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3 years ago

How tall is a building that casts a 61-fit shadow when the angle of elevation of the sun is 60 degrees?

Mathematics

1 answer:

VladimirAG [237]3 years ago

4 0

Answer:

106 ft

Step-by-step explanation:

Assuming the shadow is measured along horizontal ground.

tanθ =opp/adj = building height/shadow length

building height = shadow length(tanθ)

h = 61tan60

h = 105.65509...

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PROBLEM 6. 10 A histogram has mean 70 and standard deviation 5 If the histogram is not bell shaped but it is symmetric. Find the

blsea [12.9K]

Answer:

a. 0.4772 = 47.72 %

b. 0.7605 = 76.05 %

Step-by-step explanation:

What we must do is calculate the z value for each value and thus find what percentage each represents and the subtraction would be the percentage between those two values.

We have that z is equal to:

z = (x - m) / (sd)

x is the value to evaluate, m the mean, sd the standard deviation

a. ind the least proportion of data falls between 70 and 80 If the histogram is bell shaped:

So for 70 copies we have:

z = (70 - 70) / (5)

z = 0

and this value represents 0.5

So for 80 copies we have:

z = (80 - 70) / (5)

z = 2

and this value represents 0.9772

p (70 > x > 80) = 0.9772 - 0.5

p (70 > x > 80) = 0.4772 = 47.72 %

b. Find the proportion of data between 65 and 77

So for 65 copies we have:

z = (65 - 70) / (5)

z = -1

and this value represents 0.1587

So for 77 copies we have:

z = (77 - 70) / (5)

z = 1.4

and this value represents 0.9192

p (65 > x > 77) = 0.9192 - 0.1587

p (65 > x > 77) = 0.7605 = 76.05 %

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4 years ago

Which two numbers on the number line have an absolute value of 3? Select the location of both numbers on the number line.

mart [117]

The absolute value is how far the number is away from 0.

So, the numbers with a absolute value of 3 would be 3 and -3, which are both 3 away from 0 in opposite directions.

Hope this helps!

5 0

4 years ago

Read 2 more answers

What is the greatest common factor of the numerator and denominator

Aloiza [94]

In the numerator, we can pull a 7 out of the expression 7x + 14 to get the product 7(x + 2). In the denominator, we can factor the expression 2x² + x - 6 like this:

$2x^2+x-6=2x^2+4x-3x-6\\=2x(x+2)-3(x+2)\\=(x+2)(2x-3)$

Our fraction can now be written as

$\dfrac{7(x+2)}{(x+2)(2x-3)}$

the only factor the numerator and denominator share in this case is x + 2.

3 0

4 years ago

$1675 at 4.6% for 4 years a. Find the interest earned. $___ b. Find the balance of the account. $____

worty [1.4K]

I hope this helps, sorry it is kind of crazy. Also, I assumed it was compound interest.

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3 years ago

Consider if the following Infinite Series converges or diverges; If converges, find the sum.

kumpel [21]

<h3>Answer: 3</h3>

Step-by-step explanation:

You can immediately notice that the sum consists of the sum of two infinitely decreasing geometric progressions

$\displaystyle \large \boldsymbol {} \underline1+\underline 2+\underline {\frac{1}{2}} -\frac{2}{3} +\underline {\frac{1}{4}} -\frac{2}{9} +\underline{\frac{1}{8}} -\frac{2}{27} + \ldots = \\\\\\ \underbrace{\bigg(1+2+\frac{1}{2} +\frac{1}{4} \ldots \bigg)}_{\rm \big S_2}-2 \underbrace{\bigg(\frac{1}{3}+\frac{1}{9} +\frac{1}{27} \ldots \bigg)}_{\big S_3}$

The formula for an infinitely decreasing geometric progression:

$\displaystyle \large \boldsymbol { \rm S=\frac{b_1}{1-q} \ \ ; \ \ |q|$

Where :

q -denominator
b₁ -is the first member of the progression

Then:

Denote the sum of the numbers in the first bracket for S₂ ; and in the second bracket for S₃

$\displaystyle \large \boldsymbol {} \rm S_2=\frac{2}{1-\dfrac{1}{2} } =\frac{2}{\dfrac{1}{2} } =4 \\\\\\\ S_3=\frac{\dfrac{1}{3} }{1-\dfrac{1}{3} } = \dfrac{1}{\dfrac{3}{\dfrac{2}{3} } } =\frac{1}{2}$

Substitute the values :

$\large \boldsymbol {} \rm S_2-2S_3=4- 2\cdot \dfrac{1}{2} =\boxed{3}$

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3 years ago