Dr. Miriam Johnson has been teaching accounting for over 20 years. From her experience, she knows that 60% of her students do homework regularly. Moreover, 95% of the students who do their homework regularly generally pass the course. She also knows that 85% of her students pass the course.

a. What is the probability that a student will do homework regularly and also pass the course?

b. What is the probability that a student will neither do homework regularly nor will pass the course?

c. Are the events "pass the course" and "do homework regularly" mutually exclusive? Explain.

d. Are the events "pass the course" and "do homework regularly" independent? Explain.

Answer:

(a) The Probability that at most three lines are in use is 0.70.

(b) The Probability that fewer than three lines are in use is 0.45.

(c) The Probability that at least three lines are in use is 0.55.

(d) The Probability that between two and five lines, inclusive, are in use is 0.70.

(e) The Probability that between two and four lines, inclusive, are not in use is 0.35.

(f) The Probability that at least four lines are not in use is 0.70.

Step-by-step explanation:

The complete question is: A mail-order company business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table.

X    0          1       2       3          4             5               6

P(X)  0.10      0.15      0.20       0.25         0.20      0.05         0.05  

Calculate the probability of each of the following events.

(a) {at most three lines are in use}

(b) {fewer than three lines are in use}  

(c) {at least three lines are in use}  

(d) {between two and five lines, inclusive, are in use}

(e) {between two and four lines, inclusive, are not in use}

(f) {at least four lines are not in use}

Now considering the above probability distribution;

(a) The Probability that at most three lines are in use is given by = P(X [tex]\leq[/tex] 3)

    P(X [tex]\leq[/tex] 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

                  = 0.10 + 0.15 + 0.20 + 0.25

                  = 0.70

(b) The Probability that fewer than three lines are in use is given by = P(X < 3)

    P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

                  = 0.10 + 0.15 + 0.20

                  = 0.45

(c) The Probability that at least three lines are in use is given by = P(X [tex]\geq[/tex] 3)

    P(X [tex]\geq[/tex] 3) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

                  = 0.25 + 0.20 + 0.05 + 0.05

                  = 0.55

(d) The Probability that between two and five lines, inclusive, are in use is given by = P(2 [tex]\leq[/tex] X [tex]\leq[/tex] 5)

    P(2 [tex]\leq[/tex] X [tex]\leq[/tex] 5) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

                         = 0.20 + 0.25 + 0.20 + 0.05

                         = 0.70

(e) The Probability that between two and four lines, inclusive, are not in use is given by = 1 - P(2 [tex]\leq[/tex] X [tex]\leq[/tex] 4)

    1 - P(2 [tex]\leq[/tex] X [tex]\leq[/tex] 4) = 1 - [P(X = 2) + P(X = 3) + P(X = 4)]

                             = 1 - [0.20 + 0.25 + 0.20]

                             = 1 - 0.65 = 0.35

(f) The Probability that at least four lines are not in use is given by = 1 - Probability that at least four lines are in use = 1 - P(X [tex]\geq[/tex] 4)

    1 - P(X [tex]\geq[/tex] 4) = 1 - [P(X = 4) + P(X = 5) + P(X = 6)]

                       = 1 - [0.20 + 0.05 + 0.05]

                       = 1 - 0.30 = 0.70

Answer:

the gram

Step-by-step explanation:

casegunnell is my gram, follow if your a real g

Following are the calculation to the given points:

When the ABCD is parallelogram:

The properties of parallelogram:

[tex]\to \angle CBD = \angle ADB \\\\[/tex]

[tex]\to \angle BCA = \angle DAC \\\\[/tex]

When the Two-lines are parallel and alternate interior angles are equal:

[tex]\to \Delta BEC \cong \Delta AED \ \ \ \ \ \ \ \{ASA\} \\\\\to \overline {AE} \cong \overline{CE}\\\\ \to \overline{BE} \cong \overline{ED} \\\\[/tex]

When the properties of congruent triangle.

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Answer: the answer is c (the third answer ) ‼️

Step-by-step explanation:

The data in the given residual plot shows that model C has the best fit.

A straight line that minimizes the gap between it and some data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit.

Given:

The residual plot of the values in the graph,

The points in the first graph are very far from the x-axis and y-axis so, it is not the best fit,

The points in the second graph are very far from the x-axis and y-axis, and they are symmetric to the y-axis but not the best fit.

Most of the points are close to the x-axis, so it is the best fit,

Thus, the third graph is the best line of fit.

