Math Questions

Amanda has $21,400 in the bank. The account will earn 1.9% in simple interest for the next 4 years. How much interest will Amanda earn?

A farmer recently purchased her neighbor's farm. Before the purchase, the farmer owned a total of 343 acres of land. After the purchase, she owned a total of 501 acres of land. Determine the percent increase in the number of acres of land owned by the farmer. The number of acres of land owned by the farmer increased by about ____%

A fair die is rolled 6 times. What is the probability of having no 1 and no 2 among the rolls? Round your answer to three decimal places.

If the apprentice wishes to cut a 20-foot section of angle in seven identical lengths, what will the measurements be in fractional inches to the nearest 1/32" (assuming zero loss of metal due to cutting)?

If f(x) = -4|3x - 2| and g(x) = -20, solve the following. (a) f(x) = g(x) (b) f(x) >g(x) (c) f(x) = g(x) (a) Solve f(x) = g(x). Select the correct choice below and, if necessary, fill in the answer box to complete your answer. A. The solution set is {□ }. (Simplify your answer. Use a comma to separate answers as needed.) B. The solution set is {x| □} . (Simplify your answer. Type a compound inequality.) C. The solution set is {x|x≤□ or x≥□}. (Simplify your answer. Type inequalities.) D. The solution set is the empty set.

Mark borrowed $18,036 to help pay for expenses. If the loan carries an annual interest rate of 4.3% and he wants to be debt free in 2 years by making monthly payments, how much will each payment be?

Write the augmented matrix of the system and use it to solve the system. If the system has an infinite number of solutions, express them in terms of the parameter z. x-10y-35z=3 -5x+11y+58z=-15 x-2y-11x=3 x=________________ y=________________ z=________________

Julio reads that apples contain an average of 6 seeds. He thinks the number of seeds is greater for Granny Smith apples. He randomly samples 20 Granny Smith apples and calculates a sample mean of 6.3 seeds with a standard deviation of 1.42 seeds. Conduct a significance test for the mean with a significance level of α = 0.10 and make a conclusion. -0.945 > -2.093; Julio rejects the null hypothesis. The test suggests that Granny Smith apples have a greater mean number of seeds. -0.945 > -1.328; Julio rejects the null hypothesis. The test suggests that Granny Smith apples have a greater mean number of seeds. 0.945 < 2.093 ; Julio fails to reject the null hypothesis. The test suggests that Granny Smith apples have an average of 6 seeds. 0.945 < 1.328; Julio fails to reject the null hypothesis. The test suggests that Granny Smith apples have an average of 6 seeds.

A sample of 27 television tubes produced by a company showed a mean lifetime of 1138 hours and a standard deviation of 193 hours. Estimate the standard deviation of the population of all television tubes produced by this company. Round your answer to 3 decimal places.

The vertices of a square are H(0,2), I(2,0), J(0-2), and K(-2,0). Which statements are true of the image of HIJK after the given composition of transformations? Select all that apply. Step 1: x,y) → (-y,x) Step 2: (x,y) → (3x, 3y) a)H"(-2,0) b) HIJK = H'I'J'K' c)H'I'J'K'~H"T")"K" d)J"(6,0) e)y= x is a line of symmetry for the HIJK and H"1"J"K".

The function below gives the cost in dollars to manufacture x items: C (x) = 10,000 + 5x-x^2/10,000 Find the average cost per item over the interval [1,000, 1,010].

In an early essay draft, a student offers the following as his thesis statement: McDonald's new ad campaign for its "Healthy Choices" menu features images of happy children because the restaurant chain is trying to draw attention away from its role in depleting the rainforest. Which of the following represents the most serious problem with the claim here? The claim doesn't address why analyzing the ad campaign matters. The claim doesn't address why readers should care about McDonald's new ad campaign. The claim doesn't offer proof that McDonald's is depleting the rainforest. The claim isn't logical; why would happy children draw attention away from McDonald's environmental role?

A new fertilizer was applied to the soil of 296 bean plants. 90% showed increased growth. Find the margin of error and 95% confidence interval for the percentage of all bean plants which show increased growth after application of the fertilizer. Report answers to at least 2 decimal places.

(a) If N is the population of the colony and t is the time in days, express N as a function of t. Consider N₀ is the original amount at t= 0 and k≠0 is a constant that represents the growth rate. N(t) = □ (Type an expression using t as the variable and in terms of e.)

The plane area is bounded by the functions y=x^2 and y=4x - x^2 Find the volume generated when the plane area is revolved about the line y=6

The Happy Taco restaurant employs 12 people. If 3 people have an annual salary of $28,000, 4 people have an annual salary of $34,000, 4 people have an annual salary of $45,000, and 1 person has an annual salary of $65,500 find the average salary for the employees.

How much would you have to deposit at the end of the year in an account that pays an interest rate of 7.16% compounded monthly if at the end of 15 years you want $20,000 in the account? Use the TMV calculator to fill in the table. N_____________ I%__________ PV__________ PMT__________ FV___________ P/Y___________ C/Y_________

A fair die is rolled 6 times. What is the probability that a 4 is obtained on at least one of the rolls? Round your answer to three decimal places.

