Answer:
A sample of 499 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of 
.
The margin of error is given by:
In this question, we have that:
90% confidence level
So 
, z is the value of Z that has a pvalue of 
, so 
.
How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 90% confidence level with an error of at most 0.03
We need a sample of n, which is found when 
. So
Rounding up
A sample of 499 is needed.
Answer:
D.
Step-by-step explanation:
To find the equation of g(x), we can substitute the point into each of the equations.
A. g(x) = (1/4x)^2
1 = (1/4 * 2)^2
1 = (1/2)^2
1 = 1/4
This statement is false, so this is not the equation.
B. g(x) = 1/2 * x^2
1 = 1/2 * (2)^2
1 = 1/2 * 4
1 = 2
This statement is false, so this is not the equation.
C. g(x) = 2x^2
1 = 2 * 2^2
1 = 2 * 4
1 = 8
This statement is false, so this is not the equation.
D. g(x) = (1/2x)^2.
1 = (1/2 * 2)^2
1 = 1^2
1 = 1
This statement is true, so this is your answer.
Hope this helps!
<h3>
Answers:</h3>
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Explanation:
The scale factor is 2, which means we double each coordinate of each point. The general rule is 
with k = 2. So we can say the more specific dilation rule is 
Something like W(-2,2) moves to W ' (-4, 4) after multiplying each coordinate by 2. Do the same for the other points as well.
The given preimage points
- V = (-2, -1)
- W = (-2, 2)
- X = (0, 2)
- Y = (3, -1)
will dilate to the corresponding image points
- V ' = (-4, -2)
- W ' = (-4, 4)
- X ' = (0, 4)
- Y ' = (6, -2)
as shown below. This causes the image to be larger compared to the preimage (since the scale factor is larger than 1). Any given point is twice as far from the origin as compared to before, which in turn means the distance between any two points is twice as much.
There are 23 nickles in her purse
Answer:
x + y = -2
Step-by-step explanation:
The two primary equations to remember when dealing with graphing 2-variable equations are: ax + by = c (a & b are the x & y coefficients, respectively), and the other is y = mx + c (m = slope, x & y represent themselves). There is another equation to find the slope. If not already known, it's: ∆y/∆x {∆(aka Delta) = difference}. So, since that's all been established, we can proceed to calculate your question:
1) Find your slope: 1 - (-4) = 5 for your y-variable. And -3 - 2 = -5 for your x-variable. So your slope = 5/-5 = -1
2) Use the y = mx + c equation together with either set of (x,y) coordinates to get the equation 1 = (-1)(-3) + c. Which gives you c = -2
3) So, going back to the main equation to remember, the ax + by = c, use a one of your given sets of x,y coordinates and input your known values for x, y, & c to get: a(-3) + b(1) = (-2) and do the same with other set (these are just double-checks, coefficients are all equal to 1 anyways). So, you should arrive to the equation: x + y = -2
