The histogram represents the distributions of essay scores for high school sophomores and juniors in a contest. Which statements are true about the data used to create the histogram? Select three options.



The mean is the best comparison of the measures of center.


The juniors tended to have higher essay scores than the sophomores.


The medians of both data sets are equal.


The interquartile range is the best comparison of the measure of variability.


A histogram is the best way to show that both distributions are nearly symmetric.

To find the coordinates of the other endpoint B given the midpoint M and one endpoint A. Apply the midpoint formula and solve the equations to find the coordinates of B(-1, 5).

The midpoint coordinates are given as M(3, -2) and one endpoint is given as A(7, -9). To find the coordinates of the other endpoint, we can use the midpoint formula which states that the coordinates of the midpoint are the average of the coordinates of the two endpoints.

Let the coordinates of the other endpoint be B(x, y). Using the midpoint formula, we have:

[(x + 7) / 2, (y + -9) / 2] = (3, -2)

Simplifying the equation, we get:

(x + 7) / 2 = 3

(y - 9) / 2 = -2

Multiplying both sides by 2, we have:

x + 7 = 6

y - 9 = -4

Subtracting 7 from both sides, we get:

x = -1

Subtracting -9 from both sides, we get:

y = 5

Therefore, the coordinates of the other endpoint are B(-1, 5).

burned: 756 calories

hours: 3

same number of calories each hour

-> to find this, we must split the number of calories evenly among the hours

steps

756/3

= 252 calories per hour

Answer:

252

Step-by-step explanation: 756/3

Answer:

b

Step-by-step explanation:

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The equation can be used to find the cost of the bracelets.

5x + 22.50 + 150 = 235

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The number of bracelets sold = 5

The number of necklaces sold = 1

Cost of the necklace = $22.50

Cost of the bracelets = x

The amount left = $150

The total amount in the account after selling them = $235

Now,

The equation can be used to find the cost of the bracelets.

5x + 22.50 + 150 = 235

Thus,

The equation can be used to find the cost of the bracelets.

5x + 22.50 + 150 = 235

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Answer:

The denominator of the fraction is 2x and the answer is a= -[tex]\frac{b}{2x}[/tex]

Step-by-step explanation:

Suppose we have a quadratic equation of the form:

ax²+bx+c

The axis of symmetry of the parabola is given by:

[tex]x= \frac{-b}{2a}[/tex]

From here, we must clear the value of a.

For this, we follow the following steps:

1) Pass 2a multiplying to the other side of the equation:

2ax=-b

2) Clear the value of a by passing 2x to divide:

[tex]a= \frac{-b}{2x}[/tex]

Answer:

B.

a= -b/2x

Step-by-step explanation:

Answer:

x =  28/5

Step-by-step explanation:

Step 1: Cross-multiply

x  / 28 = 2/10

x*(10)=(2)*(28)

10x=56

Step 2: Divide both sides by 10.

10x  / 10 = 56/10

x = 28/5

The given ratios can be solved to obtain x as 5.6.

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

The given expression is x/28 = 2/10.

In order to find the equality of two ratios, the cross products of their numerators and denominators are equal which is given as,

10x = 2 × 28

⇒ x = 56/10

⇒ x = 5.6

Hence, the value of x is given as 5.6.

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Answer:

A) The increase population of town after 3 years is 1.2 times initial population

B) The increase population of town after 5 years is 1.4 times initial population .

Step-by-step explanation:

Given as :

The rate of growth of population of a town = r = 7.5%

Let The initial population of town = p

A ) Let The increase population of town after 3 years = P

The time period = n = 3 years

Now, According to question

The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]

Or, The increase population of town after 3 years  = p × [tex](1+\dfrac{\textrm 7.5}{100})^{\textrm 3}[/tex]

Or, P = p × [tex](1.075)^{3}[/tex]

Or, P = p × 1.242

So, The increase population of town after 3 years = P = 1.2 times initial population

Hence,The increase population of town after 3 years is 1.2 times initial population .  Answer

B )  Let The increase population of town after 5 years = P'

The time period = n = 5 years

Now, According to question

The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]

Or,  The increase population of town after 5 years = p × [tex](1+\dfrac{\textrm 7.5}{100})^{\textrm 5}[/tex]

