A pool holds 33500 gallons of water. The pool is filled at a constant rate of 485 gallons every 6.5 minutes. Select whether each statement is true or false.

________ The unit rate for filling the pool is 74 gallons per minute

________ It will take 4 hours and 15 minutes to fill the pool to 85% of its capacity.

________ The difference between the pool being 64% full and 48% full is 3600 gallons.

________ A slow leak has left the pool with only 19800 gallons, a 12% decrease.

________ The pool can be completely filled in less than 5 hours.

Answer:

Approximately 143 mL of 1:4 solution and 457 mL of water

Step-by-step explanation:

A 1:4 solution has a concentration of 1/(1+4) = 1/5 or 20%.

Similarly, a 1:20 solution has a concentration of 1/(1+20) = 1/21 or 4.76%.

If x is the mL of 20% solution and y is the mL of water, then:

x + y = 600

1/5 x = 1/21 (600)

Solve:

x = 5/21 (600)

x ≈ 143

y ≈ 457

You need approximately 143 mL of 1:4 solution and 457 mL of water.

Answer:

Factorization of [tex]P(x)=(x+2)(2x+1)(3x-1)[/tex]

Step-by-step explanation:

Given:

The given polynomial is [tex]P(x)=6x^3+13x^2+x-2[/tex]

Also, [tex]P(-2)=0[/tex]

Since, for [tex]x=-2[/tex], [tex]P(x)[/tex] is 0, therefore, [tex]x+2[/tex] is a factor of the polynomial.

Now, let us divide the given polynomial by [tex]x+2[/tex] using long division method. Therefore,

[tex]\frac{6x^3+13x^2+x-2}{x+2}=6x^2+x-1[/tex]

The process of long division is shown below.

Now, factoring the quotient [tex]6x^2+x-1[/tex], we get

[tex]6x^2+x-1=6x^2+3x-2x-1=3x(2x+1)-1(2x+1)=(3x-1)(2x+1)[/tex]

Therefore, the factors of polynomial [tex]P(x)[/tex] are [tex](x+2),(2x+1),\ and\ (3x-1)[/tex]

Hence, the factorization of [tex]P(x)[/tex] is:

[tex]P(x)=(x+2)(2x+1)(3x-1)[/tex]

The solutions to the equation 9x^2 - 54x = 0 are x = 0 and x = 6, found by factoring and setting each factor equal to zero.

To find the solution(s) to the equation 9x2 - 54x = 0, we can start by factoring out the greatest common factor, which is 9x. This gives us:

9x(x - 6) = 0

Now, we set each factor equal to zero:

From the first equation, we divide by 9 to isolate x:

x = 0

From the second equation, we add 6 to both sides:

x = 6

Thus, the solutions to the equation are:

Answer:

A. y = [tex]-\frac{2}{3}[/tex] x + 12

Step-by-step explanation:

Given the two points:

A = (x1, y1) =  (6, 8)

B = (x2, y2) = (9. 6)

From the photo, we can see that the line of fest fit is a straight line (linear) that go through the two points above.

We have the standard form of a linear equation is:

where m is the slope and b is the y-intercept

To find the slope, we use the following formula:

m = [tex]\frac{y2-y1}{x2-x1}[/tex]

<=> m = [tex]\frac{6-8}{9-6}[/tex] = [tex]-\frac{2}{3}[/tex]

Substitute m into the standard equation, we have:

Because the line go through point A, so we substitute A into (1), we have:

8 = [tex]-\frac{2}{3}[/tex] *6 + b

<=> b = 12

So our equation is: y = [tex]-\frac{2}{3}[/tex] x + 12

Answer: y=-2/3x+12

Step-by-step explanation:

Answer:

$2.50

Step-by-step explanation:

Let the original monthly expenses be 'x'.

Given:

Reduced monthly expenses = $2.125

Reduction in monthly expenses = 15%

Therefore, remaining percentage of monthly expenses = 100 - 15 = 85%

Now, as per question:

[tex]85\%\ of\ x=2.125\\\frac{85}{100}\times x=2.125\\0.85x=2.125\\x=\frac{2.125}{0.85}=\$2.50[/tex]

Therefore, the original monthly expenses of Mr. Wood was $2.50.

Also, we can find his monthly income using the value of 'x'.

As per question, his monthly expenses is 80% of his income.

