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pishuonlain [190]
3 years ago
6

A boiler room has the shape of a rectangular prism. The area of the floor of the room is 112 square feet. The length of the room

is 2 feet more than twice the width. The height is 1 foot greater than the width.
Mathematics
1 answer:
Naddik [55]3 years ago
5 0

Answer:

Length = 16 feet.

Width = 7 feet

Height = 8 feet

Volume = 896 cubic feet.

Step-by-step explanation:

There is a rectangular prism boiler room. 112 square feet is the floor area of the room.

Let the length of the room is L feet and width is W feet.

So, LW = 112 ...... (1)

Now, given that L = 2 + 2W ........ (2) , hence, from equation (1) we get  

(2 + 2W)W = 112

⇒ 2w + 2w² = 112

⇒ W² + W - 56 = 0

⇒ (W +8)(W - 7) = 0

⇒ W = 7 feet. {Neglecting the negative root as W can not be negative}

Hence, from equation (2) we get L = 2W + 2 = 16 feet.

Now, 1 foot more than the width is the height H.

Hence, H = 7 + 1 = 8 feet.

Therefore, the volume of the room is, V = LWH = 16 × 7 × 8 = 896 cubic feet. (Answer)

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We know, Distance = Speed * Time.

So, Equation would be: 2x + 5*2 = 6x

2x + 10 = 6x

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3 years ago
Solve the area formula for h
White raven [17]

The answer is C: h = \frac{2A}{b}

Starting with the given formula for the area, A = 1/2hb, the first step is to isolate h by using the multiplicative inverse of b, which is \frac{1}{b} on both sides of the equation:

A(\frac{1}{b})  =  \frac{1}{2}hb* (\frac{1}{b})

The result will be:

\frac{A}{b} = \frac{1}{2}h

The last step is to use the multiplicative inverse of \frac{1}{2}, which is 2 or \frac{2}{1} to further isolate the variable <em>h </em>:

\frac{A}{b} (\frac{2}{1}) = (\frac{2}{1}) \frac{1}{2} h

The formula for h will be:

h = \frac{2A}{b}  which is the option C in your question.

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3 years ago
among the 2287 respondents, 500 said that they only play hockey. what fraction of respondents said they only play hockey?
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Step-by-step explanation:

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3 years ago
Using the simple random sample of weights of women from a data​ set, we obtain these sample​ statistics: nequals45 and x overbar
Tomtit [17]

Answer: (141.1, 156.48)

Step-by-step explanation:

Given sample statistics : n=45

\overline{x}=148.79\text{ lb}

\sigma=31.37\text{ lb}

a) We know that the best point estimate of the population mean is the sample mean.

Therefore, the best point estimate of the mean weight of all women = \mu=148.79\text{ lb}

b) The confidence interval for the population mean is given by :-

\mu\ \pm E, where E is the margin of error.

Formula for Margin of error :-

z_{\alpha/2}\times\dfrac{\sigma}{\sqrt{n}}

Given : Significance level : \alpha=1-0.90=0.1

Critical value : z_{\alpha/2}=z_{0.05}=\pm1.645

Margin of error : E=1.645\times\dfrac{31.37}{\sqrt{45}}\approx 7.69

Now, the 90% confidence interval for the population mean will be :-

148.79\ \pm\ 7.69 =(148.79-7.69\ ,\ 148.79+7.69)=(141.1,\ 156.48)

Hence, the 90​% confidence interval estimate of the mean weight of all women= (141.1, 156.48)

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3 years ago
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