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-Dominant- [34]

4 years ago

12

the angle of depression from the top ski lift is 57 degrees if the vertical distance from the top and bottom ot the lift is 1200

feet, determine the length of the cable between them

1 answer:

dedylja [7]4 years ago

7 0

Answer:

1200

Step-by-step explanation:

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A recent survey of students at John Tukey High School revealed that

RoseWind [281]

Answer:

0.5234 = 52.34% probability that at least three of these students are in favor of the proposal to change the dress code.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they are in favor, or they are not. Students are independent. This means that we use the binomial probability distribution to solve this question.

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.

18% of the students are in favor of changing the dress code.

This means that $p = 0.18$

You randomly select 15 students

This means that $n = 15$

What is the probability that at least three of these students are in favor of the proposal to change the dress code?

This is

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

In which

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

$P(X = 0) = C_{15,0}.(0.18)^{0}.(0.82)^{15} = 0.051$

$P(X = 1) = C_{15,1}.(0.18)^{1}.(0.82)^{14} = 0.1678$

$P(X = 2) = C_{15,2}.(0.18)^{2}.(0.82)^{13} = 0.2578$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.051 + 0.1678 + 0.2578 = 0.4766$

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.4766 = 0.5234$

0.5234 = 52.34% probability that at least three of these students are in favor of the proposal to change the dress code.

8 0

3 years ago

What is the number of sides of a regular n gon if one of the extierior angles is 40 degrees?

sertanlavr [38]

Sum of all exterior angles = 360°

Size of one exterior angle = 40°

Number of sides = 360 ÷ 40 = 9

-----------------------------------------------------------
Answer: There are 9 sides to this polygon.
-----------------------------------------------------------

4 0

3 years ago

Which of the following illustrates a phase shift?

Natasha_Volkova [10]

<u>Answer:</u>

A. y = -2 - cos(x-π)

<u>Explanation:</u>

<u>The general form of the trig equation is:</u>

y = A sin (Bx + C) + D

where:

A is the amplitude

$\frac{2\pi}{B}$ is the period

$\frac{-C}{B}$ is the phase shift

D is the vertical shift

<u>Now, let's check the choices:</u>

<u>A. y = -2 - cos(x-π)</u>

$\frac{-C}{B} = \frac{\pi}{1} = \pi$

Therefore, the function has a phase shift of π

<u>B. y = 3 cos(4x)</u>

$\frac{-C}{B} = \frac{0}{4} = 0$

Therefore, the function has no phase shift

<u>C. y = tan(2x)</u>

$\frac{-C}{B} = \frac{0}{2} = 0$

Therefore, the function has no phase shift

<u>D. y = 1 + sin(x)</u>

$\frac{-C}{B} = \frac{0}{1} = 0$

Therefore, the function has no phase shift

<u>Based on the above,</u> the correct answer is A

Hope this helps :)

3 0

3 years ago

Read 2 more answers

What are the slope between (-5,-2) and (8,13)

Cerrena [4.2K]

Answer:

The slope:

$m = \frac{15}{13}$

Step-by-step explanation:

-To determine the slope of the following points shown, you need this formula:

$m = \frac{y_{2} - y{1}}{x_{2} - x_{1}}$

( $m$ represents the slope, $(x_{1}, y_{1})$ represents the first coordinate and $(x_{2},y_{2})$ represents the second coordinate)

-Apply the following points to the formula:

$m = \frac{13 + 2}{8 + 5}$

Then, solve:

$m = \frac{13 + 2}{8 + 5}$

$m = \frac{15}{13}$

So, the slope is $\frac{15}{13}$ .

8 0

3 years ago

He list shows the growth in centimeters of 12 plants during one week. 6, 7, 7, 8, 8, 8, 9, 9, 10, 11, 11, 14 Which box plot best

kumpel [21]

Answer:

Step-by-step explanation:

Hello!

You have the growth of 12 plants over a week (cm)

To construct a box plot you have to identify the 1st, 2nd, and 3rd Quartiles for the box and the maximum and minimum values for the whiskers.

Box

1st Quartile (Q₁)

Is the value of the data set that separates the bottom 25% from the top 75%. First, you need to calculate its position:

PosQ₁= n/4= 12/4= 3

So the first quartile is the third value.

6, 7, 7, 8, 8, 8, 9, 9, 10, 11, 11, 14

Q₁= 7

2nd Quartile/ Median (Q₂/Me)

PosMe= 12/2= 6

The second quartile in the 6th value.

6, 7, 7, 8, 8, 8, 9, 9, 10, 11, 11, 14

Q₂=Me= 8

3rd Quartile (Q₃)

PosQ₃= n*(3/4)= 12*(3/4)= 9

The third quartile is the 9th value.

6, 7, 7, 8, 8, 8, 9, 9, 10, 11, 11, 14

Q₃= 10

The left whisker extends from the Q₁ to the minimum value.

The right whisker extends from the Q₃ to the maximum value.

Min= 6

Max= 14

'------| | |-------'

6 7 8 10 14

The box plot that best displays a summary of the data, is C.

I hope this helps!

3 0

4 years ago