MATHEMATICS
MIDDLE SCHOOL

Answer: The answer is 2 1/4 because 0.25 is equal to 1/4. So 1/4 plus 2 is 2 1/4

Answer: The first thing to do here is convert it to a mixed number.

.25 should be a somewhat familiar decimal. it's created by the fraction (1/4), so instead of 2.25, you could write this as 2 1/4 (two and one-fourth).

now that you have 2 1/4, convert it to an improper fraction. remember, multiply the bottom of your fraction with the big number out front, then add to the top of your fraction. set it over your denominator.

2 1/4 ... 4*2 is 8, 8 + 1 is 9, and your resulting fraction is (9/4).

.25 should be a somewhat familiar decimal. it's created by the fraction (1/4), so instead of 2.25, you could write this as 2 1/4 (two and one-fourth).

now that you have 2 1/4, convert it to an improper fraction. remember, multiply the bottom of your fraction with the big number out front, then add to the top of your fraction. set it over your denominator.

2 1/4 ... 4*2 is 8, 8 + 1 is 9, and your resulting fraction is (9/4).

MIDDLE SCHOOL

James has 16 balloons. One fourth of them are red. How many red balloons does he have?

16 balloons or 16/1 (16 wholes) multiplied by 1/4

16*1=16

1*4=4

remake the fraction as 16/4

simplify (divide both the numerator and denominator by 4)

4/1 or 4 balloons are red

16*1=16

1*4=4

remake the fraction as 16/4

simplify (divide both the numerator and denominator by 4)

4/1 or 4 balloons are red

Answer:

Only four of his balloons are red.

Step-by-step explanation:

COLLEGE

A 1000-liter (L) tank contains 500 L of water with a salt concentration of 10 g/L. Water with a salt concentration of 50 g/L flows into the tank at a rate of Rin=80 L/minutes (min). The fluid mixes instantaneously and is pumped out at a specified rate Rout. Let y(t) denote the quantity of salt in the tank at time t. Assume that Rout=40L/min. (a) Set up and solve the differential equation for y(t). (b) What is the salt concentration when the tank overflows?

Answer:

a)

b)

Step-by-step explanation:

By definition, we have that the change rate of salt in the tank is , where is the rate of salt entering and is the rate of salt going outside.

Then we have, , and

So we obtain. , then

, and using the integrating factor , therefore , we get , after integrating both sides , therefore , to find we know that the tank initially contains a salt concentration of 10 g/L, that means the initial conditions , so

Finally we can write an expression for the amount of salt in the tank at any time t, it is

b) The tank will overflow due Rin>Rout, at a rate of , due we have 500 L to overflow , so we can evualuate the expression of a) , is the salt concentration when the tank overflows

MIDDLE SCHOOL

Consider the expressions $\frac{4x^3+2x^2+6x+7}{2x+1}$ and $2x^2+3+\frac4{2x+1}.$ a) Show that these expressions are equal when $x=10.$

b) Explain why these expressions are not equal when $x=-\dfrac12.$

c) Show that these expressions are equal for all $x$ other than $-\dfrac12.$

In parts (a) and (c), begin by explaining what your strategy for solving will be.

Part (a) We shall simplify both of them in order to find the solution to the equation.

- Once we've done that, we'll see that they have the same equation, so we can match the equation if x=10.

Part (b) When x=-1/2, the answers to the second expression, 2x2, change to -1, and we eventually arrive in 1.

- This is why the expressions are not equal at this point.

Part (c) As we can see, the expressions are identical, thus we can demonstrate that they are equal if x is any number other than -1/2.

What is an expression in maths?- An expression is a set of terms combined using the operations +, – , x or , for example 4 x − 3 or x 2 – x y + 17 .
- An equation states that two expressions are equal in value, for example 4 b − 2 = 6 .
- An identity is a statement that is true no matter what values are chosen, for example 4 a × a 2 = 4 a 3 .

- An expression is a set of numbers or variables combined using the operations +, –, × or ÷.
- Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.

- To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
- To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.

Learn more about expressions here:

brainly.com/question/723406

#SPJ2

Answer:

Part a) In order to solve the equation, we will simplify both of them. Once we do that, if we notice, they are the same equation, so therefore, if x=10, then we will be able to match the equation.

Part b) The reason the expressions are not equal when x=-1/2 is because if we see, that in the second expression, 2x^2, if x=-1/2, then the answer becomes -1, and we eventually end up with 1.

Part c) As we can see, the expressions are the same, so if x is any number other than -1/2, then we will be able to show that the expressions are equal.

Step-by-step explanation:

You can simplify the explanation, also if you play ROBLOX, follow me at my username: BAMUNJI, or 24KBlingYT

By the way, this question is from the Art of Problem Solving, and you should not just copy answers or copy of them.

HIGH SCHOOL

John runs a computer software store. Yesterday he counted 127 people who walked by his store, 58 of whom came into the store. Of the 58, only 25 bought something in the store. Estimate the probability that a person who walks into the store will buy something (put your answer as a fraction).

33/58, will buy something in the store