Basic Math Questions and Answers

The radioactive substance cesium-137 has a half-life of 30 years. The amount A (r) (in grams) of a sample of cesium-137 remaining after years is given by the following exponential function. A (t)=381 Find the initial amount in the sample and the amount remaining after 50 years. Round your answers to the nearest gram as necessary. Kimb 30

A laptop computer is purchased for $2350. After each year, the resale value decreases by 30%. What will the resale value be after 4 years? Use the calculator provided and round your answer to the nearest dollar.

4. Susan and Dan went to the roof of their 30-foot tall high school to throw their math books off the edge. The initial velocity of Susan's book was 42 feet per second while the initial velocity of Dan's book was 68 feet per second. A)Complete the equation h(t) = -16 + vt + s for both Susan and Dan where it can be used to represent the situation where h is the height of the textbook at time t seconds, v is the initial upward velocity, and s is the starting point. [1pt]

A casino hotel manager has approximated demand for two-room suites to be p = 9000 q² where p is the price (in dollars) and q is the quantity demanded. Use 18 implicit differentiation to find and interpret OA. dq dp Choose the correct answer below and fill in the answer box to complete your answer. OB. dq when q = 3. which means that if the price is increased by $1, the quantity demanded increases by approximately which means that if the price is increased by $1, the quantity demanded decreases by approximately dp suites. suites.

What is the simple interest rate on a $2450 investment paying $951.83 interest in 10.5 years? % (round to the nearest tenth of a percent)

1. For the given function: y = x²(x + 2)²(x + 1) A. What is the degree and leading coefficient? B. Determine the end behavior C. Find the y intercept if any D. Find the zeros of the polynomial E. Identify the multiplicity of these zeros F. Describe the behavior of the graph at these zeros

Compute the total cost per year of the following pair of expenses. Then complete the sentence: On an annual basis, the first set of expenses is second set of expenses. Suzanne's cell phone bill is $70 per month, and she spends $165 per year on student health insurance. On an annual basis, the money spent on her cell phone bill is% of the money spent on student health insurance. (Round to the nearest percent as needed.) % of the

If cos (0) = -1, what values could be ? Select all that apply.

Convert these numbers written in pseudo-scientific notation to scientific notation. a. 472 x 10-4 b. 61 x 10-4 c. 0.03 x 106 d. 0.0051 x 10-7

Use the formula for nºr to solve. A church has 10 bells in its bell tower. Before each church service 4 bells are rung in sequence. No bell is rung more than once. How many sequences are there? A) 151,200 B) 210 C) 5040 D) 302,400

A vector with magnitude 9 points in a direction 160 degrees counterclockwise from the positive x axis. Write the vector in component form. Give each value accurate to at least 1 decimal place

Julie is considering installing solar photovoltaic panels on the roof of her house. Her monthly electricity bills currently average $80. The cost of installing a photovoltaic system is $19,000; however, she expects a 35% reduction in this cost due to tax credits and local rebates. Assuming all of her electrical needs are met by the new system and neglecting possible revenue when the system puts electricity back into the grid, what is the approximate payback period for the photovoltaic system? The photovoltaic panels will pay for themselves in approximately months. (Round your answer to the nearest whole number as needed.) *****

The reference angle for an angle in standard position on the coordinate plane with measure 170°is: 80° 10° -10° 170°

Given the equations m(x)=x-2 and n(x)=x-4, find m(x) -n(x). When typing your answers, be sure to use the following format: • Indicate exponents with a "^" For example, write x² as "x^2." o Do not include spaces. o Write in descending order of exponents, from largest to smallest. Example: 9x² - 11x-7 would be typed in as 9x^2-11x-7 I

The expenses and income of an individual are given in table form to the right. Find the net monthly cash flow (it could be positive or negative). Assume salaries and wages are after taxes. When you need to convert between weeks and months, assume that 1 month = 4 weeks. The net monthly cash flow is $ Income Part-time job: $800/month College fund from grandparents: $500/month Scholarship: $3600/year Expenses Rent: $400/month Groceries: $50/week Tuition and fees: $3000 twice a year Incidentals: $90/week

Suppose that a box contains 8 cameras and that 5 of them are defective. A sample 2 cameras is selected at random. Define the random variable X as the number of defective cameras in the sample. Write the probability distribution for X.Write your answer in fraction form or round to 3 decimal places. What is the expected value of X?

Study this circle graph and answer the questions that follow. School Expenditures Lab fee 6% Materials fee 10% Books and lab manuals 16% Tuition 40% Tools 28% a. Which category represents the largest expenditure? b. Which category represents the smallest expenditure? c. If a student spent a total of $2500, how much of this went toward tools and lab fees combined? d. If a student spent $300 in material fees, how much would she spend on books and lab manuals? a. Which category represents the largest expenditure? Choose the correct answer below. O O O O O Materials fee Tuition Books and lab manuals Tools Lab fee b. Which category represents the smallest expenditure? Materials fee Lab fee Tuition Books and lab manuals Tools c. The student spent a total of $2500 so the combined amount that went towards tools and lab fees was. d. If a student spent $300 on materials, the amount spent on books and lab manuals was $

Investor Dan has $353,000 to invest in bonds. Bond A yields an average of 7% and the bond B yields 9.8%. Dan requires that at least 5 times as much money be invested in bond A as in bond B. You must invest in these bonds to maximize his return. How much should you invest in bond A? Round to the nearest cent.

Convert the area of 541 square meters to square feet. Include the acres-hectare conversion factor. Use the conversion factors from the table in Lesson 1.5. Show all needed conversion factors. Some spaces don't require numbers in which case enter 1. Some units will be blank in which case select the second item in the list, which is a blank space. Round final answer to 2 decimal places if needed. The setup below should look like the typical dimensional analysis that you learned. If it doesn't, resize the window on your computer, if possible.

What is the amplitude of the given function? What is the period of the given function? Which graph matches the given function? ? v Note: You can earn partial credit on this problem.

A tennis ball is dropped from the top of the building, which is 265 feet tall. The height of the ball, h, at time t seconds can be represented by the equation h(t) = -16 +265. After 3.5 seconds, did ball fall on the ground? Explain your answer mathematically.

A squirrel is 40 feet up in a tree and tosses a nut out of the tree with an initial velocity of 12 feet per second. The nuts height, h, at time t seconds can be represented by the equation h(t) = -16+ 12t+40. How long does it take for a squirrel to catch the nut on the ground?

Evaluate sin(-5π/6)

Simplify the radical. Give the exact answer in simplified radical form. √27

Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest terms. A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5,2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}. Find the probability of getting two numbers whose sum is greater than 9. A) 6 B) 1/6 C) 1/12 D)1/4

Suppose that $10,484 is invested at an interest rate of 5.6% per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time t, in years. b) What is the balance after 1 year? 2 years? 5 years? 10 years? c) What is the doubling time?

Find the monthly interest payment in the situation below. Vic bought a new plasma TV for $2400. He made a down payment of $500 and then financed the balance through the store. Unfortunately, he was unable to make the first monthly payment and now pays 4% interest per month on the balance (while he watches his TV). What is Vic's monthly interest payment? $ (Round to the nearest dollar as needed.)

Use the long division method to find the result when 16x4 + 4x³ 30x²+x+10 is divided by 4x2 + 2x - 5. If there is a remainder, express the result in the form q(x) +r(x)/b(x).

You are dealt one card from a 52 card deck. Then the card is replaced in the deck, the deck is shuffled, and you draw again. Find the probability of getting a picture card the first time and a club the second time. A)1/13 B) 3/52 C) 1/4 D) 3/13

Find the standard deviation. Round to one more place than the data. 20, 5, 13, 10, 10, 5, 7, 17, 19 A. 6.2 B. 1.5 C. 5.8 D. 5.5

Convert 5π/6 radians into degrees: Convert 2π/3 radians into degrees: Convert 7π/4 radians into degrees: Convert π radians into degrees:

(b) The distance between Moscow, Russia, and Istanbul, Turkey is 1097 miles. If lines were drawn from Moscow and Istanbul to the center of the earth, those lines would meet at an angle of 15.64°. Use this information to approximate the radius of the earth. Using this information, we can estimate that the radius of the earth is ______miles.

You must decide whether to buy a new car for $22,000 or lease the same car over a three-year period. Under the terms of the lease, you can make a down payment of $1000 and have monthly payments of $150. At the end of the three years, the leased car has a residual value (the amount you pay if you choose to buy the car at the end of the lease period) of $10,000. Assume you can sell the new car at the end of the three years at the same residual value. Is it less expensive to buy or to lease? The cost for buying the car and selling it after three years would be $

Identify each of the following as scientific or pseudo-scientific notation. 3.4 x 10^8 62.3 × 10^4 1.578 x 10^-3 0.45 x 10^-6 5.667 × 10³

Convert 40 in.³3 to cubic decimeters. Round your answer to the nearest thousandth, if necessary.

