Corresponding sides of the dilated figure and the original figure proportional true or false

David and Peter had $90 and $200 respectively. They were each given an equal amount of money. Then Peter had twice as much money

Aleksandr [31]

20 dollars each! hope it helps.

4 0

2 years ago

Suppose that F(x) = x^2 and G(x) = 2x^2-5. Which statement best compares the graph G(x) with the graph of F(x)?

notsponge [240]

I believe the correct answer from the choices listed above is option D. The graph G(x) as compared to the graph of F(x) would be that the graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units down. 2 is a stretch factor and -5 is the shift downwards of the graph. Hope this answers the question.

8 0

3 years ago

Read 2 more answers

At a new exhibit in the Museum of Science, people are asked to choose between 94 or 220 random draws from a machine. The machine

Tresset [83]

Answer:

0.0869 = 8.69% probability of getting more than 61% green balls.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

The machine is known to have 99 green balls and 78 red balls.

This means that $p = \frac{99}{99+78} = 0.5593$

Mean and standard deviation:

$\mu = p = 0.5593$

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.5593*0.4407}{99+78}} = 0.0373$

a. Calculate the probability of getting more than 61% green balls.

This is 1 subtracted by the pvalue of Z when X = 0.61. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{0.61 - 0.5593}{0.0373}$

$Z = 1.36$

$Z = 1.36$ has a pvalue of 0.9131

1 - 0.9131 = 0.0869

0.0869 = 8.69% probability of getting more than 61% green balls.

8 0

3 years ago

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

Alexandra [31]

Answer: y-axis.

Explanation:

The equation r = 3 - 4 sin θ may be graphed using cartesian coordinates (i.e. x and y) or polar coordinates.

The logical way is to graph in polar coordinates. I did it using a graphing software and obtained the attached graph.

Also, I attached the graph in cartesian coordinates.

Here you have a table that you can build by your self and use the pairs to draw the graph (either cartesian or polar coordinates).

 θ (rad) r = 3 - 4 sin θ 

0 3 
π/8 2.61731657 
 π/4 2.29289322 
3π/8 2.07612047
 π/2 2
 5π/8 2.07612047 
3π/4 2.29289322 
7π/8 2.61731657 
π 3 
9π/8 3.38268343 
5π/4 3.70710678 
11π/8 3.92387953 
3π/2 4 
13π/8 3.92387953 
7π/4 3.70710678 
15π/8 3.38268343 
2π 3 

In both of the attached graphs you can see that the left side is equal to the right side, but the upper side is not equal to the bottom side.

Therefore, the graph is symmetric about the y-axis.

7 0

3 years ago

Read 2 more answers

Gym membership costs $100 per year in a $2 fee per visit another gem charges $12 fee per visit with no yearly membership find th

Nimfa-mama [501]

Answer:

For 10 visits, both gyms charge the same

Step-by-step explanation:

Equations

Gym memberships' costs are:

G1 = 100 + 2x

G2 = 12x

Where x is the number of visits to the gym.

We need to find the number of visits for which the charges for both gyms are the same. Thus equating the costs:

12x = 100 + 2x

Subtracting 2x:

10x = 100

Dividing by 10:

x =10

For 10 visits, both gyms charge the same

3 0

3 years ago