Basic Math Questions and Answers

ΔABC is dilated by a scale factor of 0.5 with the origin as the center of dilation, resulting in the image AA'B'C. If A=(2, 2), B=(4, 3), and C= (6, 3), what is the length of B'C' ? 3 units 4 units 2 units 1 unit

In the first week of the basketball season, P.J. made 20 of his first 30 free throw attempts. Which equation models P.J.'s free throw percentage, p, if he makes his next x attempts? O A. OB. O C. O D. p = p = p = P = I 20 + 30 I + 20 I + 30 I + 20 30 201 301

Susan's math teacher assigned x homework problems on Monday. On Tuesday, she assigned 13 more problems. Over the two days, a total of 23 homework problems were assigned. Which equation could be used to find x, the number of problems assigned on Monday? A. x-13 =23 B.13x = 23 C.23 + x = 13 D.x+13=23

Select the standard form of the equation x² - 10x + y² - 6y +9=0 O (x+5)² + (y + 3)² = 21.5 (x - 5)² + (y - 3)² = 43 (x + 5)² + (y + 3)² = 43 (x - 5)² + (y - 3)² = 21.5 O

Draw an appropriate tree diagram, and use the multiplication principle to calculate the probabilities of all the outcomes. HINT [See Example 3.] Each day, there is a 40% chance that you will sell an automobile. You know that 10% of all the automobiles you sell are two-door models and the rest are four-door models. P(Sell 2-door) P(Sell 4-door) = P(No sale) =

You measure 40 textbooks' weights, and find they have a mean weight of 75 ounces. Assume the population standard deviation is 5.9 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.

A soccer team wants new uniforms. A jersey costs $42, shorts cost $26, socks cost $6, and shinguards cost $18. How much does one uniform cost? O $62 O $74 O $83 $92

You need a 60% alcohol solution. On hand, you have a 105 mL of a 40% alcohol mixture. You also have 95% alcohol mixture. How much of the 95% mixture will you need to add to obtain the desired solution?

Can the value 6 be a probability? yes no

Estimate the product. Round each number to its greatest place value, then multiply. 7.5 x 203

A student plans to take 5 courses next term. If he selects them randomly from a list of 16 courses, 8 of which are science coum Courses selected will be science courses? The probability that all 5 courses selected will be science courses is ype an integer or decimal rounded to three decimal places as needed.)

Points Q, R, S, and T are plotted on the number line. RS T 1 -2 -1 -1 -1 0 1 1/2/2 a. Which two plotted points have a sum of zero? b. Explain how the number line can be used to show that the sum of the two points you identified is zero. c. Explain how the number line can be used to determine the sum of the location of point T and -1-1/

COOKIES A cookie jar contains three types of cookies: oatmeal, chocolate chip, and sugar. Sixty percent are chocolate chip. Half of the remaining cookies are oatmeal. If there are 9 oatmeal cookies, how many cookies are in the jar? Use the draw a diagram strategy.

A statistical analysis is completed on a set of data and Pearson's and Spearman's coefficients are found as shown below: Pearson's: 0.549 Spearman's: 0.989 Which coefficient would be more appropriate to apply in this analysis?

Boxplot of Male Age (Actor), Female Age (Actress) Male Age (Actor) Female Age (Actress) 20 30 40 Ves 50 Data 60 +510 (Mac) 70 Identify three major differences between the ages of the best actor and best actress Oscar winners using the boxplot above. Look for difference in their center, shape, spread (IQR and range), and outliers. (Note: Since you are interpreting a histogram, there is some flexibility for correct responses.) 80

Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $118. Two adults and three children must pay $84. Find the price of the adults ticket and the price of a child's ticket The price of a child's ticket is $ The price of an adult's ticket is $

Which of the following is an example of the identity property of 1? 11/12 (1) = 11/12 3.11 (0) = 0 0 + 8 4/5 = 8 4/5 -2 + 3 = 1

A manufacturer produces two models of mountain bikes. Model A requires 5 hours of assembly time and 2 hours of painting time, and Model B requires 4 hours of assembly time and 3 hours of painting time. The maximum total weekly hours available in the assembly department and the painting department are 200 hours and 108 hours, respectively. The profits per unit are $25 for Model A and $15 for Model B. How many of each type should be produced to maximize profit? bikes of Model A bikes of Model B What is the maximum profit? $

A scientist discovered a new type of bacteria that will grow at a rate of 3 cells every 2 seconds. If the scientist starts with one bacteria cell in a petri dish, what equation could predict the amount of cells in the dish after x seconds?

Solve the inequality. Graph the solution on the number line and then give the answer in interval notation. - 4x + 1 ≥ − 11 -3 0 1 m 0

In January 2008, the temperature in parts of Minnesota fell from 41°F to -13°F over a 24-hour period. What was the average temperature change per hour? - (1 1/6) F -2.25°F 2.25°F (1) 1/6 F

How many ways can a president, vice-president, secretary, and treasurer be chosen from a committee of 8 people? The number of ways to choose a president, vice-president, secretary, and treasurer is

Find the mean, median, mode(s), and range of the data. 9. 16, 22, 14, 12, 20, 19, 14, 11 a. mean: 16 median: 16 mode: 14 range: 11 b.mean: 16 median: 16 mode: 14 range: 5 c.mean: 16 median: 14 mode: 15 range: 11 d.mean: 16 median: 15 mode: 14 range: 11 A B C D

To pass a course with a C grade, a student must have an average of 70 or greater. A student's grades on three tests are 69, 71, and 65. Find what score the student must get on the next test to get a C average or better.

The county administrator's office is making plans to finance the next phase of infrastructure repair to the county's roads and bridges. To help with their planning, they have developed functions that model the anticipated tax money available and planned budget for repairs, for any given year, x years from today. The expected tax money, in millions, received from the state is represented by the function 7(x) = 14x³ + 43x² + 37x+ 190. The planned budget allocating money, in millions, for infrastructure repairs in that same year is represented by the function R(x) 35x +90. Which function represents the balance, in millions, that remains in a given year, after using a portion of the tax money to pay for infrastructure repairs? DA. B(x) = 14x³ + 8x² + 37x+100 OB. B(x) = 14x³ + 8x² +37x+ 280 OC. B(x) = 14x³ + 43x² + 2x + 100 OD. B(x) = 14x³ + 43x²+2x+280

Lina is making a spreadsheet for an assignment. The spreadsheet, when completed, will be 200 lines long, and Lina has already completed 63 lines. How many lines does Lina have left to complete? OA. 263 OB. 74 OC. 137 OD. 232 X+63 = 200

Which of the following selections most closely summarizes the mother's reaction to the mummy exhibit (paragraphs 17-18)? When Mom is down, we go to see the mummies at the Field Museum of Natural History. The Egyptian dead sleep in the basement, most of them still shrouded in their wrappings. "These were people like us," my mother whispers. She pulls me into her waist. "They had dreams and intrigues and problems with their teeth. They thought their one particular life was of the utmost significance. And now, just look at them." My mother never fails to brighten. "So what's the use of worrying too hard or too long? Might as well be cheerful." A. She is frequently sad but finds perspective in the mummy exhibit B. She is not typically sad, but museum exhibits like this cause her sadness. C. The exhibit makes her think about her various problems with her teeth. D. She wants to learn as much as she can about Egyptian art and history

A fruit punch is mixed in a ratio of 3 parts orange juice, 1 part pineapple juice, and 2 parts ginger ale. If the bowl hold 96 ounces, how many ounces of orange juice are required? 16 ounces 32 ounces 96 ounces 48 ounces

Two hikers are 13 miles apart and walking toward each other. They meet in 2 hours. Find the rate of each hiker if one hiker walks 1.7 mph faster than the other.

Match the expression on the left with its simplified form on the right. Answer options on the right may be used more than once. -|- 31 | - 31 - 131 |3| -(-3) Clear 3 Question ID: 558964 -3

If a single card is drawn from a standard 52-card deck, in how many ways can a card other than a face card be obtained? A card other than a face card can be obtained in ways.

The ratio of photo developing fluid to water is given as 2:5. If the container holds 49 ounces, how much photo developing solution is required? 35 ounces 49 ounces 14 ounces 7 ounces

Approximate the following number using a calculator. 9.1(1/5)^2.6

A bottle of rubber cement weighs 210 grams. One gross (12 dozen) of the bottles is being shipped to a store in 2 boxes that weigh 1.1 kg each when empty. What is the total weight in kilograms of the shipment?

