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1 month ago

A sphere has a radius of 16 in. Which statements about the sphere are true? Check all that apply.

Mathematics

2 answers:

tester [12.3K]1 month ago

7 0

Answer:

The accurate statements are:

The sphere has a diameter of 32 inches.

The length of the radius is half that of the diameter.

The sphere's volume totals StartFraction 16,384 Over 3 EndFraction pi cubic inches.

Step-by-step explanation:

The sphere has a diameter of 8 in. False

This is incorrect because the radius is always half the diameter. Half of 8 in gives 4 in, whereas the stated radius is 16 in.

The sphere’s volume is StartFraction 2,048 Over 3 EndFraction pi cubic inches. False

This is incorrect since the formula for a sphere's volume is 4πr³/3 = (16,384/3) π cubic inches.

The sphere has a diameter of 32 in. True

This is correct as the radius is half the diameter. Half of 32 in is 16 in, aligning with the given radius.

The length of the radius is half that of the diameter. True

This is accurate because the radius, by definition, is half of the diameter.

The volume of the sphere is StartFraction 16,384 Over 3 EndFraction pi cubic inches. True

This is correct based on the volume calculation of 4πr³/3 = (16,384/3) π cubic inches.

The diameter is half the radius's length. False

Instead, it is the radius that measures half the diameter’s length.

lawyer [12.5K]1 month ago

6 0

Answer:

The sphere has a 32 in. diameter. CORRECT: A sphere's diameter equals twice its radius; therefore, if the radius is 16, then the diameter is 32.
The radius measures half the diameter's length. CORRECT: According to the definition, the diameter represents the greatest distance across the sphere, and its length is twice the radius since the radius extends from the center to the surface (imagining that distance across the sphere can connect two radii, which create the diameter).
The sphere's volume (V) can be computed as $\frac{4\pi r^3}{3}$ , where r is the radius. In this instance, the sphere's volume equals $\frac{4\pi\times16^3}{3}=\frac{4\pi\times4096}{3}$ , which can also be expressed as $\frac{16384\times\pi}{3}$ .

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Leona [12618]

Answer:

The correct answer is;

A. 0.17

Step-by-step explanation:

Here are the provided details;

The average time taken for a cashier to handle an order, μ = 276 seconds

The deviation from the average, σ = 38 seconds

The z-score for an order processing time of x = 240 seconds can be calculated as follows;

$Z=\dfrac{x-\mu }{\sigma }$

Thus;

$Z=\dfrac{240-276 }{38 } \approx -0.9474$

The resulting probability

P(z = -0.9474) = 0.17361

Hence, the estimated proportion of orders processed in under 240 seconds is roughly 0.17361 or 0.17 when rounded to two decimal places.

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2 months ago

The random variable KK has a geometric distribution with mean 16. Which of the following is closest to the standard deviation of

Inessa [12570]

Answer:

E 240

Step-by-step explanation:

Mean of the geometric distribution = (1- p) / p

16 = (1 - p) / p

16p = 1 - p; 17p = 1; thus, p = 1/17 = 0.058

Standard Deviation = (1 - p) / p^2

= (1 - 0.058) / (0.058)^2

0.942 / 0.003364

= 280, which is closest to 240

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1 month ago

Initially 5 grams of salt are dissolved into 10 liters of water. Brine with concentration of salt 5 grams per liter is added at

Svet_ta [12734]

The salt enters at a rate of (5 g/L)*(3 L/min) = 15 g/min.

The salt exits at a rate of (x/10 g/L)*(3 L/min) = 3x/10 g/min.

Thus, the total rate of salt flow, represented by $x(t)$ in grams, is defined by the differential equation,

$x'(t)=15-\dfrac{3x(t)}{10}$

which is linear. Shift the $x$ term to the right side, then multiply both sides by $e^{3t/10}$ :

$e^{3t/10}x'+\dfrac{3e^{t/10}}{10}x=15e^{3t/10}$

$\implies\left(e^{3t/10}x\right)'=15e^{3t/10}$

Next, integrate both sides and solve for $x$ :

$e^{3t/10}x=50e^{3t/10}+C$

$\implies x(t)=50+Ce^{-3t/10}$

Initially, the tank contains 5 g of salt at time $t=0$ , so we have

$5=50+C\implies C=-45$

$\implies\boxed{x(t)=50-45e^{-3t/10}}$

The duration required for the tank to contain 20 g of salt is $t$ , such that

$20=50-45e^{-3t/10}\implies t=\dfrac{20}3\ln\dfrac32\approx2.7031\,\mathrm{min}$

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1 month ago

Find the maximum value of P=3x+2y subject to the following constraints:<br> Please help me!!!

Zina [12379]

The maximum value of P is determined to be 33.

Step-by-step explanation: Start by graphing the constraints represented by the lines

5x + y = 16, which has intercepts at (16, 0) and (0, 16), and

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At (0, 0), P = 0. At (0, 16), P = 32. At (2, 6), P = 18. Finally, at (11, 0), P = 33. Thus, the maximum P value occurs when x = 11 and y = 0.

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28 days ago

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PIT_PIT [12445]

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29 days ago