The value of expression 40 divided by 160000 would be equal to 0.00025
How can we interpret the division?When 'a' is divided by 'b', then the result we get from the division is part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.
We need to find the expression of 40 divided by 160000
A negative divided by a negative is positive, then
40÷160000 = 0.00025
Therefore, The value of 40 divided by 160000 is; 0.00025
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In each of Problems 6 through 9, determine the longest interval in which the given initial value problem is certain to have a unique twice- differentiable solution. Do not attempt to find the solution. 6. ty" + 3y = 1, y(1) = 1, y'(1) = 2 7. t(t – 4)y" + 3ty' + 4y = 2, y(3) = 0, y'(3) = -1 8. y" + (cost)y' + 3( In \t]) y = 0, y(2) = 3, y'(2) = 1 9. (x - 2)y"+y' +(x - 2)(tan x) y = 0, y(3) = 1, y'(3) = 2 = ) y( = = = - =
(a) The interval (-∞, ∞).
(b) The interval (-∞, ∞).
(c) The interval (-∞, ∞).
(d) The interval (-π/2, π/2) \ {0}.
(a) The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is the interval where the coefficient function, 3t, is continuous and bounded. Since 3t is a continuous and bounded function for all t in the interval (-∞, ∞), the given initial value problem is certain to have a unique twice-differentiable solution for all t in (-∞, ∞).
(b) The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is the interval where the coefficient functions, t(t - 4), 3t, and 4, are continuous and bounded. Since t(t - 4), 3t, and 4 are continuous and bounded functions for all t in the interval (-∞, ∞), the given initial value problem is certain to have a unique twice-differentiable solution for all t in (-∞, ∞).
(c) The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is the interval where the coefficient functions, cost and In|t|, are continuous and bounded. Since cost and In|t| are continuous and bounded functions for all t in the interval (-∞, ∞), the given initial value problem is certain to have a unique twice-differentiable solution for all t in (-∞, ∞).
(d) The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is the interval where the coefficient functions, x - 2, 1, and (x - 2)tanx, are continuous and bounded. Since x - 2, 1, and (x - 2)tanx are continuous and bounded functions for all x in the interval (-π/2, π/2) \ {0} , the given initial value problem is certain to have a unique twice-differentiable solution for all x in (-π/2, π/2) \ {0}.
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The given question is incomplete, the complete question is:
determine the longest interval in which the given initial value problem is certain to have a unique twice- differentiable solution. Do not attempt to find the solution. (a) ty" + 3y = 1, y(1) = 1, y'(1) = 2 (b) t(t – 4)y" + 3ty' + 4y = 2, y(3) = 0, y'(3) = -1 (c) y" + (cost)y' + 3( In |t|) y = 0, y(2) = 3, y'(2) = 1 (d) (x - 2)y"+y' +(x - 2)(tan x) y = 0, y(3) = 1, y'(3) = 2
1. Find an equation for the line with the given properties.
Perpendicular to the line x = 5; containing the point (5,6)
y =
2. Find an equation for the line with the given properties. Use lowercase letter x for the variable.
Parallel to the line 7x - y = -7; containing the point (0,0)
y =
3. Find an equation for the line with the given properties.
Slope undefined; containing the point (8,2)
For the first question, the equation for the line is y = -x + 11. This comes from the fact that the slope for a line perpendicular to the line x = 5 is -1. From there, we can use the point (5,6) to calculate the y-intercept, which is 11.
For the second question, the equation for the line is y = 7x. This comes from the fact that the slope for a line parallel to the line 7x - y = -7 is 7. Since the point (0,0) is already on the line, the equation is already solved.
For the third question, the equation for the line is x = 8. This comes from the fact that the slope for a line with an undefined slope is 0. Since the point (8,2) is already on the line, the equation is already solved.
11/12 x 8/25 x 15/16 x 9/44
Answer the question below: *
The area of a playground is 108 yd². The width of the playground is 3 yd longer than its length. Find the
length and width of the playground.
•length = 9 yards, width = 12 yards
•length = 12 yards, width = 15 yards
•length = 12 yards, width = 9 yards
•length= 15 yards, width = 12 yards
Solving a system of equations we the length and width of the playground is length = 9 yards, width = 12 yards
How to find the length and the width?Remember that the area of a rectangle of length L and width W is:
Area = L*W
Here we know that the area is 108 square yards, and we know that he width is 3 yards longer than the length, then we can write a system of equations:
W =L + 3
108 = L*W
Replacing the first equation into the second one we will get:
108 = (L + 3)*L
108 = L² + 3L
Then we have the quadratic equation:
L² + 3L - 108 = 0
Using the quadratic formula we get the solutions:
[tex]L = \frac{-3 \pm \sqrt{3^2 - 4*1*-18} }{2}[/tex]
We only care for the positive solution, which is:
L = 9
Then the width is:
W = L + 3 = 9 + 3 = 12
Then the correct option is:
•length = 9 yards, width = 12 yards
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At Snobby Girls School, 65% of the girls are Clothes Ponies (C), 50% are Makeup Missies (M) and 30% are both. A girl from SCS is
chosen at random.
a) What is the probability she is a C?
b) What is the probability she is an M?
c) What is the probability she is both a C and an M?
d) If the chosen girl is an M, what is the probability she is also a C?
e) Are the two events C and M independent? Why or why not?
