Bruno works for Poseidon Pool Service. He needs to drain a 38,000-gallon pool so that he can repair the cracked plaster. The Pool drains 12 gallons per minute.


Write an equation to represent the pool draining in slope-intercept form.


How long will it take for the pool to fully drain? Explain using numbers and words


Bruno needs to refill the pool now that the plaster is repaired. The Pool fills 16 gallons per minute.


Write an equation in slope intercept form to represent the pool filling back up.

*

How long will it take for the pool to fill back up? Explain using words and numbers..

*

Answer:

8v - 42

Step-by-step explanation:

Distributive property: a* (b + c) = (a*b) + (a*c)

3(4v - 6) - 4(v + 6) = (3*4v) + (3*(-6) ) + (-4*v + (-4)*6) )

                             = 12v - 18 - 4v - 24

                              = 12v - 4v - 18 - 24

Combine like terms [ 12v & (-4v) ] and combine constants [ (-18) & (-24)]

                             = 8v - 42

Answer:$9.695

Step-by-step explanation:

1/4 is 0.25 so this means Allison is paying 25% of the bill. Then all you have to do is times 38.78 with 0.25 and you get $9.695 or $9.70.

Answer:

$9.70

Step-by-step explanation:

You can do this question several way on a calculator:

1/4 × 38.78

OR

.25 × 38.78

OR (I like this one)

38.78 ÷ 4

All these calculations will give you the result 9.695

Since this is a real-world money problem, we would round this number to 9.70.

Allison paid $9.70.

Answer: 1.c   2.a   3.c

Step-by-step explanation:

Answer:

first picture

1 and 2 are congruent because they are a pair of corresponding angles

second picture

A = B

This is because they are alternate exterior angles and they equal the same thing

third picture

angle 5

it is also an alternate interior angle

Answer: 2/15  in/hour

Step-by-step explanation:

[tex]\displaystyle\\1)\ 6:36=\\\\6\frac{36}{60}=\\\\6\frac{3(12)}{5(12)}=\\\\6\frac{3}{5}=\\\\\frac{6*5+3}{5}=\\\\\frac{30+3}{5}=\\\\\frac{33}{5} \ hours[/tex]

[tex]\displaystyle\\2)\ 9-\frac{33}{5} =\\\\\frac{9(5)-33}{5}=\\\\\frac{45-33}{5} =\\\\\frac{12}{5}\ hours[/tex]

[tex]\displaystyle\\3)\ \frac{8}{25}:\frac{12}{5} =\\\\\frac{8}{25}*\frac{5}{12} =\\\\\frac{8(5)}{25(12)} =\\\\\frac{2*4*5}{5*5*4*3} =\\\\\frac{2}{5*3} =\\\\\frac{2}{15}\ in/hour[/tex]

Answer:

5x-8

Step-by-step explanation:

7x-14-2x+6

-14+6=-8

7x-2x=5x

The coordinates of the other endpoint of the Line segment is (-2,-5).

If M(x.y) divides the line formed by two points A(a,b) and B(c,d) into a ratio m:n. Then the coordinates of the point M can be found out by using the formula,

x = (mc + na)/(m+n)

y = (md + nb)/(m+n)

This above mentioned formula is known as The section Formula.

The one of the End point of the line is (10,-1) and the point (7,-2) is dividing the line in the ratio of 1:3.

Let us assume the other end point to be (a,b).

Now, applying Section Formula,

7 = [(1)(a)+(3)(10)]/4 and

-2 = [(1)(b)+(3)(-1)]/4

Further solving,

a = -2 and

b = -5

So, the coordinates of the endpoint is (-2,-5).

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80 : 22 :: x : 11

x = (11 x 80) / 22

x = 880/22

x = 40

The missing number is 40

The notebook's length in centimeters is 27.94 cm.

Since we are provided that

The  desk's width is 25 inches.

Convert into cm.

There is a stated measurement of 25 inches = 63.5 cm.

As previously stated, a measurement in inches differs directly from a measurement in centimeters.

As a result, we have said that

If the notebook's length is 11 inches

Let 'x' be the length of the notebook in cm.

As a result of the question,

[tex]\frac{25}{63.5} = \frac{11}{x}[/tex]

[tex]x=\frac{698.5}{25}[/tex]

x = 27.94 cm

Hence the length of note book is 27.84 cm.

