Basic Math Questions and Answers

A street light is at the top of a 20 ft pole. A 6 ft tall girl walks along a straight path away from the pole with a speed of 6 ft/sec. At what rate is the tip of her shadow moving away from the light (ie. away from the top of the pole) when the girl is 36 ft away from the pole? Answer. How fast is her shadow lengthening?

Jamie painted a small rectangular drawing at Art Club. He then made a scale drawing of his original painting to create a similar rectangular poster. He used a scale factor of 5/3 to create the rectangular poster. If the perimeter of the smaller rectangle is 45 centimeters, what is the perimeter of the larger rectangle?

Toby owes his Great Aunt $32,000. Toby can pay his aunt $4,000 a year. How long will it take him to pay back his aunt? Function: p(x) = Slope/Meaning in context: m = y-intercept/Meaning in context: b = After five years, how much money does Tobey owe Great Aunt Mildred? How long will it take for Tobey to pay off the loan?

The half-life of Palladium-100 is 4 days. After 12 days a sample of Palladium-100 has been reduced to a mass of 5 mg. What was the initial mass (in mg) of the sample? What is the mass 6 weeks after the start?

Pizarro's Pizzeria charges $12.50 for a large pizza. Each additional topping is $1.65. Function: P(x) = Slope/Meaning in context: m = y-intercept/Meaning in Context: b = What will the charge be for a pizza with 5 toppings? If Pedro paid $24.05 for his pizza, how many toppings did he get?

The count in a bacteria culture was 700 after 20 minutes and 1600 after 30 minutes. Assuming the count grows exponentially, What was the initial size of the culture? Find the doubling period. Find the population after 65 minutes. When will the population reach 10000. K

4) Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks, A yoga studio offers memberships that cost $30 per month for unlimited classes. The studio also accepts walk-ins, charging $10 per class. If someone attends enough classes in a month, the two options cost the same total amount. What is that total amount? How many classes is that? Each option costs $___if a person takes__classes,

To find the distance from the house at A to the house at B, a surveyor measures the angle ACB, which is found to be 70°, and then walks off the distance to each house, 90 feet and 100 feet, respectively. How far apart are the houses?

One of two complementary angles Is 8 degrees less than the other. Which of the following systems of equations represents the word problem? x+y=90 and 90 - x = 8 x+y=90 and y = 8 x x+y=90 and x - y = 8

Given f(x)= 16/ x+6 and g(x)=3√x, find the following expressions. (a) (fog)(4) (b) (gof)(2) (c) (fof)(1) (d) (gog)(0) (a) (fog)(4) =

25. What is the molarity of sodium chloride in solution that is 13.0% by mass sodium chloride and that has a density of 1.10 g/mL? A) 143 B) 2.45 C) 2.56 D) 2.23 E) 1.43 x 10-2 B) 2.45 C) 2.56 E) 1.43 x 10-2 A) 143 D) 2.23

Linus sells widgets at his store. Today he has sold 21 widgets to three customers. What is the cost per widget? $2.00 $1.50 $3.00 $1.00

The explicit formula for a certain geometric sequence is f(n) =525 (20)^n-1. What is the exponential function for the sequence? Write your answer in the form shown. f(n)= a/r (r) ^n

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. f(x) = 3x² - x³ A. 0, touches the x-axis and turns around; 3, crosses the x-axis B. 0, touches the x-axis and turns around; 3, touches the x-axis and turns around C. 0, touches the x-axis and turns around; 3, crosses the x-axis; - 3, crosses the x-axis D. 0, crosses the x-axis; 3, crosses the x-axis; - 3, crosses the x-axis

A) The number of students using a certain university's online programs has been increasingly exponentially each year since 2010. The number of students n who use the university's online programs t years after 2010 can be modeled using the function n (t) = 425(1.14)^t . Interpret the meaning of 1.14 in the function n (t) in the context of this situation. The total number of students who attend the university increases by 114% each year since 2010. The number of students who study online at the university increases by 14% each year since 2010. The number of students who study online at the university increases by 114% each year since 2010. The total number of students who attend the university increases by 14% each year since 2010.

An ecologist randomly samples 13 plants of a specific species and measures their heights. He finds that this sample has a mean of 16 cm and a standard deviation of 1 cm. If we assume that the height measurements are normally distributed, find a 95% confidence interval for the mean height of all plants of this species. Then find the lower limit and upper limit of the 95% confidence interval.

A random sample of 200 individuals working in a large city indicated that 70 are dissatisfied with their working conditions. Based upon this, compute a 95% confidence interval for the proportion of all individuals in this city who are dissatisfied with their working conditions. Then find the lower limit and upper limit of the 95% confidence interval.

The length of the first loop of a spring is 20 inches. The length of the second loop is 9/10 the length of the first. The length of the third loop is 9/10 the length of the second, and so on. Suppose the spring had infinitely many loops find the length.

An existing inventory for a test measuring self-esteem indicates that the scores have a standard deviation of 11. A psychologist gave the self-esteem test to a random sample of 150 individuals, and their mean score was 63. Construct a 95% confidence interval for the true mean of all test scores. Then give its lower limit and upper limit.

Olivia's volleyball team is going on a trip to play in a tournament in Oregon. The 12 players all need to fundraise to pay for their trip. Each player needs to pay $20 for the bus plus some amount for food. The total cost of the entire trip for all 12 is $540. How much extra does each player need to fundraise for food? * (3 Points) 1 Point: equation 1 Point: solution to written equation 1 Point: solution is labeled with context

A prescription medication has a half-life of 6 hours and the recommended dosage of the medicine is 2 pills. If each pill is 500 mg, how long will it take for the amount of the medicine to remain in the body to be 200 mg if a person takes the recommended dosage?

Two factory plants are making TV panels. Yesterday, Plant A produced 8000 panels. Ten percent of the panels from Plant A and 3% of the panels from Plant B were defective. How many panels did Plant B produce, if the overall percentage of defective panels from the two plants was 7%? Number of panels produced by Plant B:

Directions: Find each sum or difference. Answers must be in standard form. 11. (x²-4x + 3) + (3x²-3x - 5) 12. (8r^2 -12r + 4)-(3r²+5r-1) 13. (2m-3+ 7m²)-(3-9m² -2m) 14. (7p² + 3p)-(5p² + 4) 15. (3a²-a + 3) + (4a²-5) 16. (5w³-w+ 2u² + 4) + (3w²+1-4w) 17. (2x² +3y^2-2z^2) — (x² − y² − z²) + (4x² − 3y²) 18. (12+ 8k³ + 3k-4k²) + (5k³ + 15-k + 2k²) 19. Find the sum of (2x² - 6x-2) and (x² + 4x). 20. Subtract (-a² - 5ab + 3b²) from (3a²- 2ab + 3b²).

A contractor finds that Crew A takes 6 1/2 - hours to construct a retaining wall and Crew B can do the same job in 5 1/2 hours. If Crew A and Crew B work together, how long will it take them to construct the retaining wall? a) Let h= the time to complete the job. Write the equation you would use to solve this problem, b) Now solve your equation. Give your answer first as a reduced fraction, and then a decimal rounded to 3 places. Working together, the two crews will construct the wall in which as a decimal is hours. hours (fraction),

Maria read in the newspaper that 59% of voters in her city were voting "no" on a local initiative measure. The newspaper article stated that 772 people were originally polled. What is the margin of error for this survey? 4.6% 2.6% 3.6% 1.6%

In testing their recording devices, a team of seismologists positioned two of the devices 2000 feet apart, with the device at point A to the west of the device at point B. At a point between the devices and 200 feet from point B, a small amount of explosive was detonated. A second explosion is to be carried out at a point directly north of point B. How far north should the site of the second explosion be chosen so it is directly north of point B? Imagine what this would look like on the coordinate plane ... what do we know about the graph and/or equation of this hyperbola?

Sam bought three folders and one notebook from the office store and spent $8.25. He went back the next day and bought two more folders and three more notebooks and spent $16. If the prices did not change between the days, find the cost of one folder.

Mrs. Browne wants to start a college fund for her newest addition, Wade. She makes a payment of $50 at the end of each month into an ordinary annuity account paying a 3.5% annual interest rate, compounded monthly. How much will be in the account after 18 years and Wade is ready to go to college?

In 2017, the number of students enrolled in a high school was 232. It is estimated that the student population will increase by 3% every year. Estimate the number of students that will be enrolled in 2027.

