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ahrayia [7]
3 years ago
5

You are measuring the height of a statue. You stand 5 feet from the base of the statue. You measure the angle of elevation from

the ground to the top of the statue to be 68º. Find the height h of the statue to the nearest foot.

Mathematics
1 answer:
sp2606 [1]3 years ago
5 0

Answer:

The height of the statue is 12 feet

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle ABC

tan(68^o)=\frac{AB}{BC} ---> by TOA (opposite side divided by the adjacent side)

substitute the given values

tan(68^o)=\frac{AB}{5}

solve for AB (the height of the statue)

AB=tan(68^o)(5)=12\ ft

therefore

The height of the statue is 12 feet

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<h2>Answer with explanation:</h2>

<u>Sample size--</u>

It is the collections of all the possible outcomes of an event.

(A)

It is given that:

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This means that the possible outcomes are given as follows:

(Red,1)          (Green,1)           (Yellow,1)

(Red,2)         (Green,2)          (Yellow,2)

(Red,3)         (Green,3)           (Yellow,3)

(Red,4)         (Green,4)           (Yellow,4)

(Red,5)         (Green,5)           (Yellow,5)

(Red,6)         (Green,6)           (Yellow,6)

This means that the total number of outcomes are: 18

Hence, the sample size for this compound event is:  18

(B)

If the spinner has four colored spaces.

Let the fourth color be: Blue

Then the possible outcomes are given by:

(Red,1)          (Green,1)           (Yellow,1)           (Blue,1)

(Red,2)         (Green,2)          (Yellow,2)          (Blue,2)

(Red,3)         (Green,3)           (Yellow,3)          (Blue,3)

(Red,4)         (Green,4)           (Yellow,4)          (Blue,4)  

(Red,5)         (Green,5)           (Yellow,5)          (Blue,5)

(Red,6)         (Green,6)           (Yellow,6)          (Blue,6)

Hence, the total number of outcomes are:  24

The sample size of this compound event would be 24.

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A fair coin is tossed three times and the events A, B, and C are defined as follows: A: \{ At least one head is observed \} B: \
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Answer:

a) P(A)=0.875

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Step-by-step explanation:

Given : A fair coin is tossed three times and the events A, B, and C are defined as follows: A: At least one head is observed, B: At least two heads are observed, C: The number of heads observed is odd.

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C: The number of heads observed is odd.

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P(A)=\frac{n(A)}{n(S)}

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b) P(A or B)

Using formula,

\text{P(A or B)}=P(A)+P(B)-\text{P(A and B)}

\text{P(A or B)}=\frac{n(A)}{n(S)}+\frac{n(B)}{n(S)}-\frac{\text{n(A and B)}}{n(S)}

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\text{P(A or B)}=\frac{7}{8}

\text{P(A or B)}=0.875

(c) P((not A)  or B  or (not C))

A={HHH,HHT,HTT,HTH,TTH,TTH,THH,THT}

not A = {TTT} = 1

B={HHH,HTT,TTH,THT}

C={HHH,HTT,THT,TTH}

not C = {HHT,HTH,THH,TTT} = 4

So, not A or B or not C = {HHH,HHT,HTH,THH,TTT}=5

\text{P((not A)  or B  or (not C))}=\frac{5}{8}

\text{P((not A)  or B  or (not C))}=0.625

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3 years ago
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