MATHEMATICS
HIGH SCHOOL

Answer: Given:

h = height

s = slant height

a = side length

e = lateral edge length

r = a/2

V = volume

L = lateral surface area

B = base surface area

A = total surface area

Pyramid 1.

h = 28 m

s = 29.1204 m

a = 16 m

e = 30.1993 m

r = 8 m

V = 2389.33 m³

L = 931.854 m2

B = 256 m²

A = 1187.85 m²

Pyramid 2

h = 112 m

s = 112.071 m

a = 7.99999 m

e = 112.143 m

r = 3.999995 m

V = 2389.33 m³

L = 1793.14 m²

B = 63.9999 m²

A = 1857.14 m²

h = height

s = slant height

a = side length

e = lateral edge length

r = a/2

V = volume

L = lateral surface area

B = base surface area

A = total surface area

Pyramid 1.

h = 28 m

s = 29.1204 m

a = 16 m

e = 30.1993 m

r = 8 m

V = 2389.33 m³

L = 931.854 m2

B = 256 m²

A = 1187.85 m²

Pyramid 2

h = 112 m

s = 112.071 m

a = 7.99999 m

e = 112.143 m

r = 3.999995 m

V = 2389.33 m³

L = 1793.14 m²

B = 63.9999 m²

A = 1857.14 m²

MIDDLE SCHOOL

Two mechanics worked on a car. The first mechanic charged $85 per hour, and the second mechanic charged $120 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1875 . How long did each mechanic work?

Let's make a system of equations.

F=First mechanic

S=Second mechanic

F+S=20

85F+120S=1875

Let's make the first equation equal S.

S=20-F; We can plug this in as S in the second equation.

85F+120(20-F)=1875

85F+2400-120F=1875

Add like terms.

-35F+2400=1875

Subtract 2400.

-35F=-525

Divide.

-525÷-35=15=F

So, the first mechanic worked 15 hours and the second one had to work 5 since they worked 20 together. Let's check.

85(15)+120(5)

1,275+600

1,875

So, the first mechanic worked 15 hours and the second mechanic worked 5 hours.

F=First mechanic

S=Second mechanic

F+S=20

85F+120S=1875

Let's make the first equation equal S.

S=20-F; We can plug this in as S in the second equation.

85F+120(20-F)=1875

85F+2400-120F=1875

Add like terms.

-35F+2400=1875

Subtract 2400.

-35F=-525

Divide.

-525÷-35=15=F

So, the first mechanic worked 15 hours and the second one had to work 5 since they worked 20 together. Let's check.

85(15)+120(5)

1,275+600

1,875

So, the first mechanic worked 15 hours and the second mechanic worked 5 hours.

HIGH SCHOOL

The regular price of some patio furniture is $230.00. Today, the patio furniture is on sale for 10% off. What is the amount of the discount?

10% * $230.00 = $23.00

The discount is $23.00.

_____

Of course, you know that 10% expressed as a decimal is 0.10. Many calculators will calculate percentages directly. If yours doesn't, you can use the decimal equivalent. If you recognize that multiplying by 1/10 simply shifts the decimal point to the left one place, you can do the arithmetic in your head.

The discount is $23.00.

_____

Of course, you know that 10% expressed as a decimal is 0.10. Many calculators will calculate percentages directly. If yours doesn't, you can use the decimal equivalent. If you recognize that multiplying by 1/10 simply shifts the decimal point to the left one place, you can do the arithmetic in your head.

MIDDLE SCHOOL

Evaluate the function f(x) = x 2 + 1 for f(2). 1 5 7

If you get a function like f(2), you have to know that the 2 in the brackets/parentheses pretty much replaces the “x” in the equation. Think about it:

If we have f(x) and f(2), that must mean x=2

So we insert the value of x into the function and we get:

f(2)= 2*2+1=4+1=5

So 5 is the answer

If we have f(x) and f(2), that must mean x=2

So we insert the value of x into the function and we get:

f(2)= 2*2+1=4+1=5

So 5 is the answer

MIDDLE SCHOOL

Solve 3(x - 2) < 18 {x | x < 8}

{x | x > 8}

{x | x < -8}

{x | x > -8}

Answer:

x < 8

Step-by-step explanation:

