The value of R500 decrease to ratio 9:8 is x = 400.
What is cross multiplication?By using the cross multiplication approach, the denominator of the first term is multiplied by the numerator of the second term, and vice versa. Using the mathematical rule of three, we may determine the answer based on proportions. The best illustration is cross multiplication, where we may write in a percentage to determine the values of unknown variables.
Given that, decrease R450 in the ratio 9:8.
Let 9 = 450
Then 8 will have the value = x.
That is,
9 = 450
8 = x
Using cross multiplication we have:
9x = 450(8)
x = 50(8)
x = 400
Hence, the value of R500 decrease to ratio 9:8 is x = 400.
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Use a triple integral to find the volume of the solid bounded below by the cone z = vx2 + y2 and bounded above by the sphere x2 + y2 + z2 = 18. (0.0.V18) x?+y+z=18 cubic units The volume of the solid is (Type an exact answer.)
The volume of the solid is given by the equation V = 36π (√2 - 1) using the triple integral.
A three-dimensional object's volume in three-dimensional space may be determined using the triple integral. The three-variable function is represented by the triple integral. If in space is a closed region, the region's entire volume may be expressed as V = Ddv, which is equivalent to V = D d x d y d z.
Cone: z = [tex]\sqrt{x^2+y^2}[/tex]
sphere: x² + y² + z² = 18
Here, we will use cylindrical coordinates to evaluate volume:
x = rcosθ , y = rsinθ, z = z
so, z = [tex]\sqrt{r^2cos^2\theta+r^2sin^2\theta} =r[/tex]
z = [tex]\sqrt{18-(x^2+y^2)} =\sqrt{18-r^2}[/tex]
r = [tex]\sqrt{18-r^2}[/tex]
r = 3
Finding limits,
[tex]Volume = \int\limits^2_0 \int\limits^3_0\int\limits^a_r {rdzdrd\theta} \, \\\\= \int\limits^2_0 \int\limits^3_0rz \ drd\theta\\\\= \int\limits^2_0 \int\limits^3_0 r(\sqrt{18-r^2}-r ) \ drd\theta\\\\[/tex]
Now, we have
[tex]\int\limits^3_0 {r\sqrt{18-r^2} } \, dr = -(9-18\sqrt{2} ) = 18\sqrt{2} -9[/tex]
Now the integral becomes,
Volume = 2π [(18√2-9) - 9]
= 2π x 18√2 - 18
V = 36π (√2 - 1)
Therefore, the volume of the solid is given by V = 36π (√2 - 1).
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What rotation centered about the origin maps (4, − 7) to (7,4) ? 90° counterclockwise 180° counterclockwise 270° counterclockwise I don't know. ←
Answer:
What rotation centered about the origin maps (4, − 7) to (7,4) ? 90° counterclockwise 180° counterclockwise 270° counterclockwise I don't know. ←
Step-by-step explanation:
To map the point (4, -7) to (7, 4) by a rotation centered about the origin, we need to find the angle of rotation and direction.
We can start by finding the vector from the origin to (4, -7), which is <4, -7>. We want to rotate this vector to the vector from the origin to (7, 4), which is <7, 4>.
To do this, we need to find the angle between these two vectors. Using the dot product, we have:
<4, -7> · <7, 4> = (4)(7) + (-7)(4) = 0
Since the dot product is zero, we know that the two vectors are orthogonal, and the angle between them is 90 degrees.
To map (4, -7) to (7, 4) with a 90-degree rotation counterclockwise, we can use the matrix:
[0 -1]
[1 0]
Multiplying this matrix by the vector <4, -7>, we get:
[0 -1] [4] = [-7]
[1 0] [-7] [ 4]
which corresponds to the point (-7, 4). This matches our desired endpoint, so the answer is 90° counterclockwise.
Answer:
90° counterclockwise
Step-by-step explanation:
I am not sure if the picture helps or not. I am trying to show that I traced the point (4,-7). Then I have a plus sign at (0,0). I start rotating the tracing paper counterclockwise until I get to the point (7,4). I needed to turn one turn of the plus sign. That would be 90°
Helping in the name of Jesus.
Help I don’t just this
The conditional relative frequency that a student rides the bus, given that the student is in middle school is 0.16 / 0.96 ≈ 0.17.
