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kvasek [131]
2 years ago
14

1. Joshua has a ladder that is 14 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is

13.8 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 78°. Will the ladder be safe at this height? Show your work and draw a diagram to support your answer.
Mathematics
1 answer:
34kurt2 years ago
8 0

Answer:

Step-by-step explanation:

θ is the angle the ladder makes with the ground.

θ = arcsin(13.8/14) ≈ 80.3° > 78°

The ladder is not safe at that height and angle.

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Vlad the Impaler promotes many of his soldiers into generals (don't ask what happened to the past generals). Haley thinks the pr
marin [14]

Using the formula for the margin of error, it is found that Haley should sample 12,724 soldiers.

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of \alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of \frac{1+\alpha}{2}.

The margin of error is of:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

Estimate of the proportion of 64%, hence \pi = 0.64.

94% confidence level

So \alpha = 0.94, z is the value of Z that has a p-value of \frac{1+0.94}{2} = 0.97, so z = 1.88.  

Margin of error of <u>less than 0.008</u> is wanted, hence, we have to find n when M = 0.008.

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.008 = 1.88\sqrt{\frac{0.64(0.36)}{n}}

0.008\sqrt{n} = 1.88\sqrt{0.64(0.36)}

\sqrt{n} = \frac{1.88\sqrt{0.64(0.36)}}{0.008}

(\sqrt{n})^2 = (\frac{1.88\sqrt{0.64(0.36)}}{0.008})^2

n = 12723.84

Rounding up, Haley should sample 12,724 soldiers.

A similar problem is given at brainly.com/question/25404151

4 0
2 years ago
The area of a rectangular rug is given by the trinomial r^2-4r-77. What are the possible dimensions of the​ rug? Use factoring.
Softa [21]
When you factor the equation...

r^2-4r-77

r^2+7r-11r-77

r(r+7)-11(r+7)

(r-11)(r+7)  so each parenthetical term is a dimension.

Note that r>11 though for any possible real solution. 
4 0
3 years ago
What is -7(x-2)=1=15-7x
Soloha48 [4]

Answer:

0

Step-by-step explanation:

Simplifying

-7(x + -2) + 1 = 15 + -7x

Reorder the terms:

-7(-2 + x) + 1 = 15 + -7x

(-2 * -7 + x * -7) + 1 = 15 + -7x

(14 + -7x) + 1 = 15 + -7x

Reorder the terms:

14 + 1 + -7x = 15 + -7x

Combine like terms: 14 + 1 = 15

15 + -7x = 15 + -7x

Add '-15' to each side of the equation.

15 + -15 + -7x = 15 + -15 + -7x

Combine like terms: 15 + -15 = 0

0 + -7x = 15 + -15 + -7x

-7x = 15 + -15 + -7x

Combine like terms: 15 + -15 = 0

-7x = 0 + -7x

-7x = -7x

Add '7x' to each side of the equation.

-7x + 7x = -7x + 7x

Combine like terms: -7x + 7x = 0

0 = -7x + 7x

Combine like terms: -7x + 7x = 0

0 = 0

Solving

0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

3 0
2 years ago
A secretary can type 56 words per minute. how much time will she need to type a 4200-word report?
tino4ka555 [31]
The answer would be D, because you do 4200÷56=75 minutes. 75 minutes= 1 hour and 15 minutes
7 0
3 years ago
ASAP!! HELP!!!
miv72 [106K]
You should put each question somewhere different so anyone can answer it and see it faster
3 0
3 years ago
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