The freshman and sophomore classes at Yardley High School are decorating floats for homecoming. The freshmen have already spent $51 on their float, plus they need to buy floral sheeting that costs $41 per roll.
The sophomores, who have spent $115 so far on theirs, still need to purchase vinyl grass at $40 per roll. Both classes plan to buy the same number of rolls, since they have the same area to cover. By coincidence, the two floats will have the same total cost in the end. How much will each class spend in total?
How many rolls will each class be buying?
The two classes will have each spend
$____
in total by buying $____ rolls

The equation that represents the total number of black and white squares on the chess board is 8 * 2² = 32

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

The chess board

From the chess board, we have

Black squares = 32

White squares = 32

When factorized, we have

Black squares = 32 = 8 * 2²

White squared = 32 = 8 * 2²

Hence, the equation that represents the squares on the chess board is 8 * 2² = 32

Read more about equation at

https://brainly.com/question/148035

#SPJ1

Answer:

312

Step-by-step explanation:

Add the area of each face together

Don't forget the units!

Let's start by finding the right face (12 by 3). From your picture, we can tell its 12m long, and 3m tall. To find the aria of any face, we multiply the length, times the width.
12 x 3 = 36.
Now let's look at where it says 8m. Since that face is just as tall as the first one, we can tell its 3m tall.
8 x 3 = 24.

We can continue this for the top face.
Since the width of the second face we did is 8m, and the width of the first one is 12m, we can tell that the top one is 8 x 12. (96).

We can do this again for the other 3 sides.
A shortcut i like to take, is to do 3 of the sides, (Like the ones we did) and add them together, then double the sum.

36+24+96=156.

156x2=312.

This shortcut should work, because by adding the aria of half the sides together, we get exactly half the answer.

When doing this, it only works to do 3 different sides. it will not work if you do the same side twice, or a parallel side.

I encourage you to let me know if this method works for you! I hope this helps!

The statement X = Y + Yxy is True.

The equation given is:

X = Y + Yxy

To find x = (X- Y) / Yy we have to substitute the value of x in X = Y + Yxy as

X = Y + Yxy

X = Y + Yy (X-Y) / Yy

To solve for x, we can rearrange the equation as:
X = Y +  X - Y

X = X

Thus, the statement is True.

Learn more about Equation here:

https://brainly.com/question/29657983

#SPJ1

Answer:

0.58 = 58% probability she passes both courses

Step-by-step explanation:

We can solve this question treating the probabilities as a Venn set.

I am going to say that:

Event A: She passes the first course.

Event B: She passes the second course.

The probability she passes the first course is 0.67.

This means that \(P(A) = 0.67\)

The probability she passes the second course is 0.7.

This means that \(P(B) = 0.7\)

The probability she passes at least one of the courses is 0.79.

This means that \(P(A \cup B) = 0.79\)

a. What is the probability she passes both courses

This is \(P(A \cap B)\).

We use the following relation:

\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)

So

\(P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.67 + 0.7 - 0.79 = 0.58\)

0.58 = 58% probability she passes both courses

Answer:

Step-by-step explanation:

Reflecting a point across the x-axis results in changing the sign of the y-coordinate, but keeping the x-coordinate the same. Reflecting a point across the y-axis results in changing the sign of the x-coordinate, but keeping the y-coordinate the same.

Reflecting (5,2) across the x-axis gives (5,-2), and reflecting it across the y-axis gives (-5,2).

Reflecting (-6,12) across the x-axis gives (-6,-12), and reflecting it across the y-axis gives (6,12).

Reflecting (2,-7) across the x-axis gives (2,7), and reflecting it across the y-axis gives (-2,-7).

Reflecting (-4,-2) across the x-axis gives (-4,2), and reflecting it across the y-axis gives (4,-2).

Reflecting (0,-2) across the x-axis gives (0,2), and reflecting it across the y-axis gives (0,-2).

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

For more questions on prime number

https://brainly.com/question/145452

#SPJ8

Answer:

26in

Step-by-step explanation:

The heights of the people in relation to their shadow lengths are proportional.

78in/63in = x/21in

The child's shadow is 1/3 the length of his mom so his height is 1/3 of hers.

78/3 = 26 in

Answer:

The son is 26 inches tall.

Step-by-step explanation:

\(\frac{x}{21} = \frac{78}{63}\)

\(x= \frac{21x78}{63}\)

21x78= 1638

1638÷63=26

Hope this helps

Sorry if I got it wrong!