Sherry needs to have at least $1600 in her bank account at the end this month. She works at a restaurant where she earns $18 an hour (h). This month she has to pay her car payment of $200. Write an inequality to represent how many hours she will need to work in order to have $1600 in her account. Inequality:

Solve the system of equations by the addition method. 3x-7y = 4 7x-2y = 4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Simplify your answer. Type an ordered pair.) OA. The solution is OB. There are infinitely many solutions; {(x,y)|3x-7y=4} or Oc. There is no solution; or Ø. or {(x,y)|7x-2y = 4}.

An apartment building currently has rented x apartments with two occupants and 17 apartments with one occupant. The apartment building has 85 total occupants. 2x+17 = 85 How many double-occupancy apartments are currently rented? A. 34 B. 68 C. 26 D. 51

Chris spent half of his money on a pair of headphones. Then he spent half of his remaining money on CDs. Finally, he spent his remaining $11.75 on a book. How much money did Chris have to begin with? Chris began with $

One pipe fills a storage pool in 20 hours. A second pipe fills the same pool in 10 hours. When a third pipe is added and all three are used to fill the pool, it takes only 5 hours. Find how long it takes the third pipe to do the job.

A person invests 9000 dollars in a bank. The bank pays 6.25% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 13600 dollars? A = P(1 + 7) n² nt

The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 30 feet and the height of the arch over the center of the roadway is 13 feet. Two trucks plan to use this road. They are both 12 feet wide. Truck 1 has an overall height of 12 feet and Truck 2 has an overall height of 11 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge. Both Truck 1 and Truck 2 can pass under the bridge. Truck 1 can pass under the bridge, but Truck 2 cannot. Truck 2 can pass under the bridge, but Truck 1 cannot. Neither Truck 1 nor Truck 2 can pass under the bridge.

People are waiting in line for a theater premiere. Every 5th person in line will receive a free theater ticket. Every 6th person will receive a gift card for $40. Which person is the first to receive both prizes? Explain.

(b) that a music download was neither tropical nor regional Next, calculate the relative frequency that a download was neither tropical nor regional. We are given that, of the 400 total downloads, 200 were regional, 110 were pop-rock, 80 were tropical, and 10 were urban. The categories of music that are not tropical and not regional are pop-rock and urban. So, the frequency of music downloads that are neither tropical nor regional is equal to the frequency of music downloads that are pop-rock or urban. The frequency of music downloads that are pop-rock or urban is 110 + 10 = 120 So the frequency of music downloads that are neither tropical nor regional is

Paul, a janitor, must move a large shipment of books from the first floor to the fifth floor. The sign on the elevator reads "maximum weight 900 pounds." If each box of books weighs 80 pounds, find the maximum number of boxes that Paul should place in the elevator if he does not ride.

The population of a certain species of oak tree in a national forest declines each year by one-fourth. So, after each year, only three-fourths of the trees present at the beginning of the year remain. Which of the following describes the rate of decline in the population of the species of oak tree? OA. neither linear nor nonlinear SOB. both linear and nonlinear OC. nonlinear O D. linear

Use the formula R = log t In May 2008, an earthquake measuring 6.8 on the Richter scale struck near the east coast of Honshu, Japan. In March 2011, a quake measuring 9.0 struck that same region. How many times more intense was the 2011 quake than the one in 2008? (Round your answer to one decimal place.) times

A large wind turbine can power 598 homes. A company had 4 turbines and then built 5 more. homes can How mar many the company power with its wind turbines?

2. (12 points) An open top box is to be constructed from rectangular pieces of cardboard. The base will be a square cut from sturdy and more expensive material, one that costs $4.00 per square foot. The four walls will be cut from more affordable material that costs $1.00 per square foot. What are the dimensions of the least expensive box one can design that will enclose 54 cubic feet of volume? How expensive will this box be to construct?

Truck #1 can haul 480 tons of steel in 24 trips. Truck #2 can haul the same amount of steel in 48 trips. How many trips would it take if both trucks are used? O 10 Trips 20 Trips 1 pt O 36 Trips O 16 Trips

A ball is thrown from a height of 164 feet with an initial downward velocity of 12 ft/s. The ball's height h (in feet) after seconds is given by the following. h=164-12t - 16t² How long after the ball is thrown does it hit the ground? Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)