Basic Math Questions and Answers

A chemist has three different acid solutions. The first acid solution contains 25 % acid, the second contains 40% and the third contains 60 %. They want to use all three solutions to obtain a mixture of 96 liters containing 50 % acid, using 3 times as much of the 60 % solution as the 40 % solution. How many liters of each solution should be used?

In an online poll, 197 people voted for Coach as the best job at the Super Bowl. The job of Announcer received 205 more votes than the Coach. Write and solve an equation to find how many votes the job of Announcer received.

Miss Crawford wants to buy a new car. She is considering elther a hybrid or an electric car. She can choose a standard or a luxury model. There are red, silver, black, and white colors available to choose from. How many possible cholces does Miss Crawford have If she chooses one Item from each group? 4 8 16 24

Samantha has some dimes and quarters. She has 7 more dimes than quarters and the collection of coins is worth $10.15. How many dimes and quarters does Samantha have? Write an equation(s) to represent the situation and then solve. Be sure to define your variable(s) and clearly answer the question.

Put the equation y = x² + 4x - 5 into the form y = (x + h)² + k

Two square pyramids are similar. If the heights of the pyramids are 9 inches and 12 inches, and the volume of the smaller pyramid is 162 in³, what is the volume of the larger pyramid (in cubic inches)?

A car bought for $13000 depreciates at 12% annually. What is its value after 9 years? Do not include the dollar sign in your answer. Round your answer to the nearest cent.

Two square pyramids are similar. If the heights of the pyramids are 9 inches and 12 inches, and the volume of the smaller pyramid is 162 in', what is the volume of the larger pyramid (in cubic inches)?

Leos total bill at the blue lobster came to $45.90. he wanted to leave a 20% tip. How much money would he need to pay in total?

A certain company's main source of income is a mobile app. The company's annual profit (in millions of dollars) as a function of the app's price (in dollars) is modeled by P(x) = -2(x-3)(x - 11) What would be the company's profit if the app price is 0 dollars?

Seema deposited $800 in a saving account earning 2.05% compounded annually. To the nearest cent, how much will she have in 17 years? Do not include the dollar sign in your answer.

The population of Bloom Falls, Mass. (population 937) is slowly moving to a bigger city. Every year the population drops by 4.5%. What is the population after 3 years? 894 people 1,069 people 854 people 816 people

An electrician charges an hourly rate of $50, but also charges a fixed fee for making house calls regardless of time spend on the job. One day, the electrician earned a total of $250 for a 2 hour job. Write an equation for C, in terms of t, representing the total cost of the electrician's services if the electrician spends t hours at the house working.

Simon has 160 meters of fencing to build a rectangular garden. The garden's area (in square meters) as a function of the garden's width 2 (in meters) is modeled by A(z) = -x(x - 80) What width will produce the maximum garden area?

Find an expression which represents the difference when (10x-8y) is subtracted from (-4x-9y) in simplest terms.

Ian is going to the amusement park, where he has to pay a set price of admission and another price for tickets to go on each of the rides. The total amount of money lan will spend is given by the equation y = 20+ 1.5a, where y represents the total amount of money, in dollars and cents, and a represents the number of rides Ian goes on. What is the meaning of the y-value when z = 1? The total amount of money lan will spend if he goes on 100 rides. The change in the total amount of money for every one additional ride he goes on. The total amount of money Ian will spend if he goes on o rides. The total amount of money Ian will spend if he goes on 1 ride.

Tanya has a garden with a trench around it. The garden is a rectangle with length 2 1/2m and width 2 m. The trench and garden together make a rectangle with length 3 1/2m and width 3 m. Find the area of just the trench. m²

Suppose Solid X and Solid Y are similar. The volume of Solid X is 5145 cm³, and the volume of Solid Y is 10,935 cm³. If Solid X has a height of 28 cm, what is the height of Solid Y in centimeters?

One pipe can fill a swimming pool 2.8 times faster than a second pipe. If both pipes are open, the pool can be filled in 3 hours. Choose the equation that can be used to determine how many hours, x, it would take to fill the pool if only the slower pipe is used to fill the pool.

Use the even-odd properties of the trigonometric functions to find the exact value of the given expression. Do not use a calculator. cos (-60°) Select the correct choice below and fill in any answer boxes in your choice. A. cos (-60°)= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The answer is undefined.

If two triangles have the same area, what additional information is needed to show that they are congruent? One triangle's altitude is congruent to the other triangle's altitude. The triangles are both isosceles. One triangle has two angles that are congruent to two angles of the other triangle. The triangles each have a right angle.

Starting at noon, Kennedy observed the amount of snow on her lawn during a blizzard. She wrote an equation to represent 8, how many inches of snow were o lawn: 8= 0.012x +4.5, where x represents the number of minutes past noon. What could the number 4.5 represent in the equation? The amount of snow on the lawn when the blizzard ended. How much more snow is added to the lawn every minute. The amount of snow on the lawn at noon. The amount of snow on the lawn at 12:01 p.m.

Sebastian signed up for a streaming music service where there's a fixed cost for monthly membership and a cost per song downloaded. His total cost per month is given by the equation c = 1.25x + 4.99, where a represents the number of songs he downloads and c represents the total cost, in dollars and cents. What is the meaning of the c-value when x = 1? The cost to use the service for one month if zero songs are downloaded. The total cost per month assuming one song is downloaded. The cost to download 100 songs. How much the streaming service charges per downloaded song.

49. Validate the biconditional statement. A game can be classified as a card game if and only if it is played with a deck of cards. The biconditional statement is false because the conditional statement and the converse are false. The biconditional statement is false because the conditional statement is false. The biconditional statement is false because the converse is false. The biconditional statement is true because the conditional statement and the converse are true.

Joseph is in the business of manufacturing phones. He must pay a daily fixed cost of $1000 to rent the building and equipment, and also pays a cost of $50 per phone produced for materials and labor. Make a table of values and then write an equation for C, in terms of p, representing total cost, in dollars, of producing p phones in a given day.

A Ferris wheel has a radius of 80 feet. Two particular cars are located such that the central angle between them is 165º. To the nearest tenth, what is the length of the intercepted arc between those two cars on the Ferris wheel?

The quadratic y = (x - 3)(x + 5) is horizontally translated left by 4 units. Which of the following gives the equation of the transformed quadratic? (A) y = (x-7)(x + 1) (B) y = (x + 1)(x + 9) (C) y = (x + 1)(x + 9) - 4 (D) y = x² + 2x - 11

The population of Dublin, Ohio, in 2013 was 43,607 people. The area of the City of Dublin in 2013 was 24.79 square miles. Find the population density of Dublin in 2013 rounded to the nearest person.

Residents of Valentine, a small city in Nebraska, meet for a city council meeting once a week. Meetings are supposed to last no more than 3 hours. However, many residents are complaining that the average meeting is significantly longer than 3 hours (180 minutes). In order to test this, the lengths of the last 15 meetings were recorded in minutes: 147.0, 155.4, 159.6, 162.6, 163.8, 165.0, 167.4, 169.2, 172.2, 172.8, 172.8, 175.8, 175.8, 196.8, 201.6. Using this data, test the null hypothesis at the alpha=0.1 level that the mean length of city council meetings is equal to 3 hours versus the alternative that the average meeting length is greater than 3 hours. Assume that the distribution of meeting lengths is normal. What is the p-value and conclusion of this test? p-value = 0.046; Fail to reject the null hypothesis p-value=0.046; Reject the null hypothesis p-value = 0.990; Fail to reject the null hypothesis p-value = 0.990; Reject the null hypothesis

The number of astronomy papers published increases by 5% every year. If 27,000 astronomy papers were published in a particular year, how many will be published 2 years later?

On a spelling test. Michelle spelled 17 words correctly. There were 20 words on the test. What percent of the words did she spell correctly.

At the gym, Diana always spends more minutes running than lifting weights. Part A Which equations describe the relationship between the number of minutes Diana runs, r, and the number of minutes she lifts weights, w. Select all that apply. 12+w=T r=w-12 w= 12 + r r-12= w r+w=12 Part B If Diana spends 25 minutes running at the gym, how many minutes does she spend lifting weights?

A basketball player has a free throw percentage of 0.75. In the first half of a game, he made 12 attempts. How can a spinner be created to simulate data collection for this experiment? Create a spinner with two halves where one side represents made shots and one side represents missed shots. Create a spinner with four quarters where two sections represent made shots and two sections represent missed shots. Create a spinner with four quarters where three sections represent made shots and one section represents missed shots. Create a spinner with twelve sections where each section represents a shot.

Caleb was given a gift card for a coffee shop. Each morning, Caleb uses the card to buy one cup of coffee. The original amount of money on the gift card was $45 and after buying 8 cups of coffee, the card had a $25 remaining balance. Write an equation for A, in terms of x, representing the amount money remaining on the card after buying x cups of coffee.

What can the unit fraction 1 meter/3 feet be used for? To convert 25 inches to meters. To convert 15 meters to inches. To convert 5 meters to centimeters. This cannot be used to convert anything.

Owen's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y = 67 + 6x, where y represents the expected quiz score and a represents hours spent on homework that week. What is the meaning of the x-value when y = 99? A student's expected quiz score if they spent 1 hour on their homework. A student's expected quiz score if they spent 99 hours on their homework. The change in expected quiz score for every additional one hour students spend on their homework. The number of hours a student should spend on their homework to expect a score of 99 on the quiz.

16. If one student can complete the decoration for the prom in five days working alone, another student can do it in three days, and a third can do it in four days, how long will it take them working together?

The path of a marble rolling off of a desk can be modeled by the parametric equations: x(t)=2.5t y(t)=-16t^2+3 In these equations, the horizontal and vertical positions of the marble x(t) and y(t) are in feet and t is measured in seconds. Use Desmos and scratch paper to complete the following prompts. A. The marble will hit the ground after how many seconds? =0.433 seconds. B. Using your answer to (A), how far (horizontally) from the edge of the table will the marble first hit the ground? C. The parametric equations above can be expressed as the following single rectangular equation:

Write the negation of the conditional statement. If she can't take out the trash, then I will. If she can take out the trash, then I can't. She can't take out the trash, and I won't. If she can't take out the trash, then I won't. She can take out the trash and I will.

The population of Columbus, Ohio, in 2013 was 822,553 people. The area of the City of Columbus in 2013 was 223.1 square miles. Find the population density of Columbus in 2013 rounded to the nearest person.

For the example below, prorate the given expenses to find the monthly cost. Sara pays $5300 for tuition and fees for each of the two semesters, plus an additional $320 for textbooks each semester. The prorated monthly cost for tuition and fees and textbooks is $ (Round to the nearest dollar as needed.)

Suppose it takes a force of 42 N to hold a spring that has been stretched from its natural length of 15 cm to a length of 18 cm. How much work (in J) is done in stretching the spring from 20 cm to 25 cm?

Emma is driving on a long road trip. She wrote an equation to represent how many gallons of gas she has left in her tank, g = 14.5-0.45h, where g represents the number of gallons and h represents time in hours. What could the number 0.45 represent in the equation? How quickly the car uses gas, in gallons per hour. The number of gallons in the tank after one hour. How long it takes Emma to run out of gas. The number of gallons of gas initially in the tank.

The value of a painting can be predicted by the expression 120(1.08)t, where t is the . number of years since 2014. What does the value 120 represent? A. the predicted value of the painting in 2014 B. the predicted change in the value of the painting each year C. the predicted percent change in the wue of the painting each year D. the number of years for which the value of the painting is predicted to continue changing

A park ranger measures the change in height of all trees of a similar species and age over a month. Half the trees are within a quarter of a mile from a large lake and half are further away. Observation Experiment

A company manufactures electronic pedometers. One out of 60 pedometers Is faulty, but the company cannot pinpoint the faulty ones until a consumer complains. Say that the company makes a profit of $10 on the sale of every pedometer but takes a loss of $100 for every faulty one, as they have to replace the unit. What is the expected average profit on the sale of a single pedometer in the long run? $7.80 -$1.20 -$7.80 $2.56

When the function f(x) is divided by 32 - 5, the quotient is 2x² + 7x + 3 and the remainder is -3. Find the function f(x) and write the result in standard form.

ATM passwords at a local bank consists of four digits. Paula remembers the first two digits of her password, but forgot the last two. What is the probably that Paula correctly guesses her password on the first try? 1/10000 1/100 1/10 1/1000

Julia just lit a new candle and then let it burn all the way down to nothing. The candle burned at a rate of 0.75 inches per hour and its initial length was 9 inches. Write an equation for L, in terms of t, representing the length of the candle remaining unburned, in inches, t hours after the candle was lit.

The number of users on a social networking site was 45 thousand in February when they officially went public and grew to 60 thousand by October. If the site is growing exponentially, and growth continues at the same rate, approximately how many users should they expect two years after they went public? 142 thousand 150 thousand 1420 thousand 107 thousand 90 thousand