Which algebraic expression has a term with a coefficient of 3?A. -2y + 5+3B. 3y + 1C. 5y - 7D. 3(y - 6)

The probability that the household owns a dog given that it owns a cat is 0.5625.

To find the probability that a household owns a dog given that it owns a cat, we can use the concept of conditional probability.

Let's denote the event that a household owns a dog as "D" and the event that a household owns a cat as "C". We are given the following probabilities:

P(D) = 0.40 (probability of owning a dog)

P(C) = 0.32 (probability of owning a cat)

P(D ∩ C) = 0.18 (probability of owning both a dog and a cat)

To find P(D|C), the probability of owning a dog given that a household owns a cat, we can use the formula:

P(D|C) = P(D ∩ C) / P(C)

Substituting the given values:

P(D|C) = 0.18 / 0.32 ≈ 0.5625

Therefore, the probability that a household owns a dog given that it owns a cat is approximately 0.5625 or 56.25%.

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The volume of the conical hole will be 154 cubic feet.

The area a cone takes up in a three-dimensional plane is known as its volume. A cone's base is circular, so it is made of a radius and a diameter.

Given that a cone-shaped hole is 3 feet deep and the circumference of the base of the hole is 44 feet,

The volume of the cone will be calculated as:-

Volume = (1/3)πr²h

The circumference of the cone is,

2πr = 44

2 x ( 22 / 7 ) x r =  44

r = 7 feet

The volume of the cone will be calculated as:-

Volume = (1/3)πr²h

Volume = ( 1 / 3 )  x ( 22 / 7 ) x 7 x 7 x 3

Volume = 22 x 7

Volume = 154 cubic feet

Therefore, the volume will be 154 cubic feet.

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According to the normal distribution, 68% of values should fall in one standard deviation from the mean.

The standard deviation and the mean of the provided data must first be determined.

Below are the standard deviation and mean

Mean = (50 + 46 + 54 + 51 + 29 + 52+ 48 + 54 + 47 + 48)/10

Mean x = 47.9

Standard deviation: √∑(x - x')²/(n - 1)

s = √(50 -  47.9)² + (46 -  47.9)² + (51 -  47.9)² + .....+ (48 -  47.9)²)/(9)

s = 7.20

We possess:

x' ± s = (47.9 ± 7.2)

x' ± s = (40.7, 55.1)

The proportion of values that are within 1 standard deviation of that mean is thus:

9/10 * 100 = 90%.

According to the normal distribution, 68% of values should fall in one standard deviation from the mean.

As a result, the percentage of values seen to be within 1 standard deviation of a mean is significantly larger than the percentage a normal distribution would predict.

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-14 is the value of the expression b - 3a at a =6 and b = 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression b - 3a

For this expression given,

a = 6 and b = 4

Thus the value of expression at given values

=> b - 3a

=> 4 - 3 * 6

=>4 - 18

=> -14

Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.

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Answer:

1)  x = -3 and y = -4

2)  x = 1/4 and y = -2

Step-by-step explanation:

for #2 you can distribute a -2 among the terms in the top equation to get:

-8x - 6y = 10  now add this to the 2nd equation to get:

-2y = 4

y = -2

substitute -2 for 'y' to get 'x' as follows:

8x + 4(-2) = -6

8x + (-8) = -6

8x = 2

x = 2/8 or 1/4

for #1 I multiplied each side by 3 to remove the denominators in each equation to get:

3y = x - 9

3y = -2x - 18

now solve for 'x':  x-9 = -2x-18    because each expression equals '3y'

3x-9 = -18

3x = -9

x = -3

plug -3 for 'x' into this equation to solve for 'y'':  3y = x-9

3y = -3 - 9

3y = -12

y = -4

The inequality representing the number of backpacks, x, that need to be sold each week for the factory to meet the profit goal is:

30x - 12,000 ≥ 980

To represent the situation, we need to consider the revenue and expenses associated with selling backpacks.

Let's break down the components:

Selling price per backpack: $40.00

Cost to make one backpack: $10.00

Operating expenses per week: $12,000.00

Profit goal per week: $980.00

To calculate the profit, we subtract the total cost (including both the cost to make the backpacks and the operating expenses) from the revenue obtained by selling the backpacks. The number of backpacks sold is denoted by 'x.'