Or, P' = p × [tex](1.075)^{5}[/tex]

Or, P' = p × 1.4356

So, The increase population of town after 5 years = P' = 1.4 times initial population

Hence,The increase population of town after 5 years is 1.4 times initial population . Answer

Answer:

24%

Step-by-step explanation:

Formula:

   x                 new price - old price

---------    =     ---------------------------------

100%                      old price

Each computer costs $225 and each printer costs $150

Step-by-step explanation:

Thomas is starting a new company. He has two quotes from a computer company for the cost of computers and printers

We need to find how much each computer and printer costs

Assume that the cost of each computer is $x and the cost of each printer is $y

∵ The cost of each computer is $x

∵ The cost of each printer is $y

∵ The cost of 3 computers and one printer is $825

- Multiply x by 3 and add the product to y, equate the sum by 825

∴ 3x + y = 825 ⇒ (1)

∵ The cost of 4 computers and 2 printers is $1200

- Add the product of 4, x and the product of 2 , y and equate the

  sum by 1200

∴ 4x + 2y = 1200 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -2 to eliminate y

∵ -6x - 2y = -1650 ⇒ (3)

- Add equations (2) and (3)

∴ -2x = -450

- Divide both sides by -2

∴ x = 225

Substitute the value of x in equation (1) to find y

∵ 3(225) + y = 825

∴ 675 + y = 825

- Subtract 675 from both sides

∴ y = 150

Each computer costs $225 and each printer costs $150

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By setting up a system of equations from the scenarios provided, we can determine that each computer costs $225 and each printer costs $150.

To determine the cost of each computer and printer, we can set up a system of equations based on the information provided. Let C represent the cost of one computer and P represent the cost of one printer. Using the first scenario where three computers and one printer cost $825, we can write the first equation as:

3C + P = $825 ... (1)

For the second scenario where four computers and two printers cost $1200, we can write the second equation as:

4C + 2P = $1200 ... (2)

Next, we'll solve this system of equations using either substitution or elimination method. To use elimination, we can multiply equation (1) by 2 to eliminate the printers:

6C + 2P = $1650 ... (3)

Now, we subtract equation (2) from equation (3) to find C:

6C + 2P - (4C + 2P) = $1650 - $1200

2C = $450

C = $225

We now know each computer costs $225. To find the cost of a printer, we can replace C in either equation (1) or (2). Let's use equation (1):

3(225) + P = $825

675 + P = $825

P = $825 - 675

P = $150

Thus, each computer costs $225 and each printer costs $150.

Note: As you missed to mention the graph for f(x) = x + 1 from where we had to check which option defines the accurate graph. But, after a little research, I was able to get the graph of this question, and hence attaching the graph. So, I am answering based on that graph which, anyways, would clear your concept about determining the domain of the function that shows in a graph.

Answer:

x > 1 is the domain of the f(x) = x + 1.

Step-by-step explanation:

A domain is the set of all x values that a function passes through. It means a domain is set of all input values where the function is defined, meaning whatever you input the x value, for every x-value there is only one y-value that corresponds to it.

So, now lets talk about the given function f(x) = x + 1 and its graph as shown in attached figure. Carefully observe the top right part of the graph of f(x) = x + 1. It is validating the condition of x > 1.

For example,

Just input some x values, greater than 1 i.e. x > 1, in f(x) = x + 1 to determine the output values.

For example, for x > 1

and so on.

So, the top right part of the graph of f(x) = x + 1 is validating the condition of x > 1 as it is passing through P(2, 3), P(3, 4) and P(4, 5) etc. and so on.

So, x > 1 is the domain of the f(x) = x + 1.

Keywords: domain, function

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Answer:

"D"  X > 1

Step-by-step explanation:

HOPE THIS HELPS!!!

Answer: [tex]x=2[/tex]

Step-by-step explanation:

Given a System of linear equations, the solution of the system is the point [tex](x,y)[/tex] in which the lines intersect, where "x" is the x-coordinate and "y" is the y-coordinate.

Having the following System of equations:

[tex]\left \{ {{9x - 6y = 12} \atop {3x + 2y =8}} \right.[/tex]

You can use the Elimination method to find the value of "x":

-Multiply the second equation by 3.

