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zimovet [89]
3 years ago
12

Jake is comparing the prices of two laundry service companies. Company A charges $20 per load and an additional $8 as service ch

arges. Company B charges $24 per load and an additional $4 as service charges.
Part A: Write an equation to represent each company's total charges for cleaning a certain number of loads of laundry. For both equations (one for Company A and one for Company B), define the variable used. (4 points)

Part B: Which company would charge less for 5 loads of laundry? Justify your answer. (3 points)

Part C: How much money is saved by using the services of Company A instead of Company B to clean 9 loads of laundry? (3 points)
Mathematics
2 answers:
madreJ [45]3 years ago
4 0
<span>Part A: Write an equation to represent each company's total charges for cleaning a certain number of loads of laundry. 
lets x = # of loads
</span><span>Company A : 20x + 8
</span><span>Company B:  24x + 4

</span><span>Part B: Which company would charge less for 5 loads of laundry? Justify your answer. (3 points)

</span>Company A : 20x + 8 = 20(5) + 8 = 100 + 8 = 108
Company B:  24x + 4 = 24(5) + 4 = 120 + 4 = 124

Company A charges $16 less than company B <span>for 5 loads of laundry
</span>
<span>Part C: How much money is saved by using the services of Company A instead of Company B to clean 9 loads of laundry? (3 points)
</span>
Company A : 20x + 8 = 20(9) + 8 = 180 + 8 = 188
Company B:  24x + 4 = 24(9) + 4 = 216 + 4 = 220

220 - 188 = $32

You would save $32 <span>by using the services of Company A instead of Company B to clean 9 loads of laundry</span>
Nat2105 [25]3 years ago
3 0
Part A:
Company A: Charges= $20x+$8
(I knew 20 was the coefficient for x instead of 8 because in the question it says $20 "per a load" which is a clue that it is multiplied by a variable. I knew that 8 did not come with a variable because it was describribed as a one time charge for using the laundry service)

Company B: Charges= $24x+$4

the variable used for both equations was "x".
variable x= number of loads of laundry that Jake has.





Part B: which company would charge less for 5 loads of laundry? (so, when x=5)

Comp. A: C= 20x+8
C= 20(5)+ 8
C= 100 +8
C= $108

For company A, the total charges for 5 loads is $108.

Comp. B: C= 24x +4
C=24(5)+4
C=120+4
C=$124

For compamy B, the total charges for five loads add up to $124. COMPANY A CHARGES LESS FOR 5 LOADS OF LAUNDRY BECAUSE 124>108.



Part C: How much money is saved by using the services of Company A instead of Company B to clean 9 loads of laundry? (so, when x=9, what is Cb-Ca = to?)

Comp.A: C=20x+8
C=20(9)+8
C=180 + 8
Ca=$188

Comp. B: C=24x+4
C=24(9)+4
C=216+4
Cb=$220


Final answer part C:
Cb-Ca= answer
220-188=$32

$32 are saved by using Company A rather than Company B.
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/// WORTH 70 points /// ASAP ////
belka [17]

A community is developing plans for a pool and hot tub. The community plans to form a swim team, so the pool must be built to certain dimensions. Answer the questions to identify possible dimensions of the deck around the pool and hot tub.


Part I: The dimensions of the pool are to be 25 yards by 9 yards. The deck will be the same width on all sides of the pool. Including the deck, the total pool area has a length of (x + 25) yards, and a width of (x + 9) yards.

Write an equation representing the total area of the pool and the pool deck. Use y to represent the total area. Hint: The area of a rectangle is length times width. (1 point)

y = (x+25)(x+9)


Rewrite the area equation in standard form. Hint: Use the FOIL method. (1 point)


y = x^2 + 9x + 25x + 9(25)


y = x^2 +34x + 225


Rewrite the equation from Part b in vertex form by completing the square. Hint: Move the constant to the other side, add to each side, rewrite the right side as a perfect square trinomial, and finally, isolate y. (4 points: 1 point for each step in the hint)


y-225 = x^2 +34x


y-225 + 17^2 = x^2 +34x + 17^2


y-225 + 289 = (x+17)^2


y = (x+17)^2 - 64


What is the vertex of the parabola? What are the x- and y-intercepts? Hint: Use your answer from Part a to identify the x-intercepts. Use your answer from Part b to identify the y-intercept. Use your answer from Part c to identify the vertex. (4 points: 1 point for each coordinate point)

The vertex is where the squared term is zero, x=-17 , y =-64, (-17,-64)


The y intercept is y at x=0, so (0,225)


The x intercepts are the zeros; so at x=-25 and x=-9, aka (-25,0), (-9,0)


Graph the parabola. Use the key features of the graph that you identified in Part d. (3 points)


[Plot the points we generated and connect the dots. I'll leave the graphing to you]

In this problem, only positive values of x make sense. Why? (1 point)

<em>x</em> is the width of the pool edge; it must be positive.


