A bike path is 8 miles. Max is 40% of the way to the end. How far is max on the path?

ycow [4]

Answer:divide the opposite sides, by the length of the hypotenuse. To get the cosine, divide the length of the adjacent side,by the length of the hypotenuse.

Step-by-step explanation:

divide the opposite sides, by the length of the hypotenuse. To get the cosine, divide the length of the adjacent side,by the length of the hypotenuse.

7 0

3 years ago

Graph the inverse circular function by hand, given f(x) = 3sin(2x) ;-pi/4 ≤ ≤pi/4

nasty-shy [4]

Part a)

a) The given function is

$f(x) = 3 \sin(2x)$

We let

$y = 3 \sin(2x)$

Interchange x and y.

$x= 3 \sin(2y)$

Solve for y;

$\frac{x}{3} = \sin(2y)$

$y = \frac{1}{2} { \sin}^{ - 1}( \frac{x}{3} )$

${f}^{ - 1}(x) = \frac{1}{2} { \sin}^{ - 1}( \frac{x}{3} )$

Part b) The range of f(x) refers to y-values for which f(x) exists.

The range of f(x) is

$- 3 \leqslant y \leqslant 3$

This is because the function is within y=-3 and y=3.

c) The range of

${f}^{ - 1} (x)$

is

$- \frac{ \pi}{4} \leqslant y \leqslant \frac{\pi}{4}$

The domain is -3≤x≤3

This is because the domain and range of a function and its inverse swaps.

Part d) The graph is shown in the attachment.

3 0

4 years ago

Mari has 3 friends who are available to go with her to the movies, but she only has 2 extra tickets. How many different choices

aliina [53]

Answer:

3 different choices

Step-by-step explanation:

This problem is a combination problem: She has 3 friends, and we want to know how many groups of 2 friends there are. We can solve this using the combination of 3 choose 2:

C(3,2) = 3!(1! * 2!) = 3*2/2 = 3 possibilities

If we call her three friends A, B and C, the groups that can be formed are:

A and B

A and C

B and C

6 0

3 years ago

The mean finish time for a yearly amateur auto race was 186.32 minutes with a standard deviation of 0.305 minute. The winning c

uranmaximum [27]

Complete Question

The mean finish time for a yearly amateur auto race was 186.94 minutes with a standard deviation of 0.305 minute. The winning car, driven by Roger, finished in 185.85 minutes. The previous year's race had a mean finishing time of 110.7 with a standard deviation of 0.115 minute. The winning car that year, driven by Karen, finished in 110.48 minutes.

Find their respective z-scores.

Who had the more convincing victory?

A. Roger had a more convincing victory because of a higher z-score.

B. Karen a more convincing victory because of a higher z-score.

C. Roger had a more convincing victory, because of a lower z-score.

D. Karen a more convincing victory because of a lower z-score.

Answer:

The correct option is D

Step-by-step explanation:

From the question we are told that

The mean of the current year is $\mu_c = 186.32 \ minutes$