In response to the stated question, we may respond that Given that she is an M, the probability that the chosen female is both a M and a C is 0.6.
What is probability?Probabilistic theory is a branch of mathematics that calculates the likelihood of an event or proposition occurring or being true. A risk is a number between 0 and 1, with 1 indicating certainty and a probability of around 0 indicating how probable an event appears to be to occur. Probability is a mathematical term for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences among equally likely alternatives that result in a certain event.
a) The girl has a 0.65 chance of being a Clothes Pony (C).
b) The girl has a 50% chance of being a Makeup Missie (M).
c) The girl has a 0.30 chance of being both a Clothing Pony and a Makeup Missie.
d) Using the conditional probability formula, we can calculate the likelihood that the chosen female is both a M and a C provided that she is a M:
P(C|M) = P(C and M) divided by P (M)
Part (c) tells us that P(C and M) = 0.30, while Part (b) tells us that P(M) = 0.50. Therefore:
P(C|M) = 0.30 / 0.50 = 0.6
Given that she is an M, the likelihood that the chosen female is both a M and a C is 0.6.
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Second chance! Review your workings and see if you can correct your mistake. The table below shows how much a healthy kitten is expected to weigh. Betsy's kitten is 2 weeks old and its mass is 113% of its expected mass. What is the mass of Betsy's kitten? Give your answer in grams (g) and give any decimal answers to 1 d.p. Age (weeks) 1 2 3 4 5 6 7 8 Mass (g) 210 310 390 460 600 680 790 910 Watch video Answer >
Answer:
350.3 g
Step-by-step explanation:
310 * 113% = 310 * 1.13 = 350.3 g
Hope this helps!
What is tangent and how do you calculate it from the unit circle?
Answer:
The unit circle has many different angles that each have a corresponding point on the circle. The coordinates of each point give us a way to find the tangent of each angle. The tangent of an angle is equal to the y-coordinate divided by the x-coordinate.
Answer this imagine please
Answer:
B) Group 2
Step-by-step explanation:
Group 1 wrote it correctly because there are 3 groups of 4x and 3 groups of 3
Group 2 wrote it incorrectly because that would mean 9 groups of 4x, which is not the case here
Group 3 wrote it correctly because 3(4x) + 3(3) = 3(4x+3) due to the Distributive Property
Group 4 wrote it correctly because it is an expansion of Group 3's expression
question 1 write an inequality and a word sentence that represent the graph. let x represent the unknown number.
The inequality is X > 0 and a word sentence represent the graph is X the graph of a number line with an open circle on zero and an arrow pointing to the right.
The inequality X > 0 represents the graph of a number line with an open circle on zero to left and an arrow pointing to the right. This means that any value of X that is greater than zero is a valid solution for the inequality.
In other words, X can be any positive number, such as 1, 2, 3, and so on. However, X cannot be zero or any negative number, as those values do not satisfy the inequality. Therefore, the word sentence that represents this inequality is "X is greater than zero."
This means that X must be a positive number, and it can be any value that is greater than zero.
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Calculate the standard deviation of ABC stock returns given the following historical series of returns. Year Rate of Return 1 −12% 2 10% 3 5% 4 −7% 5 3%
The value of standard deviation of the stock returns is 10.246%.
What is standard deviation?The variance or dispersion of a group of data points is measured by standard deviation. Finding the square root of the variance, which is the sum of the squared deviations between each data point and the mean, is how it is determined. In statistics, the term "standard deviation" is used to characterise the distribution of a data collection and to estimate the probability of certain outcomes or events.
The standard deviation is determined using the formula:
√(V).
The mean of the given data is:
(−12 + 10 + 5 − 7 + 3) / 5 = −0.2%
Now, the variance is:
Variance = [ (−12 − (−0.2))² + (10 − (−0.2))² + (5 − (−0.2))² + (−7 − (−0.2))² + (3 − (−0.2))² ] / 5
Variance = 104.96
Now, for standard deviation:
Standard deviation = √(104.96) = 10.246%
Hence, the value of standard deviation of the stock returns is 10.246%.
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t/f the mean and standard deviation are more accurate measures of center and spread when the data is skewed
When the data is skewed, it is untrue that the mean and standard deviation are better indicators of the centre and spread.
