The diameter of a dime tells us the circumference of a dime is approximately 299 times larger than human hair.
What is DiameterThe diameter of an object is used to calculated the circumference or area of the object. This also helps us to know the width of a circular object.
In this problem, the diameter tells us about the length of the each quantity.
The diameter of a dime tells us how wide the coin is and the diameter if a hair tells us the width of the hair.
Comparing both values
Dime = 17.91mm
Hair = 6.0*10^-2
Divide both quantity together.
17.91 / 6.0*10^-2 = 298.5≅299
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What is the equation of a vertical ellipse with a major axis = 14, a minor axis = 12,
and a center of (3,5) ?
The equation (x - 3)² / 144 + (y - 5)² / 196 = 1 is the standard form of the ellipse.
How to determine the standard form of the equation of the ellipse
Herein we know the main features of a vertical ellipse, that is, the center and the lengths of its axes. The standard form of the equation of the ellipse:
(x - h)² / a² + (y - k)² / b² = 1, b > a
Where:
(h, k) - Center of the ellipse.a, b - Length of the semiaxes.If we know that (h, k) = (3, 5), a = 12, b = 14, then the standard form of the equation of the ellipse is:
(x - 3)² / 12² + (y - 5)² / 14² = 1
(x - 3)² / 144 + (y - 5)² / 196 = 1
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Find x and y values that make both y=−2/3x+3 and y=2x−5 true.
What is the ordered pair for your solution?
The ordered pair is (3, 1) which is the intersecting point of these two equations.
What is the graphical solution of a system of equations?Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.
A system with two or more than two equations has a solution only when they have a common intersection point.
Given, are two equations y = -(2/3)x + 3 and y = 2x - 5.
Now the solution to this system is the common intersecting point of these equations.
With the help of graphing we conclude that the intersecting point is (3, 1) and so is the solution.
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Out of a group of 360 students, exactly 18 are on the track team. What percent of the students are on the track team?
if we take 360 to be the 100%, what's 18 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 360 & 100\\ 18& x \end{array} \implies \cfrac{360}{18}~~=~~\cfrac{100}{x}\implies 20=\cfrac{100}{x} \\\\\\ 20x=100\implies x=\cfrac{100}{20}\implies x=5[/tex]
What is the slope that passes through (1,2) and (2,6)
Answer:
4
Step-by-step explanation:
use slope formula y2-y1/x2-x1
6-2/2-1
4/1
4 is the slope
Hopes this helps please mark brainliest
What is the value of x? Show your work.
In 8 day, a ample of vanadium-48 decay to 1/√2 of it original amount. Determine the half-life of vanadium-48
The half-life of vanadium-48 is 16 days.
What is half life?
The half-life formula is used to determine the half-life of a material whose quantity is degrading or decreasing. When a substance degrades, the rate of decay varies depending on the quantity present. It is exceedingly challenging to determine the life of a decaying substance since when the quantity of the chemical decreases, the pace of decay likewise slows down. In order to offer the appropriate metrics to quantify the life of decomposing material, the half-life formula is applied.
According to law of radio active decay, IN=N
N-- amount of sample present
N1--- initial amount of sample
Decay 0 constant
Half life = 16 days
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Below are several options for the roots of a polynomial with degree 4. Consider all possibilities and combinations for the x- intercepts.
distinct x-intercepts of which one has a multiplicity of
x-intercepts and imaginary roots
distinct x-intercepts of which one has a multiplicity of
distinct x-intercepts
x-intercept with multiplicity
x-intercept with imaginary roots
distinct x-intercepts and imaginary root
distinct x-intercepts each with multiplicity
The all the possibilities and combination for the x - intercepts , of the roots of the polynomial with degree 4 are :
0 x-intercepts and 4 imaginary roots ,
4 distinct x-intercepts ,
1 x-intercept with multiplicity 4 and
2 distinct x-intercepts each with multiplicity 2 .
In the question ,
it is given that ,
there is polynomial of degree 4 ,
and some statements about the roots of the polynomial is given ,
we have to find the suitable options that are for the roots .
