Question 1

Solve the equation.

Accepted Answer

The answer of Solve the equation. 
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Question 2

The speed of the current in a stream is 2.4 mi/hr. It takes a canoeist 60 minutes longer to paddle 1.7 miles upstream than to paddle the same distance downstream. What is the canoeist's rate in still water? Round the answer to the nearest tenth of a mile per hour.

Accepted Answer

The canoeist's rate in still water can be found by setting up equations based on the distance, rate, and time for both upstream and downstream travel. Let $x$ be the canoeist's rate in still water. The effective rate downstream is $x + 2.4$ mi/hr and upstream is $x - 2.4$ mi/hr. The time to travel 1.7 miles downstream is $\frac{1.7}{x + 2.4}$ hours, and upstream is $\frac{1.7}{x - 2.4}$ hours. The problem states that it takes 60 minutes (or 1 hour) longer to paddle upstream, so we have the equation: $\frac{1.7}{x - 2.4} - \frac{1.7}{x + 2.4} = 1$. Solving this equation for $x$ gives the canoeist's rate in still water, which is approximately 3.7 mi/hr when rounded to the nearest tenth.

Question 3

A bullet is fired horizontally at a target, and the sound of its impact is heard 1.3 seconds later. If the speed of the bullet is 3,000 ft/sec and the speed of sound is 1,100 ft/sec, how far away is the target?

Accepted Answer

The time taken for the bullet to reach the target is the total time minus the time taken for the sound to travel back. Let d be the distance to the target. The time for the bullet to reach the target is d/3000, and the time for the sound to travel back is d/1100. The total time is 1.3 seconds, so d/3000 + d/1100 = 1.3. Solving this equation gives d ≈ 1,046.3 ft.

Question 4

A square vegetable garden is to be tilled and then enclosed with a fence. If the fence costs $1 per foot and the cost of preparing the soil is $0.20 per ft ², determine the width of the garden that can be enclosed for $403.20.

Accepted Answer

The answer of A square vegetable garden is to be...

Question 5

Solve the inequality.

Accepted Answer

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Question 6

British sterling silver is a copper-silver alloy that is 7.5% copper by weight. How many grams of pure copper and how many grams of British sterling silver should be used to prepare 222 grams of a copper-silver alloy that is 15% copper by weight?

Accepted Answer

The answer of British sterling silver is a copper-silver alloy...

Question 7

A person's intelligence quotient (IQ) is determined by multiplying the quotient of his or her mental age and chronological age by 100. Find the IQ of a 18 - year - old child whose mental age is 21.6.

Accepted Answer

The answer of A person's intelligence quotient (IQ) is determined...

Question 8

Solve the equation by factoring.

Accepted Answer

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Question 9

A student in an algebra course has test scores of 69, 79, 75, and 80. What score on the next test will raise the student's average to 80?

Accepted Answer

To achieve an average score of 80 over 5 tests, the total points must be 5 * 80 = 400. The sum of the first four scores is 69 + 79 + 75 + 80 = 303. Therefore, the score needed on the fifth test is 400 - 303 = 97.

Question 10

Solve the equation.

Accepted Answer

The answer of Solve the equation. 
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Question 11

A person's intelligence quotient (IQ) is determined by multiplying the quotient of his or her mental age and chronological age by 100. Find the mental age of a person 18 years old whose IQ is 140.

Accepted Answer

The answer of A person's intelligence quotient (IQ) is determined...

Question 12

The boundary of a city is a circle of diameter L = 7 miles. As shown in the figure, a straight highway runs through the center of the city from A to B. The highway department is planning to build a 8-mile-long freeway from A to a point P on the outskirts and then to B. Find the distance from A to P. (Hint: APB is a right triangle.) Round the answer to the nearest tenth of a mile.

Accepted Answer

The answer of The boundary of a city is a...

Question 13

Solve the equation

Accepted Answer

The answer of Solve the equation 
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Question 14

A consumer is trying to decide whether to purchase car A or car B. Car A costs $10,000 and has an mpg rating of 30, and insurance is $500 per year. Car B costs $12,600 and has an mpg rating of 50, and insurance is $550 per year. Assume that the consumer drives 15,000 miles per year and that the price of gas remains constant at $1.25 per gallon. Based only on these facts, determine how long it will take for the total cost of car B to become less than that of car A.

Accepted Answer

To determine how long it will take for the total cost of car B to become less than that of car A, we need to calculate the annual costs and the initial difference in purchase price.Initial cost difference: $12,600 - $10,000 = $2,600Annual fuel cost for car A: (15,000 miles / 30 mpg) * $1.25 = $625Annual fuel cost for car B: (15,000 miles / 50 mpg) * $1.25 = $375Annual savings on fuel with car B: $625 - $375 = $250Annual insurance cost difference: $550 - $500 = $50Total annual savings with car B: $250 (fuel) + $50 (insurance) = $300Time to recover initial cost difference: $2,600 / $300 = 8.67 yearsSince the options are in whole years and the calculation gives a value between 8 and 9 years, the closest provided option is 13 years, which is incorrect based on the calculation. However, given the options and the context of the question, it seems there might be a misunderstanding in the interpretation of the options or a mistake in the calculation process. The correct calculation shows that it would take less than 9 years for the total cost of car B to become less than that of car A, but since this option is not available, there might be a need to reevaluate the answer choices or the calculation.

Question 15

During a nuclear explosion, a fireball will be produced having a maximum volume V₀. For temperatures below 2,000 K and a given explosive force, the volume V of the fireball t seconds after the explosion can be estimated using the given formula. (Note that the kelvin is abbreviated as K, not ^oK.) Approximate t when V is 92% of V₀. Round the answer to the nearest thousandth of a second.

Accepted Answer

The answer of During a nuclear explosion, a fireball will...

Question 16

Solve the equation

Accepted Answer

The answer of Solve the equation 
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Question 17

Solve the equation by factoring.

Accepted Answer

The answer of Solve the equation by factoring. 
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Question 18

Write the expression  in the form  , where a and b are real numbers.

Accepted Answer

The answer of Write the expression  in the form...

Question 19

Solve the inequality.

Accepted Answer

The answer of Solve the inequality. 
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Question 20

Solve the formula for K.

Accepted Answer

The answer of Solve the formula for K. 
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Quiz 2: Equations and Inequalities

Solve the equation.

The speed of the current in a stream is 2.4 mi/hr. It takes a canoeist 60 minutes longer to paddle 1.7 miles upstream than to paddle the same distance downstream. What is the canoeist's rate in still water? Round the answer to the nearest tenth of a mile per hour.

A bullet is fired horizontally at a target, and the sound of its impact is heard 1.3 seconds later. If the speed of the bullet is 3,000 ft/sec and the speed of sound is 1,100 ft/sec, how far away is the target?

A square vegetable garden is to be tilled and then enclosed with a fence. If the fence costs $1 per foot and the cost of preparing the soil is $0.20 per ft 2 , determine the width of the garden that can be enclosed for $403.20.

Solve the inequality.

British sterling silver is a copper-silver alloy that is 7.5% copper by weight. How many grams of pure copper and how many grams of British sterling silver should be used to prepare 222 grams of a copper-silver alloy that is 15% copper by weight?

A person's intelligence quotient (IQ) is determined by multiplying the quotient of his or her mental age and chronological age by 100. Find the IQ of a 18 - year - old child whose mental age is 21.6.

Solve the equation by factoring.

A student in an algebra course has test scores of 69, 79, 75, and 80. What score on the next test will raise the student's average to 80?

Solve the equation.

A person's intelligence quotient (IQ) is determined by multiplying the quotient of his or her mental age and chronological age by 100. Find the mental age of a person 18 years old whose IQ is 140.

Solve the equation

Solve the equation

Solve the equation by factoring.

Write the expression in the form , where a and b are real numbers.

Solve the inequality.

Solve the formula for K.

A square vegetable garden is to be tilled and then enclosed with a fence. If the fence costs $1 per foot and the cost of preparing the soil is $0.20 per ft ², determine the width of the garden that can be enclosed for $403.20.