The median is a better tool to use to locate the centre when it is skewed right or left with high or low outliers. The IQR is the most accurate indicator of spread when the median is the centre. When the mean is the centre, the standard deviation should be utilised because it gauges how far a data point is from the mean.
The standard deviation will be greatly overstated in cases when the distribution of the data is highly skewed, making it a poor choice as a measure of variability.
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A large random sample of American students in seventh grade showed that
20
%
20%20, percent of them were reading below grade level.
Based on this data, which of the following conclusions are valid?
Choose 1 answer:
Choose 1 answer:
(Choice A) About
20
%
20%20, percent of all American students in seventh grade were reading below grade level.
A
About
20
%
20%20, percent of all American students in seventh grade were reading below grade level.
(Choice B)
20
%
20%20, percent of this sample was reading below grade level, but we cannot conclude anything about the population.
B
20
%
20%20, percent of this sample was reading below grade level, but we cannot conclude anything about the population.
(Choice C) About
20
%
20%20, percent of all American students were reading below grade level.
C
About
20
%
20%20, percent of all American students were reading below grade level.
The appropriate inference from the data is (B) Since [tex]20%[/tex] of this group read below grade level, we cannot draw any generalizations about the population. Thus, option B is correct.
What is the percent of the sample?A representative sample is a subset of data, often drawn from a wider population, that can show qualities that are similar.
Because the data produced contains more manageable, smaller representations of the larger group, representative sampling aids in the analysis of bigger groups.
Although the sample may be representative of seventh-grade American students, it is not necessarily representative of all seventh-graders or all American children. Hence, without additional data or research, we cannot extrapolate the sample's results to the overall population.
Therefore, 20%20, percent of all American students in seventh grade were reading below grade level.
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A blue whale is currently diving down beneath the ocean. After 4 minutes, the blue whale is 33.7 meters below sea level, and after 13mins, the blue whale is 99.4 meters below sea level. If the blue whale is diving at a constant rate, how long will it take to reach a depth of 190.65 meters below sea level? To answer this, construct a linear function.
please hurry i dont want to fail
The problem asks for the time, we know that the blue whale will reach a depth of 190.65 meters below sea level after 26.7 minutes.
How can you tell if a function is linear?If a function is linear or not, its graph can be examined to determine. A straight line results from the graphing of a linear function. A nonlinear function has some sort of curve in contrast to a linear function.
The slope and y-intercept must first be determined in order to build a linear function. The slope can be determined using the two provided locations (4, -33.7) and (13, -99.4):
slope is the product of (y-change) and (change in x)
slope = (-99.4 - (-33.7)) / (13 - 4)
slope = -65.7 / 9
slope = -7.3
We can now use the point-slope form of a linear equation to obtain the equation of the line since we know its slope:
y - y1 = m(x - x1)
y - (-33.7) = -7.3(x - 4)
y + 33.7 = -7.3x + 29.2
y = -7.3x - 4.5
The following is the linear function that plots the blue whale's depth below sea level against time (x):
y = -7.3x - 4.5
We can plug in this number for y and solve for x to get how long it will take the blue whale to descend 190.65 metres below sea level:
190.65 = -7.3x - 4.5
195.15 = -7.3x \sx = -26.7
We know that the blue whale will descend to a depth of 190.65 metres below sea level in 26.7 minutes because the problem specifically asks for the time.
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When 1.00 g potassium chlorate is dissolved in 50.0 g water in a Styrofoam calorimeter of negligible heat capacity, the temperature decreases from 25.00°C to 23.36°C. Calculate q for the water and ?H° for the process.The specific heat of water is .
The specific heat of water is [tex]+41840J . mol^{-1}[/tex].
The following formula is used to determine how much heat a substance absorbs or releases during a heat exchange between two bodies, Calculate the value of q.
Q = m.s.t
Where,
Q is equal to how much heat is received or emitted.
m = The substance's mass
t = Temperature change
s = The substance's specific heat
The starting temperature in this dissolve is,
[tex]T_{i}[/tex] = 25.00°C
(25.00 + 273.00) K
= 298.00 K
Final temperature in this dissolving is,
[tex]T_{f}[/tex] = 23.36°C
= (23.36 + 273.00) K
Specific Water's heat is, [tex]4.184\frac{J}{g.K}[/tex]
In this issue, the heat that water releases are,
[tex]Q_{released} = 50.0g*4.184\frac{J}{g.K} * (298.00 - 296.36)K[/tex]
= 343.088J
2) Molar Mass of KClO₃ is [tex]122.55g mol^{-1}[/tex]
As a result, number of moles of KClO₃ present in 1g sample is,
[tex]\frac{1.00g}{122,55g/mol} = 0.0082mols[/tex]
Hence, the standard enthalpy change of the dissolving process is determined as follows:
Δ[tex]H^{o} = +\frac{343.088J}{0.0082mol} \\= +41840J . mol^{-1}[/tex]
The plus symbol (+) denotes the absorption of heat during the dissolving phase.
