Basic Math Questions and Answers

After descending for 8 minutes, an airplane is at an altitude of 24800 feet. After descending for 20 minutes, the plane's altitude is 12800 feet. Assuming a linear function, write an equation in the form a(t) = mt+b that shows the altitude, a, after t minutes of descent. Provide your answer below: a(t) =

Ernie deposited $4000 between two savings accounts. One account paid 4% simple interest and the other paid 2%. At the end of one year, Ernie had earned $140 in interest for both accounts. How much money did Ernie deposit in the account that paid 4% interest?

Given that the degree of the polynomial f(x) is 5, which of the following most accurately describes the number of x- intercepts that f(x) has? Select the correct answer below: f(x) has at most 4 x-intercepts. f(x) has at least 4 x-intercepts. f(x) has at least 5 x-intercepts. f(x) has at least 6 x-intercepts. f(x) has at most 5 x-intercepts. f(x) has at most 6 x-intercepts.

A woman decides to invest $4000 in an IRA CD at the end of each year for 10 years. If she makes these payments and the certificates all pay 6%, compounded annually, how much will she have at the end of the 10 years?

Given that the degree of the polynomial f(x) is 4, which of the following most accurately describes the number of x- intercepts that f(x) has? Select the correct answer below: f(x) has at least 4 x-intercepts. f(x) has at most 3 x-intercepts. f(x) has at least 5 x-intercepts. f(x) has at most 4 x-intercepts. f(x) has at least 3 x-intercepts. f(x) has at most 5 x-intercepts.

I can break apart unknown facts into known facts and solve multiplication problems. Madison broke up a large array into a 3 x 4 array and a 5 x 4 array. What was the large array that Madison started with? Use evidence to justify your thinking.

The number x of printer cartridges that a store will sell per week and their price p (in dollars) are related by the equation x² = 7000 - 5p². If the price is falling at the rate of $1 per week, find how the sales will change if the current price is $30.

Each day a small business owner sells 200 pizza slices at $3.00 per slice and 85 sandwiches at $3.00 each. Business expenses come to $70 per day. What is the owner's profit for a ten-day period?

A toy shop sells baby rattles in green and yellow. For every two green rattles the toy shop sells, it sells 7 yellow rattles. If the company sells 108 rattles, how many yellow rattles did they sell?

Allistair throws a biased six-sided dice. The probability of getting a 6 with this dice is 0.4. The other numbers are equally probable. If he throws the dice 3 times, what is the probability that he gets 5, 3 and 2 in this order?

Let a and b be positive constants. If a > b, then which of the following is true? It is not possible to tell anything about the relationship between a³ and b³. a³ > b³ a³ = b³ b³ > a³

g(x)=3x²-18x+22 (a) Write the equation in the form g (x)= a (x-h)²+k. Then give the vertex of its graph. (b) Graph the function. To do this, plot five points on the graph of the function: the vertex, two points to the left of the verte of the vertex. Then click on the graph-a-function button.

The graph to the right shows that the three components of love, namely passion, intimacy, and commitment, progress differently over time. Passion peaks early in a relationship and then declines. By contrast, intimacy and commitment build gradually. What is the maximum level of intensity for passion? After how many years in a relationship does this occur?

Which description lists Earth's layers from most superficial to deepest? a Lithosphere, lower mantle, asthenosphere, outer core, inner core b Asthenosphere, Lithosphere, lower mantle, inner core, outer core c Inner core, outer core, lower mantle, ästhenosphere, lithospherea d Lithosphere, asthenosphere, lower mantle, outer core, inner core

5. A French toast recipe uses 2 eggs to make 14 slices of French toast, Brenda wants to make 98 slices of French toast to feed her family and friends. How many eggs will Brenda need to make 98 slices?

John 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 John will spend is given by the equation y = 18 + 1.5x, where represents the total amount of money, in dollars and cents, and art represents the number of rides John goes on. What could the number 1.5 represent in the equation? The total amount of money John will spend if he goes on o rides. The change in the total amount of money for every one additional ride he goes on. The total amount of money John will spend if he goes on a ride. The total amount of money John will spend if he goes on 100 rides.

