a poll of $100$ eighth-grade students was conducted to determine the number of students who had a dog, a cat or a fish. the data showed that $50$ students had a dog, $40$ students had a cat, and $20$ students had a fish. further, $19$ students had only a dog and cat, $2$ students had only a cat and a fish, $3$ students had only a dog and a fish, and $12$ students had only a fish. how many students had none of these pets?

Chloe runs her air conditioner for a total of 4 months, or 120 days. Chloe spends $176.40 per year on utility bills for the air conditioner during the four hottest months.

The reason for this expense is the need for cooling during these months, and the cost associated with running the air conditioner for 7 hours per day at a rate of $0.21 per hour.

To calculate the annual cost of running Chloe's air conditioner, we need to consider the number of hours per day, the cost per hour, and the number of days the air conditioner is used.

1. First, let's determine the total number of hours the air conditioner runs during the four hottest months:
7 hours/day * 30 days/month * 4 months = 840 hours

2. Now, we can calculate the total cost by multiplying the number of hours by the cost per hour:
840 hours * $0.21/hour = $176.40

At 7 hours per day, that's a total of 840 hours of use. At a cost of 21 cents per hour, Chloe spends 0.21 x 840 = $176.40 per year on utility bills for her air conditioner.

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The study aims to investigate whether the presence of popular cartoon characters on food packages affects the food choices of young children aged four to six. The study could be designed as an observational study or an experimental study.

In an observational study, the researchers could observe the children's food choices when presented with food packages with and without popular cartoon characters. The study could be conducted in a naturalistic setting, such as a school cafeteria or a grocery store. However, in an observational study, it may be difficult to control for other factors that could influence children's food choices, such as their previous exposure to the food and their preferences.

In an experimental study, the researchers could randomly assign children to two groups. One group would be presented with food packages with popular cartoon characters, while the other group would be presented with food packages without popular cartoon characters. The researchers could then measure the children's food choices and compare them between the two groups. By randomly assigning children to the groups, the researchers can control for other factors that could influence children's food choices.

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Yes,

It is true that if A is invertible, then det(A⁽⁻¹⁾) = det(A).

The determinant of a matrix and its inverse are closely related.

The determinant of a matrix is nonzero, then the matrix is invertible, and its inverse has the same determinant as the original matrix.

The following properties of determinants:

det(AB) = det(A)det(B) for any square matrices A and B

If A is invertible, then det(A⁽⁻¹⁾) = 1/det(A)

Using these properties, we can write:

det(A⁽⁻¹⁾) = det(A⁽⁻¹⁾)det(AI) = det(A⁽⁻¹⁾A) = det(I) = 1

And:

det(A) = det(AA⁽⁻¹⁾) = det(A)det(A⁽⁻¹⁾)

Multiplying both sides by det(A⁽⁻¹⁾), we get:

det(A)det(A⁽⁻¹⁾) = det(A⁽⁻¹⁾)det(A⁽⁻¹⁾) = det(A⁽⁻¹⁾)det(A)

det(A⁽⁻¹⁾) = det(A).

The determinant of a matrix and its inverse are closely related.

The determinant of a matrix is nonzero, then the matrix is invertible, and its inverse has the same determinant as the original matrix.

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The function f(x) = ab^x is an exponential function.

From the question, we have the following parameters that can be used in our computation:

f(x) = ab^x

As a general rule, and exponential functtion is represented as

f(x) = ab^x

Where

Hence, the function is an exponential function

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Answer:

Part A:

From the box plots, we can see that the Red Team has the least variability and spread of times, followed by the Blue Team and then the Green Team. The Red Team's box is the smallest, indicating that their times are more tightly clustered together.

