Basic Math Questions and Answers

Directions - Find the x and y-intercepts from the Standard Form equation. Write your answers as ordered pairs. -5x - 2y = 10 x-intercept = ( y-intercept = (

Sketch the graph of the inequality. 3x - 4y < 12 Step 1 To graph the given inequality, first replace the inequality symbol by an equality sign. 3x - 4y = 12 Graph the equation using a dashed line, as the solution set does not contain the boundary

The length of a rectangle is 4 inches more than its width, and its perimeter is 34 inches. Find the length and width of the rectangle. Find the width of the rectangle. 7.5 in 6.5 in 6 in

Identify the study as observational or experimental. One group of subjects was given an herbal supplement for one year, another group was given a placebo. After one year, the number of illnesses each group had was compared.

In a hydraulic system, an input piston has an area of 22.0 in² and an output piston with an area 70.6 in². A weight or resistance of 150 pounds is on the output piston. What is the pressure? 2.12 psi 5,261 psi 792.3 psi 1,445 psi

Directions - Convert the following equation to Standard Form. Make sure the leading coefficient is positive, and all integers are whole numbers. 2y = -3x+5 Standard Form:

On a second class lever, a 12 lb input force (effort force) is 30 inches from the fulcrum. Where should a 34 lb load (resistance force) be placed so it can be lifted? 5.00 in 27.4 in 10.6 in 83.9 in

Is there a correlation between the salary of a teacher and their shoe size? no correlation correlation correlation that implies causation

Rosa invests $3300 in an account with an APR of 3% and annual compounding. Julian invests $2800 in an account with an APR of 4% and annual compounding. Complete parts a through c. a. Compute the balance in each account after 5 and 20 years. After 5 years Rosa will have a balance of approximately $___After 20 years Rosa will have a balance of approximately $. (Round to the nearest cent as needed.)

Classify the following: The number letters in a city and the population of the city. Correlation only No correlation Correlation that implies causation

...... is a sample used by chance methods in statistics. Every member of the population has the same chance of being selected. control biased random independent

A hydraulic system contains one small piston with a area of 2 square inches and one large piston with an area of 10 square inches. If a force of 70 pounds is applied to the small piston, what will the system pressure be? 700 psi 74.1 psi 35 psi 4.82 psi

Factor: f(x) = x² - 4x - 12 (x-6)(x+2) (x-3)(x + 4) (x-4)(x + 3) (x-2)(x+6)

Going against the current, a boat takes 6 hours to make a 120-mile trip. When the boat travels with the current on the return trip, it takes 5 hours. If x= the rate of the boat in still water and y= the rate of the current, which of the following systems could be used to solve the problem? 6(x-yl=120 and 5(x-y)=120 6(x+y)-120 and 5(x-y)=120 6x-5y=120 and x-y=120

The function below shows the cost to attend the fair if you ride r rides. f(r)= 5+1.75r. What is the slope, and what does it mean in the context of this problem? The slope is 1.75 and it is the cost to attend the fair without riding any rides. The slope is 5 and it is the cost to attend the fair without riding any rides. The slope is 1.75 and it is the cost per ride. The slope is 5 and it is the cost per ride.

Identify the study as observational, experimental, survey or neither. An entrepreneur stands on a street corner of New York city and counts the number of people of with dogs that walks by. He used this data to decide if he wants to put in a pet store of the street none of the answer choices observational survey experimental

On a second class lever, a 80 lb input force (effort force) is 42 inches from the fulcrum. Where should a 300 lb load (resistance force) be placed so it can be lifted? 221 in 17.3 in 11.2 in 8.00 in

Find the inverse function for the following: f(x) =2+3x/5x and use your result to show that f(f-¹(x)) = x. (HINT: f(f-¹(x)) is just function notation.... you are being asked to replace the x's in f(x) with f-¹(x)).

On a first class lever, a weight of 62 lb is 1.5 feet feet from the fulcrum. How far from the fulcrum should an effort or input force of 10.1 lb be located? 13.4 feet 29.5 feet 4.60 feet 9.21 feet

The following system of equations is y=-1/3x+2/3 2x+6y=4 independent inconsistent equivalent

Given f(2)= 12, which of the following could be an equation of the function? A. f(x) = 8x-2 B. f(x) = 4x + 4 C. f(x) = 6x-4 D. f(x) = -4x - 4 Please select the best answer from the choices provided A B C D

Find the measure of the third angle of a triangle if the measures of the other two angles are given. 102.9 and 40.4 A. 43.2 B. 56.7 C. 46.7 D. 36.7

The logistic growth function f(t) = 103,000/1+4500 e^-t describes the number of people, f(t), who have become ill with influenza t weeks after its initial outbreak in a particular community. a. How many people became ill with the flu when the epidemic began? b. How many people were ill by the end of the fourth week? c. What is the limiting size of the population that becomes ill?

Point A lies outside of plane P, how many lines can be drawn parallel to plane P that pass through point A? A. 2 B. an Infinite number C. 1 D. O

An artifact originally had 16 grams of carbon-14 present. The decay model A = 16 e ^-0.000121t describes the amount of carbon-14 present after t years. Use the model to determine how many grams of carbon-14 will be present in 6311 years. The amount of carbon-14 present in 6311 years will be approximately grams. (Round to the nearest whole number.)

What types of concurrent constructions are needed to find the orthocenter of a triangle? A. Intersection of the lines drawn to the midpoint of each side of the triangle to its opposite vertex B. Intersection of the lines drawn to bisect each vertex of the triangle C. Intersection of the lines drawn from each vertex of the triangle and perpendicular to its opposite side D. Intersection of the lines drawn perpendicular to each side of the triangle through its midpoint

The areas of two similar pentagons are 32 in² and 72 in². Find the ratio of larger pentagon's perimeter to the smaller pentagon's perimeter. A. 9:4 B. 25:9 C. 5:3 D. 3:2

The logistic growth function f(t)=111,000/1+5000 e-t describes the number of people, f(t), who have become ill with influenza t weeks after its initial outbreak in a particular community. a. How many people became ill with the flu when the epidemic began? b. How many people were ill by the end of the fourth week? c. What is the limiting size of the population that becomes ill?

The areas of two similar rectangles are 540 ft2 and 135 ft2. Find the similarity ratio of smaller rectangle to the larger rectangle. A. 1:2 B. 1:3 C. 1:4 D. 2:5

Calculate the amount of money you'll have at the end of the indicated time period. You invest $3000 in an account that pays simple interest of 4% for 10 years.

Jacob and Zachary go to the movie theater and purchase refreshments for their friends. Jacob spends a total of $18.25 on two bags of popcorn and three drinks. Zachary spends a total.of $27.50 for four bags of popcorn and two drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a bag of popcorn and the price of a drink, to the nearest cent.

Subtract and simplify your answer. 7/X-6 - 6/X+5

Last summer, a group of high school students farmed a plot of land. They harvested 13 bushels of vegetables to give to a food pantry. Next year the students will use a larger, similar plot of land. The ratio of the dimensions of the original plot to the new plot is 2:5. How many bushels of vegetables can the students expect to harvest next year? A. about 81 bushels B. about 65 bushels C. about 33 bushels D. about 114 bushels

Factor by using the perfect-square trinomial formula. 25x² +20xy+4y²

If the coordinate of A is (0, -2) and the coordinate of B is (10, -6), the then midpoint of AB is: Part A The X portion of the midpoint is Part B The Y portion of the midpoint is

A population has a mean = 71 and a standard deviation a=36. Find the mean and standard deviation of a sampling distribution of sample means with sample size n=81. H = (Simplify your answer.)

Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. Also, find the APY for the account. A $7000 deposit in an account with an APR of 3.5%. The balance in the account after 1 year is approximately $

2x-y-4-0 3x+y-9-0 What is the solution set of the given system?

$8,000 is invested in two different accounts earning 3% and 4% interest. If the two accounts earn a total of $295 in interest, how much money was invested at 3%? $2.500 $3,500 $5.500

The sum of Pete's and Sam's ages is 30. Five years ago, Pete was 3 times as old as Sam. How old is Sam? Let P Pete's age, S-Sam's age, and PS= 30. Which of the following equations would complete the system? P-5=35-5 P-S=35-15 P-5=35

If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. Determine the original fraction. Which of the following equations represents "If the numerator of a fraction is increased by 3, the fraction becomes 3/4"? (Hint: cross products) 4n+ 12 = 3d 3n 9-40 4n+3=30

5x + 2y = 7 y=x+1 What is the solution set of the given system? (16/7, 9/7)) (5/7, 12/7)) ((12/7, 5/7) ((9/7, 16/7)

y-2x+3 2y-4x+6 The system of equations has solution(s). one Infinite no

The similarity ratio of two similar parallelograms is 4/5 . The area of the smaller parallelogram is 64 in². Find the area of the larger parallelogram. A. 92 in² B. 88 in² C. 100 in² D. 96 in²

A box with a square base and no top is to be made from a square piece of carboard by cutting 2 in. squares from each corner and folding up the sides. The box is to hold 10368 in³. How big a piece of cardboard is needed?

2y = x + 3 5y = x - 7 What is the solution set of the given system? ((-29/3, -10/3)] [(29/3, 10/3)]} ((-1/3, -4/3)] ((1/3, 4/3)]

What is the x-coordinate of the solution of the following system of equations 3x + y = 6 x-y=6 -3 0 3

2x + y = -2 x+y=5 The x-coordinate of the solution to the system shown is -3 7 3 -7

Solve the following system of equations by the substitution method. 8x = 2y + 5 3x = y +7 What is the solution set?

Find the sum and classify the polynomial based on degree and number of terms. 3n2(5n22n + 1) + (4n² - 11n4 -9) A 4th degree polynomial with 4 terms B. 3rd degree polynomial with 3 terms C. 3rd degree polynomial with 4 terms D. 4th degree polynomial with 3 terms