Basic Math Questions and Answers

In a binomial experiement, what does it mean to say that each trial is independent of the other trials? Choose the correct answer below. A. Each trial is independent of the other trials if the outcome of one trial affects the outcome of another trial. B. Each trial is independent of the other trials if the outcome of one trial does not affect the outcome of any of the other trials. C. Each trial is independent of the other trials if no more than one trial occurs at a time. D. Each trial is independent of the other trials if the sum of all the possible trial outcomes equals 1.

Of the cartons produced by a company, 10% have a puncture, 8% have a smashed corner, and 0.5% have both a puncture and a smashed comer. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner.

The mean scores for students in a statistics course (by major) are shown below. What is the mean score for the class? 9 engineering majors: 92 5 math majors: 94 13 business majors: 85 The class's mean score is

Solve the equation by the method of your choice. x² +8x=1

Solve the equation by the square root property. (x-3)² = 1 What is the solution set? (Use a comma to separate answers as needed.)

A depressant puts more emphasis on the inhibitory part of the brain, which can cause you to be more A. aroused B. stimulated C. dispirited

Determine whether the study is an observational study or an experiment. Explain. In a survey of 1081 adults in a country, 53% said the country's leader should release all medical information that might affect their ability to serve. The study is because it a treatment to the adults.

Friendship's soccer team purchased uniforms and equipment for a total cost of $912. equipment cost $612, and the uniforms cost $25 each. How many uniforms did the school purchase? 1. Variable: 2. Constant: 3. Rate: 4. Equation and solve:

Quadratic Equations Solve the equation by the method of your choice. (2x + 1)(x+3) = -1 The solution set is. (Simplify your answer. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

Members of the track team can run one mile in an average of 7.32 minutes. The fastest and slowest times varied from the average by 1.04 minutes. Which absolute value inequality below models the one mile running times of the track team? |x+8.36| ≤ 7.32 |x-7.32|≤ 1.04 |x+7.32| ≤ 1.04 |x-1.04| ≤ 7.32

Solve the following system of three equations and three unknowns using either substitution or linear combination. Be sure to check that your solution satisfies all three of the original equations! x-y +z = 10 3x + y + 2z = 34 -5x + 2y-z = -14

Two trains leave stations 374 miles apart at the same time and travel toward each other. One train travels at 75 miles per hour while the other travels at 95 miles per hour. How long will it take for the two trains to meet? Do not do any rounding.

You are shopping for school supplies. A store is offering a 10% discount on binders and a 20% discount on packages of paper. You want to buy 5 binders originally marked $2.50 each and 10 packages of paper originally marked $1.30 each. Write an expression that shows how much you will save after the discounts.

There are 750 toothpicks in a regular-size box. A jumbo-size box is made by doubling the length, width, and height of the regular box. How many toothpicks will the jumbo box hold? 6000 toothpicks 1500 toothpicks 2250 toothpicks 3000 toothpicks

u= <- 4,6 > and v= < 2,- 3 > a. Sketch u, v, and u + v on a pair of coordinate axes below: b. Find | u + v | and label it on your graph above. c. Find the angle that u + v makes with the positive or negative x-axis and label it on your graph above. d. Sketch u, v, and u- v on a pair of coordinate axes below:

Use the cylindrical shell method to calculate the exact volume of the solid formed by rotating the graph of f(x) = 5√x -4about the y-axis on the interval [4, 5]. Note: Round to the nearest hundredth.

The access code for a garage door consists of three digits. Each digit can be any number from 1 through 6, and each digit can be repeated. Complete parts (a) through (c). (a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c) What is the probability of not selecting the correct access code on the first try? (a) Find the number of possible access codes. The number of different codes available is 216 (b) What is the probability of randomly selecting the correct access code on the first try? The probability of randomly selecting the correct access code is 0.005 (Round to three decimal places as needed.) (c) What is the probability of not selecting the correct access code on the first try? The probability of not selecting the correct access code is (Round to three decimal places as needed.)

