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2 years ago

Find x when y=32, given that x varies inversely as y, and x = 132 when y = 4

Mathematics

2 answers:

vagabundo [1.1K]2 years ago

7 0

The answer is 16.5

i hope thsi helps!

777dan777 [17]2 years ago

7 0

Answer: 16.5

Step-by-step explanation:

We know that the equation that shows inverse variation between two quantities is given by :-

$x_1y_1=x_2y_2$

We are given that x varies inversely as y, and x = 132 when y = 4

Then , to find the value of x when y= 32 , we have the following equation :-

$x\times32=132\times4$

Now, divide 32 on both the sides , we get

$x=\dfrac{132\times4}{32}\\\\\Rightarrow\ x=16.5$

Hence, the value of x = 16.5

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Vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2 minutes to complete. W

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y = 2x + 20. The answer is A. Explanation: Vlad spends a known amount of time on his history homework (20). On top of it, he also spends an unknown amount of time on solving a number of math problems (x). Each problem takes two minutes to solve, so the amount of time that he spends solving math problems is 2*x or 2x. In total (y), Vlad spends 20 + 2x amount of time on his homework. So y = 2x + 20, where y is clearly greater or equal to 20 and x is greater or equal to 0.

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2 years ago

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Jake's morning run was a distance of 9.3 miles. He ran back and forth on one long straight street. He started at his house and r

Sergeeva-Olga [200]

Answer: the distances can be 0.65 miles (in the opposite direction to the school) or 4.65 miles (in the same direction as the school)

Step-by-step explanation:

Ok, the data that we have is:

Total distance = 9.3 mi.

The travel is:

House to school = 4 mi.

school to library = A

library to house = B

Now, we have that:

4mi + A + B = 9.3mi.

We have three possibilities:

1) The order of locations is: house, library, school

The travel from: school to library + library to house is equivalent to a travel between the school to the house = 4mi.

Then we have A + B = 4mi

4mi + A + B = 8mi ≠ 9.3mi

Then the library can not be between the house and the school.

2) The order of locations is: house, school, library.

In this case we have that the distance between the library and the house is equal to the distance between the house and the school plus the distance between the school and the library, then:

4mi + A = B.

We can replace this in our original equation:

4mi + A + B = 9.3mi

4mi + A + (4mi + A) = 9.3mi

8mi + 2*A = 9.3mi

2*A = 9.3mi - 8mi = 1.3mi

A = 1.3mi/2 = 0.65mi

Then the distance between the house and the library is:

The 4 miles between the house and the school, plus the 0.65 miles between the school and the library:

Distance = 4mi + 0.65mi. = 4,65mi

3) The third case is when the order of the locations is:

Library, house, school.

Then the distance between the house and the library is equal to the distance between the school and the library minus the distance between the house and the school, this is:

A - 4mi = B

Now we can replace this in our distance equation:

4mi + A + B = 9.3mi

4mi + A + (A - 4mi) = 9.3 mi

2A = 9.3mi

A = 9.3mi/2 = 4.65mi

Then the distance between the house and the library is:

B = A - 4mi = 4.65mi - A = 0.65mi

Then the distance between the house and the library is 0.65 miles in this case.

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2 years ago

A survey found that 89% of a random sample of 1024 American adults approved of cloning endangered animals. Find the margin of er

Kobotan [32]

Answer:

The margin of error for the survey is 0.016

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 1024

Sample proportion:

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We have to find the margin of error associated with a 90% Confidence interval.

Formula for margin of error:

$z_{stat}\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.10} = 1.64$

Putting the values, we get:

$M.E = 1.64\times (\sqrt{\dfrac{0.89(1-0.89)}{1024}})\\\\M.E=0.016$

Thus, the margin of error for the survey is 0.016

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2 years ago

Here is the scale model of a fountain at a museum the scale is 1:30 how many boulders are in the real fountain

wlad13 [49]

Answer:

When we do a scale model of something (like a building, a house, or whatever) al the properties of the original thing must also be in the model.

So for example, you want to do a model of a house, and in the backyard of the house there are 4 trees, then in the model of the house you also need to put 4 trees in the backyard (indifferent of the scale of the model).

Then the number of boulders in the really fountain should be the same as the number of boulders in the scale model of the fountain.

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2 years ago

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Consider circle O below. The length of arc BA is 8.4 cm and the length of the radius is 8 cm. The measure of angle AOC is 45°. C

denis23 [38]

Answer:

i) 60°

ii) 14.7 cm

Step-by-step explanation:

length of Arc BA = 8.4 cm

length of radius = 8 cm

angle AOC = 45°

BO = AO = CO = 8 cm

i) What is the measure of Angle BOA

= length of Arc BA / Radius

= 8.4 / 8 = 1.05 radians = 60.16° ≈ 60°

ii) what is the length of arc BAC

= radius * angle BAC * $\pi /180$

angle BAC = angle AOC + angle BOA

= 45° + 60° = 105°

hence length of arc BAC

= 8 * 105 * $\pi /180$

≈ 14.7 cm

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2 years ago

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