- Add the equations.

- Solve for "x".

Then, you get:

[tex]\left \{ {{9x - 6y = 12} \atop {9x +6y =24}} \right.\\.......................\\18x=36\\\\x=\frac{36}{18}\\\\x=2[/tex]

Answer:

9000

Step-by-step explanation:

When you are rounding to the thousands, if the hundreds place is 500 or greater you have to round up in the thousands place.

That would mean 8923 rounded to the thousands place would equal 9000

Hope This Helps!

Answer:

9000  

Step-by-step explanation:

To  round a number to the nearest thousand, you look at the number in the hundreds place.

If the number in the hundreds place is

Here's how to round 8923 to the nearest thousand.

The rounded number is 9000.

Answer:

The markup percentage is 61.2

Step-by-step explanation:

Given as :

The cost price of each ornaments = $23

The sell price of each ornament = $37.08

Let The markup percentage = x

Now, According to question

Markup percentage = [tex]\dfrac{s.p - c.p}{c.p}[/tex] × 100

Or, x% = [tex]\dfrac{37.08 - 23}{23}[/tex]

Or, x% = [tex]\dfrac{14.08}{23}[/tex]

Or, x% = 0.612

∴ x = 0.612 × 100

I.e x = 61.2

So, The The markup percentage = x = 61.2

Hence, The markup percentage is 61.2 Answer

Good evening ,

Answer:

x²-9x+12 = (x - (9/2))²- (33/4)

Step-by-step explanation:

Look at the photo below for the details.

:)

In order to find the variables p and q in the equation x^2 - 9x + 12 = (x-p)^2 - q, we first complete the square on the left-hand side which leads us to determine that p=4.5 and q=32.25.

The original equation given is x^2 - 9x + 12 = (x-p)^2 - q. To find the values of p and q, we need to rewrite the left-hand side of the equation in the format of (x-p)^2. This can be done through a process known as completing the square. Looking at the equation x^2 - 9x + 12, we have a perfect square x^2 - 9x + (9/2)^2 = (x-4.5)^2. However, remember, we added (9/2)^2 to both sides, so we have (x-4.5)^2 = x^2 - 9x + 12 + 20.25. Simplifying, (x-4.5)^2 = x^2 - 9x + 32.25, which is our original equation format. Thus, p=4.5 and q=32.25.

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Answer:

x = -5

Step-by-step explanation:

let the number be x

"five times a number" : 5x

"Six more than five times a number" : 5x + 6

"twice the number" = 2x

"Six more than five times a number = 2x - 9

"Six more than five times a number" = "Six more than five times a number

5x + 6 = 2x - 9

5x - 2x = -9 -6

3x = -15

x = -15 / 3

x = -5

Answer:

61%

Step-by-step explanation:

15.25/25

=0.61

Multiply it by 100 and you will get the answer

Whole row form: 15.25/25*100

61 percentage was received.

Hope that helps! :)

Answer: He received 61%

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

To, find the percentage (p):

p = t/T x 100

Replacing with the values given:

p = (15.25/25)x100

p= 0.61 x 100=61%

He received 61%

Feel free to ask for more if needed or if you did not understand something.

84 miles I would think

Explanation:

14 whales in all, each travelled 6 miles.

14x6=84

Hope I helped :)

Answer:

35/ 12

Step-by-step explanation:

5/6 divided by 2/7

= 5/6 x 7/2

= 35/ 12

Answer:

Okay, so the first one is" The point (0, 2.50) is on the graph" second one is "The graph has a y-intercept but no x-intercept" And the third one would be "The graph increases from left to right"

Answer:

Step-by-step explanation:

30 lbs in 3 hrs....

