Which of the following statements is true?
For a large enough sample size, the Central Limit Theorem states that the sample medians of repeated samples of a population are normally distributed.
For the Central Limit Theorem to be true, you must have a large sample, the underlying population must be normally distributed, and the standard deviation should not be finite.
For a large enough sample size, the Central Limit Theorem states that the sample means of repeated samples of a population are normally distributed.
Even with a very large sample size, the Central Limit Theorem states that the sample means of repeated samples of a population cannot be normally distributed.

The difference between the median rating for each company is approximately 0.3 times the interquartile range.

Generally speaking, the median for 20 observations is the average of the 10th and 11th number:

Median rating of Company A = (4 + 4)/2

Median rating of Company A = 8/2

Median rating of Company A = 4.

Median rating of Company B = (3 + 3)/2

Median rating of Company B = 6/2

Median rating of Company B = 3.

Difference in median = 4 - 3

Difference in median = 1

For the required expression that models the difference between the median rating for each company and the interquartile range, we have the following:

1 = 3x

x = 1/3.

x = 0.3

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The fomulas of the sequence are a(n) = 3200(1.09)^n-1 and a(n) = a(n - 1) * 1.09

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

First term, a = 3200

Increment, r = 9%

To find the explicit formula, we can use the formula for compound interest:

a(n) = a * (1 + r)^n-1

So, we have

a(n) = 3200(1.09)^n-1

For the recursive formula, we have

a(n) = a(n - 1) * 1.09

This is because the product of the current term and the incremnt rate gives the next term

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The grades that Angie need to receive in her next test so that her average is 92 is 91.

The average is defined as the mean value a given data set. The formula to calculate the mean of a given data set is:

Average = Sum of the observations / Total number of observations

Assume the marks that Angie needs in her next test is represented by x.

Given that Angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. Therefore, the grades she need to receive in her next test so her average is 92 is:

Average = Sum of the grades of all test / Total Number of test

92 = (88+96+92+93+x)/5

460 = 369+x

460 - 369 = x

x = 91

Hence, she needs 91 grades in her next test.

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The complete question is:

Angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. what grade will she need to receive in her next test so that her average of all test is 92?

The output value of y when input value x is -7:   -6

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check given expression is a function or not we can check it by a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

A graph of a function,

And input value x  = -7

output value y = ?

As it can be seen in the graph,

For input value x  = 0

output value of y = -2

Similarly,

for input value x  = -7

It can be seen in the graph that

the value of y = -6

Hence, the value of y is -6

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Some way to solve binary operations are listed below

By definition, binary operations involve performing arithmetic operations on two operands in a specific way.

An example of a binary expression is a + b

Where a and b are the operands & + is the operator

Some common binary operations and how to solve them are highlited below

Other operations are

Multiplication (*), Division (/) and Modulus

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Answer:

yes

Step-by-step explanation:

2*(4+7) = ( 2 * 4 ) + ( 2 * 7 )

Answer:

It could be [tex]x=25[/tex] and [tex]q = -5[/tex] or it could be [tex]x=-25[/tex] and [tex]q = 5[/tex]. As both x and q are variables, either of these could be correct.

The simplified form of the expression xy( x³y⁵ - x⁷ ) is x⁴y⁶ - x⁸y.

Given the expression in the question;

xy( x³y⁵ - x⁷ )

To simplify the expression, apply distributive property.

xy( x³y⁵ - x⁷ )

xy( x³y⁵ ) - xy( x⁷ )

xy( x³y⁵ ) - xy( x⁷ )

Multiply xy and ( x³y⁵ )

x⁴y⁶ - xy( x⁷ )

Multiply xy and ( x⁷ )

x⁴y⁶ - x⁸y

Therefore, the simplified form is x⁴y⁶ - x⁸y.

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Answer:

6.7 weeks.

Step-by-step explanation:

65.00 x 6.7 = 435.50

Answer:

Step-by-step explanation:

He has $65 on the first week. He’s missing $370. If he can save $18 a week. 370/18 = 20.5. But they’re asking for the total weeks it’ll take. So add the first week. 20.5 + 1 = 21.5

not mine but he did he get it right

Answer: x = -3/2

Step-by-step explanation:

-4x + 2(x+4) = -7x - (x+1)

-4x + 2x+8 = -7x -x-1

-2x + 8 = -8x - 1

+2x          +2x

8 = -6x - 1

+1           +1

9 = -6x

/-6    /-6

-9/6  = x

-3/2 = x

At x=2, the function in the graph is approaches to infinity. This is satisfied by equation 1 that models the rational function, hence option 1 is the correct answer.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

From given graph we can see that

At x=2, the function in the graph is approaches to infinity.

