Which equation can be used to solve for in the following diagram?

5 pointsWhich is the image of vertex Lafter the triangle is rotated 180 degrees about the origin?

Anastasy [175]

The image of vertex L after the triangle is rotated 180 degrees about the origin= (-2, -1).

Option B.

First let's stae the the original location of the figure on the graph.

From the graph:

L (2, 1)

W(1, -3)

O (-1, -2)

A rotation of 180 degrees about the origin will change the x and y axis of each location to the opposite of those numbers;

Positive numbers becomes negative and negative numbers becomes positive.

The new location for L = L'

L' = (-2, -1)

The new location for W = W'

W' = (-1, 3)

The new location for O = O'

O' = (1, 2)

Hence, the image of vertex L after the triangle is rotated 180 degrees about the origin= (-2, -1).

Option B.

6 0

1 year ago

We learned in Exercise 4.18 that about 90% of American adults had chickenpox before adulthood. We now consider a random sample o

liraira [26]

Answer:

a) 108 people with a standard deviation of 3.286335

b) No

c) 0.218163 or around 21.82%

d) See explanation below.

Step-by-step explanation:

This situation can be modeled with the Binomial Distribution which gives the probability of an event that occurs exactly k times out of n, and is given by

$\large P(k;n)=\binom{n}{k}p^kq^{n-k}$

where

$\large \binom{n}{k}$ = combination of n elements taken k at a time.

p = probability that the event (“success”) occurs once

q = 1-p

In this case, the event “success” is finding an American adult who had chickenpox before adulthood with probability p=0.9

and n=120 American adults in the sample.

The standard deviation for this binomial distribution is

$\large s=\sqrt{npq}$

where n is the sample size 120

a)

We consider a random sample of 120 American adults. How many people in this sample would you expect to have had chickenpox in their childhood?

If about 90% of American adults had chickenpox before adulthood, we expect to find 90% of 120 = 0.9*120=108 people in the sample who had chickenpox in their childhood.

The standard deviation would be

$\large s=\sqrt{120*0.9*0.1=3.286335}$

b)

Would you be surprised if there were 105 people who have had chickenpox in their childhood?

No, because 105 and 108 are in the interval [mean - s, mean +s]

c)

What is the probability that 105 or fewer people in this sample have had chickenpox in their childhood?

The probability that 105 or fewer people in this sample have had chickenpox in their childhood is

$\large \sum_{k=0}^{105}\binom{120}{k}0.9^k0.1^{120-k}$

We compute this value easily with a spreadsheet and we get

$\large \sum_{k=0}^{105}\binom{120}{k}0.9^k0.1^{120-k}=0.218163\approx 21.82\%$

d)

How does this probability relate to your answer to part (b)?

A binomial distribution with np>5 and nq>5 with n the sample size as is the case here, behaves pretty much like a Normal distribution with mean np and standard deviation $\large \sqrt{npq}$ , so around 60% of the data are in the interval [mean -s, mean +s] and 40% outside, so roughly 20% of the data should be in [0, mean-s]

4 0

3 years ago

If 70% of college students say they have a job what is the probability that 3 randomly selected college students say they have a

dsp73

Answer: 0.343

Step-by-step explanation:

Probability of college students that say they have a job = 70%

Number of randomly selected college students = 3

The probability that 3 randomly selected college students say they have a job will be:

= (70/100)³

= 0.7 × 0.7 × 0.7

= 0.343

4 0

3 years ago

Suppose the contestants were asked to make two batches of their recipes instead of one batch. Would the value for the amount of

kirill [66]

Answer:

yes

Step-by-step explanation:

If all contributors to the distribution are doubled, the value of any particular item in the distribution will be double what it was. That is, it will be different.

4 0

3 years ago

Tell whether the triangle with the given side lengths is a right triangle. 10in., 24in., 26in.

ra1l [238]

Answer- Yes it is a right triangle.
You can use the Pythagorean Theorem.
( a^2 + b^ = c^2 ) and replace a with 10, b with 24, and c with 26 and the equation will be balanced on both sides.

(10^2 + 24^2 = 26^2)
(100 + 576 = 676 )

4 0

3 years ago