Math Questions

Three sources of finan- cial aid are government grants, private scholarships, and the colleges themselves. Susan, a financial aid director of a private college, surveyed the records of 100 sophomores and found the following: 49 receive government grants 55 receive private scholarships 43 receive aid from the college 23 receive government grants and private scholarships 18 receive government grants and aid from the college 28 receive private scholarships and aid from the college 8 receive help from all three sources. How many of the students in the survey: (a) have government grants only? (b) have scholarships but not government grants? (c) receive financial aid from only one of these sources? (d) receive aid from exactly two of these sources? (e) receive no financial aid from any of these sources? (f) receive no aid from the college or the government?

Solve the equation x+1/x-1 = -2/x+3 + 8/x2+2x-3 List all valid solutions, separated by commas.

Teams of students compete in a robotics contest. The times for the robots to complete an obstacle course are normally distributed. The mean time for completion is 60 seconds, and the standard deviation is 4 seconds. Approximately what percentage of the robots will complete the course in 56 to 64 seconds? A. 68% B. 60% C.50% D 8%

Use Newton's method to approximate a root of the equation 4x7 + 5x4 + 2 = 0 as follows. Let x1=2 be the initial approximation. The second approximation x2 is and the third approximation x3 is Carry at least 4 decimal places through your calculations.

The fox population in a certain region has a continuous growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 9900. (a) Find a function that models the population t years after 2000 (t = 0 for 2000). Hint: Use an exponential function with base e. Your answer is P(t) (b) Use the function from part (a) to estimate the fox population in the year 2008. Your answer is (the answer must be an integer)

At the movie theater all snacks are priced the same, and all movie tickets are priced the same. Jaden, Ben, and Amal bought four snacks and three movie tickets, costing their group $40. Tiara, Lisa, and Shyanne bought two snacks and three movie tickets, costing their group $32. What is the cost of a snack and what is the cost of a movie ticket?

The Kuiper Belt is estimated to be about 3, 000, 000 meters wide. Which value represents the estimated width of the Kuiper Belt, in meters, in scie 3.0 x 10 meter 30 × 10-5 meter 30 x 105 meters 3.0 x 106 meters

In an electric circuit, the current varies inversely as the resistance. The current is 40 amps when the resistance is 12 ohms. Write a indirect variation equation for the relationship between current-c versus the resistance=r.

The larger of two numbers exceeds twice the smaller by one. Three times the smaller exceeds the larger by six. If y is the larger number, which of the following systems of equations represents the word problem? y=2x+1 and y+6= 3 x y=2(x+1) and y+6= 3 x y=2x+1 and 3 x + 6 = y

Solve the rational equation: x+56/x = 15

The circumference of a sphere was measured to be 89 cm with a possible error of 0.5 cm. Use linear approximation to estimate the maximum error in the calculated surface area. Estimate the relative error in the calculated surface area.

Mercury is 57,000,000 km from the sun. Neptune is 4.5 x 10⁹ km from the sun. What is the difference between Mercury's and Neptune's distance from the sun? 4.443 x 10⁹ 4.43 x 108 4.443 x 1010 4.443 x 108

Nick is making bread dough. • Nick wants to make the recipe using 1 cup of flour. • The recipe requires 3/4 cup of flour and 1 1/8 teaspoons of salt. To maintain the ratio, how much salt is required when 1 cup of flour is used?

A cube is expanding, with the length of an edge decreasing 2 cm every minute. At the moment the cube has a volume of 343 cm³, the rate at which the volume of the cube is changing is:

How does increasing the reserve requirement affect the money supply? It decreases the money supply because less money is on reserve in banks. It increases the money supply because more money is available for loans. It increases the money supply because more money is on reserve in banks. It decreases the money supply because less money is available for loans.

In ΔFGH, the measure of ∠H-90°, the measure of ∠F=75°, and HF = 31 feet. Find the length of GH to the nearest tenth of a foot.

Simplify the expression 1/x² + 3x + 2 - 1/x²-3x - 4 and give your answer in the form of P/Q Your answer for P is: Your answer for Q is :

Tuition for one year at a state university is about $13,500. Stephen would like to attend this university and will save money each month for the next 5 years. His grandparents will give him $7,000 for his first year of tuition. Which plan shows the minimum amount of money Stephen must save to have enough money to pay for his first year of tuition? A Save $541.67 per month for the next 5 years. B Save $225.00 per month for the next 5 years. C Save $116.67.00 per month for the next 5 years. D Save $108.33 per month for the next 5 years.

Four expressions are shown in the box. Expression 1: 3.4 x 105 Expression 2: 8.7 x 10 Expression 3: 2.1 x 106 Expression 4: 9.5 x 10³ Which expression represents the largest value? Expression 1 Expression 2 Expression 3 Expression 4

Solve the equation 3/x+1 - 3/2 = 8/3x+3

There are approximately 7.5 x 1018 grains of sand on Earth. There are approximately 7* 1027 atoms in an average human body. Are there more grains of sand on Earth or atoms in an average human body? Atoms in the human body Grains of sand on Earth

In ΔMNO, the measure of ∠0-90°, MN = 27 feet, and OM = 20 feet. Find the measure of ∠M to the nearest degree.

Multiply and simplify: x² - 2x - 8/x² - 16*x² - 25/x² + 7x + 10 Numerator preview: Denominator preview: Enter the numerator and denominator separately in the boxes below. If the denominator is 1, enter the number 1. Do not leave either box blank. Answer:

Listed below are the measured radiation emissions (in W/kg) corresponding to cell phones: A, B, C, D, E, F, G, H, I, J, and K respectively. The media often present reports about the dangers of cell phone radiation as a cause of cancer. Cell phone radiation must be 1.6 W/kg or less. Find the a. mean, b. median, c. midrange, and d. mode for the data. Also complete part e. 1.42 0.72 0.88 1.05 1.14 0.83 0.26 0.21 1.12 1.44 0.87 a. Find the mean. b. Find the median c. Find the midrange. d. Find the mode.

