Basic Math Questions and Answers

An object with initial temperature 200° F is submerged in large tank of water whose temperature is 40° F. Find a formula for F(t), the temperature of the object after t minutes, if the cooling constant is k = 0.6

Find the equation of the line with the slope m = 3/2 and passes through the point (-4,-2). y=-3/2x+4 y=3/2x-4 y=3/2x+4

If 5000 dollars is invested in a bank account at an interest rate of 10 per cent per year, Find the amount in the bank after 14 years if interest is compounded annually: Find the amount in the bank after 14 years if interest is compounded quarterly: Find the amount in the bank after 14 years if interest is compounded monthly: Finally, find the amount in the bank after 14 years if interest is compounded continuously:

Suppose that the world's current oil reserves is R= 2190 billion barrels. If, on average, the total reserves is decreasing by 21 billion barrels of oil each year, answer the following: A.) Give a linear equation for the total remaining oil reserves, R, in billions of barrels, in terms of t, the number of years since now. (Be sure to use the correct variable and Preview before you submit.) R= billions of barrels. B.) 15 years from now, the total oil reserves will be C.) If no other oil is deposited into the reserves, the world's oil reserves will be completely depleted (all used up) approximately years from now. (Round your answer to two decimal places.)

Two independent random samples resulted in the following. Find the estimate for the standard error for the difference between two means. (Give your answer correct to two decimal places.) Sample A: nA = 27, SA = 8.2 Sample B: ng= 27, SB = 11.5

The rate of a continuous flow for a company is growing exponentially. At the beginning, the rate was $10,000 per year. By the end of the first year, the rate was $10,941.74 per year. Complete parts (a) through (e) below. (a) Determine an exponential function to model the continuous money flow for this company. f(t) = (10,000) (0.09) (b) Find the total money flow for the first 8 years. The total money flow over is $ 117159.25. (c) Find the accumulated amount of money flow at the end of 8 years if the interest rate is 6%, compounded continuously. The accumulated amount of money flow is $

A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y=ax+b a=-1.053 b=21.709 r²=0.927369 r=-0.963 Use this to predict the number of situps a person who watches 5.5 hours of TV can do

With a certain medical insurance policy, the customer must first pay an annual $350 deductible, and then the policy covers 60% of the cost of x-rays. The first insurance claims for a specific year submitted by a person are for two x-rays. The first x-ray cost $640, and the second x-ray cost $940. How much, in total, will he need to pay for these x-rays?

Study the polynomial function. f(x) = 0.1x(x + 6)(4x + 10) Part A. Identify the key features for the function above. Key features include: x- and y-intercepts, end behavior, vertical stretch/shrink and degree.

Mark wants to invest $6,500.00 at an interest rate of 7.5% per year, compound daily. How long will it take his investment to grow to $8,000? Use: A (t) = P(1+) ² 1.5 years 2 years 2.7 years 1.3 years

A cake mixture is 9 parts flour to 4 parts water (by mass). How many kilograms are there each of flour and water necessary to produce a dough with a mass of 3.12 kg.

A population numbers 16,000 organisms initially and grows by 13.3% each year. Suppose P represents population, and t the number of years of growth. An exponential model for the population can be written in the form P = abt where

The phone company NextFell has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 100 minutes, the monthly cost will be $61. If the customer uses 780 minutes, the monthly cost will be $333. A) Find an equation in the form y = = mx + b, where x is the number of monthly minutes used and y is the total monthly of the NextFell plan. B) Use your equation to find the total monthly cost if 980 minutes are used.

A house was valued at $115,000 in the year 1992. The value appreciated to $150,000 by the year 2000. A) What was the annual growth rate between 1992 and 2000? Round the growth rate to 4 decimal places. B) What is the correct answer to part A written in percentage form? C) Assume that the house value continues to grow by the same percentage. What will the value equal in the year 2003?

A car rental company offers two plans for renting a car: Plan A: 30 dollars per day and 16 cents per mile Plan B: 50 dollars per day with free unlimited mileage For what range of miles will plan B save you money for a 1 day rental? To save money the mileage must be greater than Give your answer accurate to at least one decimal place miles per day.

A computer monitor is 20 inches wide. The aspect ratio, which is the ratio of the width of the screen to the height of the screen, is 16:9. What is the length of the diagonal of the screen, to the nearest whole inch?

In 2001 the population of Mountainville was 9,400. Their population increases by 0.21% per year. What is the expected population of Mountainville in 2007? Round your answer to the nearest whole number.

Shannon needs to rent a car while on vacation. The rental company charges $17.95, plus 19 cents for each mile driven. If Shannon only has $50 to spend on the car rental, what is the maximum number of miles she can drive?

Which of the following is a type of joint? trochanter fibrous tibia synapse ulna

Mathematics is like love; a simple idea, but it can get complicated. A swimming pool contains 34,000 gallons of water. How many gallons of chlorine must be added to "shock the pool" and bring the water to a 8.5 % solution?

A line passes through the point (2, 3) and has a slope of -2. Which is the equation of the line in point-slope form? A) 2x+y=7 B) y=-2x+7 Cy-3--2(x-2) E) y + 3 = -2(x - 2)

Suppose we take a sample of size 100 from a population. We find that 22 people in our sample are left-handed. Describe the shape of the sampling distribution of proportions. Why? The sampling distribution is approximately normal because np and n(1-p) are both greater than 10. The sampling distribution is skewed because np and n(1-p) are not both greater than 10. The sampling distribution is approximately normal because our sample size is larger than 30. The sampling distribution is skewed because the CLT is not met.

Make sure to justify your answer. A normal distribution has a mean of 75 and a standard deviation of 15. Determine the z- score for the data value of 85.

A sample of 200 sodas filled on a new machine showed that 22 were over-filled. The factory will get rid of the new machine if the data indicates that the proportion of over-filled sodas is significantly more than 7%. At a significance level of 10% does the factory get rid of the machine or not? Yes, the factory gets rid of the machine. There is evidence the machine is over-filling the bottles. No, the factory does not get rid of the machine. There is not evidence the machine is over-filling the bottles. Yes, the factory gets rid of the machine. There is not evidence the machine is over-filling the bottles. No, the factory does not get rid of the machine. There is evidence the machine is over-filling the bottles.

A taxi driver charges for a trip, with a base fare, using the function = 3k + 2, where t is the total cost ($) for the trip and k is the number of kilometers traveled in the trip. Find the rate of change (cost per kilometer traveled). $1 $3 $1.5

Bentley invested $26,000 in an account paying an interest rate of 6.8% compounded daily. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 11 years?

A queen-sized mattress is 20 inches longer than it is wide. A king-sized mattress is 16 inches wider than the queen-sized mattress but has the same length. The area of the king-sized mattress is 1,280 square inches more than that of the queen- sized mattress. An equation that can be used to solve for the dimensions of the king size mattress is The dimensions of the king size mattress are

When hired at a new job selling jewelry, you are given two pay options: ption A: Base salary of $12,000 a year, with a commission of 11% of your sales Option B: Base salary of $20,000 a year, with a commission of 4% of your sales In order for option A to produce a larger income, you would need sell at least $ of jewelry each year.

Brenda bought 10 dresses for 100 dollars. Find the rate of change and the cost of 15 dresses. $30 and $450 $10 and $150 $20 and $300

1,889,550. In 1995 the population was 1,885,550. Compute the slope of the population growth (or decline) and choose the most accurate statement from the following: A city's population in the year x = 1979 was y The population is decreasing at a rate of 300 people per year. The population is decreasing at a rate of 250 people per year. The population is increasing at a rate of 300 people per year. The population is increasing at a rate of 250 people per year. The population is increasing at a rate of 450 people per year. The population is decreasing at a rate of 450 people per year.

A television network, Network A, is scheduling its fall lineup of shows. For the Tuesday night 8 p.m. slot, Network A has selected its top show. If its rival network, Network B, schedules its top show during the same time slot, Network A estimates that it will get 1.1 million viewers. However, if Network B schedules a different show during that time slot, Network A estimates that it will get 1.5 million viewers. Network A believes that the probability that Network B will air their top show is 0.3 and the probability that Network B will air another show is 0.7. Determine the expected number of viewers for Network A's top show.

Automotive Design. The angle formed by a car's windshield and dashboard is such that tane = √3. If the vertical distance y between the top of the windshield and the horizontal plane of the dashboard is 5 feet, what is the length of the windshield?

Let R be the region bounded by the graphs of f(x) and g(x) as shown in the figure above. Use these graphs o answer the questions in this activity. Instructions are below: 1. sketch and label the graphs 2. Find the points of intersection using your graphing calculator and label them 3. Draw your representative rectangle on the graph to help with the questions below

Determine a polynomial equation for a graph that passes through the point (6, -196) and has three x- intercepts at (-8, 0), (-1, 0), and (5, 0). Show all your work. Points are awarded for setting up the correct equation, solving correctly and showing steps, and providing a correct answer.

Suppose a paint that is 15% gloss is mixed with a paint that is 30% gloss to make 5 gallons of a paint that is 20% gloss. How many gallons of each paint were used in the mixture? One must set a system of equations and use substitution or elimination to solve.

Suppose another drug is administered intravenously. The concentration c of the drug (in mg/L) in the bloodstream, t hours after it is administered, is modeled by the function c(t) a. Determine when the concentration will be 0.5 mg/L. -The concentration of the drug will fall to a level of 0.5 mg/L with 36 hours after the drug is given. b. Complete the table representing the concentration of the drug in the bloodstream, t hours after administration. Round to two decimal places as needed.

A popular restaurant does not take reservations. As a result, there is usually a waiting time before you can be seated. Assume the waiting time before being seated is normally distributed with a mean of 22 minutes and a standard deviation of 5 minutes. What is the probability that the waiting time will not exceed 20 minutes?

Using the water tower below, select all the shapes that could be used to model it. Pyramid Hemisphere Cone Prism Cube Cylinder

A belief based on specific observations that has not been proven or disproven is called a conjecture of Fill in the blank to complete the statement below. A belief based on specific observations that has not been proven or disproven is called a conjecture or

The solution set to a system of dependent equations is given. Write three ordered triples that are solutions to the system. ((5z, 3-z, z) | z is a real number}

If the equation of the line y = 4x - 5 is changed to y = -x - 5, how is the graph affected? A) The line is shifted up. B) The line is closer to vertical. C) The line is closer to horizontal. D) The line is now decreasing from left to right. E) The line is now decreasing from right to left.

Which transformation could NOT be used to prove that two circles are congruent to one another? A. a dilation with a scale factor of 2 B. a dilation with a scale factor of 1 C. a reflection D. a rotation

A coffee company has found that the marginal cost, in dollars per pound, of the coffee it roasts is represented by the function below, where x is the number of pounds of coffee roasted. Find the total cost of roasting 110 lb of coffee, disregarding any fixed costs. C'(x)= -0.023x + 5.50, for x ≤ 200 The total cost is $

Find the area, if it is finite, of the region under the graph of y=6x5 e over [0,00). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The area of the region is. (Type an exact answer.) B. The area is not finite.

Which of the following statements are true about the point of concurrency of the perpendicular bisectors of a triangle? I. For a right triangle, the point of concurrency lies on the triangle. II. For an obtuse triangle, the point of concurrency lies inside the triangle. III. For an acute triangle, the point of concurrency lies outside the triangle. I and III I only Ill only II only none of these

The slope of the function is -4 and y-intercept is reciprocal of the slope. Which of the following represents the linear function? 16x-4y=1 4x + 16y=1 16x + 4y = -1

"If AB + BC = 24 and AB = 10, then 10 + BC = 24" is an example of the ? Symmetric property of equality Addition property of equality Subtraction property of equality Reflexive property of equality Substitution property of equality

Solve the triangle. Round to the nearest tenth. O m∠A = 45°, m∠B = 45°, c = 7.1 O m∠A = 41.4°, m∠B = 48.6°, c = 7.1 O m∠A = 42.8°, m∠B = 47.2°, c = 7.1 Om∠A= 47.2°, m∠B = 42.8°, c = 7.1 O None of the other answers are correct

Solve the triangle. Round to the nearest tenth. In ABCA, mZB = 114°, a = 13, b = 35.3 mZC = 46.3°, m<A = 19.7°, c = 27.9 mZC = 46.3°, m<A = 19.7°, c = 26.5 None of the other answers are correct mZC = 49.6°, mZA = 16.4°, c = 27.9 mZC = 46.3°, m<A = 19.7°, c = 25

Given the following: f(x) = 3x +7x+8x¹; g(x) = -x + 12x - 212³; and h(x) = 8x³ + 12x + 6x² - 14x¹ Complete the following: h(x) - f(x) 8x³+3x+6x - 7x + 12x22x4 82³-3x+62-7x 82³-3x+6x7x 82³ + 3x + 6x + 7x