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Ivahew
2 months ago
13

A sphere with a diameter of 9 units fits exactly in the clear glass cube as shown.

Mathematics
1 answer:
babunello [11.8K]2 months ago
3 0

Answer:

347.3 cubic units

Step-by-step explanation:

To calculate the volume of the empty space, we derive the total volume of the two shapes and subtract the volume of the sphere from that of the cube.

The volume of a cube is calculated as l^3.

Here, the length is given as 9, so we compute 9x9x9, resulting in 729 cubic units.

The formula for the volume of a sphere is 4/3 pi r^3.

The radius is 4.5 (half of the diameter), thus:

4/3*91.125 pi

which becomes 121.5 pi = 381.7 (to one decimal place).

Subtracting these gives us 729-381.7 = 347.3.

The volume of the empty space equals 347.3 cubic units.

The comprehensive expression in reference to the given d:

Volume of empty space = d^3 - 4/3 pi (d/2)^3

I hope this was helpful!

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In Melanie's Styling Salon, the time to complete a simple haircut is normally distributed with a mean of 25 minutes and a standa
zzz [12365]

Answer:

b) falls between 18.4 and 31.6 minutes.

Step-by-step explanation:

Problems involving normally distributed samples can be tackled using the z-score formula.

In any set with a mean \mu and standard deviation \sigma, the z-score for a measurement X is calculated as follows:

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

The Z-score indicates how many standard deviations an observation diverges from the mean. After determining the Z-score, consulting the z-score table provides the associated p-value. This p-value represents the likelihood of observing a measure less than X, i.e., the percentile of X. Subtracting the p-value from 1 yields the probability of observing a measure greater than X.

In this question, we find that:

\mu = 25, \sigma = 4

To cover the Middle 90%

The lower limit is determined as the value of X when Z corresponds to a p-value of 0.5 - 0.9/2 = 0.05.

The upper limit corresponds to the value of X when Z has a p-value of 0.5 + 0.9/2 = 0.95.

Lower limit:

X when Z = -1.645Z = \frac{X - \mu}{\sigma}

-1.645 = \frac{X - 25}{4}

X - 25 = -1.645*4

X = 18.42

Upper limit:

X when Z = 1.645

1.645 = \frac{X - 25}{4}

X - 25 = 1.645*4

X = 31.58

Thus, the correct assessment is:

b) between 18.4 and 31.6 minutes.

3 0
1 month ago
243.875 to nearest tenth, hundredth, ten, and hundred
Inessa [12570]
When rounding 243.875: to the nearest tenth, it becomes 243.9; to the nearest hundredth, it is 243.88; to the nearest ten, it rounds down to 240; and to the nearest hundred, it rounds down to 200. The general rule in rounding states that if the decimal is less than 5, the number remains the same; if it is 5 or more, you round up.
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Jai Narayan sells two radio sets for 2288 each.
tester [12383]

Answer:

1%

Step-by-step explanation:

The selling price for each radio is $2288.

Total selling price is 2\times 2288=$4576.

Profit is 10%.

Loss is also 10%.

Cost price=\frac{S.P\times 100}{100+gain(in\;percent)}

Cost price=\frac{S.P\times 100}{100-loss(in\;percent)}

Utilizing the formula,

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The combined cost price for both radios totals 2080+2542.2=$4622.2.

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Thus, the loss is 1%.

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