math

2.56 ÷ 0.02 =

The correct answer is 128

15. If the ratio of males to females in a group of students is 3: 5, which of the following could be the total number of students in the group? (A) 148 (B) 150 (C) 152 (D) 154

There are 3x males and 5x females, where x is an integer. This means that the total number of students is 8x. Since 152 is the only multiple of 8, the only possibility is 152.

A six year old boy with a congenital heart disorder is admitted. Digoxin 0.12mg is ordered. The bottle in stock contains 0.05mg in 1mL of solution. How much should be administered?

Use rule of threes 0.12/0.05mg x 1mL Cross multiply 0.05mg*1mL And 0.12mg*1 Divide the remainding fraction to result in 2.4mL

fractions

adding fractions or subtracting: LCD Multiple fractions: straight across divide fractions: multiply the reciprocal

4. A nurse is to give the liquid medicine 3 times a day. The morning dose is 3/4 ounce, the noon dose is 1/2 ounce and the evening dose is 3/4 ounce. The nurse has 1 ounce of medicine at noon. How much more is needed?

er: 1 ounce

y=mx+b

mx= slope b= Y intercept

A nurse must mix a 20% solution of a medication in an existing container of water. If the container currently holds 12 ounces of water, how many ounces of medication should the nurse add to make the proper solution? (A) 2.5 (B) 3 (C) 3.6 (D) 4

x = 0.2 (x + 12)x = 3

A nurse must give a medication twice a day The first dose is 3/8 ounce the second dose is 2/7 ounce. She has 1 ounce of medication, will she have enough both doses?

yes Explain: find LCD and add fractions, since the result is 37/56 and the numerator is less than the denominator, 1 is a whole number which is more than 37/56.

hat is the solution to the problem -3 × 15 - 35 ÷ 5 + 25? -42 16 -6 -20

-20 since,-3 x 15 - 35 ÷ 5 + 25 -3 x 15 - 35 ÷ 5 + 32 -45 - 35 ÷ 5 + 32 -45 - 7 + 32 -20

hich step should be solved first when given the problem -4 ÷ 2 × 6 - 5 + 13? -4 ÷ 2 2 × 6 6 - 5 -5 + 13

-4 ÷ 2, because since there are not parentheses or exponents, our next step in PEMDAS is multiplication and division. These go along together that when you begin working out the problem from left to right, whatever operation you come across first is what you will work on. In this case it is division.

How to convert Celsius to Fahrenheit

-Multiply by 1.8 & add 32. Ex. 30 Celsius * 1.8 + 32 = 86 Fahrenheit

Renee's dress shop is suffering from slow business. Renee decides to mark down all her merchandise. The next day, she sells 33 winter coats. That day Renee sold 30% of the winter coats she had in stock. How many winter coats were in stock before the sale?

0.3x = 33x=110

At a diner, Joe orders 3 doughnuts and a cup of coffee and is charged $4.30. Stella orders 2 doughnuts and a cup of coffee and is charged $3.45. What is the price of 2 doughnuts?

0.85

1/3 + 1/6 - 4/9= ?

1) common denominator in the case its 18. 6/18 + 3/18 - 8/18 9/18-8/18= 1/18 answer: 1/18

What is the solution to the problem (4 - 2 × 4) - (3 × -4)3 ? -40 1,724 -1732 32

1,724 since,(4 - 2 x 4) - (3 x -4)3 (4 - 8) - (3 x -4)3 (-4) - (3 x -4)3 -4 - (-12)3 -4 - (-1728) 1724

A nurse must infuse 1.5mL of solution in x minutes and she has 650mL of solution how many minutes will it take for the medicine to be given?

1.5mL/650mL = 3 min/x min cross multiply ,to give 144. divide 144 by 60 = 2 minutes

Andrew bought a camera on sale at a 20% discount. It was marked down from it regular price of $120. If there is an 8% sales tax on the sale price, how much did Andrew pay for the camera?

103.68

Andrew bought a camera on sale at a 20% discount. It was marked down from its regular price of $ 120. If there is an 8% sales tax on the sale price, how much did Andrew pay for the camera?

103.68 The price would be (120 × 0.8) to show the 20% discount, with the result multiplied by 1.08 to include sales tax. ????

146 ÷ 12.3 =

11.87

At a certain school, if the ratio of teachers to students is 1 to 10, what would be the total number of teachers to students?

11:1 teachers to students

At a certain store, juice A costs $0.10 more per ounce than juice B. If a 12‑ounce bottle of juice A costs $5.64, what is the cost per ounce of juice B?