We know that the fourth degree polynomial will have theoretically four roots .
So , the possible situations for the roots are
it can have ,
0 x intercepts and 4 imaginary roots ( where imaginary roots must occur in pairs ) OR
it can have 4 distinct x intercepts . OR
1 x intercept that have multiplicity 4 , OR
2 distinct x intercepts that have multiplicity 2 .
Therefore , the possibilities options are (b) , (d) , (e) and (h) .
The given question is incomplete , the complete question is
Below are several options for the roots of a polynomial with degree 4. Consider all possibilities and combinations for the x- intercepts .
(a) 2 distinct x-intercepts of which one has a multiplicity of 3 ,
(b) 0 x-intercepts and 4 imaginary roots
(c) 3 distinct x-intercepts of which one has a multiplicity of 2
(d) 4 distinct x-intercepts
(e) 1 x-intercept with multiplicity 4
(f) 1 x-intercept with 3 imaginary roots
(g) 3 distinct x-intercepts and 1 imaginary root
(h) 2 distinct x-intercepts each with multiplicity 2
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If (x+r)(x+s)=x² +3x-10 for all x, then what is the value for (r+s)?
The value of (r + s) in the given equation, (x+r)(x+s) = x² + 3x - 10, is (r + s) = 3
Determining the value of an expression from an equationFrom the question, we are to determine the value of the given expression.
The expression we are to determine its value is
(r + s)
To do this, we will compare the terms of the given equation.
From the given equation
(x+r)(x+s) = x² + 3x - 10
First, we will expand the left-hand side of the equation
Expanding the left-hand side of the equation
(x+r)(x+s)
x(x + s) + r(x + s)
x² + xs + xr + rs
Factor the middle expressions
x² + x(s + r) + rs
x² + x(r + s) + rs
x² + (r + s)x + rs
Now, compare the resulting expression to the expression on the right-hand side
x² + 3x - 10
By comparison,
r + s = 3
Hence, the value is 3
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What is the y-intercept, b, of the additive relationship represented by this table?
Enter your answer as an integer in the box.
b = ?
Answer:
3
Step-by-step explanation:
For every point on the graph of F(x), there is a point on the graph of F1(x)
with exactly the same coordinates.
A. True
B. False
Select the statement below that is true about correlations.A. Correlations can only be negativeB. Correlations are a measure of how much one variable changes as the other variable changesC. Correlations are a measure used to determine the degree to which two variables are related.D. Correlations are a measure of causation between two variablesE. A negative correlation implies no relationship between variablesF. Correlations can only be positive
The statements that are True about the Correlations is , "Correlations are a measure used to determine the degree to which two variables are related" , the correct option is (c) .
In the question,
few statements about Correlation is given ,
we need to find the statement that is True .
we know that , Correlation is the term that is used to measure the degree of relationship between two variable ,
the correlation can be negative , positive or 0 ,
and the negative correlation implies that if one variable increases then other variable decreases and vice a versa .
So , from the above information about Correlation ,
we conclude that , the True statement is "Correlations are a measure used to determine the degree to which two variables are related. "
Therefore , the statement in option (c) is True .
The given question is incomplete , the complete question is
Select the statement below that is true about correlations.
(a) Correlations can only be negative
(b) Correlations are a measure of how much one variable changes as the other variable changes
(c) Correlations are a measure used to determine the degree to which two variables are related.
(d) Correlations are a measure of causation between two variables
(e) A negative correlation implies no relationship between variables
(f) Correlations can only be positive .
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a photo has a width to length ratio of 2:3. if the width of the photo is 4.8 cm, the length of the photo is
The length of the photo having a width to length ratio of 2:3 is 6.9 cm.
What is length?Length is the distance between two points.
To calculate the length of the photo, use the formula below.
Formula:
L = W/R............ Equation 1Where:
L = Length of the photoR = Width to length ratio of the photoW = Width of the photo.From the question,
Given:
W = 4.6 mR = 2:3 = 2/3Substitute these values into equation 1
L = 4.6/(2/3)L = 4.6×3/2L = 6.9 cmHence, the length of the photo is 6.9 cm.
