Basic Math Questions and Answers

Solve the given exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation for the solution. 5ex = 127 The solution set expressed in terms of logarithms is (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the equation.) Now use a calculator to obtain a decimal approximation for the solution. The solution set is () (Use a comma to separate answers as needed. Round to two decimal places as needed.)

Determine whether the given partial fraction decomposition is set up correctly. If the setup is incorrect, make the necessary changes to produce the correct decomposition. 5x A B C (x+8)(x-3)² (x+8) (x-3) (x-3) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Do not solve for the constants. A. The partial fraction decomposition is correct. B. The partial fraction decomposition is incorrect. The correct partial fraction decomposition is 5x (x+8)(x-3)

Which kind of symmetry does the letter D have? A. line symmetry, only B. neither point nor line symmetry C. both point and line symmetry D. point symmetry, only

A telephone pole casts a shadow that is 34 m long. Find the height of the telephone pole if a state that is 36 cm tall casts a shadow 77 cm long. A. 15.9 m B. 14.4 m C. 71.2 m D. 72.7 m

The count in a bateria culture was 200 after 10 minutes and 1000 after 35 minutes. Assuming the count grows exponentially, What was the initial size of the culture? Find the doubling period. Find the population after 60 minutes. When will the population reach 10000.

The local weather forecast has been accurate for 22 of the past 32 days. Based on this fact, what is the relative frequency probability that the forecast for tomorrow will be accurate?

If possible, solve the system of equations. Use any method. If there is not a unique solution to a system, say why. 2x - 8y = 1 8x - 32y = 3 Infinite number of solutions; dependent equations (2 5,-1 10) (1, 3) No solution; inconsistent system of equations

In an ad an item which retails for $400 is for sale stating "take an additional 20% off an already 30% discount" what is the sale price for this item? Type in the number and do not include: commas, decimals, dollar sign.

The best description of a dilation of a figure is: A. a mirror image of the figure B. a slide of the figure C. an enlargement or a reduction of the figure D. a turning of the figure about some fixed point

What is the sum of the interior angles of a regular polygon with 12 sides? A. 1800 B. 2160 C. 1260 D. 360

Solve the system by the addition method. x+y = -6 x-y = 4 Select the correct choice below and fill in any answer boxes present in your choice. A. The solution set is. (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

Find the factors of function f. f(x) = x4 - 5x3 - 4x² + 20x Based on the factors, which statement is true about the graph of function f? A. The graph crosses the x-axis at the point (-5,0). B. The graph crosses the x-axis at the point (4,0). C. The graph crosses the x-axis at the point (-4,0). D. The graph crosses the x-axis at the point (2,0).

To buy a car, Jessica borrowed $15,000 for 3 years at an annual simple interest rate of 9%. How much interest will she pay if she pays the entire loan off at the end of the third year? What is the total amount that she will repay?

The area of a rectangular wall in a classroom is 216 square feet. Its length is 3 feet shorter than three times its width. Find the length and width of the wall of the classroom. width = 9 ft; length = 12 ft width = 9 ft; length = 24 ft width = 9 ft; length = 30 ft width = 9 ft; length = 18 ft

Write an equation of the line with the given slope and containing the given point. Write the equation in the form y=mx+ b. Slope -2 3; through (2, 3) y=2 3x + 13 3 y=-2 3x - 13 3 y=2 3x - 13 3 y =-2 3x + 13 3

One option in a roulette game is to bet $6 on red. (There are 18 red compartments, 18 black compartments, and two compartments that are neither red nor black.) If the ball lands on red, you get to keep the $6 you paid to play the game and you are awarded $6. If the ball lands elsewhere, you are awarded nothing and the $6 that you bet is collected. Complete parts (a) through (b) below. a. What is the expected value for playing roulette if you bet $6 on red?

The coordinates of ΔABC are A(12, 8), B(10, 18), C(4, 16). After a dilation, the coordinates are A'(6,4), B'(5,9), C'(2, 8). Find the scale factor. A. 3 2 B. 5 2 C. 1 2 D. 2

Mike purchased 500 apples at the rate of $75 per hundred. 12% of them got damaged and cannot be sold. If he sold the remaining apples at $15 per dozen in a bag, did he make a profit or loss and by how much?

When compared to the graph of y = log3 x, the graph of y = 2 + log3 (x − 1): has been translated horizontally 1 unit to the left has been horizontally stretched by a factor of 2 has been vertically compressed by a factor of 0.5 has been translated vertically up 2 units

An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 31 2" by 51 4" on the drawing, how large is the bedroom? A. 20 ft by 30 ft B. 10 ft by 15 ft C. 7 ft by 10.5 ft D. 14 ft by 21 ft

Choose the best answer. The diagonals of a rectangle: A. none of these B. are double the shortest side C. are the same length D. are the not same length

Give the domain and range of the relation. {(5, -4), (1, -3), (1, 0), (10, 3), (26,5)} domain: {5, 10, 1, 26}; range: {-4, -3,0,3,5} domain: {5, 10, 1, 26}; range: {-4, -3, 3,5} domain: {-4, -3, 3, 5}; range: {5, 10, 1,26} domain: {-4, -3, 0, 3, 5}; range: {5, 10, 1, 26}

Which geometric figure has 120 rotational symmetry? A. equilateral triangle B. square C. regular pentagon D. rhombus

Make a probability distribution for the given set of events. The sums that appear when two fair four-sided dice (tetrahedrons) with sides 3, 4, 5, and 6 are tossed Complete the probability distribution below. Sum Probability Sum Probability

A car was valued at $33,000 in the year 1992. The value depreciated to $14,000 by the year 2001. A) What was the annual rate of change between 1992 and 2001? r = Round the rate of decrease to 4 decimal places. B) What is the correct answer to part A written in percentage form? r =. C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2006? value = $ Round to the nearest 50 dollars.

