A major car manufacturer wants to test a new engine to determine if it meets new air pollution standards. Safety regulations require that the mean emission of all engines of this type must be no greater than 20 parts per million (ppm) of carbon. If it is higher than that, they will have to redesign parts of the engine. A random sample of 25 engines is tested and the emission level of each is determined. The sample mean is calculated to be 20. 4 ppm and the sample standard deviation is calculated to be 2. 0 ppm. It is known that emission levels are normally distributed with standard deviation 1. 6 ppm. We would like to test whether the true mean emission level for the new engine is greater than 20 ppm. The test statistic for the appropriate test of significance is: ________

The correlation between the number of points scored by the basketball team and the weeks of the season is likely negative.

However, without seeing the actual data, it is difficult to determine the exact correlation. As for the coach's statement, it could be either correct or incorrect depending on the actual data. Based on the given information, the basketball coach's observation suggests a negative correlation between the number of weeks into the season and the points scored by his team. Without the actual data, it is impossible to determine if his observation is correct or incorrect.

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The constant hourly rate using the given data points is  $100 per hour.

To calculate the constant hourly rate, we can use the given data points. For example, let's use the 5-hour rental for $500:

Hourly rate = Total cost / Number of hours
Hourly rate = $500 / 5 hours
Hourly rate = $100 per hour

Now, we can use this hourly rate to find the cost for the missing hour value in the table:

Cost = Hourly rate × Number of hours
Cost = $100 per hour × 9 hours
Cost = $900

So, the table will look like this:

Hours: _______ 5   |   9   |   _______
Cost (in dollars): 500 | 1,250 | 3,500

Now we can calculate the missing hours for the $3,500 cost:

Number of hours = Total cost / Hourly rate
Number of hours = $3,500 / $100 per hour
Number of hours = 35 hours

Now, the completed table is:

Hours: _______ 5   |   9   |   35
Cost (in dollars): 500 | 1,250 | 3,500

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There were 490 walkers at the 10k fund-raiser.

The ratio of runners to walkers is 5:7, that means that the every five runners, there are 7 walkers so therefore we will use ratio formula.

If there have been 350 runners, we can use this ratio to discover what number of walkers there were:

5/7 = 350/x

Where x is the number of walkers.

To solve for x, we will cross-multiply:

5x = 7 * 350

5x = 2450

x = 490

Consequently, there were 490 walkers at the 10k fund-raiser.

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The carbon dioxide level in the atmosphere is modeled using two possible derivative functions. Using Model I, the level in 2050 is approximately 426.25 ppm, and using Model II, it is approximately 522.73 ppm.

Using Model I

We need to integrate the derivative function C'(t) = 0.5 + 0.025t to get C(t).

∫C'(t) dt = ∫0.5 + 0.025t dt

C(t) = 0.5t + (0.025/2)t^2 + C

Using the initial condition that C(0) = 370, we get

370 = 0 + 0 + C

C = 370

So, C(t) = 0.5t + (0.025/2)t^2 + 370

To find the carbon dioxide level in 2050 using Model I

C(50) = 0.5(50) + (0.025/2)(50)^2 + 370

C(50) = 25 + 31.25 + 370

C(50) = 426.25 ppm

Using Model II

We need to integrate the derivative function C'(t) = 0.5e^(0.025t) to get C(t).

∫C'(t) dt = ∫0.5e^(0.025t) dt

C(t) = (20e^(0.025t))/ln(10) + C

Using the initial condition that C(0) = 370, we get

370 = (20e^(0))/ln(10) + C

C = 370 - (20/ln(10))

So, C(t) = (20e^(0.025t))/ln(10) + (370 - (20/ln(10)))

To find the carbon dioxide level in 2050 using Model II

C(50) = (20e^(0.025(50)))/ln(10) + (370 - (20/ln(10)))

C(50) = 522.73 ppm (rounded to two decimal places)

Therefore, the carbon dioxide level in 2050 is approximately 426.25 ppm using Model I, and approximately 522.73 ppm using Model II.

