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Rus_ich [418]
2 years ago
6

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

Mathematics
1 answer:
SCORPION-xisa [38]2 years ago
5 0
4.8 he is 4.8 miles into the path
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How to find trigonomic ratio ​
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

   The standard deviation is  \sigma_c  =  0.305 \  minutes

   The time taken by  the winning car for the current year  is  x =  185.85 \ minutes

  The mean of the previous  year  is  \mu_p =  110.7 \  minutes

   The standard deviation the previous  year  is  \sigma_p  = 0.115  \  minutes

 The time taken by  the winning car for the previous year  is  y =   110.48 \ minutes    

Generally the z-score for current year is mathematically evaluated as

     z_c  =  \frac{x- \mu_c}{\sigma_c }

=>     z_c  =  \frac{ 185.85- 186.32}{0.305 }

=> z_c  = -1.536

Generally the z-score for previous year is mathematically evaluated as

     z_p  =  \frac{y- \mu_p}{\sigma_p }

=>     z_p  =  \frac{ 110.48-110.7}{0.115  }

=> z_p  = -1.913

From the value obtained we see that  z_p  <  z_c , Hence  Karen had a more convincing victory because of the lower z -score.

5 0
2 years ago
Draw a graph of the rose curve.<br><br> r = 4 cos 2θ, 0 ≤ θ ≤ 2π
alukav5142 [94]
See the attachment below gor graph
hope that helps 

3 0
3 years ago
Read 2 more answers
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