The amount of time t (in hours) that it takes to fill a swimming pool varies inversely with the pumping rate r(in kiloliters per hour). The constant of variation is 4. Find how long it will take to fill the pool when the pumping rate is 3.2 kL/hr
A.) 12.8 hrs
B.) 1.25 hrs - APEX
C.) 7.2 hrs
D.) 0.8 hrs

Answer:

Option d. [tex]4y+2x\leq -1[/tex]

Step-by-step explanation:

we know that

If a ordered pair is a solution of an inequality, then the ordered pair must be satisfy the inequality

Verify each case

case a) [tex]y\geq2x+8[/tex]

we have

[tex]x=5, y=-3[/tex]

Substitute the value of x and the value of y in the inequality and then compare the results

[tex]-3\geq2(5)+8[/tex]

[tex]-3\geq18[/tex] -----> is not true

therefore

the ordered pair is not a solution

case b) [tex]-2y<3x-9[/tex]

we have

[tex]x=5, y=-3[/tex]

Substitute the value of x and the value of y in the inequality and then compare the results

[tex]-2(-3)<3(5)-9[/tex]

[tex]6<6[/tex] -----> is not true

therefore

the ordered pair is not a solution

case c) [tex]y-2x>5[/tex]

we have

[tex]x=5, y=-3[/tex]

Substitute the value of x and the value of y in the inequality and then compare the results

[tex]-3-2(5)>5[/tex]

[tex]-13>5[/tex] -----> is not true

therefore

the ordered pair is not a solution

case d) [tex]4y+2x\leq -1[/tex]

we have

[tex]x=5, y=-3[/tex]

Substitute the value of x and the value of y in the inequality and then compare the results

[tex]4(-3)+2(5)\leq -1[/tex]

[tex]-2\leq -1[/tex] -----> is  true

therefore

the ordered pair is a solution

d. 4y+2x≤−1

Step-by-step explanation:

Is there supposed to be a picture

Answer:

[tex]2\frac{2}{3}[/tex]

Step-by-step explanation:

Given : BC is parallel to DE

To Find : What is the length of CE?

Solution :

AB = 3

BD = 2

AC = 4

Since BC || DE

So, [tex]\frac{AB}{BD}=\frac{AC}{CE}[/tex]

[tex]\frac{3}{2}=\frac{4}{CE}[/tex]

[tex]CE=\frac{4 \times 2}{3}[/tex]

[tex]CE=\frac{8}{3}[/tex]

[tex]CE=2\frac{2}{3}[/tex]

Hence the length of CE is [tex]2\frac{2}{3}[/tex]

The difference between the square of 80 and the square of 20 is 6000.

The student's question appears to ask for the difference between the squares of two numbers, specifically square 20 and square 80.

To find this difference, each number must be squared and then the smaller result subtracted from the larger one.

Squaring a number means multiplying the number by itself, so square 20 (which is 20²) equals 400 and square 80 (which is 80²) equals 6400.

Next, we find the difference by subtracting the smaller square from the larger one:

6400 (square 80) - 400 (square 20) = 6000

This calculation reveals that the difference between the square of 80 and the square of 20 is 6000.

Answer: C= 50.2652

Step-by-step explanation:

The circumference of a circle with an area of 201.06 square inches is approximately 50.24 inches, after calculating the radius from the area and applying it to the circumference formula.

To find the circumference of a circle when given the area, you'll want to perform a series of mathematical steps. The area of a circle is given by the formula A = πr², and the circumference is given by C = 2πr. You can rearrange the area formula to solve for the radius, r, and then substitute that into the circumference formula.

First, solve for the radius:
A = πr² → r = √(A/π) → r = √(201.06/π).

Once you have r, plug it into the circumference formula:

C = 2πr.

Using a calculator, you'll find the following values:

The circumference of a circle with an area of 201.06 square inches is approximately 50.24 inches.

