1. On Saturday morning the temperature was 76°F. The temperature dropped 9°F and then rose 13°F. How much does the temperature need to rise or fall to return to the initial temperature of 76°F?(1 point)
To find the fraction that represents the part of the adoptions for cats and dogs, we need to add the fractions for dogs and cats together.
The fraction representing the dogs is 2/3, and the fraction representing the cats is 1/4.
To add these fractions together, we need to find a common denominator, which is 12 in this case.
The fraction representing the dogs can be written with a denominator of 12 by multiplying both the numerator and denominator by 4: (2/3) * (4/4) = 8/12.
The fraction representing the cats can be written with a denominator of 12 by multiplying both the numerator and denominator by 3: (1/4) * (3/3) = 3/12.
Adding the fractions together, we get: 8/12 + 3/12 = 11/12.
Therefore, the fraction that represents the part of the adoptions for cats and dogs together is 11/12.
The temperature dropped 9°F and then rose 13°F, so it is currently 4°F higher than the initial temperature of 76°F. To return to the initial temperature, the temperature needs to fall by 4°F.
2. What is the distance between -23 and 9 on a number line?(1 point)
To find the distance between two numbers on a number line, you subtract the smaller number from the larger number and take the absolute value of the result.
So, the distance between -23 and 9 is: |9 - (-23)| = |9 + 23| = 32.
−27−(−6)
To find the result of the expression −27−(−6), you can simplify it by removing the parentheses and applying the rule of signs.
Since you have a negative sign in front of the parentheses, when you remove them, it changes the sign of each term inside.
Therefore, the expression becomes −27 + 6.
Now you can add the two numbers:
−27 + 6 = -21.
4.
13−(−19)=
To find the result of the expression 13−(−19), you can simplify it by removing the parentheses and applying the rule of signs.
Since you have a negative sign in front of the parentheses, when you remove them, it changes the sign of each term inside.
Therefore, the expression becomes 13 + 19.
Now you can add the two numbers:
13 + 19 = 32.
5.
20+(−30)
To find the result of the expression 20+(−30), you can simply add the two numbers:
20 + (-30) = -10.
6.
I. You gain 5 pounds.
II. You set your clock 5 hours ahead.
III. You use 5 gallons of gas.
The integer -5 would BEST represent which of these events?
(1 point)
7. Which of these situations is NOT an example of two quantities that combine to make zero.(1 point)
Responses
Mary collects 12 bottle caps and then loses 12.
Mary collects 12 bottle caps and then loses 12.
A business’s income is equal to its expenses.
A business’s income is equal to its expenses.
Benjamin lost 6 pounds and then gained 8 pounds.
Benjamin lost 6 pounds and then gained 8 pounds.
Madeline wins $20 and then pays the babysitter $20.
The situation that is NOT an example of two quantities that combine to make zero is Mary collecting 12 bottle caps and then losing 12.
In this situation, Mary's actions do cancel each other out and result in a net change of zero. Therefore, it is an example of two quantities combining to make zero.
The other situations - a business's income equaling its expenses, Benjamin losing 6 pounds and then gaining 8 pounds, and Madeline winning $20 and then paying the babysitter $20 - all involve two quantities that combine to make zero.
7. Which of these situations is NOT an example of two quantities that combine to make zero.(1 point)
Responses
A. Mary collects 12 bottle caps and then loses 12.
B. A business’s income is equal to its expenses.
C. Benjamin lost 6 pounds and then gained 8 pounds.
D. Madeline wins $20 and then pays the babysitter $20.
The situation that is NOT an example of two quantities that combine to make zero is option B: A business’s income is equal to its expenses.
In this situation, if a business's income is equal to its expenses, it means that the two quantities are balanced and the net result is zero. Therefore, option B is not an example of two quantities that combine to make zero.
8. Jeffrey earned $52 at his job last week. On Saturday, he bought a video game that cost $25. Which number is the additive inverse of the amount of money Jerry has left?(1 point)
To find the additive inverse of the amount of money Jerry has left, we need to subtract the amount of money he has left from 0.
Jerry earned $52 and bought a video game for $25, so the amount of money he has left is $52 - $25 = $27.
The additive inverse of $27 is -$27.
Therefore, the number that is the additive inverse of the amount of money Jerry has left is -$27.
9. John used his debit card to withdraw $55 from the ATM. Then, he wrote a check for $18.00. Which equation represents the total change to John's account for these two transactions?(1 point)
To represent the total change to John's account for these two transactions, you need to subtract the amounts of money he withdrew and wrote the check for from his account balance.
Let x represent John's account balance.
The equation that represents the total change to John's account is:
x - $55 - $18.00 = 0.
Therefore, the equation that represents the total change to John's account for these two transactions is: x - $55 - $18.00 = 0.
9. John used his debit card to withdraw $55 from the ATM. Then, he wrote a check for $18.00. Which equation represents the total change to John's account for these two transactions?(1 point)
A. 55−18 = 37
B. −55 + (−18) = −73
C. -55 + 18 = -37
D. 55 - (-18) = 73
To represent the total change to John's account for these two transactions, you need to subtract the amounts of money he withdrew and wrote the check for from his account balance.
John withdrew $55 from the ATM, which should be subtracted from his account balance. Then, he wrote a check for $18, which should also be subtracted from his account balance.
The correct equation that represents the total change to John's account for these two transactions is:
x - $55 - $18.00 = 0
Simplifying this equation, we get:
x - $73.00 = 0
To isolate x, we need to add $73 to both sides of the equation:
x = $73
Therefore, the equation that represents the total change to John's account for these two transactions is D. 55 - (-18) = 73.
10. Macy and Bill were painting the shed. Macy painted 2/3
of the shed and Bill painted 1/4
of the shed. Which statement is TRUE?(1 point)
A. Together they painted a little more than half the shed.
B. Together they painted almost the entire shed.
C. Together they didn’t even paint half of the shed.
D. Together they painted three-fourths of the shed.
To find the total fraction of the shed painted by Macy and Bill together, we need to add up their individual fractions.
Macy painted 2/3 of the shed, and Bill painted 1/4 of the shed.
To add these fractions, we need to find a common denominator, which is 12 in this case.
Macy's fraction can be written with a denominator of 12 by multiplying both the numerator and denominator by 4: (2/3) * (4/4) = 8/12.
Bill's fraction can be written with a denominator of 12 by multiplying both the numerator and denominator by 3: (1/4) * (3/3) = 3/12.
Adding the fractions together, we get: 8/12 + 3/12 = 11/12.
Therefore, the statement that is TRUE is B: Together, Macy and Bill painted almost the entire shed. They painted 11/12 of the shed, which is almost the entire shed.
11. Sally runs an animal rescue company that allows families to adopt homeless pets. Last month, 2/3
of the adopted animals were dogs and 1/4
of the adoptions were cats. Rabbits and reptiles were also adopted. Which fraction represents the part of the adoptions for cats and dogs?(1 point)
12.
1.567−11.83+2.3
(1 point)
To find the result of the expression 1.567 - 11.83 + 2.3, you can simply subtract and add the numbers:
1.567 - 11.83 + 2.3 = -10.263 + 2.3 = -7.963.
Therefore, the result of the expression is -7.963.
13. The admiral is in a submarine that is 550 feet below sea level. The submarine then descends 108 feet. What is the new position of the submarine?(1 point)
To find the new position of the submarine after descending 108 feet, you need to subtract 108 feet from its initial position.
The initial position of the submarine is 550 feet below sea level.
Subtracting 108 feet from 550 feet, we get:
550 - 108 = 442.
Therefore, the new position of the submarine is 442 feet below sea level.
14. The Becker Department Store's basement is 15 feet below ground. If the total length of the building from basement to roof is 70 feet, what is the building's elevation above ground?(1 point)
To find the building's elevation above ground, you need to subtract the depth of the basement (15 feet) from the total length of the building (70 feet).
70 - 15 = 55.
Therefore, the building's elevation above ground is 55 feet.
15. Simplify: 8⋅9−2⋅5
Remember to use the order of operations (PEMDAS).
(1 point)
To simplify the expression 8⋅9−2⋅5, you need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
Starting from left to right, first, you multiply 8 and 9, and then you multiply 2 and 5. After that, you subtract the second product from the first product.
8⋅9−2⋅5 = 72 - 10 = 62.
Therefore, the simplified expression is 62.
8. Jeffrey earned $52 at his job last week. On Saturday, he bought a video game that cost $25. Which number is the additive inverse of the amount of money Jerry has left?(1 point)
To find the additive inverse of the amount of money Jerry has left, we need to find the opposite of the amount of money he has left.
Jerry earned $52 and bought a video game for $25, so the amount of money he has left is $52 - $25 = $27.
The additive inverse of $27 is -$27.
Therefore, the number that is the additive inverse of the amount of money Jerry has left is -$27.
1. On Saturday morning the temperature was 76°F. The temperature dropped 9°F and then rose 13°F. How much does the temperature need to rise or fall to return to the initial temperature of 76°F?(1 point)
The temperature dropped 9°F and then rose 13°F, so it is currently 4°F higher than the initial temperature of 76°F. To return to the initial temperature, the temperature needs to fall by 4°F.
What is the distance between -23 and 9 on a number line?(1 point)
Responses
32
32
14
14
-14
-14
-32
To find the distance between two numbers on a number line, you subtract the smaller number from the larger number and take the absolute value of the result.
