8 True or False: The substitution method is a method of solving systems of equations by adding equations together in such a way that the variables are set aside, one by one.

The difference between the population means - 3.4 and -1.84 when calculated is found to be -2.62 years.

The 95% confidence interval for the difference in true mean ages of cars owned by students and faculty is between -3.4 and -1.84 years.

We know that the sample of 138 cars which belongs to the students have an average age of 5.13 years. The standard deviation = 3.45 years.

Then again,

A sample of 111 cars which belongs to the faculty have an average age of 7.75 years.  The standard deviation= 2.08 years.

So the difference between them will be , s - f

= 3.45 - 2.08 = 1. 37

and the mean will be , mean of students - mean of faculty =

-2.62.

This is the point of difference between their means.

The SD is found to be as 0.3961.

and MOE is 0.78

with these details now we will calculate the required intervals,

The lower end is found to be as  -2.62 - 0.78 = -3.4

The upper end is found to be as  -2.62 + 0.78 = -1.84

Therefore, the mean difference between the cars is - 3.4 and -1.84.

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Answer:

True, explanation, lets hope I had a good math teacher lol

An inequality that can be written in the form ax + by < c (where a and b are not both zero) is called a linear inequality in two variables.

An inequality that represents a line in a two-dimensional coordinate system is referred to as a linear inequality. The set of points that satisfies the inequality is a half-plane bounded by a line that may be dashed or solid.

In contrast to a linear equation, which represents a line, a linear inequality represents a half-plane. The points on one side of the line, rather than the points on the line, are solutions to the inequality.

The method of shading is used to graph a linear inequality in two variables. First, graph the boundary line, which is usually represented by a solid or dashed line, and then select a test point on one side of the line. Shaded regions of the half-plane containing the test point satisfy the inequality.

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x is the unknown remaining edge of the base.

Using Pythagoras theorem in the base, we have:

\(8 {}^{2} + x {}^{2} = 10 {}^{2} \)

\( = > \: x = \sqrt{10 {}^{2} - 8 {}^{2} } = 6\)

with x = 6, the perimeter of the base is 10 + 8 + 6 = 24

Answer:

Step-by-step explanation:

There is no picture so I can’t answer

Answer and Step-by-step explanation:

24 goes into 171

7 times, with a remainder of 3.

24 times 7 is equal to 168.

171 minus 168 is 3.

So, 7 is the maximum amount of times 24 (whole number) can go into 171.

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The doctor will use 960 minutes on the patients before it is your turn.

If there are 8 patients before you and the doctor says you have to wait 2 hours for your turn, we need to calculate the total time the doctor will spend with all the patients before you.

Since there are 60 minutes in an hour, 2 hours would be equal to 2 * 60 = 120 minutes.

To find the total time the doctor will use on the patients, we need to multiply the number of patients by the time per patient. In this case, there are 8 patients before you, so:

Total time = Number of patients * Time per patient

= 8 * 120

= 960 minutes

It's important to note that this calculation assumes equal time spent with each patient. In reality, the time spent with each patient may vary depending on their medical needs and the complexity of their cases.

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The pizza restaurant uses 858 individual toppings. A pizza restaurant advertises 286 different 3-topping pizzas. To find out the total number of individual toppings used in the restaurant, we can multiply the number of pizza variations by the number of toppings per pizza.

Each pizza has three toppings. Therefore, the number of individual toppings per pizza is 3.To find out how many individual toppings are used in the restaurant, we multiply the number of pizzas by the number of individual toppings per pizza as follows:286 (different pizzas) × 3 (toppings per pizza) = 858Therefore, the pizza restaurant uses 858 individual toppings.

A pizza restaurant advertises 286 different 3-topping pizzas. A pizza restaurant advertises 286 different 3-topping pizzas. To find out the total number of individual toppings used in the restaurant, we can multiply the number of pizza variations by the number of toppings per pizza.

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Answer:

1

Step-by-step explanation:

The slope of this line is -1 or -1/1, and to find the perpendicular slope you find the opposite of the reciprocal, which in this case would be 1/1 which simplifies to 1.

The relationship is that number sense can be used to solve area models or partial products.

Number sense refers to a set of important numerical skills. It includes the capacity to comprehend numbers and concepts such as more and less. Some people have a better sense of numbers than others.

