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To find the number of items, x, for which the total daily cost, C, of each machine will be the same, we can set up an equation and solve for x. The number of items x for which the total daily cost C of each machine will be the same is 20. For 20 items produced, the total daily cost per machine is $60.

To find the number of items, x, for which the total daily cost, C, of each machine will be the same, we can set up the following equation:

40 + 1x = 30 + 1.5x

Simplifying, we get:

0.5x = 10

Dividing both sides by 0.5, we find:

x = 20

Therefore, the number of items x for which the total daily cost C of each machine will be the same is 20.

To find the total daily cost per machine for this number of items, we can substitute x = 20 into the equations for each machine:

Machine A: C = 40 + 1(20) = 60

Machine B: C = 30 + 1.5(20) = 60

So, for 20 items produced, the total daily cost per machine is $60.

Final answer:

Mrs. Smith will donate $20 for Sam walking 20 miles, illustrating a direct proportional relationship with a constant of proportionality of $1 per mile, which is a simple yet effective example of how constants of proportionality function in everyday scenarios.

Explanation:

In the fundraiser mentioned, Mrs. Smith pledges $1 for each mile walked. If Sam walks 20 miles, Mrs. Smith will donate $20. The constant of proportionality in this problem is $1 per mile.

You can see this relationship as a simple formula: total donation = $1 × number of miles walked. So, if we replace "number of miles walked" with 20, the formula would be total donation = $1 × 20 = $20. This illustrates how the initial pledge creates a directly proportional relationship between the money donated and the miles walked.

The constant of proportionality here is crucial because it tells us how much money will be donated per mile that Sam walks. It is a straightforward example of how constants of proportionality work in real-life scenarios, similar to being paid for each call made in a phone drive or being charged per hour of tutoring.

Answer:

(-∞,-3), (-1,2), and (4,∞)

Step-by-step explanation:

If f(x) is increasing on (a,b), then f(a)<f(b) on (a,b).

From the given graph, the graph is increasing on (-∞,-3), (-1,2), and (4,∞).

Think of it as the portion of the graph that slopes forward.

The correct options are A, C, an E

Answer:

(-∞,-3), (-1,2), and (4,∞)

Answer: X= 83°

Step-by-step explanation: If we observe closely, the angle between 41° and X° is an angle opposite angle 56° (opposite angles are equal)

So what we have are three angles on a straight line, which are

41°, 56° and X.

Sum of angles on a straight line = 180°

Therefore,

41 + 56 + X = 180

97 + X = 180

Subtract 97 from both sides of the equation

X = 180 - 97

X = 83°

Step-by-step explanation:

Given by question,

(x, y) = (5, 15)

Here, x = 5 and y = 15

To find, the value of [tex]\tan \theta[/tex] = ?

We know that,

[tex]\tan \theta[/tex] = Sope = [tex]\dfrac{y}{x}[/tex]

∴ [tex]\tan \theta[/tex]  = [tex]\dfrac{15}{5}[/tex]

⇒ [tex]\tan \theta[/tex]  = [tex]\dfrac{3}{1}[/tex]

⇒ [tex]\tan \theta[/tex]  = 3

∴ The value of [tex]\tan \theta[/tex] = 3

Thus, the value of [tex]\tan \theta[/tex] is equal to 3.

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The total amount of money Camden owes is $1550

Hello! remember you have to write complete questions in order to get good and exact answers. Here the question is incomplete so I'll assume you need to know the total amount of money Camden owes. From the statement, we know two facts:

Let:

x: Debt on his credit card

y: Debt on his rent

z: Total debt

Then:

[tex]z=x+y \\ \\ x=800 \\ \\ y=750 \\ \\ \\ z=800+750 \\ \\ z=1550[/tex]

So the total amount of money Camden owes is $1550.

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The equation according to the given verbal sentence is [tex]\frac{2 t+2}{2 s^{3}}[/tex] (after solving this [tex]\frac{t+1}{s^{3}}[/tex] ).

Step-by-step explanation:

Rewrite the given verbal sentence and so it will be easier to translate.

Given: The quotient of the sum of 2 t and 2 and twice the cube of s

sum of 2 t and 2 can be written as

       2 t + 2

twice the cube of s

      [tex]2 s^{3}[/tex]

Now, combine the above according to the given verbal. The quotient of the sum of 2 t and 2 and twice the cube of s  means,

             2 t + 2  divided by [tex]2 s^{3}[/tex]

Now, the equation would be [tex]\frac{2 t+2}{2 s^{3}}[/tex]

When solving this equation, we get

         [tex]\frac{2(t+1)}{2 s^{3}}=\frac{t+1}{s^{3}}[/tex]

The quotient of the sum of 2t and 2 and twice the cube of s is [tex]\frac{t + 1}{s^3} [/tex].