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The length of the hypotenuse is approximately 7.21 ft.

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse). In mathematical terms, it looks like this:

a² + b² = c²

Where "a" and "b" are the lengths of the legs, and "c" is the length of the hypotenuse.

In your case, we can substitute the given values into the equation:

6² + 4² = c²

Simplifying:

36 + 16 = c²

52 = c²

To solve for "c," we need to take the square root of both sides of the equation:

√(52) = c

We can simplify the square root of 52 to be 2 times the square root of 13. Therefore:

c ≈ 7.21 ft

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Complete Question:

Find the value of hypotenuse of the given triangle by using the Pythagoras theorem.

Any measurement below 435 inches qualifies as a value less than 435 inches.

To find measurements less than 435 inches, you simply need to consider any value below 435 inches. Here's a step-by-step explanation:

1. Understand the question: You are looking for measurements less than 435 inches.
2. Identify the range: The range includes all values below 435 inches.
3. Provide examples: Examples of measurements less than 435 inches can be 400 inches, 350 inches, 250 inches, 100 inches, and so on.

Remember, any measurement below 435 inches qualifies as a value less than 435 inches.

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Hi! To find the area of the similar polygon after finding the area of the first polygon and the similarity ratio, follow these steps:

1. Find the dimensions of the first polygon.
2. Calculate the area of the first polygon using the dimensions.
3. Determine the similarity ratio between the first polygon and the similar polygon.
4. Use the similarity ratio to find the corresponding dimensions of the similar polygon.
5. Calculate the area of the similar polygon using the new dimensions.

In your answer: After finding the area from the dimensions of the first polygon, find the area of the similar polygon by determining the similarity ratio and using it to calculate the corresponding dimensions of the similar polygon. Then, calculate the area of the similar polygon using the new dimensions.

To find the area of the similar polygon, you'll need to use the similarity ratio, which compares the corresponding lengths of the sides of two similar figures. Once you have the similarity ratio, you can multiply the area of the first polygon by the ratio squared to get the area of the similar polygon.

Remember, the area of a polygon is found by multiplying the base by the height (or using another appropriate formula depending on the shape of the polygon). So, to summarize, you would first find the area of the first polygon using its dimensions, then use the similarity ratio to find the corresponding sides of the similar polygon, and finally use these sides to find the area of the similar polygon.

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The probability that Nguyen will choose a can of chicken noodle soup is 1/3. Therefore, the correct option is B.

To find the probability, you need to divide the number of favorable outcomes (chicken noodle soup cans) by the total number of possible outcomes (total cans of soup). Hence,

1. Count the total number of cans of soup: 4 chicken noodle + 2 tomato + 3 vegetable + 3 potato = 12 cans in total.

2. Count the number of chicken noodle soup cans: 4 cans.

3. Divide the number of chicken noodle soup cans (4) by the total number of cans (12): 4/12.

4. Simplify the fraction: 4/12 can be simplified to 1/3.

Therefore, the probability of choosing a chicken noodle soup is option B: 1/3.

Note: The question is incomplete. The complete question probably is: Nguyen has the following cans of soup in his pantry: 4 cans of chicken noodle soup; 2 cans of tomato soup; 3 cans of vegetable soup; 3 cans of potato soup. He randomly chooses a can of soup for lunch. What is the probability that he will choose chicken noodle soup? a. ½ b. 1/3 c. 1/6 d. ¼.