12-ounce bottle of juice A costs $5.64, then the cost per ounce of the juice A is $5.64÷12=$0.47 it follows that the cost per ounce of juice B is $0.47−$0.10=$0.37 =0.37

John bought a camera on sale that normally costs $ 160. If the price was reduced 20% during the sale, which was the sale price of the camera?

128 The price would be (160 × 0.8) to show the 20% discount.

A syringe contains 16mL of a medication and the nurse was ordered to give 20% less. How much medication should the nurse have in the syringe?

128mL Explain: 16mL/xmL = 100%/80% = 12.8mL

12. If 13 + a = 25 + b, then b − a = ? (A) 38 (B) 12 (C) 8 D) − 12 .

13+a=25+b 13+a-a=25+b-a 13=25+b-a 13-25=25-25+b-a -12=b-a

Edward has $ 400 more than Robert. After Edward spends $ 60 on groceries, he has 3 times more money than Robert. How much money does Robert have?

170 After Edward spends $ 60, he has $ 340 more than Robert, which is three times as much as Robert. x + 340 = 3x. step 1) 400-60=340 ????

Ruth has finished 3 chapters of an 8-chapter novel in just one evening of reading. If she reads an additional 1/10 of the novel tomorrow night, what part of the novel will she have finished? (A) 1/10 (B) 1/2 (C) 19/40 (D) 36/80

19/40

5 2/3 x 1/2 -5/12

2 5/12

2. A worker earns $ 16 per hour for the first 40 hours she works each week, and one and a half times this much for every hour over 40 hours. If she earned $ 700 for one week's work, how many hours of overtime did she work? A) 3.3 (B) 3 (C) 2.5 (D) 4

2.5 hours

Which is the value of a( b − 2) + 3c if a = 2, b = 6 and c = 4?

20

The price of a stock decreased by 20%. By what percent must the price increase to return to its original value? .

25%

Which is the value of x in the equation 6x − 7 = y, if y = 11?

3

33 - 6 ÷ (2 + 1) + 15

33 - 6 ÷ (2 + 1) + 15 Step 1: Solve the parentheses 33 - 6 ÷ (3) + 15 Step 2: Solve the exponents 27 - 6 ÷ 3 + 15 Step 3: Divide. 27 - 2 + 15 Step 4: Subtract, then add and find answer. 40

4. When z is divided by 8, the remainder is 5. Which is the remainder when 4z is divided by 8??

4 The easiest way to solve this problem is to substitute an actual number for z. The number 13 yields a remainder of 5 when divided by 8, so (4 × 13) ÷ 8 = 6 with a remainder of 4.

4 + -5 × 4 +(5-3)2

4 + -5 × 4 +(5-3)2 Step 1: Solve the parentheses 4 + -5 × 4 +(2)2 Step 2: Solve the exponents 4 + -5 × 4 + 4 Step 3: Multiply. 4 + -20 + 4 Step 4: Add and find answer. -12

What is 25% of 25% of 72??

4.5

ratio of 4:9 is the same as

4/13 or 9/13 Explain: add 4+9= 13, divide 4 or 9 by 13 to give desired answer

If 1/3 of people are elderly men and 2/8 are young women, what percent of people is older women?

41% Explain: 1 represents the entire amount of people. set up problem as follows: 1-1/3-2/8 find LCD, 24/24-8/24-6/24=10/24= 0.41x100= 41%

The physician orders codeine 60mg & aspirin x grains. Each codeine contains 15mg of codeine. Each aspirin tablet contains 325mg of aspirin. Which should be given?(round to the nearest whole number)

4mg codeine and 2.5 mg of aspirin Explain: 60mg/15mg x t (tablet) =4 10 grains/4mg x t (tablet)=2.5

2/3+ 3/8 -5/12

5/8

You are ordered to administer 250mg tablet of medicine to a patient that is 95% as effective as the house before. How long will it take before the medicine reaches the dangerous level of 52mg?

52=250(.95)^t .208=.95^t log .208=log.95^t log .208= t(log .95) log .208 / log .95 =t 30.61 hours =t

If a microbiologist cultured 3000 cells at a rate of 7% how many days will it take for 360 new cells to reproduce?

5days Explanation: use rule of threes, set up word problem as an equation. 3000/360 = 1/0.7 cross multiply and simplify fraction.

x/5 -3 = 1 4/5 then x ='s what? 0.5 4 6 8

6

16. If 48 of the 60 seats on a bus were occupied, what percent of the seats were not occupied? (A) 12% (B) 15% (C) 20% (D) 25% n

60-48 = 1212/60 = 0.2020%

if 1/4 of a bag equals 4 ounces, how many ounces are in 5 1/2 bags?

