A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 224 cars owned by students had an average age of 5.06 years. A sample of 233 cars owned by faculty had an average age of 7.19 years. Assume that the population standard deviation for cars owned by students is 3.42 years, while the population standard deviation for cars owned by faculty is 2.81 years. Determine the 95% confidence interval for the difference between the true mean ages for cars owned by students and faculty. Step 2 of 3 : Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.

Answer:

"If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular."

Step-by-step explanation:

No, 16x2 40x 25 is not a perfect square trinomial.

Perfect squares are numbers that are the result of multiplying a number by itself. Examples of perfect squares include 4, 9, 16, 25, 36, and 49. Perfect squares are also known as "square numbers" or "whole numbers." Perfect squares are not just limited to whole numbers; some decimals and fractions can also be perfect squares.

A perfect square trinomial is an expression of the form a2 + 2ab + b2, where a and b are constants. 16x2 40x 25 does not fit this form, and is therefore not a perfect square trinomial.

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The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.

Volume is the measure of the amount of 3-dimensional space occupied by an object or substance. It is usually measured in cubic units, such as cubic centimeters (cm3) or cubic meters (m3). Volume is an important concept in mathematics, physics, chemistry, and engineering, and is used to calculate the amount of material needed for a given project.

The volume of the box can be calculated by multiplying the area of the base with the height of the box. The area of the base is 58 cm² and the height of the box is x - 2 cm. Therefore, the volume of the box can be expressed as:
Volume = 58 cm² x (x - 2 cm)
     = 58 cm³
The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.

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The area, in square units, of the region where the two triangles overlap is found as 1 square units.

We can determine the equation for each line with in diagram using its coordinates.

We can determine the coordinates for each point. (1/4,3/4) is one of the intersections.

d² = 2² + 2² = 8

A₁ = (1/3d + 1/6d )/2 * 1/4d

A₁ = 1/4d * 1/4d

A₁ = 1/ 16 d²

Now,

A = 2A₁

A = 2.(1/16)d²

A = 1/8d²

A = 1/8 *8

A  = 1

Thus, the area, in square units, of the region where the two triangles overlap is found as 1 square units.

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Answer:

1 square unit

Step-by-step explanation:

2a+b=15.7 is the formula used to get the base's length and b has a value of 3.

Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and Skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.

An isosceles triangle has 2 equal sides that are longer than the length of the base

perimiter=15.7

equation is 2a+b=15.7

so if the longer side is 6.3

we know that identical sides are bigger so 6.3 is one of the identical sides

2a means the 2 identical sides

2(6.3) + b = 15.7

12.6 + b = 15.7

subtract 12.6 from both sides

b = 3.1

therefore, The equation used to find the length of the base is 2a+b=15.7

and the value of b is 3.1

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Answer:

12.6 + b = 15.7

The function G(x) = 3 tan(x) does not have a minimum value.

The relative extremas of a function are the values of x for which the derivative of the function assumes a value of zero.

The extremas are classified as local minimum or local maximum, as follows:

The tangent function does not have a local minimum, as it is increasing over it's entire domain.

The function G(x) = 3 tan(x) is a vertical stretch by a factor of 3 of the tangent function, which changes only the range, thus the function continues without a local minimum.

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Therefore , the solution of the given problem of tractable problem comes out to be halting problem claims that no computer can be created that can anticipated.

an algorithm that takes a polynomial amount of time to solve a tractable issue. The upper bound is described by a polynomial. Any issue that cannot be addressed in a polynomial period of time is considered to be intractable. The lowest limit is exponential.

Here,

The halting problem claims that no computer can be created that can anticipated.

the likelihood that any other program will halt after a certain number of steps, making it an unsolved algorithmic challenge.

Software development is directly affected in practice by the stopping problem's insoluble nature.

Therefore , the solution of the given problem of tractable problem comes out to be halting problem claims that no computer can be created that can anticipated.

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Answer:

Below

Step-by-step explanation:

x - 6 = 12      add 6 to both sides of the equation

x - 6 + 6 = 12 + 6     simplify

x = 18

3x-1 = 11        add  1  to both sides of the equation

3x -1 + 1 = 11 + 1

3x = 12          now divide both sides by 3

3x/3 = 12 / 3   simplify

x = 4

The correct answer is (D) 0.75. The probability of rolling a number greater than 4 on a fair, eight-sided number cube is 0.75 or 75%

We know that there are 8 possible outcomes when rolling the number cube (1, 2, 3, 4, 5, 6, 7, 8). Of these 8 outcomes, 5 of them are numbers greater than 4 (5, 6, 7, 8). So, the number of favorable outcomes is 5.

To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes: P(number greater than 4) = 5/8. As a decimal, this is 0.625. However, the question asked for P(number greater than 4) which means we have to add 0.125 to 0.625, the answer is 0.75.

Therefore, the probability of rolling a number greater than 4 on a fair, eight-sided number cube is 0.75 or 75%. This means that if we roll the cube many times, we expect 75% of the rolls to be numbers greater than 4.

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The inequality be -4 ≤ x ≤ 2,300

If x is a real number, we have infinite solutions.

