Basic Math Questions and Answers

A box contains 30 widgets, 4 of which are defective. If 4 are sold at random, find the probability that (a) all are defective (b) none are defective. A)1/30;2/15 B)1/657720;1/164430 C)2/15;13/15 D)1/27405;2990/5481

Consider the quadratic equation 3x²-2x+10=0. Choose the words or phrases that complete the statement. The discriminant of the equation is .This means the equation has because the discriminant is zero.

The speed of a passenger train is 14 mph faster than the speed of a freight train. The passenger train travels 310 miles in the same time it takes the freight train to travel 240 miles. Find the speed of each train. The speed of the passenger train is mph. The speed of the freight train is

Solve y + 3xyz - 2yz = 0 for z z=-y³/(3xy² - 2y) z=-y/(3x - 2y) z=(-y²-2)/3xy z=1/3x

A car's windshield wiper is 10 inches long and rotates through an angle of 60°. If the rubber part of the wiper only covers the last 9 inches of the blade, find the area of the windshield cleaned by the blade.

Multiply (8.1 × 10³) (4.7 × 10¹). Write your answer in scientific notation. For example, you'd enter 2.3*10^4 for 2.3 - 10¹ Invalid use of a comma.syntax incomplete.

Mr. Wolf throws a basketball vertically upward from a height of 2 m with initial velocity of 25 m/s. a. How long does it take to reach the maximum height? b. What is the maximum height? c. What is the velocity when the basketball hits the ground?

A car rental agency advertised renting a car for $28.95 per day and $0.26 per mile. If Shawn rents this car for 2 days, how many whole miles can he drive on a $150 budget?

Hana walks 12/3 miles to school. After school she walks 1 1/2 miles to work. How many miles does she walk before and after school? 3 1/3 miles 2 5/6 miles 2 3/5 miles 3 1/6 miles

According to the United Nations Office for Outer Space Affairs, in 2016 there were 4, 256 satellites orbiting the planet. Round this number to the nearest ten. 4,300 4,000 4, 260 5,000

Micah is twice as old as Richard. Richard is four times as old as Ken. Ken is six years old. How old is Micah? 48 years old 24 years old 8 years old 12 years old

Write the expression as a function of x, with no angle measure involved. sin(2π/3-x) sin (2π/3-x)-0 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression..

In 2021, Forsyth County in North Carolina had a population of 388,453 with an area of 413 square miles. Rounded to the nearest hundredth, what was Forsyth County's population density in 2021? Hint for review only: Population density Is a measurement of population per unit area. The population density for Forsyth County in 2021 was

You can use prime factorization or the list method to find the greatest common numerical factor. The numerical factors are -49 and -343. Because -1 is a common factor of each coefficient, find the GCF of 49 and 343. Factors of 49: 1, 7, 49 Factors of 343: 1, 7, 49, 343 What is the GCF of 49 and 343? Multiplying the GCF of 49 and 343 by -1 gives the GCF of -49 and -343. What is the GCF of -49 and -343?

Which of the following are true? Select ALL that are true. □ If f(x) has an absolute maximum at a = □ If g" (2) = 0, then a = 2 can be a point of inflection. -3 then f'(-3) must exist and be equal to zero. h(x) = 4x²/3 - 24/3 is concave down on its domain. It is possible for a continuous and decreasing function on a closed interval to have a local minimum.

2) Naya thinks that the inverse of f(x)=x-2 is g(x)=2-x. To justify her answer, she calculates f(2)=0 and then substitutes the output 0 into g to get g(0)=2, which gives back the original input. Show that Naya is incorrect by using other examples from the domain and range of f.

Suppose that a loan of $3000 is given at an interest rate of 13% compounded each year. Assume that no payments are made on the loan. Follow the instructions below. Do not do any rounding. (a) Find the amount owed at the end of 1 year. (b) Find the amount owed at the end of 2 years.

The federal budget in 2012 included $471 billion for Medicare and $47 billion for International Affairs. Complete the statement below that compares the two quantities. The budget of $471 billion for Medicare is about times larger than the $47 billion budget for International Affairs.