Describe conditional relative frequency ?Conditional relative frequency is a statistical measure that describes the proportion or percentage of a specific group or category within a subset of data. It is calculated by dividing the frequency of the specific category in the subset by the frequency of the total subset.
To find the conditional relative frequency that a student rides the bus, given that the student is in middle school, we need to divide the frequency of middle school students who ride the bus by the total number of middle school students.
From the table, we see that the frequency of middle school students who ride the bus is 0.16. The total number of middle school students is the sum of the frequencies in the first row, which is 0.20 + 0.16 + 0.12 + 0.48 = 0.96.
So, the conditional relative frequency that a student rides the bus, given that the student is in middle school is:
0.16 / 0.96 ≈ 0.17
Rounded to the nearest hundredth, the answer is 0.17. Therefore, about 17% of middle school students ride the bus.
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A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books isA 1 / 21B 10 / 21C 11D 21 / 11
If 2 books are chosen at random, then the probability that both are statistics books is (a) 1/21.
The number of statistics book in bookcase is = 2;
The number of biology books in bookcase is = 5;
So, the total number of books is = 7;
The Probability of choosing a statistics book on the first draw is 2/7, since there are 2 statistics books out of a total of 7 books.
After the first book is chosen, there will be 6 books left, including 1 statistics book out of a total of 6 books.
So, the probability of choosing another statistics book on the second draw is 1/6.
In order to find the probability of both events happening together (i.e. choosing 2 statistics books in a row), we multiply the probabilities of each event:
So, P(choosing 2 statistics books) = P(1st book is statistics) × P(2nd book is statistics given that the 1st book was statistics);
⇒ (2/7) × (1/6)
⇒ 1/21
Therefore, the required probability is (a) 1/21.
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The given question is incomplete, the complete question is
A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books is
(a) 1/21
(b) 10/21
(c) 11
(d) 21/11
How do you write 0.38 as a percentage?
Write your answer using a percent sign (%).
Answer:
38%
Step-by-step explanation:
I learned in class on Friday.
Multiply both numerator and denominator by 100. We do this to find an equivalent fraction having 100 as the denominator.
[tex]0.38\times \dfrac{100}{100}[/tex]
[tex]= (0.38 \times 100) \times \dfrac{1}{100} =\dfrac{38}{100}[/tex]
Write in percentage notation: 38%
In circle � W, � � = 3 WX=3 and m ∠ � � � = 8 0 ∘ ∠XWY=80 ∘ . Find the length of � � ⌢ XY ⌢ . Express your answer as a fraction times � π. X W Y Answer: Length of X Y ⌢ = Length of XY ⌢ =
The Length of arcXY is 4π/3
Define the term Circle identities?The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.
Given, (radius) WX =3, it means, r = 3
given, m∠XWY = 80°
So, the length of arc XY;
arcXY = [tex]\frac{80}{360}* 2\pi r[/tex] (by formula: length of arc)
arcXY = [tex]\frac{2}{9}* 2\pi *3[/tex]
arcXY = [tex]\frac{4}{3}\pi[/tex]
Therefore, the Length of arcXY is 4π/3
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Complete question-
A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 1 unit of protein, 2 units of carbohydrates, and 1 unit of fat. Each ounce of nuts will supply 1 unit of protein, 1 unit of carbohydrates, and 1 unit of fat. Every package must provide at least 8 units of protein, at least 11 units of carbohydrates, and no more than 10 units of fat. Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package.
Let x be the number of ounces of fruit and y the number of ounces of nuts. Referring to the chart, give the three inequalities that x and y must satisfy because of the package's requirements for protein, fat, and carbohydrate.
__ _ 8
__ _ 11
__ _ 10
Give the inequalities that x and y must satisfy because they cannot be negative.
y ≥ __
x ≥ __
Answer:
Step-by-step explanation:
The three inequalities that x and y must satisfy because of the package's requirements for protein, fat, and carbohydrate are:
Protein: 1x + 1y ≥ 8 (at least 8 units of protein)
Carbohydrates: 2x + 1y ≥ 11 (at least 11 units of carbohydrates)
Fat: 1x + 1y ≤ 10 (no more than 10 units of fat)
The inequalities that x and y must satisfy because they cannot be negative are:
x ≥ 0
y ≥ 0
Step-by-step explanation:
To satisfy the requirements for protein, fat, and carbohydrates, the following three inequalities must be satisfied:
1. 1x + 1y ≥ 8 (At least 8 units of protein)
2. 2x + 1y ≥ 11 (At least 11 units of carbohydrates)
3. 1x + 1y ≤ 10 (No more than 10 units of fat)
To ensure that x and y are non-negative, the following inequalities must be satisfied:
x ≥ 0y ≥ 0
Therefore, the complete set of inequalities for x and y are:
x + y ≥ 82x + y ≥ 11x + y ≤ 10x ≥ 0y ≥ 0
What gravitational force does the moon produce on the Earth if their centers are 3.88x108 m apart and the moon has a mass of 7.34x1022 kg?
The gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]
What is gravitational force?
Gravitational force is the force of attraction that exists between any two objects in the universe with mass. This force is directly proportional to the masses of the objects and inversely proportional to the square of the distance between their centers.
The gravitational force that the moon produces on the Earth can be calculated using the formula:
[tex]F = G \cdot \frac{m_1 \cdot m_2}{r^2}[/tex]
where:
[tex]G$ = gravitational constant = $6.67430 \times 10^{-11}\ \mathrm{N(m/kg)^2}$[/tex]
[tex]m_1$ = mass of the moon = $7.34 \times 10^{22}\ \mathrm{kg}$[/tex]
[tex]m_2$ = mass of the Earth = $5.97 \times 10^{24}\ \mathrm{kg}$ (approximate)[/tex]
[tex]r$ = distance between the centers of the Earth and the moon = $3.88 \times 10^8\ \mathrm{m}$[/tex]
Substituting these values into the formula, we get:
[tex]F &= 6.67430 \times 10^{-11} \cdot \frac{7.34 \times 10^{22} \cdot 5.97 \times 10^{24}}{(3.88 \times 10^8)^2} \&= 1.98 \times 10^{20}\ \mathrm{N}[/tex]
Therefore, the gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]
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Use the slope and y-intercept to identify the equation of this line.
Answer:
D. y = -2x
Step-by-step explanation:
slope = rise/run = 2/-1 = -2
y-intercept = (0,0)
y = mx + b
y = -2x + 0
y = -2x
Please answer the attached question
The values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.
How are radicals solved?Equations containing radicals can be made simpler by solving the resultant equation after squaring both sides of the equation to remove the radical. Nonetheless, caution must be exercised to guarantee that any solutions found are reliable and adhere to any variables' limitations.
The given equation is [tex](e - 2\sqrt{3} )^2[/tex] = f - 20√3.
Expanding the left side of the equation we have:
[tex](e - 2\sqrt{3} )^2[/tex] = (e - 2√3)(e - 2√3)
= [tex]e^2[/tex] - 2e√3 - 2e√3 + 12
= [tex]e^2[/tex] - 4e√3 + 12
Substituting back in the function
[tex]e^2[/tex] - 4e√3 + 12 = f - 20√3
[tex]e^2[/tex] - 4e√3 - f + 20√3 - 12 = 0
Using the quadratic formula:
e = [4√3 ± √(16*3 + 4(f - 20√3 + 12))] / 2
e = [4√3 ± √(4f - 64√3)] / 2
e = 2√3 ± √(f - 16√3)
Now for,
(e - 2√3)² = f - 20√3
(2√3 + √(f - 16√3) - 2√3)² = f - 20√3
f - 20√3 = f - 16√3
f = 4√3
Hence, the values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.
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PLEASE HELP FAST !! 30 POINTS + BRAINLIEST
I have two fair dice each numbered 1 to 6. I am going to throw the two dice. What is
the probability that the sum of the numbers on the dice will be a square number?
The probability that the sum of the numbers on the dice will be a square number is 1/6.
What is the mathematical probability?The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.