So, 80% of income = 2.5

Income = [tex]\frac{2.5}{0.80}=\$3.125[/tex]

So, his monthly income is $ 3.125

Answer:

It would be 11.333 minutes

Step-by-step explanation:

I solved this by setting up a cross multiplication.

60%/17 so then 40/x.

Then here cross multiplying. 60x=680. divide by 60 and x would = 11.33

To find (f o h)(4), substitute h(4) into f(x) and evaluate the expression.

To find (f o h)(4), we need to first find h(4) and then substitute that value into f(x). Let's start by finding h(4).

h(x) = - x + 3

h(4) = -4 + 3 = -1

Now, we substitute h(4) into f(x).

f(x) = -3x - 1

f(h(4)) = f(-1) = -3(-1) - 1 = 2

Therefore, (f o h)(4) = 2.

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Answer:

1002

Step-by-step explanation:

Answer:

165 additional messages

Step-by-step explanation:

$47.25 - $6.00 for 600 messages and 0.25/each additional message= $47.25-$6.00=41.25/0.25 per message =165 additional messages for a total of 765

Answer:

The slope is 3.

Step-by-step explanation:

y=-1+3x

y=3x-1

y=mx+b where m=slope and b=y-intercept

Answer:

1.22

its obvious, lets say 100% of 1 is 1. 22% of 1 is 0.22. 1+0.22=1.22

The percent 122% as a decimal will be 1.22.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol 'percent' is used to symbolize it.

The expression is given below.

⇒ 122%

Then the percent 122% as a decimal will be

⇒ 122 / 100

⇒ 1.22

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Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

c = 7/5

Decimal Form:

c = 1.4

Mixed Number Form:

c = 1/2/5

Edit: I answered this on Jan 7th, 2021.

Answer:

7 is width

Step-by-step explanation: i got it right

The length of the rectangle is 7 unit.

A rectangle is a plane shape that has pair of opposite sides equal.

To calculate the length of the rectangle, we use the formula below

Formula:

Where:

From the question,

Assuming the width of the rectangle is y unit

Substitute these values into equation  1

Solving the quadratic equation,

Since length can not be negative,

Hence The length of the rectangle is 7 unit.

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The solution involves calculating the average speed for each driver (distance travelled divided by time). Deena's average speed was 65 mph and Kristen's was 55 mph, therefore, Deena drove at a faster rate.

To solve this question, we need to compute each driver's average speed. Average speed is calculated by dividing the total distance traveled by the total time taken to cover that distance. Mathematically, average speed = total distance/total time.

For Deena, we calculate her average speed by dividing her total distance traveled (585 miles) by the time she took to cover this distance (9 hours). Doing the division, we find Deena's average speed to be about 65 mph.

Similarly, for Kristen, we divide her total distance traveled (605 miles) by the time she took to cover this distance (11 hours). Kristen's average speed comes out to be approximately 55 mph.

By comparing the average speeds, we find Deena drove at a faster rate than Kristen.

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Answer:

x=2

Step-by-step explanation:

2x+4=8

2x=8-4

2x=4

x=4/2

x=2

Answer:

  x = 2

Step-by-step explanation:

The equation shown is a perfectly good equation.

___

Look at what is being done to the variable. It is multiplied by 2, and 4 is added to the product.

To find the value of the variable, we reverse these operations, in reverse order. We undo the addition by adding the opposite of 4 (to both sides of the equation).

  2x +4 -4 = 8 -4

  2x = 4 . . . . . simplify

We undo the multiplication by multiplying by the inverse value, 1/2 (to both sides of the equation).

  (1/2)(2x) = (1/2)(4)

  x = 2 . . . . . simplify

_____

The rules of equations are pretty simple: whatever you do to one side, you must also do to the other side.

_____

Comment on this equation

You may notice that all of the numbers in this equation are divisible by 2. Another way to solve it is to start by dividing (both sides!) by 2:

  x + 2 = 4

Now, you have a 2nd-grade problem in addition facts: what added to 2 gives 4? Since you know your addition facts, you know the answer is 2. In algebra, we solve this by subtracting 2 (from both sides!).

  x = 2

Answer:

in 2hrs =  -6°C

in 5hrs = -15°C

in half an hr = -1.5°C

Step-by-step explanation:

in an hr, the temperature falls by 3°C = 0 -3 = -3°C

in 2hrs = 2*-3°C = -6°C

in 5hrs = 5*-3°C = -15°C

in half an hr = 0.5 * -3°C = -1.5°C

The required continues to fall at this rate of the temperature in 2 hours -6°C ,5hours in -15°C and in half an hour -1.5°C.