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The values of the variables are:

c = 86 degrees

d = 168 degrees

a = 57 degrees

b = 94 degrees

Since the polygon is inscribed in a circle, the opposite angles of the polygon are supplementary. Thus, we have:

The top and bottom angles of the polygon are supplementary to angle "d":

c + 92 + 123 = 180 + d

The left and right angles of the polygon are supplementary to angle "c":

c + 94 = 180, so c = 86

The angle "a" is supplementary to angle "d":

a + 123 = 180 + d

The angle "b" is supplementary to angle "c":

b + 86 = 180

Substituting the values of "c" and solving the system of equations, we get:

d = 168

a = 57

b = 94

Therefore, the values of the variables are:

c = 86 degrees

d = 168 degrees

a = 57 degrees

b = 94 degrees

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The answer is (C) 67.20.

Charlie saved 30% off of the original price, which means he paid 70% of the original price.

Let x be the sale price of the skateboard.

We have:

0.7 * 96 = x

x = 67.20

Therefore, the sale price of the skateboard was $67.20.

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1 is linear variation and 2 is direct proportionality. In 1 it is linear variation since from the beginning the zeros do not correspond and in 2 if the zeros correspond.

Variation refers to the differences that exist among individuals or groups within a population. These differences can be genetic, environmental, or a combination of both, and can manifest in various traits, such as physical characteristics, behavior, or disease susceptibility.

Genetic variation arises from differences in the DNA sequence among individuals, which can result in different traits being expressed. This variation can occur naturally or be induced by mutations, genetic recombination, or genetic drift. Environmental variation arises from differences in the conditions experienced by individuals or groups, such as differences in climate, nutrition, or exposure to toxins. Environmental variation can also interact with genetic variation to produce complex traits.

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Complete Question:-

Look at the following tables and analyze the values ​​they contain. Then, pose a problem that can be solved with these data, also argue why one table corresponds to linear variation and the other to direct proportional variation.​

TABLE 1:

X 0 1 2 3

and 2 17 32 47

TABLE 2:

X 0 1 2 3

AND 0 15 30 45​

The weight of Harry Skyes on Mercury is 32.8 kg, under the condition that Mercury's gravity = 3. 70 m/s².

The weight of astronaut Harry Skyes on Mercury can be evaluated using the formula:

Weight on Mercury = (Weight on Earth / 9.81 m/s²) × 3.7 m/s²

Given that Harry Skyes has a mass of approximately 85.0 kg, his weight on Mercury would be:

Weight on Mercury = (85.0 kg / 9.81 m/s²) × 3.7 m/s²

Weight on Mercury = 32.8 kg

Gravity affects weight severely and causes its change . Objects have mass, which is specified as how much matter an object contains. Weight is known as the pull of gravity on mass. The relation between weight and gravitational pull is such that, when on another celestial body, the difference in gravity would alter a person’s weight.

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Applying the Equidistant Chords Theorem, the value of x in the circle given above is calculated as: b. 50.

The Equidistant Chords Theorem states that If two chords in a circle, or in congruent circles, are equally distant from the center, then the chords are congruent.

The image given reveals that the two chords are equidistant from the center of the circle, therefore:

x = 2(25)

x = 50.

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Answer:

The Fourier series of a periodic function f(x) with period 2L can be expressed as:

f(x) = a0/2 + Σ[n=1 to ∞] (ancos(nπx/L) + bnsin(nπx/L))

where

a0 = (1/L) ∫[-L,L] f(x) dx

an = (1/L) ∫[-L,L] f(x)*cos(nπx/L) dx

bn = (1/L) ∫[-L,L] f(x)*sin(nπx/L) dx

In this case, we have f(x) = 1 for 2k - 0.25 <= x <= 2k + 0.25, and f(x) = 0 otherwise. The period is 0.5, so L = 0.25.