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#SPJ2

Answer:

Top to bottom, splits it in half

Step-by-step explanation:

Answer: 7.0596 x 10^2

Explanation: I used a scientific calculator to type in the equation. If you were to type the equation in like that, it'd be 705.96. To covert into scientific notation, you would press the 2nd button, and then press DRG. If you see the options FLO, SCI, and ENG, you want to press SCI, and then you get the answer.

I hope this helps!

Answer:

[tex]n=(\frac{2.58(0.34)}{0.05})^2 =307.79 \approx 308[/tex]

So the answer for this case would be n=308 rounded up to the nearest integer

Step-by-step explanation:

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =0.1/2 =0.05 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex]   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution since the sample size is large enough to assume the estimation of the standard deviation as the population deviation. The critical value for this case is [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:

[tex]n=(\frac{2.58(0.34)}{0.05})^2 =307.79 \approx 308[/tex]

So the answer for this case would be n=308 rounded up to the nearest integer

Answer:2

Step-by-step explanation:

v= is the midpoint of xn and wy

Answer:

Option 1

Step-by-step explanation:

The line XZ and line WY parallelogram have a midpoint or center. That is point V.

The lines are the two diagonals of a parallelogram.

Since the diagonals XZ and WY divide each other into equal segments, the diagonals bisect each other. Since the diagonals XZ and WY bisect each other at point V, point V is the midpoint of each diagonal. That is the definition of midpoint.

Answer : The number of capfuls of liquid soap needed to fill the rectangular soap dispenser are 12.

Step-by-step explanation :

First we have to calculate the volume of soap dispenser which is a cuboid.

Volume of cuboid = l × b × h

where,

l = length of cuboid = 16 cm

b = width of cuboid = 9 cm

h = height of cuboid = 4 cm

Now put all the given values in the above formula, we get:

Volume of cuboid = 16 cm × 9 cm × 4 cm

Volume of cuboid = 576 cm³

Now we have to calculate the volume of cap which is a cylinder.

Volume of cylinder = π r² h

where,

r = radius of cylinder = 2 cm

h = height of cylinder = 4 cm

Now put all the given values in the above formula, we get:

Volume of cylinder = 3.14 × (2 cm)² × 4 cm

Volume of cylinder = 50.24 cm³

Now we have to calculate the number of capfuls of liquid soap are needed to fill the rectangular soap dispenser.

Number of capfuls of liquid soap needed =  [tex]\frac{\text{Volume of soap dispenser}}{\text{Volume of cap}}[/tex]

Number of capfuls of liquid soap needed =  [tex]\frac{576cm^3}{50.24cm^3}[/tex]

Number of capfuls of liquid soap needed = 11.46 ≈ 12

Therefore, the number of capfuls of liquid soap needed to fill the rectangular soap dispenser are 12.

Answer:

The amount of interest for this loan is 16.6%.

Step-by-step explanation:

Since Levi will make a purchase for $ 3000 with your credit card, you should explore the two options you have:

-On the one hand, a down payment of $ 1000, with fees of $ 125.

-on the other, a down payment of $ 1,300, with fees of $ 110.

In both cases, the fees are the same, and the interest too. Therefore, to determine the amount of installments and interest, the difference between the down payment of one option and the other must be taken and divided by the difference between the value of the installments of either option.

Thus, the difference of the down payment of 300 (1300 - 1000) must be divided by 15 (125 - 110). This yields a result of 20 (300/15), with which that will be the total of quotas until both have paid the same amount of money.

Thus, given that 1300 + 110 x 20 = 3,500, and that 1000 + 125 x 20 = 3,500, in both cases the total value to be paid is $ 3,500. Since 500 is 16.6% of 3000, the total purchase interest will be 16.6%.

Answer:

See explanation below

Step-by-step explanation:

1) Prove or disprove that if [tex] x^y[/tex] is an irrational number, then x or y is also an irrational number.

Let's take the following instances:

i) When x= 2 and y=[tex] \sqrt{2} [/tex] we have: [tex] 2^\sqrt^{^2^} [/tex]

ii) When [tex] x=2\sqrt{2} [/tex] and y=3, we have: [tex] (x=2\sqrt{2})^3 [/tex]

iii) When [tex] x=2\sqrt{2} [/tex] and [tex] y = \sqrt{2}[/tex], we have: [tex] (2\sqrt{2})^\sqrt^{^2^}[/tex]

It is proven because, in scenario

i) x is rational and y is irrational

ii) x is irrational and y is rational

iii) x and y are irrational

2) Prove tha x² is irrational, then x is irrational.

Use contradiction here.

Thus, x² is irrational and x is rational.

[tex] x =\frac{b}{a} [/tex] when x is rational, a & b are integers.