If $8000 is invested at 3% interest, compounded annually, then after n years the investment is worth an = 8000(1.03)" dollars. Find the first five terms of the sequence {a}. Step 1 For an = 8000(1.03), we have a₁ = 8000(1.03)¹ = a2 = 8000(1.03)² = and

Suppose that an object is dropped from a height of h meters and hits the ground with a velocity of v meters per second. Then v= 19.6h. If an object hits the ground with a velocity of 18.3 meters per second, from what height was it dropped? Carry your intermediate computations to at least four decimal places, and round your answer to the nearest tenth.

In 2012, the population of a city was 5.91 million. The exponential growth rate was 2.48% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 9 million? d) Find the doubling time.

The formula for the surface area of a rectangular solid is: S = 2HW + 2LW + 2LH, where S, H, W, and L represent surface area, height, width, and length, respectively. Solve this formula for L.

You were offered either a simple interest note or a simple discount note with the following terms: $39,242 at 9% for 18 months. a. Calculate the effective interest rate. (Do not round intermediate calculations. Round your final answer to the nearest tenth percent.) Effective interest rate %

The lengths of the sides of a right triangle are such that the shortest side is 7 in. shorter than the middle side, while the longest side (the hypotenuse) is 1 in. longer than the middle side. Find the lengths of the sides.

Victoria counts this week's food donations at a pet shelter. There are 16 full cases of canned food. There are 4 cases of canned food that are each missing 5 cans. Victoria records a total of 220 cans of food. a. Use c to represent the number of cans in a full case. What expression could represent the number of cans in each case that is missing cans? b. Write an equation you could use to find c. c. How many cans are in a full case? How many cans are in each of the 4 other cases? Show your work.

A factory manufactures parts for a new television at a cost of $30 per part, and also has a monthly fixed cost of $600. If P represents the number of parts the factory manufactures in a month, and C is the total cost, write the linear equation that represents the relationship between P and C.

Given that the polynomial f(x) has 4 turning points, which of the following most accurately describes the degree of f(x)? Select the correct answer below: The degree of f(x) is at most 3. The degree of f(x) is at most 5. The degree of f(x) is at least The degree of f(x) is at most 4. The degree of f(x) is at least 3. The degree of f(x) is at least 5.

27 boxes of coconut creams for $14.95 each 36 boxes of pralines for $11.39 each 14 boxes of raspberry bites at $8.50 each Round the cost of each box to the nearest dollar, and then estimate the amount of money that the class earned. $927 $963 $1,025 $913

There are 240 students going on a field trip. Each school bus can hold 48 students. Complete the equation to show which operation to use and how many school buses are needed. Then complete the sentence to explain your reasoning. because 240 students need to be split into equal groups of 48 students.

For a total accumulated amount of $3687.52, a principal of $2000, and a time period of 9 years, use the compound interest formula to find r, if interest is compounded monthly.

In a race in which seven automobiles are entered and there are no ties, in how many ways can the first three finishers come in?

Andrew is watching the stock market. He recorded the changes every day, as follows: • Day 1: Opened at 4,798.68 points Day 2: Lost 125.07 points Day 3: Lost 36.5 points Day 4: Gained 52.71 points ● ● Round each number to the nearest whole number. Then, add the values to find the value on Day 5. O O 4,690 4,689 4,691 4.584

Find the vertex, focus, and directrix of the following parabola. Graph the equation. Verify your graph using a graphing utility. (y-2)² = 8(x+3) The vertex of the parabola is (-3,2). (Type an ordered pair.) The focus of the parabola is. (Type an ordered pair.)

A can of tennis balls has a diameter of 3 in. and a height of 9 in. Find the volume of the can to the nearest cubic inch.

A survey of a random sample of voters shows that 66% plan to vote for Katie and 34% plan to vote for Casey. The survey has a margin of error of ±2%. What is the range for the percentage of voters who plan to vote for Katie?

