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# Solving a set of basic mathematical questions

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1. Write in radical notation and simplify if possible.
253/2

2. Assume all variables are positive real numbers. Write the following radicands with rational exponents and simplify if possible.

3. Solve for x
(x + 2)(x - 2) = 15 + (x +1)(x - 7)

4. Solve for x
Cancel x-5.
4x=20
4(5)=20 , x=5

5. Compute the slope of the line determined by the given equations.
5x + 4y = 1

6. Compute the slope of the line determined by the given points. Use ∆ y and ∆ x notation.
(12, 8), (0, 16)

7. Graph the following using the x and y-intercepts.

8x + 10y = 12

8. Find the equation of the following lines. Write your answer in slope-intercept form.

Through (-1, 5) with m = -1

9. Find the area bounded by the following. y = |x| and y = 4

10. Let h(x) = x2-1.
Evaluate (b) h(-2)

11. Solve each system using either the elimination method or the substitution method. Verify your
result by graphing each system. Indicate the point of intersection on your graph.
2x + y = 7
-2x + 3y = 5

12. Two people set out simultaneously from two locations 12 miles apart and walk toward each other. One person walks 5 miles an hour faster than the other. Find the rate of speed of each person if they meet in one hour and ten minutes.

https://brainmass.com/math/basic-calculus/solving-set-basic-mathematical-questions-582728

#### Solution Preview

1. Write in radical notation and simplify if possible.
253/2
A: 253/2=(52)3/2=53=125

2. Assume all variables are positive real numbers. Write the following radicands with rational exponents and simplify if possible.

A:
Note: x and y are both positive as mentioned in the question.

3. Solve for x

(x + 2)(x - 2) = 15 + (x +1)(x - 7)

A: (x+2)(x-2)=x2-4 and 15+(x+1)(x-7)=15+x2-6x-7=8+x2-6x
So x2-4=8+x2-6x.
So 6x=12 and x=2.
Check: when x=2, left side=(4)(0)=0, right side=15+(2+1)(2-7)=15-15=0.
So x=2 is the ...

#### Solution Summary

The solution gives detailed steps for solving a set of mathematical questions including solving system of linear equations, finding slope and intercept of equations and so on.

\$2.19

## Several basic statistics and finite math problems

Attached are the math/algebra problems that I am having a hard time solving. Please show your work so I have an understanding of how to solve future problems of these sorts....Thanks!

(Please see the attachment rather than the copied material here.)

____________________________________________________

Use the following to answer questions 1-2:

Continent or Region Land Area
(1,000 mi2)
% of Earth Population
1900 Population
1950 Population
2000
North America 9,400 16.2 106,000,000 221,000,000 305,000,000
South America 6,900 11.9 38,000,000 111,000,000 515,000,000
Europe 3,800 6.6 400,000,000 392,000,000 510,000,000
Asia (including
Russia) 17,400 30.1 932,000,000 1,591,000,000 4,028,000,000
Africa 11,700 20.2 118,000,000 229,000,000 889,000,000
Oceania (including
Australia) 3,300 5.7 6,000,000 12,000,000 32,000,000
Antarctica 5,400 9.1 Uninhabited ? ?
World Total 57,900 1,600,000,000 2,556,000,000 6,279,000,000

1. Use the world population and land area table.
What was the mean population of all inhabited areas except Asia in 2000?

A) 510,000,000 B) 193,000,000 C) 133,600,000 D) 450,200,000

2. Use the world population and land area table.
What is the total land area of South America?

A) 6,900,000 mi2 B) 38,000,000 mi2 C) 6,900 mi2 D) 11.9 mi2

Use the following to answer question 3:

3. The pie chart shows the distribution of a person's total yearly income of \$36,000. Find the amount budgeted for utilities.

A) \$4,320 B) \$1,800 C) \$3,600 D) \$2,880

4. Find the median of the following set of numbers.

4, 5, 6, 9, 11

A) 6 B) 4 C) 7 D) 5

5. The following scores were recorded on a 100-point examination:
95, 75, 76, 86, 96, 71, 68, 81, 95, 76, 69, 82, 93, 88, 94

Find the mean and median final examination scores.

A) mean: 83; median: 81 C) mean: 82; median: 83
B) mean: 81; median: 83 D) mean: 83; median: 82

6. Find the median of the following set of numbers.

33, 72, 23, 27, 77, 68, 85

A) 72 B) 27 C) 55 D) 68

Use the following to answer question 7:

7. Use the bar graph, showing the attendance at a circus for 7 days in September, to find the median attendance over the 7 days.

A) 4,000 B) 5,600 C) 3,200 D) 4,800

8. Find the first and third quartiles, Q1 and Q3, of the following set of numbers.

13, 4, 12, 16, 8, 14, 8, 3, 10, 8

A) 3; 16 B) 4; 14 C) 4; 12 D) 8; 13

9. Find the mean of the following set of numbers.

13, 15, 18, 18, 18, 19, 22, 26, 28, 33

A) 21 B) 20.6 C) 20 D) 20.3

10. Find the mode of the following set of numbers.

15, 14, 10, 15, 16

A) 14 B) no mode C) 15 D) 10

11. The following pie chart shows the budget for a local company. The total budget is \$560,000. Find the amount budgeted in the category of miscellaneous.

A) \$56,000 B) \$140,000 C) \$224,000 D) \$84,000

12. Find the first and third quartiles, Q1 and Q3, of the following set of numbers.

0.16, 0.08, 0.27, 0.20, 0.22, 0.32, 0.25, 0.18, 0.28, 0.27

A) 0.16; 0.28 B) 0.18; 0.27 C) 0.16; 0.27 D) 0.18; 0.28

A) B) C) D)

14. Evaluate

A) 14 B) C) D)

15. Subtract

A) -15.4 B) 1.2 C) 15.4 D) -1.2

16. Multiply

A) 273.6 B) -45.6 C) -456 D) 7.6

17. Divide

A) 4 B) C) 5 D)

18. Find the reciprocal of

A) B) C) D)

19. Perform the indicated operation.

A) B) C) Undefined D) 180

20. Place the following set of numbers in ascending order.

25, -13, 8, -2, 13, 3, 18

A) -13, -2, 3, 13, 8, 18, 25 C) -13, 3, -2, 8, 13, 18, 25
B) 25, 18, 13, 8, 3, -2, -13 D) -13, -2, 3, 8, 13, 18, 25

21. Divide

22. Place the following set of numbers in ascending order.

23. Multiply

24. Which of the following numbers are integers?

25. Divide

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