Simplify algebraically ​

Answer:

[tex]\huge\bold\purple{ 2a•3b }[/tex]

Question:

A company produces boxes of DVDs at a rate of 52 boxes per hour they begin to produce boxes when they first opened for the day and after 3 hours have 400 boxes in stock.

- How many boxes were in stock when they opened?

- Write a linear model for the amount of boxes, b, as a function of the number of hours since they opened, h.

- Use your model to predict the number of boxes in stock at the end of an 8 hour shift.

Answer:

1. [tex]Initial = 244[/tex]

2. [tex]b = 244 + 52h[/tex]

3. 660 boxes

Step-by-step explanation:

Given

[tex]Rate = 52\ per\ hour[/tex]

[tex]Total\ boxes\ in\ 3\ hours = 400[/tex]

Solving (a): Initial Number of boxes

First, we calculate the number of boxes made in 3 hours

[tex]Boxes = Rate * Hours[/tex]

[tex]Boxes = 52 * 3[/tex]

[tex]Boxes = 156[/tex]

If they had 400 boxes at the 3rd hour.

Then, the number of boxes when they opened is:

[tex]Initial = 400 - 156[/tex]

[tex]Initial = 244[/tex]

Solving (b): Linear function

[tex]b = boxes[/tex]

[tex]h = hours[/tex]

Since, we have the rate and the initial number of boxes.

The linear function is:

[tex]Boxes = Initial + Rate * Hours[/tex]

i.e.

[tex]b = 244 + 52 * h[/tex]

[tex]b = 244 + 52h[/tex]

Solving (c): Boxes at the end of the 8th hour

We have:

[tex]b = 244 + 52h[/tex]

In this case:

[tex]h = 8[/tex]

Substitute 8 for h

[tex]b = 244 + 52 * 8[/tex]

[tex]b = 244 + 416[/tex]

[tex]b = 660[/tex]

Hence, there are 660 boxes at the end of the 8th hour

Answer:

1800

Step-by-step explanation:

600x300

Answer:15

Step-by-step explanation:trust me

Answer:

The absolute of x would be 15

Answer:

Step-by-step explanation:

Start with a point at -7 on the y axis, and move up 2 right one repeatedly and keep making points. Then, connect them and you'll have your line.

Answer:

It's an equilateral triangle.

Step-by-step explanation:

For starters, the angle measures of any triangle all add up to 180 degrees. Because 2 sides of this triangle are 60 degrees, the two sides added up would be 120 degrees. Because 180 - 120 = 60, the unknown side is 60 degrees. Because an equilateral triangle is a triangle where all the angles or sides are equal, and all of the angle measures of the triangle are equal, it is an equilateral triangle.

Answer:

50%

Step-by-step explanation:

Answer:

70 mins

Step-by-step explanation:

Lets first convert the 4.5 hours to minutes. We know that there's 60 mins in an hour, so we can just multiply 4.5 by 60 to get 270 minutes. Now we know the total time spent at the mall.

Then, we can add the times given in the question.

130 mins + 70 mins + walking mins = 270 mins

To solve, simply collect like terms:

200 mins + walking mins = 270 mins

walking mins = 270 mins - 200 mins

walking mins = 70 mins

Answer:

20

Step-by-step explanation:

Answer:

[tex]t=7.85 years[/tex]

Step-by-step explanation:

We can write this rate as an ordinary differential equation.

[tex]\frac{dP}{dt}=aP[/tex]

Where a is proportional constant, P the population variable, and t the time.

[tex]\frac{dP}{P}=adt[/tex]

Integrating each side of the equation.

[tex]\int \frac{dP}{P}=\int adt[/tex]

[tex]ln(P)=at+c[/tex]

[tex]P=e^{at+c}[/tex]

[tex]P=e^{c}e^{at}=Ce^{at}[/tex]

To find C we need to use the initial condiction, it means evaluae P at t=0.

[tex]P_{0}=Ce^{0}=C[/tex]

[tex]P=P_{0}e^{at}[/tex]

Now, we use the sentence  the population has doubled in 5 years.

[tex]2P_{0}=P_{0}e^{a5}[/tex]

We can find "a" in this condition.

[tex]2=e^{a5}[/tex]

[tex]ln(2)=a5[/tex]

[tex]a=\frac{ln(2)}{5}[/tex]

[tex]a=0.14[/tex]

Finally, let's find how long will it take to triple.

[tex]3P_{0}=P_{0}e^{0.14t}[/tex]

[tex]3=e^{0.14t}[/tex]

[tex]t=\frac{ln(3)}{0.14}[/tex]

[tex]t=7.85 years[/tex]

I hope it helps you!

Answer:

There are no options but I guess C

Step-by-step explanation:

Answer:

Variance= (Standard deviation)^2=

✓6.25=Standard deviation

✓(625/100)= Standard deviation

25/10= Standard deviation

2.5= Standard deviation

Step-by-step explanation:

Answer:

d.) sinθ=0.763; tanθ=1.181

c. 21/x=9/x−4; Terran walks at 4 miles per hour and runs at 8 miles per hour.

Step-by-step explanation:

Given that:

θ is in the IV quadrant (All is positive) that is sin, cos and tan are all positive.

Cosθ = 0.646

Θ = Cos^-1(0.646)

θ = 49.75930

Hence,

Tanθ = tan(49.75930) = 1.1816365 = 1.182

Sinθ = sin(49.75930) = 0.7633373 = 0.763

2.)