A 28 ft ladder leans against a wall so that the base of the ladder is 5 ft away from the base of the wall. How far up the wall does the ladder reach? Round to the nearest tenth. Enter your answer, as a decimal, in the box.

Kristina needs to mix a 10% alcohol solution with a 60% alcohol solution to create 100 millileters of a 10% solution. How many millileters of each solution must Kristina use? Answer: Kristina must mix millileters of 10% solution and millileters of 60% solution.

Hannah can paint a room in 20 hours. Destiny can paint the same room in 12 hours. How long does it take for both Hannah and Destiny to paint the room it they are working together.

A town's population has been growing linearly. In 2003, the population was 57000, and the population has been growing by 700 people each year. Write an equation for the population years after 2003. P(x) =

In a chemistry class, 7 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

A solution is prepared by dissolving 25.0 g of NaCl in 500.0 g of water. What is the molality (m) of NaCl in the solution? The density of the solution is 1.0 g/mL. A) 0.000856 B) 0.0500 C) 50.0 D) 8.56 E) 0.856

Solve and check the linear equation. 3(x-5)+16=2(x+4) What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The solution set is {7}. B. The solution set is {x|x is a real number}. C. The solution set is Ø.

The difference of two numbers is 3 and the sum of their squares is 45. Find the numbers. List any unique pairs of numbers that satisfy the given conditions. (Type an ordered pair, with the larger number listed first. Use a comma to separate answers as needed.)

A store sells cashews for $6.00 per pound and peanuts for $3.00 per pound. The manager decides to mix 20 pounds of peanuts with some cashews and sell the mixture for $4.00 per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as would selling the nuts separately? There should be pounds of cashews in the mixture. (Type an integer or a decimal.)

A wireless store owner takes presale orders for a new smartphone and tablet. He gets 160 preorders for the smartphone and 190 orders for the tablet. The combined sale of the preorders is $181,250. If the price of a smartphone and a tablet together is $1,055, find the cost of one smartphone and the cost of one tablet. What is the cost of one smartphone? What is the cost of one tablet?

A landscaping company charges $40 per cubic yard of mulch plus a delivery charge of $29. Find a linear function which computes the total cost C (in dollars) to deliver x cubic yards of mulch. C(x) =

Gordon has paper strips that are all equal in length. He lines them up end to end. When the line of paper strips is 3 feet long, Gordon says there are 12 paper strips. What is the length, in feet, of one paper strip if Gordon is correct?

In a Northwest Georgia County, the speed limit is 35 miles per hour. The speeding fines are determined by the formula: F(s) = 8(s 35) + 95 where F(s) is the cost, in dollars, of the fine if a person is caught driving at a speed of s miles per hour. If a fine comes to $303, how fast in mph was the person driving?

A group of scientists is studying Streptococcus lactis, which is used in the production of cheese. The initial population for a colony of bacteria is 15,000, and the population can double every 50 minutes under certain conditions. Which graph represents the bacteria's population as a function of time, in minutes? (1 point)

New York City is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 1 van and 6 buses with 324 students. High School B rented and filled 9 vans and 3 buses with 264 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?

The midpoint of AB is at (-1, -1). If A = (9,5), find B. B is:(

A solution is prepared by disserving 15.0 g of NH3 in 250.0 g of water. The density of the resulting solution is 0.974 g/mL. The molarity of NH3 in the solution is M. A) 0.00353 B) 0.882 C) 60.0 D) 3.24 E) 3.53

The number of girls varied directly as the number of boys and inversely as the number of teachers. When there were 50 girls, there were 20 teachers and 10 boys. How many boys were there when there were 10 girls and 100 teachers?

The current population of a town is 10,000. If the population, P, increases by 20% each year, which equation could be used to find the population after t years? P= 10,000(0.2)t P = 10,000(1.8)t P = 10,000(0.8)t P= 10,000(1.2)t

William and Debra Pierce are celebrating their 20th anniversary by having a reception at a local reception hall. They have budgeted $4,000 for their reception. If the reception hall charges a $80 cleanup fee plus $39 per person, find the greatest number of people that they may invite and still stay within their budget.

Kyle spent more than 37 minutes swimming last night. Which of the following amounts of time could Kyle have been swimming? Select all that apply. Choose all that apply: 2350 seconds 2050 seconds 2250 seconds 2150 seconds