Answer:

Step-by-step explanation:

Good evening ,

P(A|B) = P(A∩B)/P(B)

P(B|A) = P(A∩B)/P(A)

:)

Answer:

option C. [tex]KL=2*JL[/tex]

option D. [tex]JK=\frac{\sqrt{3}}{2}*KL[/tex]

option F. [tex]JK=\sqrt{3}*JL[/tex]

Step-by-step explanation:

step 1

we know that

In the right triangle JKL

[tex]sin(30\°)=\frac{JL}{KL}[/tex]

[tex]sin(30\°)=\frac{1}{2}[/tex]

so

[tex]\frac{1}{2}=\frac{JL}{KL}[/tex]

[tex]KL=2*JL[/tex]

step 2

[tex]cos(30\°)=\frac{JK}{KL}[/tex]

[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]

so

[tex]\frac{\sqrt{3}}{2}=\frac{JK}{KL}[/tex]

[tex]JK=\frac{\sqrt{3}}{2}*KL[/tex]

step 3

[tex]tan(30\°)=\frac{JL}{JK}[/tex]

[tex]tan(30\°)=\frac{1}{\sqrt{3}}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{JL}{JK}[/tex]

[tex]JK=\sqrt{3}*JL[/tex]

Answer:

Pretty sure it's 2 strides

Step-by-step explanation:

To get from 7 to 5 you minus by 2, and look how many spaces there are. There are 2

Answer: option b.

Step-by-step explanation:

Based on the information given, you know that:

- The ground is at 0 feet.

- The initial posititions of both elevators were at 0 feet (because both moved from the ground level).

Therefore:

- If the final position of Elevator 1 is at +17 feet (positive) means that it moved 17 feet above the ground level.

- If the final position of Elevator 2 is at -22 feet (observe the negative sign) means that it moved 22 feet below the ground level.

Answer:

I  -3/20

Step-by-step explanation:

-3       2

---- * -----

8       5

Multiply the numerators

-3*2 = -6

Multiply the denominators

8*5= 40

The fraction is

-6/40

Both the top and the bottom can be divided by 2

-6/2 = -3

40/2 =20

The fraction becomes

-3/20

Answer:

The height is given by: 776.5 / 34.5 = about 22.5 yards. So....10 times this is about 225 yards.

Two lines y = -x + 3 and y = 2x - 5 are graphed to find their intersection, which gives the x and y values that satisfy both equations.

To find x and y values that satisfy both equations y = -x + 3 and y = 2x - 5, we need to graph these equations and look for their point of intersection.

The intersection represents the x and y values that make both original equations true simultaneously. Use the graph to identify the coordinates of this point for the exact solution.

Out of the choices provided, only [tex]$(-3,5)$[/tex] lies on the intersection of the two lines. Thus the answer is a. [tex]$(-3,5)$[/tex].

Here's a step-by-step solution to find the x and y values that satisfy both equations:

1. Graph the Equations:

    Take the first equation, y = -2/3x + 3. This equation is in slope-intercept form (y = mx + b), where m (slope) is -2/3 and b (y-intercept) is 3.

     -   Plot the y-intercept (3) on the y-axis.

      -  Since the slope is -2/3, remember "rise over run." So in this case for every 2 positions you move down (because it's negative), you move  3 positions to the right. Plot another point based on this movement.

       - Connect these two points with a straight line.

  -  Repeat the process for the second equation, y = 2x - 5. This equation is also in slope-intercept form with m (slope) as 2 and b (y-intercept) as -5.

       - Plot the y-intercept (-5) on the y-axis.

       - The slope is 2, so for every 2 positions you move up, you move 1 position to the right. Plot another point based on this movement.

       - Connect these two points with a straight line.

2. Find the Intersection Point:

   - Observe the graph. The point where the two lines intersect represents the solution where both equations are true simultaneously.

   - In this case, the lines intersect at the point (-3, 5).

Verification:

   - You can substitute x = -3 and y = 5 in both the original equations and see if they hold true.

      - For y = -2/3x + 3, substituting x = -3 gives you y = (-(2/3) [tex]\times[/tex] (-3)) + 3 = 2 + 3 = 5 (which is true).

      - For y = 2x - 5, substituting x = -3 gives you y = (2 [tex]\times[/tex] -3) - 5 = -6 - 5 = -11 (which is not true).

Therefore, the solution (x, y) that makes both equations true is (-3, 5). This is the point where the two lines intersect on the graph.

The graph is provided below.

Answer:

lol

Step-by-step explanation:

Answer:

The answer is (-3, 4).

Step-by-step explanation:

(3, 4) is located in Quadrant I, which is (+, +). Since you're reflecting the point across the x-axis, you'll be in Quadrant IV, which is (-, +). The point will now be (-3, 4).

