Basic Math Questions and Answers

Hudson is blocking off several rooms in a hotel for guests coming to his wedding. The hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 6 people. Hudson booked a total of 19 rooms which can accommodate 87 guests altogether. Write a system of equations that could be used to determine the number of small rooms reserved and the number of large rooms reserved. Define the variables that you use to write the system.

A photographer points a camera at a window in a nearby building forming an angle of 42° with the camera platform. If the camera is 52 m from the building, how high above the platform is the window, to the nearest hundredth of a meter? 0.9 m 46.82 m 57.75 m 1.11 m

Determine the simple interest. Assume 360 days in a year. p=$39,632, r=0.0625% per day, t = 90 days The simple interest is $. (Do not round until the final answer. Then round to the nearest cent as needed.)

Use the power reducing formulas to rewrite sin3x in terms of the first power of cosine. Simplify your answer as much as possible. To indicate your answer, first choose one of the four forms below. Then fill in the blanks with the appropriate numbers.

If you inflate a beach ball with 14,130 cubic inches of air, what will its radius be? Use 3.14 for π. Round to the nearest whole number if necessary. 15 inches 17 inches 24 inches 58 inches

Jessica is collecting aluminum cans during the summer for a recycling project. She collected 120 aluminum cans in June and 150 aluminum cans in July. What is the percentage change of the number of cans she collected in June to the number of cans she collected in July? A. a 25% increase B. a 20% decrease C. a 20% increase D. a 25% decrease

What is the factored form of the trinomial below? 25x² +10 xy + y²=0 (Note: When factoring polynomials with two variables, one of them can be treated as a constant.) (5x-y)² (5x + y)² (25x + y)² (25x - y)²

Determine the effective annual yield for $1 invested for 1 year at 7.3% compounded quarterly. The effective annual yield is %.

Claire is writing a report about kangaroos. The report must bedwo full pages. If she can fit 20 lines on each page with about 20 words per line, approximately how many words in all will Claire's report be?

Reason A race is 10 kilometers long. Markers will be placed at the beginning and end of the race-course and at each 500-meter mark. How many markers are needed to mark the course for the race?

A cylinder has a radius of 25 cm and a height of 2 cm. Find the height of another cylinder that has a radius of 5 cm and the same surface area as the first cylinder. The other cylinder has a height of cm.

A couple found a house selling for $112,500. The taxes on the house are $1300 per year, and insurance is $320 per year. They are requesting a conventional loan from the local bank. The bank is currently requiring a 15% down payment and 3 points, and the interest rate is 10%. The couple's gross monthly income is $4850. They have more than 10 monthly payments remaining on a car, a boat, and furniture. The total monthly payments for these items is $430. Their bank will approve a loan that has a total monthly mortgage payment of principal, interest, property taxes, and homeowners' insurance that is less than or equal to 28% of their adjusted monthly income. Complete parts a) through g) below. a) Determine the required down payment. The required down payment is $.

A company determined that for each $1 increase in the price of their product, the number of items sold will decrease by 2. Their predicted weekly profit with a price increase of x dollars is represented by the function f(x)=-3x²+18x+120. By how many dollars should they increase the price of their product to maximize their weekly profits? 3 147 10 120

Which could describe two quadrilaterals that have all pairs of corresponding angles congruent but are not similar? Two rectangles, both having a perimeter of 3.5 feet A square with a perimeter of 14 feet and a square with a perimeter of 54 centimeters Two rhombi, each having at least one 90° angle A parallelogram with adjacent sides 9 and 12 centimeters and an angle of 88, and a parallelogram with adjacent sides 9 and 12 inches and an angle of 92°

A local high school held a two-day fundraiser selling lunches. The equations shown represent the amount of money the school collected during the two days. 12x + 4y = 152 32x+12y = 420 In the equations, x represents the cost of a chicken lunch and y represents the cost of a vegetarian lunch. Which is the cost of the vegetarian lunch? $9 $11 $13 $21

Based on f(x) = lxl, describe the transformations of the function g(x) = -|x +4| +3 a. g(x) is f(x) translated 4 units to the left and 3 up units b. g(x) is f(x) reflected across the x-axis translated 4 units to the left and 3 up units c. g(x) is f(x) reflected across the x-axis translated 3 units to the left and 4 up units d. g(x) is f(x) reflected across the y-axis translated 4 units to the right and 3 up units

Determine the simple interest. (The rate is an annual rate unless otherwise stated. Assume 360 days in one year.) p=$775, r= 6.5%, t = 90 days The simple interest is $ (Round to the nearest cent as needed.)

