3. 07 Quiz: Combine Functions Nearpod i H George has opened a new store and he is monitoring its success closely. He has found that this store's revenue each month can be modeled by r(x) = x2 + 5x + 14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x) = x2 - 4x + 5 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars. What does (r - c)(5) mean about George's new store? -O The new store will sell 900 items in its fifth month in business.

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The p-value of the test is 0.017 > 0.01, which means that there is not convincing evidence that the mean time behind the whell for all U.S drivers is less than 51 minutes.

We are told that:

Time spent by U.S. drivers on average each day = 51 minutes behind the wheel

Thus, the null hypothesis is:

H₀: μ = 51

The alternate hypothesis is:

Hₐ: μ < 51

The formula for the test statistic is:

z = (x' - μ)/(σ/√n)

where:

x' is sample mean

n is sample size

μ is population mean

σ is standard deviation

Thus:

z = (46.4 - 51)/(18.8/√75)

z = -2.12

From online p-value from z-score calculator, we have:

The p-value of the test is referred to as the probability of finding a sample mean that is less than 46.4, which is the p-value of z when X = 46.4.

Looking at the z-table, z = -2.12 has a p-value of 0.017.

Decision:

The p-value of the hypotheses test is seen to be0.017 > 0.01.

Thus, this tells us that we don't have convincing evidence that the mean time spent behind the wheel for all U.S drivers is less than 51 minutes.

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Answer:

Acute triangle

Step-by-step explanation:

angles that are less than 90° are called acute

This triangle has 3 acute angles, so it is an acute triangle

Answer:

The first one is B & H
2nd one is A & G

3rd one is D & E

4th one is C & F

Step-by-step explanation:

The box plot that represents these data is Option B because the centre of measure falls on 4.

To find the median, we first arrange the study hours in ascending order:

2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7.

From here, we have 15 numbers, so the median is the 8th number in the list which is 4.

As the median study hours for Mr. Jeffer's math class is 4 hours per week, then, the box plot that represents these data is B because the centre of measure falls on 4.

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Answer:

Step-by-step explanation:

By the figure, it would mean:

67, 67, 68

72, 72, 73, 76, 76, 77, 78

80, 81, 83, 83, 85, 85, 85, 87, 88

91, 91, 93, 95, 99

a) 2 students

b) 9 students

c) 2 students

Explanation : 5 students (90s) - 3 students (60s) = 2 students

d) 81

Explanation : (67 + 67 + 68 + 72 + 72 + 73 + 76 + 76 + 77 + 78 + 80 + 81 + 83 + 83 + 85 + 85 + 85 + 87 + 88 + 91 + 91 + 93 + 95 + 99) ÷ 24 = 81.33

Answer: To calculate the total amount a buyer should save each month to cover these fees, we need to add up all the costs and divide by 12 (the number of months in a year).

Annual real estate taxes = $2046

Insurance premiums = $1236

Flood insurance premiums = $380

Annual special assessment landfill fee = $125

Quarterly trash collection costs = $65 x 4 = $260

Annual homeowner's association fee = $720

Quarterly pool maintenance costs = $45 x 4 = $180

Monthly termite and pest protection costs = $39 x 12 = $468

Total annual costs = $2046 + $1236 + $380 + $125 + $260 + $720 + $180 + $468 = $5405

Total monthly costs = $5405 / 12 = $450.42

Therefore, a buyer should save $450.42 each month to cover these fees.

Step-by-step explanation:

Hamid's soccer game starts at 10:00 am with players warming up 45 minutes earlier and ends by 1:15.

Hamid's soccer game is scheduled to start at 10:00 am, but the players must arrive at the field 45 minutes early to warm up. This means that they need to be there at 9:15 am. The duration of the game is not given, but we know that it must end by 1:15 pm.

Assuming that the game will last for 90 minutes, it would end at 11:30 am. This would give the players ample time to change, clean up, and leave the field by 12:00 pm. However, if the game were to last longer, say for 2 hours, it would end at 12:00 pm, leaving only 15 minutes for the players to get ready to leave.

Therefore, it is important for the players to play efficiently and within the time allotted so that they have enough time to change and leave before the deadline. It is also important for the players to arrive at the field on time to ensure that they have enough time to warm up and prepare for the game.

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To find dy/dx for y = 1/3x³ + 7x, we need to take the derivative with respect to x using the power rule and the sum rule, which gives dy/dx = x² + 7.

The given equation is y = 1/3x³ + 7x. To find dy/dx, we need to take the derivative of y with respect to x. We can do this by using the power rule and the sum rule of differentiation.

