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Arturiano [62]
1 year ago
13

Wo Internet service providers charge an installation fee plus a monthly service fee. The table shows the total costs in dollars)

for different numbers of months at Company A. The total cost y (in dollars) for x months of service at Company B is represented by y=45x+50 . Which company charges less per month?
Company A
Months, x Total cost, y
2

3

4

5

6

$180

$220

$260

$300

$340


Company A
Company A

Company B
Company B
Question 2
After how many months of service are the total costs the same?
After___ months of service, the total costs are the same.
Mathematics
1 answer:
natka813 [3]1 year ago
3 0

Using linear equations, we determined that:

1. Company A charges less per month

2. After <u>10 months</u> of service, the total costs are the same.

<h3>How to Write Linear Equations?</h3>

We are given that:

  • Number of months is represented as x
  • Total cost is represented as y

Total cost for Company B is represented as y = 45x + 50.

Company B charges $45 per month.

Write an equation in slope-intercept form, y = mx + b, to represent the total cost y (in dollars) for x months of service at Company A. From the table given, using two pairs of values, (2, 180) and (3, 220), find the slope (m).

Slope (m) = change in y/change in x = (220 - 180)/(3 - 2)

Slope (m) = 40

Company A charges $40 per month.

Plug in m = 40 and (x, y) = (2, 180) into y = mx + b, to find the y-intercept, b:

180 = 40(2) + b

180 - 80 = b

b = 100

Substitute m = 40 and b = 100 into y = mx + b:

y = 40x + 100 (equation for Company A)

Make both equations equal to find the value of x, which is the number of months of service that will make the total costs of both company the same.

45x + 50 = 40x + 100

45x - 40x = -50 + 100

5x = 50

x = 10

Therefore, number of months would be 10.

In summary, using linear equations, we determined that:

1. Company A charges less per month

2. After <u>10 months</u> of service, the total costs are the same.

Learn more about linear equation on:

brainly.com/question/2030026

#SPJ1

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Four cards are dealt from a standard fifty-two-card poker deck. What is the probability that all four are aces given that at lea
elena-s [515]

Answer:

The probability is 0.0052

Step-by-step explanation:

Let's call A the event that the four cards are aces, B the event that at least three are aces. So, the probability P(A/B) that all four are aces given that at least three are aces is calculated as:

P(A/B) =  P(A∩B)/P(B)

The probability P(B) that at least three are aces is the sum of the following probabilities:

  • The four card are aces: This is one hand from the 270,725 differents sets of four cards, so the probability is 1/270,725
  • There are exactly 3 aces: we need to calculated how many hands have exactly 3 aces, so we are going to calculate de number of combinations or ways in which we can select k elements from a group of n elements. This can be calculated as:

nCk=\frac{n!}{k!(n-k)!}

So, the number of ways to select exactly 3 aces is:

4C3*48C1=\frac{4!}{3!(4-3)!}*\frac{48!}{1!(48-1)!}=192

Because we are going to select 3 aces from the 4 in the poker deck and we are going to select 1 card from the 48 that aren't aces. So the probability in this case is 192/270,725

Then, the probability P(B) that at least three are aces is:

P(B)=\frac{1}{270,725} +\frac{192}{270,725} =\frac{193}{270,725}

On the other hand the probability P(A∩B) that the four cards are aces and at least three are aces is equal to the probability that the four card are aces, so:

P(A∩B) = 1/270,725

Finally, the probability P(A/B) that all four are aces given that at least three are aces is:

P=\frac{1/270,725}{193/270,725} =\frac{1}{193}=0.0052

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K:A
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since the total number of stamps didn't change, the total ratio should be the same.

7:5(after)
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so this means 1 unit is 10stamps.

14-10=4
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₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋

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