Part B:

Blue Team:

Q1: 75

Q2: 82

Q3: 87

IQR: 12

Upper fence: Q3 + 1.5IQR = 87 + 1.512 = 105

There are no outliers

Green Team:

Q1: 70

Q2: 75

Q3: 80

IQR: 10

Upper fence: Q3 + 1.5IQR = 80 + 1.510 = 95

There is one outlier at 90

Red Team:

Q1: 80

Q2: 83

Q3: 87

IQR: 7

Upper fence: Q3 + 1.5IQR = 87 + 1.57 = 98.5

There are no outliers

Step-by-step explanation:

N/A

A triangle is a closed figure with three sides, and the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

This is known as the triangle inequality theorem. Using this theorem, we can determine whether the given segments can form a triangle.

In this case, the segments measuring 34 cm, 13 cm, and 38 cm can form a triangle if and only if:

- 34 + 13 > 38
- 34 + 38 > 13
- 13 + 38 > 34

We can simplify these inequalities to:

- 47 > 38
- 72 > 13
- 51 > 34

All of these inequalities are true, so the given segments can form a triangle.

Now, we need to determine how many triangles can be formed using these segments. To do this, we can use the formula:

number of triangles = (n-2)

where n is the number of sides (or segments, in this case). Plugging in n=3, we get:

number of triangles = (3-2) = 1

In conclusion, using the triangle inequality theorem, we determined that the given segments can form a triangle. However, only one triangle can be formed using these segments.

The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case:

1. 34 cm + 13 cm > 38 cm (47 > 38)
2. 34 cm + 38 cm > 13 cm (72 > 13)
3. 13 cm + 38 cm > 34 cm (51 > 34)

Since all three conditions are satisfied, only one triangle can be formed using these segments.

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Step-by-step explanation:

To determine the type of association shown in the scatterplot, we need to plot the data points and examine the trend.

When we plot the data points, we will see that as the length of the string increases, the frequency it creates decreases. This means that there is a negative association between the length of the string and the frequency it creates.

Therefore, the scatterplot will show a negative association.

Step-by-step explanation:

Let's start by setting up the problem. We know that one side of the rectangle is 11 cm, and we'll call the other side x (which is increasing at a rate of 3 cm per minute). The formula for the area of a rectangle is A = l x w, where l is the length and w is the width. In this case, the length is 11 cm and the width is x. So:

A = 11x

To find how fast the area is changing, we need to take the derivative with respect to time (t):

dA/dt = 11(dx/dt)

Now we can plug in the values we know:

x = 26 cm

dx/dt = 3 cm/min

So:

dA/dt = 11(3) = 33 cm^2/min

Therefore, the area of the rectangle is changing at a rate of 33 cm^2/min at the instant when the other side is 26 cm and increasing at a rate of 3 cm per minute.

Ben used wrong the Pythagorean's theorem, the solution that he should have got is x = 2√5

The Pythagorean's theorem says that for a right triangle, the sum of the squares of the cathetus is equal to the square of the hypotenus.

Then the rule that Ben should have written is:

x² + 4² = 6²

So he started wrong.

Solving that we will get:

x = √(6² - 4²) = √20 = 2√5

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The total shelf area of the bookcase is given as follows:

A = 1846.32 in².

The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:

A = πr²

The radius is half the diameter, hence it is given as follows:

r = 14 inches.

There are three shelves, hence the total shelf area of the bookcase is given as follows:

A = 3 x 3.14 x 14²

A = 1846.32 in².

(there are 3 bookcases, hence we obtain the area of one bookcase and then multiply by 3 to obtain the total area).

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Answer:

A = (1/2)(4)(5) + 7(7) + 3(2) = 65 mm^2

The volume of the composite solid, can be found to be C. 22. 53mm ³.

Seeing as this is a composite solid, we can find the volume by finding the volumes of the constituent shapes which are a triangular prism and a cuboid.

Volume of triangular prism :

= 1 / 2 x base x h x l

= 1 / 2 x 2. 1 x 2. 4 x 2. 9

= 7. 308 mm ³

The volume of the cuboid would be:

= Length x height x width

= 2. 1  x 2. 5 x 2. 9

= 15. 225 mm ³

The volume is therefore:

= 15. 225 + 7. 308

= 22. 53 mm ³

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The calculated value of the temperature at 2 hours is -6 °C

From the question, we have the following parameters that can be used in our computation:

This means that we have

Initial value = 0

Rate of change = 3

The equation of the fuction is represented as

f(x) = Initial value - Rate of change * x

Where

x = hours

substitute the known values in the above equation, so, we have the following representation

f(2) = 0 - 3 * 2

Evaluate

f(2) = -6

Hence, the temperature at 2 hours is -6 °C

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The standard deviation of a sample mean is a measure of how much the sample mean varies from the true population mean.

