Suppose each data value in a data set is multiplied by 8. What will
happen to the mean?

Select one:
- It will be 4 times as much.
- It will increase by 4.
- It will be 8 times as much.
It will increase by 8, as well.

The reduced fraction is 6/7 using GCF method.

What is GCF method?

The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)

Given,

the fraction = 24/28.

the factors of 24  = 2×2×2×3

The factors of 28 = 2×2×7

The gcf is 2 × 2 = 4

divide the denominator and numerator by 4

24 ÷ 4 = 6

28÷ 4 = 7

We get,

the fraction = 6/7.

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Both  2/3m=-4 and -4m=24 have a solution of 1/6 and are equivalent

Algebraic expressions are described as expressions that contains terms, variables, coefficients, constants and factors.

They are also known to be made up of some arithmetic operations, such as;

We have the equations;

2/3m=4 and -4m=24

Let's solve for m in the first equation

12m = 2

Divide both side by coefficient of m

m = 2/ 12  = 1/ 6

For the second equation

-4m = 24

Divide both sides by - 4

m = 24/-4

m = 6/ -1

Take inverse

m = 1/6

Hence, the equations are equivalent

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The sinusoid that models 4° = A cos B(x - C) and 68° = A cos B(x - C) the change in temperature in the house.

The heater turns on when the house is 4° below the set temperature and turns off when the house is 4° above the set temperature. The temperature is set at 68°. At 10:15 am the heater turns on, and at 10:30 am the heater turns off.

Temperature fluctuations can be modeled using the sine and cosine functions throughout the day.

The equations that can be used to model these data is of the form:

At 10:30 am the heater turned off,

⇒ 4° = A cos B(x - C)

At 10:15 am the heater turned on,

⇒68° = A cos B(x - C)

where A, B, and C are constants, y is the temperature in °C and x is the time

Thus, The sinusoid that models 4° = A cos B(x - C) and 68° = A cos B(x - C) is the change in temperature in the house.

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Answer: D

Step-by-step explanation: Took the test

The p - value is d ) a probability .

Defining P - Value

P - Value : It is the probability of obtaining results at least as extreme as the  observed results of a statistical hypothesis test , assuming that the null hypothesis is correct . The p - value does not , in itself , establish probabilities of hypotheses . Rather , it is a tool for deciding , whether to reject null hypothesis or not .

A smaller p - value means that there is stronger evidence in favor of alternative hypothesis .

Hence , the p - value is d ) a probability .

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Yes, it is reasonable for her to use a normal model for the sampling distribution of the sample​ proportion. In this case, less than ten efforts have been successful. Since 5 is a lot less than 10, this is the case.

Because the data don't fit the success and failure criteria, it is not appropriate to adopt a normal model for a sampling of the sample distribution.

50 students make up the sample. The probability that she assumes 10% of the group will attend is 10%.

It will be demonstrated by:

1 - p = 1 - 10% = 1 - 0.10 = 0.90

np = 50 × 0.1 = 5. This suggests the number of victories.

Less than 10 attempts have succeeded in this instance. 5 is much less than 10, hence this case. As a result, the data does not satisfy the requirement.

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The question is -

For her final project, Stacy plans on surveying a random sample of 50 students on whether they plan to go to Florida for spring break. from past years, she guesses that about 10% of the class goes. is it reasonable for her to use a normal model for the sampling distribution of the sample proportion? why or why not?

The correct graph for each of the equations are respectively;

5) Graph C

6) Graph A

7) Graph B

The general form of equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

5) We are given the linear equation as;

-9x + 3y = 0

3y = 9x + 0

y = 3x + 0

The slope is 3 and y-intercept is zero. Thus, the correct graph for this function is; Graph C

6) We are given the linear equation as;

4x - 6y = 12

Rearranging we have;

6y = 4x - 12

y = ⁴/₆x - 2

y = ²/₃x - 2

Thus, slope is 2/3 and y-intercept is -2. The correct graph is graph A

7) The correct graph of the function 25x - 10y = -50 is the graph B.

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The required diameter of the circle is given as 15 in. Option B is correct.

Given that,
The circumference of a circle is given 47.1 in, we have to determine the diameter of the circle.

Perimeter is the measure of the figure on its circumference.

Here,
As per the given condition,
First, write the formula for the circumference of the circle,
Circumference of the circle = πD
now substitute the value in the above equation,
47.1 = 3.14 D
D = 47.1/3.14
D = 15 in

Thus,  the required diameter of the circle is given as 15 in. Option B is correct.

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Answer: 151.8

Step-by-step explanation:
330/100 x 54 = 178.2

330- 178.2 = 151.8

For the given equation 4x + 3y =21 the slope intercept form is given by y = (-4/3)x + 7.

Graph is attached.