First, we can find the value of a0:

a0 = (1/0.5) ∫[-0.25,0.25] 1 dx = 1

Next, we can find the values of an and bn:

an = (1/0.5) ∫[-0.25,0.25] 1*cos(nπx/0.25) dx = 0

bn = (1/0.5) ∫[-0.25,0.25] 1*sin(nπx/0.25) dx

Since the integrand is odd, we have:

bn = (2/0.5) ∫[0,0.25] 1*sin(nπx/0.25) dx

Using the substitution u = nπx/0.25, du/dx = nπ/0.25, dx = 0.25du/(nπ), we get:

bn = (4/nπ) ∫[0,nπ/4] sin(u) du = (4/nπ) (1 - cos(nπ/4))

Therefore, the Fourier series of f(x) can be written as:

f(x) = 1/2 + Σ[n=1 to ∞] [(4/nπ) (1 - cos(nπ/4))] * sin(nπx/0.25)

for 2k - 0.25 <= x <= 2k + 0.25, and f(x) = 0 otherwise.

The correct expression to use to find how many meters it is from Washington, D.C., to Baltimore is:

C. 57 x 1,000.

An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.

In the given question,

The correct expression to use to find how many meters it is from Washington, D.C., to Baltimore is:

C. 57 x 1,000

Since 1 km equals 1,000 meters, we can convert the distance of 57 km to meters by multiplying it by 1,000. This gives us:

57 km x 1,000 meters/km = 57,000 meters

Therefore, the distance from Washington, D.C., to Baltimore is 57,000 meters.

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Answer:

The answer for x is 2

z is 100°

Step-by-step explanation:

80=6x+68

6x=80-68

6x=12

divide both sides by 6

6x/6=12/6

x=2

z=?(empty space)

?(empty space)=z

80+z+z+6x+68=360

Note:6x+68=80

80+80+2z=360

160+2z=360

2z=360-160

2z=200

divide both sides by 2

2z/2=200/2

z=100°

The weight of the component is of length of 12 feet, a width of 13. 5 feet, and a height of 15 feet, and weighs on average 0. 47 pounds per cubic foot is 1142 lbs.

To find the weight of the contents in the container, we need to first find the volume of the container.

The formula for the volume of a right rectangular prism is length x width x height.

So, the volume of the container is:
12 ft x 13.5 ft x 15 ft = 2430 cubic feet

Next, we need to multiply the volume by the weight per cubic foot:
2430 cubic feet x 0.47 lbs/cubic foot = 1141.1 lbs

Rounding to the nearest pound, the weight of the contents in the container is approximately 1142 lbs.

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The equation of the line that is parallel to the graph of 2x-3y=7 and contains the point (-3, -3) is expressed as: y = (2/3)x - 1.

To find the equation of a line that is parallel to the graph of 2x - 3y = 7, we need to determine the slope of the given line. We can rewrite the equation in slope-intercept form:

2x - 3y = 7

-3y = -2x + 7

y = (2/3)x - 7/3

This implies that the slope of this line is m = 2/3.

Thus, the equation of the line we are to find will take the following form:

y = (2/3)x + b

where b is the y-intercept of the line.

To find the y-intercept (b), substitute (x, y) = (-3, -3) and m = 2/3 into y = mx + b:

-3 = (2/3)(-3) + b

-3 = -2 + b

b = -1

Substitute m = 2/3 and b = -1 into y = mx + b:

y = (2/3)x - 1

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The coordinates of the other trees that must also be on the boundary are (-5, 12), (5, -12), (-5, -12), (12, 5), (12, -5), (-12, 5), and (-12, -5).

The coordinates of the other trees that must be on the boundary of the circular orchard, given that the tree at (5, 12) is on the boundary and the center of the orchard is at (0, 0) can be determined as follows.

1. Calculate the radius of the orchard using the distance formula:

sqrt((x2-x1)^2 + (y2-y1)^2).

In this case, (x1, y1) = (0, 0) and (x2, y2) = (5, 12).

2. Radius = sqrt((5-0)^2 + (12-0)^2) = sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13.

Now, we know the radius of the orchard is 13. To find the other boundary points, we can use the property of circles that states that the points on the boundary are equidistant from the center.

