Teresa, Charlie, and Justin served a total of 153 orders Monday at the school cafeteria. Justin served 4 times as many orders as Charlie. Teresa served 9 more orders than Charlie. How many orders did they each serve?

Answer:

20%

Step-by-step explanation:

let the percent be p

rewriting the expression:

p% of 170 is 34

or mathematically,

p% x 170 = 34

(p / 100) x 170 = 34   (divide both sides by 170)

p/100 = 34/170  (multiply both sides by 100)

p = (34 / 170)  x 100

p = 20

hence 34 is 20% of 170

75 % free throws are made by Morton

Solution:

Given that Morton made 36 out of 48 free throws last season

To find: Percent of free throws made by Morton

From given statement,

total number of throws = 48

throws made by morton = 36

Thus the percent of free throws made by Morton is given as:

[tex]percent = \frac{\text{number of throws made}}{\text{total number of throws}} \times 100[/tex]

Substituting the values, we get

[tex]percent = \frac{36}{48} \times 100\\\\percent = 0.75 \times 100 = 75 %[/tex]

Thus 75 % of his free throws are made by Morton

I think it's histograms for the first blank; distribution for the second blank; frequency for the third and final blank.

Hope this helps please let me know if I'm wrong :)))

Histograms show the distribution and frequency for a set of values. Distribution is how the values are spread out or grouped, and frequency is how often a value occurs in a set of numbers.

A frequency distribution is like a detailed count of all the different values or groups of values in a data set. When data are collected, a histogram provides a visual representation of this distribution. The distribution of the data can be divided into various classes or bins, where the count or frequency of data falling into each bin is tallied. This tally helps to visualise patterns such as the center, spread, and overall shape of the data.
The histogram consists of contiguous rectangles, with the height of each bar corresponding to the frequency of data points within that class interval. The horizontal axis (x-axis) typically represents the values or categories of the dataset, while the vertical axis (y-axis) represents the frequency of occurrences. This graphical tool allows us to quickly ascertain which values are more prevalent and identify the spread or variability of the data, as well as the center, which is considered the middle or typical value of the dataset.

Answer:

  D.  123.9 - 20.886x

Step-by-step explanation:

Using the distributive property, we find the expansion to be ...

  5.9(21) +5.9(-3.54x) = 123.9 -20.886x

_____

The distributive property tells you ...

  a(b+c) = ab +ac

The factor outside parentheses multiplies each of the individual terms inside parentheses.

Answer:

True

Step-by-step explanation:

Answer:

their sum: 2.8m

their difference: 1.2m

the third side's length should be smaller than their sum, larger than their difference

it could be: 1.3-1.4-1.5-1.6-1.7-1.8-1.9-2-2.1-2.2-2.3-2.4-2.5-2.6-2.7 but since it has to be a whole number, 2m is the only eligible answer.

Using the Pythagorean theorem, we can calculate the third side of the triangle considering both positions for the side: as the hypotenuse and one of the two remaining sides. In both cases, the result is rounded to a whole number due to the constraints of the question.

In this case, we need to calculate the third side of the triangle based on the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, which can be written as: a² + b² = c². To find the possible lengths of the third side, we need to consider that it should be a whole number, and use both possible positions: once as a hypotenuse and once as the other side of the triangle.

If the third side is the longest (hypotenuse), then based on the Pythagorean theorem: (1.9m)² + (0.7m)² = c². The answer should be rounded to a whole number.

If the third side is not the longest one, then we could subtract the square of the shorter side from the square of the longer one: (1.9m)² - (0.7m)² = (c)². Again, the answer should be rounded to a whole number.

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Answer:

The volume in cubic millimeter is 16182.

Step-by-step explanation:

Given:

Rectangular prism has base area 522 square millimeters and height 31 millimeters.

Now, to find the volume in cubic millimeter.

Base area = 522 square millimeters.

Height = 31 millimeters.

Now, to get the volume we put formula:

[tex]Volume=base\ area\times height[/tex]

[tex]Volume=522\times 31[/tex]

[tex]Volume=16182\ cubic\ millimeter.[/tex]

Therefore, the volume in cubic millimeter is 16182.

