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3 years ago

A dilation maps the point (24,36) to (16,24). The scale factor of the dilation is

Mathematics

1 answer:

Vika [28.1K]3 years ago

7 0

Answer:

The scale factor of the dilation is 2/3

Step-by-step explanation:

point (24,36) to (16,24)

16/24 = 2/3

24/36 = 2/3

Answer

The scale factor of the dilation is 2/3

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The annual rainfall (in inches) in a certain region is normally distributed with mean 43.2 and variance 20.8. Assume rainfall in

Wittaler [7]

Answer:

92.24% probability that out of 15 years, at most 2 have rainfall of more than 50 inches.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the binomial probability distribution.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation(which is the square root of the variance) $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Binomial probability distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem, we have that:

$\mu = 43.2, \sigma = \sqrt{20.8} = 4.56$

Probability that a year has rainfall of more than 50 inches.

pvalue of Z when X = 50. So

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

$Z = \frac{50 - 43.2}{4.56}$

$Z = 1.49$

$Z = 1.49$ has a pvalue of 0.9319

1 - 0.9319 = 0.0681

Find the probability that out of 15 years, at most 2 have rainfall of more than 50 inches.

This is $P(X \leq 2)$ when $n = 15, p = 0.0681$ . So

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{15,0}.(0.0681)^{0}.(0.9319)^{15} = 0.3472$

$P(X = 1) = C_{15,1}.(0.0681)^{1}.(0.9319)^{14} = 0.3805$

$P(X = 2) = C_{15,2}.(0.0681)^{2}.(0.9319)^{13} = 0.1947$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.3472 + 0.3805 + 0.1947 = 0.9224$

92.24% probability that out of 15 years, at most 2 have rainfall of more than 50 inches.

8 0

3 years ago

Read 2 more answers

Hey surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 150 feet from a Pi

AleksAgata [21]

Answer: 87 feet

Step-by-step explanation:

The angle between the pilling is 60°

The adjacent side of the right angle is 150

So let the distance between the pilling be y, that is opposite side.

Opposite / adjacent = tan (60°)

y / 150 = tan (60)

y × tan (60°) = 150

Divide both side by tan (60°)

y = 150 / tan (60°)

y = 150 / 1.7321

y = 87 feet

4 0

3 years ago

A bacteria cell splits into two cells every hour. Write and evaluate an exponential expression to find how many cells there will

ryzh [129]

Easy

equation is
f(x)=2ˣ

where x=number of hours elapsed

after 6 hours
f(6)=2⁶=64 bacteria

to solve for 1024

1024=2ˣ
take ln of both sides
ln(1024)=ln(2ˣ)
ln(1024)=x(ln(2))
divide both sides by ln(2)
ln(1024)/ln(2)=x
using calculator
10=x

or you could recognize that
1024=2¹⁰
or keep divising 1024 by 2

10 hours for 1024 bacteria

4 0

3 years ago

PLEASE HURRY Read a text trailer for the movie Harry Potter and the Sorcerer’s Stone. Harry Potter seems at first glance normal,

V125BC [204]

Answer:

Step-by-step explanation:

Which statement in the trailer is the hook?

A) Harry Potter seems at first glance normal, a boy living an unusual life with his dull and rather mean Dursley relatives.

B) However, on Harry’s eleventh birthday, he learns from a mysterious stranger, Rubeus Hagrid, that he is actually a famous wizard.

C) Forbidden by his uncle from seeking out his magical destiny, letters rain down inviting Harry to attend the magic school of Hogwarts.

D) What follows is an adventure story of intrigue, discoveries, and sacrifice.

In order of events:

A, C, B, D

A is where the story begins so it would be the best chose. It should catch you and make you want to know more. Also, the hook is usually the first sentence.

6 0

3 years ago

If x = 2 and y = 1, then 3(y – 1) + 2x2 =

abruzzese [7]

3(1-1) +2x2

3-1+4

2+4=6

6 0

3 years ago

Read 2 more answers