Math Questions
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Math
Basic MathA space shuttle is made using a scale of 1 inch : 12 feet. If the actual space shuttle has a height of 84 feet, then the model is inches tall.
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Basic Math(11.5) In a survey of 42 U.S. children, 72% said they plan to complete a summer reading list this year. Give an interval that is likely to contain the exact percent of all U.S. children who plan to complete a summer reading list this year. Round to the nearest tenth of a percent. It is likely that the exact percent is between % and %.
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AreaA blueprint of a house shows a bedroom with an area of 12 square inches. If the blueprint's scale is 1 inch : 3 feet, what would be the actual square footage of the bedroom? square feet
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Basic MathA map's scale is 1 inch : 3.5 miles. If the actual distance between two places is 77 miles, then they will be__________ inches away from each other on the map.
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Basic MathIf you borrow $400 for 3 years at an annual interest rate of 4%, how much will you pay altogether?
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Basic MathAt work, Chris used 117 inches of tape to seal 9 boxes for shipping. The equation x/15 = 117/9 can be used to determine how many inches of tape, x, it will take him to seal 15 boxes. How many inches of tape will Chris need to seal 15 boxes for shipping?
A) 182 hours
B) 195 inches
C) 208 inches
D) 225 inches
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Basic MathWhich two consecutive whole numbers does √39 lie between? Why?
5 and 6 because 39 falls between 5² =25 and 6² = 36.
4 and 6 because 39 falls between 4² = 16 and 6² = 36.
6 and 7 because 39 falls between 6² = 36 and 7² = 49.
5 and 7 because 39 falls between 5² = 25 and 7² = 49.
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TrigonometryA construction worker leans a ladder against a building. The ladder is 27 ft long and the distance between the base of the ladder and the bottom of the building is 9 ft. Find the angle formed between the ground and the base of the ladder.
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Basic MathOn a map, the scale shown is 1 inch : 5 miles. If an island is 2.5 square inches on the map, what is the actual area of the island? The actual island's area is square miles.
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Basic MathΔABC is located in Quadrant I. Point A is 5 units to the right of the line of reflection. If ΔA'B'C' is the image created by reflection, where is A' relative to the line of reflection?
A. 0 units away, directly on the line of reflection
B. 2.5 units to the left
C. 5 units to the left
D. 10 units to the right
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LogarithmsSuppose a house that costs $270,000 appreciates by 5% each year. In about how many years will the house be worth $350,000? Use the equation 350 = (270)(1.05)* and round the value of x to the nearest year.
6
5
7
4
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AreaA carpenter is framing a wall that is 8 feet high and 15 feet long. If the carpenter wants to be sure that
the sides of the wall meet at right angles, then what should the diagonal measurement of the wall be?
13 feet
19 feet
17 feet
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Basic MathJan is looking at a map of Roaring River. The map was created using the scale 1 inch : 25 miles. If the river is 5.5 inches long on the map, then it is actually miles long.
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Basic MathAlexandra owns a small business selling bagels. She knows that in the last week 95 customers paid cash, 4 customers used a debit card, and 31 customers used a credit car. Based on these results, express the probability that the next customer will pay with something other than a credit card as a fraction in simplest form.
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Basic MathMembers of a school sports team are raising money by selling custom water bottles at school activities. They plan to sell each bottle for $11. Each bottle costs them $4. They spend $40 for advertising. Use n to represent the number of bottles they sell. Multiply this by the money they make for each bottle, then subtract the advertising cost. Which expression represents the money that the group raises?
A. (11-4)n - 40
B. 11n - 4 - 40
C. 40 - (11 - 4) n
D. 11 - 4n - 40
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Basic MathWhat is the length of the hypotenuse of a right triangle whose legs have lengths of 5 and 12?
13
17
15
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Basic MathA gas that exerts a pressure of 215 torr in a container with a volume of 51.0 mL will exert a pressure of torr when transferred to a container with a volume of 18.5 mL.
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Basic MathOn a map, the scale shown is 1 inch: 20 miles. If a city is 900 square miles, what is the area of the city on the map? The city's area is square inches on the map. (Do NOT round your answer.)
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Basic MathPostcards cost $2.50 for six. What's the price for 1 postcard?
A. $7.10
C. $0.42
B. $6.25
D. none of the above
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Basic MathThe milligrams of aspirin in a person's body is given by the equation a = 500 (3/4)^t, where t is the number of hours since the patient took the medicine.
a. How much aspirin will be in the patient's body after two hours?
b. In the equation, what does the 500 tell us about the situation?
c. In the equation, what does the % tell us about the situation?
d. Graph the equation for values of t between 0 and 4.
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Basic MathEvaluate each logarithm. Round to the nearest thousandth when necessary.
(Use a calculator for "log" and "In." If the log as a base number, use the Change of Base Formula:
loga c= logc/loga
9) log 17
10) In 0.5
11) log3 4
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Basic MathA blueprint of a house shows a living room that is 15 square inches. If the blueprint's scale is 1 inch : 4 feet, what is the actual square footage of the living room space?
square feet
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Basic MathIf triangle LMN has an obtuse angle at vertex M, which statements could be true? Check all that apply.
Triangle LMN is an obtuse triangle.
The angle at vertex L is acute.
The angle at vertex L is right.
The angle at vertex N is right.
The angle at vertex N is acute.
Triangle LMN is a right triangle.
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Basic MathImagine a very large connected graph that has 650 even vertices and no odd vertices.
a) Does an Euler path exist for this graph? Explain.
b) Does an Euler circuit exist for this graph? Explain.
a) Choose the correct answer below.