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Answer:

Step-by-step explanation:

ŷ = − 2.6s + 1.1.

residual value = Measured value - Predicted value

Measured value = actual y-coordinate of the point, y

Predicted value = value of y from the equation, y1

residual value = (actual y-coordinate of the point, y) - (value of y from the equation, y1)

residual value = y - y1

For s = 1.3

     y  = 1.2

value of y from the equation, y1:

y1 = -2.6*(1.3) + 1.1

y1 = -3.38 + 1.1

y1 = -2.28

residual value = y - y1

residual value = 1.2 -  -2.28

residual value = 1.2 + 2.28

Since the predicted value is far less than the observed value, the line of best fit underpredicts the temperature change.

Answer:

3.48; The line of best fit underpredicts the temperature change.

Step-by-step explanation:

i took the test :)

Simply put, probability is the likelihood that something will occur.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.Statistics is the study of events that follow a probability distribution.

Calculate probability ?

Therefore,

p = 0.43

if, in fact, 43% of shoppers make a purchase before leaving a store;

p = 78/200

=  0.39

if, in a sample of 200 shoppers, 78 make a purchase.

The sample proportion is a random variable that can't be predicted with certainty because it fluctuates from sample to sample.

It will be represented as a random variable by the letter P.

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Answer: the answer to that problem is

X=2

The third term of the sequence is 41.

Given,

Tn = 50 - n²

Tn = 50 - (3)²

Tn = 50 - 6

Tn = 41

As the third term is required substitute the value in the main equation 50 - n² which gives T3 = 41.

As the third term is necessary, replace 50 - n² in the main equation, yielding T3 = 41.

Arithmetic Progression is a series of numbers in which the difference between consecutive terms is constant. One approach is to calculate the arithmetic mean. To do this, sum all the values ​​and divide the sum by the number of values. For arithmetic sequences, use the expression a = a1 + (n1) d. where a is the term, a1 is the difference of the first term, and d is the difference of the subsequent term.

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The decimal notation of 4.93 x 10³ will be 4930.00.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The expression is;

4.93 x 10³

Now, Solve for decimal notation as;

4.93 x 10³ = 4.93 x 10 x 10 x 10

               = 49.3 x 10 x 10

               = 493 x 10

              = 4930.00

Thus, The decimal notation of 4.93 x 10³ will be 4930.00.

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Answer: Similar by SAS

Step-by-step explanation:

Note that [tex]\frac{AC}{AB}=\frac{JG}{HG}=\frac{1}{4}[/tex].

So, the triangles are similar by SAS (since the congruent angle is included between the proportional sides).

Answer:

B

Step-by-step explanation:

All the rest = 3/5, 3 shaded out of 5

:]

The ratios aren't proportional as D. No, because one ratio reduces to different values.

A ratio is simply used to show the comparison between the numbers that are illustrated in a data.

In this case, the fractions that are given include 46/48 and 69/84.

To have an equivalent ratio, it's important to have the numerator and the denominator divided by the same number.

In this case, this isn't possible with 46/48 and 69/84.

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Rose walks 3.2 miles every day. How many miles will she have walked in 5 days?

3.2*5 = 16 miles

Christie was on a road trip. She travelled 320.95 miles on day one, 231.45 miles on day two, and 120.32 miles on day three. How many miles did she travel during her three-day trip?

320.95 + 231.45 + 120.32 = 672.72 miles

Hugh drove 774.4 miles. His car averaged 24.2 miles per gallon of gas. How many gallons of gas did the car use?

774.4/24.2 = 32 gallons

Answer:

Step-by-step explanation:

There are 9 squares filled halfway, and 5 squares filled completely.

9 x 0.5 = 4.5

4.5 + 5 = 9.5

There are 25 squares in the shape.

9.5  / 25 = 0.38

38% of the square is shaded.

Answer:

2x44/7

Step-by-step explanation:

Answer:

Step-by-step explanation:

well it very confusing to some but,...31.7142857143 and i don't know the other one :) ;).

Answer:

A

Step-by-step explanation:

17 < 9 + x ( subtract 9 from both sides )

8 < x , then

x > 8

The variable y has a value of 72 when x equals 9

The variation statement is given as

x and y are in direct proportion

This means that

y = kx

Where k represents the constant of variation

Using the values given from the question, we have

(x, y) = (7, 56)

This gives

56 = 7k

Divide both sides by 7

k = 8

So, we have

y = 8k

The value of y when x = 9 is calculated as

y = 8 * 9

Evaluate the products

y = 72

Hence, the value of y is 72

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Answer:

php 40,000

Step-by-step explanation:

In the ratio, Marvin corresponds to 12 and Victor to 2.

