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Umnica [9.8K]
3 years ago
8

A rectangular prism has a length of 5 1/8 feet, a width of 7 1/2 feet, and a height of 2 feet. What is the volume of the prism?

Enter your answer in the box. ft³
Mathematics
1 answer:
maksim [4K]3 years ago
6 0

For this case we have that by definition, the volume of a rectangular prism is given by:

V = A_ {b} * h

Where:

A_ {b}: It is the area of the base

h: It's the height

According to the data we have:

length = 5 \frac {1} {8} = \frac {8 * 5 + 1} {8} = \frac {41} {8}

width = 7 \frac {1} {2} = \frac {2 * 7 + 1} {2} = \frac {15} {2}

Then:

A_ {b} = \frac {41} {8} * \frac {15} {2} = \frac {615} {16}

Thus, the volume is:

V = \frac {615} {16} * 2 = \frac {1230} {16} = 76.875

Answer:

76.875 \ ft ^ 3

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nika2105 [10]

Answer:

The best point of estimate for the true mean is:

\hat \mu = \bar X = 2.55

2.55-1.96\frac{12}{\sqrt{76}}=-0.148    

2.55+1.96\frac{12}{\sqrt{76}}=5.248    

Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.

Step-by-step explanation:

Information given

\bar X=2.55 represent the sample mean for the late time for a flight

\mu population mean

\sigma=12 represent the population deviation

n=76 represent the sample size  

Confidence interval

The best point of estimate for the true mean is:

\hat \mu = \bar X = 2.55

The confidence interval for the true mean is given by:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

The Confidence level given is 0.95 or 95%, th significance would be \alpha=0.05 and \alpha/2 =0.025. If we look in the normal distribution a quantile that accumulates 0.025 of the area on each tail we got z_{\alpha/2}=1.96

Replacing we got:

2.55-1.96\frac{12}{\sqrt{76}}=-0.148    

2.55+1.96\frac{12}{\sqrt{76}}=5.248    

Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.

7 0
3 years ago
Take the horse to overtake the
S_A_V [24]

Answer:

  • 120 km/h

Step-by-step explanation:

  • Speed in one direction = 40 km/h
  • Speed on return = x
  • Average speed = 60 km/h

Let the distance be d

<u>Average speed </u>

  • 2d/(d/40 + d/x) = 60
  • d/40 + d/x = 2d/60
  • 1/40 + 1/x = 1/30
  • 1/x = 1/30 - 1/40
  • 1/x = (4-3)/120
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6 0
3 years ago
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IgorLugansk [536]

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4 0
3 years ago
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 6 small boxes has a t
Olin [163]

Answer:

  • large: 18.5 kg
  • small: 15.75 kg

Step-by-step explanation:

Let b and s represent the weights of the big and small boxes, respectively. Then the two delivered weights can be summarized as ...

  5b +6s = 187

  3b +2s = 87

We can eliminate the "s" variable by subtracting the first equation from 3 times the second:

  3(3b +2s) -(5b +6s) = 3(87) -(187)

  4b = 74 . . . . . collect terms

  b = 18.5 . . . . . divide by 4

Using this value in the second equation, we find ...

  3(18.5) +2s = 87

  2s = 31.5 . . . . . . . . subtract 55.5

  s = 15.75 . . . . . . . . divide by 2

The large box weighs 18.5 kg; the small box weighs 15.75 kg.

5 0
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lesantik [10]

Answer:

24

Step-by-step explanation:

In a deck of 52 cards, there are 4 kings and 4 queens

Selection of 3 kings out of 4 = 4 C 3 = 4

Selection of 2 queens out of 4 = 6

So, total number of selections = 4 x 6 = 24

7 0
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