The distance between Paris, France, and Rio de Janeiro, Brazil is 5720 miles. If lines were drawn from Paris and Rio to the center of the earth, those lines would meet at an angle of 82.24°. Use this information to approximate the radius of the earth. Using this information, we can estimate that the radius of the earth is miles.

Carlie's stock rose by 1 points in trading today. Let Y represent yesterday's stock price at closing and T represent today's stock price at closing. i) What is a formula that correctly relates Y and T? ii) If yesterday's closing price was 3213, what was today's closing price? 16 i) Y = T + 1² 7 ii) Today's closing price was 33- 16 i) T = Y + 1/² ii) Today's closing pric was 337. 16 i) T = Y + 1²/ ii) Today's closing price was 34. i) Y = T + 1/² ii) Today's closing price was 34 16

11 1 point If the function f (x) = x³ is transformed to f (x) = (x + 5)³ + 2, what will the effect be on the function's graph? The graph will be translated 5 units left and 2 units up The graph will be translated 5 units right and 2 units down The graph will be translated 2 units left and 5 units up The function's graph will be vertically stretched

Mr. Jones is 4 times as old as his son. In 16 years, he will be only twice as old. At the present time, how old is Mr. Jones? O 8 years old O 32 years old O 24 years old 48 years old

A hotel puts out 3 apples for every 1 orange as the fruit for their breakfast buffet. A. Write a ratio of apples compared to all the fruit. B. What percent of the fruit in the breakfast buffet are apples?

This question: 1 point(s) possible Due to random variations in the operation of an automatic hot chocolate machine, not every cup is filled with the same amount of hot chocolate. Assume that the mean amount dispensed is 10 ounces with a standard deviation of 0.8 ounces. What percentage of the cups should have more than 10.8 ounces of hot chocolate? Assume that the given distribution is normal. ties OA. 25% OB. 16% OC. 34% OD. 32%

3 Mary walks the 3 day breast cancer walk. They break the 62-miles evenly for each day. How many miles 4 does she walk in one day? ○ 21¹ miles 4 O 20. miles 11 O 20- miles 12 3 21-miles

During a regular baseball season, Player A hit 22 home runs and was paid an annual salary of $510,000. During the same regular season, Player B hit 25 home runs and was paid an annual salary of $20,000,000. Express the salary of each player as a unit rate in terms of dollars paid to home runs hit. Player A's salary as a unit rate in terms of dollars paid to home runs hit is (Simplify your answer. Round to the nearest dollar as needed. Do not include dollars/home run. home runs/dollar. *****

Change the equation to slope - intercept form (y = mx + b) and show your work and label each step with the correct Properties of Equalities. Given: 6x + 8y = 16 What is the slope - intercept form of the equation (y=mx+b)? What is the slope? What is the y-intercept? Draw the graph of the slope-intercept equation.

Ven because questions can be worth more or less (including zero) depending on your answe Match each number on the left with the correct description of the number on the right. Answer options on the right may be used more than once. - 10 This is an integer. √5 This is a rational number, but not an integer. -5.6 This is an irrational number. 3 1/4 π

A car rental agency advertised renting a car for $27.95 per day and $0.27 per mile. If Kevin rents this car for 2 days, how many whole miles can he drive on a $150 budget? MOCNO miles (Round down to the nearest whole mile.)

points). Two students try to solve the equation 4* = 26: Student 1's work 4* = 26 (22)* = 26 22+x= 26 2 + x = 6 x = 4 Student 2's work 4x = 26 log(4*) = log(26) xlog(4) = log(64) X = log(64) log(4) x = 3 Which student(s) solved the equation correctly? Explain.

test. You have held 1 questions so far. A school needs 1, 860 pencils for its students. The pencils are sold in boxes of 12. How many boxes does the school need to order? The solution is I

During 2014, there was an Ebola breakout in West Africa. On April 1, 2014, there had been 130 cases reported. A month later there had been 234 cases reported. Question 5 Find the absolute and relative change between the two reported values. Absolute change: Relative change: As a decimal: As a percent:

When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 10 kg, the acceleration of the object is 7 m/s². If the same force acts upon another object whose mass is 35 kg, what is this object's acceleration?

A KHS class ring is dropped from an upper-room window (1600 feet high) at NRG Stadium in Houston. a. Find the position function. b. Find the velocity function. c. Find the time required for the ring to reach ground level.

Suppose that an amount of $1600 is invested into an account that earns 3.2% compounded continuously. a) How much is in the account after 7 years? b) How long does it take for the balance in the account to reach $3000? c) Suppose that after a period of four years, the balance is withdrawn and invested into a new account that earns 4.6% compounded monthly. How much would be in that new account 7 years from now?

Two cars leave from the same location. Car #1 travels north at 60 mph and car #2 travels south at 54 mph. How long will it take for the cars to be 342 mile apart? 5.7 hours 6.3 hours 0.6 hours 3 hours

A missile was fired from a submarine from 170 feet below sea level. If the missile reached a height of 16400 feet before exploding, what was the change in the altitude of the missile?

1 point The vertices of a triangle are at (0, 0), (4,4), and (6,2). What is the volume in cubic units of the figure created by rotating the triangle about y = ? O 64√2 32√2 16x √2 O 32x O 3² √2

5. Each group in Anh's math class is making up a secret math code, where unfamiliar symbols (heart, star, raindrop, lightning bolt, & bullseye) stand for five different mathematical operations. Anh's group is going to challenge Aurora's group to crack the code used in the following equations: (540) * 3 = 15 (1425) / 2 = 4 40 (146) 0 2 = 64 Aurora's group's results will be verified by asking them to evaluate this expression: 23 ★ (40310) 620 (41) * (1 4 0 20) What should they get? Be sure to explain your solution.

The sum of the measures of two angles is 135°. If the measure of one angle is xº, which of the following algebraic expressions best represents the measure of the other angle? THE Choose the correct answer below. OA. x-135 OB. 135-x OC. 135 + x OD. 135-x

To estimate the number of manatees in Florida waters, 180 are tagged. A few months later, a random sample of manatees is selected and examined. Of the 110 manatees in the sample, 3 are tagged. Assuming that the sample is representative of the population, the number of manatees in Florida waters is: 5800 6600 6200 7000

From a hot-air balloon, Zoe measures a 37° angle of depression to a landmark that's 1441 feet away, measuring horizontally. What's the balloon's vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.

Two lines are given. Look at the pictures and determine if such lines exist. Can they exist in the same plane? Explain your reasoning. If such lines exist, how would you call them? front view top view

can be worth more or less (including zero) depending on your answer. Which of the following statements is true about the numbers below? (i) 0.12345678901234567890... (the digits cycle through repeatedly) (ii) 0.101001000100001000001000001... (i) is irrational and (ii) is irrational. (i) is rational and (ii) is irrational. (i) is irrational and (ii) is rational. (i) is rational and (ii) is rational. (the number of Os inbetween the 1s increases by one each time)

Jasmine has 3 cup of flour in a mixing bowl. 4 After adding more flour to the mixing bowl, Jasmine says that she now has 5 cup of flour. 3+56 Which of the following explains why Jasmine's statement is incorrect?

What is the length of the altitude? (also called the geometric mean) O 2.45 O 3.46 O 4.90 O 2.83

An ornithologist is studying hawks in the mountains. She catches 24 hawks over a period of one month, tags them, and releases them back into the wild. The next month, she catches 30 hawks and finds that 10 are already tagged. Estimate the number of hawks in this part of the mountains. There are hawks in this part of the mountains. *****

If the APR is 2.4% per year, how much is the interest per month (Remember Periodic Rate from 1.9)? % Now write this as a decimal.

A particle is moving on a horizontal line according to the equation s(1) = -91 +24r +3. a.Write an equation for velocity. b. Write an equation for acceleration. c. At what time(s) does the particle change direction? d. Find the position(s) of the particle when it turns. e. Make a motion graph. f. Find the velocity when the acceleration is zero. g. Find the displacement of the particle during the first 5 seconds. h. Find the total distance traveled during the first 5 seconds.

wo 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 2.3 mph faster than the other. That is the speed of the slower hiker? ype an integer or a decimal.) That is the speed of the faster hiker? ype an integer or a decimal.) FERRE