Given that,

A weather station on the top of a mountain reports that the temperature is currently 0°C and has been falling at a constant rate of 3°C per hour.

We have to find,

If it continues to fall at this rate, what will the temperature be in 2 hours 5 hours and in half an hour.

According to the question,

A weather station on the top of a mountain reports that the temperature is currently 0°C and has been falling at a constant rate of 3°C per hour.

In an hour the temperature falls by 3°C = 0 - 3 = -3°C

The temperature fall in 2hrs = (2)(-3°C) = -6°C

The temperature fall in 5hrs = (5)(-3°C) = -15°C

The temperature fall in half an hour = (0.5)(-3°C) = -1.5°C

Hence, The required continues to fall at this rate of the temperature in 2 hours -6°C ,5hours in -15°C and in half an hour -1.5°C.

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Answer:

Slope=9, y-intercept= 39

Step-by-step explanation:

The equation is already in y=mx+b form, where m is the slope and b is the y-intercept

(rearrange positions of 9m and 39 to get t=9m + 39)

So, the slope is 9 and the y-intercept is 39

Answer:

The solution of the given system is given as  L = -12, d =16.5

Step-by-step explanation:

7 L+  5.5 d  = 6.75

L +  d  =  4.5

From (2), we get:

L +  d  =  4.5

⇒  d = 4.5 - L

Substitute the above value of d is the above first equation:

7 L+  5.5 d  = 6.75   ⇒  7 L+  5.5 (4.5 - L)  = 6.75

⇒ 7 L  +  24.75  - 5.5 L = 6.75

or, 1.5 L = 6.75 -   24.75  =  -18

or, L  = -18/1.5 =  12

or, L = -12

Now,  d = 4.5 - L  = 4.5  - (-12)  = 16.5

 or,  d = 16.5

Hence, the solution of the given system is given as  L = -12, d =16.5

Let's begin by understanding your initial position, which is the school, located at coordinates (2, -1). The school is 2 blocks east and 1 block south of the center of town. This means that if you were to go to the center of town, you would travel 2 blocks west and 1 block north from the school. Now, to find out where your house is in relation to the school, we can reverse the steps you take to get from your house to the school. You’ve said you walk 5 blocks west and 2 blocks north to reach the school. Since you walk west to reach school, your house must be to the east of the school. Similarly, since you walk north to reach school, your house must be to the south of the school. To get back to your house from the school, then, you'd need to reverse both of these movements. To find the house’s position, we start with the school's position at (2, -1): 1. Since you walk 5 blocks west to get to school, let's go 5 blocks east from the school to get back to your house. Moving east means increasing the x-coordinate. So, starting from the x-coordinate of the school, which is 2, we add 5 to find the x-coordinate of your house. This gives us 2 + (-5) = -3. 2. Next, since you walk 2 blocks north to get to school, let's go 2 blocks south from the school to reach your house. Moving south means decreasing the y-coordinate. So, starting from the y-coordinate of the school, which is -1, we subtract 2 to find the y-coordinate of your house. This gives us -1 + 2 = 1. Therefore, the coordinates of your house are (-3, 1), which means your house is 3 blocks west and 1 block north of the center of town.

Final answer:

To locate the student's house on a grid, you need to reverse the movements made from the school to the house. By subtracting 5 blocks west and adding 2 blocks north from the school's coordinates (2, -1), the house's coordinates are determined to be (-3, 1).

Explanation:

The question involves a two-dimensional path on a grid, similar to the coordinates and movements given in the examples provided. To solve the problem, imagine that you start at the center of town, move 2 blocks east and 1 block south to reach the school at (2, -1), and then move from your house to the school by walking 5 blocks west and 2 blocks north.

To find your house's coordinates, you need to reverse the movements. Starting from the school's location at (2, -1), moving 5 blocks west means subtracting 5 from the x-coordinate, and moving 2 blocks north means adding 2 to the y-coordinate. Thus, the coordinates of your house would be (2 - 5, -1 + 2) which simplifies to (-3, 1).