Fill in the blank. The of a data set is the difference between the largest and smallest data values in the set. The_____of a data set is the difference between the largest and smallest data values in the set.

A grocery store orders 4 large containers of milk for every 7 small containers of milk. Which ratio could represent the number of large containers of milk to small containers of milk in an order from the grocery store? F. 18:21 G 14:8 H 16:49 J None of these

Select all of the valid conditions for proving similarity. Angle-Angle Angle-Side-Angle Side-Side-Side Angle-Side-Side Side-Angle-Side

Suppose the typical texting response time is between 2 seconds and 6 seconds. That could be written as a compound inequality for time t as: 2 < t < 6 seconds. If a car is travelling at 35 mph what is the typical distance a car would travel during a typical texting response? Round values to the nearest whole foot. Express your answer as an inequality using < or >, using d as the variable to represent the distance traveled. feet

Agriculture: Farmers use Fertilizers imported from China and each bag of fertilizer (20 kg) is marked the direction how to use the fertilizer and the unit is given in terms of Kilograms per hectare(kg/ha). In United States it is customary for farmers to use the unit in terms of pounds per acre(lb./A) (1 Lb./ac = 0.892 kg/ha) a) How many bags of fertilizers are needed if the farmer had done cultivation in 20 acres land? Challenge: b) The direction in the bag say 240 grams of fertilizer can be mixed with 1 Liter of water for spraying. How will the U.S. farmer use this direction if he uses Lb. and gallons? (1 U.S. gal =3.79 LB, 100 grams = 0.22 LB)

A 5-ounce container of Greek yogurt contains 135 calories. Find the unit rate of calories per ounce. 27 ounces/ 1 calorie 135 calories / 5 ounces 27 calories /1 ounce 27:1

Convert a person's weight of 202 pounds to kilograms.

Particles A and B are moving along a plane. Their velocities are represented by vectors a and 6, respectively. Which option best describes the meaning of the following statement? ||ā||> ||b|| Choose 1 answer: Particle A is heavier than particle B. Particle A's speed is greater than particle B's speed. Particle A's movement creates a greater counterclockwise angle with the eastward direction than particle B's movement.

A migrating salmon heads in the direction N 45 E, swimming at 5 mi/h relative to the water. The prevailing ocean currents flow due east at 3 mi/h. Find the true velocity of the fish as a vector. Justify your work.

There are 3 more gallons of yellow paint than brown paint. If there are 6 gallons of yellow paint, how many gallons of brown paint are there? 9 gallons 3 gallons 6 gallons 2 gallons

A golf ball is struck across a flat fairway at an angle of 60° with an initial speed of 135ft/s. a.). Write a set of parametric equations for the motion of the golf ball. b.). Determine how long the golf ball was in the air. c.). Determine how far the golf ball traveled in the air.

Gas mileage is rated for either city driving or highway driving. Most of Jenna's travel will take place on the highway. For one trip, she drives 150 miles and the price of gas is $3.67/gallon. Her 4Runner gets 22 miles/gallon. If Jenna rents, she can request a small, fuel-efficient car such as the Hyundai Elantra, which gets 40 miles/gallon. What is the cost of the gas for each vehicle? (Round to the nearest cent) Try the problem on your own first. If you are having trouble after 2 tries, we will break it down. Cost of gas for the 4Runner: $ Cost of gas for the Elantra: $

The physician orders a medication to be administered q8h. The first dose is given at 6:00 a.m. What times will this medication be given throughout the day in military time? a. 0600h - 1300h - 2200h b. 0200h - 1000h - 1800h c. 0800h - 1800h - 2400h O d. 0600h - 1400h - 2200h

You have one type of candy that sells for $2.60/lb and another type of candy that sells for $5.10/lb. You would like to have 15 lbs of a candy mixture that sells for $5.00/lb. How much of each candy will you need to obtain the desired mixture? You will need lbs of the cheaper candy and lbs of the expensive candy.

Fiona is going to jog once around the block she lives on. The block is rectangular, and it is 130 yards long and 200 feet wide. How far will Fiona jog (in feet)? 590 feet 1, 180 feet 393 1/3feet 660 feet