Solve 3sin(π 6x) = 2 for the four smallest positive solutions x = Give your answers accurate to at least two decimal places, as a list separated by commas

Perform the indicated operation and simplify. x 4 - x2-16 x2+5x+4 x2+3x+16 (x-4)(x+4)(x+1) x2-3 (x-4)(x+4)(x+1) x2-3x+16 (x-4)(x+4) x2-3x+16 (x-4)(x+4)(x+1)

Eric has a treehouse 28ft above the ground. How long would it take a water balloon dropped from the treehouse to hit the ground if the path of the balloon is modeled by the function d = 16t2 where d is measured in feet and time in seconds a) 12544 seconds b) 5.3 seconds c) 3.1 seconds d) 1.3 seconds

I bought my home in Clemmons for $250,000, and now it is worth $345,000. What is the percent increase? Type in the number: no decimals, no commas, no percent sign.

Discuss the statement and tell what possible misuse or misinterpretation may exist. There are more empty spaces in the parking lot of a Mexican restaurant than at an Italian restaurant. Therefore, more people prefer Italian food than Mexican food. Discuss the statement and tell what possible misuse or misinterpretation may exist. Choose the correct answer below. A. The statement is not valid because the Italian restaurant might be closed on Sundays and the Mexican restaurant might be open on Sundays. B. The statement is not valid because more people may walk to the Mexican restaurant than the Italian restaurant. C. The statement is not valid because Mexican food is always more popular than Italian food. D. The statement is valid because there are more empty spaces in the parking lot of the Mexican restaurant than at the Italian restaurant.

Choose the best answer. The diagonals of a square bisect each other at angles. A. right B. obtuse C. reflex D. acute

At a hockey game, a vender sold a combined total of 132 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold. Number of sodas sold: Number of hot dogs sold:

Under which transformation can the image be a different size than the original figure? A. dilation B. rotation C. reflection D. translation

You can afford a $1250 per month mortgage payment. You've found a 30 year loan at 3.2% interest. How big of a loan can you afford? $199,102.51 $189,153.49 $289,039.49 $255,456.51

A parallelogram whose angles measure 90° is called: A. rectangle B. trapezold C. kite D. rhombus

The area of a square is 81 cm² If the same amount is added to one dimension and removed from the other, the resulting rectangle has an area 9 cm² less than the area of the square. How much is added and subtracted?

Find the time it takes for $9,300 to double when invested at an annual interest rate of 9.4%, compounded continuously. Give your answer to 2 decimal places. years Find the time it takes for $911,400 to double when invested at an annual interest rate of 9.4%, compounded continuously. Give your answer to 2 decimal places. years

At the beginning of an experiment, a scientist has 184 grams of radioactive goo. After 60 minutes, her sample has decayed to 11.5 grams. What is the half-life of the goo in minutes? Find a formula for G(t), the amount of goo remaining at time t. G(t) = How many grams of goo will remain after 80 minutes?

Which of the following statements is false? A. The parallel sides of an isosceles trapezold are congruent. B. The base angles of an isosceles trapezold are congruent. C. Opposite sides of a parallelogram are congruent. D. The diagonals of a rhombus are perpendicular and bisect each other.

Which of the following statements is false? A. A rhombus is a parallelogram. B. A rhombus is a quadrilateral. C. A parallelogram is a rhombus. D. The diagonals of a rhombus are perpendicular and bisect each other.

Solve the system for x and y, expressing either value in terms of a, if necessary. Assume that a≠0. 6ax + 7y= 31 ax+6y= 10 Select the correct choice below and fill in any answer boxes present in your choice. A. The solution set is. (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

The cost C(in dollars) for a company to produce and sell x thousand gadgets is given by the equation: C=1/40x²-2x+1040 (a) What is the company's start-up cost? (The start up costs is the amount they have to pay even if they don't produce any gadget.) (b) What is the minimum cost? (c) How many gadgets must the company produce and sell in order to incur the least cost? (Be careful with your units!)

The perimeter of rectangle A is 10 cm and its area is 6 cm². The perimeter of rectangle B is 20 cm. What is the area of rectangle B assuming these two rectangles are similar? [?] cm²

Find the measure of one interior angle of a regular 12-gon. A. 128.6 B. 147.3 C. 150 D. 135

Simply -36x^8-20x^5+16x²/4x² -9x^445x³+4 -9x^6-5x³+4 -9x^6-5x³ + 16x² -36x^4-5x²5 +4

The exponential model A=617.2 e 0.008t describes the population, A, of a country in millions, t years after 2003. Use the model to determine the population of the country in 2003. The population of the country in 2003 was .... million.

A twin-engined aircraft can fly 960 miles from city A to city B in 3 hours with the wind and make the return trip in 8 hours against the wind. What is the speed of the wind? 140 mph 100 mph 80 mph 120 mph

The cost, in dollars, to produce x vats of ice cream is C (x ) = 5x + 2. When selling them to ice cream shops, the price-demand function, in dollars per vat, is p(x) = 125 -3x. Find the revenue function. R(x) =

Use the discriminant to determine whether the equation has two rational solutions, one rational solution, two irrational solutions or two non-real solutions x² + 7x - 2 = 0 a) Two rational solutions b) Two non-real solutions c) Two irrational solutions d) One rational solution

A radioactive substance decays exponentially. A scientist begins with 170 milligrams of a radioactive substance. After 19 hours, 85 mg of the substance remains. How many milligrams will remain after 29 hours? ... mg Give your answer accurate to at least one decimal place.