Answer:

uoyhhgvooihyjug

Step-by-step explanation:

uyfiuyf

Answer:

y = \(\frac{1}{3}\)x + 1 \(\frac{1}{3}\)

Step-by-step explanation:

y = -3x - 1

1. Perpendicular line needs the opposite (reciprocal) of the slope.

             reciprocal of -3 is -1/3, slope 1/3.                    y = 1/3x + b

2. Now find the b (y-intercept).                                     1 = 1/3(-1) + b

                                                                                       1 = -1/3 + b

                                                                                 + 1/3  +1/3

                                                                                    1 1/3 = b

3. Answer         y = \(\frac{1}{3}\)x + 1 \(\frac{1}{3}\)

Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.

Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.

Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.

At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.

To learn more about equilibrium of demand and supply:

https://brainly.com/question/30237240

The graph for the linear equation y = - 4 x + 2 has been obtained.

We are given a linear equation:

y = - 4 x + 2

We need to graph this linear equation.

We will first find out some points that satisfies this equation.

So, the points are:

 x           y

- 2         10

- 1           6

0           2

1          - 2

2         - 6

Now plotting these points on the graph, we can obtain the graph of the linear equation.

Therefore, the graph for the linear equation y = - 4 x + 2 has been obtained.

Learn more about equation here:

https://brainly.com/question/1214333

#SPJ1

Answer:

0.3542 = 35.42% probability that the third light is red

Step-by-step explanation:

For each light:

If it is green, 77% probability that the next is green.

If it is red, 77% probability that the next is red.

If the first light is green, what is the probability that the third light is red?

These following outcomes are desired, for the second and third lights:

G - R(0.77, then 1 - 0.77 = 0.23 probability)

R - R(0.23, then 0.77 probability).

So the desired probability is:

\(p = 0.77*0.23 + 0.23*0.77 = 0.3542\)

0.3542 = 35.42% probability that the third light is red

Answer:

i tried but it said "This survey has been moved or deactivated by the survey owner" :(

Answer:

Step-by-step explanation:

find "q'

first take 2 as common

solution .

2(-9q+9q+q+7)=4

Now divided 2 by both sides.

2(-9q+9q+q+7) ÷2

=4÷2

-9q+9q+q+7 =2

q+7=2

q=2-7

q=-5 Answer.

Answer:

aã/fjd &dsjf éfbcsçvn bñßã

Answer:

Step-by-step explanation:

Full question is:

Number of bowls is:

Profit made:

The remainder is 5 + c, which means that the expression P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) divided by (x + 1) results in a quotient of\(5x^3 + 2x^2 - 4x + 4\) and a remainder of 5 + c.

To divide the polynomial P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) by the binomial (x + 1), we can use polynomial long division.

Let's set up the long division:

    \(5x^3 + 2x^2 - 4x + 4\)

_______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

We start by dividing the highest degree term of the dividend (5x^4) by the divisor (x + 1), which gives us 5x^3. We then multiply this quotient by the divisor (x + 1) and subtract it from the dividend:

              \(5x^3(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- (\(5x^3 + 5x^2)\)

This leaves us with a new polynomial:\(2x^3 - 7x^2 - 3x + c\). We repeat the process by dividing the highest degree term of this polynomial (2x^3) by the divisor (x + 1), resulting in 2x^2. We then multiply this quotient by the divisor and subtract it from the polynomial:

              \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

-\((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

We continue this process until we reach the constant term, resulting in the remainder of the division.

At this point, we have:

               \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- \((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

-\((2x^2 + 2x)\)

_______________________

- 5x + c

- (-5x - 5)

_______________________

5 + c

For more such questions on remainder visit:

https://brainly.com/question/29347810

#SPJ8

Answer:

the first car has 25 gallons of gases while the second car has 35 gallons of gases

One example is if a guy studied 8 hours a day and score 75 marks and another studied 8 hours and scored 95 marks.

A function is a relation that states that each input should have only one output (or) a special type of relation (a collection of ordered pairs) that follows a rule, i.e., every X-value should be connected with only one y-value.

The Cartesian product is a subset of it. Alternatively, a collection of points (ordered pairs). In other words, the collection of the ordered pair is defined as the relationship between the two sets, where the ordered pair is generated by the object from each set.

One example of an everyday situation between relations that is not a function is if a guy studied 8 hours a day and score 75 marks and another studied 8 hours and scored 95 marks.

To know more about relations and functions follow

https://brainly.com/question/25638609

#SPJ1

The probability that a person chosen at random, who lives in the city, lives in the central or north region is 0.56

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Given that, the Probability distribution table shows the proportion of people living in five different regions of a city

Probability = Favourable Outcomes/Total Outcomes

Probability(of selecting a person from central or north region) = 0.44 + 0.12 = 0.56

Hence, probability that a person chosen at random, who lives in the city, lives in the central or north region is 0.56

For more references on probability, click;

https://brainly.com/question/11234923

#SPJ2

Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.

A variable is anything that may be altered in the context of a mathematical notion or experiment. Variables are frequently denoted by a single symbol. .

a. Input variables: hours worked as a cashier, payroll clerk, and assistant.

The total amount earned each week is the output variable.

b. To determine the weekly total, multiply the number of hours worked at each job by the hourly rate and put them together. As a result, the equation would be:

Total weekly wage = (hours worked as a cashier x cashier hourly rate) + (hours worked as a payroll clerk x payroll clerk hourly rate) + (hours worked as an aide x rate per hour as an aide)

c. The amount of hours worked as an assistant is always 10 hours fewer than that of a payroll clerk. Therefore, if x denotes the number of hours worked as a payroll clerk, then the number of hours worked as an assistant may be denoted as (x - 10).

d. The equation describing the total money earned each week is as follows:

(20 x 9.5) + (x x 9) + ((x - 10) x 7) = y

This expression is simplified as follows:

y = 190 + 9x - 70 + 7x

y = 16x + 120

Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.

f. The realistic replacement values for x would be determined by the maximum number of hours you may work at each job as well as the amount of time available to work. Working 8 hours as a payroll clerk may be a reasonable substitute value if you have restricted availability, but 50 hours is unlikely.

g. If you do not work as an aide, you may calculate your total weekly income by setting the number of hours worked as an aide to zero in the calculation for the total amount earned each week. This results in:

y = 16x + 120 + 0

y = 16x + 120

As a result, the total weekly wage would be determined only by the number of hours performed as a cashier and payroll clerk.

To know more about variable visit:

https://brainly.com/question/2466865

#SPJ1

Answer:

190

Step-by-step explanation:

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

Work Shown:

1 gallon = 3.785 liters ..... given info

50*(1 gallon) = 50*(3.785 liters) .... multiply both sides by 50

50 gallons = 189.25 liters

50 gallons = 189 liters .... round to the nearest whole number

Solution:

Given:

From the graph above, a frequency table can be made as shown below;

To calculate the mean;

Therefore, the mean is 9.45

To calculate the median;

Median is the middle term when the data is arranged in rank order.

Since we have 20 terms, then the middle terms will be the 10th and 11th terms.

The median will be the mean of these two numbers.

Therefore, the median is 9.5

To calculate the mode;

The mode is the data that appears most in the set. It is the data with the highest frequency.

From the graph

From the graph

Answer:

the radius is 16 and the diameter is 32

Step-by-step explanation:

diameter is always radius times two

Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.

A cylinder is three-dimensional. It's not a flat thing. There are parallel circular bases in this shape. These bases have a curved face affixed to them. A cylinder in this instance has three faces. Along both end of a curved face, which rounds back to the face's origin, are two spherical bases.

Given that-

Volume of cylinder = πr²h

Volume of cylinder = 3.14 *5²*18

Volume of cylinder = 3.14*25*18

Volume of cylinder = 1413 ft³

Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.

Know more about the cylinder:

https://brainly.com/question/23935577

#SPJ1

Answer:

\(\frac{623}{8}\)

Step-by-step explanation:

\(\frac{78.875x1000}{1 x 1000} =\frac{77875}{1000}\)\(= \frac{623}{8}\)

Answer:

623/8

Step-by-step explanation:

steps to convert decimal into fraction

Write 77.875 as  

77.875

1

Multiply both numerator and denominator by 10 for every number after the decimal point

77.875 × 1000

1 × 1000

=  

77875

1000

Reducing the fraction gives

623

8

Based on the figures given in the table, the rate of change of the function is b. 5.

This can be found as:

= (Y₂ - Y₁) / (X₂ - X₁)

Use points:

(0, 1/2) and (1, 5/2)

Solving gives:

= (5/2 - 1/2) / (1 - 0)

= 5

Find out more on the rate of change at https://brainly.com/question/25184007.

#SPJ1

Answer:2x+1

Step-by-step explanation:

Answer: Increases in X tend to be accompanied by increases in Y

Step-by-step explanation:

The option given that indicates a positive value for a correlation is that an increases in X tend to be accompanied by increases in Y.

When two variables are said to be positively correlated, it simply means that the variables move along the same direction. As one variable increase, the other variable too will slow increase and vice versa.