As the sample size increases, the standard deviation of the sample mean decreases. This is because larger samples are more representative of the population and are less likely to contain extreme values that can skew the sample mean.

The decrease in standard deviation is due to the central limit theorem, which states that as sample size increases, the distribution of sample means approaches a normal distribution with a mean equal to the true population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

This means that the standard deviation of the sample mean decreases as the square root of the sample size increases. Therefore, the correct answer to the question is b) decreases as the sample size increases. This is an important concept to understand in statistical analysis, as it affects the precision and accuracy of estimates made from sample data.

A larger sample size generally leads to more reliable and accurate estimates of population parameters. The standard deviation of a sample mean decreases as the sample size increases. As the sample size gets larger, the sample mean becomes a more accurate estimate of the population mean,

And the spread of the sample means around the population mean becomes smaller. This decrease in variability is captured by the standard deviation of the sample mean, which is calculated as the population standard deviation divided by the square root of the sample size. So, the correct answer is option b.

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To represent a 15 yard-gain in football, we can use the integer +15. This means that the team has moved forward 15 yards from their starting point. The meaning of zero in this situation would be that the team did not gain or lose any yards and stayed at their starting point.

Step-by-step explanation:
1. You start at 0 yards (the meaning of zero in this context).
2. You gain 15 yards, which is a positive value (+15).


In both cases, zero serves as the starting point from which gains or losses are measured using positive or negative integers.

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It is true that, Statistically, using z-scores, a group mean can be compared to a population mean to ascertain whether or not the group mean is different from the population mean.

Hypothesis testing is a statistical method for making inferences about a population based on sample data.

It involves formulating a null hypothesis, which is a statement about the population that we want to test, and an alternative hypothesis, which is a statement that contradicts the null hypothesis.

Here we have a statement

Statistically, using z-scores, a group mean can be compared to a population mean to ascertain whether or not the group mean is different from the population mean.

The above statement is true

Z-scores are a measure of the distance between a sample mean and the population mean in standard deviation units.

By using z-scores, we can compare a group mean to a population mean and determine whether the difference is statistically significant.

To do this, we calculate the z-score using the formula:

z = (x - μ) / (σ / sqrt(n))

If the resulting z-score falls in the rejection region of the standard normal distribution, we can reject the null hypothesis that the sample mean is not significantly different from the population mean.

In summary, comparing a group mean to a population mean using z-scores is a common statistical technique to determine whether there is a significant difference between the two means.

Therefore,

It is true that, Statistically, using z-scores, a group mean can be compared to a population mean to ascertain whether or not the group mean is different from the population mean.

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There are six possible arrangements of the letters in the word "mat": "mat", "mta", "am t", "atm", "tam", and "tma". The tree diagram is attached.

To create a tree diagram of all possible arrangements of the letters in the word "MAT," we start with the first letter, which can be either "M," "A," or "T." Then, for each of these possibilities, we add the next letter, and so on until we have included all three letters. The resulting tree diagram shows all possible combinations of the letters in the word "MAT."

There are a total of 6 possible arrangements of the letters in the word "MAT," as we can see from the tree diagram. Out of these 6 arrangements, only one has the letters in the order "M-A-T," which is "MAT." Therefore, the fractional probability of writing the letters in that order is 1/6 or approximately 0.1667.

This means that if we randomly order the letters of "MAT" many times, we can expect to get the letters in the order "M-A-T" about 16.67% of the time.

