1. (you may get teacher with this during tutoring)
solve this expression: 6x7-3^2x9+4^3 (the “^” means raise to the power of)

insert parentheses in expression 2 so that it has a value of 19. then show why your expression has a value of 19.
5+4x2+6-2x2-1

2. (you must try this one on your own and show all your work)
solve this expression: 3x7-3^3x9+4^2 (the “^” means raise to the power of)

insert parentheses in expression 2 so that it has a value of 19. then show why your expression has a value of 25.
5+3x2+6-2x3-7

3. (you may ask your teacher for on this one)
the average distance from the sun to the planet mercury is about 58,000,000 km. the diameter of a human hair is about 0.0025 cm.
(a) what is the distance from the sun to mercury written in scientific notation?

(b) what is the diameter of a human hair written in scientific notation?

4. (you must show your work and try this one on your own)
(a) what is 46,700,000,000,000 written in scientific notation?

(b) what is 0.0035 written in scientific notation?

5. (you may ask your teacher for on this question)
solve:
a.) (4.5x10^3) x (2x10^3)
b.) (1.4x10^5)/(1.2x10^5)

the average mass of an adult human is about 65 kilograms while the average mass of
an ant is approximately grams. the total human population in the world is
approximately 6.84 billion, and it is estimated there are currently about 10,000 trillion
ants alive.
based on these values, how does the total the total mass of all living ants compare to
the total mass of all living humans?

6. (on your own; show all work)
a.) (2.5x10^6) x (3x10^6)
b.) (1.1x10^7)/(1.2x10^7)

7. see additional worksheet. can ask for on odds; evens are independent.

1A --- 25

1B --- (5 + 4) x 2 + 6 - 2 x 2 - 1 = 19

2A --- -206

2B --- ?

3A --- 5.8 × 10⁷

3B --- 2.5 × 10⁻³

4A --- 4.67 × 10¹³

4B --- 3.5 × 10⁻³

5A --- 9 × 10⁶

5B --- 1.68 × 10¹⁰

5C --- All ants combined weigh 112.46 times more than all humans combined

Step-by-step explanation:

(I am using PEMDAS for Order of Operations)

1A

6 × 7 - 3² × 9 + 4³

Parenthesis

No parenthesis.

Exponents

6 × 7 - 3² × 9 + 4³

6 × 7 - 9 × 9 + 64

Multiplication

6 × 7 - 9 × 9 + 64

42 - 81 + 64

Division

No division.

Addition

42 - 81 + 64 (the 81 is negative)

42 + -17

25

1B

5 + 4 x 2 + 6 - 2 x 2 - 1 = 14

(5 + 4) x 2 + 6 - 2 x 2 - 1 = 19

9 x 2 + 6 - 2 x 2 - 1

18 + 6 - 2 x 2 - 1

18 + 6 - 4 - 1

24 - 5

19

2A

3 × 7 - 3³ × 9 + 4²

Parenthesis

No parenthesis

Exponents

3 × 7 - 27 × 9 + 16

Multiplication

21 - 27 × 9 + 16

21 - 243 + 16

Addition

21 - 243 + 16

21 - 227

Subtraction

21 - 227

-206

2B

5 + 3 × 2 + 6 - 2 × 3 - 7 = 4

(sorry cant figure this one out)

3A

Move the decimal point in 58,000,000.0 over x times until you have 5.8000000. It was moved to the left 7 times, so the answer is 5.8 × 10⁷.

3B

Move the decimal point in 0.0025 over x times until you have 2.5. It was moved to the right 3 times, so the answer is 2.5 × 10⁻³.

4A

Move the decimal point in 46,700,000,000,000.0 x times until you have 4.67. It was moved to the left 13 times so the answer is 4.67 × 10¹³.

4B

Move the decimal point in 0.0035 x times until you have 3.5. It was moved to the right 3 times, so the answer is 3.5 × 10⁻³.

5A

(4.5 × 10³)(2 × 10³)

4.5 × 2 = 9

10³ × 10³ = 10⁶

9 × 10⁶

5B

(1.4 × 10⁵)(1.2 × 10⁵)

1.4 × 1.2 = 1.68

10⁵ * 10⁵ = 10¹⁰

1.68 × 10¹⁰

5C

An adult human is 65 kilograms.

6.5 × 10¹ grams

An ant is (you didnt say how many so im going with) 5 grams.

5 × 10⁰ grams

6.84 billion humans

6,840,000,000.0 humans

6.84 × 10⁹ humans

10,000 trillion ants

1 × 10¹⁶ ants

Weight of humans:

(6.5 × 10¹)(6.84 × 10⁹)

44.46 × 10¹⁰

All humans weigh 4.446 × 10¹¹ kilograms

Weight of ants:

(5 × 10⁰)(1 × 10¹⁶)

All ants weigh 5 × 10¹⁶ grams

1000 grams per kilogram

1000 = 1 × 10³

5 × 10¹⁶ ÷ 1 × 10³

5 ÷ 1 = 5

16 - 3 = 13

All ants weigh 5 × 10¹³ kilograms

All humans weigh 4.446 × 10¹¹ kilograms

5 × 10¹³ ÷ 4.446 × 10¹¹ = 112.46

All ants combined weigh 112.46 times more than all humans combined

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.