Marvin invested php 240,000.

His part of the ratio is 12.

240,000/12 = 20,000

Victor's part in the ratio is 2.

Victor's investment amount is 2 × php 20,000 = php 40,000

Based on the complete question, the Normal Distribution Graph will resemble the one in the figure attached.  

Also, note that using the 68-95-99.7 rule, the proportion of runners between 48.7 and 67.9 kg is 0.8385.

The 68-95-99.7 rule, also known as the empirical rule, is a statistician's shorthand for remembering the percentage of values in a normal distribution that fits within an interval estimate: 68%, 95%, and 99.7% of the variables lie within one, two, and three standard deviations of the mean, correspondingly.

To compute the proportion of runners whose body weight is between 48.7 and 67.9 kg with the help of the 68-95-99.7 rule:

We know given that:

The mean = 63.1 and

the standard deviation (SD) = 4.8.

Where the weight is 67.9kg, we know that the distance between this and the mean is 4.8, that is;

67.9 - mean

= 67.9 - 63.1

= 4.8 [1*SD]

In the same way,
48.7 corresponds to 48.7-63.1 = -14.4 [ -3*SD]

Hence, based on the rule,

= 83.85%

= 0.8385.

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Full Question:

A study of elite distance runners found a mean body weight of 63.1 Kilograms (kg), with a standard deviation of 4.8kg.

If you have saved some money to purchase five different songs to download to your portable music device. The inequality that represents the prices you can pay for each song if you have saved no more than 20 dollars is : 5 x ≤ 20.

Given:

Numbers of different songs to download = 5

Cost = $20

Hence,

The inequality  is ; 5 x ≤ 20

Now let solve the inequality

5 x ≤ 20

x = 20 /5

x = 4

So,

=  x ≤ 4

Therefore the inequality is  5 x ≤ 20.

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The assumption that the sample means follow a roughly normal distribution is used to calculate a confidence interval for a population mean with a known standard deviation.

A confidence interval gives a range of values that will probably include the actual mean. For example, let's say that our sample has a mean of x=10 and we have generated the 90% confidence interval (5, 15), with EBM = 5. For instance, we might not be able to speak to everyone in Colorado if we wanted to find out the typical age of Colorado residents who enjoy bananas. However, we could conduct in-depth interviews with a representative sample and make an educated guess or calculation to provide us with a range of ages.

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Answer:

-32

Step-by-step explanation:

m=3 , n=-1 ( given )

then, -4(m-n)2 = -4(3-(-1))2 = -32

Rounding off to nearest ten thousand gives the most accurate answer as 240,000 cans.

Given that, the number of cans collected during September = 32,537 and the number of cans collected during October = 207,492.

Rounding numbers means adjusting the digits (up or down) to make rough calculations easier. The result will be an estimated answer rather than a precise one.

a) Now, the number of cans were collected during September and October = 32537+207492 = 240,029

To the nearest thousand is 240,000

b) Rounding 32,537 to the nearest thousand is 32000 and rounding 207,492 to the nearest thousand is 207,000

Sum = 32000+207000 = 239,000

Rounding 32,537 to the nearest ten thousand is 30000 and rounding 207,492 to the nearest ten thousand is 210,000

Sum = 30000+210,000 = 240,000

Therefore, rounding off to nearest ten thousand gives the most accurate answer as 240,000 cans.

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a) The mean of this distribution is 7 min

b) The standard deviation is 4.0414 min

a) The mean is the midpoint between the ends or 7 min

variance is (b-a)^2/12 or 196/12 or 16.3333 min

b) standard deviation is sqrt(V)= 4.0414 min

the complete question is

a bus comes by every 14 minutes. the times from when a person arives at the bus stop until the bus arrives follows a uniform distribution from 0 to 14 minutes. a person arrives at the bus stop at a randomly selected time. round to 4 decimal places where possible.

a) The mean of this distribution is

b) The standard deviation is

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The two whole numbers  between which is √12 are 3 and 4.

What is an example of a whole number?

Any positive number that does not contain a fractional or decimal component is referred to as a whole number. The numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all whole numbers, for instance, as a result. -3, 2.7, or 3 12 are examples of non-whole numbers.

The closest perfect squares near 12 are 16 and 9 which are the perfect squares of 4 and 3 respectively Therefore the root of 12 lies between 3 and 4.

i.e  3 < √12 < 4

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