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Answer: The value of the marginal product of the ninth worker is $400

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The maximum value of f (x, y, z) =  [tex](xyz)^{1/3}[/tex] given that x, y, and z are non- negative numbers and x + y + z = 4 is 4/3

Using arithmetic mean and geometric mean relation

Arithmetic mean is dividing the sum of the values of a set by the number of values in the set

Geometric mean is the nth root of the product of the n values

AM ≥ GM

AM = [tex]\frac{x+y+z}{3}[/tex]

GM = [tex](xyz)^{1/3}[/tex]

[tex]\frac{x+y+z}{3}[/tex] ≥ [tex](xyz)^{1/3}[/tex]

x + y + z = 4

[tex]\frac{4}{3}[/tex] ≥ [tex](xyz)^{1/3}[/tex]

maximum possible value is 4/3

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The median of the triangle is a segment that runs from the vertex of a triangle to the midpoint of the opposing side.

A median is a line segment that extends from a vertex of a triangle to the midpoint of the opposite side. The centroid has several interesting properties. It is always located inside the triangle, and it divides each median into two segments in a 2:1 ratio.  Additionally, the centroid is the center of mass of the triangle, meaning that if the triangle were a physical object with uniform density, it would balance perfectly on the centroid. The centroid is also equidistant from the three vertices of the triangle.

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The definite and indefinite integral are both important concepts in calculus. The indefinite integral represents the antiderivative of a function,

which means finding a function whose derivative is the original function. It is often denoted by the symbol "∫" followed by the function to be integrated. The indefinite integral is not unique, as it can have an arbitrary constant of integration.

On the other hand, the definite integral is the signed area between the curve and the x-axis over a specified interval. It is often denoted by the symbol "∫" with limits of integration at the upper and lower bounds of the interval. The definite integral has a definite value, as it is a single number obtained by evaluating the antiderivative at the limits of integration.

In summary, the indefinite integral is a family of functions while the definite integral is a single number. The indefinite integral is used to solve differential equations while the definite integral is used to calculate the area under a curve. Understanding the difference between these two concepts is crucial for success in calculus.

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The 95% confidence interval for the population mean is (16.426, 26.574

To find the 95% confidence interval, we can use the formula:

Confidence interval = sample mean ± (z-score)*(population standard deviation/√n)

where the z-score for a 95% confidence level is 1.96.

Plugging in the values given in the question, we get:

Confidence interval = 21.5 ± (1.96)*(19.4/√49)

Simplifying this expression, we get:

Confidence interval = 21.5 ± 5.074

Therefore, the 95% confidence interval for the population mean is (16.426, 26.574) as an open-interval.

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The volume of given sphere is 3054 cm³

Given that a sphere with diameter of 18 cm we need to find its volume,

Volume of a sphere = 4/3 × π × radius³

So,

Volume = 4/3 × 3.14 × 9³

= 9156.24 / 3

= 3053.08

≈ 3054 cm³

Hence the volume of given sphere is 3054 cm³

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Answer:

I think 270m

Step-by-step explanation:

450x60=27.000 so 270 m

Yes, it is true that if matrix B is formed by adding to one row of matrix A a linear combination of the other rows, then the determinant of B is equal to the determinant of A.

Proven using elementary row operations are operations that can be performed on the rows of a matrix without changing its determinant.

One such operation is adding a multiple of one row to another row.

A linear combination of the other rows to a particular row of A to form B, we can express this operation as a matrix multiplication:

B = P × A

P is a matrix that represents the elementary row operation.

P is an identity matrix with the (i, j)-th entry equal to 1 if i = j or equal to a constant c if i is the row being modified and j is the row being added to, and 0 otherwise.

Since P is an elementary matrix, it has determinant equal to 1 or -1, depending on whether an odd or even number of row swaps were performed.

Therefore,

det(B) = det(P × A) = det(P) × det(A) = ±det(A)

det(P) is either 1 or -1.

P is formed by adding a linear combination of the other rows to a particular row, we can easily see that P is a triangular matrix with 1's on the diagonal, and thus its determinant is equal to 1.

Therefore, we have

det(B) = det(A)

as claimed.

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The approximate height of kite above the ground will be 150 feet.

The correct answer is an option (b)

Let us assume that in the attached diagram of right triangle the angle A represents the ideal angle to fly a kite and this angle measures 45 degrees.

Here, the hypotenuse of right triangle measures 225 ft

We need to find the height of the kite above the ground.

i.e., we need to find the length of side opposite to angle A.

Let us assume that x represents this height.

We know that in right triangle, the sine of angle θ is nothing but the ratio of opposite side of angle θ to the hypotenuse.

Consider the sine of angle A

sin(A) = opposite side of angle A / hypotenuse

sin(45°) = x / 225

We know that from the standard trigonometric table the value of sin(45°) is [tex]\frac{1}{\sqrt{2} }[/tex]

Substitute this value in above equation we get,

[tex]\frac{1}{\sqrt{2} }[/tex] =  x / 225

We solve this equation to find the value of x.

x =   [tex]\frac{225}{\sqrt{2} }[/tex]

x = 159.09 ft

x ≈ 150 ft

Therefore, the correct answer is an option (b)

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Answer:

D

Step-by-step explanation:

have a good day God bless :)

The graph correctly shows the solution to the problem 4x + 3y ≤ 50 is D. X, Y graph. X range is -30 to 30, and y range is -30 to 30. Solid line on the graph has a negative slope and runs through (-10, 30), (5, 10), and (20, -10). Below the line is shaded.

To examine the points on the graph:

Point (-10, 30): Substituting x = -10 and y = 30 into the inequality: 4(-10) + 3(30) = -40 + 90 = 50 ≤ 50. So, the point satisfies the inequality.

Point (5, 10): Substituting x = 5 and y = 10 into the inequality: 4(5) + 3(10) = 20 + 30 = 50 ≤ 50. The point satisfies the inequality.

Lastly, Point (20, -10): Substituting x = 20 and y = -10 into the inequality: 4(20) + 3(-10) = 80 - 30 = 50 ≤ 50. The point satisfies the inequality.

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Since ABCD is an isosceles trapezoid, we know that AB = CD. Additionally, we know that AD = BC. Therefore, we can set up two equations:

AB = CD

AD = BC

Using the fact that B = x + 10 and C = 2x - 30, we can substitute those values into the equations:

AB = CD

x + 10 + AD = 2x - 30 + BC

Since AD = BC, we can simplify the second equation to:

x + 10 + AD = 2x - 30 + AD

x + 10 = 2x - 30

x = 40

Now that we know x, we can find the measures of angles B and C:

B = x + 10 = 50

C = 2x - 30 = 50

Since ABCD is an isosceles trapezoid, we know that angles B and C are congruent. Therefore, each of them measures 50 degrees. Since the sum of the angles in a quadrilateral is 360 degrees, we can set up the equation:

A + B + C + D = 360

Substituting in the values we have:

A + 50 + 50 + D = 360

Simplifying the equation:

A + D = 260

Since ABCD is an isosceles trapezoid, we know that angles A and D are congruent. Therefore, we can set up the equation:

A + D = 2D

Substituting in the value we have:

2D = 260

Simplifying the equation:

D = 130

Therefore, the measure of angle D is 130 degrees.

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A z-score of 2.14 indicates that Katie's score on the test is quite high and unusual, and places her in the top 2% of the scores in the population.

Katie scored a 93 on a test and her calculated z score was 2.14, that means that her score is 2.14 standard deviations above the mean of the test scores.

A z score represents the number of standard deviations a data point is from the mean of the data set.

A positive z score means that the data point is above the mean, while a negative z score means that the data point is below the mean.

The mean of the test scores was, 80 with a standard deviation of 5, then Katie's z score would be calculated as:

z = (x - μ) / σ

= (93 - 80) / 5

= 2.6

Z scores are useful for comparing data points from different data sets or for comparing data points within the same data set that are measured on different scales.

Katie's score is 2.6 standard deviations above the mean.

A z score of 2.14 would mean that Katie's score is slightly below this value, but still significantly above the mean.

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