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Complete Question:
When 1.00 g potassium chlorate (KCIO₃) is dissolved in 50.0 g water in a Styrofoam calorimeter of negligible heat capacity, the temperature decreases from 25.00°C to 23.36°C. Calculate q for the water and AH° for the process. KCIO: (s) → K* (aq) + CIO (aq) The specific heat of water is 4.184 J K-1 g¯!.
Intercept form 4x + 5y = 20
By answering the question the answer is So the slope intercept expression 4x + 5y = 20 in intercept form is: x/5 + y/4 = 1
what is slope intercept?The slope-intercept form of a linear equation in mathematics is an equation of the form y = mx + b. where m is the slope of the line and b is the y-intercept, the point where the line crosses the y-axis. The slope-intercept format is a convenient way to plot equations for straight lines because it allows you to quickly see the line and determine the slope and y-intercept. The slope indicates how steep the line is, and the y-intercept indicates where the line crosses the y-axis.
The intercept form of a linear equation in two variables (x and y) is given by
x/a + y/b = 1
where a and b are the intercepts of x and y respectively.
To convert the given expression 4x + 5y = 20 to intercept form, we need to solve for the intercepts for x and y.
For x = 0, 4x + 5y = 20 becomes
0 + 5 years old = 20
y = 4
So the y-intercept is 4.
For y = 0, 4x + 5y = 20 becomes
4x + 0 = 20
x = 5
So the x-intercept is 5.
So the expression 4x + 5y = 20 in intercept form is:
x/5 + y/4 = 1
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Suppose
X1
is a numerical variable and
X2
is a dummy variable with two categories and the regression equation for a sample of
nequals=1919
is
ModifyingAbove Upper Y with caret Subscript iYiequals=77plus+33X1iplus+22X2i.
a.
Interpret the regression coefficient associated with variable
X1.
b.
Interpret the regression coefficient associated with variable
X2.
c.
Suppose that the
tSTAT
test statistic for testing the contribution of variable
X2
is
3.213.21.
At the
0.100.10
level of significance, is there evidence that variable
X2
makes a significant contribution to the model?
Interpret the regression coefficient associated with variable
X1.
Holding constant the effect of
▼
Upper X 2 commaX2,
Upper X 1 commaX1,
for each increase of one unit in
▼
Upper X 2 commaX2,
Upper X 1 commaX1,
the predicted mean value of Y
▼
increases
decreases
by a positive change of nothing unit left parenthesis s right parenthesis . unit(s).
The regression coefficient associated with X1 and X2 interpret it increased by 33 and 22.
Test statistic represents that X2 makes a significant contribution to the model.
The regression coefficient associated with variable X1 is 33.
This means,
Holding all other variables constant, for every one unit increase in X1, Y is expected to increase by 33 units.
The regression coefficient associated with variable X2 is 22.
This means ,
Compared to the reference category ,
Average value of Y for the category represented by X2 is expected to be 22 units higher.
Holding all other variables constant.
Null hypothesis for testing the contribution of variable X2 is that the coefficient of X2 is equal to zero,
X2 does not make a significant contribution to the model.
Alternative hypothesis is that the coefficient of X2 is not equal to zero,
X2 does make a significant contribution to the model.
The t-statistic for X2 is 3.21, and the p-value associated with this statistic is less than 0.10.
Reject the null hypothesis at the 0.10 level of significance.
p-value is less than 0.10,
Conclude evidence that variable X2 makes a significant contribution to the model.
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The above question is incomplete, the complete question is:
Suppose X1 is a numerical variable and X2 is a dummy variable with two categories and the regression equation for a sample of n =1919
is Modifying Y with Y = 77 + 33X1 +22X2
a. Interpret the regression coefficient associated with variable
X1.
b. Interpret the regression coefficient associated with variable
X2.
c. Suppose that the test statistic for testing the contribution of variable
X2 is 3.213.21.
At the 0.100.10 level of significance, is there evidence that variable
X2 makes a significant contribution to the model?
Interpret the regression coefficient associated with variable X1?
What is the equation of the circle in the standard (x, y) coordinate plane that has a radius of 4 units and the same center as the circle determined by x^2 + y^2 - 6y + 4=0?
A. x² + y^2 = -4
B. (x+3)^2 + y^2 = 16
C. (x-3)^2 + y^2 = 16
D. x^2 + (y+3)^2 = 16
E. x^2 + (y-3)^2 = 16
Answer:
E. x² + (y - 3)² = 16
Step-by-step explanation:
The equation of a circle in the standard (x, y) coordinate plane with center (h, k) and radius r is given by:
[tex]\boxed{(x - h)^2 + (y - k)^2 = r^2}[/tex]
To find the equation of the circle with a radius of 4 units and the same center as the circle determined by x² + y² - 6y + 4 = 0, we need to first write the equation of the second circle in the standard form.
