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3 years ago

Rectangle JKLM is rotated 90° clockwise about the origin.

Mathematics

1 answer:

shusha [124]3 years ago

4 0

Answer:

Clockwise rotation 90 ° about origin

R_{90, clockwise, origin}(x,y) -> (y,-x)

J(-4,1) therefore

R_{90, clockwise, origin}J(-4,1) -> J'(1,+4) this answer was form other person credits to him/her

Step-by-step explanation:

You might be interested in

Write the equation in standard form y-4= -3(x-3)

Crazy boy [7]

Y - 4 = -3x + 9

y = -3x + 13

standard form: 3x + y = 13

3 0

3 years ago

Read 2 more answers

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

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

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

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]

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

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

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

Can someone explain the process of getting to Angle A? I know the answer is 44.1 but I need to show my work so can someone show

dsp73

Answer:

Step-by-step explanation:

First you have to calculate CB in order to use sin law to calculate ∠A

CB= $\sqrt{18.4^{2} -13.2^{2} }$

CB=12.8(correct to nearest tenth)

After that, use sin law to calculate ∠A,

$\frac{18.4}{sin90} =\frac{12.8}{sinA}$ or $\frac{sin90}{18.4} =\frac{sinA}{12.8}$

sinA=0.695...

A=44.079...

=44.1(corrext to the nearest tenth)

Is that clear enough for you?

4 0

2 years ago

A recipe used 2/3 cup of sugar for every 2 teaspoons of butter. How much sugar was used per teaspoon of butter

myrzilka [38]

Answer:

2/3cups 2 teaspoons

(2/3 )cups/2teaspoons =1/3 cups per teaspoon

Answer= 1/3 cups per teaspoon

8 0

3 years ago

Read 2 more answers

A golf ball is hit off a tee toward the green. The height of the ball is modeled by the function h(t) = −16t2 + 96t, where t equ

Ierofanga [76]

Answer:

t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.

Step-by-step explanation:

To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.

h(t) = -16t² + 96t

= -16(t² - 6t)

= -16(t² - 6t + 9) - (-16) * 9

= -16(t - 3)² + 144

Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum. We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground. The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".

6 0

3 years ago