Math Questions

Solve this problem by using a two order system. A man invests $5,200, part at 4% and the balance at 3%. If his total income for the two investments is $194, how much money did he invest at each rate? $ at 4% and $ at 3%

Tony invested his savings in two investment funds. The $6000 that he invested in Fund A returned a 3% profit. The amount that he invested in Fund B returned a 10% profit. How much did he invest in Fund B, if both funds together returned a 7% profit? Amount invested in Fund B: $

McKenna plans on attending a four-year university that costs $16,000 per year. Her parents have agreed to contribute $2,000 each year. Her grandparents have a college savings account that will be worth $30,900 when she graduates high school. How much more money will she need in scholarships, loans, or work programs to attend this university for four years? A $16,900 B $32,900 C $31,100 D $25,100

(a) Complete the square by writing ² - 16-11 in the form (x-h)² + k. Note: the numbers hand k can be positive or negative.

Suppose h" is continuous at x = 2.h' (2) = 0, and h" (2) < 0. What can you say about the behavior of h at x = 2? Inflection point Inflection point at a horizontal tangent Relative (local) minimum Relative (local) maximum

Danielle and her family are discussing how to pay for her college education. The cost of tuition at the college that Danielle wants to attend is $12,000 per year. Danielle's parents will pay 75% of the tuition cost every year, and she will pay the rest. Danielle has one year to save enough money to attend her first year of college. What is the minimum amount of money she should save every month in order to reach her goal? A $3,000.00 B $750.00 C $40.00 D $250.00

Charles's pay varies directly with the number of words he writes for Two Cities Magazine. The first story he wrote was 4,929 words and he was paid $345.03. How much will he be paid for his next story, which is 3,825 words? A $110.40 B $267.75 C $319.97 D $546.43

A chemist weighs samples obtained from a production run. The weights of the samples are 11 g, 10 g, 6 g. 11 g. 15 g. 13 g. 14 g, 12 g. 13 g. 12 g, 14 g, and 18 g. find the outlier(s) if there are any. Describe how any outlier affects the mean and the standard deviation. Q1-1.5(IQR) Q3+1.5(IQR)

Lupita deposited $5,000 into a savings account that earns 2% interest compounded annually. Rounded to the nearest cent, how much interest will Lupita have earned after 48 months? The answer is $

Suppose the area of square A is 15 cm² and the area of square C is 42 cm². What is the area of square B if the three squares create a right triangle? A 27 cm² B 39 cm² C 52 cm² D 57 cm²

The mass of a textbook is approximately 0.00165 metric ton. How is this number written in scientific notation? F 165 x 10^-5 G 1.65 x 10^-3 H 16.5 x 10^-4 J 0.165 x 10^-2

John is 5 years older than Mary. In 10 years, twice John's age decreased by Mary's age Is 35, and John's age will be twice Mary's current age. Find their ages now. If x Is Mary's age now and yis John's age now, which system of equations could not be used to solve the problem? y=x+ 5 and 2(y + 10) = x y=x+ 5 and 2(y+10)-(x+10) = 35 y=x+5 and y + 10 = 2x

Frank earns $40,000 one year and receives a 6% raise in salary. What is his new salary? Frank's new salary is $. (Simplify your answer.)

A trade magazine routinely checks the drive-through service times of fast-food restaurants. A 90% confidence interval that results from examining 595 customers in one fast-food chain's drive-through has a lower bound of 159.3 seconds and an upper bound of 162.9 seconds. What does this mean? Choose the correct answer below. A. One can be % confident that the mean drive-through service time of this fast-food chain is seconds. B. The mean drive-through service time of this fast-food chain is seconds % of the time. C. There is a 90% probability that the mean drive-through service time of this fast-food chain is between seconds and seconds. D. One can be 90% confident that the mean drive-through service time of this fast-food chain is between seconds and seconds.

Let f(x) = (3x - 1)² (3x - 7)² on [1,3]. Answer the following. (a) Find all critical numbers of f. (b) Find the intervals on which f is increasing. (c) Find absolute extreme value of f.

James is investing $15,000 in the bank. The investment has an interest rate of 6% compounded monthly. After ten years, how much will James have made? The answer is $ Make sure to round correctly. Think MONEY.

A kitchen is shaped like a rectangle with dimensions of 11(1/2) ft by 9(1/2) ft. The floor of the room is made of square tiles with a side length of 1/2 ft. What is the number of tiles that will cover the kitchen floor?

A guy wire that is used to support a pole is attached at a height of 55 ft and at an angle of 62.1° above the ground. How far from the base of the pole is the guy wire attached to the ground? a. 29.12 ft b. 48.61 ft c. 117.54 ft d. 62.23 ft

A principal is ordering pizza for a school pizza party. He knows that 9 pizzas will feed 25 students. If there are 300 students in the school, how many pizzas will he need to order? 108 pizzas 102 pizzas 105 pizzas 99 pizzas

Ahmad and his wife are each starting a saving plan. Ahmad will initially set aside $650 and then add $135 every month to the savings. The amount A (in dollars) saved this way is given by the function A = 650+ 135N, where N is the number of months he has been saving. His wife will not set an initial amount aside but will add $495 to the savings every month. The amount B (in dollars) saved using this plan is given by the function B=495N. Let I be total amount (in dollars) saved using both plans combined. Write an equation relating I to N. Simplify your answer as much as possible.

A toy manufacturing company's monthly profit in its first two months of operation is given by the profit function P(x) = x³ -6x2 +9x+6, where is the number of toys sold and P(x) is In thousands of dollars (for example, if P(x) = 3, then the company's profit is $3000). What is the company's maximum profit during the first two months?

In a given year, residents of a country spent approximately $50.4 billion on their pets. Of this amount, $18.9 billion was for veterinarian bills. What percent of the total was spent on veterinary care? About % of the total was spent on veterinary care.

State the order and type of each transformation of the graph of the function f(x) = (5(x - 1))3 - 2 as compared to the graph of the base function. right 1 unit, horizontal compression by a factor if 1/5 down 2 units Oright 1 unit, vertical stretch by a factor if 5, down 2 units right 1 unit, down 2 units, vertical stretch by a factor if 5 right 1 unit, down 2 units, horizontal compression by a factor if 1/5

The shape of the distribution of the time required to get an oil change at a 10-minute oil-change facility is unknown. However, records indicate that the mean time is 11.1 minutes, and the standard deviation is 4.3 minutes. Complete parts (a) through (c) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required? Choose the required sample size below. O A. Any sample size could be used. OB. The normal model cannot be used if the shape of the distribution is unknown. C. The sample size needs to be less than 30. D. The sample size needs to be greater than 30. (b) What is the probability that a random sample of n = 35 oil changes results in a sample mean time less than 10 minutes? The probability is approximately (Round to four decimal places as needed.) (c) Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 35 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, at what mean oil-change time would there be a 10% chance of being at or below? This will be the goal 'established by the manager. Click to select your answer(s).

The local Art Club has 5 members. Their ages are 19, 25, 30, 63, and 30. Find the mode, mean, and standard deviation. Make sure you label each answer.

Write the expression in rectangular form, x+y i, and in exponential form, reiθ (√13-i)4 The rectangular form of the given expression is. and the exponential form of the given expression is (Simplify your answers. Use integers or decimals for any numbers in the expressions. Round the final answer to three decimal places as needed. Round all intermediate values to four decimal places as needed.)

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.