Find the domain of the function. (10 Points) f(t) = √√√r +2 all real numbers t such that 1 ≥ 2 all real numbers t except t = 2 all real numbers t O all real numbers t such that t ≤ 2 all real numbers t except t = - 2

Decide if the situation involves permutations, combinations, or neither. Explain your reasoning. The number of ways 19 people can line up in a row for concert tickets. Does the situation involve permutations, combinations, or neither? Choose the correct answer below. A. Permutations. The order of the 19 people in line matters. B. Combinations. The order of the 19 people in line does not matter. C. Neither. A line of people is neither an ordered arrangement of objects, nor a selection of objects from a group of objects.

A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 600 cubic centimeters of soup. The sides and bottom of the containe will be made of styrofoam costing 0.04 cents per square centimeter. The top will be made of glued paper, costing 0.06 cents per square centimeter. Find the dimensions for the package that will minimize production cost. Helpful information: h: height of cylinder, r: radius of cylinder Volume of a cylinder: V = Tr²h 2πrh Area of the top/bottom: A = ² To minimize the cost of the package: Radius: Area of the sides: A Height: Minimum cost: = cm cm cents

From a balloon 1197 feet high, the angle of depression to the ranger headquarters is 50°21'! How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)? 997 ft O 987 ft 992 ft O 982 ft

There are 250 toothpicks in a regular-size box. A jumbo-size box is made by tripling the length, width, and height of the regular box. How many toothpicks will the jumbo box hold? 750 toothpicks 2250 toothpicks 6750 toothpicks 9000 toothpicks

About 50% of babies born with a certain ailment recover fully. A hospital is caring for six babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. Is the experiment a binomial experiment? Yes O No What is a success in this experiment? O Baby doesn't recover Baby recovers PIE

Construct a confidence interval for p₁ -P2 at the given level of confidence. X₁ = 366, n₁ = 516, x₂ = 439, n₂ = 597, 95% confidence The researchers are confident the difference between the two population proportions, p₁ -P₂, is between (Use ascending order. Type an integer or decimal rounded to three decimal places as needed.) and

C: The Linear Correlation Coefficient a) Give an example of two variables that you believe would be positively correlated. Explain your reasoning. b) Give an example of two variables that you believe would be negatively correlated. Explain your reasoning.

A 159 foot tower is located on a hill that is inclined 36° to the horizontal. A guy-wire is to be attached to the top of the tower and anchored at a point 74 feet downhill from the base of the tower. Find the length of wire needed. You may want to refer to p 511 for a diagram.

Solve the equation by factoring. 3x(x-2)=8x²-8x Rewrite the equation in factored form.

Heather has been given a list of 5 bands and asked to place a vote. Her vote must have the names of her favorite, second favorite, and third favorite bands from the list. How many different votes are possible?

The given scatter plot shows x = age versus y test score data on a test: a) Determine the equation of the approximate line of best fit drawn on the graph. Use (20, 220) and (35, 280) for the coordinates of the points marked on the line with a +: line b) What do the slope and the y-intercept of your indicate? c) Use your equation to predict the test score for a 24 year- old test taker. d) Use your equation to predict the age of someone scoring 260 points on the test.

What is the exact volume of the solid stretching over the x-interval [0, 2] whose cross-sections are equilaterial triangles where the length of the side of a cross-section at is given by the function f(x)=√√√36-x²? Note: Maintain fractions if applicable.

In f(x) = k(x)², if k = 1 for the original graph, what happens to the graph of f(x) as k decreases toward 0? The graph of f(x) is shrunk horizontally by a factor of k. The graph of f(x) is stretched horizontally by a factor of k. The graph of f(x) is shrunk vertically by a factor of k. The graph of f(x) is stretched vertically by a factor of k.

A wooden artifact from an ancient tomb contains 65 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.)

A tank that is 5 feet deep, with a square bottom with sides 4 feet each, has 2 feet of water that weighs 62.3 lb/ft³ in it. How much work (in ft-lbs) will it take to pump the water to the rim of the tank? Note: Enter your answer without the use of commas. Round to the nearest integer.

Suppose a long rectangular sheet of metal, 12 inches wide and 10 feet long, is to be made into a rain gutter by turning up two sides so they are perpendicular to the sheet. How many inches should each side be turned up to give the gutter its greatest capacity?

