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3 years ago

Surface area question:

Mathematics

1 answer:

Dafna1 [17]3 years ago

3 0

Answer:

190π (not part of the answer choices)

Step-by-step explanation:

The surface area of a cylinder can be found using the formula below:

$SA=2\pi r^2+\pi dh$ where $r$ is the radius of the base, $d$ is the diameter of the base and $h$ is the height of the cylinder.

Plug in the given values

$SA=2\pi (\frac{10}{2}) ^2+\pi (10)(14)\\SA=2\pi (\frac{100}{4})+140\pi\\SA=2\pi (25)+140\pi\\SA=50\pi+140\pi\\SA=190\pi$

Therefore, although this answer isn't one of the choices, the surface area of the cylinder is 190π.

I hope this helps!

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Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately norm

iragen [17]

Answer:

a. 0.691

b. 0.382

c. 0.933

d. $88.490

e. $58.168

f. 5th percentile: $42.103

95th percentile: $107.897

Step-by-step explanation:

We have, for the purchase amounts by customers, a normal distribution with mean $75 and standard deviation of $20.

a. This can be calculated using the z-score:

$z=\dfrac{X-\mu}{\sigma}=\dfrac{85-75}{20}=\dfrac{10}{20}=0.5\\\\\\P(X$

The probability that a randomly selected customer spends less than $85 at this store is 0.691.

b. We have to calculate the z-scores for both values:

$z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{65-75}{20}=\dfrac{-10}{20}=-0.5\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{85-75}{20}=\dfrac{10}{20}=0.5\\\\\\\\P(65$

The probability that a randomly selected customer spends between $65 and $85 at this store is 0.382.

c. We recalculate the z-score for X=45.

$z=\dfrac{X-\mu}{\sigma}=\dfrac{45-75}{20}=\dfrac{-30}{20}=-1.5\\\\\\P(X>45)=P(z>-1.5)=0.933$

The probability that a randomly selected customer spends more than $45 at this store is 0.933.

d. In this case, first we have to calculate the z-score that satisfies P(z<z*)=0.75, and then calculate the X* that corresponds to that z-score z*.

Looking in a standard normal distribution table, we have that:

$P(z$

Then, we can calculate X as:

$X^*=\mu+z^*\cdot\sigma=75+0.67449\cdot 20=75+13.4898=88.490$

75% of the customers will not spend more than $88.49.

e. In this case, first we have to calculate the z-score that satisfies P(z>z*)=0.8, and then calculate the X* that corresponds to that z-score z*.

Looking in a standard normal distribution table, we have that:

$P(z>-0.84162)=0.80$

Then, we can calculate X as:

$X^*=\mu+z^*\cdot\sigma=75+(-0.84162)\cdot 20=75-16.8324=58.168$

80% of the customers will spend more than $58.17.

f. We have to calculate the two points that are equidistant from the mean such that 90% of all customer purchases are between these values.

In terms of the z-score, we can express this as:

$P(|z|$

The value for z* is ±1.64485.

We can now calculate the values for X as:

$X_1=\mu+z_1\cdot\sigma=75+(-1.64485)\cdot 20=75-32.897=42.103\\\\\\X_2=\mu+z_2\cdot\sigma=75+1.64485\cdot 20=75+32.897=107.897$

5th percentile: $42.103

95th percentile: $107.897

5 0

3 years ago

Prove the identity with steps.

Sav [38]

Remember that a double angle formula for cosine is
$\cos(2x)=\cos^{2}x-\sin^{2}x$

So
$\cos^{2}(2x)-\sin^{2}(2x)=\cos(4x)$
$\rightarrow \cos^{2}(2x)-\sin^{2}(2x)=\cos(2*2x)$
$\rightarrow \cos^{2}(2x)-\sin^{2}(2x)=\cos^{2}(2x)-\sin^{2}(2x)$

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3 years ago

the formula F=9/5C+32 changes a temperature reading from the Celsius scale C to the Fehrenheit scale F. What temperature measure

cestrela7 [59]

Answer:

Step-by-step explanation:

F=(9/5)c + 32

F=(9/5)(-5) + 32

F=(-9) + 32

F=23

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3 years ago

Help me please .-. tyyy

Ket [755]

4/3
explanation : just write it in fraction form

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A water tank contains 100 fluid Ounces of water. Jacob fills up cups that hold 8 fl. oz. each. How many cups has he filled when

Kamila [148]

7 and a half cups.

Step-by-step explanation:

Dvide 60 by 8

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