If x is an integer number, we have 2,305 solutions.

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality in mathematics. On the number line, it is most frequently used to compare the sizes of two numbers.

The term "inequality" in mathematics refers to a relationship between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus.

Let the given data be 3, -4, 0, and 2,300 are solutions.

If we order these numbers from smallest to largest, we get: {-4, 0, 3, 2,300}

Let the inequality be -4 ≤ x ≤ 2,300

The four values in the set {-4, 0, 3, 2,300} exists solutions for our inequality.

Here x exists a real number, then we contain infinite solutions.

If x exists an integer, then the total number of solutions will be equivalent to the number of negative solutions (4) and number of positive solutions (2,300)

the number zero (1)

We would have: 4 + 2,300 + 1 = 2,305 integer solutions.

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The inequality be -4 ≤ x ≤ 2,300

If x is a real number, we have infinite solutions.

If x is an integer number, we have 2,305 solutions.

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality in mathematics. On the number line, it is most frequently used to compare the sizes of two numbers.

The term "inequality" in mathematics refers to a relationship between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus.

Let the given data be 3, -4, 0, and 2,300 are solutions.

If we order these numbers from smallest to largest, we get: {-4, 0, 3, 2,300}

Let the inequality be -4 ≤ x ≤ 2,300

The four values in the set {-4, 0, 3, 2,300} exists solutions for our inequality.

Here x exists a real number, then we contain infinite solutions.

If x exists an integer, then the total number of solutions will be equivalent to the number of negative solutions (4) and number of positive solutions (2,300)

the number zero (1)

We would have: 4 + 2,300 + 1 = 2,305 integer solutions.

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No, the sine ratio of an acute angle cannot be greater than 1.

What is an acute angle?

Each angle in an acute triangle must be less than 90 degrees. A triangle is not an acute triangle even if one of its angles is 90 degrees. Because all angles (60°) are less than 90°, an equilateral triangle, for instance, is always sharp.

Here,

We have to determine whether the sine ratio of an acute angle can be greater than 1 or not.

We concluded that the value of the Sine ratio will always be between zero and one.

The Sine ratio is related to one of the acute angles of a right triangle such that the sine of the acute angle is the ratio of the side opposite the specific acute angle (the reference angle) to the hypotenuse.

Hence, the sine ratio of an acute angle cannot be greater than 1.

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Answer:

Regular megagon

Step-by-step explanation:

Regular megagon is a shape called with 1000000000 sides.

Answer:

Alex deleted 37.5 selfies

Step-by-step explanation:

Let X be the number of selfies that Vic deleted.

Alex deleted 3X selfies.

After deleting selfies, Alex has 90-3X selfies left.

Vic has 75-X selfies left.

Since Alex has half as many selfies as Vic, we can set up the equation: 90-3X = (75-X)/2

Multiplying through the parentheses on the right side, we get: 90-3X = 75-X/2

Combining like terms, we get: 2X = 15

Dividing both sides by 2, we get: X = 7.5

Since X represents the number of selfies that Vic deleted, Vic deleted 7.5 selfies.

Since Alex deleted 3 times as many selfies as Vic, Alex deleted 37.5 = <<37.5=22.5>>22.5 selfies.

The number of selfies deleted by Alex is 51.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that Alex took 90 selfies and Vic took 75 selfies. Today, they each decided that some of these selfies were not very good and deleted them. Alex deleted three times as many selfies as Vic. Now, Alex has half as many selfies as Vic.

Let Vic deleted x selfies and number of selfies deleted by Alex is 3x,

Therefore,

Since, Alex has half as many selfies as Vic, we can set up the equation: 90-3x = (75-x)/2

180 - 6x = 75 - x

5x = 105

x = 17

3x = 51

Hence, the number of selfies deleted by Alex is 51.

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Answer:

Step-by-step explanation:

we know the 30% off the marked price.

so the sale price is 60-60*30%=42

Answer:$42.00

Step-by-step explanation:

There were 481 people that utilized the public swimming pool that day, including 217 children and 264 adults.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter.

given

The number of children =X=217

The number of adults=264

Let say the number of children are denoted by X

Then the number of adults are (481-X)

Price for children =1.25X

Price for adults=2.25(481-X)

Price for children +Price for adults=865.25

1.25X+2.25(481-X)=865.25

Solving for X:

1.25X+1082.25-2.25X=865.25

-X=865.25-1082.25

-X=-217

X=217

The number of children =X=217

The number of adults=(481-X)

The number of adults=(481-217)

The number of adults=264

There were 481 people that utilized the public swimming pool that day, including 217 children and 264 adults.

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Joshua will need 7 additional customers.

The parameters that will help us to determine the number of customers is give as follows:

Joshua's goal is to sell more than 20 items at a farmers' market. So far, he has sold 6 items. Each customer buys 2 items.

Since Joshua's goal is to sell more than 20 items at a farmers' market and he has sold 6 items. and If each of his customers buys 2 items, the number of additional customers needed will be:

= (20 - 6) / 2

This is given as  14 / 2

The the number of customers needed = 7

In conclusion He will  need 7 additional customers.