We can first make a list of every conceivable result when rolling two dice in order to determine the likelihood that the sum of the numbers on the two dice will be a square number:
[tex](1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6[/tex])
[tex](2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)[/tex]
[tex](3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)[/tex]
[tex](4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)[/tex]
[tex](5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)[/tex]
[tex](6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)[/tex]
The sums can then be listed, and the square numbers can be identified:
2, 3, 4, 5, 6, 7
3, 4, 5, 6, 7, 8
4, 5, 6, 7, 8, 9
5, 6, 7, 8, 9, 10
6, 7, 8, 9, 10, 11
7, 8, 9, 10, 11, 12
The likelihood that the sum of the numbers on the dice will be a square number is 6 out of a total of 36 potential outcomes.
P(square sum) = 6/36 = 1/6.
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he buys a 5kg lwisa samp and repacks the samp into 125g packets. determine how many packets will be able to get from one pack of 5kg samp?
Answer:5
Step-by-step explanation:5555555
Interpret the slope of this function in the context of the situation. Use complete sentences.
Jennifer is painting an office complex. One wing has a large reception area with several equal-sized offices. Before painting, she must put tape on the baseboards. The amount of tape needed is given by the equation, y=12x+25 where y is total number of meters of tape, and x is the number of offices.
The slope of the function is 12. Because of the slope, Jennifer will require 12 extra meters of tape for each additional office she needs to tape the baseboards in.
What is slope?A line's slope on a graph is its steepness or inclination. It may be derived from any two locations on a line by dividing the vertical change (rise) by the horizontal change (run). Positive, negative, zero, or undefinable slopes are all possible for lines. A line on a graph with a positive slope is growing as you travel from left to right, while one with a negative slope is declining. A line has a slope of zero when it is horizontal and a slope of infinity when it is vertical.
The given function is y = 12x + 25.
The standard equation of the line is given as:
y = mx + b
where, m is the slope.
Comparing the equation with the given equation the slope of the function is 12.
Because of the slope, Jennifer will require 12 extra metres of tape for each additional office she needs to tape the baseboards in. In other words, if more offices need to be painted, the amount of sellotape required also grows linearly.
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The table shows some points on the graph of exponential function g(x)
0 1 2 3 4 g(x) 1 3 9 27 81 What is the range of g?
the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.
How to solve and what is graph?
The range of a function refers to the set of all possible output values. Looking at the table, we can see that the output values of g(x) increase rapidly as x increases.
In fact, the output values of g(x) are the result of raising 3 to the power of x, which means that g(x) can never be negative. Therefore, the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.
A graph is a visual representation of data or mathematical functions. It is a diagram made up of points, lines, and curves that show the relationship between different variables or data points.
Graphs are used to display and analyze data, to illustrate trends and patterns, and to communicate complex information in an easily understandable way. There are many different types of graphs, including bar graphs, line graphs, pie charts, scatter plots, and more, each suited to different types of data and analysis.
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Twelve of the workers received the following salaries: three of them earn P12,500 a month, four of them earn P11,000; twoearn P10,500 and the rest earn P9,000 a month. What is the median salary of the workers?
The median salary of the workers is P11,000.
What is median?In statistics, the median is a measure of central tendency that represents the middle value of a data set when the data set is ordered from least to greatest (or vice versa). If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values. The median is used as a measure of central tendency when the data set has outliers or is not normally distributed.
How to calculate median?To calculate the median of a set of numbers:
Put the numbers in order from lowest to highest.If the number of items in the list is odd, the median is the middle number. For example, if the list is 3, 5, 7, 9, 11, the median is 7.If the number of items in the list is even, the median is the average of the two middle numbers. For example, if the list is 4, 6, 8, 10, the median is (6 + 8)/2 = 7.In the given question,
To find the median salary of the workers, we need to arrange the salaries in order from lowest to highest.
The salaries are:
P9,000, P9,000, P10,500, P10,500, P11,000, P11,000, P11,000, P11,000, P12,500, P12,500, P12,500, P12,500
There are 12 workers, so the median salary will be the average of the 6th and 7th salaries when arranged in order.
Median salary = (P11,000 + P11,000)/2
= P11,000
Therefore, the median salary of the workers is P11,000.
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A TRIANGLE HAS TWO SIDES OF LENTHS 6 AND 9. WHAT VALUE COULD THE LENGTH OF THE THIRD SIDE BE
Answer:
The value could be any length between 3 and 15
Step-by-step explanation:
9 - 6 = 3
and
9 + 6 = 15
Help pleaseeee!!
