Basic Math Questions and Answers

A recent report indicated that twenty percent of the households in a certain community speak a language other than English at home. A reporter will randomly select a household from the community until the first household that speaks a language other than English at home is selected. Let random variable L represent the number of attempts needed until the first household that speaks a language other than English at home is selected. The random variable L has a geometric distribution with p=0.22. What is the expected number of attempts needed until the first household that speaks a language other than English at home is selected?

Boris plays a game of tennis. He serves from the base line to his opponent, Steffi. The path of the ball may be modelled by the quadratic curve H(x) = 2.103 +0.1455x -0.01932x² for 0 ≤ x ≤ X. a Find the maximum height of the ball during its motion. (2 marks) b The height of the net is 1.07 m. Boris is standing on the baseline of the court, at a horizontal distance of 11.98 m from the net. Show that the ball just passes over the net. c Suggest a maximum value for X and explain why this would be a sensible value to take.

Use a finite sum to estimate the average value of f on the given interval by partitioning the interval into four subintervals of equal length and evaluating f at the subinterval midpoints. f(x)= x³ on [2,4] The average value is. (Type an integer or a simplified fraction.)

Approximate the following number using a calculator. 6-2.1

Solve the exponential equation. Write the exact solution and the approximation to the 4 decimal places. Type "DNE" if there is no solution. 109x-9 = 5 1) Exact solution: 2) Approximation:

Car A is traveling at a speed of 61 mph and is increasing its speed 0.2 mph each second. Car B is traveling at a speed of 75 mph and is decreasing its speed 0.5 mph each second. After how many seconds will the cars be traveling the same speed, and how fast will they be going? After 10 seconds, the cars will both be traveling at 66 mph. After 65 seconds, the cars will both be traveling 20 mph. After 18 seconds, the cars will both be traveling at a speed of 70 mph. After 20 seconds, the cars will both be traveling at 65 mph.

Eddie found a store that sells cell phone cases for $18.50 plus $0.15 per letter engraved on the case. A second store sells cases for $18.00 plus $0.25 per letter engraved on the case. How many letters would Eddie have to engrave on his case for it to cost the same at either store? 5 letters 50 letters 7 letters 10 letters

The data manager for a state political party gathered data to determine how many citizens would support the party's senate candidate. He polled citizens in 30 similarly sized senate districts and found a sample mean of 70,438 citizens. Statewide data shows that the population standard deviation is 645.3. What is the approximate 90% confidence interval for this situation? 70,134 and 70,742 70,403 and 70,473 70,244 and 70,632 70,207 and 70,669

Select the correct answer from each drop-down menu. Marjory works at a commercial bakery. She is conducting an experiment to test the results of two yeast activators for making bread. The Rapid Prove activator claims to increase the rise of dough by at least 30%. The Quick Rise activator claims to increase the rise of dough by at least 26%. Marjory and her team bake 60 loaves of bread, 30 using the Rapid Prove activator and 30 using the Quick Rise activator. After the loaves were baked, Marjory evaluated the rise of the breads as compared to previous doughs with no activator used. She reported that, on average, the rise of those made with the Rapid Prove activator increased by 25% and the rise of loaves made with the Quick Rise activator increased by 28%. The Rapid Prove activator claim is The Quick Rise activator claim is The activator is more effective because the increase in rise was ✓that of the other activator.

A researcher for a travel company is looking into the prices people are willing to pay for airplane tickets. The company has communicated that the overall population mean is $265 with a standard deviation of $40.93. The researcher has a sample of 130 ticket purchases from one location By the Central limit theorem, which interval can the researcher be 95% certain that the sample mean will fall within? A. $264.37 and $265.63 $254.23 and $275.77 $261.41 and $268.59 $257.82 and $272.18

Which statement about the graph of y = 8(0.25)x is true? F The coordinates of the x-intercept are (0.25, 0). G The coordinates of the y-intercept are (0, 8). H The equation of the asymptote is x = 0. J The graph includes the point (2, 1).

What is the solution to the following system? 3x+3y+6z=9 x+3y+2z=5 3x+12y+ 12z = 18 (3, 1, 0) (0, 1, 0) (2, 1, 0) (-2, 1, 0)

In order to fairly set flat rates for auto mechanics, a shop foreman needs to estimate the average time it takes to replace a fuel pump in a car. How large a sample must he select if he wants to be 99% confident that the true average time is within 15 minutes of the sample average? Assume the standard deviation of all times is 30 minutes. 27 5 26 6

A student took out a simple interest loan for $2200 for 2 years at an annual rate of 5.6%.. (a) What is the interest on the loan? $ (b) How much will the student have to repay at the end of 2 years? $

Susan is conducting a survey about the electric bills of households in her city. From the electric company, she found that the population mean is $98.75 with a standard deviation of $10.45. Susan has a sample size of 60. Complete the equation that Susan can use to find the interval in which she can be 68% sure that the sample mean will lie. 88.3 10.45 7.75 109.2 60 98.75

The parent function f(x) = x² is reflected across the x-axis, vertically stretched by a factor of 3, and translated right 7 units to create g. Use the description to write the quadratic function in vertex form. g(x) = 7(x+3)² g(x)=-3(x-7)² g(x) = -3(x+7)² g(x) = 3(x-7)²

Eric's bicycle tires have a 29-inch diameter and Maggie's bicycle tires have a 26-inch diameter. How much farther do Eric's tires travel compared to Maggie after 10 complete revolutions? Use = 3.14 Enter your answer correct to one decimal place.

