How do you do a question like this? 80% as a fraction in simplest form.


Answer 1
Answer: Take away 0.20 of the amount.

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Paula knows the total cost for 100 students will be $750, and the cost total cost for 150 students is $1050. What is the caterer’s fixed cost and the rate per student served?


The caterer’s fixed cost and the rate per student served is $6 and $150

How to choose what quantity to multiply the first equation?

This method is actually called method of elimination to solve a system of linear equations.

We make one specific variable's coefficients of equal magnitude so that we can subtract or add the equations and eliminate that variable to make it easy to get the value of the other variable which will then help in getting the value of the first variable (if working in dual variable system).

If we have equations:

a_1x + b_1y = c_1\na_2x + b_2y = c_2

then, if we want to eliminate variable x, then we have to multiply equation 1 with


which will make coefficient of x in first equation as

a_1 * - (a_2)/(a_1) = -a_1

Then adding both equation will eliminate the variable x.


Cost of 100 students= $750

Cost of 150 students= %1050

Let the fixed cost of caterer be x

and the cost per student be y



solving the above equations;




The fixed cost is $150, while the per-student cost is $6.

Learn more about linear equations;


Step-by-step explanation:

the price charged for 100 students reflects the cost per student that applies to the order as a whole.

100 * 6 = $600, so the fixed cost is 750-600 = 150.


We can check this by substituting in the other equation.

Does 150*6 + 150 = 1050?


900+150 = 1050.

Yes, it does


We can express this relationship by the equation:

y = mx + b


y = total cost

m = $6 per student

x = number of students

b = fixed costs = 150

y = 6x + 150

your softball team has 8, 10, 9, and 3 hits during four games. Write and solve an equation to find how many hits the team needs in the fifth game to have a total of 40 hits​




Step-by-step explanation:

8+10+9+3=30. So, 40-30=10


Step-by-step explanation:

Add 9 to 10 to get 19, then add 3 to get 22, then add 8 to get 30.

A coral reef grows 0.14 m every week. How much does it grow in 14 weeks? Write your answer in millimeters.​



0.14*14= 1.96

Step-by-step explanation:

Must multiply 0.14 times 14 for the answer.

A box contains 5 plain pencils and 5 pens. A second box contains 3 color pencils and 7 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected


The events 'select a plain pencil' and 'select a color pencil' are independent. therefore the probability of both occurring is the product of their probabilities:
P(plain\ pencil\ and\ color\ pencil)=(5)/(10)*(3)/(10)=(3)/(20)
The answer is 3/20 or 0.15.

Order of operation and mathematical con vent ion


PEMDAS - Parenthesis, exponent, multiply, divide, add, subtract

Final answer:

In mathematics, the order of operations and mathematical conventions are vital to ensure the correct solution of equations. This includes principles like scientific notation for handling large or small numbers, and dimensional analysis for ensuring the validity of equations involving different units of measurement.


The order of operations and mathematical convention are fundamental in accurately solving mathematical equations or expressions. This involves following certain rules, such as the use of scientific notation or the principles of dimensional analysis, to ensure equations and operations are performed correctly and yield valid results.

Take for example scientific notation, used for expressing very large or small numbers. When multiplying two numbers expressed in scientific notation, the process is simplified: you multiply coefficients and add exponents. E.g., (3 × 105) × (2 × 109) = 6 × 1014.

Alternatively, dimensional analysis is a technique used to check the validity of equations involving mathematical operation on quantities. It works on the premise that the units of these quantities have to undergo the same mathematical operations as their numbers. This ensures consistency and coherence of dimensions and units in the expression or equation, preventing impossible situations such as adding length to time.

Learn more about Order of Operations here:


AC is a straight segment as shown in the diagram below. If the distance between points A and C is 67 miles, determine the distance between points A and B.


Final answer:

Without additional information such as the location of point B along line segment AC, or the distances from B to either A or C, it is impossible to determine the distance between points A and B based on the provided details.


The problem here is lacking some necessary information to accurately determine the distance between points A and B. Given that AC is a straight line segment and the distance between A and C is 67 miles, we still need further details to conclude the distance from A to point B, such as knowing the position of point B along segment AC, or the distances from B to either A or C. Without these specifics, it's impossible to determine the distance between points A and B based upon the given information.

Learn more about Distance here: