Basic Math Questions and Answers

Ms. O'Malley's cousin lives 1,650 miles away. Ms. O'Malley won a gift card for 100 gallons of gas. If her car can travel 35 miles on each gallon, can she drive roundtrip to see her cousin on the free gas? Explain how you know.

In a class of 30 IB students, 20 study mathematics SL, 12 study physics and 8 study both of these subjects. Find the probability that a randomly selected student does not study both of these subjects.

Employees at an office were surveyed about what types of hot beverages they drank that day. It was found that 50% of them drank coffee and 25% drank tea. The survey showed that 10% of the employees drank both coffee and tea. For these employees, are the events "drank coffee" and "drank tea" mutually exclusive? Choose 1 answer: AYes B No Find the probability that a randomly selected person from this group drank coffee OR drank tea. P (coffee OR tea):=

Identify the property that justifies each step asked about in the answer area below. Line 1: (7x) (10y) Line 2: 7. (x 10) y Line 3: 7.(10 x) y Line 4: (7.10)(x - y) Line 5: 70xy Line 1 to Line 2: Line 2 to Line 3: Line 3 to Line 4:

What is the equation, in standard form, of a parabola that contains the following points? (-2,-16), (0, -4), (4, -28) a y = 2x² - 2x - 4 b y = 2x² - 2x + 4 c y = 4x² + 2x + 2 d y = -2x² + 2x - 4

Ron needs 17 gallons of gas to get to and from work every week. Last week gas cost $2.44 per gallon. This week it dropped to $2.32 per gallon. How much less money did Ron spend this week on gas for work?

Four employees of Papa Tony's Pizza are cleaning up at the end of a busy night. There is a list of 43 clean-up tasks that need to be completed. If each employee does the same number of tasks, how many tasks should each employee do? Solve. Explain how you interpreted the remainder.

A rock thrown vertically upward from the surface of the moon at a velocity of 20 m/sec reaches a height of s=20t-0.8t meters in t sec. a. Find the rock's velocity and acceleration at time t. b. How long does it take the rock to reach its highest point? c. How high does the rock go? d. How long does it take the rock to reach half its maximum height? e. How long is the rock aloft? a. Find the rock's velocity at time t. Find the rock's acceleration at time t. (Simplify your answer. Use integers or decimals for any numbers in the expression.) b. How long does it take the rock to reach its highest point? (Simplify your answer.)

The weekly pay that Crystal receives varies directly with the number of hours she works. If she works 37 hours she makes 463.61, How much money would she make if she works 29 hours?

A town's population of children increased from 376 to 421 during the past year. Which equation shows how to find the percent increase? A.p =(421-376)/376 B.p =(421-376)/421 C.p =376/(421-376) D.p =(376+421)/376

Solve for q in terms of r and s. r = -qs q=

What is the image of (1, -1) after a dilation by a scale factor of 4 centered at the origin?

A sinusoidal function has an amplitude of 3, a period of π, and a maximum > 3. Which of the following functions could represent this data? y = 3 sin 2x + 1 y = 4 sin(x - π) + 3 y = 3 sin 2x - 1 y = 4 sin 2(x - π) + 3 y = 3 sin 2(x - π) + 4

To transmit information on the internet, large files are broken into packets of smaller sizes. Each packet has 1,500 bytes of information. An equation relating packets to bytes of information is given by b= 1,500p where p represents the number of packets and b represents the number of bytes of information. Type the answers in the boxes below. 1. How many packets would be needed to transmit 30,000 bytes of information? 2. How much information could be transmitted in 30,000 packets? 3. Each byte contains 8 bits of information. Write an equation to represent the relationship between the number of packets, p and the number of bits, z.

Members of a lacrosse team raised $1814.75 to go to a tournament. They rented a bus for $1168.50 and budgeted $58.75 per player for meals. Which equation could be used to determine x, the number of players the team can bring to the tournament?

The test scores of 32 students are listed below. Find Q 3. 32 37 41 44 46 48 53 55 56 57 59 63 65 66 68 69 70 71 74 74 75 77 78 79 80 82 83 86 89 92 95 99 79.5 24 80 79

The measure of an angle is 1°. Find the measure of the complement. The complement is

There are 3 neighboring orchards, K, L, and M. Orchard K has 4 times as many fruit trees as Orchard L. Orchard M has 60 fewer fruit trees than Orchard K. If Orchards K and L together have 430 fruit trees, how many fruit trees does Orchard M have?

Graph the function by using transformations of the graph of y=1/x² Plot all necessary asymptotes. For vertical asymptotes, make sure there are at least two points on each side. g(x)=(1/(x+4)²)-2

Find the relative extrema, if any, of the function. Use the Second Derivative Test if applicable. (Enter your answers as a comma- separated list. If an answer does not exist, enter DNE.) f(t) = 2t + 1/t Relative maximum value(s): Relative minimum value(s):

Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. What is the number of ships Astrid can build, assuming she receives the maximum possible amount of wood?

Penelope needs to borrow $9000. She can borrow the money at 4.5% simple interest for 3 yr or she can borrow at 5% with interest compounded continuously for 3 yr. (a) How much total interest would Penelope pay at 4.5% simple interest? (b) How much total interest would Penelope pay at 5% interest compounded continuously? (c) Which option results in less total interest?

Ursula has a mortgage of $88,000 at 6 3/4% for 25 years. Find the total interest. $79,184.27 $86,924.00 $94,424.00 $109,514.42

Of 26 employees at a local supermarket, 15 work as cashiers and 11 stock shelves. If 4 employees are selected at random to work overtime, determine the probability that all 4 are cashiers.

A student has some $1 and $5 bills in his wallet. He has a total of 14 bills that are worth $50. How many of each type of bill does he have?

Use the formula S = P(1 + r)t to complete parts (a) and (b). a. Graph the function that gives the future value of $70,000 invested at 3%, compounded annually, for t years, 0≤ts 12. b. Find the future value of $70,000 invested for 10 years at 3% compounded annually.

Bear Valley already had 4 centimeters of snowcover when a snowstorm moved in. The storm is increasing the amount of snowcover by 2 centimeters per hour. Write an equation that shows the relationship between the number of hours it has been snowing, x, and the total snowcover in centimeters, y. y =

Find an equation of the line with the slope m = -7 that passes through the point (-2,-4). Write the equation in the form Ax+By = C. Choose the correct answer below. A. 7x+y=18 B. 18x+y=7 C. 18x+y= -7 D. 7x+y=-18

When Sarah left her house this morning, her cell phone was 80% charged and it then started to lose 8% charge for each hour thereafter. Write an equation for B, in terms of t, representing the charge remaining in Sarah's battery, as a percentage, t hours after Sarah left her house.

Arsenic is a compound that occurs naturally in very low concentrations. Arsenic blood concentrations in healthy individuals are normally distributed, with mean u 3.2 micrograms per deciliter (μg/dl) and standard deviation = 1.5 (μg/dl). Some areas are known to have naturally elevated concentrations of arsenic in the ground and water supplies. We take a random sample of adults residing in a high-arsenic area and ask whether the data provide good evidence that the mean blood arsenic concentration in this population is elevated compared with the 3.2 µg/dl mean of the population of healthy individuals. Define the parameter examined and select the appropriate null and alternative hypotheses. Ho: μ = 3.2 μg/dl; Ha: μ> 3.2 µg/dl None of the options are correct. Ho: μ = 3.2 µg/dl; Ha: μ< 3.2 μg/dl Ho: H=3.2 μg/dl; Ha: ## 3.2 μg/dl

Evaluate the expression when x= 1 and y=4. Hint: the 2x term changes to 2(1), a multiplication problem. 2x+y select one: 4 3 7 6

Let f(x)=2/(x-5) Pick the correct a and y values of the inverse function at x = 1 in the original function. A.y=-1 B.y = 1 C.X=-1/2 D.x = 1

The total cost of 2 bracelets and 3 necklaces is $15.50. The total cost of 4 bracelets and 1 necklace is $13.50. Let b represent the cost of each bracelet and n represent the cost of each necklace. This situation can be represented by the following system of equations. 2b+ 3n = 15.50 4b+ n = 13.50 What is the cost of one bracelet? $7.75 $2.50 $5.00 $3.50

Kayla's school is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 3 senior citizen tickets and 5 child tickets for a total of $70. The school took in $216 on the second day by selling 12 senior citizen tickets and 12 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

A survey of salaries of employees in a business shows that the mean is greater than the median. Which conclusion is valid? The data distribution is skewed right. The data distribution is symmetric. The data distribution is constant. The data distribution is skewed left.