30/3 = 10 lbs per hr <==

Answer:

10 pounds

Step-by-step explanation:

if you divide 30 by 3 you will get 10 and becuase there are three hours you will have the answer as 10

30÷3=10

10×3=30

Answer:

see the explanation

Step-by-step explanation:

we know that

The y-intercept is the value of the function when the value of x is equal to zero. Also is called the initial value of the function

I will analyze two cases

Part 1) we have

[tex]f(x)=-3x[/tex]

so

For x=0

substitute

[tex]f(0)=-3(0)=0[/tex]

therefore

The y-intercept is the point (0,0)

Part 2) we have

[tex]f(x)=-3^x[/tex]

so

For x=0

substitute

[tex]f(0)=-3^0=-1[/tex]

therefore

The y-intercept is the point (0,-1)

Answer:

[tex]\large\boxed{x=\dfrac{50y-585}{156}}[/tex]

Step-by-step explanation:

[tex]y=0.39(8x+30)\qquad\text{use the distributive propety}\\\\y=(0.39)(8x)+(0.39)(30)\\\\y=3.12x+11.7\qquad\text{multiply both sides by 100}\\\\100y=312x+1170\qquad\text{subtract 1170 from both sides}\\\\100y-1170=312x\qquad\text{divide both sides by 312}\\\\\dfrac{100y-1170}{312}=x\\\\x=\dfrac{100y:2-1170:2}{312:2}\\\\x=\dfrac{50y-585}{156}[/tex]

Answer:

f(x) = (2x + 1)(2x − 1)

Explanation:

As we can see from the above function f(x) = 4[tex]x^{2}[/tex] − 1, we need to find x-intercept, i.e., the value of x where this function's value is zero.

So let us Equate the function with zero

4[tex]x^{2}[/tex] - 1 = 0 => 4[tex]x^{2}[/tex] = 1 => [tex]x^{2}[/tex] = 1/4 => x = [tex]\sqrt{1/4}[/tex]

Hence we get 2 values of x, i.e., +1/2, and -1/2.

So now we need to check out the functions which are zero at this values of x, so let us substitute values of x in each and every option and see the values of functions.

Option A - f(x) = (4x + 1)(4x − 1) = 3, -3

Option B - f(x) = (2x + 1)(2x − 1)  = 0

Option C - f(x) = 4(x2 + 1)  = 5

Option D - f(x) = 2(x2 − 1) = -3/2

Hence answer is Option B

Answer:

200g of sugar, 600g of flour, 400g of butter

Step-by-step explanation:

50g sugar = 15 biscuits

3 x 50g = flour --) 150g = flour

2 x 50g = butter --) 100g = butter

60/15 = 4; 4 times as much

4 x 50g = 200g of sugar

4 x 150g = 600g of flour

4 x 100g = 400g of butter

The amount of flour she needed is 600g.

Given that,

Based on the above information, the calculation is as follows:

50g sugar = 15 biscuits

[tex]= 3 \times 50g\\\\ = 150g\ flour[/tex]

And.  

[tex]= 2 \times 50g \\\\= 100g \ butter[/tex]

Now  

[tex]= 60\div15[/tex]

= 4 times

Therefore, the amount of floor should be

[tex]= 150 \times 4[/tex]

= 600 grams.

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Answer:

2x^2-16x+34

Step-by-step explanation:

Since Y is equal to -5

And  you substitute -5 in the equation.

You now have -5=2x^2-16x+29

Add 5 to both sides

5-5=2x^-16x+29+5

The solution of the system of equations will be given as x = 4 ± i.

The solution of the equation means the value of the unknown or variable.

The equations are given below.

y = – 5                      ....1

y = 2x² – 16x + 29    ....2

From equation 1 and 2, we have

2x² – 16x + 29 = –5

2x² – 16x + 34 = 0

x² – 8x + 17 = 0

Then the value of x will be

[tex]\rm x = \dfrac{-(-8) \pm \sqrt{(-8)^2 - 4 * 1 * 17}}{2*1}\\\\x = \dfrac{8\pm \sqrt{-4}}{2}\\\\x = \dfrac{8 \pm 2\iota}{2}\\\\x = 4 \pm \iota[/tex]

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Answer:5x+7y

Step-by-step explanation:

Your welcome

Answer:

Mean= 59.8 and median = 59.5

Step-by-step explanation:

Mean  = Summation of values/ No. of Values

Mean of Girls' height= 61+58+63+57+58+59+62+64+60+56/10

Mean=  598/10= 59.8

Arranged Data = { 56, 57,58,58,59, 60, 61,62,63,64}

As the number of observations is even so the 5th and 6th value will be added and divided by 2

59+60/2= 59.5

Median = 59.5