As given in the question,

Given equation is equal to :

4x + 3y = 21

To get the slope intercept form of the given equation we have,

Subtract 4x from both the sides of the given equation we have,

4x + 3y - 4x = 21 - 4x

⇒ 3y = 21 - 4x

Now divide by 3 on both the sides of the equation we get,

3y / 3 = (-4/3)x + (21/3)

⇒ y = (-4/3) x + 7

Graph of the given equation in slope intercept form y = (-4/3) x + 7 is attached.

When x = 0 ⇒ y = 7

y= 0 ⇒ x = 21 /4

Therefore, for the given equation 4x + 3y =21 the slope intercept form is given by  y = (-4/3)x + 7.

Graph is attached.

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Answer:

y = - [tex]\frac{1}{3}[/tex] x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{1}{3}[/tex] , then

y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (6, - 5 ) into the partial equation

- 5 = - 2 + c ⇒ c = - 5 + 2 = - 3

y = - [tex]\frac{1}{3}[/tex] x - 3 ← equation of line

the required sample size for the interval estimate with a 95% level of confidence  is 385

since we are given the margin of error which is f $10 and a standard deviation which is $1,000,  and we are also given the level of confidence which is 95%

so the formula we are  referring to calculate the sample size is :

n=z(0..95)*s²/ E

here, E is the margin of error, S is the standard deviation

so z score of 0.95 is 1.96

so n = 1.96*1000^2/100

        = 384.16 ,which is almost 385

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Answer:

p = -1 ; p= 3

Step-by-step explanation:

10p^2 - 20p - 34 +4 = 0

10p^2 -20p - 30 = 0

10/10 p^2 - 20/10 p - 30/10 = 0

p^2 - 2p - 3 = 0

(p-3)(p+1) = 0

p = 3

p = -1

Answer:

b = 3

Step-by-step explanation:

Given that,

→ a = 27

Forming the equation,

→ 27 = 3b²

Now the value of b will be,

→ 27 = 3b²

→ b² = 27/3

→ b = √9

→ [ b = 3 ]

Hence, the value of b is 3.

⇒Given that a=27 in the equation [tex]a=3b^{2} \\[/tex] in the place of a plug in 27 and solve for b

[tex]27=3b^{2} \\\frac{27}{3} =\frac{3b^{2}}{3} \\b^{2} =9\\b^{2}-9=0\\(b+3)(b-3)=0\\b+3=0\\or\\b-3=0\\b=-3\\or\\b=3[/tex]

⇒Note b can also be -3 but the only option available as the answer is 3

∴ b=3 in this case.

Answer:

Hey, hope it helps my friend

Step-by-step explanation:

In the image

The function rule in slope-intercept form is y = -4x - 2

Mathematically, the slope-intercept form of a straight line can be calculated by using this equation:

y = mx + c

Where:

From the graph of this line, we have the following data points:

Point (x, y) = (-1, 2)

Point (x, y) = (0, -2)

In Mathematics, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (-2 - 2)/(1 - 0)

Slope, m = -4/-1

Slope, m = -4

Note: The y-intercept occurs at the point where the x-value is equal to zero (0).

Now, we can write the function rule for this line in slope-intercept form as follows:

y = mx + c

y = -4x - 2

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The two values of x which are root of the given equation are; x = (-3 + √29)/2 and x = (-3 - √29)/2.

It follows from the task content that the two values of x which are roots of the given quadratic equation be determined.

Recall that the roots of quadratic equations are given by the formula;

x = {-b ± √(b² - 4ac)} / 2a

Since the given equation is; x² + 3x - 5; it follows that; a = 1, b = 3 and c = -5.

Therefore, the roots are as follows;

x = {-3 ± √(3² - 4•1•-5)} / 2(1)

x = (-3 ± √29)/2

Therefore, the required roots are;

x = (-3 + √29)/2 and x = (-3 - √29)/2

Ultimately, the roots of the given quadratic equation x² + 3x - 5 are; x = (-3 + √29)/2 and x = (-3 - √29)/2.

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Answer:

Step-by-step explanation:

3b(2x - z^3)  = 2h - 7gx      Distribute 3b

6bx - 3bz^3 = 2h - 7gx      Add 3bz^3 to both sides

6bx = 3bz^3 + 2h - 7gx    Add 7gx to both sides

6bx + 7gx = 3bz^3 + 2h     Factor left side, factor out a gcf of x

x(6b + 7g) = 3bz^3 + 2h     Divide both sides by (6b + 7g) to isolate x

x = (3bz^3 + 2h)/ (6b + 7g)

Identifying the domain and range is important when defining a function because domain gives all the input values and range gives all the output values a function can take. It is very essential to know domain and range of a function.

Domain are represented by independent variable and are graphed on x coordinate of the axis.

Range are dependent values and are graphed on y axis of the graph.

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the quotient as a power. a^21/a is a^20.

What is Power?

In mathematics, power defines a base number raised to the exponent, where base number is the factor which is multiplied by itself and exponent denotes the number of times the same base number is multiplied.

What is quotient?

The number we obtain when we divide one number by another is the quotient.

What is exponential function?

An exponential function is a mathematical function of the following form: f ( x ) = a x. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.

