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Ostrovityanka [42]
2 years ago
8

A boy climbs to the top of a tree and sees his friend 100 feet from the base of the tree. If the tree is 25 feet tall, what is t

he angle of depression to his friend?
Mathematics
1 answer:
QveST [7]2 years ago
7 0
It would be helpful to draw the figure for this system. We would see that a right triangle is made where the base is equal to 100 ft and the height is equal to 25 ft. Using trigonometric functions we can easily calculate for the angle as follows:

tan (theta) = 25 / 100
theta = 14.04 degrees
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A veterinarian does research on the causes of enteroliths, stones that develop in the colon of horses. She suspects that feeding
skad [1K]

Answer: 8

Step-by-step explanation:

The degree of freedom for t-distribution of testing the differnce between the two population mean is given by :-

df= n_1+n_2-2

, where n_1 = Size of first sample.

n_1 = Size of second sample.

As per given ,

Veterinarian selects five horses that are known to have enteroliths and compares the number of flakes of alfalfa they have eaten over a month with the number of flakes eaten by five horses free of enteroliths.

i.e. n_1=5 and n_2=5

Now , If she calculates a two-sample confidence interval by hand for the difference in the mean number of flakes fed to horses with and without enteroliths the degrees of freedom she should use are

df= 5+5-2=8

Hence, the correct answer is 8.

8 0
1 year ago
Brenda earns $1,700 per month after taxes. She is working on her budget and has the first three categories finished.
Zigmanuir [339]

Answer:

B

Step-by-step explanation:

Recommended for housing: 30%

X/100 = 612/1700

= 36%

Recommended for food: 10%

X/100 = 238/1700

= 14%

Recommended for transportation 15%

X/100 = 370/1700

= 21.8%

6 0
1 year ago
Which statement describes function composition with respect to the commutative property? Given f(x) = x² – 4 and g(x) = x – 3, (
Paraphin [41]

Answer:

The correct option are;

f(x) = x² - 4 and g(x) = x - 3, (f ο g)(2) = -3 and (g ο f)(2) = -3, so the function is commutative

Given f(x) = 4·x and g(x) = x², (f ο g)(x) = 4·x² and (g ο f)(x) = 16·x²

So the function is not commutative

Step-by-step explanation:

For the equations f(x) = x² - 4 and g(x) = x - 3, we have;

(f ο g)(x) = f(g(x)) = (x - 3)² - 4 = x² - 6·x + 9 - 4 = x² - 6·x + 5

At x = 2, we have;

(f ο g)(2) = f(g(2)) = 2² - 6×2 + 5 = - 3

Similarly, we have;

(g ο f)(x) = g(f(x)) = x² - 4 -3 = x² - 7

At x = 2, we have;

(g ο f)(2) = g(f(2)) = 2² - 7 = 4 - 7 = -3

Therefore, by commutative property, we have that the result of an operation does not change by changing the order of the operands such that we have;

a + b = b + a or a·b = b·a from which we have resolved also the following operation is commutative

(f ο g)(2) = (g ο f)(2)

Similarly given f(x) = 4·x and g(x) = x², (f ο g)(x) = 4·x² and (g ο f)(x) = 16·x²

So the function is not commutative

(f ο g)(x) = f(g(x)) = 4·x²

(f ο g)(x) = 4·x²

(g ο f)(x) = g(f(x)) = (4·x)² = 16·x²

(g ο f)(x) = 16·x²

∴ (f ο g)(x) = 4·x² ≠ (g ο f)(x) = 16·x²

(f ο g)(x)  ≠ (g ο f)(x) the function is not commutative.

8 0
2 years ago
Read 2 more answers
Which statements are true about the graphs of all nth degree polynomials?
vova2212 [387]

The statements are true about the graphs of all nth degree polynomials are B and D.

B. It goes up and down at most a total of n times.

D. The number of x-intercepts is at most n.

6 0
2 years ago
Read 2 more answers
Hugger Polls contends that an agent conducts a mean of 53 in-depth home surveys every week. A streamlined survey form has been i
bonufazy [111]

Answer: 4

Step-by-step explanation: yep

8 0
2 years ago
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