Using the power rule, the derivative of x³ is 3x². Using the sum rule, the derivative of 7x is 7. Therefore, the derivative of y with respect to x is:

dy/dx = d/dx (1/3x³ + 7x)

= d/dx (1/3x³) + d/dx (7x)

= (1/3) d/dx (x³) + 7 d/dx (x)

= (1/3) (3x²) + 7

= x² + 7

Hence, we have found that the derivative of y with respect to x is x² + 7.

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Samantha determines the answer as cos(θ) = -√(3/4).

Based on the information given, I can help you with this problem. Samantha is correct in using the Pythagorean identity and substitution, but she made an error in identifying the quadrant. Here's the correct process:

1. Given sin(θ) = 1/2 and tan(θ) < 0.
2. The correct quadrant where sin(θ) is positive and tan(θ) is negative is the second quadrant, not the first.
3. Using the Pythagorean identity: sin^2(θ) + cos^2(θ) = 1.
4. Substitute sin(θ) = 1/2 into the equation: (1/2)^2 + cos^2(θ) = 1.
5. Simplify: 1/4 + cos^2(θ) = 1.
6. Solve for cos^2(θ): cos^2(θ) = 3/4.
7. Since we are in the second quadrant, cos(θ) is negative: cos(θ) = -√(3/4).

Your answer: cos(θ) = -√(3/4).

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Answer:

Pens=13

Pencils=27

Step-by-step explanation:

1. Pens = x, Pencils = y

x+y=40

2. y+5 & x-5 --> y=4x

3. Rearrange the x+y=40 to y=40-x. Then substitute y=4x and y=40-x to 4x=40-x.

4. Solve. 4x=40-x, 5x=40, x=8

5. Plug in x=8 to y=4x -> y=32.

6. Reverse the y+5 & x-5. y=27, x=13.

The surface area be 243 square feet.

Hence option (d) is correct.

In the given regular pyramid

Slant height = l = 6 ft

Edge of base = s = 9ft

Then,

Area of base = a = 9x9 = 81 square ft

Perimeter of base = p = 4x9 = 36 ft

Since surface area of regular pyramid = A  = a + (1/2)ps

                                                                       = 81 + (36x9)/2

                                                                       = 81 + 162

                                                                       =  243

Hence, A = 243 square ft.

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Answer:

The surface area be 243 square feet.

Step-by-step explanation:

Percentage of gumballs that are within standard deviations of the mean is 68% and have a diameter between 2.20 cm and 2.22 cm.

To find the percentage of gumballs that are within one standard deviation of the mean, we need to use the empirical rule, also known as the 68-95-99.7 rule. According to this rule, for a normal distribution:

Here we want to find the percentage of gumballs that are within one standard deviation of the mean. So we can use the first part of the empirical rule and say that approximately 68% of the gumballs have a diameter between:

Mean - Standard deviation = 2.21 - 0.01 = 2.20 cm and Mean + Standard deviation = 2.21 + 0.01 = 2.22 cm

Therefore, approximately 68% of the gumballs have a diameter between 2.20 cm and 2.22 cm.

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The location where the fourth child will stop running in the relay race is 4/5 of the way.

To determine the location where the fourth child will stop running in the relay race, we need to find out the total distance covered by the first four children.

Since each child runs 1/5 of a mile, we can find the total distance for the first four children by multiplying their individual distances.

Total distance = (Number of children) * (Distance run by each child)
Total distance = 4 * (1/5)

Now, let's multiply:
Total distance = 4/5

So, the fourth child will stop running at a location 4/5 of a mile from the starting point. To plot this point on a number line, locate the point between 0 and 1 that is 4/5 of the way. This point represents the location where the fourth child will stop running in the relay race.

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The missing values are:

Given Integral:

[tex]\int\limits^1_0 \int\limits^{2-x}_x {F(x,y)} \, dydx = \int\limits^b_a \int\limits^{g(y)}_{f(y)} {F(x,y)} \ dxdy + \int\limits^c_b \int\limits^{h(y)}_{k(y)} {F(x,y)} \ dxdy \\[/tex]

To write the equivalent integral with the order of integration reversed, express the limits of integration and functions appropriately.

Reversed integral:

[tex]\int\limits^b_a \int\limits^{g(y)}_{f(y)} {F(x,y)} \ dxdy + \int\limits^c_b \int\limits^{h(y)}_{k(y)} {F(x,y)} \ dxdy \\[/tex]

Now, let's determine the values of the variables:

a = 0: The lower limit of the outer integral remains the same as the original integral.

b = 1: The upper limit of the outer integral also remains the same as the original integral.

c = 1: The upper limit of the second inner integral is determined by the limits of integration of the original integral, which is 1.

f(y) = y: The lower limit of the first inner integral is the same as the original integral, which is y = x.

g(y) = 2 - y: The upper limit of the first inner integral is determined by the limits of integration of the original integral, which is 2 - x.

h(y) = 0: The lower limit of the second inner integral remains the same as the original integral.

k(y) = y: The upper limit of the second inner integral remains the same as the original integral.