Therefore, [tex] x^2 =\frac{b^2}{a^2} [/tex]. This x² is rational.

This contradicts the statement that x² is irrational.

Therefore, if x² is irrational, x is also irrational.

Answer:

x= -3 +√2 ≈ -0.1716,  and x = - 3 -2√2 ≈ -5.8284

Step-by-step explanation:

y= -1/2(x+3)² +4

For x -intercept, y = 0.

0 = - 1/2(x+3)² + 4 /*(-2)

0 = (x+3)² - 8

(x+3)² = 8

√(x+3)² = +/-√8

x+3 = +/-√8

x = - 3+/- 2√2

x= -3 +√2 ≈ -0.1716,  and x = - 3-2√2 ≈ -5.8284

Answer:

Y = 3√2 +4

Step-by-step explanation:

y = acosxº + b

Let's look for the values of a and b first.

Let's get values of x and y and solve simultaneously

When x= 0 ,y=10

When x = 120, y= 1

10 =acos0 + b

10 = a +b..... equation 1

1 = acos120 + b

1= -0.5a + b ..... equation 2

10 = a +b

1= -0.5a + b

10-1= a +0.5a

9 = 1.5a

9/1.5 = a

6 = a

1= -0.5a + b ..... equation 2

1 = -0.5(6) +b

1= -3 + b

1+3 = b

4 =b

So

y = acosxº + b equal to

Y = 6cosx° + 4

So value of y when x= 45 is

Y= 6cos45° +4

Y =6(√2/2) +4

Y = 3√2 +4

The value of y when x = 45 degree is,  [tex]y=3\sqrt{2}+4[/tex]

Given function is,

                            [tex]y = a cos(x)+ b[/tex]

From given table, It is observed that,

          x = 0, y = 10 and x = 90, y = 4

Substitute above values in above equation.

                          [tex]a+b=10\\\\b=4[/tex]

         [tex]a=10-b=10-4=6[/tex]

Now, our equation become,

                                [tex]y = 6 cos(x)+ 4[/tex]

Substitute x = 45 in above equation.

                  [tex]y=6cos(45)+4\\\\y=6*(\frac{\sqrt{2} }{2} )+4\\\\y=3\sqrt{2} +4[/tex]

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Answer:

6 pounds

Step-by-step explanation:

Answer:

t1 = S / (15 + 2)      time to cross with wind

t2 = S / (15 -2)       time to cross against wind

t = t1 + t2 = S / 17 + S / 13 = 30 S / 221 = .136 S    where t is in hours

S = .667 hrs / .136 hrs/mi = 4.90 mi

Avg speed = 2 * 4.90 mi / .667 hr   = 14.7 mph

Answer:

Jomo Kenyatta

Step-by-step explanation:

Jomo Kenyatta was a Kenyan politician, who was one of the first African anti-colonial figures. He became the prime minister of Kenya from 1963 to 1964, and after Kenyan independence in 1964, he became president of Kenya. Jomo Kenyatta was born into a family of Kikuyu farmers in Kiambu, present day Kenya which was then, British East Africa. He had his basic schooling in a missionary school before proceeding to study at Moscow's Communist University of the Toilers of the East, University College London, and the London School of Economics.

Answer:

Jomo Kenyatta

Step-by-step explanation:

took the test

Answer:

83.29% probability that at least 2 flights arrive late.

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either they arrive late, or they do not. The probability of a flight arriving late is independent of other flights. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

80 % of its flights arriving on time.

This means that 100-80 = 20% arrive late, so [tex]p = 0.2[/tex]

A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time.

This means that [tex]n = 15[/tex]

Find the probability that at least 2 flights arrive late.

Either less than 2 arrive late, or at least 2 does. The sum of the probabilities of these events is decimal 1. So

[tex]P(X < 2) + P(X \geq 2) = 1[/tex]

We want [tex]P(X \geq 2)[/tex]. Then

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which

[tex]P(X = 2) = P(X = 0) + P(X = 1)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{15,0}.(0.2)^{0}.(0.8)^{15} = 0.0352[/tex]

[tex]P(X = 1) = C_{15,1}.(0.2)^{1}.(0.8)^{14} = 0.1319[/tex]

[tex]P(X = 2) = P(X = 0) + P(X = 1) = 0.0352 + 0.1319 = 0.1671[/tex]

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.1671 = 0.8329[/tex]

83.29% probability that at least 2 flights arrive late.

Answer:

if your asking for letter option it would be B if it is a choice between the two in each it is xxx and cx.