Answer:

Part a) [tex]y=0.05x+1.50[/tex]

Part b) [tex]y=0.50x+0.50[/tex]

Part c) The graph in the attached figure

Part d) see the explanation

Step-by-step explanation:

The complete question is

A restaurant sells tea for $1.50 plus $0.05 per refill. A gas station store sells tea for $0.50 plus $0.50 per refill.

Part a) Write a linear function for the price of tea at restaurant

Part b) Write a linear function for the price of tea at gas station store

Part c) Graph both equations

Part c) Compare the lines in terms of slope and y-intercept

Let

y -----> the price of tea in dollars

x -----> the number of refills

we know that

The linear equation in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value (value of y when the value o x is equal to zero)

Part a)

At restaurant

we have that

The slope or unit rate is equal to

[tex]m=\$0.05\ per\ refill[/tex]

The initial value or y-intercept is equal to

[tex]b=\$1.50[/tex]

substitute

[tex]y=0.05x+1.50[/tex]

Part b)

At gas station store

we have that

The slope or unit rate is equal to

[tex]m=\$0.50\ per\ refill[/tex]

The initial value or y-intercept is equal to

[tex]b=\$0.50[/tex]

substitute

[tex]y=0.50x+0.50[/tex]

Part c) Graph both equations

we know that

The easiest way to graph a line is with two points

Find the intercepts of the line

At restaurant

[tex]y=0.05x+1.50[/tex]

The y-intercept is the point (0,1.50)

The x-intercept is the value of x when the value of y is equal to zero

For y=0

[tex]0=0.05x+1.50[/tex]

[tex]x=-30[/tex]

The x-intercept is the point (-30,0)

Plot the points and join to graph the line

see the attached figure

At gas station store

[tex]y=0.50x+0.50[/tex]

The y-intercept is the point (0,0.50)

The x-intercept is the value of x when the value of y is equal to zero

For y=0

[tex]0=0.50x+0.50[/tex]

[tex]x=-1[/tex]

The x-intercept is the point (-1,0)

Plot the points and join to graph the line

see the attached figure

Part c) Compare the lines in terms of slope and y-intercept

The slope or unit rate at the restaurant is less than the slope at the gas station store

[tex]\$0.05\ per\ refill < \$0.50\ per\ refill[/tex]

The initial value or y-intercept at the restaurant is greater than the initial value at the gas station store

[tex]\$1.50 > \$0.50[/tex]

Turn percentage into a decimal.

3% = 0.03

Multiply.

40,400 * 0.03 = 1,212

Subtract.

40,400 - 1,212 = $39,188

_______

Alice earned $39,188 last year.

_______

Best Regards,

Wolfyy :)

Answer:

The correct answer is 39,188.

Step-by-step explanation:

Alice Swanson's current earnings for this year are 40,400. Her earnings were 3% less than this last year. To find her earnings for last year, we will use the "Percent • Whole = Part" formula. But first, we must put 3% into a decimal form: 3 ÷ 100 = 0.03. Now let's solve:

40,400 • 0.03 = 1,212

1,212 is 3% of 40,400. To find Alice's earnings for last year, we will subtract her raise from her current earnings:

40,400 - 1,212 = 39,188

Hope this helps,

♥A.W.E.S.W.A.N.♥

871 miles ........... 13 hours

469 miles ............x hours

x = 469×13/871 = 7 hours

Answer:

3:10

Step-by-step explanation:

1. Find the total number of students by doing

14 + 6= 20

2. Now make your ratio

6:20

3. To make it in simplest form, divide both sides by 2

6 divided by 2 is 3

20 divided by 2 is 10

4. Your answer is

3:10

Answer:

3:10

Step-by-step explanation:the answer would be 6:20, but that can be simplified by 2. 6 divided by 2 equals 3, 20 divided by 2 equals 10. 3:10

1. 60 tablets

2. 120 tablets

Step-by-step explanation:

1. Order: Alprazolam 2 mg take 1 tab by mouth twice a day for 30days. How many total tablets will the patient take for 1 month (30days)

As the patient has to take 1 tablet twice a day, that will be 2 tablets per day so the total number of tablets will be:

[tex]30*2 = 60\ tablets[/tex]

And

60*2 = 120 mg

2. Order: Tramadol Hychloride 10mg take 1 tab by mouth 4 times a day before meal for 30days. How many total tablets will the patient take for 30days?