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9.
3/5
+
3
20
please answer
Answer:9/10
Step-by-step explanation:
make 3/4 equal to 3/20 by multiplying by 5
15/20 + 3/20 = 18/20
18/20 = 9/10
A candidate for office claims that "there is a correlation between television watching and crime." Criticize this statement on statistical grounds.
There may be an association, but not a correlation unless the variables are quantitative. There could be a correlation between the average number of hours of TV watched per person and number of crimes committed per year. Even if there is a relationship, one does not cause the other.
What is correlation?Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate).
What are qualitative and quantitative variables?
The variables are classified as qualitative or quantitative as follows:
Qualitative variables assume labels as values.
Quantitative variables assume numbers as values.
The relevance of the variables according to association and correlation are given as follows:
Qualitative variables can have association.
Quantitative variables can have correlation.
The variables in this problem are given as follows:
Television watching -> yes/no -> qualitative.
Crimes committed -> yes/no -> qualitative.
As they are qualitative variables, they can have association, and thus there is no correlation between the two variables
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David's iPod has about 10,000 songs. The distribution of the play times for these songs is heavily skewed to the right with a mean of 225 seconds and a standard deviation of 60 seconds. Suppose we choose an SRS of 10 songs from this population and calculate the mean play time
x
of these songs. What are the mean and the standard deviation of the sampling distribution of
x?
Explain.
The mean and the standard deviation of the sampling distribution of x are given as follows:
Mean: 225 seconds.Standard deviation: 19 seconds.How to obtain the mean and the standard deviation of the sampling distribution of x?The mean and the standard deviation of the sampling distribution of x are defined according to the Central Limit Theorem, which states that:
The mean is the same as the population mean.The standard deviation is the division of the population standard deviation by the square root of the sample size.The parameters for this problem are given as follows:
Population mean of 225 seconds.Population standard deviation of 60 seconds.Sample size of 10 seconds.Hence the standard deviation for the sampling distribution of x is given as follows:
s = 60/sqrt(10) = 19 seconds.
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ABCD is a rectangle, where AB= x cm and
BC is 1.5 cm less than AB.
If the area of the rectangle is 52 cm³, form
an equation in x and solve it to find the
dimensions of the rectangle.
Answer:
AB = 8cm ; BC = 6.5 cm
Step-by-step explanation:
BC = x- 1.5
x * (x-1.5) = 52
x^2 - 1.5x - 52 = 0
Discriminant = 2.25 -4(-52) = 2.25 + 208 = 210.25
We are searching only positive value
(1.5 + 14.5)/2 = 16 / 2 = 8 cm
AB = 8 cm
BC = 8 - 1.5 = 6.5 cm
Tracy is saving to buy a new guitar that costs $253. 77 (including tax). Tracy has saved $136. 27, and she can save $23. 50 each week. How many more weeks will it take her to save enough money?.
Tracy need 5 weeks to save enough money to buy a new guitar.
Given that,
Tracy is saving to buy a new guitar. Which having costs $253.77(including tax).
Tracy has already saved $136. 27.
Now she needs = 253. 77- 136. 27
= $117.50
she can save each week = $23. 50
Tracy will take weeks to save enough money
= [tex]\frac{117.50}{23.50}[/tex]
= 5 weeks.
Therefore, Tracy need 5 weeks to save enough money to buy a new guitar.
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14. On the test, Zeke answered 85% of the
questions correctly. If there were 60 problems
on the test, how many did Zeke answer
correctly?
I need help please im so confused
Step-by-step explanation:
the x-intercept is the point, where the curve intercepts the x-axis (that means y = 0).
the y-intercept is the point, where the curve intercepts the y-axis (that means x = 0).
y = 10 - 2x
when x = 0, that means y = 10 - 2×0 = 10.
when y = 0, that means 0 = 10 - 2x, 2x = 10, x = 5
x-intercept = (5, 0)
y-intercept = (0, 10)
4y + 9x = 18
x = 0, 4y = 18, y = 18/4 = 9/2 = 4.5
y = 0, 9x = 18, x = 18/9 = 2
x-intercept = (2, 0)
y-intercept = (0, 4.5)
6x - 2y = 44
3x - y = 22
x = 0, -y = 22, y = -22
y = 0, 3x = 22, x = 22/3 = 7 1/3
x-intercept = ( 7 1/3, 0)
y-intercept = (0, -22)
2x = 4 + 12y
x = 2 + 6y
x = 0, 6y = -2, y = -2/6 = -1/3
y = 0, x = 2 + 6×0 = 2
x-intercept = (2, 0)
y-intercept = (0, -1/3)
Which of the following are essential elements of hypothesis testing?