On January 1, 2014, the federal minimum wage was $7.25 per hour. Which graph has a slope that best represents this rate?
The horizontal line at $7.25 on the y-axis of the graph is the one with a slope that most accurately depicts the federal minimum wage of $7.25 per hour as of January 1, 2014.
Which federal minimum wage was the highest?Although it varies from state to state, the federally mandated minimum wage in the United States is $7.25 per hour. The District of Columbia had the highest minimum wage in the US as of January 1, 2023, at 16.50 dollars per hour.
How are minimum wages determined?The variable dearness allowance (VDA) component, which takes into account inflationary trends, such as an increase or fall in the Consumer Price Index (CPI), and, if applicable, the housing rent, are included in the computation of the monthly minimum salary.
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The question is in the picture.
The composite function is obtained applying the inner function as the input to the outer function.
The functions for this problem are defined as follows:
Inner function: T(t) = 6t + 1.2.Outer function: N(T) = 20T² - 128t + 77.Hence the composite function is obtained replacing the two instances of T on the function N(t) by the definition of T(t), hence:
N(T(t)) = 20(6t + 1.2)² - 128(6t + 1.2) + 77
N(T(t)) = 720t² + 288t + 28.8 - 768t - 204.6.
N(T(t)) = 720t² - 480t - 175.8.
For a population of 18413 bacteria, we have that N(T(t)) = 18413, hence:
720t² - 480t - 175.8 = 18413
720t² - 480t - 18588.8 = 0.
The coefficients of the quadratic function are given as follows:
a = 720, b = 480, c = -18.588.8.
Using a quadratic function calculator, the positive solution is given as follows:
t = 4.76 hours.
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HELP ME ASAPPP!!! Ill mark you brasinlisest
Step-by-step explanation:
Theoretical probabilities can be calculated using the concept of probability. Each student has a 0.5 chance of selecting either List A or List B. Therefore, the probability of getting 27 heads and 33 tails can be calculated as:
P(27 heads and 33 tails) = (60 choose 27) * (0.5)^27 * (0.5)^33 where (60 choose 27) is the number of ways to select 27 students out of 60.
Using a calculator, we can compute the above probability as approximately 0.109. This means that if we were to repeat this experiment many times, we would expect to get 27 heads and 33 tails about 10.9% of the time.
Comparing this theoretical probability to the experimental results, we see that the observed proportion of heads (27/60 = 0.45) is lower than the expected proportion of heads (0.5) and the observed proportion of tails (33/60 = 0.55) is higher than the expected proportion of tails (0.5).
However, it is important to note that due to the random nature of the experiment, we would not expect the exact theoretical probabilities to match the experimental results exactly. In other words, there is always some amount of variation expected in the results. Nonetheless, the experimental results are consistent with the theoretical probabilities, and we can conclude that there is no significant deviation from what we would expect by chance.
The odometer in Mr. Washington's car does not work correctly. The odometer recorded 14.3 miles for his last trip to the hardware store,but he knows the distant traveled is 17 miles.What is the percent error. Show steps
Find the percent errors, use the formula a-x/x ×100%
Answer:
15.8823% error
Step-by-step explanation:
Percent Error Formula
abs([tex]\frac{(a-x)}{x}[/tex]) * 100%
abs: absolute value
a: actual value
x: expected value
Percent Error = abs([tex]\frac{14.3 - 17}{17}[/tex]) * 100%
= abs(-0.158823) * 100%
15.8823% error
a
21 units squared
b
27.6 units squared
c
32.2 units squared
d
42 units squared
The area of the right triangle given in this problem is given as follows:
21 units squared -> Option A.
How to obtain the area of a triangle?To calculate the area of a triangle, you can use the formula presented as follows:
Area = (1/2) x base x height
In which the parameters are given as follows:
"base" is the length of the side of the triangle that is perpendicular to the height."height" is the length of the perpendicular line segment from the base to the opposite vertex.For a right triangle, we can consider one side to be the base and the other side to be the height, hence the parameters are given as follows:
Base of 7 units.Height of 6 units.Hence the area of the triangle is given as follows:
A = 0.5 x 7 x 6 = 21 units squared.
Missing InformationThe complete problem is defined as follows:
"Calculate the area of the given triangle".
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What does the point (5, 10) represent on the
graph?