A helicopter is hovering 2500ft above the ground. The pilot looks down at a 43-degree angle with respect to the horizon to see a pedestrian. If the helicopter lands by descending directly down, how far away from the pedestrian will the helicopter have landed?

Mary forgot the security code to her home. She knows there is a 0, 2, and 8 in some order. a.) List all the possible three-digit security codes. b.) What percent of the security codes start with the number 2 or 8?

Write an algebraic equation and use it to solve the problem. Five-sevenths of a number is -20. What is the number? The equation is.

If a linear combination is the method used to solve the system of equations, what is the result of the first step? x + y = 6 x - y = 2 A. 2y = 8 B. 2x = 8 C. x + y = 8 D. x - y = 8

Fern bought groceries that cost $14.38. She paid the store clerk, Ping, with a $20 bill. 2 pennies makes the total $14.40. 6 dimes makes it $15.00, and 6 dollars makes it $20. Did the clerk make a mistake in giving Fern her change? You may use the scratchpad to show your work. A No, she received $6.62 in change. B Yes, Ping should give Fern 6 pennies and 2 dimes. C Yes, Ping should give Fern 3 dimes and 8 pennies. D Yes, Ping should give five one-dollar bills, not six.

A shirt priced at x dollars is discounted before tax is added. The final price in dollars is described by the expression below. 1.05(x -0.6x) What is the sales tax for the shirt? 0.05(0.4x) 1.05 (0.6x) 1.05 (0.4x) 0.05(0.6x)

Given y = 4x + 21-3 if a is multiplied by 3 what happens to the vertex? a. The vertex remains the same. b. The vertex shift to the right 3 units. c. The vertex shifts to the left 3 units. d. The vertex shifts down 3 units.

The price of a dress is reduced by 60%. When the dress still does not sell, it is reduced by 60% of the reduced price. If the price of the dress after both reductions is $80, what was the original price? The original price of the dress was $ (Type an integer or a decimal.)

agrees to pay a student 6¢ for every problem in this chapter that the student solves correctly, and fines the student 5¢ for every problem done incorrectly. If at the end of 33 problems they do not owe each other any money, how many problems did the student solve correctly? problems correctly.

In a circle with radius 8.8, an angle intercepts an arc of length 32.9. Find the angle in radians to the nearest 10th.

- The coordinates of quadrilateral JKLM plotted on a coordinate plane are J(-2,3), K(3, 7), L(6,5) and M(1, 1). Enter a number in the box to complete the sentence. The perimeter of the quadrilateral is || the nearest tenth. units. Round your answer to

Convert the following angle from degrees to radians. Express your answer in simplest form. 405°

Elijah is building a deck. He has enough wood to build a 35 ft2 deck. Elijah wants the deck to be 2 ft longer than it is wide. He sets up the following equations to help him determine the dimensions of the deck. x(x+2) = 35 x²+2x-35 = 0 where x is the width of the deck in feet. How wide should Elijah make his deck? To solve for x, first factor the left side of the equation. Note: The width of the deck must be positive. Ignore negative values for x. x = 7 feet x = 3 feet x = 5 feet x = 6 feet

Estimate the sum. Choose the mixed number that is closest to the estimate. 5.5 +4.2

In a circle with radius 0.8, an angle measuring 6.3 radians intercepts an arc. Find the length of the arc to the nearest 10th.