Revenue from selling x backpacks: $40.00 × x

Total cost (including operating expenses) for x backpacks: $10.00 ×x + $12,000.00

The profit is given by the difference between revenue and cost:

Profit from selling x backpacks: Revenue - Total Cost

Profit from selling x backpacks: $40.00× x - ($10.00× x + $12,000.00)

To meet the factory's profit goal of at least $980.00, we set up the following inequality:

$40.00× x - ($10.00× x + $12,000.00) ≥ $980.00

Now we simplify the inequality:

$40.00× x - $10.00 × x - $12,000.00 ≥ $980.00

$30.00 × x - $12,000.00 ≥ $980.00

Thus, the inequality representing the number of backpacks, x, that need to be sold each week for the factory to meet the profit goal is:

30x - 12,000 ≥ 980

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Answer:

The answer is the 1

Step-by-step explanation:

She has a less chance because there are 4 questions with 4 answers so that decreased her chances.

The value of the expression -13+√70 to the nearest tenth is -4.6

Arithmetic operations involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

The expression -13+√70 comprises of addition of -13 and √70

The value of √70 is 8.4(to the nearest tenth).

Therefore the value of -13+√70

=-13+8.4

= -4.6( nearest tenth)

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We can substitute this back into the expression for the average value of f:

avg(f) = (1/4) * ∫[2,6

What is the average?

This is the arithmetic mean and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

To find the average value of a function f(x) on a closed interval [a,b], we use the formula:

avg(f) = (1/(b-a)) * ∫[a,b] f(x) dx

where ∫[a,b] f(x) dx denotes the definite integral of f(x) with respect to x over the interval [a,b].

In this case, we are given the function f(x) = 3ln(2+x²)cos(x), and we want to find its average value on the interval 2 ≤ x ≤ 6.

Using the formula above, we have:

avg(f) = (1/(6-2)) * ∫[2,6] 3ln(2+x²)cos(x) dx

= (1/4) * ∫[2,6] 3ln(2+x²)cos(x) dx

We can evaluate this integral using integration by parts:

u = ln(2+x²) dv = 3cos(x) dx

du/dx = (2x)/(2+x²) v = 3sin(x)

Using the formula for integration by parts, we have:

∫ 3ln(2+x²)cos(x) dx = 3ln(2+x²)sin(x) - ∫ (6x/(2+x²))sin(x) dx

Next, we use integration by parts again:

u = (6x)/(2+ x²) dv = sin(x) dx

du/dx = (6 - 6x²)/(2+x²)² v = -cos(x)

Using the formula for integration by parts again, we have:

∫ (6x/(2+x²))sin(x) dx = -(3/2)cos(x) + (3/2) ∫ (6 - 6x^2)/(2+x²)² cos(x) dx

We can simplify this integral by using a substitution:

u = 2 + x²

du/dx = 2x

dx = du/(2x)

Substituting this into the integral and simplifying, we have:

∫ (6 - 6x²)/(2+x²)² cos(x) dx = ∫ (6 - 6u)/(u²) cos(arctan(√(u-2)/2)) du

We can evaluate this integral using integration by substitution:

v = arctan(√(u-2)/2)

dv/du = (1/2) * (1/√(u-2)) * (1/2)

du = 4(u-2)/(u-4)² * dv

Substituting this into the integral and simplifying, we have:

∫ (6 - 6u)/(u²) cos(arctan(√(u-2)/2)) du = -6 arctan(√(u-2)/2) + 3∫ (4/(u-4)) sin(v) dv

= -6 arctan(√(u-2)/2) - 12 ln(u-4) cos(v)

Substituting back for u and v, we have:

∫ (6 - 6x²)/(2+x²)² cos(x) dx = -6 arctan(√(x²+2)/2) - 12 ln(x²) cos(x-arctan(√(x²+2)/2))

Hence, we can substitute this back into the expression for the average value of f:

avg(f) = (1/4) * ∫[2,6

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Answer:

D Reflect across the line y = -3

Step-by-step explanation:

The only way you can divide the trapezoid so that there are two congruent parts is when you draw a line on y=-3.

Answer:

C (u=5)

B ( angle 4)

Step-by-step explanation:

Answer:

-1.3333333333333

Step-by-step explanation:

Answer:

y = x(2.50)+3.25

Step-by-step explanation:

y (total cost )= x (miles rode) * 2.50 (cost per mile) + 3.25 (initial cost)

The empirical probability that a consumer will like this brand of sausage is 0.9 or 90%.

The ratio of the number of times an event occurs to all possible trials is the empirical probability that the event will occur. The occurrence in this instance is comparable to the brand of sausage.

The total number of consumers who tested was 700, and 630 of them rated the sausage favorably. As a result, the empirical likelihood that a customer will enjoy this brand of sausage is:

Empirical Probability = Number of consumers who liked the sausage / Total number of consumers tested

Empirical Probability = 630 / 700

Empirical Probability = 0.9

Therefore, the empirical probability that a consumer will like this brand of sausage is 0.9 or 90%.

