Basic Math Questions and Answers

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.

Solve the radical equation. Check all proposed √2x+5=x-5 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution set is (Use a comma to separate answers as needed. Simplify your answer.) OB. The solution set is the empty set.

The 1906 San Francisco earthquake had a magnitude of 7.9 on the MMS scale. Around the same time there was an earthquake in South America with magnitude 4.9 that caused only minor damage. How many times more intense was the earth movement in San Francisco earthquake than the South American one?

Sherrie takes 35/6 hours to clean a pool; Jose takes 2 5/9 hours. Calculate the time difference in hours. Express your answer in mixed number form, and reduce if possible.

You give up a full-time salary of $52,000 a year to go to school for 2 years. The total cost of going to school is $36,000. If you want to be able to recover your investment in 4 years or less, what is the minimum salary you would need to earn upon earning your degree?

Solve the linear inequality. When the solution is other than Ø, use interval notation to express the solution set and graph the solution set on a number line. 5(x+1)+124x + 7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution is (Type the solution using interval notation.) OB. The solution set is Ø. ***

Use graphs to find the set. (-5,0) U[-1,3] Select the correct choice below and fill in any answer boxes within your choice. OA. The set is (Type your answer in interval notation.) OB. The answer is the empty set.

Other than Ø, use interval notation to express the solution set and graph each solution set on a number line. 2(8-5x)>30-3x Select the correct answer below and, if necessary, fill in the answer box to complete your choice. O A. The solution set expressed in interval notation is (Simplify your answer. Use integers or fractions for any numbers in the expression.) OB. The solution set is Ø. www

Solve the compound inequality. -8≤x-4< -1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution set is OB. The solution set is the empty set. (Type your answer in interval notation.)

A wooden artifact from an ancient tomb contains 40 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.) years.

A construction worker, 24 feet up on a scaffold, lifts a 4-lb rope hand over hand up to the scaffold to raise a cement block weighing 6 pounds off the ground. (Assume the rope is 24 feet long.) How much work (in ft-lbs) is required to pull the rope and the block up to the scaffold?

A physics class has 40 students. Of these, 14 students are physics majors and 18 students are female. Of the physics majors, four are female. Find the probability that a randomly selected student is female or a physics major. - The probability that a randomly selected student is female or a physics major is www..

Any of the following may contribute to over- training, with the exception of which? A. Training too intensely. B. Training with supervision. C. Training too much. D. Training too quickly.

If you see an argument getting out of control and heading towards violence, you should leave and notify someone asap. Who would be the best people to notify? A. the relations of those involved B. people in positions of responsibility C. the first peers you see

Some healthcare products are advertised to be effective without much behind them, which makes them questionable. A. money B. guarantee C. scientific research

At the beginning of an experiment, a scientist has 268 grams of radioactive goo. After 210 minutes, her sample has decayed to 4.1875 grams. What is the half-life of the goo in minutes? Find a formula for G(t), the amount of goo remaining at time t. G(t) = How many grams of goo will remain after 47 minutes?

Living in a large city which has bad air quality from pollutants can negatively affect your health. A. environmental B. social C. emotional D. spiritual

Use the basic proportion P/10 - A/B to solve the following problem for the unknown quantity. Round your answer to the nearest hundredth, if necessary.

A tractor pull contest is held at a county fair. The tractors in the contest pull a sled on which two more people get on every 10 feet. The force function to move the sled feet is given by F(x) = 400x + 1500 lbs. How much work (in ft-lb) is required to pull the sled 50 feet?

The half-life of Palladium-100 is 4 days. After 20 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 7 weeks after the start?

What term describes when there is an increase, often sudden, in the number of cases of a disease above what is normally expected in a population? A. endemic B. anemic C. pandemic D. epidemic