So, to find the distance between -23 and 9, we have:
|9 - (-23)| = |9 + 23| = |32| = 32.
Therefore, the distance between -23 and 9 on a number line is 32.
−27−(−6)
(1 point)
Responses
21
21
33
33
-33
-33
-21
To simplify the expression −27−(−6), you can remove the parentheses and apply the rule of signs.
When you remove the parentheses, it changes the sign of the term inside.
Therefore, the expression becomes −27 + 6.
Now you can add the two numbers:
−27 + 6 = -21.
Therefore, the simplified expression is -21.
13−(−19)=
(1 point)
Responses
32
32
-6
-6
6
6
-32
To simplify the expression 13−(−19), you can remove the parentheses and apply the rule of signs.
When you remove the parentheses, it changes the sign of the term inside.
Therefore, the expression becomes 13 + 19.
Now you can add the two numbers:
13 + 19 = 32.
Therefore, the simplified expression is 32.
20+(−30)
(1 point)
Responses
10
10
-10
-10
50
50
-50
To simplify the expression 20+(−30), you can simply add the two numbers:
20 + (-30) = -10.
Therefore, the simplified expression is -10.
I. You gain 5 pounds.
II. You set your clock 5 hours ahead.
III. You use 5 gallons of gas.
The integer -5 would BEST represent which of these events?
(1 point)
Responses
I only
I only
III only
III only
I and III only
I and III only
II and III only
The integer -5 would best represent the event of gaining 5 pounds.
Gaining weight is commonly represented using negative numbers because in most cases, gaining weight is seen as an undesirable or negative event. Therefore, the integer -5 would best represent the event of gaining 5 pounds.
Which of these situations is NOT an example of two quantities that combine to make zero.(1 point)
Responses
Mary collects 12 bottle caps and then loses 12.
Mary collects 12 bottle caps and then loses 12.
A business’s income is equal to its expenses.
A business’s income is equal to its expenses.
Benjamin lost 6 pounds and then gained 8 pounds.
Benjamin lost 6 pounds and then gained 8 pounds.
Madeline wins $20 and then pays the babysitter $20.
The situation that is NOT an example of two quantities that combine to make zero is option B: A business's income is equal to its expenses.
In this situation, if a business's income is equal to its expenses, it means that the two quantities are balanced and the net result is zero. Therefore, option B is not an example of two quantities that combine to make zero.
effrey earned $52 at his job last week. On Saturday, he bought a video game that cost $25. Which number is the additive inverse of the amount of money Jerry has left?(1 point)
Responses
27
27
-25
-25
-37
-37
-27
To find the additive inverse of the amount of money Jerry has left, we need to subtract the amount he spent on the video game from his earnings.
Jerry earned $52 and spent $25 on the video game, so the amount he has left is $52 - $25 = $27.
The additive inverse of $27 is -$27.
Therefore, the number that represents the additive inverse of the amount of money Jerry has left is -$27.
John used his debit card to withdraw $55 from the ATM. Then, he wrote a check for $18.00. Which equation represents the total change to John's account for these two transactions?(1 point)
Responses
55−18 = 37
55−18 = 37
−55 + (−18) = −73
−55 + (−18) = −73
-55 + 18 = -37
-55 + 18 = -37
55 - (-18) = 73
To represent the total change to John's account for these two transactions, we need to subtract the amounts of money he withdrew and wrote the check for from his account balance.
Let x represent John's account balance.
The equation that represents the total change to John's account is:
x - $55 - $18.00 = 0.
Therefore, the equation that represents the total change to John's account for these two transactions is: x - $55 - $18.00 = 0.
1.567−11.83+2.3
(1 point)
Responses
−7.95
negative 7 point 9 5
−7.963
negative 7 point 9 6 3
2.773
2 point 7 7 3
7.96
To simplify the expression 1.567 - 11.83 + 2.3, you can subtract and add the numbers:
1.567 - 11.83 +
Simplify: 8⋅9−2⋅5
Remember to use the order of operations (PEMDAS).
(1 point)
Responses
280
280
62
62
350
350
46
The admiral is in a submarine that is 550 feet below sea level. The submarine then descends 108 feet. What is the new position of the submarine?(1 point)
Responses
658 feet
658 feet
442 feet
442 feet
-442 feet
-442 feet
-658 feet
The Becker Department Store's basement is 15 feet below ground. If the total length of the building from basement to roof is 70 feet, what is the building's elevation above ground?(1 point)
Responses
55 feet
55 feet
85 feet
85 feet
65 feet
65 feet
70 feet
The integer -5 would best represent the event of gaining 5 pounds.
Gaining weight is commonly represented using negative numbers because in most cases, gaining weight is seen as an undesirable or negative event. Therefore, the integer -5 would best represent the event of gaining 5 pounds.