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The new limits of integration are from u=0 to u=6sin(6) after the substitution u=6x is applied. The integral evaluates to (1/6)[cos(6sin(6))+1].

Let us assume the substitution u = 6x.

First, we need to find the new limits of integration by substituting u=6x into the original limits of integration:

When x=0, u=6(0) = 0.

When x=sin(6), u=6sin(6).

Therefore, the new limits of integration are from u=0 to u=6sin(6).

Next, we need to express the integral in terms of u by substituting x back in terms of u:

When x=0, u=6(0) = 0, so x=u/6.

When x=sin(6), u=6sin(6), so x=u/6.

Therefore, we have:

∫0sin(6) dx = (1/6) ∫0⁶ sin(6u/6) du

Simplifying, we get:

(1/6) ∫0⁶ sin(u) du

which evaluates to:

(1/6) [-cos(u)] from 0 to 6sin(6)

Plugging in the limits of integration, we get:

(1/6) [-cos(6sin(6)) + cos(0)]

which simplifies to:

(1/6) [-cos(6sin(6)) + 1]

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The new limits of integration are from u=0 to u=6sin(6) after the substitution u=6x is applied. The integral evaluates to (1/6)[cos(6sin(6))+1].

Let us assume the substitution u = 6x.

First, we need to find the new limits of integration by substituting u=6x into the original limits of integration:

When x=0, u=6(0) = 0.

When x=sin(6), u=6sin(6).

Therefore, the new limits of integration are from u=0 to u=6sin(6).

Next, we need to express the integral in terms of u by substituting x back in terms of u:

When x=0, u=6(0) = 0, so x=u/6.

When x=sin(6), u=6sin(6), so x=u/6.

Therefore, we have:

∫0sin(6) dx = (1/6) ∫0⁶ sin(6u/6) du

Simplifying, we get:

(1/6) ∫0⁶ sin(u) du

which evaluates to:

(1/6) [-cos(u)] from 0 to 6sin(6)

Plugging in the limits of integration, we get:

(1/6) [-cos(6sin(6)) + cos(0)]

which simplifies to:

(1/6) [-cos(6sin(6)) + 1]

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Answer: 8 short response questions and 12 multiple choice questions

Step-by-step explanation:

Let m represent multiple choice questions

Let s represent short response questions

m + s = 20 --> Amount of questions

3 m + 8 s = 100 --> Total number of points for each question

Solve using elimination, multiply the first equation by -3

-3m-3s=-60

3 m + 8 s = 100

----------------------

5s=40

s=8

m+8=20

m=20-8

m=12

Therefore, there are 8 short response questions and 12 multiple choice questions

The angle 1 can be named as follows:

∠RST

∠TSR

∠S

There are various ways to name an angles. You can name an angle by its vertex, by the three points of the angle (the middle point must be the vertex), or by a letter or number written within the opening of the angle.

Therefore, let's name the angle 1 indicated on the diagram as follows:

Hence, the different ways to name the angle 1 is as follows:

∠RST or ∠TSR

Or

∠S

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Answer:

Step-by-step explanation:

56.1,12.1,23.6

Therefore, the discount factor for one period with a rate of return of 6 percent is approximately 0.9434.

To calculate the discount factor for one period with a rate of return equal to 6 percent, you can use the formula:

Discount Factor = 1 / (1 + Rate of Return)

Substituting the rate of return of 6 percent (0.06) into the formula:

Discount Factor = 1 / (1 + 0.06) = 1 / 1.06 ≈ 0.9434

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The finite correction factor is used in the calculation of standard deviation when the ratio of sample size to population size is less than 0.05. For ratios greater than or equal to 0.05, the finite correction factor is not necessary.

When calculating the standard deviation of the sample mean or the standard deviation of a population, the finite correction factor is used to adjust for potential biases that can arise when the sample size is relatively large compared to the population size.

The finite correction factor takes into account the impact of sampling without replacement, meaning that once an item is selected from the population for inclusion in the sample, it cannot be selected again. This can introduce some degree of variability in the sample statistics, especially when the sample size is a large proportion of the population.

The general rule of thumb is that if the ratio of the sample size (n) to the population size (N) is less than 0.05 (or equivalently, n/N < 0.05), the finite correction factor should be applied. This suggests that the sample is small enough compared to the population that the impact of sampling without replacement is negligible.

On the other hand, if the ratio of n/N is greater than or equal to 0.05 (or n/N ≥ 0.05), the finite correction factor can be safely ignored because the sample size is relatively large compared to the population, and the impact of sampling without replacement is considered minimal.

In summary, the finite correction factor should be used when n/N < 0.05, and the correct answer to the initial question is option a. less than 0.05.