Solve the system of linear equations by graphing. (2x-y=0 3x+y=5

Points: U of 1 In triangle ABC, the angles A and B have the same measure, while the measure of angle C is 18° larger than the measure of each of A and B. What are the measures of the three angles? The measure of angle A and the measure of angle B are each (Type a whole number.)

For some particular website, the password must start with one of the letters A, B, C, D, E, or F. Then there must be 2 more charaters, and each of those characters may be a numeric digit or a letter of the alphabet. How many different passwords are possible?

Find the sum, in degrees, of the six labeled angles. The sum of the six labeled angles is:.

A local health clinic surveys 50 patients about their water drinking habits. It found the data is normally distributed with a mean of 62 ounces and a standard deviation of 5.2. Estimate how much water, to the nearest hundredth of an ounce, do all of the clinic's patients drink each day, using a 99% confidence interval.

Solve the following expression when k = 12 and v=6 k V + 5 - 4v + 12

Solve for y. 3y² +12y=0 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

Question A television company uses a factory to manufacture one of its parts. The factory has a monthly fixed cost of $700 and an additional cost of $60 per part. If C is the total cost of using the factory for a month, and P represents the number of par the factory manufactures in a month, which of these is the correct relationship between P and C? Select the correct answer below: OP=700C+60 OC=700P+60 OP=60C+700 OC=60P+700

Rebecca has 30 paintings to sell. The amount of money Rebecca makes from selling x paintings is represented by a function. f(x) = 25x What is the practical domain of the function? all multiples of 25 between 0 and 750, inclusive all integers from 0 to 30, inclusive all real numbers all integers from 0 to 25, inclusive

Question Given that the polynomial f(x) has 5 turning points, which of the following most accurately describes the degree of f(x) Select the correct answer below: O The degree of f(x) is at most 6. O The degree of f(x) is at most 5. The degree of f(x) is at least 6. O The degree of f(x) is at most 4. O The degree of ƒ(x) is at least 4. The degree of f(x) is at least 5. FEEDBACK MORE INSTRUCTION SUBMIT

Julia is solving a system of equations using elimination. The first two steps of her solution are shown below. List a property of equality to justify each of her steps. Then, find the solution of the system of equations. 4x + 3y = 6 2x - 5y = 16 Multiply by -2. 4x + 3y = 6 -4x+10y=-32 0 + 13y =-26

GRAVITATION The height h(t) in feet of an object t seconds after it is propelled straight up from the ground with an initial velocity of 60 feet per second is modeled by the equation h(t) = -16t² + 60t. At what times will the object be at a height of 56 feet?

Question 2 of 19 The population of India was about 1,380,000,000 people in 2020. Which number best approximates the population as a single digit times a power of 10? A. 1 × 10⁹ OB. 3 × 108 OC. 1 × 10-9 OD. 3 × 10⁹

An rock is thrown downward from a platform that is 215 feet above ground at 55 feet per second. Use the projectile formula h - 16t² + vot + ho to determine when the rock hit the ground. -[Recall that vo is the initial velocity of the object and he is the inital height of the object.] Answer: The rock will hit the ground after Note: Round any numerical responses to two decimal places. If there are multiple answers, separate them with commas. Select an answer

An rock is thrown upward from a platform that is 191 feet above ground at 65 feet per second. Use the projectile formula h 16t² + vot + ho to determine when the rock hit the ground. -[Recall that vo is the initial velocity of the object and he is the inital height of the object.] Answer: The rock will hit the ground after Select an answer Note: Round any numerical responses to two decimal places. If there are multiple answers, separate them with commas.

Which expression is equivalent to sec α (1 - cos²α) for all values of α for which secα(1- cos²α) is defined? Select the correct answer below: sin² α sin α tan α tan α csc²α sec² α

Let S be the universal set, where: S = {1, 2, 3, 18, 19, 20} 9 Let sets A and B be subsets of S, where: Set A = {1, 2, 3, 5, 6, 8, 9, 13, 14, 16, 17, 18} Set B = {5, 6, 9, 13, 15, 16, 17, 18, 19, 20} Find the following: LIST the elements in the set (A U B): (AUB) = { } Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set (AN B): (An B) = { } Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE You may want to draw a Venn Diagram to help answer this question.