MATHEMATICS
MIDDLE SCHOOL

Answer: 355÷5=

__71________

5(355

35 l

0 5

5

0

__71________

5(355

35 l

0 5

5

0

COLLEGE

A toll bridge charges $1.00 for passenger cars and $2.50 for other vehicles. Suppose that during daytime hours, 65% of all vehicles are passenger cars. If 20 vehicles cross the bridge during a particular daytime period, what is the resulting expected toll revenue? [Hint: Let X = the number of passenger cars; then the toll revenue h(X) is a linear function of X.]

65% of all vehicles are passenger cars......20 vehicles crosses the bridge

this means that 65% of 20 are passenger cars..

0.65(20) = 13 cars are passenger cars.....leaving (20 - 13) = 7 that are other vehicles.

toll bridge charges $ 1 for passenger cars and 2.50 for other vehicles...

expected toll revenue is : 13(1) + 7(2.50) = 13 + 17.5 = $ 30.50

this means that 65% of 20 are passenger cars..

0.65(20) = 13 cars are passenger cars.....leaving (20 - 13) = 7 that are other vehicles.

toll bridge charges $ 1 for passenger cars and 2.50 for other vehicles...

expected toll revenue is : 13(1) + 7(2.50) = 13 + 17.5 = $ 30.50

HIGH SCHOOL

I see that the amount i owe has been reduced from $90.00 to $75.00."

Answer:

its debt decreased by 16.6%

Step-by-step explanation:

If you decreased your debt from $ 90 to $ 75, it means that the rebate was $ 15

In percentage terms, you can calculate debt abatement in two ways:

Let x denote the value

1) By rule of 3

90 ---- 100%

15 = x%

x = 1500/90

x = 16.6%

2) Divide the discounted value by the total value

15/90 = 0.166

Then, simply multiply by 100 to reach the percentage

0.166 x 100 = 16.6

Therefore, its debt decreased by 16.6%

Then your amount was reduced to $15 less

COLLEGE

If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple are written in decreasing order but are not necessarily distinct? In other words, how many 5-tuples of integers (h, i, j, k, m) are there with n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1?

Answer:

Step-by-step explanation:

Lets divide it in cases, then sum everything

Case (1): All 5 numbers are different

In this case, the problem is reduced to count the number of subsets of cardinality 5 from a set of cardinality n. The order doesnt matter because once we have two different sets, we can order them descendently, and we obtain two different 5-tuples in decreasing order.

The total cardinality of this case therefore is the Combinatorial number of n with 5, in other words, the total amount of possibilities to pick 5 elements from a set of n.

Case (2): 4 numbers are different

We start this case similarly to the previous one, we count how many subsets of 4 elements we can form from a set of n elements. The answer is the combinatorial number of n with 4

We still have to localize the other element, that forcibly, is one of the four chosen. Therefore, the total amount of possibilities for this case is multiplied by those 4 options.

The total cardinality of this case is

Case (3): 3 numbers are different

As we did before, we pick 3 elements from a set of n. The amount of possibilities is

Then, we need to define the other 2 numbers. They can be the same number, in which case we have 3 possibilities, or they can be 2 different ones, in which case we have possibilities. Therefore, we have a total of 6 possibilities to define the other 2 numbers. That multiplies by 6 the total of cases for this part, giving a total of

Case (4): 2 numbers are different

We pick 2 numbers from a set of n, with a total of possibilities. We have 4 options to define the other 3 numbers, they can all three of them be equal to the biggest number, there can be 2 equal to the biggest number and 1 to the smallest one, there can be 1 equal to the biggest number and 2 to the smallest one, and they can all three of them be equal to the smallest number.

The total amount of possibilities for this case is

Case (5): All numbers are the same

This is easy, he have as many possibilities as numbers the set has. In other words, n

Conclussion

By summing over all 5 cases, the total amount of possibilities to form 5-tuples of integers from 1 through n is

I hope that works for you!

MIDDLE SCHOOL

How do you fine the slope of a line represented by the points in a table

By using the rise/run method.

Answer:

Step-by-step explanation:

Identify the changes in the y values of the table and the x values on the table.

so for example:

x y

1 -2

3 8

5 18

7 28

In this case the changes in the x values are 2,2,2

And the changes in he y values are 10,10, and 10.

So now you write them as fractions like y changes/ x-changes.

So now it is 10/2, 10/2, and 10/2 all of these simplify to 5.

Therefore you slope is 5.

MIDDLE SCHOOL

Find the GCF of each number.

75 ¢, 25¢, $1.50, $3.00

So,

To find the G.C.F. of $0.75, $0.25, $1.50, and $300,

Think of them as 75, 25, 150, and 300.

Find the prime factored form (P.F.F.) of each number.

P.F.F. of 75: 3*5*5

P.F.F. of 25: 5*5

P.F.F. of 150: 2*3*5*5

P.F.F. of 300: 2*2*3*5*5

Find common groups.

5*5 is in all of them.

5(5) = 25

25 is the G.C.F. of 75, 25, 150, and 300 ($.75, $.25, $1.50, and $3.00).

To find the G.C.F. of $0.75, $0.25, $1.50, and $300,

Think of them as 75, 25, 150, and 300.

Find the prime factored form (P.F.F.) of each number.

P.F.F. of 75: 3*5*5

P.F.F. of 25: 5*5

P.F.F. of 150: 2*3*5*5

P.F.F. of 300: 2*2*3*5*5

Find common groups.

5*5 is in all of them.

5(5) = 25

25 is the G.C.F. of 75, 25, 150, and 300 ($.75, $.25, $1.50, and $3.00).

The gcf of 75 cents, 25 cents ,$1.50 and $3.00 is 25 cents

COLLEGE

A student group investigates the relationship between iq and gpa, measured on a 12-point scale. they find the equation of the least-squares line to be gpa = –6 + 0.15*iq. along comes marilyn vos savant with an iq of 200. what does this regression say her gpa should be?

Gpa = -6 +0.15*200 = 24

HIGH SCHOOL

Evaluate the function f(p) = p2 + 3p + 1 for p = -2

Answer: -1

Step-by-step explanation:

The given function :

To find : The value of the given function ( ) at p =-2.

We substitute the value of p=-2 in the given function, we get

Therefore , the value of the given function at p=-2 = -1

P2 + 3p + 1

(-2)2 + 3(-2) +1

-4 +(-6) +1

-9

(-2)2 + 3(-2) +1

-4 +(-6) +1

-9

MIDDLE SCHOOL

If a cone shaped water cup holds 23 in.³ and has a radius of 1 inch what is the height of the cup use 3.14 for pie round into the nearest hundredth

The voolume of a cone is given by the formula:

You know the volume, the radius, and pi. Substitute those values into the formula and solve for h, the height.

h = 21.97 in.

You know the volume, the radius, and pi. Substitute those values into the formula and solve for h, the height.

h = 21.97 in.

MIDDLE SCHOOL

This is for my little brother Which equation is FALSE? A. 3+6=12-3

B. 6+6=12-0

C. 3+8=12-2

D. 7+2=14-5

C because 8+3 is 11 and 12-2 is 10

Answer:

3+6=9 12-3= 9 True

6+6=12 12-0=12 True

3+8=11 12-2=10 False

7+2=9 14-5=9 True