Math

8. Can negative numbers have square roots? Explain.

No, because a negative times a negative, or a negative number to the 2nd power, is positive, and a positive number times a positive number is a positive.

A. 0.3

Rational, Real

B. 1/7

Real, Irrational

D. pi

Real, Irrational

E. 42

Real, Rational, Integer, Natural, Whole

C. 0

Real, Rational, Integer, Whole

27) Jayden and his father baked 10 dozen cookies. He left 1/8 of the baked cookies home and took the rest to the Prep beach day picnic. How many cookies did Jayden take to beach day? (t = taken cookies)

t = (10 x 12) x (1 - 1/8) t = 120 x ⅞ t = (120 x 7) / 8 t = 840/8 t = 105

b. −17

x − 15. 15 + -17 = 15 - 17 = -2. x = -2

d. 2(n + 5)

−2. 2n + 10 = -2. -2 - 10 = -12. 2n = -12, so n = -6

a. 17x

−204. (17x)/17 = -204/17. x = -12

√ 48

√16 x 3 = 4√3

√175

√25 x 7 = 5√7

√294

√49 x 6 = 7√6

f. -2 - 2

-4. -4 x 4 = -16. V = -16

x^-3

-4^-3 = 1/-4^3 = 1/-64

−33v − 49v

-82v

Write 5.6% as a decimal. 0.056

0.056

100,000

1 x 10^5

Cost of a computer: $1,850.00 Markup: 75%

1,850.00 x 0.75 = 1387.50. 1850.00 + 1387.50 = 3237.50

77a²

7 x 11 x a x a

77,777.7

7.77777 x 10^4

Original price of a book: $18.50 Discount: 45%

$18.50 x 0.45 ≈ 8.33. $18.50 - 8.33 = $10.17

From 141 grams to 142 grams

(142 - 141) / 141 = 1/141 = 0.7%

From 43 minutes to 160 minutes

(160 - 43) / 43 = 117/ 43 ≈ 272.1

(2.3 x 10⁻⁴) - (6 x 10⁻⁶)

(2.3 - 0.06) x 10^-6 = 2.24 x 10^-6

(4.72 x 10⁵) + (3.3 x 10⁶)

(4.72 + 33) x 10^5 = 37.72 x 10^5 = 3.772 x 10^6

From 70 to 62

(62 - 70) / 70 = -8/70 ≈ −11.4%

a. b.

(m3n) / 5; 1 / (2a2)

105.0076

1.050076 x 10^2

11

1.1 x 10

12. There are 24,000 voters in Millville. If only 37.5% of them voted in the last election, how many of the registered voters did not vote?

100 - 37.5 = 62.5. 62.5% of 24,000 = 15,000 voters.

Write 0.123 as a percent

12.3

(3.5 x 10³) x (4 x 10⁵)

14 x 10^8 = 1.4 x 10^9

11. Bill works at an electronics store. He gets a 15% discount on equipment sold in the store. How much can he save on a VCR that sells for $165?

15% of 165 = $24.75

−9r + 10r

1r

24.79

2.479 x 10^1

e. 8 x 3

24. 24 - 9 = 15. v = 15

c. ⅕v

25. 25 / (⅕) = 25 / 0.2 = 125. v =125

13. By Thursday, the cutters and sewers in a clothing factory had made 280 jackets. This is 87.5% of the total number of jackets they were expected to make for the week. What is the total number of jackets the workers had to make that week? 280/0.875

280/0.875 = 320 jackets

y^-7

2^-7 = 1/(2^7)

(7.5 x 10⁵) / (2.5 x 10³)

3 x 10^2

What percent of 65 is 23?

35.38

⅜ ⅔ 1 ¾ ⅛ 2 ⅗

37.5% 66.7% 175% 12.5% 260%

12.5% of what number is 48?

384

3^x

3^-4 = 1/3^4 = 1/81

3(x-2)

3x- 6

7. What is the approximate cube root of -28? Estimate to the nearest hundredth, and justify your answer with a written explanation. (Three points)

3√-28 ≈ -3.04 because -28 is about -33, which is -27.

4 − 5(−4n + 3)

4 - (-20n) - 15 = 4 + 20n - 15 = -11 + 20n = 20n - 11

132

4 x 33 = 2 x 2 x 33 = 2 x 2 x 3 x 11 = 22 x 3 x 11

0.4521 0.0307 3.63 0.1 0.7

45% 3% 363% 10% 70%

4y - 7(y-1)

4y - 7y - (-7) = -3y - (-7) = -3y + 7

23. Asanji took a trip to Mexico. Upon leaving he decided to convert all of his Pesos back into dollars. How many dollars did he receive if he exchanged 42.7 Pesos at a rate of $5.30 = 11.1 Pesos?

5.30/(11.1) = x/42.7. Since x/42.7 times 42.7 = x, (5.30/11.1) x 42.7 ≈ 20.39 dollars, which is about 20 dollars.

0.056

5.6 x 10^2

d

50 / 1.25

Find 11.3% of 460.

51.98

Write 7/12 as a percent

58.3

22. Ming was planning a trip to Western Samoa. Before going, she did some research and learned that the exchange rate is 6 Tala for $2. How many Tala would she get if she exchanged $6?

6/2 = 18/6 (Multiply by 3/3). 18 Tala

15 is 24% of what number?

62.5

8y^-4

8(2)^-4 = 8 x 2^-4 = 8 x 1/2^4 = 8 x 1/16 = 8/16 = 1/2

Write 82.5% as a fraction 82.5/100

82.5/100 = 3.3/4 = 33/40

Original price of a toy: $90.50 Tax: 4%

94.12

Solve the following using algebra. FIrst translate the prose into an expression, then solve for the unknown. Include a key.

98% = 88 points. 88 x 0.98 = 86.24 points.

Cost of a sled: $99.50 Markup: 95%

99.50 x 0.95 = 94.525 or $94.53. 99.50 + 94.53 = 194.03

Can negative numbers have cube roots? Explain.

Yes, because a negative number multiplied by itself 3 times, gives you a negative number. If you have an odd number as a exponent and a negative number as a base, then you have a negative number.

28) When an alligator is born it is about 8 inches long. Each year alligators grow about 12 inches. Determine the age of a 116 inch long alligator.

a = (116 - 8) / 12. a = 108 / 12 a = 9 The alligator will be 9 years old when it is 116 inches long.

a² x a⁷

a9

(b⁴)³

b12

26) Albert must take 1.25 milliliters of medicine every day. How many days will the medicine last if Albert was given a prescription of the medicine in a bottle containing 50 milliliters? d = amount of days the medicine will last. 1.25 is the amount of medicine per day. 50 is the quantity of medicine.

d = 50 / 1.25 Factors of 50: 1, 2, 5, 10, 25, 50 Multiples of 1.25 : 1.25, 2.5, 3.75, 5, 6.25.... Five is a common number; 5 d = 40

d⁴ x d⁻⁶

d^-2 = 1/d^2

(e⁻³)³

e^-9 = 1/e^9

f⁴ f ⁻⁷

f(4 - (-7) ) = f 4 + 7 = f11

25) Amelia wanted to buy a new computer and printer which had a total cost of $1099.95. She had saved $389.85 for her purchase. How much more does she need to save to buy the computer and printer she wants? m = (how much more she needs to save). 1099.95 = total cost. 389.85 = much she saved right now.

m = 1099.95 - 389.85. = $710.10