I hope this helped! :-)

Answer:

[tex]\boxed{\bold{\left(3x-2\right)^2}}[/tex]

Step By Step Explanation:

[tex]\bold{\left(3x\right)^2-2\cdot \:3x\cdot \:2+2^2}[/tex]

[tex]\bold{\left(3x\right)^2-2\cdot \:3x\cdot \:2+2^2}[/tex]

[tex]\bold{\left(3x-2\right)^2}[/tex]

ANSWER

[tex]9 {x}^{2} - 12x + 4 = (3x - 2) ^{2} [/tex]

EXPLANATION

The given expression is

[tex]9 {x}^{2} - 12x + 4[/tex]

This is in the form

[tex]a {x}^{2} + bx + c[/tex]

[tex]a=9,b=-12 ,c=4[/tex]

[tex]ac=9 \times 4 = 36[/tex]

Split with -6x-6x

[tex]9 {x}^{2} - 6x - 6x + 4[/tex]

[tex] = 3x( 3x - 2) - 2(3x - 2)[/tex]

Factor further to obtain,

[tex] = (3x - 2)(3x - 2)[/tex]

[tex] = (3x - 2) ^{2} [/tex]

The area of the tile is 9 square inches.

The area of the tile is given by a product of length and width.

Given

The length of the tile = 3 inches

The width of the tile = 3 inches

The area of the tile is defined as the length of the tile and width of the tile.

[tex]\rm Area \ of \ the \ tile=Length \times Width\\\\[/tex]

Substitute all the values in the formula;

Area of the tiles = length × width

Area of the tile = 3 × 3

Area of the tile = 9

Hence, the area of the tile is 9 square inches.

To know more about Area click the link given below.

https://brainly.com/question/15442893

The area of a square (side*side) tile with sides of 3 inches is 9 square inches.

The question is asking for the area of a square tile with a side length of 3 inches. In mathematics, the area of a square can be found using the formula Area = side².

So, in this case, the area would be 3² = 9.

This means that the area of the tile is 9 square inches.

https://brainly.com/question/34380164

#SPJ3

Answer:   [tex]\bold{\dfrac{2}{65}}[/tex], Dependent

Step-by-step explanation:

[tex]\dfrac{\text{\# of vowels}}{\text{total \# of letters}}[/tex]

1st draw  and   2nd draw

     [tex]\dfrac{5}{26}[/tex]        x           [tex]\dfrac{4}{25}[/tex]     =     [tex]\dfrac{20}{650}[/tex]

[tex]\dfrac{20}{650}\div\dfrac{10}{10}=\dfrac{2}{65}[/tex]

This is dependent because the number of vowels remaining for the 2nd draw is dependent on whether or not a vowel was chosen on the 1st draw.

∴(108+27) cubic feet = 135 cubic feet of concrete are required.

The dimension of lower step is 6 ft× 3 ft× 1.5 ft

and the dimension of upper step is 6 ft ×(9-3)ft × (1.5+1.5)ft = 6 ft × 6 ft ×3 ft

Therefore concrete are required to make lower step = (6×3×1.5) cubic feet

                                                                                      = 27 cubic feet

and concrete are required to make upper step = (6×6×3) cubic feet

                                                                              =108 cubic feet

∴(108+27) cubic feet = 135 cubic feet of concrete are required.

complete questions

Tony needs to create a platform shaped like the diagram with the labeled dimensions.

How many cubic feet of concrete are required?

A) 60 cubic feet

B) 81 cubic feet

C) 108 cubic feet

D) 135 cubic feet

the slope is 2

4/2= 2

Answer:

-4

Step-by-step explanation:

Okay so basically with functions you are gonna wanna substitute 7 where x is since x=7.

10-2(7) = ?

2 x 7 = 14

10-14=-4

Have a nice day hope this helps :)

:)

Answer:

Step-by-step explanation:

Just put 7 in the place of x

[tex]f(7)=10-2(7)\\f(7)=10-14\\f(7)=-4[/tex]

Answer:

D

Step-by-step explanation:

5/5 -1/5=4/5

Answer:

x and see others below

Step-by-step explanation:

To find the equivalent expression, multiply the terms using exponent rules.

Exponent rules state to add the exponent of same bases being multiplied.

[tex]x^{\frac{1}{2}} *x^{\frac{1}{2}} =x^{\frac{1+1}{2}} =x^{\frac{2}{2}} = x^1 = x[/tex]

Each of the parts of the expression are equivalent. The simplified equivalent expression is x.

Answer:

2 1/3 yards each

Step-by-step explanation:

8 yards / 3 equal pieces = 8/3 yards for each piece or 2 1/3.