Find the circumference of a circle with radius= 30 mm. A. about 47.12 mm B. about 282.74 mm C. about 188.4 mm D. about 109.67 mm

Which equation has the same solution as x² + 16x - 11 = 4? (x-8)²=-49 (x+8)² = 79 (x+8)² = -49 (x-8)² = 79

Which of the following can be used to check that (x-4) and (x+7) are factors of the polynomial below? x² + 3x-28 x(x+7)-4 x.x+7x-4x -4.7 x+(x+7) 4+ (x+7) x.x-4-7

The governor of state A earns $52,765 more than the governor of state B. If the total of their salaries is $297,595, find the salaries of each. The governor of state A earns $ and the governor of state B earns $

In a circle with radius 9, an angle intercepts an arc of length 9π/2. Find the angle in radians in simplest form.

In 2016, there were approximately 4. 46 x 10⁹ people in Asia. On average, a person takes 8.4 x 106 breaths per year. Using this data, what was the number of breaths of all the people in Asia in 2016? Expressing your answer i scientific notation in the form a x 10, what are the values of a and b? What is the value of a? What is the value of b?

Find the critical value(s) for a left-tailed z-test with α = 0.08. Include a graph with your answer. The critical value(s) is(are) (Round to two decimal places as needed. Use a comma to separate answers as needed.)

A new car is purchased for 23700 dollars. The value of the car depreciates at 13.5% per year. What will the value of the car be, to the nearest cent, after 10 years?

An electronics store advertises that one lucky customer will be given a television at the store's 10th anniversary celebration. On the day of the celebration, 150 customers, of which 82 are less than 30 years old and 68 are 30 years old or more, complete a form to enter for the chance to win the television. The manager of the store wants to select the winner by drawing a form out of a box, but the box can only hold 100 forms. Which method ensures both that the manager can use the box for the selection and that each customer has a fair chance of winning? A Divide the forms into two lots based on age. Then, randomly select one of the lots and place it in the box. Randomly select the winning customer's form out of the box. B. Randomly divide the 150 forms into five equal-sized groups. Then randomly select 4 of the groups and place them in the box. Randomly select the winning customer's form out of the box. C. Sort the forms alphabetically by last name. Then, place the first 100 forms into the box. Randomly select the winning customer's form out of the box. D. Randomly divide the 150 forms into three equal-sized lots. Then, randomly select two of the lots and place them in the box. Randomly select the winning customer's form out of the box.

For the given principal, interest rate, and time period, determine the amount of interest that would be earned in an account paying simple interest. Also determine the amount of interest that would be earned in an account paying compound interest with interest compounded monthly. Determine how much more interest would be earned in the account paying compound interest. Round to the nearest cent. Principal: $6720 Rate: 4.25% Years: 9 1/2

Which of the following events are most likely independent of each other Your homework average in Geometry and your grade on this test Your grade on this test and your grade on another teacher's test The number of hours of sleep you had last night and your grade on this test Your grade on this test and the number of hours you spent studying for it

A lumber mill is preparing pieces of wood that meet these requirements. A finished piece of wood is shaped like a rectangular prism. The width of each piece of wood will vary (w). • The height of each piece of wood must be twice the width (2w). . The length of each piece of wood must be 10 inches more than 30 times the width (30w + 10). Which expression represents the volume in terms of the width, in cubic inches, of each piece of finished wood? Use V= /hw

Mildred sold magazine subscriptions with three prices: $27, $13, and $18. She sold 8 fewer of the $27 subscriptions than of the $13 subscriptions and sold a total of 32 subscriptions. If her total sales amounted to $556, how many $18 subscriptions did Mildred sell?

In a circle with radius 10, an angle intercepts an arc of length 5π/3. Find the angle in radians in simplest form.

A road map has a scale where 16 miles of actual distance is represented by 1 inch on the map. Two cities are 9.5 inches apart on the map. How far is the actual distance between the two city centers? 104 miles 136 miles 120 miles 152 miles

Use the FOIL method to find the terms of the following multiplication problem. (4+6i)-(4-6i)

A researcher is examining the claims made by a water softener salt manufacturer. He performs an experiment using water from a variety of sources. For each water source, he has a sample with no treatment and a sample treated with the recommended amount of the water softener salt. He then tests each sample to measure the softness and compares the results, determining that the claims made by the manufacturer are true.

A rectangular prism has a length of 20 meters, a height of 12 meters, and a width of 12 meters. What is its volume, in cubic meters?