Which of the following statements are true? (Select all that apply)

Correlation coefficients are negative when the relationship is weak and positive when they are strong.

Correlation coefficients show the relationship of the x and y values.

Correlation coefficients can be any value less than 1 or greater than −1.

Correlation coefficients show the x and y intercepts of the best fit line.

Correlation coefficients can be represented by the variable r.

Question:

A lighthouse is located on an island 3 miles from the closest point on a straight shoreline. If the lighthouse light rotates clockwise at a constant rate of 9 revolutions per minute, how fast does the beam of light move towards the point on the shore closest to the island when it is 52 miles from that point

Answer:

The beam of light moves at [tex]16278\pi[/tex] miles/min

Step-by-step explanation:

This question is illustrated with the attached image

Taking the instructions in the question, one at a time.

A revolution of 9 per minute implies that:

[tex]\frac{d\theta}{dt} = \frac{9 * 2\pi\ rad}{1\ min}[/tex]

[tex]\frac{d\theta}{dt} = 18\pi \frac{rad}{min}[/tex]

Take tan of the angle in the attachment:

[tex]tan(\theta) =\frac{52}{3}[/tex]

Differentiate both sides with respect to time

[tex]\frac{d\ tan(\theta)}{dt} =\frac{52}{3} * \frac{dx}{dt}[/tex]

Rewrite as:

[tex]\frac{d\ tan(\theta)}{d\theta} * \frac{d\theta}{dt} =\frac{52}{3} * \frac{dx}{dt}[/tex]

In calculus:

[tex]sec^2(\theta) =\frac{d\ tan(\theta)}{d\theta}[/tex] -- Chain rule

So:

[tex]sec^2(\theta) *\frac{d\theta}{dt} =\frac{52}{3} * \frac{dx}{dt}[/tex]

In trigonometry:

[tex]sec^2(\theta) = tan^2(\theta) + 1[/tex]

So:

[tex](tan^2(\theta) + 1)\frac{d\theta}{dt} =\frac{52}{3} * \frac{dx}{dt}[/tex]

Recall that:

[tex]tan(\theta) =\frac{x}{3}[/tex]

[tex]((\frac{52}{3})^2 + 1)\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]

[tex](\frac{52^2}{9} + 1)\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]

[tex](\frac{2704}{9} + 1)\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]

[tex](\frac{2704+9}{9})\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]

[tex](\frac{2713}{9})\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]

Recall that: [tex]\frac{d\theta}{dt} = 18\pi \frac{rad}{min}[/tex]

[tex](\frac{2713}{9}) * 18\pi =\frac{1}{3} * \frac{dx}{dt}[/tex]

[tex]2713 * 2\pi =\frac{1}{3} * \frac{dx}{dt}[/tex]

Multiply both sides by 3

[tex]3 * 2713 * 2\pi =\frac{1}{3} * \frac{dx}{dt} * 3[/tex]

[tex]3 * 2713 * 2\pi =\frac{dx}{dt}[/tex]

[tex]16278\pi =\frac{dx}{dt}[/tex]

[tex]\frac{dx}{dt} = 16278\pi[/tex] miles/min

Hence:

The beam of light moves at [tex]16278\pi[/tex] miles/min

Answer:

14

Step-by-step explanation:

126/9=14

Answer:

NO you only got 70 percent

Step-by-step explanation:

Answer:

I dont see the question...

Step-by-step explanation:

Answer:

62.857142857143%

Step-by-step explanation:

Answer:

0.1171875;

0.171875

Step-by-step explanation:

It is either a person is right handed or left handed

P(right handed) = 1/2

Probability of having 3 right handed people in a sample of 10 ;

P(x =x) = nCx * p^x * (1 - p)^(n - x)

P(x = 3) = 10C3 * 0.5^3 * 0.5^7

P(x = 3) = 120 * 0.125 * 0.0078125

P(x = 3) = 0.1171875

Using R ;

P(x ≤ 3)

We can obtain these from R using ;

pbinom( r, n, p)

pbinom(3, 10, 0.5) = 0.171875

Answer:

True

Step-by-step explanation:

It is true because the graph of [tex]y=x-12[/tex] passes through the point [tex](16,4)[/tex]

x = 16

y = 4

Substitute

4 = 16 - 12

4 = 4

Therefore, the answer is true.