The given parameters:

The sum of 2t and 2 is written as follows;

sum = 2t + 2

The cube of s is written as follows;

cube = s³

twice the cube of s = 2s³

The quotient of the sum of 2t and 2 and twice the cube of s is calculated as follows;

[tex]= \frac{2t + 2}{2s^3} \\\\ = \frac{2(t + 1)}{2s^3}\\\\ = \frac{t + 1}{s^3} [/tex]

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Answer:

Step-by-step explanation:

1,3,9,27, and 81

17)

Find how many more pencils are needed:

250 - 108 = 142

Divide by the number of pencils in a box:

142 / 16 = 8.875 = 9 more boxes.

18) 5/4x - 3(8x-1/4)

Use the distributive property:

5/4x - 24x - 3/4

Rewrite 24x as 96/4x

Now you have:

5/4x - 96/4x-3/4

Combine like terms:

-91/4x - 3/4

19)

Car: 3 feet in 4 seconds

60 seconds / 4 = 15

3 feet x 15 = 45 feet per minute

Truck: 2 feet in 6 seconds

60 seconds / 6 = 10

2 feet x 10 = 20 feet per minute

45 - 20 = 25 feet

The car travels 25 feet per minute faster.

Answer:

The answer would be 0.2

Step-by-step explanation:

Because there is five numbers and if you split 1 into five equal parts there is 0.2 which leads to the answer being 0.2

The required probability of Keisha first picking a yellow marble and then an orange marble is 0.04. Option c is correct.

A bag contains marbles and has an equal number of marbles in 5 colors.
The probability of Keisha first picking a yellow marble and then an orange marble is to be determined.

Probability is the ratio of a favorable number of events to the total number of events.

The total number of samples is = 5
Probability for yellow marble = 1/5 = 0.2
Probability for orange marble = 1/5 = 0.2
Probability for first picking yellow than orange = 0.2*0.2
                                                                                = 0.04

Thus, the required probability of Keisha first picking a yellow marble and then an orange marble is 0.04.

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The length of the arc is 4π.

Step-by-step explanation:

Given,

Arc length = ∅/360° (2πr)

⇒ 60°/360° (2π[tex]\times[/tex]12)

⇒ 24π/6

⇒ 4π

∴ The length of the arc is 4π.

Answer:area = x^2 +15x +36

Step-by-step explanation:

Answer:

$68.60

Step-by-step explanation:

If the original price is $98

30% = 0.03

0.30*98=29.40

Then, 98−29.40=$68.60

Final answer:

To calculate the travel time from Lubbock to San Antonio at 60 miles per hour, divide the distance (394 miles) by the speed, resulting in about 7 hours when rounded to the nearest hour.

Explanation:

The question is about calculating the travel time from Lubbock to San Antonio when driving at a speed of 60 miles per hour. Based on the provided chart, the distance between Lubbock and San Antonio is 394 miles. To find the travel time, we use the formula time = distance ÷ speed. Therefore, the travel time is calculated as 394 miles ÷ 60 miles/hour = 6.5667 hours. Rounding this to the nearest hour gives us approximately 7 hours. So, it will take about 7 hours to drive from Lubbock to San Antonio at a speed of 60 miles per hour.

Answer:

x = 6/1.1

Step-by-step explanation:

hello :

1,331x^3 -216=0  means : x^3 = 216/1.331

x^3 = (6^3)/(1.1)^3   because : 216 = 6^3  and  1.331 = (1.1)^3

so : x^3 = (6/1.1)^3

x = 6/1.1

Answer:

The answer is W

Step-by-step explanation:

The answer is W because it is included in both angles.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation:

Let he owes x amount in taxes

He made amount last year = $68,000

His tax rate = 27%

So, he pays tax = 27% of the earning

So, A.T.Q.

27% times 68000 = x

{27}{100} times 68000 = x

27times 68000 = 100 times x

The first equation can be multiplied by 5 and the second equation by 3.

3x - 3y = 3 | × 5

4x + 5y = 13 | × 3

15x - 15y = 15

12x + 15y = 39  +

________________

15x + 12x - 15y + 15y = 15 + 39

27x = 54

x = 54 : 27

x = 2

4·2 + 5y = 13

5y = 13 - 8

5y = 5

y = 5 ; 5

y = 1

Answer:

a

Step-by-step explanation:

The random variables in this situation will be:

It should be noted that a random variable simply means the numerical description of the outcome of a statistical experiment.

In this case, the distance that the basketball lands from the hoop and the distance the basketball lands from the person are the random variables.

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Answer:

The distance the basketball lands from the hoop.