Step-by-step explanation: if its roman numerals

Answer:

The proportion of infants with birth weights between 125 oz and 140 oz is 0.1359 = 13.59%.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 110, \sigma = 0.15[/tex]

The proportion of infants with birth weights between 125 oz and 140 oz is

This is the pvalue of Z when X = 140 subtracted by the pvalue of Z when X = 125. So

X = 140

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{140 - 110}{15}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

X = 125

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{125 - 110}{15}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413

0.9772 - 0.8413 = 0.1359

The proportion of infants with birth weights between 125 oz and 140 oz is 0.1359 = 13.59%.

Answer:

if the sequence is:

12, 13, 13, 14, 14 etc, and each term keeps growing up, the sequence obviusly diverges.

Now, if the sequence is

1/2, 1/3, 1/3, 1/4, 1/4, 1/5 , 1/5

so the terms after the first one repeat, we could group the terms with the same denominator and get:

1/2, 2/3, 2/4, 2/5..... etc.

So the terms after the first one are aₙ = 2/n.

Now, a criteria to see if a sequence converges if seing if:

[tex]\lim_{n \to \infty} a_n = 0[/tex]

and here we have;

[tex]\lim_{n \to \infty} 2/n[/tex]

that obviusly tends to zero, so we can conclude that this sequence converges.

then the limit is:

There exist a n' such that for any n > n' then IL -aₙI < ε

where L is the limit

I2/n - 0I = I2/nI < ε

then this is true if n > 2/ε = n'

Answer:

42.115 ft/s  

Step-by-step explanation:

The distance from the point closest to the light is given by

 d = (13 ft)tan(α)

where,

α=angle from perpendicular.

Since the light travels through an angle of 2π radians in 5 seconds, the angle can be represented by

 α = πt . . . . radians      

and the rate of change of α is dα/dt = π (radians/second)

The rate of change of distance is:

dd/dt = (13 ft)sec(α)²(dα/dt) = (13π)(sec(10°)²) ft/s ≈ 42.115 ft/s  

Answer:

-3-7e/3e

Step-by-step explanation:

d - 4d=3/e +7

-3d= 3/e +7

-3d=(3+7e)/e

d=(-3-7e)/3e

Answer:

The second graph.

Step-by-step explanation:

0-9: 6 numbers

10-19: 2 numbers

20-29: 1 number

30-39: 3 numbers

40-49: 1 number

50-59: 2 numbers

60-69: 0 numbers

70-79: 5 numbers

80-89: 3 numbers

90-99: 1 number

Answer:

C (the third graph)

Step-by-step explanation:

This graph's function has a domain and range that both exclude one value, which is 0. The x and y values are never 0 in the function, as it approaches 0 but never meets it.

Answer:

see below

Step-by-step explanation:

This graph has an asymptote at y = 0 and x=0

This excludes these values

The domain excludes x =0

The range excludes y=0

Answer:

240

Step-by-step explanation:

The average rate of a function f(x) is interval [a,b] is given by :-

R = (f(b) - f(a)) / (b-a)

Now, the given function : F(x) = 4(5)^x

Interval : [1,3]

Now, the average rate of change over the interval [1, 3]  is given by :-

R = F(3) - F(1) / (3 - 1)

= 4(5)^3 - 4(5)^1 / 2

= 4(5^3 - 5) / 2

= (4(125 - 5) / 2) = 240

Hope It helped

Answer:

The visitor needs to run 5.5 miles before he starts swimming to minimize the time it takes to reach the island.

Step-by-step explanation:

The sketch of the setup described is drawn on the attached image to this question.

Let the distance the visitor has to run be x miles

The distance from that endpoint of running to the closest point on the shoreline to the island is then (7 - x) miles

Using Pythagoras theorem, we can then calculate the distance the visitor has to swim

Let that distance be y

y² = 2² + (7 - x)²

y² = 4 + 49 - 14x + x²

y² = x² - 14x + 53

y = √(x² - 14x + 53)

Speed = (distance/time)

Time = (distance/speed)

Running time = (running distance)/(running speed) = (x/5)

Swimming time = (swimming distance)/(swimming speed) = [√(x² - 14x + 53)]/3

Total time to reach the island

= Running time + Swimming time

T = (x/5) + [√(x² - 14x + 53)]/3

we now want to find the distance that the visitor will run to minimize the time to reach the island

At minimum value of T, (dT/dx) = 0

(dT/dx) = (1/5) + [(2x - 14)(x² - 14x + 53)⁻⁰•⁵]/6

multiplying through by 15

15(dT/dx) = 3 + 5[(x - 7)(x² - 14x + 53)⁻⁰•⁵]