Given that,

a^21/a

quotient as power = a^21/a

                             =  a^(21-1)

                             = a^20

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For the given triangle STU all the angles of ΔSTU are not equal to each other is the true statement .

As given in the question,

In the given triangle STU,

TU = 11

US = 17

ST = 18

we can see that

     TU < US < ST

⇒   11 < 17 < 18

⇒   11 + 17 = 28

⇒   28  > 18

All the sides of the triangle are not equal to each other.

This implies that all the angles opposite to the unequal sides are also not equal to other.

Therefore, for the given triangle STU all the angles of ΔSTU are not equal to each other is the true statement .

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The slope Using the formula will be h = -100t + 4000

This is a linear function because for every 5 seconds that pass, the height of the plane drops 500 feet, or -500 to be exact. So that's the slope of the line.

If we look at the table we can determine where the graph goes through the h axis. The h axis is the y axis, and the t axis is the x axis. So where the graph goes through the h axis is also the y-intercept.

If your teacher is any good at all, he/she would make sure that you understand beyond a shadow of a doubt that the y-intercept exists where x = 0. Looking at the table, where x (t) is 0, y (h) is 4000 feet.

Writing the linear equation then is super easy. In the form y = mx + b, we already know both the slope (-100) and the y-intercept (4000), so we fill in accordingly:

h = -100t + 4000 which appears to be choice a.

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When binomial distribution is used, the probability that at least 275 rooms are occupied is 0.96

Option b. is correct

We have the following parameters:

sample, n=300

proportions of rooms reserved, p=6%

We first get the sample mean,

Sample mean=n*p

                       =300*6%

                        =18

Now, we get population mean according to binomial distribution, μ'

μ=n-sample mean

   =300-18

   =282

We get the standard deviation, σ

σ=(sample mean*(1-p))^1/2

 =(18*(1-6%))^1/2

 =4.11

We now, calculate z-score:

z=(x-μ)/σ, given x should be at least 275

z=(275-282)/4.11

 =-1.703

Now, we have p(x>275)=p(z>-1.703)

From z-score of probabilities, we have p(z>-1.703) as 0.95572

So, p(x>275)=0.95572

                    =0.96

Hence, the probability that at least 275 rooms are occupied is 0.96

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(a) The scatter plot and the line of fit are shown in the graph.

(b) The equation of the line of fit is y = -2.5x+18.3.

(c) The slope is -2.5 which indicates that the gamer losses 2.5 every week after getting a new game.

A scatter plot is a graph of the given points or given data.

(a)

To make a scatter plot of the data, plot the points (x,y) on a graph.

To draw the line of fit, draw a line such that the distance between the line and the plotted points is minimum.

(b) The line passes through points (7.3,0)and (0,18).

The equation of the line is given by:

[tex]y-y_1=\frac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)[/tex]

Substitutes the points (x₁,y₁) = (7.3,0) and (x₂,y₂)=(0,18) into the above equation:

[tex]y-0=\frac{18-0}{0-7.3}(x-7.3)\\y=-2.5(x-7.3)\\y=-2.5x+18.3[/tex]

(c) The slope of a line of the form y=mx+c is m.

Therefore, the slope of the line y=-2.5x+18.3 is m = -2.5.

The slope indicates the change in y with respect to the change in x.

Therefore, the slope -2.5 indicates that the gamer losses 2.5 every week after getting a new game.

Hence,

(a) The scatter plot and the line of fit are shown in the graph.

(b) The equation of the line of fit is y = -2.5x+18.3.

(c) The slope is -2.5 which indicates that the gamer losses 2.5 every week after getting a new game.

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Marsha deposited $5500 into savings with 5% interest rate

1st year, Marsha will earn : [tex]0.05 \times 5500 = 275[/tex]

2nd year, Marsha will earn: [tex]0.05 \times 5775 = 288.75[/tex]

3rd year, Marsha will earn: [tex]0.05 \times 6063.75 = 303.19[/tex]

4th year, Marsha will earn: [tex]0.05 \times 6366.94 = 318.35[/tex]

Answer:

See attached worksheet.

Step-by-step explanation:

The worksheet summarizes the steps for analyzing the data on the graph.  Note that a "line of best fit" was drawn to help illustrate the linear behavior of the data, and to better the question concerning hours of sunshine in another British town.  There are techniques for ensuring a line such as this fits the actual data as closely as possible.  These techniques draw a line that has the least overall deviation from the actual data.  For our purposes, a hand-drawn line appears to match the data reasonably well, so we are able to concule that the relationship is liner:  There is a proportional change in y for every set change in x.  That change is known as the slope.  The slope of this liner would represent the direct relationship between hours of sun and maximum temperature.

Answer:

Reflection

Step-by-step explanation:

Reflection is like looking at yourself through a mirror, so it would be the same for sound.

Tell me if this is correct.!

Answer:

Reflection

Step-by-step explanation:

i took this quiz

Answer:plot the point (2,5)

Step-by-step explanation: