Basic Math Questions and Answers

Consider the following implication: "If you drink coffee then you won't be able to sleep." Which of the following is the contrapositive of this statement? If you can't sleep then you drank coffee. If you can sleep then you didn't drink coffee. If you don't drink coffee then you will be able to sleep. Which of the following is the inverse of this statement? If you can sleep then you didn't drink coffee. If you don't drink coffee then you will be able to sleep. If you can't sleep then you drank coffee. Which of the following is the converse of this statement? If you can sleep then you didn't drink coffee. If you don't drink coffee then you will be able to sleep. If you can't sleep then you drank coffee.

The given point is on the curve. Find the lines that are (a) tangent and (b) normal to the curve at the given point. 9x² + 4xy + 6y² + 11y-9=0,(-1,0) (a) Give the equation of the line that is tangent to the curve at the given point. y = 18/7x + 18/7 (b) Give the equation of the line that is normal to the curve at the given point.

You are going to the mall with your friends and you have $200 to spend from your recent birthday money. You discover a store that has all jeans for $25 and all dresses for $50. You really, really want to take home 6 items of clothing because you "need" that many new things. How many jeans and dresses can you buy? Define your variables and show all your work below.

You are at Pie 5 ordering a one toppling pizza. You have 5 options for the crust, 4 choices for the sauce, 5 options for cheese, and 10 options for the topping. How many different pizzas can you make?

At a certain zoo, the average mass of one blue whale is measured to be,190000 kilograms. Use scientific notation to express the mass of 60 blue whales.

Which of the following is typically the least important factor to consider when conducting a statistical analysis of data? Context of the data Formula calculation Source of the data Sampling method

1) Find dy/dx for 2y² - 144 = 22² 2) Sales, x, of Michael Myers masks and their price, p, are related by p = 20. x² 4500 - 5p². If the price is decreasing at a rate of $1 per day, find the rate at which sales will change per day if

A given line has the equation 10x+2y=-2. What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y=-5x+12. 5x+y=12 y-12=5(x-0) 5x+y=-1

Find the difference. - 67x² +68x + 25) - (31x² + 49) =

At a certain zoo, the average mass of one elephant is measured to be 3800 kilograms. Use scientific notation to express the mass of 160 elephants.

You give a test to 100 students and determine the median score. After grading the test, you realize that the 10 students with the highest scores did exceptionally well. You decide to award these 10 students a bonus of 5 more points. The median of the new score distribution will be that of the original score distribution. A. lower than B. equal to C. higher than D. depending on skewness, higher or lower than

Find the sum. (36x5 + 21x³ - 15) + (7x5 + 15x³ + 25) =

You look at an ant under a magnifying glass. Find the actual length of the ant. The image of the ant is 5 times the ant's actual size and has a length of 2.5 cm. The ant's actual length is (Type an integer or a decimal)

The sum of 36 times a number and the reciprocal of the number is positive. Find the numbers which satisfy this condition.

An engineer measured the dimensions for a rectangular site by using a wooden pole of unknown length x. The length of the rectangular site is 2 pole measures increased by 3 feet, while the width is 1 pole measure decreased by 4 feet. If the perimeter of the site is 70 ft., what are the real dimensions of the site?

Find the vertex and axis of symmetry of the quadratic function. (b) Determine whether the graph is concave up or concave down. (c) Graph the quadratic function. g(x) = -2(x - 2)² +1 (a) The vertex is (2,1). (Type an ordered pair.) The axis of symmetry is (Type an equation.)

Find the amplitude, the period, any vertical translation, and any phase shift of the graph of the following function. y=8-sin 6x + ( 6x + π/4) What is the amplitude of the function? (Type an integer or a simplified fraction.) *****

Last year 762 students voted in the student council election at San Bruno Middle School. This year 721 students voted. What was the percent of change in the number of students that voted to the nearest tenth?

For the equation x/3 = 15, a student found the value of x to be 5. Complete the explanation of the error. What is the correct answer?

A party rental company has chairs and tables for rent. The total cost to rent 12 chairs and 2 tables is $43. The total cost to rent 3 chairs and 5 tables is $40. What is the cost to rent each chair and each table?

Consider the following functions. f(x)= x³ + 2 and g(x) = x - 3 Step 1 of 2: Find the formula for (f + g)(x) and simplify your answer. Then find the domain for (f + g)(x). Round your answer to two decimal places, if necessary.

George was absent for the last accounting test, For those who took the test, the mean was 75.8, the median was 74, and the mode was 81. When George took the test later, his score was different from all the other students' scores, and the class mean went up to exactly 76.6. What effect, if any, did George's score have on the class mode? A. None, the mode stayed the same. B. It decreased the mode exactly 0.8 points. C. It increased the mode exactly 0.8 points. D. It increased the mode more than 0.8 points. E. The effect of George's score on the mode cannot be determined from the given informa- tion.

Yusuf broke a cell sample into 8 batches, each weighing 4.2 x 10-⁹ grams. How much did the original sample weigh? Use scientific notation to express your answer.

Stock in Company A sells for $87 a share and has a 3-year average annual return of $23 a share. The beta value is 1.06. Stock in Company B sells for $81 a share and has a 3-year average annual return of $19 a share. The beta value is 1.18. Derek wants to spend no more than $14,000 investing in these two stocks, but he wants to earn at least $2100 in annual revenue. Derek also wants to minimize the risk. Determine the number of shares of each stock that Derek should buy.

Suppose you are the president of a student government. You wish to conduct a survey to determine the student body's opinion regarding student services. The university provides you with a list of the names and phone numbers of the 19,935 students. Discuss the procedure you would follow to obtain a simple random sample of 25 students.

You are offered two different sales jobs. The first company offers a straight commission of 3% of the sales. The second company offers a salary of $ 450 per week plus 2% of the sales. How much would you have to sell in a week in order for the straight commission offer to be at least as good?

Express each phrase as a rate and unit rate. (Round your answer to the nearest hundredth.) 1) 9 pencils for 11 dollars 2) 110 miles on 9 gallons of gas 3) 4 calculators cost $160.00 4) 8 dollars for 4 cans of tuna 5) 19 dollars for 6 books

Wendy is a waitress and has $15,000 to invest, and wishes to gain $4,200 in interest over the next eight years. Approximately what is the minimum simple interest rate Wendy needs to reach her goal?

The zeros of a fifth-degree polynomial function, Q, include -5(multiplicity 3) and 3+i. In addition, Q(0)=2500. Write the function in standard form. 2x5 +22x4 - 20x³ +300x² + 2500 2x5+21x4+ 25x3 + 75x² + 1250 2x5 + 9x4 - 5x3 - 175x² + 1250 2x5 + 18x4 - 10x3 - 350x² + 2500

Mary's car will go 319 miles on 14.5 gallons of gasoline in highway driving. a) How many gallons will it take to drive 2049 miles from her house to a friend's house? b) How far can the car be driven on 133 gallons of gasoline? a) How many gallons are needed to drive 2049 miles? gallons (Round up to the nearest integer as needed.) b) How far can Mary drive on 133 gallons of gasoline? miles (Round down to the nearest integer as needed.)

Find an angle that is coterminal with an angle measuring -285°, where 0° ≤ 0 < 360°. Do not include the degree symbol in your answer. For example, if your answer is 20°, you would enter 20. Provide your answer below:

Bill Baxter has $24,000 to invest for a year. He can lend it to his sister who has agreed to pay 10% simple interest for the year. Or, he can invest it with a bank at 8% compounded quarterly for the year. How much additional interest would the simple interest loan to his sister generate? Find the effective interest rate for both investments.

Determine whether the object is a permutation or a combination. a 10-digit telephone number (including area code) Choose the correct answer below. A. This is a permutation because repetition is not allowed and the order of the items matters. B. This is a combination because repetition is not allowed and the order of the items does not matter. C. This is neither a permutation nor a combination because repetition is allowed. D. There is not enough information given to make a decision.

A construction worker needs to pour a rectangular slab 23 ft long, 28 ft wide, and 9 in. thick. How many cubic yards of concrete does the worker need? (Assume that the construction worker cannot buy a fraction of a cubic yard of concrete.) The worker needs cubic yards of concrete. (Type a whole number, rounded up to the nearest full cubic yard of concrete.) .....

a) Make a truth table for statement: (p^q) → (pVg). b) Make a truth table for statement: (pv q) → (p^q). c) Which of these statements is a tautology? Explain. d) Could you have answered part c without using a truth table? Explain.

Ellie bought snacks for her team's practice. She bought a bag of popcorn for $3.47 and a 10-pack of juice bottles. The total cost before tax was $23.47. Write and solve an equation which can be used to determine j, how much each bottle of juice costs.

Divide the following. Give your answer in the form quotient+ remainder/divisor 20x3-10x2 -18x -4/4x + 2

It takes Terrell 69 minutes to weed his garden if he does it every 2 weeks, while his wife can get it done in 49 minutes. How long would it take them working together? Round to the nearest tenth of a minute. Select one: a. 34.5 minutes b. 29.5 minutes c. 24.5 minutes d. 28.7 minutes

What is the perpendicular bisector of a triangle? the segment from one vertex perpendicular to the opposite side the perpendicular segment that bisects one side of a triangle the side with the middle length measure a segment from one vertex to the midpoint of the opposite side

In the lab, Jane has two solutions that contain alcohol and is mixing them with each other. Solution A is 20% alcohol and Solution B is 6% alcohol. She uses 800 milliliters of Solution A. How many milliliters of Solution B does she use, if the resulting mixture a 14% alcohol solution?

1. For the first 7 days of January, the daily low temperatures for Burlington were 20°, 14°, 9º, 8°, -8°, -11°, and -4° Fahrenheit. What was the average daily low temperature, in degrees Fahrenheit, for those 7 days?

Find the domain and range of the function y = f(x) = x² – 6. Domain: Range:

A teacher gives a 15 item science test. For each item, a student receives one point for a correct answer; 0 points for no answer, and loses one point for an incorrect answer. Total test scores could range from +15 points to -15 points. The teacher computes the standard deviation of the test scores for the class to be -2.30. What do we know? A. The standard deviation was calculated incorrectly. B. Most students received negative scores. C. Most students scored below the mean. D. None of the above.

Miguel bikes 23 km per hour and starts at mile 10. Gabby bikes 28 km per hour and starts at mile 0. Which system of linear equations represents this situation? A. Gabby: d=23t+10 Miguel: d = 28t B. Miguel: d = 10t+23 Gabby: 28d = t C. Miguel: d= 23t+10 Gabby: d = 28t D. Miguel: d= 10t +23 Gabby: d = 28t

Solve the equation using the quadratic formula. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.) 18x - 6 = 9x² (a) Give real answers exactly.

Solve for v. |3v-6|=9 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

Grace is an hourly employee, and the line that models her total pay in dollars as it relates to the number of hours she has worked has a slope of 45 and a y intercept of 35. Which statement is true?

Order: Sandostatin (octreotide acetate) 40 mcg subcut. Q.6h. Read the label in the figure. If the recommended dose is 100-600 mcg/d in 2-4 divided doses titrate to response, is the prescribed dose safe? If the prescribed dose is safe, how many milliliters will you administer? Select one: a. Yes; 0.8 mL b. No, the dosage is not safe. c. Yes; 1.2 mL d. Yes; 0.5 ml

(a) Suppose an analog clock strikes 6:00. How many degrees separate the hour hand from the minute hand, measuring clockwise from the hour hand to the minute hand? (Drawing a picture might help.) (b) How many radians separate the hour hand from the minute hand, measuring clockwise from the hour hand to the minute hand? (c) How many degrees will separate the hour hand from the minute hand when the clock strikes 4:30, measuring clockwise from the hour hand to the minute hand? (Remember that the hour hand moves gradually from 4 to 5 as the minutes go by after 4:00.) The number of degrees that separates the hour hand from the minute hand when the clock strikes 4:301s

Suppose two researchers wanted to determine if aspirin reduces the chance of a heart attack.Researcher 1 studied the medical records of 500 randomly selected patients. For each patient, he recorded whether the person took aspirin every day and if the person had ever had a heart attack. Then he reported the percentage of heart attacks for the patients who took aspirin every day and for those who did not take aspirin every day. What type of study did Researcher 1 conduct? A. Observational B. Experimental C. Survey D. None of the above