Sarah wants to save for a car that costs $5000. She has $4250 in a savings account earning 1.49% compounded quarterly. If Sarah has four years until she gets her driver's license, will she have enough to buy a car? Use the TVM calculator to solve Explain.

Consider the autonomous first-order differential equation dy/dx = y - y³ and the initial condition y(0) = y₀. Sketch the graph of a typical solution y(x) when y₀, has the given values. (a) y₀ > 1

Noise levels at various area urban hospitals were measured in decibels. The mean of the noise levels in 88 randomly selected corridors was 81.1 decibels, and the standard deviation of the population was 8.06. Find the upper bound limit of the 90% confidence interval of the true mean.

Find the general indefinite integral. (Use C for the constant Integration.) ∫(x^5)^1/4 dx

A group of geometry students wrote the following definitions for parallel lines. Jennifer: Two lines that never intersect. Bethany: Two lines whose perpendicular distance between points remains constant. Darius: Two lines are parallel if and only if they lie in the same plane and corresponding points are equidistant. Which definition(s) is/are the most precise? a)Bethany b)Darius c)Jennifer d)All are precise definitions.

An equation of an ellipse is given. (a) Identify the center of the ellipse. (b) Determine the value of a. (c) Determine the value of b. (d) Identify the vertices. (e) Identify the endpoints of the minor axis. (f) Identify the foci. (g) Determine the length of the major axis. (h) Determine the length of the minor axis. (i) Graph the ellipse. Express numbers in exact, simplest form. 9x^2 + 64y^2 = 576

Translation A maps (x, y) to (x +r,y+s). Translation B maps (x, y) to (x – a,y+b). Translate a point using Translation B, then Translation A. Write a rule for the final image of the point. (x,y) → (._____________ ___________) a). type x coordinate. Don't type parenthesis. * b). type y coordinate. Don't type parenthesis.

Measurements of the diameters of a random sample of 205 ball bearings made by a certain machine during one week showed a mean of 0.873 inch and a standard deviation of 0.481 inch. Find a lower bound 99% confidence limit for the mean diameter of all the ball bearings. Round your answer to 4 decimal places.

What does Gelman mean by a "straw-man" null hypothesis? a)A hypothesis with less than a .01 probability of being supported in a study b)A null hypothesis known or suspected to be false, set up to be rejected c)A hypothesis that is full of straw d)A hypothesis about gender differences among farmers

Solve the triangle with α= 55°, γ = 69°, and c = 25.91. β= degress a= b= Round all answers to 2 places after the decimal point. Give angles in degrees (but do not type "degrees" in the answer box). As in the text, side a is opposite from angle α, side b is opposite from angle β , and side c is opposite from angle γ. If no such triangle exists, then enter DNE in each answer box. If multiple triangles exist, then enter the values of the missing sides and angles for each triangle, separated by commas.

The table below cross classifies the price of 486 stocks in a particular stock exchange, with whether the earnings per share ratio was positive or not. Use the data in the table find the probability that the price of the stock is $50.00-$99.99 or the earnings per share ratio is positive. Earnings per Share Price of Stock Negative or 0 Positive $0-$49.99 25 123 $50.00-$99.99 18 180 $100.00 or higher 2 138 A). P(E)=180/100 b)P(E) =18/(123+180 +138) C). P(E)= 180/486 D). P(E)=(123+18+180 +138)/486 The probability that the price of the stock is $50.00-$99.99 or the earnings per share ratio is positive is

4. X(-1, 2, 6) and Y(5, 5, 12) are two points in R³. a). Determine the components of a position vector equivalent to YX. b). Determine the components of a unit vector that is in the same direction as YX.

Which of the following is the best definition for a circle? a)The set of points on a plane, with an enclosed arc which has 360° b))The set of points on a plane, which are equidistant from a given point. c)one-sided figure which has no beginning or end. D)A one-sided figure with a total of 360° in the interiorangles.

Suppose that you are testing the hypotheses Ho: = 19 vs. HA: > 19. A sample of size 25 results in a sample mean of 18.5 and a sample standard deviation of 1.5. a) What is the standard error of the mean? b) What is the critical value of t for a 90% confidence interval? c) Construct a 90% confidence interval for μ. d) Based on the confidence interval, at a = 0.05 can you reject Ho? Explain. a) The standard error of the mean is 3 b) The critical value is t

Which refers to the null hypothesis for this new test? Ho: population mean of differences is zero He: population mean of differences is not zero Ho: sample mean of differences is zero He.: sample mean of differences is not zero

7 students took a test which was conducted by a public school. Their test scores are 85, 96, 78, 84, 97, 48, and 60. Find the median of the test scores. 84 78.2 85

Find the LCD for the list of rational expressions. 8x+1/x2 + 5x-6 . 4x / x2+4x-5 The LCD is

Simplify the difference b - 4 / b2+ 2b-8 -b+2 / b2-16] State any restrictions on the variable. A. -4(2b – 5)/(b + 4); b≠-4 B. -4(2b -3)/ (6 – 4)(b + 4)(b + 2); b≠-2 or ±4 C. -4(2b – 3)/(b – 4)(b + 4)(b - 2); b≠2 or ±4 D.-4(2b – 3)/(b – 4)(b + 4)(b − 2); b ≠2 or ± 4

Ana drew a map of the Panama Canal. In the scale Ana used for the map, 4 centimeters represents 20 kilometers. The actual length of the Panama Canal is 82 kilometers. What is the length in centimeters of the Panama Canal on Ana's map?

5) Does the equation x² - 10x + y² - 6y = -30 intersect the x-axis? A) Yes, because the center is a (5, 3) and the radius is 4. B) Yes, because the center is a (5, 3) and the radius is 2. C) Yes, because the center is a (-5, -3) and the radius is 2. D) No, because the circle is entirely in the first quadrant.

The weights, in grams, of 30 randomly selected apples from a large bin are shown below. The mean weight is 112 grams and the standard deviation is 5.5 grams. Does the data appear to be normally distributed? 103 116 104 123 111 112 108 115 114 101 112 120 106 98 110 119 109 111 110 112 110 109 114 107 110 105 106 102 111 108

One year Perry had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 3.17. Also, Susan had the lowest ERA of any female pitcher at the school with an ERA of 3.16. For the males, the mean ERA was 4.242 and the standard deviation was 0.873. For the females, the mean ERA was 3.949 and the standard deviation was 0.874. Find their respective Z-scores. Which player had the better year relative to their peers, Perry or Susan? (Note: In general, the lower the ERA, the better the pitcher.) a)Perry had an ERA with a Z-score of b)Susan had an ERA with a Z-score of

Jack and Jill deposited $1000 in a savings account with an annual interest rate of 8.3% compounded semiannually when they got engaged to be married. It took them 2 years to plan their wedding. If they withdraw the money on their wedding day, how much money will Jack and Jill have to take on their honeymoon? a)$1089.32 b)$1176.62 c)$1305.25 d) $1324.15

solve by graphing x + 2y=6 3x + 6y=18 Select the correct answer below: a) Infinite solutions in the form (x,-2-3) b)Infinite solutions in the form (x,-3) c)Infinite solutions in the form (x,- +3) d)Infinite solutions in the form (x, +3) e)One solution: (2, 2) f)No solution:

Cheryl wants to save for a car. She has $4050 in a savings account earning 2.2% compounded quarterly. If Cheryl has four years until she gets her driver's license, will she have enough to buy a used car that costs $4500? If not, how much more does she need?

You are running a business that manufactures sneakers. A women's size 9 sneaker is known to have a length of 10 inches. You are concerned that the sneakers being produced are too large. You randomly sample 24 sneakers and calculate a sample mean of 10.31 inches with a standard deviation of 0.87 inches. Using this data, you conduct a significance test with a significance level of α = 0.05 and calculate a t-value of 1.75. Make a strategic decision based on the result of this test. You should continue producing the sneakers using the current methods. You should redesign the shoe to be slightly larger and recalibrate them machines producing them. You should redesign the shoe to be slightly smaller and recalibrate the machines producing them. You should continue producing the sneakers but relabel them to be a different size.

A company discovers that to produce x = 660 new electronic parts, it will cost y = $51,080. To produce 850 new electronic parts, it will cost $63,050. Compute the slope of the costs and choose the most accurate statement from the following: Costs are decreasing at a rate of $63 per item. Costs are increasing at a rate of $64 per item. Costs are decreasing at a rate of $57 per item. Costs are increasing at a rate of $57 per item. Costs are increasing at a rate of $63 per item. Costs are decreasing at a rate of $64 per item.

Sarah invested $3,800 in an account paying an interest rate of 3.6% compounded daily. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 15 years?

How long would it take, in days, to spend $200,000 if a person spent $1 a second until the $200,000 is used up? Complete parts (a) and (b) below. a) Estimate the time it would take, in days. Choose the correct estimate below. A. 200 B. 4 C. 20 D. 2 b) Calculate the actual time it would take, in days. days (Type an integer or a decimal. Round to the nearest tenth as needed.)

Eve is 20 years old and wants to save $2 million for retirement at age 60. Assume she invests in a savings account that earns 5.1% interest compounded semiannually. How much does Eve need to invest to get started? a) $273,477.34 b)$266,794.47 c) $66,794.26 d) $173,277.43

Suppose you are depositing an amount today in an account that earns 5% interest, compounded quarterly. If your goal is to have $5000 in the account at the end of six years, how much must you deposit in the account today? Round to the nearest dollar. $3711 $1289 $703 $985

Jackie and Billy are saving for their first child. They know he/she will be expensive and would like an extra $5000 in the bank when the baby comes. Jacke and Billy are not planning to have a baby for at least 3 years. They found a savings account that will earn 5.2% interest compounded quarterly. How much money should they invest to be financially prepared for their first child? Round to the nearest dollar