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podryga [215]
1 year ago
11

Fruit juice comes in two types of containers. The first is a rectangular prism that is 9 inches tall and has a rectangular base

that measures 2 inches by 3 inches. The second container is a cylinder that is 8 inches tall and has a radius of 1.5 inches. Which of the following statements is valid? A. The volumes are the same. B. The prism has the greater volume. C. The cylinder has the greater volume. D. The volumes cannot be determined.
Mathematics
1 answer:
My name is Ann [436]1 year ago
3 0

The volume of a rectangular prism:

V_p=Bh\\\\B=wl\\\\w=2\ in;\ l=3\ in;\ h=9\ in

substitute

V_p=2\cdot3\cdot9=54\ in^3

The volume of a cylinder:

V_c=\pi r^2h\\\\r=1.5\ in;\ h=8\ in

substitute:

V_c=\pi\cdot(1.5)^2\cdot8=\pi\cdot2.25\cdot8=18\pi\ in^3\approx18\cdot3.14=56.52\ in^3

Answer: C. The cylinder has the greater volume.

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Electricity bills: According to a government energy agency, the mean monthly household electricity bill in the United States in
GuDViN [60]

Answer:

18.67% of bills are greater than $131

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 109.72, \sigma = 24

What proportion of bills are greater than $131

This proportion is 1 subtracted by the pvalue of Z when X = 131. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{131 - 109.72}{24}

Z = 0.89

Z = 0.89 has a pvalue of 0.8133

1 - 0.8133 = 0.1867

18.67% of bills are greater than $131

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In the trapezoid ABCD ( AB ∥ CD ) point M∈ AD , so that AM:MD=3:5. Line l ∥ AB and going trough point M intersects diagonal AC a
geniusboy [140]

Answer:

BC:BN=8:3

Step-by-step explanation:

ABCD is a trapezoid and there is a point m which belongs to AD such that AM:MD=3:5.Line "l" parallel to AB intersects the diagonal AC at p and BD at N.

Now, we know that the parallel lines divide the transversal into the segments with equal ratio, therefore, BN:NC=AM:MD

But, BC= BN+NC

Therefore, BC:BN=(BN+NC):BN

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⇒BC:BN=8:3


4 0
1 year ago
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