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2 years ago

A tree casts a shadow that is 18 feet in length. If the angle of elevation is

1 answer:

8 0

It forms a Triangle, in which base is shadow, and height of the tree is perpendicular.

So, Tan Ф = P / B
Tan 28 = P /18
0.53 * 18 = P [ Tan 28 = 0.53 ]
P = 9.6

In short, Your Answer would be Option D

Hope this helps!

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Find the 21st term in the arithmetic sequence. 3, 7, 11, 15, 19, ...

NNADVOKAT [17]

The 21st term of the given arithmetic sequence is 83. The nth term of an arithmetic sequence is applied to find the required value where n = 21.

<h3>What is the nth term of an arithmetic series?</h3>

The nth term of an arithmetic sequence is calculated by the formula

aₙ = a + (n - 1) · d

Here the first term is 'a' and the common difference is 'd'.

<h3>Calculation:</h3>

The given sequence is an arithmetic sequence.

3, 7, 11, 15, 19, ....

So, the first term in the sequence is a = 3 and the common difference between the terms of the given sequence is d = 7 - 3 = 4.

Thus, the required 21st term in the sequence is

a₂₁ = 3 + (21 - 1) × 4

⇒ a₂₁ = 3 + 20 × 4

⇒ a₂₁ = 3 + 80

∴ a₂₁ = 83

So, the 21st term in the given arithmetic sequence is 83.

Learn more about the arithmetic sequence here:

brainly.com/question/6561461

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5 0

10 months ago

The perimeter of a rectangle is 84 inches. The width of the rectangle is 12 inches. What is the length of the rectangle?

german

The length of the rectangle is 30

5 0

1 year ago

A simple random sample of 36 men from a normally distributed population results in a standard deviation of 10.1 beats per minute

Katyanochek1 [597]

Answer:

Step-by-step explanation:

Given that:

sample size n = 36

standard deviation = 10.1

level of significance ∝ = 0.10

The null hypothesis and the alternative hypothesis can be computed as follows:

$H_0 : \sigma = 10$

$H_1 : \sigma \neq 10$

The test statistics can be computed as follows:

$X^2 = \dfrac{(n -1)s^2 }{\sigma ^2}$

$X^2 = \dfrac{(36 -1)10.1^2 }{10^2}$

$X^2 = \dfrac{(35)102.01 }{100}$

$X^2 = \dfrac{3570.35 }{100}$

$X^2 =35.704$

degree of freedom = n - 1 = 36 - 1 = 35

Since this test is two tailed .

The P -value can be determined by using the EXCEL FUNCTION ( = 2 × CHIDIST(35.7035, 35)

P - value = 2 × 0.435163515

P - value = 0.8703 ( to four decimal places)

Decision Rule : To reject the null hypothesis if P - value is less than the 0.10

Conclusion: We fail to reject null hypothesis ( accept null hypothesis) since p-value is greater than 0.10 and we conclude that there is sufficient claim that the normal range of pulse rates of adults given as 60 to 100 beats per minute resulted to a standard deviation of 10 beats per minute.