-It uses probability theory to determine if a hypothesis is a reasonable statement.
-It makes use of sample data.
The following are crucial factors in hypothesis testing:
It employs probability theory to evaluate if a hypothesis is a valid claim.It employs sample data.Explain the term hypothesis testing?In statistics, the process of hypothesis testing involves putting an analyst's presumption about a population parameter to the test.
The type of data being used and purpose of the study will determine the methodology the analyst uses. A basic hypothesis can anticipate a causal relationship between variables, i.e., that one has an impact on the other. This is known as hypothesis testing, and it uses sample data to determine the plausibility of a hypothesis.It is a technique for analysis that evaluates presumptions and establishes the likelihood of something based on a predetermined level of accuracy. Testing hypotheses offers a technique to determine whether the outcomes of an investigation are reliable.Thus, before conducting the hypothesis testing, a null hypothesis as well as an alternative hypothesis are established.
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Which expression is equivalent to log2-log6
Answer: log2-log6=-log3
Step-by-step explanation:
[tex]\displaystyle\\log2-log6=\\\\log\frac{2}{6} =\\\\log\frac{2(1)}{2(3)}=\\\\log\frac{1}{3} =\\\\log3^{-1}=\\\\-log3[/tex]
Select all correct answers. one solution to a quadratic equation is . what is true about any remaining solutions? there are at least two more real solutions. there are no other real solutions. there is exactly one complex solution. there are two or more complex solutions. there are no complex solutions. there is exactly one more real solution.
There is exactly one more real solution or there is exactly one more complex solution
Given,
One solution to a quadratic equation is x = -5/3
We have to find the correct statements from the given ones;
A polynomial of degree two is a quadratic equation.
This implies that a polynomial has two solutions.
We already have an answer to the query, which is a true root.
Then, the additional response that we lack can appear in the form of two responses.
It may be a real root or a complicated root, depending on the situation.
The following is the response to this query:
There is exactly one more real solution or there is exactly one more complex solution
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what algebraic expression represents a number increased by 5
Answer: x+5
Step-by-step explanation:
Because we don't have a number so we call it x. And to increase by 5 just need to +5. So x+5
The area of a triangle is always one half the base b times the height h.
If the base is represented by the expression 4x + 2 and the height is represented by 3x, which expression gives the area of the triangle?
9x
9x2
12x2 + 6x
6x2+ 3x
The correct option is [tex]6x^2+3x[/tex] which is the area of triangle. It can be obtained by the formula of area of triangle and algebriac multiplication.
What is the are formula of area of a triangle?
Area of any shape is the measure of the 2 dimentional space occupied by that shape. Its SI unit is [tex]m^2[/tex]. Area of the triangle is given by the following formula:
[tex]A=\frac{1}{2}bh[/tex]
Here, A is the area, b is the base, and h is the height.
Substitute 4x+2 for b and 3x for h in the above equation.
[tex]A=\frac{1}{2}(4x+2)(3x)[/tex]
Now, multiply using algebriac multiplication as follows:
Initially, use distributive property as follows:
[tex]A=\frac{1}{2}[(4x)(3x)+(2)(3x)][/tex]
Now, multipliy and again open brackets as follows
[tex]A=\frac{1}{2}(12x^2+6x)\\=6x^2+3x[/tex]
This gives the area of the triangle is [tex]6x^2+3x[/tex]. Hence, the correct option is the last option.