Answer:
It means the point x = 5 and y = 10
Answer: The place 5 units right and 10 units up from the center of the graph (the origin).
Step-by-step explanation:
Starting at the origin, the 5 represents moving right 5, and the 10 represents going up 5.
Does anyone know what x equals?
Answer:
X=18
Step-by-step explanation:
Answer:
x = 3.5 units (nearest tenth)
Step-by-step explanation:
The given triangle has a one right angle and two angles each measuring 45°. Therefore, it is a 45-45-90 triangle.
A 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : 1 : √2.
Therefore, the formula for the ratio of the sides is x : x : x√2 where:
x is each side opposite the 45 degree angles (legs).x√2 is the side opposite the right angle (hypotenuse).As the hypotenuse of the given right triangle is 5 units:
[tex]\implies x\sqrt{2} = 5[/tex]
To find the measure of x, solve for x:
[tex]\implies \dfrac{x\sqrt{2}}{\sqrt{2}} = \dfrac{5}{\sqrt{2}}[/tex]
[tex]\implies x = \dfrac{5}{\sqrt{2}}[/tex]
[tex]\implies x =3.5355339...[/tex]
[tex]\implies x=3.5\; \sf units\;(nearest\;tenth)[/tex]
Therefore, the length of side x to the nearest tenth is 3.5 units.
the circumference of a circle is 4.8m. Calculate the area of the circle
Answer:
A≈1.83m²
Step-by-step explanation:
Using the formulas
A=πr2C=2πr
Solving forAA=C24π=4.824·π≈1.83346m²
Answer:
1.83 (approximate)
Step-by-step explanation:
First, we need to find the radius of the circle.
Using the formula:
[tex]C=2 \pi r[/tex]
We have to reorganize terms:
[tex]r=\frac{C}{2\pi}[/tex]
[tex]\frac{4.8}{2 \times \pi}[/tex]
r ≈ 0.76
Now we have the radius and the circumference in order to find the area.
Use the formulas:
[tex]A= \pi r^2[/tex]
[tex]C=2 \pi r[/tex]
A = C^2/4[tex]\pi[/tex] = 4.8^2 / 4 * pi = 1.83
find the lenght of each side of a rohmbus with permeter of 40 meters
Answer:
10 metres
Step-by-step explanation:
All sides are equal in Rhombus
So, the length of one side= 40m÷4
=10 metres
HERE IS THE SEQUENCE OF NUMBERS 3,6,11,18,27...
FIND THE NTH TERM OF THE SEQUENCE
3, 6, 11, 18, 27, 38, 51 , Next term 51 in the sequence is nth term .
What does math sequence mean?
An arrangement of numbers in a specific order is referred to as a sequence. The sum of the components of a sequence, on the other hand, is what is referred to as a series.
SEQUENCE 3,6,11,18,27...
the series follows the odd counting.
for example:
we have odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, etc.
now
3 + 3 = 6
6 + 5 = 11
we can see adding odd numbers in a series results in the solution of the proceeding number of series.
similarly,
11 + 7 = 18
18 + 9 = 27
27 + 11 = 38
now adding 13 to 38 according to the series will result in the next number.
38 + 13 = 51
hence, 51 is the next number in the series.
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Census data for a certain county shows that 19% of the adult residents are Hispanic. Suppose 92 people are called to jury duty and only 11 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection process? Again run a test using the PHANTOMS method to complete all parts of your problem.
Yes, the apparent under representation of Hispanics on the jury duty calls into question the fairness of the jury selection system, as the results of the hypothesis test suggest that the system may be systematically excluding Hispanics.
To determine whether the apparent underrepresentation of Hispanics on the jury selection system is statistically significant and calls into question its fairness, we need to perform a hypothesis test.
First, we set up the null hypothesis, which is the assumption that there is no difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool. That is, the proportion of Hispanics in the jury pool is expected to be equal to 19%.
The alternative hypothesis is that there is a difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool.
We can use a one-tailed z-test to test the null hypothesis, where the test statistic is calculated as:
z = (p - P) / sqrt(P(1-P)/n)
where p is the proportion of Hispanics in the jury pool, P is the proportion of Hispanics in the county population (0.19), and n is the sample size (72).