Consider the following scenario: Joe woke up one morning and found he was bitten all over by some sort of mystery bug. The next night, he felt itchy, especially on his torso, near where he'd gotten the other bites. He did not feel the same sensation on his legs, and he knew it must be psychosomatic. He treated his bed for a variety of different bugs, and the bites stopped, but he associated his bed with feelings of itchiness for several weeks. Eventually the response went away, only to suddenly show back up six months later! l

Ronald and his friends are at an arcade and are redeeming their tickets for prizes. The number of prizes they can get is calculated based on how many tickets they have won. p= the number of prizes the friends can get t = the number of tickets the friends have won Which of the variables is independent and which is dependent? t is the independent variable and p is the dependent variable p is the independent variable and t is the dependent variable

The city transit authority surveyed 1,000 citizens who regularly use public transportation. Of those surveyed, 658 users said they paid using a monthly subscription as opposed to paying for each ride individually. The transit authority's report claims, "We can be 95% confident that the percentage of citizens using public transportation with a monthly subscription is between 63.33% and 68.27%. " Which statement best describes this claim? A. There is not enough information to evaluate the report's claim. B.The report's claim is false because the margin of error is 3.87%. C. The report's claim is true. D. The report's claim is false because the margin of error is 2.94%.

The population of Suffolk County in Massachusetts decreased from 663,906 in 1990 to 641,695 in 1999. b. Use your equation to predict the population of Suffolk County in 2020.

Camila invested $9,100 in an account paying an interest rate of 4.6% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 14 years?

A friend lends you $175 for a week, which you agree to repay with 4.8% one-time interest. How much will you have to repay, including the amount you borrowed? Round your answer to two decimal places if necessary. $

According to statistics, a person will devote 34 years to sleeping and watching TV. The number of years sleeping will exceed the number of years watching TV by 22. Over the lifetime, how many years will the person spend on each of these activities?

After a 70% reduction, you purchase a new clothes dryer on sale for $150. What was the original price of the clothes dryer? The original price was $

Which of the following is a possible description for the function below? y=2x+15 The function represents the tax on a pizza order if the tax is 2% of every $15 pizza, x, that is ordered. The function represents the total cost of a pizza if the sales tax, x, is 2 times the cost of a $15 pizza. The function represents the cost of each additional topping on a pizza if the pizza is $15 plus 2% sales tax, X. The function represents the total price of a pizza which is $15 plus $2 for each additional topping, X.

Two secondary fuel tanks are needed, one within each wing. The space available in each wing is 4' 7" by 3' 2", by 10". How many total gallons of fuel could be added to the aircraft? 90.48 gal. 180.95 gal. 68.5 gal.

A student has an average (arithmetic mean) score of 88 for the first 3 tests in a class. What is the lowest score the student can earn on the fourth test to have an average score of at least 90 for the 4 tests?

A grocery store manager notices that this month her store sold a total of 849 gallons of ice cream, which represents a decrease of 17% from last month. How much ice cream did the store sell last month?

The half-life of the radioactive element unobtanium-53 is 10 seconds. If 32 grams of unobtanium-53 are initially present, how many grams are present after 10 seconds? 20 seconds? 30 seconds? 40 seconds? 50 seconds? The amount left after 10 seconds is The amount left after 20 seconds is The amount left after 30 seconds is The amount left after 40 seconds is The amount left after 50 seconds is

Suppose that W = span{V₁, V2, V3} where each v; is in R³. Consider the following statements. (i) If x is in W then x = C₁V₁1 + C2V2 + C3V3 for some scalars C1, C2, C3. (ii) 3v₁ - 2v2 is in W. (iii) W is a subspace of R³. Which of the above statements are always true? (a) (i) only (b) (ii) only (c) (ii) and (iii) only (d) (i) and (ii) only (e) (i), (ii), and (iii)

A manufacturer of face masks found out that the marginal revenue function is r(q) = 0.059q + 47.79 while the marginal cost function is c(q) = 0.0118q² - 1.18g + 59 where is the quantity of masks in thousands. Find the area between these two curves and the y-axis. Round your answer to 2 decimal(s).