Suppose that your bank pays 8% interest, compounded semiannually. Use Table 12-2 of your text to find how much should be deposited now to yield an annuity payment of $700 at the END of every six months, for 6 years. $3,669.50 $6,569.55 $6,832.34 $7,394.18

However many tennis rackets the gym teacher, Mr. Marquez, buys for his class, he must buy five more than three times as many tennis balls. Rackets cost $20 each and balls cost $1.50 each. How much does Mr. Marquez spend if he needs 17 tennis rackets 5+ 3x A) $340.00 B) $352.00 C) $421.50 D) $424.00

Ming and Carlos are selling cookie dough for a school fundraiser. Customers can buy packages of chocolate chip cookie dough and packages of gingerbread cookie dough. Ming sold 8 packages of chocolate chip cookie dough and 12 packages of gingerbread cookie dough for a total of $364. Carlos sold 1 package of chocolate chip cookie dough and 4 packages of gingerbread cookie dough for a total of $93. Find the cost each of one package of chocolate chip cookie dough and one package of gingerbread cookie dough.

The commuting times of ten employees (in minutes) are listed below. Find the mode score. 65 66 67 66 67 70 67 70 71 68 67 minutes 65 minutes 66 minutes 68 minutes

According to a New York Times/CBS poll, 54% agreed that Social Security taxes should be raised if necessary to keep the system afloat, and 42% agreed that it would be a good idea to invest part of their Social Security taxes on their own. What is the largest percentage of people who could have agreed with at least one of these statements? What is the smallest percentage of people who could have agreed with at least one of these statements?

Suppose that WHAT is a square where WH=2-20x and AT = 28 + 6x. What is the length of HA? 1 22 -1 18

If two indistinguishable dice are rolled, what is the probability of the event {(4, 4), (6, 4), (1,4)}? What is the corresponding event for a pair of distinguishable dice? {(4,4), (6, 4), (1,4)} {(4, 4), (6, 4), (1, 4), (4, 1), (4, 6)} {(4, 4), (6, 6), (1, 1), (4, 1), (4, 6)} .{(6, 4), (1, 4), (4, 1), (4, 6)} {(6, 4), (1,4)}

Form the converse of each of the following statements. State whether the converse is true or false. (a) If I live in New York, then I live in the United States. (b) If two angles are congruent, then the angles are equal in measure. (c) If two angles are vertical angles, then they are congruent. (d) If two angles are complementary, then the sum of their measures is 90. (e) If two angles are adjacent, then they have the same vertex. (f) If two lines are perpendicular to the same line, then they are parallel.

What is the image of (-1, -8) after a dilation by a scale factor of 4 centered at the origin?

Use an Euler diagram to determine whether the syllogism is valid or invalid. All swimmers float. Duchess does not float. Duchess is not a swimmer. Is this syllogism valid or invalid? Valid Invalid

Claudia invests $2400 in one account and $800 in an account paying 2 % higher interest. At the end of one year she had earned $80 in interest. At what rates did she invest? $2400 invested at $800 invested at

An organization rents a commercial kitchen for an event. The cost to rent the kitchen is $375. The cost will be divided equally among the people who attend. Each person who attends will also pay $20 for expenses. Write a function that represents f(x), the total cost in dollars, for each person who attends the event, based on x, the number of people who attend. Use the on-screen keyboard to enter the function in the box below. f(x) =

An automobile manufacturer is preparing a shipment of cars and trucks on a cargo ship that can carry 21,600 tons. The cars weigh 3.6 tons each and the trucks weigh 7.5 tons each. 1. Write an equation that represents the weight constraint of a shipment. Let c be the number of cars and t be the number of trucks. 2. For one shipment, trucks are loaded first and cars are loaded afterwards. (Even though trucks are bulkier than cars, a shipment can consist of all trucks as long as it is within the weight limit.) Find the number of cars that can be shipped if the cargo already has: a. 480 trucks b. 1,500 trucks c. 2,736 trucks d.t trucks

Eric is planning to build a raised garden. He sketches a plan with a scale of 1.5 inches = 4 feet. If the garden has a width of 4 inches on the drawing, what will be the actual width of the garden?

Classify the variable as qualitative or quantitative. the weights of cases loaded onto an airport conveyor belt qualitative quantitative