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The formula for the area of a rectangle is length times width, or in this case (x+6)(x+2) or x^2 + 8x + 12 in standard form.

To simplify this expression, we can use the distributive property to multiply the two binomials:

(x+6)(x+2) = x(x+2) + 6(x+2)

= x² + 2x + 6x + 12

= x² + 8x + 12

To express the area of the entire rectangle, we need to multiply the length (x + 6) by the width (x + 2). This will give us a polynomial in standard form.

Step 1: Write down the expression for the area of the rectangle.
Area = (x + 6)(x + 2)

Step 2: Use the distributive property (also known as the FOIL method) to expand the expression.
Area = x(x + 2) + 6(x + 2)

Step 3: Continue to expand and simplify the expression.
Area = (x² + 2x) + (6x + 12)

Step 4: Combine like terms.
Area = x² + 8x + 12

So the area of the entire rectangle is expressed as the polynomial x² + 8x + 12 in standard form.

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Ms. Paquette used approximately 0.73 gallons of paint for one coat on the rectangular wall.

To determine how many gallons of paint Ms. Paquette used for one coat on the rectangular wall, we first need to calculate the total area of the wall.

Area of the wall = length x width
= 25.5 feet x 10 feet
= 255 square feet

Now, to find out how many gallons of paint are needed for one coat, we need to know the coverage rate of the paint. This information is usually provided on the paint can label. Let's assume that the coverage rate for the paint Ms. Paquette used is 350 square feet per gallon.

To calculate how many gallons of paint are needed, we can divide the total area of the wall by the coverage rate of the paint:

255 square feet ÷ 350 square feet per gallon = 0.7286 gallons

This means that Ms. Paquette used approximately 0.73 gallons of paint for one coat on the rectangular wall. Since paint is typically sold in 1-gallon containers, she would need to purchase at least one gallon of paint to complete one coat on this wall.

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Answer:

x=3, Adding and dividing. (Im not too sure how to answer that question, Are there some options that you learned in class?)

Step-by-step explanation:

4x-5=7

+5       +5

4x=12

/4      /4

x=3

The p-value is less than the significance level so reject the null hypothesis and concluded percentage of the students volunteer their time is different from receiving financial aid students.

Percentage of college students who volunteer their time = 20%

Perform a hypothesis test.

Null hypothesis H₀: p = 0.20,

where p is the proportion of college students who volunteer their time.

The alternative hypothesis is Hₐ: p ≠ 0.20.

Indicating that the proportion of college students who volunteer their time is different for students receiving financial aid.

57 out of 381 randomly selected students who receive financial aid volunteered their time.

Test the hypothesis,

Calculate the sample proportion of volunteers among the students receiving financial aid,

p₁ = 57 / 381

    = 0.149

Using Test statistic,

which follows a normal distribution under the null hypothesis .

Mean = 0  

Standard deviation σ = √(p(1-p)/n),

where p = 0.20 is the proportion under the null hypothesis

n = 381 is the sample size.

z

= (p₁ - p) /√(p×(1-p)/n)

= (0.149 - 0.20) / √(0.20(1-0.20)/381)

= -2.55

Using attached table of p-value from z-score.

Calculated test statistic of -2.55 corresponds to a p-value of 0.0054,

which is less than the significance level α = 0.01.

Reject the null hypothesis .

Therefore, we conclude that there is evidence to suggest that the percentage of college students who volunteer their time is different for students receiving financial aid.

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The above question is incomplete, the complete question is:

20% of all college students volunteer their time. is the percentage of college students who are volunteers different for students receiving financial aid? of the 381 randomly selected students who receive financial aid, 57 of them volunteered their time. what can be concluded at the α = 0.01 level of significance?

A. To obtain the position of EFGH, Johnny translated ABCD by 3 units to the right and 4 units up. To draw and label EFGH, simply shift each vertex of ABCD by this translation vector (3, 4).

B. Tom rotated ABCD by 90º clockwise about the origin, O, to get the position of IJKL. To draw and label IJKL, rotate each vertex of ABCD 90º clockwise around the origin. This can be achieved by switching the x and y coordinates of each vertex and negating the new x value.

C. Tony placed a smaller car, MNOP, on the coordinate plane. MNOP is a dilation of ABCD with its center at the origin and a scale factor of -0.5. To draw and label MNOP, multiply the coordinates of each vertex of ABCD by the scale factor -0.5, keeping the origin as the center.

(1) it takes about 10 hours to thaw a 20-pound turkey in cold water.(2) it takes an additional 0.25 hours (or 15 minutes) to thaw in the refrigerator.