Plugging in the values, we get
z = (9/72 - 0.19) / sqrt(0.19*(1-0.19)/72) = -2.39
Assuming a significance level of 0.05, we compare the calculated z-value with the critical z-value of -1.645 (obtained from a standard normal distribution table). Since the calculated z-value is less than the critical z-value, we reject the null hypothesis and conclude that the proportion of Hispanics in the jury pool is significantly different from the proportion of Hispanics in the county population.
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A simple random sample with n = 25 provided a sample mean of 30 and a sample standard deviation of 4. Assume the population is approximately normal. a. Develop a 90% confidence interval for the population mean. b. Develop a 95% confidence interval for the population mean. c. Develop a 99% confidence interval for the population mean. d. What happens to the margin of error and the confidence interval as the confidence level is increased?
Conversely, as the confidence level decreases, the margin of error becomes smaller, and the confidence interval becomes narrower.
What is confidence interval?In statistics, a confidence interval is a range of values that is likely to contain the true value of a population parameter (such as a mean or a proportion), based on a sample from that population. The confidence interval is typically expressed as an interval around a sample statistic, such as a mean or a proportion, and is calculated using a specified level of confidence, typically 90%, 95%, or 99%.
Here,
To develop a confidence interval, we need to use the following formula:
Confidence Interval = sample mean ± margin of error
where the margin of error is calculated as:
Margin of Error = z* (sample standard deviation/ √n)
where z* is the critical value from the standard normal distribution table based on the chosen confidence level.
a. For a 90% confidence interval, the critical value (z*) is 1.645. Thus, the margin of error is:
Margin of Error = 1.645 * (4 / √25) = 1.317
So, the 90% confidence interval for the population mean is:
30 ± 1.317, or (28.683, 31.317)
b. For a 95% confidence interval, the critical value (z*) is 1.96. Thus, the margin of error is:
Margin of Error = 1.96 * (4 / √25) = 1.568
So, the 95% confidence interval for the population mean is:
30 ± 1.568, or (28.432, 31.568)
c. For a 99% confidence interval, the critical value (z*) is 2.576. Thus, the margin of error is:
Margin of Error = 2.576 * (4 / √25) = 2.0656
So, the 99% confidence interval for the population mean is:
30 ± 2.0656, or (27.9344, 32.0656)
d. As the confidence level increases, the margin of error also increases, because we need to be more certain that our interval includes the true population mean. This means that the confidence interval becomes wider as the confidence level increases.
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Martin Pincher purchased a snow shovel for $28.61, a winter coat for $23.27, and some rock salt for $7.96. He must pay the state tax of 5 percent, the county tax of 0.5 percent and the city tax of 2.5 percent. What is the total purchase price?
Hi Martin,
To calculate the total purchase price of your items, you'll need to apply the state, county, and city taxes to the total purchase cost of all three items.
The total purchase cost of all three items is:
Snow shovel: $28.61
Winter coat: $23.27
Rock salt: $7.96
Total purchase cost: $59.84
Now, we apply the applicable taxes:
State tax: 5% of $59.84 = $2.99
County tax: 0.5% of $59.84 = $0.30
City tax: 2.5% of $59.84 = $1.49
Total taxes: $2.99 + $0.30 + $1.49 = $4.78
Therefore, the total purchase price is:
Total purchase cost + Total taxes = $59.84 + $4.78 = $64.62
Andy has 4 red cards, 3 blue cards, and 2 green cards. He chooses a card and replaces it before choosing a card again. How many possible outcomes are in the sample space of Andy's experiment?
A) 18
B) 9
C)81
D)3
There are 81 potential outcomes in Andy's sample space.
What are the potential results?Potential Outcomes is a list of every scenario that could happen as a result of an occurrence. For instance, while rolling a dice, the possible results are 1, 2, 3, 4, 5, and 6. 6. Favorable Result - the intended outcome. For instance, if you roll a 4 on a dice, the only possible result is 4.
The total number of cards (i.e., 4 + 3 + 2 = 9) determines the number of outcomes that can occur in each draw.
We must multiply the total number of results for each draw in order to determine the total number of possible outcomes for the two draws.
For two draws with replacement, there are exactly as many outcomes available as the product of the amount of outcomes that could occur in each draw.
9 × 9 = 81.
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