Answer:

100 times

Step-by-step explanation:

doesn't matter if the number is in the same place value so, the answer is 100 times.

Answer:

3

Step-by-step explanation:

Answer:

The answer to this question is X=3

Step-by-step explanation:

15x3=45

45+1=46

Hope my answer helps you!!!

Answer:

Step-by-step explanation:

yes that is correct!-2

Answer:

Step-by-step explanation:

I can't see the statements

Answer:

confess and believe are the two main words.

Step-by-step explanation:

Just got this right :')

Answer:

H

Step-by-step explanation:

This is because a rectangle can be divided into two triangles.

Answer:

this is confusing. I'll try my best to sort it out for you. I'll tap in once I figure it out

Answer:your

Step-by-step explanation:

mom

Answer:

  c) parabola and circle: 0, 1, 2, 3, 4 times

  d) parabola and hyperbola: 1, 2, 3 times

Step-by-step explanation:

c. A parabola can miss a circle, be tangent to it in 1 or 2 places, intersect it 2 places and be tangent at a 3rd, or intersect in 4 places.

__

d. A parabola must intersect a hyperbola in at least one place, but cannot intersect in more than 3 places. If the parabola is tangent to the hyperbola, the number of intersections will be 2.

If the parabola or the hyperbola are "off-axis", then the number of intersections may be 0 or 4 as well. Those cases seem to be excluded in this problem statement.

Answer:

1 times 89 = 89 lol    1 x 7= 7

Step-by-step explanation:

hope this helps lol

Answer:

Ava's

Step-by-step explanation:

To find whose plot of land is smaller, compare the sizes of their plots.

Jason's is 2/5 of an acre, while Ava's is 2/8 of an acre.

Because they have the same numerator, we can look at the denominator to see which is smaller.

The number with the larger denominator will be smaller. So, this means 2/8 is smaller than 2/5.

So, Ava's plot of land is smaller

Answer:

13 weeks because he loses 3 pounds per week

Step-by-step explanation:

269-251=39

39 divided by 3 = 13

13 weeks is your answer!

please mark brainliest please!!!

NO SPEAK ENGLISH SORRYYYY

The inequality explains the value of -4°C is greater than -9°C

It is known as inequality when both sides of a mathematical statement contain mathematical signs that are either less than or larger than one another.

It is given that,

-4°C >  -9°C

We utilize the "Greater than or equal to" sign in linear inequalities when the value of a variable is greater than or equal to a certain value. The "greater than" symbol (>), which has a sleeping line beneath it, is used to denote it. It is represented by the character (≥). 

Thus, the inequality explains the value of -4°C is greater than -9°C.

Learn more about inequality here:

brainly.com/question/19491153

#SPJ2

Answer:

-1 and -3

(n+7)(n-8)

Step-by-step explanation:

1. Find the Zeros

[tex]f(x)=x^{2} +4x+3[/tex]

[tex]f(x)=\left(x+1\right)\left(x+3\right)[/tex]

[tex]x+1=0\\x=-1\\x+3=0\\x=-3[/tex]

2. Factoring Trinomials

[tex]f(x)=n^{2} -n-56[/tex]

[tex]f(x)=\left(n+7\right)\left(n-8\right)[/tex]

[tex]n+7=0\\n=-7\\n-8=0\\n=8[/tex]

Answer:

The diameter of the pond is 8.

Step-by-step explanation:

Diameter formula   d = 2r

So d = [tex]2*4[/tex]

d = 8

Answer:

the answer is 8

Step-by-step explanation:

so 4r x 2=8d

or

2(4r)=8d

Answer:

C. 30%

Have a great day! Good luck.

Answer:

C. 30%

Step-by-step explanation:

All you have to do is 45/150 to get the answer. Simplify that and get 3/10 which is also equal to 30%.

Hope this helps you

Answer: m=3

Step-by-step explanation:

This could be written as m+5=8

You would then do the inverse to 'undo' the equation. So instead of adding 5 you would take away 5 from 8.

8-5=3

Hope this helps :)

Answer:

Explanation:

f  (  − 3 )  basically means substitute  − 3  for  x  in the function  − 5 x

f

(

−

3

)

=

−

5

(

−

3

)

−

7

f

(

−

3

)

=

15

−

7

f

(

−

3

)

=8

Step-by-step explanation: