Each of 36 students at a school play bought either a cup of orange juice or a sandwich. A cup of orange juice costs $1 and a sandwich costs $3. The total amount collected was $76. How many students bought orange juice, and how many bought a sandwich?

Let x represent the number of students who bought a cup of orange juice and y represents the number of students who bought a sandwich. Then the problem can be represented by this system of equations:
x + 3y = 76
x + y = 36

Answer the questions to solve the problem.

1. Explain what you should do with the two equations to eliminate one of the variables. (2 points)

4. Interpret the solution and check the values in the system. (3 points)

equations of the line in slope intercept form:

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given two linear function,

For first equation:

2x +y = -3

in slope intercept form

y = -2x - 3

For second equation:

Given second line passes through the origin

thus, equation of the line.

y = mx

where m is slope

m = (y₂ - y₁)/(x₂ - x₁)

in our case,

m = (0 -2)/(0-(-4))

m = -1/2

Thus, equation of second line;

y  =-1/2x

Therefore, equations of the line in slope intercept form:

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If Mr. Rankin put $120 on the table, the change he would receive $8.82

What is Percentage ?

Percentage can be defined as the product ratio of given value, total value and hundred.

Mr. Rankin took his family out to dinner last night and their subtotal was $88.24. The sales tax was 5% and he left a 20% tip after the tax was added.

If Mr. Rankin put $120 on the table, the change he would receive

tax = 5/100 * 88.24

tax = 4.412

tip = 20/100 * 88.24

tip = 17.648

Total amount = 88.24 +4.412+17.648

= 111.18

So, If Mr. Rankin put $120 on the table, the change he would receive

= 120 -111.18 =  8.82

Therefore,  If Mr. Rankin put $120 on the table, the change he would receive $8.82

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I year of weekends= 105days therefore 105, therefore you need 105 ice cream bars? hoped this helped

Answer:(8 x r)+(8 x 1)

Step-by-step explanation:

[tex]8(r+1)[/tex]

Distribute:

[tex](8)(r)+(8)(1)[/tex]

[tex]\fbox{8r + 8}[/tex]

The total dinner bill was $177.90 including a tip of 20%.

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"

Given that, a restaurant adds a 20% gratuity (or tip), a dinner bill for a large party comes to $148.25, we need to find the total dinner bill with tip.

The total bill will be = 148.25 + 20% of 148.25

= 148.25 + 20/100 × 148.25

= 148.25 + 0.2 × 148.25

= 148.25 + 29.65

= 177.90

Hence, the total dinner bill was $177.90 including a tip of 20%.

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[tex]\dfrac{k}{0.1} =36[/tex]

Multiply both sides by 0.1:

[tex](\dfrac{k}{0.1} )\times0.1=(36)\times0.1[/tex]

[tex]\fbox{k = 3.6}[/tex]

the remaining soup at Adya's place is 24/114 liters As per the given ratio.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, Adya makes 9/38 liters of soup for a party. The guests eat 3/57 liters.

Since the total soup was 9/38 liters

Thus,

Remaining soup at Adya = 9/38 -3/57

LCM of 38 and 57 are 114

Remaining soup at Adya = 27/114 - 6/114

Remaining soup at Adya = 27/114 liters

Therefore, the remaining soup at Adya's place is 24/114 liters.

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Answer: No they are not.

Step-by-step explanation:

1/2x and -5/8x are like terms, if subtracted you get 1 1/8x. But then you are left with an unlike term, 3/4 so your first equation would equal out to 1 1/8x + 3/4

Now for equation 2, you use your distributive property and get 1/8(x)=1/8x

Then you must distribute 1/8(1)=1/8

1/8x + 1/8

So, 1 1/8x + 3/4 ≠ 1/8x + 1/8

62 points, he would need to improve his credit score in order to take a mortgage for $150,000.

What is a mortgage?

It is an agreement between you and a lender that allows you to borrow money to purchase or refinance a home and gives the lender the right to take your property if you fail to repay the money you've borrowed. A mortgage is a type of loan that's used to finance the property. A mortgage is a type of loan, but not all loans are mortgages. Mortgages are “secured” loans.

To calculate the monthly payment, we can use the formula:

M = P [i(1 + i)^n] / [(1 + i)^n – 1]

Where M is the monthly payment, P is the loan amount, i is the interest rate, and n is the number of payments (in this case, the number of months in 30 years)

Plugging in the values,

M = 150000 * (0.0929 / 12) / [ (1 + (0.0929 / 12))^(12 * 30) - 1]

This gives a monthly payment of $1238.

To find out how many points he needs to improve his credit score, we can compare this monthly payment to the maximum monthly payment he can afford, which is $14,000.

If $1238 is more than $14,000, he would need to improve his credit score to a point where the monthly payment would be less than $14,000. By looking at the table, we can see that the interest rate for credit score of 620-674 is 7.40%.

Hence, (D) option is the correct answer.

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Answer: the answer is A SO WERE IS MY COOKIE :(

Step-by-step explanation:

As per the collinear point, the common endpoint is called the vertex of the angle, and the rays are called the sides of the angle.

The term collinear point in math is defined as a set of three or more points that exist on the same straight line

Here we have given that an angle is two collinear rays with a common endpoint.

And we need to find an example that contradicts this definition.

Here we also know that an angle is the union of two noncollinear rays with a common endpoint.

Then the common endpoint is called the vertex of the angle and the rays are called the sides of the angle.

And it is measure of an angle is a number representing the spread of the two arms of the angle.

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The probability that the track star wins at least one race is 0.8, the probability that she wins the first race but not the second is 0.2, and the probability that she wins the second race but not the first is 0.1

Let A be the event that the track star wins the first race, B be the event that the track star wins the second race.

The probability that the track star wins at least one race is: P(A U B) = P(A) + P(B) - P(A ∩ B)

The probability that the track star wins the first race but not the second race: P(A ∩ B') = P(A) - P(A ∩ B)

The probability that the track star wins the second race but not the first race: P(A' ∩ B) = P(B) - P(A ∩ B)

Given:

P(A) = 0.7

P(B) = 0.6

P(A ∩ B) = 0.5

P(A U B) = 0.7 + 0.6 - 0.5 = 0.8

P(A ∩ B') = 0.7 - 0.5 = 0.2

P(A' ∩ B) = 0.6 - 0.5 = 0.1

So the probability that the track star wins at least one race is 0.8, the probability that she wins the first race but not the second is 0.2, and the probability that she wins the second race but not the first is 0.1.

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Answer:

y = 2/3x + 6

Step-by-step explanation:

for this problem, we need to find the value of b (the y-intercept). to do so, all we have to do is plug in the x and y values of the given ordered pair into  the x and y values of the function. this will give us:

[tex]4=\frac{2}{3}(-3)+b[/tex]

solve for b and we get 6.

so, our slope-intercept equation is  [tex]y=\frac{2}{3}x +6[/tex] .

hope this helped, good luck!

Answer: The formula for population growth of bacteria with a constant doubling time is P = Po*2^(t/d), where P is the population after t hours, Po is the initial population, t is the time in hours, and d is the doubling time.

Given the initial population of 8600 bacteria and a doubling time of 5 hours, we can substitute these values into the formula:

P = 8600 * 2^(7/5)

To find the population after 7 hours, to the nearest whole number, we can use a calculator to calculate 2^(7/5) which is approximately 3.7 and then multiply it with the initial population.

P = 8600*3.7

P = 31420

So, the population of bacteria in the culture after 7 hours will be around 31420.

Step-by-step explanation:

Any pair of positive numbers x and y that satisfy the inequality x * y > 50 will be the sides of rectangle.

If the area of rectangle P is greater than 50 square units, then the product of its length and width must be greater than 50. Let the length of the rectangle be x and the width be y. Then, we have:

x * y > 50

Since the missing side length is unknown, we cannot solve for a specific value. But we can say that any pair of positive numbers x and y that satisfy the inequality will represent a rectangle with an area greater than 50 square units.

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The cost to rent each chair and table, based on the total cost to the party rental company, is:

Let x be the cost of renting one chair and y be the cost of renting one table.

From the first piece of information given, we can write the equation:

3x + 2y = 25

From the second piece of information given, we can write the equation:

5x + 6y = 65

Solving these equations using elimination gives:

3x + 2y = 25

5x + 6y = 65

15x + 10y = 125

15x + 18y = 195

Subtracting gives:

0x + 8y = 70

y = $ 8.75

The cost to rent a chair is:

3x + 2 (8.75) = 25

3x + 17.5 = 25

3x = 7.5

x = $ 2.5

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Answer: A, B, E

Step-by-step explanation:

For A:

None of the factors have one same factor they can be divided by besides 1.

For B:

Both 20a and 24b can be divisible by 1,2,4.

For E:

Both 20a and 15ab are divisible by 1,5 and a.

If John bought 9 bags and spent $5.00, using simultaneous equations, the number of each kind of bag he bought is 7 bags of popcorn and 2 bags of caramel corn.

Simultaneous equations are two or more equations solved simultaneously or concurrently.

When two or more equations are solved at the same time, they are described as simultaneous equations or a system of equations.

The cost of popcorn per bag = $0.50

The cost of caramel corn per bag = $0.75

The total number of bags bought = 9

The total cost of the 9 bags = $5

Let the number of bags of popcorn = p and the number of caramel corn = c

0.5p + 0.75c = 5 ... Equation 1

p + c = 9 ... Equation 2

Multiply Equation 2 by 0.5:

0.5p + 0.5c = 4.5  ... Equation 3

Subtract Equation 3 from Equation 1:

0.5p + 0.75c = 5

-

0.5p + 0.5c = 4.5

0.25c = 0.5

c = 2

p = 9 - 2

= 7

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Answer:

When y = 3, we can substitute 3 for y in the expression 3 y^2 - 4 y + 8

3(3^2) - 4(3) + 8

= 3(9) - 12 + 8

= 27 - 12 + 8

= 15

Therefore, the value of the expression 3 y^2 - 4 y + 8 when y = 3 is 15.

Answer:

Basically since y = 3 we just have to remove the 'y' from the equation and replace it with the number 3. (Also pretty sure you wrote the equation twice)

Original Equation:

3 y^2 - 4 y + 8

Modified Equation:

→ 3 (3²) - 4(3) + 8

→ 3 (9) - 12 + 8

→ 27 - 12 + 8

→ 15 (answer)

Equation with 'y' included:

→ y (y²) - 4 (y) + 8

→ y (9) - 12 + 8

→ 27 - 12 + 8

→ 15 (answer)

Answer:

The remaining distance will be "56 km".

Step-by-step explanation:

Speed and Time:

The speed (s) of an object seems to be the rate at which it travels from one location to some other. It's also calculated by dividing the distance (d) traveled by the timeframe (t) or duration.

According to the question,

Average speed when cross a late, 108 km/h

On particular day, average speed 94 km/h

Time taken, 4 hours

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^^^^^^

not my work

where I found the answer

Answer: y = -4x -2

Step-by-step explanation:

For a linear equation, we can use this formula:

y - y_1 = m(x - x_1)

We have the slope and the coordinates, so we can just plug everything in:

y - 14 = -4( x + 4)

y - 14 = -4x -16

y = -4x -2

Answer:

C

Step-by-step explanation:

This looks like a case of multiplying the number of X's by the respective number below it.

For example: the 1/2 has 3 X's, so we multiple (1/2)(3), making it (3/2) or 1.5

Next is the 1 having 2 X's, so (2)(1) is 2

Continuing that trend we get the following

1.5, 4, 2.5, and 3.

So all of our totals are 1.5, 2, 1.5, 4, 2.5, and 3.

Our last step will be adding all these answers together.

1.5 + 2 = 3.5

+ 1.5 = 6

+ 4 = 10

+ 2.5 = 12.5

and finally +3 = a grand total of 15.5 or 15 1/2

Answer: 599 times

Step-by-step explanation: 3594/6=599

If the pizza is divided in to four equal parts , then each equal part is named as "one fourth" .

The fraction is defined as a numerical value that is part of a whole. Fraction is evaluated by dividing a whole into number of parts.

For Example : 1/2 represents the half part of the whole .

The pizza is divided into four equal part ;

So , the total number of parts in the pizza is = 4 parts ,

one part of the pizza will be written in fraction form as : 1/4 ;

We can say that each pizza slice is 1/4 of whole pizza and  1/4 is read out  as "one fourth".

The given question is incomplete , the complete question is

What fraction names the 4 equal parts of the whole pizza ?

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The line inside the circle depicted in the figure is radius.

A circle is defined as the round shape lacking corners and line. However, it does comprise of all the points in a plane. The center of the circle is the middle point which is equidistant from the outer surface of the circle. The outer surface or boundary of circle is called circumference.

A line joining the centre of the circle with circumference is called radius and the same is exhibited in the adjoining figure. A line that passes through the centre of the circle and touches the circumference at two ends is called diameter. Diameter is double in size to the radius.

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The complete question is attached in the figure.

The first equation, 3^x = 12, is an exponential equation. To solve for x, we would take the logarithm of both sides with base 3:

x = log3(12)

The second equation, x^3 = 12, is a polynomial equation of degree 3. To solve for x, we would take the cube root of both sides:

x = ∛12

The similarity between these two equations is that both are equations with one variable and are looking for the value of that variable.

The main difference between these two equations is the type of function they represent. The first equation is an exponential function, represented by 3^x, while the second equation is a polynomial function, represented by x^3.

As a result, the methods used to solve these equations are also different. The first equation is solved by taking the logarithm of both sides and the second equation is solved by taking the cube root of both sides.

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An algebraic expression for each verbal expression, and simplified indication of the properties are

1. 10t² + 2

2. d² + 2r

Arithmetic operations including subtraction, addition, division, multiplication, and exponentiation are used to build any algebraic expression from a combination of variables and integers. The word can be either a variable, a number, or the result of multiplying a variable by a number and adding an exponent.

Mathematical formulas like 3x + 4 are examples of algebraic expressions. They are distinct from algebraic equations because they lack the equals sign (=). The mathematics curriculum and mathematics in general place a lot of emphasis on algebraic expressions.

1. 9t² + 2 + t²

= 10t² + 2

2. 3d² + r - 2d² + r

= 3d²- 2d² + r + r

= d² + 2r

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120% can be expressed as a decimal by dividing it by 100: 120 / 100 = 1.2 So, 120% of 5x can be expressed as: 1.2 * 5x = 6x The expression simplifies to 6x.

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient. An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).These expressions are represented with the help of unknown variables, constants and coefficients. The combination of these three (as terms) is said to be an expression.

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the fireworks will be 612 feet high when it explodes.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, Pyrotechnicians can use polynomials to plan complex fireworks displays. A firework is launched from a platform 6 feet above the ground at a speed of 200 feet per second.

Expression that represents the height of firework = -16t² + 200t + 6

Since The firework has a 5-second fuse.

Thus, the firework will explode at t = 5

So, height at t= 5:

height of firework = -16 * 5² + 200*5 +6

height of firework = -16 * 25  + 1000 +6

height of firework = - 400 + 1000 + 6

Height of firework = 606

Since it started at 6 feet height

Thus total height at firework starts = 606 +6

total height at firework starts = 612

Therefore, the firework will explode at 612 feet in height.

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