Since the coordinates are integers and symmetric, we can list the other points as follows:

3. The coordinates of the other trees on the boundary are:

(-5, 12), (5, -12), (-5, -12), (12, 5), (12, -5), (-12, 5), and (-12, -5).

These points are also 13 units away from the center, making them equidistant from the center and thus on the boundary of the circular orchard.

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Answer:

Step-by-step explanation:

We can simplify the fractions first:

(3r + 9)(r+6) / (r+6) = 3r + 9

6r + 3 / (r + 6) = 3(2r + 1) / (r + 6)

(r^2 + 9r + 18) / (2r + 1) = (r^2 + 6r + 3r + 18) / (2r + 1) = [(r+3)(r+6)] / (2r + 1)

So the expression becomes:

[3(2r + 1) / (r + 6)] * [(r+3)(r+6) / (2r + 1)]

We can now cancel out the common factors:

[3 * (r+3)] = 3r + 9

Therefore, the simplified product is:

(3r + 9)(r+6) / (r+6) = 3r + 9

To find the derivative of sin(y²)+x=eʸ using implicit differentiation, we need to differentiate both sides of the equation with respect to x.

Starting with the left side, we use the chain rule and the derivative of sin(u), which is cos(u) times the derivative of u with respect to x:

d/dx(sin(y²)) = cos(y²) * d/dx(y²)

Using the power rule, we get:

d/dx(y²) = 2y * d/dx(y)

Putting it all together:

d/dx(sin(y²)) = 2y * cos(y²) * d/dx(y)

Now let's move on to the right side of the equation. The derivative of implicit function eʸ with respect to x is simply eʸ times the derivative of y with respect to x:

d/dx(eʸ) = eʸ * d/dx(y)

Putting it all together, we have:

2y * cos(y²) * d/dx(y) + 1 = eʸ * d/dx(y)

We can now solve for d/dx(y):

d/dx(y) = (1 - 2y * cos(y²)) / eʸ

Therefore, the derivative of sin(y²)+x=eʸ is:

d/dx(y) = (1 - 2y * cos(y²)) / eʸ.

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The statement that must be true is the original prices of the refrigerator and the stove were the same. So the answer is option B.

Let x represent the original cost of the refrigerator and y represent the original cost of the stove. The refrigerator's sale price is 0.6x (40% off means paying 60% of the original price), while the stove's sale price is 0.8y (20% off means paying 80% of the original price).

To get the overall discount, multiply the total cost after the discount by the original total cost:

(0.6x + 0.8y) / (x + y)

We want this fraction to equal 0.7 (or 30% off), so we can set up the equation:

(0.6x + 0.8y) / (x + y) = 0.7

Simplifying this equation, we get:

0.6x + 0.8y = 0.7(x + y)

0.6x + 0.8y = 0.7x + 0.7y

0.1x = 0.1y

x = y

Therefore, the statement that must be true to conclude that Alfonso received a 30% overall discount on the refrigerator and stove together is: The original prices of the refrigerator and the stove were the same.

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The best estimate of the charge Zachary will later find on his credit card statement is $20

The formula to be used is -

Amount in USD = Amount of MYR/Value of one MYR

As, 3.04 MYR is 1 USD performing money conversion of 58 MYR

So, 58 MYR will be = 58/3.04

Divide the values in Right Hand Side of the equation to find the value of MYR in USD

Value in USD = $19.07

Hence, the credit card statement will reflect usage of $20 (since it is the closes correct option and we have been asked the best estimate).

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The inequalities in the given options are: B) t > 0, C) 3 < a, E) k < -5/7, The correct option is B,C,E.

B) t > 0: This represents an inequality because the symbol ">" indicates "greater than." It states that the variable "t" is greater than zero. In other words, it means that "t" has to be a positive number and cannot be zero or negative.

C) 3 < a: This represents an inequality because the symbol "<" indicates "less than." It states that the number 3 is less than the variable "a." In other words, it means that "a" has to be greater than 3 for the inequality to hold true.