What point on your graph shows a total area that includes the pool but not the pool deck? (1 point)


x=0, y=225 i.e. (0,225)



The community decided on a pool area that adds 6 yards of pool deck to both the length and the width of the pool. What is the total area of the pool and deck when x = 6 yards? (2 points)


(9+6)(25+6)=15(31)=465



Part II: A square hot tub will be placed in the center of an enclosed area near the pool. Each side of the hot tub measures 6 feet. It will be surrounded by x feet of deck on each side. The enclosed space is also square and has an area of 169 square feet. Find the width of the deck space around the hot tub, x.

Step 1: Write an equation for the area of the enclosed space in the form y = (side length)2. Hint: Don't forget to add x to each side of the hot tub. (1 point)



y=(x+6)(x+6)=(x+6)^2



Step 2: Substitute the area of the enclosed space for y in your equation. (1 point)


169 = (x+6)^2


Step 3: Solve your equation from Part b for x. (3 points)


x + 6 = \pm \sqrt{169}


x = -6&#10; \pm 13


x= 7 \quad \textrm{ or } \quad x= -19


Step 4: What is the width of the deck around the hot tub? Hint: One of the answers from Part c is not reasonable. (1 point)


Only the positive root works,


x=7 feet


5 0
3 years ago
A cyclist rides her bike at a speed of 10 kilometers per hour. What is this speed in miles per hour? How many miles will the cyc
SashulF [63]
6.25 miles per hour
12.5 miles in 2 hours
6 0
2 years ago
I NEED HELP FAST what is y+1=5/6(x-2) in standard form?
Irina18 [472]

Answer:

\large\boxed{5x-6y=16}

Step-by-step explanation:

The standard form of an equation of a line:

Ax+By=C

We have the equation in the point-slope form. Convert:

y+1=\dfrac{5}{6}(x-2)\qquad\text{multiply both sides by 6}\\\\6y+6=6\!\!\!\!\diagup^1\cdot\dfrac{5}{6\!\!\!\!\diagup_1}(x-2)\\\\6y+6=5(x-2)\qquad\text{use the distributive property}\\\\6y+6=(5)(x)+(5)(-2)\\\\6y+6=5x-10\qquad\text{subtract 6 from both sides}\\\\6y+6-6=5x-10-6\\\\6y=5x-16\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\-5x+6y=5x-5x-16\\\\-5x+6y=-16\qquad\text{change the signs}\\\\\boxed{5x-6y=16}

6 0
2 years ago
After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only five women among the last
Georgia [21]

Answer:

The probability that 5 or fewer women are hired, assuming no gender discrimination, is 0.0317; we can use this result to support her charge of gender discrimination.

Step-by-step explanation:

If we are assuming that the women and the men are equally qualified, then the probability for each employee that is hired the probability for it to be a women should be 1/2. Note that the fact that more men that women are hired in a sample might not be disctrimination: for example, if 2 men are hired out of 2 employees, that can happen with probability 1/4, so it is quite common. In order to support her charge for gender discrimination, we need at least a probability less that 0.05 that 5 (or less) women are hired out of 19 employees.

Since each configuration is equally probable, we will count the total amount of possible cases that 5 or less women are hired, and dividide it by the total amount of cases, 2¹⁹.

  • 0 women hired: one possible case: every employee is male
  • 1 women hired: 19 possible cases
  • 2 women hired: {19 \choose 2} = 171 possible cases
  • 3 women hired: {19 \choose 3}  = 969 possible cases
  • 4 women hired: {19 \choose 4} = 3876 possible cases
  • 5 women hired: {19 \choose 5} = 11628 possible cases

Thus, there are a total of 11628+3876+969+171 = 16644 possible cases out of 2¹⁹ ones. All of them with seemingly equal probability. As a consequence, the probability of 5 or less women to be hired out of 19 employees, assuming that the probability to hire 1 is 1/2, is

16644/2¹⁹ = 0.0317 < 0.05

The probability that 5 or fewer women are hired, assuming no gender discrimination, is 0.0317. Since the probability is so low, we can conclude that for the employer, a woman equally qualified as a man is less likely to be hired, therefore, we can support her charge of gender discrimination.

6 0
2 years ago
9x10^7 is how many times as large as 3x10^-2
lianna [129]

Answer:

3000000000 times bigger

Step-by-step explanation:

5 0
3 years ago
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