Which of the following choices is NOT a healthy way to deal with stress? A. drinking with friends or alone B. meditating C. exericising regularly

2. A marble paperweight shaped similar to a prism weighs 0.3 lb. How much does a similarly shaped marble paperweight weigh if its length, width, and height are doubled? O () O 2.4 lb 2.7 lb 1.2 lb 0.6 lb

Logan is solving an a real world problem using absolute value inequalities. Below is the question Logan is solving with his steps to solve inequality. The Question The ideal weight of a certain toy car is 22.35 ounces. The actual weight may vary from the ideal by at most 0.12 ounce. Find the range of acceptable weights for this engine. Logan's steps: Step 1: The equation he created was |x-.12 |≤ 22.35 Step 2: x- - .12 ≤ 22.35 and - (x-.12) ≤ 22.35 Step 3: x 22.47 and x > -22.23 Solution: -22.23 ≤ x ≤ 22.47 Which is true about Logan's work? O Step 2 is incorrect: The second inequality that Logan should have set up should have been x-.122-22.35. O Step 3 is incorrect. Logan solved the inequality wrong for the second inequality and the inequality should be 22.23 making the solution 22.23 ≤x≤ 22.47. O All steps and the solution is correct. O Step 1 is incorrect. Logan should have used the equation x 22.35 | .12.

Use interval notation to express the solution set and graph the solution set on a number line. - 3x≤ 15 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type your answer using interval notation.) B. The solution set is Ø.

A certain manufacturing industry has 63.1 thousand job in 2008, but due to the economy, declined at an average annual rate of 1.7 thousand jobs per year from 2008-2018. Assuming this was true, what was this industry's percent change from 2008 to 1018?

Determine whether the random variable x is discrete or continuous. Explain. Let x represent the exact time it takes to evaluate 27 + 72. Choose the correct answer below. ***** A. The random variable is continuous, because it has an uncountable number of possible outcomes. OB. The random variable is discrete, because it has a countable number of possible outcomes. OC. The random variable is continuous, because it has a countable number of possible outcomes. D. The random variable is discrete, because it has an uncountable number of possible outcomes.

An 8-in pendulum moves according to the function 0 = 0.4 cos (2t) where is the angular displacement from the vertical in radians and tis time in seconds. What is the rate of change (in radians/s) of when t = Note: Round to the nearest hundreth. 4 seconds?

Suppose it takes a force of 30 N to hold a spring that has been stretched from its natural length of 6 cm to a length of 8 cm. How much work (in J) is done in stretching the spring from 7 cm to 9 cm?

Given the function f(x) below, determine for what x value(s) the function is discontinuous, if any. 3x-2 if -3 < x < 2 if 2<x< 4 2 if a 4 Hint: Try graphing the piecewise function to help visualize. f(x) H The function is discontinuous at x = 2 and x = 4. The function is discontinuous at x = 4. The function is discontinuous at x = 4 and x = -1. The function is continuous over all x values in the domain of f(x).

The radius of a disc is measured to be 14 in. The measurement of the radius at worst could be inaccurate up to 0.2 inches. Use differentials to estimate the maximum error in the calculated area of the disc (in in²). Note: Round to the nearest hundreth.

If you borrow $4,500 at 4% interest, what is the amount that you will owe in five years if compounding is continuous?

The count in a bateria culture was 900 after 15 minutes and 1300 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 13000.

Suppose a hiker finds himself in a forest 4 miles directly east of the nearest point along a road that runs north to south. He wants to walk to his car which is parked on the road 10 miles south of the point on the road that is nearest to the hiker. He can walk 2 miles per hour through the forest and 4 miles per hour along the road. Toward what point, in miles north of the car, should the hiker walk in order to minimize the time it takes to reach his car? Note: Round to the nearest thousandth.

Tyrone's hourly wage is $20 and his net pay is 72% of his earning. Tyrone spends about $1,900 on his monthly expenses. If Tyrone works 40 hours per week and has no other sources of income, what is his total monthly cash inflow? (Hint: Assume there are 4 pay periods per month)

On April 1st, 2020 there were 736 COVID-19 cases recorded in Oregon state. And on April 30th (29 days later), there were 2,510 cases. (Source: KGW8 News) Assume exponential growth. Use this data to determine what day in May the number of recorded cases should have been 3200. According to an exponential model, the number of cases should have reached 3200 on May 2020. (Round so there are no decimals in your answer.)

100 minutes, the bacterial The doubling period of a bacterial population is 10 minutes. At time t = population was 70000. What was the initial population at time t = 0? Find the size of the bacterial population after 4 hours.