It means function is not defined at x=2

We know that a rational function is undefined when denominator is equal to zero.

For equation 1:

f(x)= 2(x+2)/(x-2)

Equating the denominator:

x-2=0

x=2

It means function is not defined at x=2

The y-intercept is: y= -2

The function is passing through the point (1,-6).

When we substitute x=1

Hence, option 1 is true.

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The intervals of each behavior of the function are given as follows:

a) Increasing: (-∞, -1).

b) Decreasing: (-1, 1).

c) Constant: (1, 3).

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable .

here, we have,

to classify the function as increasing, decreasing or constant:

The function is increasing when the graph moves right and up.

The function is decreasing when the graph moves right and down.

The function is constant when the graph of the function is an horizontal line.

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The system of linear equations representing the given situation is: 2x + y = 10 and 2x + 3y = 22. Solving this system, we find that it takes 6 minutes to jog around the park.

a. Let's use x to represent the number of minutes it takes to jog around the block and y to represent the number of minutes it takes to jog around the park.

From the problem statement, we know that:

2x + y = 10 (jog around the block twice and the park once in 10 minutes)

2x + 3y = 22 (jog around the block twice and the park three times in 22 minutes)

These are the two linear equations that represent the given situation.

b. We can solve this system of equations to find the value of y, which represents the number of minutes it takes to jog around the park.

We can start by eliminating x from the equations. Subtracting the first equation from the second, we get:

(2x + 3y) - (2x + y) = 22 - 10

2y = 12

y = 6

So, it takes 6 minutes to jog around the park.

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Complete question:

You can jog around your block twice and the park once in 10 minutes. you can jog around your block twice and the park 3 times in 22 minutes.

a. write a system of linear equations that represents this situation. let x represent the number of minutes it takes you to jog around your block and y represent the number of minutes it takes you to jog around the park. system of equations:

b. how long does it take you to jog around the park? it takes you minutes to jog around the park.

The new tuition 4 years from now is $6962.68.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].

Given that, principal =$6691, rate of interest=1% and time period=4 years.

Now, A=6691(1+1/100)⁴

=6691(1+0.01)⁴

=6691(1.01)⁴

= 6691×1.04060401

= $6962.68

Therefore, the new tuition 4 years from now is $6962.68.

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Answer:

The rate of change of the velocity of the wave with respect to the depth of the water is 3/2 meters per second per meter when the depth is 2 meters. This can be found by taking the derivative of v(h) with respect to h, which is 3/2√h. When h is 2, the rate of change is 3/2√2, which is equal to 3/2 meters per second per meter.

The driver increased altitude is 517 feet.

A right triangle is a triangle with one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the road is inclined at an angle of 6 degrees.  After driving 4950 feet along this​ road, let's find the altitude as follows:

using trigonometric ratios,

sin 6° = opposite / hypotenuse

Therefore,

sin 6° = a / 4950

cross multiply'

a = 4950 sin 6°

a = 4950 × 0.10452846326

a = 517.415893175

Therefore,

a = 517 feet

Altitude = 517 feet

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25,591 cans are still in use after 4 years of recycling and re-using. The solution has been obtained by using functions.

What is a function?

A function is a connection between a set of inputs and one output for each input. The usual notation for a function is f(x), where x represents the input. Usually, a function is written as y = f(x).

We are given a function as N = 350,000 [tex](0.52)^{t}[/tex]

t is given to be 4 years.

Substituting this in the function, we get

⇒N = 350,000 [tex](0.52)^{4}[/tex]

⇒N = 350,000 * 0.07311616

⇒N = 25,590.6

⇒N = 25,591

Hence, 25,591 cans are still in use after 4 years of recycling and re-using.

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Full question has been attached below

Answer:

Step-by-step explanation:

To simplify the expression X^(12/7) * Y^(35/7) into its simplest form, we need to find the greatest common divisor (GCD) of the exponents 12/7 and 35/7 and divide both exponents by the GCD. Here's the step-by-step process:

Find the GCD of 12/7 and 35/7. To do this, we'll use the Euclidean algorithm method:

a. Divide the larger number, 35, by the smaller number, 12, and get the remainder: 35 ÷ 12 = 2 with a remainder of 11.

b. Divide the smaller number, 12, by the remainder, 11, and get the quotient and remainder: 12 ÷ 11 = 1 with a remainder of 1.

c. The last non-zero remainder, 1, is the GCD of 12/7 and 35/7.

Divide both exponents by the GCD, 1:

a. X^(12/7) becomes X^(12/7 ÷ 1) = X^12.

b. Y^(35/7) becomes Y^(35/7 ÷ 1) = Y^35.