We can complete the square for y to rewrite this equation in standard form. To do this move the constant to the right side of the equation:
[tex]\implies x^2 + y^2 - 6y + 4 = 0[/tex]
[tex]\implies x^2 + y^2 - 6y = -4[/tex]
Add the square of half the coefficient of the term in y to both sides of the equation:
[tex]\implies x^2 + y^2 - 6y +\left(\dfrac{-6}{2}\right)^2= -4+\left(\dfrac{-6}{2}\right)^2[/tex]
[tex]\implies x^2 + y^2 - 6y +9= -4+9[/tex]
[tex]\implies x^2 + y^2 - 6y +9=5[/tex]
Factor the perfect square trinomial in y:
[tex]\implies x^2+(y-3)^2=5[/tex]
[tex]\implies (x-0)^2 + (y-3)^2=5[/tex]
So the center of this circle is (0, 3) and its radius is √5 units.
Since the new circle has the same center, its center is also (0, 3).
We know its radius is 4 units, so we can write the equation of the new circle as:
[tex]\implies (x - 0)^2 + (y - 3)^2 = 4^2[/tex]
[tex]\implies x^2 + (y - 3)^2 = 16[/tex]
Therefore, the equation of the circle in the standard (x, y) coordinate plane with a radius of 4 units and the same center as the circle determined by x² + y² - 6y + 4 = 0 is x² + (y - 3)² = 16.
To find:-
The equation of circle which has a radius of 4units and same centre as determined by x² + y² - 6y + 4 = 0.Answer:-
The given equation of the circle is ,
[tex]\implies x^2+y^2-6y + 4 = 0 \\[/tex]
Firstly complete the square for y in LHS of the equation as ,
[tex]\implies x^2 + y^2 -2(3)y + 4 = 0 \\[/tex]
Add and subtract 3² ,
[tex]\implies x^2 +\{ y^2 - 2(3)(y) + 3^2 \} -3^2 + 4 = 0 \\[/tex]
The term inside the curly brackets is in the form of a²-2ab+b² , which is the whole square of "a-b" . So we may rewrite it as ,
[tex]\implies x^2 + (y-3)^2 -9 + 4 = 0 \\[/tex]
[tex]\implies x^2 + (y-3)^2 - 5 = 0 \\[/tex]
[tex]\implies x^2 + (y-3)^2 = 5\\[/tex]
can be further rewritten as,
[tex]\implies (x-0)^2 + (y-3)^2 = \sqrt5^2\\[/tex]
now recall the standard equation of circle which is ,
[tex]\implies (x-h)^2 + (y-k)^2 = r^2 \\[/tex]
where,
(h,k) is the centre.r is the radius.So on comparing to the standard form, we have;
[tex]\implies \rm{Centre} = (0,3)\\[/tex]
Now we are given that the radius of second circle is 4units . On substituting the respective values, again in the standard equation of circle, we get;
[tex]\implies (x-h)^2 + (y-k)^2 = r^2 \\[/tex]
[tex]\implies (x-0)^2 + (y-3)^2 = 4^2 \\[/tex]
[tex]\implies \underline{\underline{\red{ x^2 + (y-3)^2 = 16}}}\\[/tex]
and we are done!
PLEASE HELP WITH EXPLANATION!
The volume of the square pyramid is 9.12 m.
What is square pyramid?A square pyramid is a pyramid, in geοmetry, that has a square base and fοur lateral faces. A Pyramid is a pοlyhedrοn that has a base and 3 οr greater triangular faces that meet at a pοint abοve the base (the apex). A square pyramid is a three-dimensiοnal shape that has a tοtal οf five faces, hence called a pentahedrοn. A mοst famοus example οf such a pyramid in real life is the Great Pyramid οf Giza.
[tex]$ \rm V = \frac{1}{3} a^2H[/tex]
Where v is the volume
a is the base side and
H is the height
Here,
a = 12 cm
H = 19 cm
Then,
[tex]$ \rm V = \frac{1}{3} 12 \times 12 \times 19[/tex]
[tex]$ \rm V = 4 \times 12 \times 19[/tex]
V = 912 cm or 9.12 m
Thus, The volume of the square pyramid is 9.12 m.
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Esmanol A spinner with 12 equally sized slices has 4 yellow slices, 3 red slices, and S blue slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a slice that is not yellow?
The probability of spinning a slice that is not yellow is equal to the total number of non-yellow slices divided by the total number of slices.
Total number of non-yellow slices = 9 (3 red + 5 blue)
Total number of slices = 12
Therefore, the probability of spinning a slice that is not yellow is 9/12 or 75%.
The rectangle can be made to have rotation symmetry of order 2 by colouring one of the squares blue. Put a cross in the middle of the square which would have to be made blue.
