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Bess [88]
3 years ago
15

7.

Mathematics
1 answer:
Iteru [2.4K]3 years ago
7 0

Answer:

a. 45 π

b. 12 π

c. 16 π

Step-by-step explanation:

a.

If a 3×5 rectangle is revolved about one of its sides of length 5 to create a solid of revolution, we can see a cilinder with:

Radius: 3

Height: 5

Then the volume of the cylinder is:

V=π*r^{2} *h= π*(3)^{2} *(5) = π*(9)*(5)=45 π

b. If a 3-4-5 right triangle is revolved about a leg of length 4 to create a solid of revolution. We can see a cone with:

Radius: 3

Height: 4

Then the volume of the cone is:

V=(1/3)*π*r^{2} *h= (1/3)*π*(3)^{2} *(4) = (1/3)*π*(9)*(4)=12 π

c. We can answer this item using the past (b. item) and solving for the other leg revolution (3):

Then we will have:

Radius: 4

Height: 3

Then the volume of the cone is:

V=(1/3)*π*r^{2} *h= (1/3)*π*(4)^{2} *(3) = (1/3)*π*(16)*(3)=16 π

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Assume that​ women's heights are normally distributed with a mean given by mu equals 62.3 in​, and a standard deviation given by
Salsk061 [2.6K]

Answer: a)  0.6141

b) 0.9772

Step-by-step explanation:

Given : Mean : \mu= 62.3\text{ in}

Standard deviation : \sigma = \text{2.4 in}

The formula for z -score :

z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}

a) Sample size = 1

For x= 63 in. ,

z=\dfrac{63-62.3}{\dfrac{2.4}{\sqrt{1}}}=0.29

The p-value = P(z

0.6140918\approx0.6141

Thus, the probability is approximately = 0.6141

b)  Sample size = 47

For x= 63 ,

z=\dfrac{63-62.3}{\dfrac{2.4}{\sqrt{47}}}\approx2.0

The p-value = P(z

=0.9772498\approx0.9772

Thus , the probability that they have a mean height less than 63 in =0.9772.

8 0
3 years ago
HELP ASAP PLZ &THANK YOU :)
Andre45 [30]

The standard form:

Ax+By=C

The slope-intercept form:

y=mx+b

m - slope

m=\dfrac{y_2-y_1}{x_2-x_1}

b - y-intercept (0, b).

We have the point (0, 43) → b= 43.

Next point (2, 55). Substitute to the slope formula:

m=\dfrac{55-43}{2-0}=\dfrac{12}{2}=6

Therefore we have:

y=6x+43      <em>subtract 6x from both sides</em>

\boxed{-6x+y=43}


8 0
3 years ago
Please help ASAP!!! Step by step <br> translation : 3units right , 4 units down
xenn [34]

Answer:

C'=(-1,0)

B'=(-2,1)

A'=(-4,1)

D'=(-4,0)

Step-by-step explanation:

each point moves 3 right and 4 down ( follow the pattern)

Hope i helped :)

6 0
3 years ago
If two marbles are randomly selected from the bag without replacement, what is the probability that the first marble is blue?
joja [24]

Answer:1,0.5, or 0 it depends

Explanation:

The probability that one event occurred depends on the total of random event, being 1 the most of the probabilities

If the two marbles are blue the probability to select a marble blue is 1

If one of the marbles is blue and the other marble is of any color the probability to select the blue marbles is:

P=1 - 1/2=1/2

Being 1/2 or 0.5 the answer

If any of the marbles are blue then the probabilities are 0

8 0
3 years ago
Questions 1&amp;2 I need help with who can help me
gayaneshka [121]
What do you need help with? it helps us to know the question!
7 0
3 years ago
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