Answer: 2 2/3 yards

Step-by-step explanation:

The ribbon is 8 yards long

it is cut in 3 equal pieces so

8 yards divided by 3 yards = 2 2/3 yards

The simplified expression is x + 46.

To simplify the expression, let's distribute and simplify each term:

4(-8x + 5) - (-33x - 26)

First, distribute 4 into -8x + 5:

= -32x + 20

Then, distribute -1 into -33x - 26:

= -32x + 20 + 33x + 26

Now, combine like terms:

= (-32x + 33x) + (20 + 26)

= 1x + 46

= x + 46

So, the simplified expression is x + 46.

Answer:

Step-by-step explanation:

"A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in the social sciences (such as economics, psychology, sociology, political science).

A model may help to explain a system and to study the effects of different components, and to make predictions about behavior."

Step-by-step explanation:

Use the distributive formula to solve for x:

a(b + c) = ab + ac

-3(4x - 2) = 21 - 4(1 + 4x)

1. Use distributive property:

-12x + 6 = 21 - 4 - 16x

2. Simplify:

-12x + 6 = 17 - 16x

3. Add 16x to both sides

-12x + 16x + 6 = 17 - 16x + 16x

4. Simplify:

4x + 6 = 17

5. Subtract 6 from both sides

4x + 6 - 6 = 17 - 6

6. Simplify

4x = 11

7. Now, divide both sides by 4

4x/4 = 11/4

8. Simplify:

x = 11/4 <------ Answer

Hope this Helped!!

~Shane

Answer:

x = 2.75

Explanation:

Solve for x:

Use distributive property.

−3(4x − 2) = 21 − 4(1 + 4x)  

Combine like terms.

-12x + 6 = 21 - 4 - 16x

Add -12x on both sides.

-12x + 6 = 17 - 16x

+ 12x             + 12x

Subtract 17 on both sides.

6 = 17 - 4x

-17  -17

Divide -4 on each side to get x alone.

-11 = -4x

----   -----

-4      -4

And you get your solution to x.

2.75 = x

Check:

Substitute 2.75 to x.

−3(4(2.75) − 2) = 21 − 4(1 + 4(2.75))  

Multiply 2.75 by 4.

-3(11 - 2) = 21 - 4(1 + 11)

Distribute.

-33 + 6 = 21 - 4 - 44

Subtract 21 by 4.

-33 + 6 = 17 - 44

Subtract.

-27 = -27

Answer

So, Sam only asked 20 people in his entire middle school. That is a very small fraction of the amount of kids attending that school. He cannot say that video games is 75% of the entire school's favorite weekend activity if he only asked 20 people. To get a better, more valid result, he should ask around 100+ kids.

Step-by-step explanation:

Answer:

Option A. $1713.98

Step-by-step explanation:

You have to calculate your parents' monthly fixed expenses by the given expenses list.

Rent = $998.50

Groceries ( bi-weekly ) = $195.40 Monthly groceries = (195.40×2)

Charge card = $258.90

Cell phone = $65.78

Name brand Khakis for work (store brand optional ) = $34.95

Total expenses are 998.50 + (195.40×2) + 258.90 + 65.78

= $1713.98

Option A. $1713.98

Answer:

Consumer Math Exam Part 1 Answers:

1. Barter

2. Charge Card

3. Principal

4. Interest accrued

5. Exchange Rate

6. Debtor

7. Debit Card

8. High Interest Rate

9. Credit Score

10. Collateral

11. Cash

12. Lower your mortgage interest rate

13.brand name khakis

14. $1,213.13

15 9 oz

16. $111.59

17. $183.09

18. $2803.86

19. $52.12

20. $413.83

21. $62.43

22. 10 dozen

23. $25.46

24. $825.75

25. $24.05

26.$52.74

27. $5.25

28. $35.86

29.$16.27

30. $1580.16

31. $3.72

32. $1344.32

33. $18.50 hour

34. $1748.13

35. $510.01

36. the debt ration remains the same

Step-by-step explanation:

Answer:

S = 36

Step-by-step explanation:

s/3 +  14= 26

s/3 = 12

s = 36

Answer:

Step-by-step explanation: (1/3)*s+14 = 26 // - 26

(1/3)*s-26+14 = 0

1/3*s-12 = 0 // + 12

1/3*s = 12 // : 1/3

s = 12/1/3

s = 36

s = 36