Number sense is a set of abilities that enable humans to work with numbers. These abilities are essential for performing math as well as many other jobs.

In this case, partial products model of multiplication. This is a model which breaks numbers down into their factors. or place values in order to make multiplication easier. This depicts number sense.

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By calculating speed of each person we can find who is faster.

Speed can be defined as the distance covered with respect to time. It is a scalar quantity. It is calculated as follows

Speed  = Distance / Time taken

The time taken by each person is 20 seconds.

Distance covered by Jan = 50 meter

Speed of Jan = Distance / Time taken

Speed of Jan = 50 / 20

Speed of Jan = 2.5 meters per second

Distance covered by Dingh = 60 meter

Speed of Dingh = Distance / Time taken

Speed of Dingh = 60 / 20

Speed of Dingh = 3 meters per second

Since the speed of Dingh is more than Jan, we can say that Dingh is faster.

Distance = Speed × Time taken

Here, time taken = 1 second

This implies Distance Covered = Speed

Therefore, Jan covers 2.5 meters in one second while Dingh covers 3 meters in one second.

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a) The events are not mutually exclusive. If one event occurs, the other one can still occur.

b) The probability of picking either a purple marble or a black marble from the bag is 38.75%.

a) Mutually exclusive events: Two events are mutually exclusive if they cannot occur simultaneously, meaning if one event occurs, the other one cannot occur. If P(purple) = 25 and P(black) = 14%, picking a purple marble and picking a black marble from the bag are not mutually exclusive events. It's possible to pick a purple marble and a black marble from the bag. Therefore, the events are not mutually exclusive. If one event occurs, the other one can still occur.

b) It is possible to work out P(purple or black) because the events are not mutually exclusive. This means that it is possible to pick both a purple marble and a black marble from the bag. The formula for the probability of the union of two events is P(A or B) = P(A) + P(B) - P(A and B).

Here, A = picking a purple marble from the bag and B = picking a black marble from the bag.P(purple or black) = P(purple) + P(black) - P(purple and black)Where, P(purple and black) = P(purple) * P(black) [Because the events are independent]

Therefore, P(purple or black) = 0.25 + 0.14 - (0.25 * 0.14) = 0.3875 = 38.75%

Therefore, the probability of picking either a purple marble or a black marble from the bag is 38.75%.

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Answer: A 14-Pound bag will feed 21 dogs.

Step-by-step explanation: Because 14 is half of 28 all you need to do is divide 42 by 2 like this 42/2=21 you can check your answer by adding the answer twice like this 21+21=42

Answer:

its 21 good day

Step-by-step explanation:

Answer: The answer is 1.8 or 1.83 repeating

Step-by-step explanation: When you do 44 divided by 24 (2 years) it gives you how much she needs to pay per month.

Answer:

Angela pays $1.83 for each magazine.

Step-by-step explanation:

Considering that there are 12 months in 1 year, there would be 12 * 2 = 24 months in 2 years. If she gets one magazine per month, she would get 24 magazines.

She would be paying $44 / 24 magazines = 11/6 ≈ 1.83.

So, she is paying about $1.83 for each magazine.

The probability that at least half of the voters contacted supported the current governor is approximately 0.3322 or 33.22%.

The proportion of voters who voted for the current governor in the election can be determined using the formula

\(P=\frac{x}{n}\)

p is the proportion,

x is the number of voters who supported the current governor

n is the number of voters in the sample.

In this case, the sample size is 342, and we don't know the number of voters who supported the current governor.

Therefore, we can estimate the proportion using the sample proportion.

The sample proportion is obtained by dividing the number of voters who supported the current governor by the sample size.

Let us assume that half of the voters contacted supported the current governor.

Since we know that the sample size is 342, the number of voters who supported the current governor is 171, which is half of 342.

Therefore, the sample proportion is  \(p=\frac{171}{342}=0.5\)

In order to calculate the probability that at least half of the voters contacted supported the current governor, we need to use the normal distribution.

The normal distribution is a continuous probability distribution that is widely used to model real-world phenomena.

The normal distribution is characterized by two parameters: the mean and the standard deviation.

In this case, the mean of the normal distribution is given by the sample proportion, which is p = 0.5.

The standard deviation of the normal distribution can be calculated using the formula:

\(σ=sqrt\frac{p(1-p)}{n}\)

σ is the standard deviation,

p is the proportion, and

n is the sample size.

Using the values we have, we can calculate the standard deviation:

\(σ=sqrt\frac{0.5(1-0.5)}{342} =0.0253\)

We want to find the probability that at least half of the voters contacted supported the current governor, which means we want to find the probability that the sample proportion is greater than or equal to 0.5.

Using the normal distribution, we can standardize the sample proportion and find the probability that it is greater than or equal to 0.5.

The standardized score is given by the formula

\(z= \frac{(p-μ)}{σ}\)

z is the standardized score,

p is the proportion,

μ is the mean,

σ is the standard deviation.

Using the values we have, we can standardize the sample proportion:

\(z=\frac{0.5 - 0.5}{0.0253} =0\)

The probability of a standardized score being 0 is 0.5.

Therefore, the probability that the sample proportion is greater than or equal to 0.5 is 0.5 + (1 - 0.5) x 0.5 = 0.75.

However, this probability is for a normal distribution with a mean of 0.5 and a standard deviation of 0.0253.

We want the probability for a sample of 342 voters, so we need to adjust our answer using the continuity correction factor.

The continuity correction factor is used when we are approximating a discrete distribution with a continuous distribution.

In this case, the sample proportion is a discrete distribution because it can only take on certain values (such as 0.5, 0.51, 0.52, etc.).

However, we are using a continuous distribution (the normal distribution) to approximate the sample proportion.

Therefore, we need to adjust our answer using the continuity correction factor.

The continuity correction factor is given by the formula 0.5 - 0.5/n, where n is the sample size.

Using the continuity correction factor, we can adjust our answer:

\(0.75-\frac{0.5-0.5}{342} =0.3322\)

Therefore, the probability that at least half of the voters contacted supported the current governor in the last election when a telephone survey contacts 342 voters from the last election and asks if they voted for the current governor is approximately 0.3322 or 33.22%.

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Answer:

Step-by-step explanation:

The value if T(290) is 330.6

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.

Given:

T(x) = x + 0.14x

T ( 290)= 290+ 0.14* 290

            = 290+ 40.6

           = 330.6

Hence, the value of T(290) is 330.6.

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The sides are 20 and 21 in   right triangle.

What defines a right triangle?

The term "right triangle" refers to a triangle with an interior angle of 90 degrees.

                 The hypotenuse, the side of the right triangle that is opposite the right angle and is also its longest side, and the height and base are the two arms of the right angle.The term "right triangle" refers to a triangle with an interior angle of 90 degrees. The hypotenuse, the side of the right triangle that is opposite the right angle and is also its longest side, and the height and base are the two arms of the right angle.

29² = x²  + (x+1)²

x²+ x² +2x +1 = 841

2x² +2x -840 =0

x² + x -420 =0

(x+21)(x-20)=0

x=20

the sides are 20 and 21

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1) The statement "When dummy coding qualitative variables, the level with the lowest mean value should always be the base level" is FALSE.

2) we will not divide the p-value by 2.

1. Dummy coding qualitative variables: The statement "When dummy coding qualitative variables, the level with the lowest mean value should always be the base level" is FALSE. The choice of the base level in dummy coding is arbitrary, and it does not have to be the level with the lowest mean value.

2. Testing a quadratic model: Since you are unsure whether the curvature would be negative or positive, the appropriate alternative hypothesis is that the beta for the quadratic term is not equal to zero (i.e., it has an effect). In this case, you will perform a two-tailed test, which means you will not divide the p-value by 2.

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Explanation:

Let L = 4x-2 be the length and W = 2x+1 be the width. The order of L and W doesn't matter.

The goal is to find the area = L*W

We could simply say L*W = (4x-2)*(2x+1) and be done. Though I have a feeling your teacher wants you to expand that out.

Let's do so

(4x-2)*(2x+1)

L(2x+1) .... replace "4x-2" with L

2xL + L .... distributive property

2x( L ) + 1( L )

2x( 4x-2 ) + 1(4x - 2) .... L replaced with 4x-2

2x*4x + 2x*(-2) + 1*4x + 1*(-2) .... distributive property twice more

8x^2 - 4x + 4x - 2

8x^2 - 2 is the final answer

Side note: you can use the FOIL rule or the box method as two alternatives to get the same answer.

If lines A, B and C shows proportional relationships, then the line A has a constant of proportionality between y and x is 5

Given the line A, B and C

The constant of proportionality is the ratio of the y coordinates to the x coordinate

k = y /x

Where k is the constant of proportionality

Consider the line A

One point on the line = (1, 5)

Constant of proportionality K = 5/1

= 5

Consider the line B

One point on the line = (3, 5)

Constant of proportionality k = 5/3

Consider the line C

One point on the line = (7, 5)

Constant of proportionality = 5/7

Therefore, the line A has the constant of proportionality of 5

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The given question is incomplete, the complete question is

Lines A, B, and C show proportional relationships. Which line has a constant of proportionality between y and x of 5?

The function is discontinuous at x = 5, i.e., the point of discontinuity is x = 5 for the given function.

The abrupt change in the function's value over a small change in its independent variable is known as discontinuity.

The following are the types of discontinuity:

Removable Discontinuity: When a function has a hole at a certain value of x, the discontinuity is known as removable discontinuity.

Jump Discontinuity: When a function has a sudden jump from one value to another at a certain value of x, the discontinuity is known as jump discontinuity.

Infinite Discontinuity: When a function has an infinite gap (vertical asymptote) at a certain value of x, the discontinuity is known as infinite discontinuity.

Other types of discontinuity are Oscillating Discontinuity and Essential Discontinuity.

Here, the function is continuous from both sides for x = 5.

But it is not continuous at x = 5 as the left and right-hand limits are not equal; the function has a jump discontinuity at x = 5.

The function is discontinuous at x = 5, i.e., the point of discontinuity is x = 5.

Hence, the result is S - if x < 5 if x ≥ 5.

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The correct option that indicates how Christa sliced the rectangular pyramid is the second option.

Christa sliced the pyramid perpendicular to its base through two edges.

A rectangular pyramid is a pyramid with a rectangular base and four triangular faces.

The height of the cross section indicates that the location where Christa sliced the shape is lower than the apex of the pyramid.

The trapezoid shape of the cross section of the pyramid indicates that the top and base of the cross section are parallel, indicating that Christa sliced the pyramid parallel to a side of the base of the pyramid, such that it intersects two of the edges of the pyramid

The correct option is therefore the second option;

Christa sliced the pyramid perpendicular to its base through two edges

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A one-way ANOVA is a statistical test used to compare the means of four populations in this case. Thus, the degrees of freedom for the F-statistic in this one-way ANOVA are (df1, df2) \(= (3, 78)\).

The degrees of freedom are essential for calculating the F-statistic, which helps determine whether there are significant differences among the population means.

To calculate the degrees of freedom for the F-statistic, we need to determine the numerator degrees of freedom (df1) and the denominator degrees of freedom (df2). For df1 (numerator degrees of freedom), it is equal to the number of populations (groups) minus 1.

In this case, there are four populations,

So: df1 \(= 4 - 1 = 3\)

For df2 (denominator degrees of freedom), it is equal to the total sample size (N) minus the number of populations (groups).

The total sample size is given as \(18 + 22 + 20 + 22 = 82\).

So: df2 \(= 82 - 4 = 78\)

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Using the range concept, it is found that the method used to find it is:

Find the difference between the maximum and minimum values.

The range of a data-set is given by the difference between the maximum value in the data-set and the minimum value in the data-set.

Hence, the correct option about the method used to find the range is:

Find the difference between the maximum and minimum values.

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Answer:

(B)  Find the difference between the upper and lower quartiles.

Answer:

24

Step-by-step explanation:

Answer:

x greater than or equal to 12cm^2

Step-by-step explanation:

From greatest to least, the sides of the triangle are: b. ST, RS, TR.

In a triangle, the side opposite the largest angle is the longest side and the side opposite the smallest angle is the shortest side. Also, the side opposite the middle-sized angle is the medium-length side.

Therefore:

m<S = 20°, and is opposite to side TR.

m<T = 40°, and is opposite to side RS.

m<R = 180 - 40 - 20 = 120°, and is opposite to side ST.

Therefore, the order from greatest to least is: b. ST, RS, TR.

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