The distance the basketball lands from the person.

Answer:

The perimeter of a rectangle is found by using this equation: P = 2 (L + W)

Step-by-step explanation:

I cannot see the picture that you posted, but that is the above equation. Take the length of the rectangle, and the width... plug that in for (L and W), and you have your formula! :)

Hope this helps!

Answers:

x = -5

y = 9

============================================

Work Shown:

Start by solving the second equation for x.

3x = -15

3x/3 = -15/3 .... divide both sides by 3

x = -5

Then plug this into the first equation and isolate y.

6x + 4y = 6

6(-5) + 4y = 6 .... every x replaced with -5

-30 + 4y = 6

-30+4y+30 = 6+30 .... add 30 to both sides

4y = 36

4y/4 = 36/4 .... divide both sides by 4

y = 9

Answer: vertex

Step-by-step explanation:

Answer:

Vertex. The vertex is the point where two points meet, and the point 12 is where the lines meet.

Length = 34 cm

Width= 9 cm

Step-by-step explanation:

Let the width of the rectangle to be.........w

Length is 7 more than three times the width..........3w+7

Perimeter = 86 cm

Perimeter of a rectangle = 2(l+w)

Perimeter of the rectangle = 2 (w + 3w +7)

                                             = 2w +6w + 14

                                      86= 8w +14

                                       86-14 =8w

                                        72=8w

                                        72/8 =8/8w

                                          9=w

Width= 9 cm

Length = 3*9 + 7= 27+7 = 34 cm

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Answer:

4 44/49

Step-by-step explanation:

7 7/9 is 70/9

then u use 70/9 multiply by 7/4(I call it keep, change, flip method for division of fraction)

You keep the 1st fraction and because it is a mixed fraction, changing it to improper fraction is easier to solve it later on.

after that, you change the division sign to multiply sign(÷ to ×)

then you flip the 2nd fraction, which means 7/4 becomes 4/7

So overall it becomes 60/7 × 4/7 =240/49,4 44/49 as a mixed fraction.

Answer is 4 44/49

Answer:

you add -8 to 13

Step-by-step explanation:

-8+13=5

p=5

Answer: 5 = p

Step-by-step explanation: To solve the equation -8 = p - 13, notice that the variable is on the right side of the equation,

don't let this throw you off.

To solve for p, we need to get p by itself on the right side of the equation by adding 13 but if we add 13 to the right side of the equation, we also must add 13 to the left side of the equation.

On the right side of the equation, the -13 and + 13 cancel eachother out and we have p. On the left side of the equation, -8 + 13 is 5 so we have 5 = p which is the solution to our equation.

Answer:

x=15

Step-by-step explanation:

This is a simultaneous equation

2x-3y=45 ------------------------------ equation i

x+y=10    -------------------------------equation ii

from equation ii

x+y=10

make x the subject of the matter

we have,

x=10-y

in equation i

substitute x for 10-y

2x-3y=45----------------------i

since x=10-y

we have,

2(10-y) - 3y=45

20-2y=3y=45

collect like terms

-2y-3y=45-20

-5y=25

divide both sides by -5

we have y=-5

substitute y for-5 in equation i

x+y=10

x+-5=10

collect like terms

x=10+5

x=15

therefore

x=15

Answer:

  x = 15

Step-by-step explanation:

Use the second equation to write an expression for y:

  y = 10 -x

Then, substitute this into the first equation and solve for x.

  2x -3(10 -x) = 45

  5x -30 = 45 . . . . . eliminate parentheses

  x -6 = 9 . . . . . . . . .divide by 5

  x = 15 . . . . . . . . . . .add 6

The given image is a triangle.

Property of triangle:

A triangle has three sides.

A triangle has three angles.

A triangle has three vertices.

To find the sides, angles and vertices of the triangle RST:

Sides of the triangle SRT:

RS, ST and RT

Angles of the triangle RST:

∠A, ∠B and ∠C

Vertices of the triangle RST:

A, B and C

These are sides, angles and vertices of the triangle.

Answer:

12X+10

Step-by-step explanation:

It's easy. Just combine like terms. Like terms must have the same variable and to the same power in this case all the terms  have a power of 1, but it doesnt show it because it doesn't really matter. So 4x,6x, and 2x all have the same variable so add them together. That gets you 10x. Since nothing else in the expression has the same variable with 10, you leave the 10 at the end resolving in 12x+10

Answer:

12x+10

Step-by-step explanation:

Collect the like terms to one side.  

Answer:

89

Step-by-step explanation:He bought 89 items because 20 + 3 is 23, 23 + 12 is 35, 35 + 11 is 46, 46 + 24 is 70, and 70 + 11 is 89.