E) k < -5/7: This represents an inequality because the symbol "<" indicates "less than." It states that the variable "k" is less than -5/7. In other words, it means that "k" has to be a value smaller than -5/7 for the inequality to be true.

The other options, such as -3 = y, g = 5 and one-half, and x = 1, do not represent inequalities because they either show an equation (equality) or simply assign values to variables without any comparison.

Therefore the correct option is B,C,E.

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The estimated contribution for Rosemary's first-year college fee is $6,500 including all her savings and available funds.

Savings of Rosemary = $2,500

Savings from bond = $1000

To calculate the contribution needed for Rosemary from other sources, to pay her college fee, we need to add all the available funds and subtract the money for her college fee.

Let us imagine that the total cost of Rosemary's college = $10,000

Total available funds = $2,500  + $1,000

Total available funds = $3500

The remaining amount needed = $10,000 - $3,500 = $6,500

Therefore, we can conclude that Rosemary would need an estimated contribution of $6,500.

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The unit rate for planting is 1 1/6 acres per day.

To find the unit rate, we need to divide the total area planted by the number of days taken to plant it. We can convert the mixed number of days to an improper fraction by multiplying the whole number by the denominator and adding the numerator.

Therefore, 4 1/2 days can be converted to 9/2 days.

Now we can divide the total area of 5 1/4 acres by the number of days it took to plant it, which is 9/2 days. To divide fractions, we invert the second fraction and multiply, so:

5 1/4 ÷ 9/2 = 21/4 ÷ 9/2 = 21/4 x 2/9 = 42/36

We can simplify 42/36 by dividing both the numerator and denominator by their greatest common factor, which is 6.

42/36 = 7/6

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Check the picture below.

a. The probability that exactly 90 people say they use the Internet is 0.0391

b. The probability that at least 90 people say they use the Internet is 0.1933

c. The probability that fewer than 90 people say they use the Internet is 0.8067

d. The first probability is unusual

(a) Find the probability that exactly 90 people say they use the Internet.

P(X = 90) = C(100, 90) * (0.93)^90 * (0.07)^10

P(X = 90) ≈ 0.0391

(b) Find the probability that at least 90 people say they use the Internet.

P(X ≥ 90) = P(X = 90) + P(X = 91) + ... + P(X = 100)

To calculate this, we can use cumulative binomial probability:

P(X ≥ 90) ≈ 1 - P(X ≤ 89) ≈ 1 - 0.8067 = 0.1933

(c) Find the probability that fewer than 90 people say they use the Internet.

P(X < 90) = P(X ≤ 89)

P(X < 90) ≈ 0.8067

(d) Are any of the probabilities in parts (a)-(c) unusual? Explain.

A probability is generally considered unusual if it is less than 0.05 or greater than 0.95. Based on the calculated probabilities:

P(X = 90) ≈ 0.0391: This probability is unusual since it is less than 0.05.

P(X ≥ 90) ≈ 0.1933: This probability is not unusual.

P(X < 90) ≈ 0.8067: This probability is not unusual.

So, only the probability of exactly 90 people saying they use the Internet is considered unusual.

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Lindsey can put together 27 different outfits if she has 3 tops, 3 bottoms, and 3 scarves to choose from. The answer is (D) 27 outfits.

To find the number of different outfits that Lindsey can put together, we need to use the counting principle, which states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things together.

In this case, there are 3 ways for Lindsey to choose a top, 3 ways to choose a bottom, and 3 ways to choose a scarf. To find the total number of outfits, we multiply these numbers together:

Total number of outfits = number of tops x number of bottoms x number of scarves

Total number of outfits = 3 x 3 x 3

Total number of outfits = 27

Therefore, Lindsey can put together 27 different outfits if she has 3 tops, 3 bottoms, and 3 scarves to choose from. The answer is (D) 27 outfits.

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