88 ounces Explain: 1/4oz over 5 1/2oz= 0.25/5.5= 4oz/x = 88 ounces

Jim's car gets 32.5 miles per gallon of gas. If Jim drove 314 miles, how many gallons of gasoline did he use?

9.66 314/32.5=9.66

Angles

A Right Angle is 90°. Lines that intersect to form Right Angles are Perpendicular. Angles that form a straight line add up to 180° An angle greater then 90° is Obtuse, an angle smaller then 90° is Acute.(i.e a°__/__b° a is Obtuse, b is Acute) If two Lines Intersect (i.e X) the adjacent angles are Supplementary and add up to 180°. Angles around the point are 360°.

6. If 90 ÷ x = 9n, then what is the value of nx? (A) 10 (B) 9x (C) 900 (D) 90xn

A)A or d

Robin sees that a jacket at the mall has been marked down 20% from an original price of $49.99. Taking into account the sales tax of 8%, which is applied after taking the discount, how much will Robin have left over if she brought $60 to the mall? 10.01 $16.81 $16.02 $15.01 $6.02

After the discount, she will pay for the remaining cost of the jacket. This cost will be equal to the percent remaining after the discount. 100% - 20% = 80% She will pay for 80% of the original cost. 80% = 0.80 $49.99∗(0.80)=$39.99 Add in the sales tax. 8% = 0.08 $39.99+($39.99∗0.08)=$39.99+($3.20)=$43.19 Subtract the final price from Robin's budget of $60. $60.00−$43.19=$16.8

5 × (-3 + 2) - 112 = ?

Answer is -116 since, -5 × (-3 + 2) - 112 -5 × (-1) - 112 -5 × (-1) - 121 5 - 121 -116

-43 + (2 - 7) ÷ 5 = ?

Answer is -44 since, -43 + (2 - 7) ÷ 5 -43 + (-5) ÷ 5 -43 + -1 -44

-3 - 9) + 63 ÷ 23 = ?

Answer is 15 since, (-3 - 9) + 63 ÷ 23 (-12) + 63 ÷ 23 -12 + 216 ÷ 23 -12 + 216 ÷ 8 -12 + 27 15

27 + 16 x 2 ÷ 8 - 11

Answer is 20 since, 27 + 16 x 2 ÷ 8 - 11 27 + 32 ÷ 8 - 11 27 + 4 - 11 20

-6 + -9 × 5 ÷ -5)3 = ?

Answer is 27 since, (-6 + -9 x 5 ÷ -5)3 (-6 + -45 ÷ -5)3 (-6 + 9)3 (3)3 27

14. Brad bought a music player on sale at a 20% discount from its regular price of $ 118. If there is an 8% sales tax that is calculated on the sale price, how much did Brad pay for the music player? (A) $ 86.85 (B) $ 94.40 (C) $ 101.95 (D) $ 127.44

C

Define median, mode, and range

Define median, mode, and range Median: middle number/averageMode: how often the number appearsRange: positive difference between largest and smallest numbers

13. If a kilogram is equal to approximately 2.2 pounds, which of the following is the best approximation of the number of kilograms in one pound? 5/11 3/7 3/8 1/3

Divide both sides by 2.2 to get 1 lb = .4545... kg A

A delivery service charges $ 25.00 per pound for making a delivery. If there is an additional 8% sales tax, what is the cost of delivering an item that weighs of a pound? (A) $ 20.00 (B) $ 21.60 ( C) $ 22.60 (D) $ 24.00

Let x = the number of pounds (Note: * means "times") Cost = (25 x) * 1.08 Plug in 4/5 for x. (4/5 = 0.8) Cost = (25*0.8) * 1.08 Cost = 20 * 1.08 = 21.6 The charge would be $21.60. The reason the subtotal is multiplied by 1.08 is because the 8% sales tax is added to the subtotal. Alternatively, we could have done it this way: Cost of item = 25 * 0.8 = 20 Delivery cost = 20 + (20 * 0.08) = 20 + 1.6 = 21.6

The width-to-height ratio of a certain computer monitor is 16 to 9. The monitor's height is 13.5 inches. What is the width, in inches, of the monitor? A7.6 B10.7 C20.520.5 D24.0

Set up as a proportion 16/9 = x/13.5 = 24.0

9. If a woman earns $ 600 for her first 40 hours of work in a week and then is paid one-and one-half times her regular rate for any additional hours, how many hours must she work to make $ 690 in a week? (A) 43 (B) 44 (C) 45 (D) 46

She makes $15 / hour ($600 / 40 hour) For overtime she makes $22.50 $90 / $22.50 = 4 She must work 44 hours