All categories

2 years ago

What is the ratio of the volumes of two similar rectangles, if the ratio of their perimeters is 2:9?

Mathematics

1 answer:

erma4kov [3.2K]2 years ago

8 0

Answer:

Step-the base is equal to length * width.

the formula for the volume of a rectangular prism becomes length * width * height.

the ratio of the volume of a three sided figure is the ratio of their corresponding sides cubed.

so if the ratio of their volumes is 125/64, then the ratio of their corresponding sides id 5/4 because 5^3 = 125 and 4^3 = 64.

since the base area is equal to length * widfth, then the ratio of the areas becomes 5^2 / 4^2 which is equal to 25/16.

the ratio of the base area becomes 25/16.

to confirm, use an example:

original prism has dimensions as shown below:

length = 20

width = 40

height = 60

volume = 20 * 40 * 60 = 48000

base area = 20 * 40 = 800

prims that has sides in a ratio of 5/4 to original prism is shown below:

length = 20 * 5/4 = 25

width = 40 * 5/4 = 50

height = 60 * 5/4 = 75

volume = 25 * 50 * 75 = 93750

base area = 25 * 50 = 1250

ratio of the volumes = 93750 / 48000 = 1.953125

ratio of the base areas = 1250 / 800 = 1.5625

125/64 = 1.953125

25/16 = 1.5625

the formulas work.

the ratio of the volume is 125/64

the ratio of the base area is 25/16by-step explanation:

volume = 20 * 40 * 60 = 48000

base area = 20 * 40 = 800

prims that has sides in a ratio of 5/4 to original prism is shown below:

length = 20 * 5/4 = 25

width = 40 * 5/4 = 50

height = 60 * 5/4 = 75

volume = 25 * 50 * 75 = 93750

base area = 25 * 50 = 1250

You might be interested in

Someone pls help me ill give out brainliest pls don’t answer if you don’t know

Akimi4 [234]

Answer:

$\sqrt{256} \: and \: \sqrt{289}$

Step-by-step explanation:

Explanation:

$\sqrt{256 } = 16 \\ \sqrt{289} \: = 17$

5 0

2 years ago

A. 231<br> B. 39<br> C. 129<br> D. 51

VladimirAG [237]

Answer:

the answer is

129

Step-by-step explanation:

cyclic

3 0

3 years ago

Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41 % of the viewing audience in the a

ZanzabumX [31]

Answer:

1) Null hypothesis: $p\geq 0.41$

Alternative hypothesis: $p < 0.41$

2) $\hat p=0.36$ estimated proportion of people indicated that they watch the late evening news on this local CBS station

3) $z_{crit}=-2.33$

And we can use the following excel code to find it: "=NORM.INV(0.01,0,1)"

4) $z=\frac{0.36 -0.41}{\sqrt{\frac{0.41(1-0.41)}{1000}}}=-1.017$

5) $z_{crit}=-1.28$

And we can use the following excel code to find it: "=NORM.INV(0.1,0,1)"

6) We see that $|t_{calculated}|$ so then we have enough evidence to FAIL to reject the null hypothesis at 1% of significance.

7) Null hypothesis: $p\geq 0.41$

Step-by-step explanation:

Data given and notation

n=100 represent the random sample taken

X represent the people indicated that they watch the late evening news on this local CBS station

$\hat p=0.36$ estimated proportion of people indicated that they watch the late evening news on this local CBS station

$p_o=0.41$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v{/tex} represent the p value (variable of interest) Part 1We need to conduct a hypothesis in order to test the claim that 11:00 PM newscast reaches 41 % of the viewing audience in the area: Null hypothesis:[tex]p\geq 0.41$

Alternative hypothesis: $p < 0.41$

Part 2

$\hat p=0.36$ estimated proportion of people indicated that they watch the late evening news on this local CBS station

Part 3

Since we have a left tailed test we need to see in the normal standard distribution a value that accumulates 0.01 of the area on the left and on this case this value is :

$z_{crit}=-2.33$

And we can use the following excel code to find it: "=NORM.INV(0.01,0,1)"

Part 4

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.36 -0.41}{\sqrt{\frac{0.41(1-0.41)}{1000}}}=-1.017$

Part 5

Since we have a left tailed test we need to see in the normal standard distribution a value that accumulates 0.1 of the area on the left and on this case this value is :

$z_{crit}=-1.28$

And we can use the following excel code to find it: "=NORM.INV(0.1,0,1)"

Part 6

We see that $|t_{calculated}|$ so then we have enough evidence to FAIL to reject the null hypothesis at 1% of significance.

Part 7

Null hypothesis: $p\geq 0.41$

4 0

3 years ago

A rectangular lot is 70 yards wide and 115 yards long.

forsale [732]

Answer: 165 in length 20 in width

Step-by-step explanation: :)

5 0

2 years ago

Find the remainder when f(x) = x3 − 14x2 + 7x − 10 is divided by x − 3. 184 164 −88 −122

Fudgin [204]

Answer:

122

Step-by-step explanation:

For this case we must build a quotient that, when multiplied by the divisor, eliminates the terms of the divide until it reaches the remainder.

It must be fulfilled that:

Dividend = Quotient * Divisor + Remainder

we have that the remainder is 122.

have a good day

5 0

3 years ago

What is the ratio of the volumes of two similar rectangles, if the ratio of their perimeters is 2:9? ​

What is the ratio of the volumes of two similar rectangles, if the ratio of their perimeters is 2:9?