To make a rectangle with a rotation symmetry of order 2, first draw the rectangle on a piece of paper. Then draw a cross in the middle of one of the squares in the rectangle. This is the square that needs to be coloured blue in order to create the rotation symmetry. Finally, colour the square with the cross blue to create the rotation symmetry.
Mr. James is enlarging a logo for printing
on the back of a T-shirt. He wants to enlarge a logo that is 3 inches by
5 inches so that the dimensions are 3 times larger than the original. How
many times as large as the original logo will the area of the printing be?
The area of the enlarged logo will be 9 times larger than the original logo.
When an object is enlarged or scaled up how does it area change ?
When an object is enlarged or scaled up by a factor of [tex]k[/tex], both its length and width are multiplied by [tex]k[/tex]. Therefore, the new length is [tex]k[/tex] times the original length, and the new width is [tex]k[/tex] times the original width.
The area of the new object is the product of the new length and width, which is ([tex]k[/tex] times the original length) multiplied by ([tex]k[/tex] times the original width), or [tex]k^2[/tex] times the original area.
Therefore, the area of an object increases by a factor of [tex]k^2[/tex] when the object is enlarged or scaled up by a factor of [tex]k[/tex].
Calculating how many times larger the area of the enlarged logo will be :
The original logo has dimensions of 3 inches by 5 inches, so its area is 3 x 5 = 15 square inches.
Mr. James wants to enlarge the logo so that the dimensions are 3 times larger than the original. This means the new dimensions will be 9 inches by 15 inches.
To determine how many times larger the area of the enlarged logo will be, we need to compare the areas of the original logo and the enlarged logo. The area of the enlarged logo is 9 x 15 = 135 square inches.
To find out how many times larger the area of the enlarged logo is compared to the original logo, we divide the area of the enlarged logo by the area of the original logo:
135 square inches ÷ 15 square inches = 9
Therefore, the area of the enlarged logo will be 9 times larger than the area of the original logo.
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A screen has a zoom of 140%, which means that images on the screen are 140% as long and 140% as wide as when they are printed on a sheet of paper. An image of a house is 17 cm tall when printed on a sheet of paper. How tall would the image of the house be on the screen? Give your answer in centimetres (cm).
Answer:
23.8 cm
Step-by-step explanation:
17 * 140% = 17 * 1.4 = 23.8 cm
The image of the house would be 23.8 cm tall on the screen.
To calculate the height of the image of the house on the screen, we can use the given zoom factor of 140%.
The zoom factor of 140% means that the images on the screen are 140% as long and 140% as wide compared to when they are printed on a sheet of paper.
To calculate the height of the image on the screen, we need to multiply the printed height by the zoom factor (140% or 1.4).
Height on the screen = Printed height * Zoom factor
Height on the screen = 17 cm * 1.4
Height on the screen = 23.8 cm
Therefore, the image of the house would be 23.8 cm tall on the screen.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Step-by-step explanation:
my previous answer assumed we need a kind of average change rate.
but it seems you need the immediate change rate ?
or what ? the question does not specify.
I would appreciate if you would leave a comment, when you find that my answer is seemingly not matching some expected answers.
so, let's try now the immediate change rate (as I have no information to go - I have also no information about what you are currently learning in your class, and if you do already derivatives or not, so, this might be now above your learning level ...) :
again, the area between the inner circle and the outer square is
A = As - Ac = s² - pi×r²
where s is the square's side length, and r is the radius of the circle.
the immediate change rate of that area is the sum of first derivatives of A based on both used variables multiplied by their individual change rates :
dA/dt = dAs/ds × ds/dt - dAc/dr × dr/dt
and this is then calculated for the given data point (s = 16, r = 3) and the individual change rates of the variables (ds/dt = 2 meters/minute, dr/dt = 1 meter/minute).
so, we have
dA/dt = 2s × 2 - 2×pi×r × 1
as (s²)' = 2s, (pi×r²)' = 2×pi×r
dA(16, 3)/dt = 2×16×2 - 2×pi×3×1 = 64 - 6pi =
= 45.15044408... meters²/minute ≈
≈ 45.15 meters²/minute
so, you see, for a curved function (not a line) there has to be a difference between the average change rate between 2 points and the immediate change rate directly at a point.
I hope this works now for you.
and here now the original answer for an average change rate :
right now the radius is 3 m, and the square side lengths are 16 m.