Answer:

D

Step-by-step explanation:

700/7= 100

100*2= 200

200+ (756-700)= 256

256 closest to 216 than to 204 or any other answer.

Answer:216.

Step-by-step explanation:

if ur doing the scantron so am i i hate it as much as you do

Answer:

C

Step-by-step explanation:

area if squre is πr^2

so...

[tex]\pi {r}^{2} = 3.14 \times 7 \times 7 = 153.86 {ft}^{2} [/tex]

r means radius and...radius is diameter/2

now we must subtract the area of the square

[tex] {a}^{2} = 10 \times 10 = 100 {ft}^{2} [/tex]

[tex]153.86 - 100 = 53.86 {ft}^{2} [/tex]

nearest answer is 50

Answer:

Step-by-step explanation:

r = 14/2 = 7 feet

Area of circle=πr²=22*7*7/7 = 22*7= 154 sq. feet

Area of square = side*side = 10*10 =100

Area of shaded region = Area of circle - Area of square

    =154 - 100 = 54 sq. feet ≈ 50 sq. feet

Answer:

1) 5.6 cents

2) 30 cds

Step-by-step explanation:

For both problems we can use the Rule of Three:

1) If 3 ounces of tomato sauce cost [tex]\$1.68[/tex], how many will cost 1 ounce?:

3 oz ---[tex]\$1.68[/tex]

1 oz --- ?

Then:

[tex]?=\frac{(1 oz)(\$1.68)}{3 oz}[/tex]

[tex]?=\$ 0.056[/tex]

This is the price in dollars, now we have to calculate it in cents, taking into account that [tex]100 cent=\$1[/tex]:

[tex]$ 0.056 \frac{100 cent}{\$1}=5.6 cents[/tex]  This is the price in cents of 1 ounce of tomato sauce

2) If Edward buys 60 cds for [tex]\$ 7[/tex] each, what is the cost of 60 cds?:

60 cds ---?

1 cd --- [tex]\$7[/tex]

[tex]?=\frac{(60 cds)(\$7)}{1 cd}[/tex]

[tex]?=\$ 420[/tex] This is what Edward spends in 60 cds for [tex]\$7[/tex] each

Now, we have to calculate how many cds Edward can buy for [tex]\$14[/tex] each and spend the same [tex]\$ 420[/tex]:

1 cd --- [tex]\$14[/tex]

? cds ---[tex]\$ 420[/tex]

[tex]?=frac{(\$ 420)(1 cd)}{\$14}[/tex]

Finally:

[tex]?=30 cds[/tex]

Answer:

5.3x − 8.14 + 3.6x + 9.8

group the numbers on one side and the x's on the other

5.3x + 3.6x - 8.14 + 9.8

solve

8.9x +  1.66

Brainliest pls ;)

The given algebraic expression simplifies to 8.9x + 1.66 by combining like terms.

The question you've asked appears to be a linear algebraic expression. Here is how you would simplify it. First, you should group like terms together. So, the equation becomes 5.3x + 3.6x - 8.14 + 9.8. You will add together the x-terms and the constants separately, resulting in 8.9x + 1.66. Therefore, the simplified form of the given algebraic expression is 8.9x + 1.66.

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Final answer:

The equation representing the total cost for an adult and five children renting skates, with the adult's rental at $4 and the total at $16, is 4 + 5x = 16.

Explanation:

The question is asking for an equation that represents the total cost for an adult and five children renting skates where the adult's rental costs $4 and the total cost is $16. To write this equation, we let x be the cost for renting skates for a child. Since there are five children, the cost for the children's skates is 5x. Adding the adult's cost, we have the total cost expressed as 4 + 5x = 16.

Explanation: We know that the cost for one adult is $4, so that's a fixed amount. Since we don't know the individual cost for a child's skate rental, that's our variable x. We have five children, so we multiply x by 5. Adding up the adult's cost and the children's cost gives us the total cost, which is $16, and thus we arrive at our final answer, 4 + 5x = 16.

Answer:

Krutika get 21

Alex get 21

Gordon get 7

Step-by-step explanation:

Given: Total amount= 49

           Ratio= 3:3:1

Now, finding the amount received by Krutika, Alex and Gordon.