MIDDLE SCHOOL

What is 5d=470 and what is 8a=47

5d=470:

in this case we have to divide both sides by 5:

d=94

8a=47:

in this case we have to divide both sides by 8:

a=5.875

as a general rule, if you want to find out a value of a in

ab=c

you have to divide both sides of the equation by b (if it's not zero); then you will have left:

a=c/b

and if you calculate c/b, this will give you the answer

in this case we have to divide both sides by 5:

d=94

8a=47:

in this case we have to divide both sides by 8:

a=5.875

as a general rule, if you want to find out a value of a in

ab=c

you have to divide both sides of the equation by b (if it's not zero); then you will have left:

a=c/b

and if you calculate c/b, this will give you the answer

MIDDLE SCHOOL

A barge can safely haul no more than 400 tons across the river. The barge has an empty weight of 24 tons. The average weight of the railroad cars is 4 tons each. How many railroad cars can the barge haul?

Answer:

The barge can caul 94 railroad cars.

Step-by-step explanation:

As the barge can safely haul no more than 400 tons across the river, and the barge itself has an empty weight of 24 tons, it has an available capacity of 376 tons (400-24). So, as every railroad car weighs 4 tons, in order to know how many railroad cars the barge can haul we have to divide the available capacity by the weight of each railroad car.

According to it, we have to divide 376 by 4 (376 / 4), which gives us a result of 94, which is the maximum number of railroad cars that the barge can haul.

Answer:

94

Step-by-step explanation:

t = tons

Here's your initial equation. 400-24=4t

The empty weight means how much the barge itself weighs, so I've got to get rid of that.

I'm solving for the left side... 400-24 = 376

376=4t

Now I'll divide both sides by 4.

376/4=94

The barge can haul 94 railroad cars.

HIGH SCHOOL

Multiply the fractions and simplify the answer 2/5 ×5/7×1/2

Let's write it as fractions:

we can simplify whatever is both in the nominator and the denominator: so fist, 5:

now, 2:

so:

this is the answer!

we can simplify whatever is both in the nominator and the denominator: so fist, 5:

now, 2:

so:

this is the answer!

If you would like to multiply the fractions 2/5 * 5/7 * 1/2, you can calculate this using the following steps:

2/5 * 5/7 * 1/2 = (2 * 5 * 1) / (5 * 7 * 2) = 1/7

The correct result would be 1/7.

2/5 * 5/7 * 1/2 = (2 * 5 * 1) / (5 * 7 * 2) = 1/7

The correct result would be 1/7.

MIDDLE SCHOOL

83023007 expanded form

80,000,000 + 3,000,000 + 20,000 + 3,000 + 7

HIGH SCHOOL

Eric deposits $100 into a savings account at time 0, which pays interest at a nominal rate of i, compounded semiannually. Mike deposits $200 into a different savings account at time 0, which pays simple interest, at an annual rate of i. Eric and Mike earn the same amount of interest during the last 6 months of the 8th year. Calculate i. Choose one of the following. Source: Society of Actuaries.

(a) 9.06%

(b) 9.26%

(c) 9.46%

(d) 9.66%

(e) 9.86%

Answer:

Option (c) 9.46%

Step-by-step explanation:

Amount deposited by Eric = $100

Amount deposited by Mike = $200

Interest rate = i

Now,

For Eric

Amount after 7.5 years, A = Principle ×

= $100 ×

thus,

for the last 6 months i.e 0.5 year = A ×

= A ×

therefore,

Interest earned = A × - A

= A ×

= $100 ×

= $50i ......(1)

For Mike

Interest = Principle × i × Time

= $200 × i × 0.5

= $100i .........(2)

Equating (1) and (2)

$50i = $100i

or

= 2

or

= 1.0473

or

= 1.0473 - 1

or

= 0.0473

or

i = 0.0946

or

i = 0.0946 × 100% = 9.46%

Hence,

Option (c) 9.46%