1 minute ago the radius was 2 m, and the square side lengths were 14 m.
the area between the circle and the square is always the area of the square minus the area of the circle.
these areas are right now
circle : pi×3² = 9pi m²
square : 16² = 256 m²
area between = 256 - 9pi = 227.7256661... m²
these areas were one minute ago
circle : pi×2² = 4pi m²
square : 14² = 196 m²
area between = 196 - 4pi = 183.4336294... m²
the change rate of the area between the circle and the square is
227.7256661... - 183.4336294... = 44.29203673... m² per minute
HELP what is the answer to this using systems of equations
y=1/8x−1
−5x+4y=−13
Answer:
x = 2
y = -3/4
Step-by-step explanation:
1. Substitute y=1/8x -1 in −5x+4y=−13
-5x+4(1/8x -1) = -13
2. Solve for x
-5x + 4/8x - 4 = -13
-9/2x - 4 = -13
-9/2x = -9
x = 2
3. Now that you know x = 2, plug it into y=1/8x - 1 to find what y is.
y= 1/8(2) - 1
y= 2/8 - 1
y= -3/4
T
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View Instructions
Interpreting a Dot Plot
DAR
3 4 5
1 2
Number of pets at home
6
How many people have 2 pets at home?
How many people have at least 3 pets at home?
How many more people have 2 pets than 5 pets?
How many people have less than 3 pets at home?
11
10 HELP MEEE
If we total up the dots plot for 3, 4, and 5 pets, we find that 3 people have 2 pets at home, 10 individuals have at least 3 pets at home.
What is the 1 pet in the world?The fact that dogs are the most common pet in the world shouldn't be shocking. There is a reason why there are tens of millions of dogs living in the United States alone, which is why some people say that dogs are a man's greatest friend. Around the world, at least one dog is kept in one-third of all households.
What exactly is a house pet?A fully domesticated animal kept constitutes a "household pet." a pet kept by you for personal company, like a dog, cat, reptile, bird, or mouse. Any kind of horse, cow, pig, sheep, goat, chicken, turkey, other captive fur-bearing animal is not considered a household pet, nor is any animal that is typically kept for food or profit.
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The total number of people with pets at home is 11, which is the sum of the heights of the columns.
What is equation?
A math equation is a method that links two claims and represents equivalence using the equals sign (=). An equation is a mathematical statement that establishes the equivalence of two mathematical expressions in algebra.
Based on the given dot plot, we can answer the following questions:
How many people have 2 pets at home?
Answer: Two people have 2 pets at home, as indicated by the two dots in the second column.
How many people have at least 3 pets at home?
Answer: Six people have at least 3 pets at home, as indicated by the dots in the third column and beyond.
How many more people have 2 pets than 5 pets?
Answer: There are no dots in the last column, which represents 5 pets. Therefore, the difference between the number of people with 2 pets and those with 5 pets is 2 - 0 = 2.
How many people have less than 3 pets at home?
Answer: Three people have less than 3 pets at home, as indicated by the dots in the first two columns.
Therefore, the total number of people with pets at home is 11, which is the sum of the heights of the columns.
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PLS HELP ME with all 4 questions!!
By answering the presented question, we may conclude that so by SAS congruency property we have said that all these triangles are similar.
What precisely is a triangle?A triangle is a closed, a double geometric shape made up of three line segments known as sides that connect at three parameters known as vertices.
Triangles are differentiated by their angles and their sides. Triangles can be collinear (all sides equal), angles, or scalene dependent on their sides.
Triangles are classed as acute (all angles just under 90 degrees), right (one angle of approximately to 90 degrees), or ambiguous (all angles greater than 90 degrees).
The area of a triangle may be determined with the formula A = (1/2)bh, where A is the surface, b is really the right triangle base, and h is the triangle's height
here, from the figure, we have
Two sides of the triangle are equal.
And also all angles are also same.
Therefore, so by SAS congruency property we have say that all these triangles are similar.
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What is the equation of the line that is parallel to the
given line and passes through the point (-3, 2)?
V(o, 3)
O 3x - 4y = -17
(-3,2
O 3x - 4y = -20
4x + 3y = -2
4x + 3y = -6
The equation of the line that is parallel to the given line and passes through the point (-3, 2) is 3x - 4y = -17.
What is the formula for a parallel line equation?If the line's equation is axe + by + c = 0 and the coordinates are (x1, y1).
To find the equation of a line parallel to a given line, we must first understand that parallel lines have the same slope. As a result, we must first determine the slope of the given line.
3x - 4y = -17 is the given line. To determine its slope, solve for y and write the equation in slope-intercept form:
-3x - 4y = -3x - 17 y = (3/4)x + (17/4)
This line has a 3/4 slope.
Now we want to find the equation of a parallel line that passes through the point (-3, 2). Because the new line is parallel to the given line, it has a slope of 3/4.
We can write the equation of the new line using the point-slope form of the equation of a line as:
y - y1 = m(x - x1)
where m represents the slope and (x1, y1) represents the given point (-3, 2).
When m = 3/4, x1 = -3, and y1 = 2, we get:
y - 2 = (3/4)(x - (-3))
y - 2 = (3/4)(x + 3)
Divide both sides by 4 to get rid of the fraction.
4y - 8 = 3x + 9
3x - 4y = -17
As a result, the equation of the parallel line that passes through the point (-3, 2) is 3x - 4y = -17.