So, at minimum value of T, (dT/dx) = 0

0 = 3 + 5[(x - 7)(x² - 14x + 53)⁻⁰•⁵]

-3[(x² - 14x + 53)⁰•⁵] = 5(x - 7)

-3[(x² - 14x + 53)⁰•⁵] = (5x - 35)

Squaring both sides

9(x² - 14x + 53) = (5x - 35)² = 25x² - 350x + 1225

9x² - 126x + 477 = 25x² - 350x + 1225

25x² - 350x + 1225 = 9x² - 126x + 477

16x² - 224x + 748 = 0

Solving this quadratic equation

x = 8.5 or x = 5.5 miles

Since the Total distance from the cabin to the closest shore point to the island is 7 miles, the only feasible answer is x = 5.5 miles.

Therefore, the visitor needs to run 5.5 miles before he starts swimming to minimize the time it takes to reach the island.

Hope this Helps!!!

Answer:

Center: (1, 5)

Radius: r = 5

Step-by-step explanation:

Step 1: Rewrite equation

x² - 2x + y² - 10y = -1

Step 2: Complete the Square (x2)

x² - 2x + 1 + y² -10y + 25 = -1 + 1 + 25

(x - 1)² + (y - 5)² = 25

Step 3: Find answers

Center = (h, k)

(1, 5) as Center

Radius = r

r² = 25

r = 5

Answer: Center = (1, 5)

               Radius = 5

Step-by-step explanation:

The standard form for a circle is: (x - h)² + (y - k)² = r²     where

First, group the x's and group the y's in order to complete the square.

x² - 2x        + y² - 10y         = -1

     ↓                    ↓

   (-2/2)²=1         (-10/2)²=25

Add those values to BOTH sides:

x² - 2x + 1      +  y² - 10y + 25    = -1 + 1 + 25

Rewrite the left side as perfect squares and simplify the right side.

  (x - 1)²       +     (y - 5)²         = 25

We end up with (h, k) = (1, 5)   this is the center

        and r² = 25 --> r = 5         this is the radius

To graph the circle, place an x at the center (1, 5).  Plot a point 5 units (the radius) to the right of the center, another point 5 units up from the center, a third point 5 units left from the center, and a fourth point 5 units down from the center. "Connect the dots" to create a circle.

Answer:

[tex]8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6[/tex]

Step-by-step explanation:

Step 1: Distribute the negative

[tex]8r^6s^3-9r^5s^4+3r^4s^5-2r^4s^5+5r^3s^6+4s^5s^4[/tex]

Step 2: Combine like terms

When you do so, you should get your answer.

Answer:

[tex]\frac{27}{64}[/tex]

Step-by-step explanation:

[tex]( \frac{3}{4} )^3[/tex]

Distribute the exponent to the numerator and denominator.

[tex]\frac{3^3}{4^3}[/tex]

Evaluate the value.

[tex]\frac{27}{64}[/tex]

Answer:

[tex]z=-0.253<\frac{a-100}{15}[/tex]

And if we solve for a we got

[tex]a=100 -0.253*15=96.205[/tex]

And for this case the value would be 96.2 for the P40

Step-by-step explanation:

Let X the random variable that represent the IQ scores of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(100,15)[/tex]  

Where [tex]\mu=100[/tex] and [tex]\sigma=15[/tex]

We want to find the P40 ( a) so we need to satisfy the following condition:

[tex]P(X>a)=0.60[/tex]   (a)

[tex]P(X<a)=0.40[/tex]   (b)

For this case we can look for the critical value in the normal standar ddistirbution who accumulate 0.4 of the area in the left and 0.6 in the right and we got z=-0.253.

If we use condition (b) from previous we have this:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.40[/tex]

And we can set up the following equationL

[tex]z=-0.253<\frac{a-100}{15}[/tex]

And if we solve for a we got

[tex]a=100 -0.253*15=96.205[/tex]

And for this case the value would be 96.2 for the P40

Answer:

Movie: $4.25

Video Game: $5.25

Step-by-step explanation:

For this problem, we can use system of equations to solve for the rental costs of the movies and video games. Let's use x for movies and y for video games.

Equation 1

5x+3y=37

Equation 2

2x+6y=40

To start, we can use elimination to solve for x and y. Let's cancel out y. To do so, we have to multiply the first equation by 2 to get the y equal.

10x+6y=74

Now that the y are equal, we can subtract both equations.

8x=34

x=4.25

The movie rental cost is $4.25.

Now that we know x, we can plug in to find y.

2(4.25)+6y=40

8.5+6y=40

6y=31.5

y=5.25

The rental cost for video games is $5.25.