A linear function is a function that represents a straight line in the coordinate plane. For example, y = 3x - 2 represents a straight line in the coordinate plane and thus a linear function. Since y can be replaced by the function f(x), this function can be written as f(x) = 3x - 2.

 a. A typical thawing rate when thawing in the refrigerator  is about 1 day per 4-5 kilograms of turkey meat. So if you have a 20 pound turkey, it will take about 4-5 days to thaw in the fridge. In cold water, the thawing rate  is about 30 minutes per pound, so it takes about 10 hours to thaw a 20-pound turkey in cold water.

b) The initial value may represent the weight of the frozen turkey before thawing begins. c. Let y be the time it takes to thaw the turkey in hours and let x be the weight of the turkey in pounds. Assuming a linear relationship between melting time and weight, we can write:

y = mx + b

where m is the thaw rate (in hours per pound) and b is the intercept (the time it takes to thaw a 0-pound turkey, which is 0). From part a, we know that the refrigerator thaw rate  is about 1 day per 4-5 pounds of turkey, or about 0.25-0.2 hours per pound. So we can use m = 0.25 in our linear function:

y = 0.25x + 0

This means that for every additional pound of turkey, it takes an additional 0.25 hours (or 15 minutes) to thaw in the refrigerator.

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Answer:

LCM = 2^4 x 3^2 x 5^2 x 7 = 25200

Step-by-step explanation:

Prime factorization of 720:

720 = 2^4 x 3^2 x 5

Prime factorization of 1575:

1575 = 3^2 x 5^2 x 7

Answer:

720 = 2 × 2 × 2 × 2 × 3 × 3 × 5

1,575 = 3 × 3 × 5 × 5 × 7

LCM of 720 and 1,575 =

2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 × 7 = 25,200

The relative frequency for selecting a teen out of all the people who like chocolate is calculated by dividing the number of teens who like chocolate (N) by the total number of people who like chocolate (T).

To find the relative frequency for selecting a teen out of all the people who like chocolate, you need to follow these steps:

Step 1: Determine the total number of people who like chocolate (let's call this T).
Step 2: Determine the number of teens who like chocolate (let's call this N).
Step 3: Calculate the relative frequency by dividing the number of teens who like chocolate (N) by the total number of people who like chocolate (T).

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The only option left is −5°F, which is colder than −3°F and thus could be the temperature on her thermometer this morning.

The temperature on Skylar's thermometer is measured using a scale that indicates the degree of hotness or coldness of the atmosphere. In this case, we know that the temperature on her thermometer last night was −3°F. The negative sign indicates that the temperature was below the freezing point of water.

We are asked to determine what the temperature could be on her thermometer this morning. Since we are told that the temperature is colder than −3°F, we can eliminate 0°F and 2°F as possible options, as they are warmer than −3°F.

Similarly, −1°F is only slightly colder than −3°F, so it is unlikely to be the temperature on Skylar's thermometer this morning. Therefore, the only option left is −5°F, which is colder than −3°F and thus could be the temperature on her thermometer this morning.

It is important to note that temperature can have a significant impact on our daily lives. Extreme cold temperatures can cause frostbite, hypothermia, and other health hazards, while hot temperatures can lead to dehydration, heat exhaustion, and heat stroke. It is important to dress appropriately and take necessary precautions when the temperature is too low or too high.

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Answer:

I believe the distance between these points is (2, 7), because the difference between -5 and -7 is 2, and the for -9 and -2, it's 7.  Hope I helped.

The solution to this system of equations are x = 7 and y = -3.

In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.

Given the following system of linear equations:

3y = 26 - 5x               .........equation 1.

6x + 7y = 21               .........equation 2.

Rewriting in standard form, we have:

5x + 3y = 26

6x + 7y = 21

By multiplying equation 1 by 6 and dividing by 5, we have:

6x + 3.6y = 31.2   .........equation 3.

By subtracting equation 3 from equation 2, we have:

3.4y = -10.2

y = -3.

x = (26 - 3y)/5

x = (26 - 3(-3))/5

x = 7

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The fraction of Juan's shifts with a total sales of $225 or more can be found by looking at the box plot.

We can see that the top line of the box represents the third quartile (Q3) which is the value where 75% of the data falls below.

In this case, Q3 is at approximately $250. This means that 75% of Juan's shifts had total sales less than $250. To find the fraction of shifts with sales of $225 or more, we need to determine how many shifts fall within the range of $225 to $250.

Looking at the box plot, we can see that the distance between Q1 and Q3 (the interquartile range) is approximately $100. Therefore, the distance between Q1 and $225 is approximately one-third of the interquartile range or $33.33. So, any shift with total sales of $225 or more would fall within one-third of the distance between Q1 and Q3.

Therefore, the fraction of Juan's shifts with total sales of $225 or more is approximately one-third of 75%, which is 25%.

In summary, approximately 25% of Juan's shifts at the Bayview community pool had total sales of $225 or more, based on the box plot.

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