Replace the original exponents in the expression with the simplified exponents: X^12 * Y^35.

So, the expression X^(12/7) * Y^(35/7) is simplified as X^12 * Y^35, which is written as a single radical in its simplest form.

[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ x^{\frac{12}{7}}y^{\frac{35}{7}}\implies \left( x^{12} y^{35} \right)^{\frac{1}{7}}\implies \sqrt[7]{x^{12} y^{35}}\implies \sqrt[7]{x^{7+5} (y^5)^7} \\\\\\ \sqrt[7]{x^7 x^5 (y^5)^7}\implies {\Large \begin{array}{llll} x y^5\sqrt[7]{x^5} \end{array}}[/tex]

The amount of money the company makes per shirt  $18.90

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The chances that event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes

                                 = X/n

To calculate the expected profit per shirt, we need to consider the two possible outcomes:

the shirt is defective or not defective.

If the shirt is not defective, the company makes a profit of $20.

If the shirt is defective, the company incurs a cost of $35 and no profit.

The probability of a shirt being defective is 0.02, so the probability of a shirt not being defective is:

= 1 - 0.02

= 0.98.

Therefore, the expected profit per shirt can be calculated as:

Expected profit = (probability of not defective) x (profit per non-defective shirt)

+ (probability of defective) x (cost per defective shirt)

Expected profit = 0.98 x $20 + 0.02 x (-$35)

Expected profit = $19.60 - $0.70

Expected profit = $18.90

So the company really makes $18.90 per shirt, taking into account the cost of defective shirts.

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By the given graph we can conclude that the solution of the equation (i.e point of intersection of lines) is (-2, -2).

To solve the system of equations, graph the given two lines' first equation. Now determine whether the lines are parallel, intersect, or are the same line.

In the next step, we need to Identify the solution to the system.

If the lines are intersected, the point of intersection is the solution.

If the lines are parallel, the system will have no solution.

If the lines are the same or coincident, then the system will have an infinite number of solutions.  

Here we have

y = x  ----- (1)

y = 2x+2 ---- (2)

From (1) and (2)

=> y = 2y + 2

=> 2y - y = -2

=> y = - 2

Hence, the solution of the given system of the equation is (-2, -2)

We can check it by graphing the lines as shown figure.  

Therefore,

By the given graph we can conclude that the solution of the equation (i.e point of intersection of lines) is (-2, -2).

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Relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides

a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

To widen or enlarge an opening or hollow structure beyond its usual size in simple way changes the the size.

The scale factors is the factor in which each linear measure of the figure is multiplied.

AC is a smaller triangle which is dilated to get A'C' and this A'C' is dilated to get A''C''.

the relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides with a scale factor.

Hence,  relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides

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Answer:12

Step-by-step explanation:30-6=24

24 divided by 2 =12

radius = 9 cm

height = 26,5 cm

as we know that

volume of cylinder = πr^2h

= 3,14x9x9x2x26,5

= 13.480 cm cubic

The value of the variable y is 3

From the information given, we have that;

ACDF∼VWYZ

Given that the lengths are;

Since the diagrams are equivalent, then,

A/VZ = CD/YW

substitute the values, we have;

12/3y - 1 = 9/6

cross multiply

3y - 1 = 12(6)/9

divide the values

3y - 1 = 8

collect like terms

3y = 9

Make 'y' the subject

y =3

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If the temperature dropped at a constant rate, it would have dropped 4°C per hour. This can be calculated by taking the difference in temperature (24°C) and dividing it by the number of hours that passed (4 hours).

The value of x for the angle C in the triangle ABC is equal to 42.5

A triangle formed by the diameter of a circle is a right triangle, with one side being the diameter of the circle and the other two sides being radii of the circle. Since the diameter of a circle bisects the circle into two equal halves, it also bisects the right angle formed by the radii into two equal angles of 45 degrees each.

The angle C is equal to 90° and we shall solve for the value of x as follows:

2x + 5 = 90°

2x = 90° - 5 {subtract 5 from both sides}

2x = 85°

x = 85°/2 {divide through by 2}

x = 42.5

Therefore, the value of x for the angle C in the triangle ABC is equal to 42.5

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Four rational numbers between 1/5 and 1/6 are; 41/240, 42/240, 43/240, 44/240

A rational number is defined as a number that can be expressed as the quotient of fraction p/q of two integers, a numerator p, and a non-zero denominator q.

First, we have to make the denominators the same.

We multiply 1/5 by 48 and 1/6 by 40 to get:

48/240 and 40/240

Thus, the other rational numbers between them are;

41/240, 42/240, 43/240, 44/240

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Complete question is;

Find four rational numbers between 1/5 and 1/6 ​