Let

Walking rate = x mph

Running rate = x + 4 mph

21 miles run time = 9 miles walk time

Recall :

Time = distance / speed or rate

21 / (x + 4) = 9 / x

Cross multiply :

21 * x = 9(x + 4)

21x = 9x + 36

21x - 9x = 36

12x = 36

x = 36 /12

x = 4 mph = walking rate

Running rate = x + 4 = 4 + 4 = 8 mph

Answer:

C. 1

Step-by-step explanation:

Use the formula to find slope:

(y2-y1)/(x2-x1)

Plug in the numbers you have.

(9 - 2)/(3 - -4)

7/7

1

Slope of the line shown below is option C. 1

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.

Given is a line.

Slope must be positive since the line is drawn in the positive direction.

Consider two points along the line.

Consider (-4, 2) and (3, 9).

Slope = change in y coordinates / change in x coordinates

          = (9 - 2) / (3 - -4)

          = 7 / 7

          = 1

Hence the slope is 1.

To learn more about Slope, click :

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Answer:

No.

9 Is rational.

Step-by-step explanation:

I'm 100% sure.

9514 1404 393

Answer:

  3/5

Step-by-step explanation:

Let a, b, c represent the probability of a win by Kaden, Keith, and Kipp, respectively.

  P(bc' | a') = P(a'bc')/P(a')

  P(bc' | a') = (1/2)/(1 -1/6) = (3/6)/(5/6) = 3/5

The probability is 3/5 that Keith beats Kipp when Kaden doesn't win.

Answer:

[tex] \frac{1}{2} \: cup \: for \: each \: dumpling \\ 10 \: cups \: for \: \frac{ \frac{10}{1} }{ \frac{1}{2} } = 20 \: dumplings[/tex]

Answer:

Slope: -1, y-intercept: 2.

Step-by-step explanation:

3x + 3y = 6 in slope intercept form is y = -x + 2. Slope-intercept form is y = mx + b. As we know, m is slope and b is y-intercept. This means the slope is -1 and the y-intercept is 2.

Answer:

x=5

Step-by-step explanation:

4×3x=12x

4×-2=-8

(12×x)-8=52

So you balance it to make it:

12x=60

60÷12=5

I hope this helps and please give brainliest and thank me

Step-by-step explanation:

Open bracket

use 4 to multiply what is in the bracket

12x - 8 = 52

collect like terms (CLT)

12x = 52 + 8

12x = 60

divide both sides by 12

x = 5

Answer:

Farmer Bill sold 120 lb of potatoes

Step-by-step explanation:

Suppose farmer Bill had x lb of potatoes. He sold a quarter to the first person. A quarter is written as (1/4)x. After that, Bill had x-(1/4)x = (3/4)x.

Then he sold 4/9 of what was left to the second person, thus it was left 1-4/9=5/9 of the remaining potatoes. Multiplying both factors:

[tex]\frac{5}{9}*\frac{3}{4}x=\frac{5}{12}x[/tex]

This is the remaining portion of the potatoes.

Finally, he sold 4/5 of it and the last 10 lb. This means 1 - 4/5 = 1/5 of the remaining is equivalent to 10 lb:

[tex]\frac{1}{5}*\frac{5}{12}x=\frac{1}{12}x[/tex]

Thus:

[tex]\frac{1}{12}x=10[/tex]

x = 120 lb

Farmer Bill sold 120 lb of potatoes

The Farmer will sold 120 lb of potatoes.

Let us consider that farmer have x lb of potatoes.

He sold a quarter to the first person, that is  [tex]\frac{x}{4}[/tex]

Potatoes left,[tex]=x-\frac{x}{4} =\frac{3x}{4}[/tex]

4/9 of what was left to the second person,

 Potatoes sell to second person is, [tex]\frac{3x}{4} *\frac{4}{9} =\frac{x}{3}[/tex]

the third buyer bought 4/5 of what was left

       that is,          [tex]\frac{4}{5}*(\frac{3x}{4} -\frac{x}{3} ) =\frac{x}{3}[/tex]

Potatoes left [tex]=\frac{5x}{12} -\frac{x}{3} =\frac{x}{12}[/tex]

Since, Potatoes left = 10 lb

So,   [tex]\frac{x}{12} =10\\\\x=12*10=120[/tex]

Thus, The Farmer will sold 120 lb of potatoes.

Learn more:

https://brainly.com/question/2785554

Answer: Proportional

Step-by-step explanation: 8 goes into 36, 2 goes into 24, and 5 goes into 10

Answer:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Because the points are going up by 10 :)

Answer:

  [1]    x - 6y = 3

  [2]    x + 2y = 5

Graphic Representation of the Equations :

   -6y + x = 3        2y + x = 5  

Solve by Substitution :

// Solve equation [2] for the variable  x

 [2]    x = -2y + 5

// Plug this in for variable  x  in equation [1]

  [1]    (-2y+5) - 6y = 3

  [1]     - 8y = -2

// Solve equation [1] for the variable  y

  [1]    8y = 2

  [1]    y = 1/4

// By now we know this much :

   x = -2y+5

   y = 1/4

// Use the y  value to solve for  x

   x = -2(1/4)+5 = 9/2

Solution :

{x,y} = {9/2,1/4}

Answer:

33433.2

Step-by-step explanation:

504 - 300 = 204

204 + 800 = 1004

100 / 3 = 33.3

1004 x 33.3 = 33433.2

Answer:

1/2 or one half

Step-by-step explanation:

Answer:

The slope is 1/2.

Step-by-step explanation:

To find the slope of a line, divide yB - yA by xB - xA.

(yB - yA)/(xB - xA)

(2 - 5)/ (-2 - 4)

-3/-6

Dividing two negatives make a positive.

0.5

The slope is 0.5, or 1/2.

Answer:

2

Step-by-step explanation:

Add 7 to both sides.

7x=7+7

2 Simplify  7+7 to  14.

7x=14

3 Divide both sides by 7.

x= 14 divided by 7

x=2