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ipn [44]
3 years ago
10

Alexa pays 7/20 of a dollar for each minute she uses her pay-as-you-go phone for a call, and 2/5 of a dollar for each minute of

data she uses. This month, she used a total of 85 minutes and the bill was $31. Which statements are true? Check all that apply.
The system of equations is x + y = 31 and 7/20x+2/5y=85
The system of equations is x + y = 85 and 7/20x+2/5y=31
To eliminate the y-variable from the equations, you can multiply the equation with the fractions by 5 and leave the other equation as it is.
To eliminate the x-variable from the equations, you can multiply the equation with the fractions by 20 and multiply the other equation by -7.
A-She used 25 minutes for calling and 60 minutes for data.
B-She used 60 minutes for calling and 25 minutes for data.
C-She used 20 minutes for calling and 11 minutes for data.
D-She used 11 minutes for calling and 20 minutes for data.
Mathematics
2 answers:
9966 [12]3 years ago
7 0

Answer:

  • The system of equations is x + y = 85 and 7/20x+2/5y=31
  • To eliminate the x-variable from the equations, you can multiply the equation with the fractions by 20 and multiply the other equation by -7.
  • B-She used 60 minutes for calling and 25 minutes for data.

Step-by-step explanation:

It is always a good idea to start by defining variables in such a problem. Here, we can let x represent the number of calling minutes, and y represent the number of data minutes. The the total number of minutes used is ...

  x + y = 85

The total of charges is the sum of the products of charge per minute and minutes used:

  7/20x + 2/5y = 31.00

We can eliminate the x-variable in these equations by multiplying the first by -7 and the second by 20, then adding the result.

  -7(x +y) +20(7/20x +2/5y) = -7(85) +20(31)

  -7x -7y +7x +8y = -595 +620 . . . . eliminate parentheses

  y = 25 . . . . . . . . simplify

Then the value of x is

  x = 85 -y = 85 -25

  x = 60

aksik [14]3 years ago
4 0

Answer:

The second, fourth and B option are correct.

Step-by-step explanation:

In order to solve this problem, we are going to define the following variables :

X: ''Minutes she used her pay-as-you-go phone for a call''

Y: ''Minutes of data she used''

Then, we are going to make a linear system of equations to find the values of X and Y.

''This month, she used a total of 85 minutes'' ⇒

X+Y=85  (I)

(I) is the first equation of the system.

''The bill was $31'' ⇒

(\frac{7}{20})X+(\frac{2}{5})Y=31 (II)

(II) is the second equation of the system.

The system of equations will be :

\left \{ {{X+Y=85} \atop {(\frac{7}{20})X+(\frac{2}{5})Y=31}} \right.

The second option ''The system of equations is X+Y=85 and (\frac{7}{20})X+(\frac{2}{5})Y=31 .'' is correct

Now, to solve the system, we can eliminate the x-variable from the equations by multiplying the equation with the fractions by 20 and multiplying the other equation by -7. Then, we can sum them to obtain the value of Y :

X+Y=85 (I)

(\frac{7}{20})X+(\frac{2}{5})Y=31 (II) ⇒

(-7)X+(-7)Y=-595 (I)'

7X+8Y=620 (II)'

If we sum (I)' and (II)' ⇒

(-7)X+(-7)Y+7X+8Y=-595+620 ⇒ Y=25

If we replace this value of Y in (I) ⇒

X+Y=85\\X+25=85\\X=60

The fourth option ''To eliminate the x-varible from the equations, you can multiply the equation with the fractions by 20 and multiply the other equation by -7'' is correct.

With the solution of the system :

\left \{ {{X=60} \atop {Y=25}} \right.

We answer that the option ''B-She used 60 minutes for calling and 25 minutes for data'' is correct.

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Complete question is;

After examining daily receipts over the past year, it was found that the green parrot italian restaurant has been grossing over $2200 a day for about 85% of it's business days. Using this as a reasonably accurate measure, find the probability that the green parrot will gross over $2200:

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Step-by-step explanation:

This is a binomial probability distribution problem and as such we will use the formula;

P(X = k) = C(n, k) × p^(k) × (1 - p)^(n - k)

A. At least 5 of the next 7 business days will be;

P (X ≥ 5) = P(X = 5) + P(X = 6) + P(X = 7)

P(X = 5) = C(7, 5) × 0.85^(5) × (1 - 0.85)^(7 - 5)

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Thus;

P(X ≥ 5) = 0.20965 + 0.396 + 0.320577

P(X ≥ 5) = 0.9262

B. Probability of at least 5 of the next 10 business days will be;

P(X ≥ 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

From online binomial calculator attached, we can see that the answer is;

P(X ≥ 5) = 0.9986

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From online binomial calculator attached, we can see that the answer is;

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P(X = 7) = 0.1298

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P(X ≥ 1) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

From third image attached using online binomial calculator, we have;

P(X ≥ 1) = 0.9999

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