A. Yes. There are no odd vertices.
B. Yes. The graph is sufficiently large that an Euler path will exist regardless of the number of even and odd vertices.
C. No. There are too many even vertices for an Euler path to exist regardless of the number of odd vertices.
D. Yes. There are sufficiently many even vertices that an Euler path will exist regardless of the number of odd vertices.
E. No. The graph is too large for an Euler path to exist regardless of the number of even or odd vertices.
F. No. There are no odd vertices.
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Basic MathAmy wants to paint the ceiling of her restaurant. The ceiling is in the shape of a square. Its side lengths are 44 feet. Suppose each can of paint will cover 242 square feet. How many cans will she need to paint the ceiling?
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Basic MathA furniture store bought a couch for $425 and marked the price up by 70%. Angela bought the couch with a 6% tax. How much did Angela pay for the couch?
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Straight linesEquation x-x1/cosθ = y-y1/sinθ = r, may represents -
(A) Equation of straight line, ife is constant and r is variable.
(B) Equation of a circle, if r is constant & is variable.
(C) A straight line passing through a fixed point & having a known slope
(D) A circle with a known centre and given radius.
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Basic MathMatthew purchased a desk that was on sale for 45% off the original price of $480. If the sales tax was 8% (of the sale price), how much did Matthew spend on the desk?
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Basic MathCarmen uses 2/7 of a bag of flour to make 1/2 of a batch of her special homemade cookies. How many bags of flour does it take to make 3 batches of the cookies? Simplify your answer completely.
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Basic MathWhen 2 grams of Helium are added to a weather balloon, its volume is 8.0 L. If the pressure and temperature do not change, and 1 more gram is added, what is the final volume of the balloon?
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Basic MathA gas that exerts a pressure of 537 torr in a container with a volume of 5.30 L will exert a pressure of 255 torr when transferred to a container with a volume of L.
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Basic MathWhen the volume of a gas is changed from 800.0 cm³ to 400.0 cm3, the temperature will change from 115°C to °C.
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Coordinate systemThe revolving restaurant on top of a hotel in San Francisco, California takes 45 minutes to complete a full counterclockwise rotation. A table that is 30 ft from the center of the restaurant starts at position (30, 0). What are the coordinates of the table after 9 minutes? Round to the nearest tenth.
(9.3, 28.5)
(11.3, 17.3)
(28.5.9.3)
(23, 19.3)
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Straight linesA line has a slope of and passes through the point (-1, -10). What is its equation in point-slope form?
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
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Matrices & DeterminantsUse Cramer's rule to find the solution to the following system of linear equations.
5x-4y=-8
3x+y=3
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Basic MathMia works at a bakery. Mia prepared 10 kg of dough after working 2 hours. How many kilograms (x) of dough did Mia prepare if she worked for 9 hours? Assume the relationship is directly proportional.
A) 45 kg
B) 50 kg
C) 55 kg
D) 60 kg
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Sequences & SeriesWhich of the following is a feature of the pattern? Select all that apply.
A. All of the house numbers are even.
B. All of the house numbers are odd.
C. The house numbers alternate odd and even.
D. The house numbers are multiples of 3.
E. The house numbers increase by 3.
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Basic MathFind the scale factor that was used to change the Original (O) to the Scaled Image (S).
S 7.8"
O 2.6"
A. 3
B. 0.33
C. 2.8
D. 5.2
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Basic MathIn a 30-60-90 triangle how do we go from the longer leg to the shorter leg? *
divide by the square root of 2
multiply by the square root of 2
multiplyby the square root of 3
divide by the square root of 3
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Sequences & SeriesAt the beginning of April, a colony of ants has a population of 5,000 ants.
a. The colony decreases by 1/5 during April. Write an expression for the ant population at the end of April.
b. The colony continues to decrease by % of its size each month. Write an expression for the ant population after 6 months.
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Basic MathAn organization will give a prize to a local artist. The artist will be randomly chosen from among 6 painters, 2 sculptors, and 9 photographers. What is the probability that the artist chosen will be a painter or a sculptor?
Write your answer as a fraction in simplest form.
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Basic MathA couple needs to get a loan of $5,000 and has to choose between three options.
Option A: 21% compounded quarterly
Option B: 3% compounded every 4 months
Option C: 4-1% compounded semi-annually
If they make no payments for 5 years, which option will give them the least amount owed after 5 years? Use a mathematical model for each option to explain your choice.
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ProbabilityJulian owns a small business selling ice-cream. He knows that in the last week 52
customers paid cash, 22 customers used a debit card, and 5 customers used a credit
card.
Based on these results, express the probability that the next customer will pay with a
credit card as a fraction in simplest form.
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Basic MathTara has 19 feet of yarn. She is making friendship bracelets that each need 1/2 of a foot of yarn. How many bracelets can Tara make?
A.9 1/2
B.10
C.18 1/2
D. 38
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Basic MathA ticket to the state fair cost $15. The equation y = 15x relates the total cost of tickets (y) to the number of tickets purchased (x). Identify the unit rate in the equation.
x
y
15
15x
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Basic MathDavis can read 4/5 of a page in one minute. How many pages can he read in 4 1/2 minutes?
Simplify your answer completely.
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VectorsLet u = -5i +2j and v=-5i-5j. Decompose u into two vectors u1, and u₂, where u1, is parallel to v and u2, is orthogonal to v.
Write your answers in the form ai+bj.
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Basic MathCory can eat 21 boiled eggs in 6 minutes. He wants to know how many minutes (m) it would take him to eat 35 boiled eggs if he can keep the same pace.
How many minutes would Corey need to eat 35 boiled eggs?
8 minutes
9 minutes
10 minutes
12 minutes