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3 years ago

15

The table below shows the number of hours some college athletes in two states spend on indoor sports each week:

1 answer:

svet-max [94.6K]3 years ago

5 0

Arrange the data set in ascending order:
State A:   4,   5, 6, 6, 7, 8,   9, 21, 25
State B: 10, 11, 12, 13, 14, 14, 15, 15, 16

5 number summary:
State A State B
minimum 4 10
Q1 5.5 11.5
median    7 14
Q3 15 15
maximum 25   16
IQR 9.5 3.5

The box plot are not symmetric. The distance of the median from each Q1 and Q3 should be equal for the box plot to be symmetric.

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the runner's time to complete the marathon is 45 minutes. The time to complete the last marathon was 49.5 minutes. What is the p

Lana71 [14]

Answer:

9.09%

Step-by-step explanation:

To find percent decrease you have to use this equation:

$Percent Decrease = \frac{Initial -New}{Initial} x 100$

Initial = 49.5

New = 45

Plug in and solve:

$PD = \frac{49.5-45}{49.5} x 100\\\\PD = \frac{4.5}{49.5} x 100 \\\\PD = 0.0909 x 100\\\\PD = 9.09$

The percent decrease is 9.09%

<em>Hope this helps!!</em>

<em>- Kay :)</em>

6 0

3 years ago

Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______

Ludmilka [50]

Answer:

$(a)\ \sec^2(\theta) = 82$

$(b)\ \cot(\theta) = \frac{1}{9}$

$(c)\ \cot(\frac{\pi}{2} - \theta) = 9$

$(d)\ \csc^2(\theta) = \frac{82}{81}$

Step-by-step explanation:

Given

$\tan(\theta) = 9$

Required

Solve (a) to (d)

Using tan formula, we have:

$\tan(\theta) = \frac{Opposite}{Adjacent}$

This gives:

$\frac{Opposite}{Adjacent} = 9$

Rewrite as:

$\frac{Opposite}{Adjacent} = \frac{9}{1}$

Using a unit ratio;

$Opposite = 9; Adjacent = 1$

Using Pythagoras theorem, we have:

$Hypotenuse^2 = Opposite^2 + Adjacent^2$

$Hypotenuse^2 = 9^2 + 1^2$

$Hypotenuse^2 = 81 + 1$

$Hypotenuse^2 = 82$

Take square roots of both sides

$Hypotenuse =\sqrt{82}$

So, we have:

$Opposite = 9; Adjacent = 1$

$Hypotenuse =\sqrt{82}$

Solving (a):

$\sec^2(\theta)$

This is calculated as:

$\sec^2(\theta) = (\sec(\theta))^2$

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

Where:

$\cos(\theta) = \frac{Adjacent}{Hypotenuse}$

$\cos(\theta) = \frac{1}{\sqrt{82}}$

So:

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

$\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2$

$\sec^2(\theta) = (\sqrt{82})^2$

$\sec^2(\theta) = 82$

Solving (b):

$\cot(\theta)$

This is calculated as:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

Where:

$\tan(\theta) = 9$ ---- given

So:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

$\cot(\theta) = \frac{1}{9}$

Solving (c):

$\cot(\frac{\pi}{2} - \theta)$

In trigonometry:

$\cot(\frac{\pi}{2} - \theta) = \tan(\theta)$

Hence:

$\cot(\frac{\pi}{2} - \theta) = 9$

Solving (d):

$\csc^2(\theta)$

This is calculated as:

$\csc^2(\theta) = (\csc(\theta))^2$

$\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2$

Where:

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

$\sin(\theta) = \frac{9}{\sqrt{82}}$

So:

$\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2$

$\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2$

$\csc^2(\theta) = \frac{82}{81}$

4 0

2 years ago

Find the solution to the equation 4x + 17 = 23

Ann [662]

Answer:

x= 3/2 or x=1.5

Step-by-step explanation:

subtract 17 to the other side of the equation.

Next you divide both sides of the equation by 4.

You have your answer :)

7 0

2 years ago

Please help, i will give brainliest

Galina-37 [17]

Answer:

13. (E) all of the above 14. (E) the diagonals bisect the angles at the vertices

Step-by-step explanation:

3 0

2 years ago

The model shows the expression 20 + 16. Which expression is equivalent to this sum?

Natali5045456 [20]

Answer:

4(5+4)

Step-by-step explanation:

4(5+4) equals 36, and 20 + 16 equals 36 as well, so therefore 20 + 16 is equivalent to 4(5+4)

4 0

2 years ago

Read 2 more answers