Sarah earned $36.00 mowing lawns. She saved 1/6 of her money. After saving, how much money does Sarah have left?

A water tank in the shape of an inverted circular cone has a base radius of 3 m and height of 7 m . If water is being pumped int

Wittaler [7]

The water level increases by 0.608 meters per minute when the water is 3.5 m deep

<h3>How to determine the rate?</h3>

The given parameters are:

Radius, r = 3
Height, h = 7
Rate in, V' = 4.3m^3/min

The relationship between the radius and height is:

r/h = 3/7

Make r the subject

r = 3h/7

The volume of a cone is;

$V = \frac 13\pi r^2h$

This gives

$V = \frac 13\pi (\frac{3h}{7})^2h$

Expand

$V = \frac{3h^3}{49}\pi$

Differentiate

$V' = \frac{9h^2}{49}\pi h'$

Make h' the subject

$h' = \frac{49}{9\pi h^2}V'$

When the water level is 3.5.

We have:

$h' = \frac{49}{9\pi * 3.5^2}V'$

Also, we have:

V' = 4.3

So, the equation becomes

$h' = \frac{49}{9\pi * 3.5^2} * 4.3$

Evaluate the products

$h' = \frac{210.7}{346.36}$

Evaluate the quotient

h' = 0.608

Hence, the water level increases by 0.608 meters per minute

Read more about volumes at:

brainly.com/question/10373132

#SPJ1

7 0

2 years ago

X+y=5 3x-4y=8 please i need the steps

grandymaker [24]

Answer:

x + y = 5

3x - 4y = 8

3x + 3y = 15

3x - 4y = 8 -

7y = 7

y = 1

x + y = 5

x + 1 = 5

x = 4

x = 4

y = 1

Hope it helps!

6 0

2 years ago

An education researcher claims that 58% of college students work year-round. In a random sample of 400 college students, 232

Hatshy [7]

Answer:

The proportion of college students who work year-round is 58%.

Step-by-step explanation:

The claim made by the education researcher is that 58% of college students work year-round.

A random sample of 400 college students, 232 say they work year-round.

To test the researcher's claim use a one-proportion z-test.

The hypothesis can be defined as follows:

H₀: The proportion of college students who work year-round is 58%, i.e. p = 0.58.

Hₐ: The proportion of college students who work year-round is 58%, i.e. p ≠ 0.58. C

Compute the sample proportion as follows:

$\hat p=\frac{232}{400}=0.58$

Compute the test statistic value as follows:

$z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.58-0.58}{\sqrt{\frac{0.58(1-0.58)}{400}}}=0$

The test statistic value is 0.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

Compute the p-value for the two-tailed test as follows:

$p-value=2\times P(z$

*Use a z-table for the probability.

The p-value of the test is 1.

The p-value of the test is very large when compared to the significance level.

The null hypothesis will not be rejected.

Thus, it can be concluded that the proportion of college students who work year-round is 58%.

6 0

4 years ago

What is the slope of any parallel to the line 8x + 9y = 3 in the standard (x,y) coordinate plane?

iris [78.8K]

Answer:y=−8x9+13 y = - 8 x 9 + 1 3 have the same slope of −89 .

Step-by-step explanation: Just do it.

8 0

3 years ago

How do you convert this decimal 0.3333 to a fraction?

torisob [31]

Answer:

1/3

Step-by-step explanation:

To convert a decimal to percent, we multiply the decimal by 100. To convert a fraction to decimal, we divide the numerator by the denominator using long division and to convert a fraction to percent, we convert the fraction to decimal and the decimal to percent.

8 0

3 years ago