If a cup of coffee has temperature 93°C in a room where the ambient air temperature is 20°C, then, according to Newton's Law of Cooling, the temperature of the coffee after t minutes is T(t) = 20 + 73e-t/45. What is the average temperature of the coffee during the first 22 minutes?

Multiply and simplify: 4d/w. 3w/2r Be sure to use parentheses as needed when entering your answer.

The loudness, L, of a sound, (measured in decibels, dB) is inversely proportional to the square of the distance, d, from the source of the sound. When a person 5 feet from a jetski, it is 100 decibels loud. How loud is the jetski when the person is 49 feet away?

In ΔPQR, the measure of ∠R-90°, RP = 3.7 feet, and PQ = 9.5 feet. Find the measure of ∠Q to the nearest tenth of a degree.

Simplify the expression 5/x2+1/x² + x and give your answer in the form of f(x)/g(x) Your answer for the function f(x) is: Your answer for the function g(x) is:

Garrison deposited $480 in an account that earns 3% interest compounded annually. How much interest will the account earn after 72 months?

Find the future value and interest earned if $8804.56 is invested for 8 years at 4% compounded (a) semiannually and (b) continuously. (a) The future value when interest is compounded semiannually is approximately $ (Type an integer or decimal rounded to the nearest hundredth as needed.) The interest earned is approximately $ (Type an integer or decimal rounded to the nearest hundredth as needed.) (b) The future value when interest is compounded continuously is approximately $ (Type an integer or decimal rounded to the nearest hundredth as needed.) The interest earned is approximately $ (Type an integer or decimal rounded to the nearest hundredth as needed.)

In ΔSTU, the measure of ∠U=90°, US = 5.9 feet, and TU = 2.6 feet. Find the measure of ∠T to the nearest tenth of a degree.

Carly deposited $800 in an account that earns 2.5% compounded annually. How much will Carla have in her account at the end of 8 years if she makes no withdrawals or deposits? The answer is $

The sum of the digits of a two digit number is 14. The difference between the tens digit and the units digit is 2. If x is the tens digit and y is the ones digit, which system of equations represents the word problem? x+y=14 and x-y=2 x+y=14 and y-x=2 xy-14 and x-y=2

Suppose you deposit $4000 at 8% interest compounded continuously. Find the average value of your account. during the first 4 years.

You decide that you want to make sure your estimate from part a is correct. You go out and gather 10 simple random samples of 25 people in your school and calculate the proportion of students within each sample whose Amazon packages arrive within two business days of ordering. The proportion of customers that receive their packages within two days of ordering are given below. 0.70, 0.75, 0.6, 0.95, 0.90, 0.73, 0.87, 0.86, 0.92, 0.97 a. Explain why all of the sample proportions are not the same. b. Find the average of all 10 proportions above.

A fireman invests $40,000 in a retirement account for 2 years. The interest rate is 6%. The interest is compounded monthly. What will his final balance be? The answer is $

If 1700 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Volume = (include units)

A farmer has 380 feet of fencing and wants to fence off a rectangular field that borders the back of his property. The back of the property already has a fence. What is the largest possible area of the field in square feet?

A model rocket is launched with an initial upward velocity of 70 m/s. The rocket's height h (in meters) after t seconds is given by the following. h=70t-5t² Find all values of t for which the rocket's height is 35 meters. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)

In ΔNOP, the measure of ∠P-90°, NO = 83 feet, and OP = 49 feet. Find the measure of ∠0 to the nearest tenth of a degree.

Suppose a universal set consists of natural numbers that are at most 16. Two subsets are created from the universal set; Set A contains the multiples of 3 and Set B contains the odd numbers. Correctly place each element of the universal set in the Venn diagram to the right.

Suppose 30 cars start at a car race. In how many ways can the top 3 cars finish the race? The number of different top three finishes possible for this race of 30 cars is (Use integers for any number in the expression.)

A mall has four escalators, one elevator, and three stairwells to travel from the second floor to the first floor. They have six doors on the first floor to exit the mall. If Jane is on the second floor, how many ways can she exit the mall?

If you were going to use the distributive property as the first step in the equation, 4 − 2 (x + 1) = 10, what would your next step be? 4-2x+1=10 4-2x-2 = 10 4-2x-1-10 -2x+5 = 10

Consider the curve y = 5x3 - 3x. (a) Find dy/dx. The curve has a tangent at the point P(-1.-2). (b) Find the gradient of this tangent at point P. (c)Find the equation of this tangent. Give your answer in the form y = mx + c.

In Exercises 1-4, find the indicated measure. 1. area of a circle with a radius of 6.8 feet 2. area of a circle with a diameter of 19.2 centimeters 3. radius of a circle with an area of 1017.9 square meters 4.diameter of a circle with an area of 707 square inches

A manufacturer is making cylindrical cans that hold 300 cm³. The dimensions of the can are not mandated, so to save manufacturing costs, the manufacturer wants to make the can that uses the least material. What are the dimensions, to the nearest three decimal places, of the can that has the smallest surface area? Radius= Height =

Select the correct answer. The designers of a standardized test are interested in knowing how long people take, on average, to complete the writing portion of the test. They decide to conduct an observation study at a testing facility. To avold blas in their study, they create a list of the test takers scheduled to take the test this week. Then, they randomly select 50 test takers from the list to be part of the study. In this situation, what does the list of test takers represent? A. the frame B. a control group C. a sample D. the population

At a hockey game, a vender sold a combined total of 228 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.