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Daniel opens a new savings account and makes an initial deposit of $1,200.
If the account earns 2.5%
annual interest, which equation shows how much money is in the account in 9
months?
Responses
A x=1,200+1,200(0.25)(0.75)
x is equal to 1 comma 200 plus 1 comma 200 0 point 2 5 0 point 7 5
B x=1,200+1,200(0.025)(0.75)
x is equal to 1 comma 200 plus 1 comma 200 0 point 0 2 5 0 point 7 5
C x=1,200+1,200(0.25)(9)
x is equal to 1 comma 200 plus 1 comma 200 0 point 2 5 9
D x=1,200+1,200(0.025)(9)
Answer:
D) x = 1,200 + 1,200(0.025)(9)
In this equation, 1,200 is the initial deposit, 0.025 is the decimal representation of the annual interest rate, and 9 represents the time period in months. The multiplication of 0.025 and 9 gives the proportion of interest earned in 9 months, which is then multiplied by the initial deposit and added to it to give the total amount in the account after 9 months.
Simplifying the equation:
x = 1,200 + (1,200)(0.025)(9)
x = 1,200 + 270
x = 1,470
Therefore, there would be $1,470 in the account after 9 months
two cards are drawn at random from an ordinary deck of 52 cards what is the probability that thee are no sixes
there is an 85% chance that the two cards drawn at random from an ordinary deck of 52 cards will not be sixes.
The probability of drawing a card from an ordinary deck without replacement can be determined using the concept of conditional probability. Conditional probability is the probability of an event occurring, assuming that another event has already occurred.
In order to calculate the probability that the two cards drawn are not sixes, we can use the formula:
P(A and B) = P(A) x P(B|A)
Where A and B represent two independent events, P(A) is the probability of event A occurring, and P(B|A) is the conditional probability of event B occurring given that event A has already occurred.
The probability of drawing the first card that is not a six is:
P(A) = 48/52 = 0.9231
The probability of drawing the second card that is not a six, given that the first card drawn was not a six, is:
P(B|A) = 47/51 = 0.9216
Therefore, the probability of drawing two cards at random from an ordinary deck of 52 cards and having neither of them be a six is:
P(A and B) = P(A) x P(B|A) = 0.9231 x 0.9216 = 0.8503 or approximately 85%.
This means that there is an 85% chance that the two cards drawn at random from an ordinary deck of 52 cards will not be sixes.
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Can Anyone Help?
A poster is to have a total area of 245cm2. There is a margin round the edges of 6cm at the top and 4cm at the sides and bottom where nothing is printed.What width should the poster be in order to have the largest printed area?
The poster should have width ____ cm
Answer: The poster should have width 17.50 CM
Step-by-step explanation:
Given that boasted I have a total area 245 cm square area of a poster is 200 and 45 20 m square. And it is in the rectangle format. So we know that the poster is always in the rectangle format and the area of rectangular area is equal to L N T W. So 245 will be equal to Ln tW. From this. We need to find L. So L is equal to 245 divided by W. Now consider the diplomatic representation of the poster. So it has mentioned that there is a margin around the edges of six cm at the top. This is 6cm and four cm at the sites. All the four sides 3 sides are four cm. So from this we need to find land and the doctor posted area that is printed area. The first wine printed with www. Z. Quilter. Now let this be total birth will be W. And this will be four and this will be four. Therefore posted with will be we need to find this part alone. So W -4 -4 will give the this part with. So W -4 -4. So post printed with PW will be equal to W -8. Similarly printed lunch will be equal to The total length is already we have found 245 by W. And we need to find this part length. So we have to subtract six and four from the total length so that that will give them this part length, So -6 -4. So printed length will be equal there 245 Divided by W -10. And we know that formula for area of a rectangle. Urz D is equal to L W. Now substitute the printed with and printed length in the area formula. We have to find the printed area. So Printed area Zeke Walter W -8 into 245 Divided by W -10. To simplify this, we get 325 minus 10. W -100 and 30,960 W. to the power of -1. Now fine D A by D. T. Not D D. This is D. W. So this is equal to differentiation of constant alma zero, this is minus 10 plus 900 and 60 W. to the power of -2 and equate this to be equal to zero. We out to find the maximum width so D A by D W is equal to zero, therefore minus 10 1960 W. To the power of -2 will be equal to zero. To simplify this, we get them maximum with value the W is equal term I wrote off 196. Therefore the value of W. Z quilter plus or minus 14. We will neglect the negative values since we cannot be negative. So one we assume the positive values. So what will be equal to 14 and length will be equal to 245 divided by 14, So which will be equal to 17.50 centimeters. And they have concluded that At W is equal to 14 cm and lunch will be equal to 17.50 cm needed to print the largest area. I hope you found the answer to school. Thank you.
