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3 years ago

5.40 is 9% of what price? Please show step by step

1 answer:

3 0

$p\%=\dfrac{p}{100}\\\\9\%=\dfrac{9}{100}=0.09\\\\9\%\ of\ x\ is\ 5.4\to0.09x=5.4\ \ \ \ |divide\ both\ sides\ by\ 0.09\\\\\boxed{x=60}$

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The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 m

jeka94

9514 1404 393

Answer:

8000π mm^3/s ≈ 25,133 mm^3/s

Step-by-step explanation:

The rate of change of volume is found by differentiating the volume formula with respect to time.

V = 4/3πr^3

V' = 4πr^2·r'

For the given numbers, this is ...

V' = 4π(20 mm)^2·(5 mm/s) = 8000π mm^3/s ≈ 25,133 mm^3/s

_____

<em>Additional comment</em>

By comparing the derivative to the area formula for a sphere, you see that the rate of change of volume is the product of the area and the rate of change of radius. This sort of relationship will be seen for a number of different shapes.

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3 years ago

Nancy found that x=1 is one solution to the quadratic equation (x 2)2=a. what is the value of a? -9 -3 3 9

AlladinOne [14]

The value of the <em>a, </em>in the provided quadratic equation for which Nancy found one solution as x=1 is 9.

<h3>What is the solution of equation?</h3>

The solution of the quadratic equation is the solution of the variable of the equation, for which the equation satisfies.

Nancy found that x=1 is one solution to the quadratic equation. The quadratic equation is,

$(x +2)^2=a$

For this equation, one solution is <em>x</em>=1. Put this value in the above equation to get the value of <em>a,</em>

$(1 +2)^2=a\\(3)^2=a\\9=a\\a=9$

Thus, the value of the <em>a, </em>in the provided quadratic equation for which Nancy found one solution as x=1 is 9.

Learn more about the solution of the equation here;

brainly.com/question/21283540

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2 years ago

Read 2 more answers

Determine whether y varies directly with x. If so, find the constant of variation k.

kumpel [21]

Direct variation is y=kx, inverse variation is y=k/x....

-5y=-2x divide both sides by -5

y=2.5x

So this is a direct variation with a constant of 2.5

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3 years ago

Find the GCF of -10c2d and 15 ca2

jonny [76]

Answer:

Step-by-step explanation:

5c is the only value you can take out of both factors

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3 years ago

Construct a 99% confidence interval to estimate the population proportion with a sample proportion equal to 0.36 and a sample s

vivado [14]

Using the z-distribution, the 99% confidence interval to estimate the population proportion is: (0.2364, 0.4836).

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which:

$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

In this problem, we have a 99% confidence level, hence $\alpha = 0.99$ , z is the value of Z that has a p-value of $\frac{1+0.99}{2} = 0.995$ , so the critical value is z = 2.575.