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Answer:
d
Step-by-step explanation:
a spring has a spring constant of 283 n/m. how far is the spring compressed to the right if 129 n of force are used
The spring is compressed to 95.5 cm to the right if 129 N of force are used.
In this question, we have been given the spring constant k = 283 N/m
if 129 N of force are used then we need to find distance that the spring compressed to the right.
Let the spring stretch from the equilibrium position x.
An equation for the spring's potential energy is,
PE = 1/2 kx^2
129 = 1/2 * 283 * x^2
2 * 129 = 283 * x^2
258/283 = x^2
x^2 = 0.9117
x = 0.9548 m
x = 95.5 cm
Therefore, the spring is compressed to 95.5 cm to the right if 129 N of force are used.
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T/F the proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the .
The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the coefficient of determination.
What is coefficient of determination?
The effectiveness of a statistical model in forecasting a result is shown by the coefficient of determination (R²). The dependent variable in the model is a representation of the result.
R² can have a value of 0 or 1, with 1 being the maximum achievable. Simply said, a model's R² will be closer to 1 the more accurate its predictions are.
R² is a more precise measure of goodness of fit. The amount of volatility in the dependent variable that the model can account for.
You can typically tell whether your linear regression data's R² is high or low by graphing it. The graphs below, for instance, display two sets of simulated data:
Dots represent the observations.
The line of best fit, or predictions of the model, is displayed as a black line.
Purple lines represent the deviations (the residuals) between the data and their expected values.
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Use synthetic division to solve (2 x cubed + 4 x squared minus 35 x + 15) divided by (x minus 3). What is the quotient?.
The quotient is 2x² + 10x − 5, and the remainder is 0.
What is synthetic division?
Synthetic division is a method in algebra for manually performing Euclidean division of polynomials that requires less writing and fewer calculations than long division. It is typically taught for division by linear monic polynomials, but the method can be applied to any polynomial.
The given polynomial is (2x³ + 4x² - 35x + 15) and we have to divide this polynomial by (x - 3).
By using synthetic division
2x³ + 4x² - 35x + 15
Take the constant term of the divisor with the opposite sign and write it to the left
3 | [tex]x^3[/tex] [tex]x^2[/tex] [tex]x^1[/tex] [tex]x^0[/tex]
| 2 4 -35 15
----|----------------------------
Write down the first coefficient as it is
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
3 | 2 4 -35 15
| 3.2 = 6
----|----------------------------
2 10
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
3 | 2 4 -35 15
| 6 30
-----|----------------------------
2 10 -5
Again, we get
3 | 2 4 -35 15
| 6 30 -15
-----|----------------------------
2 10 -5 0
We have completed the table and have obtained the following resulting coefficients: 2,10,−5,0.
Thus, the quotient is 2x² + 10x − 5, and the remainder is 0.
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If θ i an angle in tandard poition and it terminal ide pae through the point (-9,-1), find the exact value of tan theta implet radical form
The exact value of tan(θ ) in simplest radical form is 1/9 .
What is the trigonometric ratio?
Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.
Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.
(-9,-1), is a point with x= -9 = adjacent side, y= -1 = opposite side
tan(θ ) = opposite side/adjacent side = -1/-9 = 1/9
1/9 can't be simplified further
So, the exact value of tan(θ ) in simplest radical form is 1/9 .
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Solve the system. Explain your answer using words, symbols, or both. please show your work thank you.
x+3y=8
x+y=2
The value of x and y is 3
What is meant by mathematical equation ?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equals sign =. [2] [3] In other languages, the word equation and its cognates may have slightly different meanings; for example, in French, an équation is defined as containing one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.
Let the equations be
x + 3y = 8 ..............(1)
x + y = 2 ..............(2)
substracting equation 1 from 2
(x + 3y) - (x + y ) = 8 - 2
x + 3y - x + y = 6
3y - y = 6
2y =6
y = 6/2
y = 3
multiply the equation 2 with value of 3
x + y=2*3
x+y =6
x+3 = 6
x = 6 - 3
x = 3
Therefore the value of x and y is both are 3
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➤ Solve the inequalities.
T -3 is less than or equal to 2
-3 is less than 2
< is the symbol