First, lets find the sum of ratio

Sum of ratio= [tex]3+3+1= 7[/tex]

We know now that amount will be distributed in the following fraction:

Krutika= [tex]\frac{3}{7}[/tex]

Alex= [tex]\frac{3}{7}[/tex]

Gordon= [tex]\frac{1}{7}[/tex]

∴ Amount received by Krutika= [tex]\frac{3}{7}\times 49= 21[/tex]

Alex,

Amount received by Alex= [tex]\frac{3}{7}\times 49= 21[/tex]

Gordon,

Amount received by Gordon= [tex]\frac{1}{7}\times 49= 7[/tex]

Hence, they get 21,21 and 7 respectively out of 49.

KKrutika and Alex each get £21, and Gordon gets £7.

To find out how much money each person gets, you need to divide the total amount of money (£49) in the ratio of 3:3:1.

First, add up the parts of the ratio to find the total number of parts: 3 + 3 + 1 = 7.  

Next, divide the total amount of money (£49) by the total number of parts (7) to find the value of one part: £49 ÷ 7 = £7.  

Finally, multiply the value of one part (£7) by each part of the ratio to find out how much money each person gets: KKrutika and Alex each get £7 × 3 = £21, and Gordon gets £7 × 1 = £7.

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Answer:

a.III

Step-by-step explanation:

We solve for x:

4x > 15

it gives

x > 3.75

Now we have to analyze our choices and see which solutions satisfy this inequality.

[tex]3\frac{1}{2} =3.5[/tex]

is not greater than 3.75; this isn't a solution.

[tex]3\frac{3}{4}=3.75[/tex]

is not greater than 3.75; this isn't a solution.

[tex]4\frac{1}{4}=4.25[/tex]

is greater than 3.75; this is a solution.

Thus only choice III is correct.

[tex]-3-2(5+1)-1-1\\-3-(2)(6)-(1-1)\\-3-12-(1-1)\\15-(1-1)\\15-0\\{Answer=-15 \checkmark[/tex]

Answer:

The algebraic expression for this problem is [tex]T=15x+3y[/tex].

Step-by-step explanation:

Given:

15 students fit in a van and 3 students will be traveling in a car.

So we can say that;

Number of students travelling by van = 15

Number of students travelling by car = 3

Now Let the number of vans be 'x'.

also Let the number of cars be 'y'.

Let the Total number of students bayside middle school be 'T'.

Solution:

now we can say that;

Total number of students going on field trip is equal to sum of Number of students travelling by van multiplied by the number of vans and Number of students travelling by car multiplied by the number of cars.

framing in equation form we get;

[tex]T=15x+3y[/tex]

Hence, The algebraic expression for this problem is [tex]T=15x+3y[/tex].

There are 43 nickels in the piggy bank.

Step-by-step explanation:

Given,

Amount in piggy bank = $6.95 = 6.95*100 = 695 cents

Total coins = 91

One nickel = 5 cents

One dime = 10 cents

Let,

x be the number of nickels

y be the number of dimes

According to given statement;

x+y=91          Eqn 1

5x+10y=695    Eqn 2

Multiplying Eqn 1 by 10

[tex]10(x+y=91)\\10x+10y=910\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](10x+10y)-(5x+10y)=910-695\\10x+10y-5x-10y=215\\5x=215[/tex]

Dividing both sides by 5

[tex]\frac{5x}{5}=\frac{215}{5}\\x=43[/tex]

There are 43 nickels in the piggy bank.

Keywords: linear equation, elimination method

Learn more about linear equations at:

#LearnwithBrainly

Final answer:

To find the number of nickels in the piggy bank, you can set up a system of equations. By solving the system, it is determined that there are 43 nickels.

Explanation:

To find the number of nickels in the piggy bank, we need to set up a system of equations. Let's assume that the number of nickels is 'x' and the number of dimes is 'y'.

We know that there are a total of 91 coins, so we can write the equation: x + y = 91.

We also know that the value of the nickels is 5 cents and the value of the dimes is 10 cents. The total value of the coins is $6.95, so we can write the equation: 5x + 10y = 695.

Solving this system of equations will give us the number of nickels.

First, let's multiply the first equation by 5 to eliminate 'x'.

5x + 5y = 455

Next, subtract this new equation from the second equation.

(5x + 10y) - (5x + 5y) = 695 - 455

5y = 240

y = 48

Finally, substitute the value of 'y' back into the first equation to find 'x'.

x + 48 = 91

x = 43

Therefore, there are 43 nickels in the piggy bank.

Answer:

C

Step-by-step explanation:

Slope-intercept form is y=mx+b. Y is y, m is the slope, x is x, and b is the y-intercept. The first thing you do is figure out the slope. The equation is (y2-y1)/(x2-x1). Then take 2 points from the table and substitute them in. I'll use the bottom two points: (4-2)/(2-1). You should get 2 as your answer. Substitute this in for m. Take a point from the table and substitute y in for y, x in for x. I'll use the last point: 4=2(2)+b. If I simplify further, I get 4=4+b, which means b is 0, and we won't need to put it in the equation.

Figure out the answer using the process of elimination: we know that because b=0, the answer can't be A or B. The slope is positive 2, which means that the answer can't be D. So it has to be C.

Answer:

i think the answer is Option D...

The 15th Amendment was necessary to address the barriers African Americans faced in voting, including discriminatory voting districts, poll taxes, literacy tests, and legal prohibitions against voting.

The necessary amendment referred to in the question is the 15th Amendment to the United States Constitution. This amendment was necessary because African Americans were facing significant barriers to voting, particularly in the Southern states. These barriers included the establishment of discriminatory voting districts, poll taxes, literacy tests, and legal prohibitions against African Americans voting in some states. The 15th Amendment aimed to address these issues by granting African American men the right to vote.

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Answer:

7/10

Step-by-step explanation:

4 1/2=9/2

3 4/5=19/5

9/2-19/5=45/10-38/10=7/10

Answer:

Option C. is the correct option.

Step-by-step explanation:

Clara found the product of (3 - 6y²) and (y² + 2) and she did it as below

(3 - 6y²)(y² + 2) = 3(y²) + (-6y²)×2 = 3y² - 12y² = -9y²

She did the step wrong as highlighted above. She did not use the distributive property correctly.

Now we will do it in a correct way.

(3 - 6y²)(y²+2) = 3(y² + 2) - 6y²(y² + 2)

= 3y^{2}+6-6y^{4}-12y^{2}=-6y^{4}-9y^{2}+6

Therefore Option C. is the correct answer.

Hope it helps:)

Answer:

-7/12

Step-by-step explanation:

An equation can be made out of this problem.

Sum means adding, so in this problem, you are adding 7 to the product of x and 12.

Product means multiplying, so you are multiplying x by twelve to get 12x.

Since you are adding all of this to 7, you get the equation 7 + 12x = 0.

Now, you just need to solve for x by subtracting the 7 over, giving you 12x = -7.

Now, to isolate x, divide both sides by 12. The twelves on the left cancel each other out, leaving you with -7/12.

Answer:

False

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b

where m is the slope and c the y- intercept

Answer:

The correct answer is:  Option 3.

Step-by-step explanation:

To begin the problem asks to find [tex]f[/tex]· [tex]g[/tex] which can be defined as [tex][f*g](x)[/tex]. Now we are given that:

[tex]f(x)=-5x+3\\g(x)=6x-2[/tex]

So now we need to 'multiply' our two algebraic expressions as follow:

[tex]fg(x)=(-5x+3)(6x-2)\\fg(x)=(-5x)(6x) +(-2)(-5x)+(3)(6x)+(3)(-2)\\fg(x)=-30x^2+10x+18x-6\\fg(x)=-30x^2+28x-6[/tex] Eqn.(1)

The domain of Eqn. (1) is all real numbers of [tex]x[/tex].

Which according to the given options , Option 3 is correct.

Answer: fog(x) = -30x + 13.

The domain is all the real  numbers.

Given that f(x)= -5x + 3 and g(x) = 6x - 2.

fog(x)

[tex]=f(g(x))\\=f(6x-2)\\=-5(6x-2)+3\\=-30x+10+3\\=-30x+13[/tex]

The domain is all the real numbers.

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Answer: (5,-4)

Step-by-step explanation: if u meant x^2-10x+21, the minimum point is (5,-4)

Answer: $7,864.32

Step-by-step explanation:

First you would do 100% -20% which would give you 80% (0.8)

1st year : $24,000 x 0.8 = 19,200

Then take your answer and times it by 0.8 again until you get to the 5th year

2nd year : $19,200 x 0.8 = $15,360

3rd year : $15,360 x 0.8 = $12,288

4th year : $12,288 x 0.8 = $9,830.40

5th year : $9,830.40 x 0.8 = $7,864.32

Therefore your final answer is $7,864.32

Final answer:

The resale value of the car after 5 years will be approximately $7,864.32.

Explanation:

To find the resale value of the car after 5 years, we need to calculate the depreciation rate each year and then apply it to the original purchase price. Since the resale value decreases by 20% each year, we can calculate the resale value after 5 years as follows:

After the first year, the resale value will be 80% of the original purchase price: $24,000 * 0.8 = $19,200.

After the second year, the resale value will be 80% of the previous year's resale value: $19,200 * 0.8 = $15,360.

After the third year, the resale value will be 80% of the previous year's resale value: $15,360 * 0.8 = $12,288.

After the fourth year, the resale value will be 80% of the previous year's resale value: $12,288 * 0.8 = $9,830.40.

After the fifth year, the resale value will be 80% of the previous year's resale value: $9,830.40 * 0.8 = $7,864.32.

Therefore, the resale value of the car after 5 years will be approximately $7,864.32.

Answer:

The correct answer is C. 30 percent

Step-by-step explanation:

What percent of the total overhead expense should be allocated to Department B?

For answering this question, we should make the following calculations this way:

Company's footprint = Department A + Department B + Department C

Company's footprint = 10,000 + 6,000 + 4,000

Company's footprint = 20,000 square feet

Overhead expense allocated to Department B = Department B footprint/Company's footprint

Overhead expense allocated to Department B = 6,000/20,000

Overhead expense allocated to Department B = 0.3 = 30%

The correct answer is C. 30 percent

Answer: The shortest side is 9ft

Step-by-step explanation: If the longest side is identified as 15 ft, then we already have our hypotenuse (the longest side in a right angled triangle).

If the shortest side is labelled as x, then the third side of the triangle would be labelled as 3x - 15 (15 less than three times the shortest side).

Now we have three sides of a triangle which we can label as 15, x and 3x - 15

By applying the Pythagoras theorem, AC² = AB² + BC²

(Where AC is the hypotenuse and AB and BC are the other two sides)

15² = X² + (3x-15)²

By expansion, (3x-15)² becomes 9x² - 90x + 225

Hence, 225 = X² + 9X² - 90X + 225

225 = 10X² - 90X + 225

Subtract 225 from both sides of the equation

10X² - 90X = 0

Factorize the left hand side of the equation by 10x

10x (x - 9)= 0

Therefore, either

10x = 0 OR

x - 9 = 0

If 10x=0, then x=0. OR

If x - 9 = 0, then x = 9

The length of the shortest side is 9ft.

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

Work Shown for part (i)

One base of triangle PQR is QR = 4

If the base is QR, then the height is PL = 5, which is perpendicular to QR.

area of triangle PQR = (1/2)*base*height

area of triangle PQR = (1/2)*QR*PL

area of triangle PQR = (1/2)*4*5

area of triangle PQR = 10

---------------------------------

Work Shown for part (ii)

Another base for triangle PQR is PR = 8

Imagine rotating triangle PQR so that PR is completely horizontal and flat.

Note: the diagram implies that MR = 8, but instead it's actually PR = 8

For the base PR, the perpendicular height is QM, which we'll label as x for now

area of triangle PQR = (1/2)*base*height

area of triangle PQR = (1/2)*PR*QM

area of triangle PQR = (1/2)*8*x

area of triangle PQR = 4*x

From part (i), we can set 4x equal to 10 since we know the triangle PQR has area 10 square cm.

4x = 10

4x/4 = 10/4

x = 10/4

x = (5*2)/(2*2)

x = 5/2

x = 2.5