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Q1Solve the given equation for x. −5x + 17 = 112
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✓ Correct answer: X = −19
On the left, an order of operations demands that we first multiply x by −5, then add 17. To solve this equation for x, we must “undo” each of these operations in an inverse order. Thus, we will first subtract 17 from both sides of the equation, then divide both sides of the resulting equation by −5. <br/><br/>Original equation. <br/><br/>−5x + 17 = 112<br/><br/>To “undo” adding 17, subtract 17 from both sides of the equation. <br/><br/>−5x+ 17 − 17 = 112 − 17<br/><br/>Simplify both sides. <br/><br/>−5x = 95<br/><br/>To “undo” multiplying by −5, divide both sides of the equation by −5. <br/><br/><img src="asset:assets/questions/21fbf59b80efca5e.png"/><br/><br/>Simplify both sides. <br/><br/>x = −19.
Q2Which is NOT an example of an independent event?
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✓ Correct answer: Drawing 3 cards from a deck without replacing the cards
Not replacing the card makes the next draw dependent on the previous draw because there is always 1 less card in the deck.
Q3A paper bag contains 3 blue marbles, 2 red marbles, 4 green marbles and 1 white marble. Without replacement what is the probability of drawing a red marble on first attempt and green marble on the second attempt?
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✓ Correct answer: 4/45
On the first draw there are 10 marbles therefore the probability is getting a red is 2/10 or 1/5. On the second draw there are 9 marbles the probability of getting a green is 4/9. The events are independent thus multiply the two probabilities to determine first ball is red and second is green. 1/5 * 4/9 = 4/45.
Q4Determine k so that the point (−1, k) is a solution of y = −5x+ 3.
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✓ Correct answer: K = 8
Substitute (x, y) = (−1, k) into the equation y = −5x+ 3. <br/><br/>Original equation. <br/><br/>y = −5x+ 3<br/><br/>Substitute: −1 for x, k for y. <br/><br/>k = −5(−1) + 3<br/><br/>Multiply: −5(−1) = 5. <br/><br/>k = 5 + 3<br/><br/>Add: 5 + 3 = 8. <br/><br/>k = 8<br/><br/>Thus, k = 8.
Q5Jackson leased a new car for 3 years. He agreed to pay $1,900 down and a $269 payment each month. He also agreed to pay $0.125 per mile he drove over 30,000 miles. During the 3-year lease period, Jackson drove the car 32,458 miles. Excluding taxes, what was the cost of leasing this car for 3 years?
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✓ Correct answer: $11,891.25
Add the three costs: down payment ($1,900), total monthly payments and mileage over 30,000 (<img src="asset:assets/questions/a62cfae3ba16c4fa.png"/>) to get $11,891.25.
Q6When the sum of 1.8912 and 3.1846 is rounded to the nearest hundredth, the result is:
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✓ Correct answer: 5.08
First, add the two values together without rounding.<br/><br/>1.8912 + 3.1846 = 5.0758<br/><br/>Next, round to the nearest hundredth, which is two decimal places. Since the 5 digit in the thousandths place indicates that you need to round up, the correct answer is 5.08.
Q7The rectangular dining room table is 3.5 feet wide by 8 feet long.<br/><br/>What is the perimeter of the table?
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✓ Correct answer: 23 feet
The perimeter of the table is the distance around it. Thus, the perimeter equals 3.5 feet + 8 feet + 3.5 feet + 8 feet, or 23 feet.
Q8Point X is halfway between points A and B. Point Y is halfway between points C and D.<br/><br/>What is the distance between point X and point Y?
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✓ Correct answer: 2.5
Find the midpoint between A and B then find the midpoint between C and D then evaluate the absolute value of their difference to find the distance from point Y to Z.<br/><br/>Halfway between A and B: −1.75<br/><br/>Halfway between C and D: 0.75<br/><br/>The absolute value of the difference between them:<br/><br/>= |−1.75−0.75|<br/><br/>= |−2.5|<br/><br/>= 2.5.
Q9Mechanical advantage is a measure of the force amplification that is achieved by using a tool, mechanical device, or machine system. The formula for mechanical advantage is shown below.<br/><br/>A crowbar can be used to remove a nail from a board. If the crowbar has a mechanical advantage of 8, and the a force of 40 Newtons is applied to it, what will be the output force?
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✓ Correct answer: 320 Newtons
The question provides the mechanical advantage and the input force. The first step is to plug these numbers into the equation:<br/><br/>8 = x/40<br/><br/>To solve this, multiply each side by 40:<br/><br/>8 × 40 = x x = 320.
Q10Nora makes soup by adding some spices to a pot of boiling water and stirring the spices until completely dissolved. Next, she adds several chopped vegetables.<br/><br/>What is the solute in her mixture?
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✓ Correct answer: Spices
A solute is a substance that is dissolved in another substance. In this case, the solute is the spices.
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