I can find common factors and multiples. D Jerrie practices the piano every three days, and practices the trumpet every four days. Jerrie practices both the piano and the trumpet on May ST. When is the next day Jerrie will practice both Instruments at the same time?

Let u = (0, -2, 2) and v= (1,3,-1). Which of the following vectors are in span {u, v}? (i) (1,-1,2) (ii) (1, 1, 1) (iii) (5, 3, 7) (a) all of them (b) (ii) only (c) (iii) only (d) (i) and (iii) only (e) (ii) and (iii) only

The element plutonium-239 is highly radioactive. Nuclear reactors can produce and also use this element. The heat that plutonium-239 emits has helped to power equipment on the moon. If the half-life of plutonium-239 is 24,360 years, what is the value of k for this element?

The results of a statewide exam for assessing the mathematics skills of realtors were normally distributed with a mean score of 72 and a standard deviation of 12. The realtors who scored in the top 10% are to receive a special certificate. What score does a realtor need in order to receive a certificate?

The sides of a triangle are 12 inches, 15 inches, and 8 inches. Does the triangle contain a right angle? No, the sides of 8 inches and 12 inches do not add up to 15 inches. No, the sides of 8 inches and 12 inches squared and added together does not equal the side of 15 inches squared. Yes, the sides of 8 inches and 12 inches squared and added together equal the side of 15 inches squared. Yes, the sides of 8 inches and 12 inches are less than 15 inches.

A bacterial culture contains 200 cells initially and grows at a rate proportional to its size. After half an hour there were 400 bacteria. When will the population reach 1000?

The members of a youth football program are required to sell tickets to chicken dinners for the program's fundraiser. They can sell adult tickets for $10 and child tickets for $5. Each athlete must bring in at least $350 from the ticket sales. a. Write an expression to represent the total amount of money an athlete makes from ticket sales. Let x represent the number of adult tickets sold and let y represent the number of child tickets sold. b. Write an inequality in two variables to represent the amount an athlete must make. c. Graph the inequality from part (b). d. Use the graph to determine whether an athlete will bring in at least $350 if they sell 10 adult tickets and 30 child tickets. Explain your reasoning.

Dave bought a new car 8 years ago for $8400 to buy a new car comparably equipped new would cost $12,500. Assuming a steady rate of increase, what was the yearly rate of inflation in car prices over the 8-year period?

What factors must be taken into account in order to form a meaningful conclusion? Randomization Replication and treatments Controlling variables, randomization, and replication and treatments Controlling variables

Emma's Pet Shop sells aquariums in the shape of a right rectangular prism. Each aquarium measures 50 inches long, 20 inches wide, and 30 inches tall. The recommended density of each aquarium is no greater than 0.002 fish per cubic inch. Based on the recommendation, what is the greatest number of fish that should be in one aquarium? 15 fish 60 fish 600 fish 15,000,000 fish

Find the equation of the plane containing the point P(3, 0, -1) and the line (x, y, z) = (2, 1, 3) + t(3, -1, -2). (a) 2x 6y + 2z = 4 (d) 3x - 17y + 5z = 4 (b) x + 5y-z = 4 (c) x+6y-z = 4 (e) 16y - 4z = 4

Manny is deciding between two packages of yogurt. YoFruit costs $4.48 for 16 ounces. Yummy Yogurt costs $2.64 for 8 ounces. How much more does Yummy Yogurt cost per ounce? per ounce

Dakota and Justine are training to be in the Sweat for Fun Run. They ran the same distance on Saturday, but Dakota finished in less time. They each plan to run for the same amount of time on Sunday. If their average speeds are consistent, who will run farther on Sunday?

Exponential models and applications The number of bacteria in a culture is given by the function n(t) = 960e0.25t where t is measured in hours. (a) What is the relative rate of growth of this bacterium population? Your answer is percent (b) What is the initial population of the culture (at t=0)? Your answer is (c) How many bacteria will the culture contain at time t=5? Your answer is

Find the absolute maximum and absolute minimum values of f(t) = t√/9-t2 on the interval [-3, 3]. 1. Find the absolute maximum of f on the interval. 2. Find the absolute minimum of f on the interval.

On November 1st, Ben owes $500 on his credit card. On November 5th, Ben pays $60 towards the balance of the card. On November 12th, Ben makes $90 in purchases. On November 22nd, Ben pays $150 towards the balance of the card. The average daily balance of the card for the month of November is Question Help: Message instruct

The electromotive force V of an alternating current circuit at time t can be describe by the following function, where V is volts and t is in seconds. V(t) = 110sin (120) How many cycles will the circuit run through in 1 minute? 120 1320 1200 3600

A company observes the lifespan of 560 lightbulbs and finds that their data follows a normal distribution. What is the approximate number of light bulbs that fall within two standard deviations from the mean?