As the patient has to take 4 tablets each day, that means the total tablets for one month or 30 days will be:

[tex]30* 4 = 120\ tablets[/tex]

And

120*10 = 1200 mg

Hence,

1. 60 tablets

2. 120 tablets

Keywords: Multiplication,

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Answer:

$5175 per meal

Step-by-step explanation:

10% of $23.00 is $2.30, now you subtract $2.30 from $23.00 which makes $20.70. Now your getting four meals, so you split the money four ways which would be $20.70/4 which would equal $5.175 per meal

Step-by-step explanation:

Answer:

2/6

Step-by-step explanation:

Answer:

The time taken by ball to hit the ground is 5.10 seconds .

Step-by-step explanation:

Given as :

The height cover by ball to move upward = 7 feet

The initial velocity = u = 50 feet per sec

Let the time taken by ball to hit the ground = t sec

Let the deacceleration rate = - 9.8 m/s²

The final velocity of the ball = v=  0 at the top

So, From equation

v = u + at

I.e v = u + a × t

Or, 0 = 50 + ( - 9.8) × t

Or, 9.8 t = 50

∴ t = [tex]\frac{50}{9.8}[/tex]

I.e t = 5.10 seconds

So, time taken = 5.10 sec

Hence The time taken by ball to hit the ground is 5.10 seconds . Answer

1) There is 233.33% increase in the quantity.

2) There is 122.22% increase in the quantity.

3) There is 15% decrease in the quantity.

Step-by-step explanation:

1) Start: 3 End: 10

Change = End - Start

Change = [tex]10-3=7[/tex]

As the change is positive, therefore, it shows an increase

Percent increase = [tex]\frac{Change}{Start}*100[/tex]

Percent increase = [tex]\frac{7}{3}*100 = 233.33\%[/tex]

There is 233.33% increase in the quantity.

2) Start: 9 End: 20

Change = [tex]20-9=11[/tex]

As the change is positive, it shows an increase.

Percent increase = [tex]\frac{Change}{Start}*100[/tex]

Percent increase = [tex]\frac{11}{9}*100 = 122.22\%[/tex]

There is 122.22% increase in the quantity.

3) Start: 100 End: 85

Change = 85-100 = -15

Negative sign shows that it is a decrease in quantity.

Percent decrease = [tex]\frac{Change}{Start}*100[/tex]

Percent decrease = [tex]\frac{15}{100}*100 = 15\%[/tex]

There is 15% decrease in the quantity.

Keywords: Percentage, increase

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Answer:

1. 233.333%

2.122.2%

3.-12%

Step-by-step explanation: Hopes this helps you :)

Answer:

It is.

Step-by-step explanation:

1. Multiply 2x *x and 2x* -3 ;

2. Multiply 1*x and 1*(-3) ;

You should get: 2x^2 -6x +x -3 = 2x^2 -5x -3;

3. Add -6x +x;

In the end you get : 2x^2 -5x -3=2x^2 -5x -3

Answer:

Step-by-step explanation:

Use FOIL:

(a + b)(c + d) = ac + ad+ bc+ bd

(2x + 1)(x - 3)

= (2x)(x) + (2x)(-3) + (1)(x) + (1)(-3)

= 2x² - 6x + x - 3          combine like terms

= 2x² + (-6x + x) - 3

= 2x² - 5x - 3

Answer:

0.7

Step-by-step explanation:

7 millimiters equals 0.7 centimeters

Answer:

0.7 cm

Step-by-step explanation:

1 mm=0.1 cm

7 mm=0.1*7=0.7 cm

The given expressions are solved and matched

To match the given expressions we need to solve the expressions with the given values of g and h and find their value.

Given that g = -7 and h = 3

[tex]\begin{array}{l}{\text { 1) } g+h=-7+3=-4} \\\\ {\text { 2) } g-h=-7-3=-10} \\\\ {\text { 3) } h-g=3+7=10} \\\\ {\text { 4) } g h=-7 \times 3=-21} \\\\ {\text { 5) } g+h^{2}=-7+3^{2}=-7+9=2} \\\\ {\text { 6) } g^{2}-h=(-7)^{2}-3=49-3=46}\end{array}[/tex]

The expressions are evaluated by substituting g = -7 and h = 3 into each one. After calculation, the matching values are found for each expression.

To evaluate each expression for g = -7 and h = 3, we'll substitute these values into the equations and perform the operations step by step.

Then, you can match each expression to its corresponding value that has been calculated: