Basic Math Questions and Answers

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

Mary's car will go 330 miles on 16.5 gallons of gasoline in highway driving. a) How many gallons will it take to drive 2183 miles from her house to a friend's house? b) How far can the car be driven on 149 gallons of gasoline?

On the planet Maximillian live Sprogs and Graks. Initially there were 2400 sprogs and 300 Graks. The population of Sprogs doubles every 6 years and that of Graks doubles every 3 years. a. How many Graks were there after 1/2 years? b. When are there as many Sprogs as Graks?

The dean of a college would like to determine the feelings of students concerning a new registration fee that would b used to upgrade the recreational facilities on campus. All registered students would pay the fee each term. Which of the following data collection plans would provide the best representation of students' opinions at the school? A. Survey every 10th student who enters the current recreational facilities between the hours of 1:00 and 5:00 pm until 100 students have been asked. B. Randomly sample fifty student ID numbers and send a survey to all students in the sample. C. Place an ad in the campus newspaper inviting students to complete an online survey. Collect the responses of the first 200 students who respond. D. All of the above would be equally effective.

An art teacher made a copy of a small painting. To make the painting easier to see, the teacher enlarged the area of the painting by 48%. Let c represent the area of the original painting. The expression below is one way to represent the area of the new painting. Find two equivalent expressions that would give the area of the new painting. c+0.48c Which expressions will give the area of the new painting? Select all that apply. A. c(1+0.48) B. 148c C. 0.48c D. c +48c E. 1.48c

Use the fact that the derivative of the function f(x) = 3/x is f'(x) = -3/x2 to find the equation of the tangent line to the graph of f(x) at the point x = -7. The equation of the tangent line to the graph of f(x) at the point x = -7 is

Use the discriminant to determine the type and number of solutions. -2x2 + 5x + 5 = 0 Select one: a. One rational solution b. Two imaginary solutions c. Two rational solutions d. Two irrational solutions

Carl is making a garden that is half as long as it is wide. He wants to cover 271 square feet with the garden. Which equation best represents the situation if x represents the length of the garden? x-2x = 271 x. 1/2x=271 x+1/2x = 271 x+ 2x = 271

In a class of 60 students, on average, 8 will be left-handed. If a class includes 20 "lefties", estimate how many students are in the class. The class has approximately students.

Diana has 1600 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area?

A light display has three colored lights, each of which flashes on for an instant at regular intervals. The yellow one flashes 15 times per minute, the blue one flashes 6 times per minute, and the red one flashes 12 times per minute. You see all three lights flash on simultaneously. How much longer must you wait before the three lights flash on simultaneously again? The correct answer is 20 seconds. Solve this problem and explain each step of your process so that a 5th grader will understand.

Select the correct answer from each drop-down menu. A cash card has a starting value of $25. If the card is not used within the first year of its purchase, the value on the card begins to decrease by $2.50 per month. The relationship between the number of months after the first year and the amount remaining on the card is T he Independent variable is the The dependent variable is the

An English instructor asserted that students' test grades are directly proportional to the amount of time spent studying. Lisa studies 9 hr for a particular test and gets a score of 75. At this rate, how many hours would she have had to study to get a score of 94? She would have had to study hr to get a score of 94. (Round to the nearest hundredth as needed.)

Dante runs each lap in 7 minutes. He will run at least 11 laps today. What are the possible numbers of minutes he will run today? Use t for the number of minutes he will run today. Write your answer as an inequality solved for t.

Leo's Lawn Mowing Service has $300 in start-up expenses, and charges $30 for each yard. Yan's Yards does not have any start-up expenses and charges $20 for each yard. After how many yards will the profits of the two businesses be the same?

The graph of y = 5x6 - 3x4 + 2x-9 has at most how many turning points? Choose the correct answer below. 5 -9