Danny drove to Yosemite Park from his home at 60 mph. on his trip home, his rate was 10 mph less and ...?

Response:

option D

Step-by-step reasoning:

Provided in the prompt is a right-angled triangle FGH.

Base of triangle = 12

Height of triangle = 5

Hypotenuse of triangle = 13

To solve the question, we'll apply trigonometric identities.

cos(F) = adjacent / hypotenuse

cos(F) = height / hypotenuse

cos(F) = 5 / 13

Thus, the cosine ratio for angle F is 5 / 13

Let C denote the quantity of compost

T represent the quantity of topsoil

Each cubic yard of compost is priced at $25

Thus, the cost of C cubic yards of compost is 25C

Each cubic yard of topsoil costs $15

Therefore, the cost for T cubic yards of topsoil is 15T

Together, the amount of compost plus topsoil equals 10

C + T = 10 -------> Equation 1

The total cost for compost and topsoil is $180

25C + 15T = 180 --------> Equation 2

Rearranging the first equation to find C

C + T = 10

results in

C = 10 - T

Now substitute into the second equation

25C + 15T = 180

25 ( 10 - T) +15T = 180

Using like terms: 250 - 25T + 15T = 180

From which we can simplify to 250 - 10T = 180 by removing 250 from both sides

-10T = 180 - 250

yielding -10T = -70 (dividing both sides by -10)

results in T = 7

104 ft total

If Evelyn had not lost any dolls, she would have had a total of 9 dolls. Initially, Evelyn owned 9 dolls and lost 1/3 of them, which equals 3 dolls. As a result, after the loss, she had 6 dolls left. Consequently, had all the dolls remained with her, she would possess 9 dolls.

Given:
Total girls in class = 16.
Total boys in class = 14.
To determine:
The various combinations for selecting one girl and one boy.
Solution:
We have,
Total girls = 16
Total boys = 14
Thus,
The total combinations for selecting one girl from 16 girls = 16.
The total combinations for selecting one boy from 14 boys = 14.
Now, the various ways to select one girl and one boy amount to:
Therefore, the total number of combinations is 224.