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ExtremeBDS [4]
2 years ago
9

Kent has two similar cylindrical pipes, Pipe A and Pipe B. The radius of Pipe A is 6 cm, and the radius of Pipe B is 2 cm. What

is the ratio of the
volume of Pipe A to the volume of Pipe B?
A)3:1
B)6:2
C)27:1
D)9:3​
Mathematics
1 answer:
Alchen [17]2 years ago
7 0

Answer: C)27:1

Step-by-step explanation:

Given, Kent has two similar cylindrical pipes, Pipe A and Pipe B. The radius of Pipe A is 6 cm, and the radius of Pipe B is 2 cm.

Volume of cylinder = \pi r^2h, where r= radius and h = height.

Also, If two figures are similar then ratio of volume is equal to the cube of any dimension .

The ratio of the volume of Pipe A to the volume of Pipe B is given by :-

\dfrac{\text{Volume of pipe A}}{\text{Volume of pipe B}}=\dfrac{6^3}{2^3}\\\\=\dfrac{216}{8}=\dfrac{27}{1}

Thus, the ratio of the volume of Pipe A to the volume of Pipe B = 27:1

So, the correct option is C)27:1.

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The diagram represents a difference of squares. A 2-column table with 2 rows. The labels for the columns and rows are blank. Fir
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I think its fisrts one

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2 years ago
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21. Given directed line segment WV , find the coordinates of R
Jobisdone [24]

Answer:

R\left(\frac {4x_1+3x_2}{7} , \frac {4y_1+3y_2}{7}\right)

Step-by-step explanation:

Let the coordinate of the points W, V and R are (x_1,y_1), (x_2,y_2), and (x_s,y_s)respectively.

The coordinate of the section point, (x_s,y_s), which divides the line joining the two points (x_1,y_1) and (x_2,y_2) in the ration m:n is

x_s=\frac {nx_1+mx_2}{m+n} and

y_s=\frac {ny_1+my_2}{m+n}.

The given ration is, m:n=3:4

R(x_s,y_s)=R\left(\frac {nx_1+mx_2}{m+n} , \frac {ny_1+my_2}{m+n}\right)

=R\left(\frac {4x_1+3x_2}{7} , \frac {4y_1+3y_2}{7}\right).

The exact point can be determined by putting the value of the exact coordinate in the above-obtained formula.

6 0
2 years ago
32​% of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find t
Lorico [155]

Answer:

A.  21.06%

B. 66.88%

C. 81.56%

Step-by-step explanation:

There are two possible answer for the question asked, yes(more likely to make purchases) or no. The probability for a random adults answer yes to the question is 32% so the probability that the adults answer no is 68%.

(a) exactly​ two

There is only one case for this question, 2 people say yes and 8 people say no. The calculation for this problem will be:

2P10 * P(yes)^2 * P(no)^8= 10!/2!8!* 32%^2  * 68%^8 = 0.21066= 21.06%

(b) more than​ two

There are a lot of case for more than two, its easier to find out the negation of the probability which is "two or less". Case that fulfill "two or less" will be: 2 yes and 8 no

1 yes and 9 no

0 yes and 10 no

The calculation for the negation will be:

~P(X)= 0P10 * P(yes)^0 * P(no)^10   +   1P10 * P(yes)^1 * P(no)^9   +  2P10 * P(yes)^2 * P(no)^8  =

10!/0!10!* 32%^0  * 68%^10    +   10!/1!9!* 32%^1  * 68%^9   +   10!/2!8!* 32%^2  * 68%^8

0.02113 + 0.09947 + 0.21066  =  0.33126= 33.12%

Since its the negation, you need to subtract 1 with the negation

P(X)= 1 - ~P(X)

P(X)= 1 - 33.12%= 66.88%

(c) between two and​ five, inclusive

Same formula as above, but the case is:

2 yes and 8 no

3 yes and 7 no

4 yes and 6 no

5 yes and 5 no

The calculation will be:

2P10 * P(yes)^2 * P(no)^8 + 3P10 * P(yes)^3 * P(no)^7 + 4P10 * P(yes)^4 * P(no)^6 + 5P10 * P(yes)^5 * P(no)^5 =

10!/2!8!* 32%^2  * 68%^8    +   10!/3!7!* 32%^3  * 68%^7   +   10!/4!6!* 32%^4  * 68%^6  +  10!/5!5!* 32%^5  * 68%^5

0.21066 + 0.26435 + 0.21770 + 0.1229= 0.81561= 81.56%

8 0
2 years ago
A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50. In a random
Harlamova29_29 [7]

Answer with explanation:

Given : Sample mean =\overline{x}=\text{48.47 pounds}

Standard deviation : \sigma=\text{ 3.1 pounds.}

Sample size : n = 36

Claim : \mu\neq50

∴ H_0:\mu=50

H_1:\mu\neq50

Since the alternative hypothesis is two tail , then the test is two tail test.

By using a z statistic and a 0.05 level of significance. Reject  H_0 if z < -1.960 or is z> 1.960.

Then , the test static for population mean is given by :-

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

z=\dfrac{48.47-50}{\dfrac{3.1}{\sqrt{36}}}\approx-2.96

We reject H_0 since -2.96\leq -1.96. We have statistically significant evidence at \alpha=0.05 to show that the mean amount of garbage per bin is not different from 50.  

5 0
2 years ago
Liza's cousin Marie bought her a ring for 250 euros in France. Liza wants to pay Marie for it in U.S. dollars. If the foreign ex
EleoNora [17]

Answer:

416.67 dollars

Step-by-step explanation:

the exchange rate between U.S. dollar and euro is given as

Exchange rate = 1:0.6

1 U.S. dollar /1 euro = 0.6

cross-multiplying both side

1 x 1 U.S. dollar = 0.6 x 1 euro

1 U.S. dollar = 0.6 euro

multiplying both side by 10

10 U.S. dollar = 0.6 x 10 euro

10 U.S. dollar = 6 euro

dividing both side by "6"

10 U.S. dollar/6 = 6 euro/6

(10/6) U.S. dollar = 1 euro

1 euro = (10/6) U.S. dollar

the ring was bought for 250 euros , we need to convert 250 euros in dollars.

multiplying both side by 250

250 x 1 euro = (250 x 10/6) U.S. dollar

250 euro = 416.67 U.S. dollar

so liza should pay 416.67 U.S. dollar to marie.

4 0
2 years ago
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