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The system of linear equations has no solution for any value of a.

The equations Ax + 3y = a and 3x + 3y = a can be written in matrix form as

[A  3]   [x]   [a]

[3  3] * [y] = [a]

By using the Gaussian elimination method, the reduced form of the matrix is

[A  3]   [x]   [a]

[0  0] * [y] = [0]

This implies that the system has no solution for any value of a.

The system of linear equation

Ax + 3y = a and 3x + 3y = a can be written in matrix form as

[A  3]   [x]   [a]

[3  3] * [y] = [a]

We can use the gaussian method to solve this system. First, we subtract 3 times the first equation from the second equation to get

[A  3]   [x]   [a]

[0  0] * [y] = [0]

This implies that the system has no solution for any value of a.

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Answer:

X = 1 and below

Step-by-step explanation:

since X is less than 2.

the value of X will be 1 and below.

Answer:

zero is the simplified answer

Step-by-step explanation:

it's just as adding -5 to 5 which are additive inverse to each other so they cancel each other out ,, so -5 + 5 = 0

same for -5x +5X =0

[tex]\begin{array}{|c|c|} \cline{1-2}\text{Class} & \text{Frequency}\\\cline{1-2}20-29 & 5\\\cline{1-2}30-39 & 12\\\cline{1-2}40-49 & 9\\\cline{1-2}50-59 & 6\\\cline{1-2}60-69 & 3\\\cline{1-2}\end{array}[/tex]

=====================================================

Explanation:

The given data set is

{37, 60, 35, 38, 59, 34, 56, 42, 55, 48, 39, 33, 36, 35, 43, 52, 39, 64, 41, 35, 20, 31, 29, 45, 32, 54, 66, 44, 47, 45, 27, 24, 48, 28, 55}

It sorts to

{20, 24, 27, 28, 29, 31, 32, 33, 34, 35, 35, 35, 36, 37, 38, 39, 39, 41, 42, 43, 44, 45, 45, 47, 48, 48, 52, 54, 55, 55, 56, 59, 60, 64, 66}

The five values 20,24,27,28,29 are between 20 and 29. This means the first class or bin will have a frequency of 5.

The next interval spans from 30 to 39. There are 12 items in this interval, and those 12 items are this subset {31, 32, 33, 34, 35, 35, 35, 36, 37, 38, 39, 39}. This means we have a frequency of 12 for the interval from 30 to 39.

Keep this process going until you get to the end of the data set.

Answer:

1.  $76,000

2. $58,000 + $2,000 * t

Step-by-step explanation:

2. Now, you might be questioning why we are going with the second question first, but this will be useful as it sets up our equation to make the first question easier. So, we will start with Luke's base salary of $58,000. Then, we will add $2,000 for every year he works at the company. If he works for t years and gains $2,000 on his salary per year, our equation will look like this:

$58,000 + $2,000 * t

That is the equation.

1. Now, using our previous equation, $58,000 + $2,000 * t, we will substitute 9 in for t. We get:

$58,000 + $2,000 * 9

Then, we simplify, giving us:

$58,000 + $18,000 = $76,000

This type of blinding is used to prevent a potential source of bias in the experiment. By keeping the subjects unaware of the treatment they are receiving, the researchers can eliminate the possibility of any psychological effects influencing the outcome of the study. This is particularly important in cases where a treatment is being evaluated for subjective outcomes such as pain, anxiety, or depression, as the subjects' expectations and beliefs can influence their perception of the treatment's effectiveness. By keeping the subjects blinded to their treatment, researchers can ensure that the results of the study are as unbiased as possible.

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The statements that are true, based on the multiples of 3 and 6 are:

When a number is a multiple of a smaller number, then all the multiples of that larger number, will be the multiples of the smaller number.

This means that all the multiples of 6 ( including b ) will be multiples of 3 as well because 6 is a multiple of 3.

It is also interesting to note that the difference between the multiples of 3 are also multiples of 3. This means that a - b will result in a number that is a multiple of 3.

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Answer:

it must be less than 90 degrees

Column A and B matching the results with the operations

Answer:1

Step-by-step explanation:;

Answer:

f(-7) = -33

Step-by-step explanation:

f(x) = − x² - 4x – 12

f(-7) = ?

We put -7 in for x and solve

f(-7) = -(-7)^2 -4(-7) - 12

f(-7) = -(49) + 28 - 12

f(-7) = -49 + 28 - 12

f(-7) = -33

Answer:

28.2, 27.63, 27.54, 27.5, 27.22

Answer: 28.2, 27.62,27.5,27.22

Step-by-step explanation:

Answer:

p = 81

Step-by-step explanation:

9 = [tex]\frac{p}{9}[/tex]  Multiply both sides by 9

9(9) = [tex]\frac{p}{9}[/tex][tex](\frac{9}{1})[/tex]  another name for 9  is [tex]\frac{9}{1}[/tex]

81 = p

Answer:

Step-by-step explanation:

1) 6.2

2)12.4

3) 18.6