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Triss [41]
3 years ago
13

A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. A pyramid with the same

base and half the height of the prism is placed inside the prism, as shown in the figure.
The volume of the space outside the pyramid but inside the prism is cubic centimeters

Mathematics
2 answers:
Vadim26 [7]3 years ago
6 0
The answer is 250 cm³

We need to calculate V = Vr - Vp
V - the <span>volume of the space outside the pyramid but inside the prism
Vr - the volume of the rectangular prism.
</span>Vp - the volume of the pyramid<span>

Vr = w * l * h
w = l = 5 cm
h1 = 12 cm
Vr = 5 * 5 * 12 = 300 cm</span>³<span>


Vp = w * l * h / 3
w = l = 5 cm
h2 = h1/2 = 12/2 = 6 cm
Vp = 5 * 5 * 6 / 3 = 50 cm</span>³


V = Vr - Vp = 300 cm³ - 50 cm³ = 250 cm³
Arlecino [84]3 years ago
6 0
I hope this helps you

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<u>Given</u>:

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To determine the percentage of tickets sold to seniors we need to determine the total number of tickets sold to each category.

<u>To determine the percentage of tickets sold to seniors:</u>

In order to determine the percentage of tickets sold to the seniors, we divide the tickets sold to seniors by the total number of tickets sold to children, adults, and seniors.

This value is multiplied with 100 to convert it into a percentage.

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The percentage of tickets sold to seniors = \frac{100}{722} (100) = 0.1385(100)=13.85\%.

Rounding this off, we get the value as 13.9%

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A balloon artist creates balloon hats for children at a store’s grand opening. The graph shows the number of balloons the artist
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Answer:

The phrase that best describes the the line representing the relationship between the number of balloons remaining and the number of hats created is:

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Clearly from the graph we could that it is  a linear function.

Also, the function is a decreasing function since with the increase of one variable that is the number of Balloon hats produced the other variable i.e. Balloons remaining is decreasing.

Also, we can calculate the slope of the line.

as the line is passing through (0,500) and (100,0)

Hence, the slope of line is:

Slope=\dfrac{0-500}{100-0}\\\\Slope=\dfrac{-500}{100}\\\\Slope=-5

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The owner of Matt’s Gas Station wants to study gasoline purchases of customers at his station. In 2017, the mean amount of gas
gulaghasi [49]

Answer:

Step-by-step explanation:

a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 9

For the alternative hypothesis,

µ ≠ 9

This is a 2 tailed test

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 9

x = 9.9

σ = 2.5

n = 50

z = (9.9 - 9)/(2.5/√50) = 2.55

Looking at the normal distribution table, the probability corresponding to the area above the z score is 1 - 0.99461 = 0.00539

Recall, population mean is 9

The difference between sample sample mean and population mean is 9.9 - 9 = 0.9

Since the curve is symmetrical and it is a two tailed test, the x value for the left tail is 9 - 0.9 = 8.1

the x value for the right tail is 9 + 0.9 = 9.9

These means are higher and lower than the null mean. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area. We already got the area above the z score as z = 0.00539

We would double this area to include the area in the left tail of z = - 2.55. Thus

p = 0.00539 × 2 = 0.01078

Since alpha, 0.01 < 0.01078, we would reject the null hypothesis

But we are told to use the critical value approach, then

Since α = 0.01, the critical value is determined from the normal distribution table.

For the left, α/2 = 0.01/2 = 0.005

The z score for an area to the left of 0.005 is - 2.575

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The z score for an area to the right of 0.995 is 2.575

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b) we would assume normal distribution because the sample size is sufficiently large and the population standard deviation is known.

c) Confidence interval is written in the form,

(Sample mean ± margin of error)

Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.

Margin of error = z × σ/√n

The z score for confidence level of 99% is 2.58

Margin of error = 2.58 × 2.5/√50 = 0.91

Confidence interval = 9.9 ± 0.91

The lower end of the confidence interval is

9.9 - 0.91 = 8.99

Therefore, p = 9 will be contained in the interval.

4 0
2 years ago
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