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Answer:

0.15

Step-by-step explanation:

Multiply 30 by 0.005 to get the number which is 0.15 in which 0.15 is 0.5% of 30.

a) Any value outside of Q1 - 1.5(IQR) and Q3 + 1.5(IQR) can be considered a potential outlier.

b) This will give us a visual representation of the distribution of income among the full-time students.

c) It is important to analyze outliers carefully to ensure that they are not artificially skewing the results of our analysis.

(a) To check for outliers in the data set, we can use the box-and-whisker plot or the z-score method. However, since we do not have the exact data, we cannot use these methods. One way to identify potential outliers is to calculate the quartiles (Q1, Q2, and Q3) and the interquartile range (IQR).

(b) To draw a histogram of the data, we can use the frequency distribution table given in the question. The x-axis should represent the income ranges (e.g. $0-$100, $100-$200, etc.) and the y-axis should represent the frequency (i.e. the number of students who earned income within each range).

(c) If there are any outliers in the data set, we need to investigate them further to determine the reason for their unusual values. Possible reasons for outliers could be data entry errors, extreme values due to high- or low-income jobs, or unique situations such as unexpected windfalls or emergencies.

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Answer:

392 min

Step-by-step explanation:

convert to seconds every turn:

60(3) + 16 = 180 + 16 = 196 seconds

multiply the number of laps by this time:

\(120(196)=23520\) seconds

Equivalent to:

\(\frac{23520}{60} =392\) minutes

or:

6 hours 32 minutes

Hope this helps

Answer:

Step-by-step explanation:

Sandra, Deacon, and Breanna read a total of 5 + 6 + 7 = 18 books. Since one book was read by all three children, we need to subtract it once from the total. Therefore, they read 18 - 1 = 17 different books.

Sara needed 8 test tubes for 3 different experiments. The first experiment required 2 test tubes, leaving 8 - 2 = 6 test tubes for the other two experiments. Since the two experiments required the same number of test tubes, each one required 6/2 = 3 test tubes.

It is unclear what the question is asking. Please provide more information or a specific question.

Branson and his sister Beatrice combined their allowance of $7 each to buy a movie for $12. They spent a total of 7 x 2 = $14 on the movie. Therefore, they had 14 - 12 = $2 left to buy fruit salad. They bought 2 containers of fruit salad for $1 each, leaving them with $0. They split the containers evenly between them, so each of them got 2/2 = 1 container of fruit salad.

Before Cam broke his right arm, he could type 9 words per minute on his phone. After he broke his arm, he could only type 6 words per minute. The difference between the number of words he could type in 5 minutes before and after he broke his arm is 5 x (9 - 6) = 5 x 3 = 15 words.

Gisselle saved $6 every week for 8 weeks, so she saved a total of 6 x 8 = $48. She found a used bicycle for $50, so she did not have exactly enough for the bicycle. She was $50 - $48 = $2 short.

Answer:

244 if the difference

Step-by-step explanation:

Answer:

180º Fahrenheit

Answer:

y = 4x - 2

Step-by-step explanation:

m = y-y/x-x

m = 6-(-2)/2-0

m = 8/2

m = 4

Answer:

y=4x-2

Step-by-step explanation:

Answer:

WX

Step-by-step explanation:

The distance between vertex X and vertex W is much smaller then from X to Y or W to Y.

To find the value of j - i, we need to determine the relationship between the surface areas (An) and volumes (Vn) of the unit ball in Rn for different positive integers n.

For the unit ball in Rn, the formula for surface area (An) and volume (Vn) are given by:

An = (2 * π^(n/2)) / Γ(n/2)

Vn = (π^(n/2)) / Γ((n/2) + 1)

where Γ denotes the gamma function.

To find the value of j - i, we need to identify the positive integers i and j such that Ai > Ak for all k not equal to i, and Vj > Vk for all k not equal to j.

First, let's analyze the relationship between An and Vn. By comparing the formulas, we can see that:

An / Vn = [(2 * π^(n/2)) / Γ(n/2)] / [(π^(n/2)) / Γ((n/2) + 1)]

      = 2 / [n * (n-1)]

From this equation, we can deduce that An / Vn > 1 if and only if 2 > n * (n-1).

To find the positive integer i, we need to identify the highest positive integer n for which 2 > n * (n-1) holds true. We can observe that this condition is satisfied for n = 2. Therefore, i = 2.

Now, let's find the positive integer j. We need to identify the lowest positive integer n for which 2 > n * (n-1) does not hold true. We can observe that this condition is no longer satisfied for n = 3. Therefore, j = 3.

Finally, we can calculate j - i as follows:

j - i = 3 - 2 = 1

Therefore, j - i equals 1.

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