The Snake Eyes Roller Coaster climbs 125 feet from ground level then drops 60 feet before climbing another 135 feet. How far does the coaster need to drop or climb to be back at ground level? (Hint: Draw a picture or use a number line.)
To solve this problem, we can use a number line. Let's assume that ground level is represented by the number 0 on the number line.
The roller coaster starts at ground level, then climbs 125 feet. This takes it to a height of +125 on the number line.
Next, the roller coaster drops 60 feet. This takes it down to a height of +125 - 60 = +65 on the number line.
Finally, the roller coaster climbs another 135 feet. This takes it to a height of +65 + 135 = +200 on the number line.
To find out how much the coaster needs to either drop or climb to be back at ground level, we need to determine how far the coaster is from 0 on the number line.
The coaster is currently at +200, which is 200 feet above ground level. Therefore, it needs to drop 200 feet to be back at ground level.
Simplify |-7| + |6|.
:)
|-7| + |6| simplifies to 7 + 6, which equals 13.
Before it started to rain, Amnar cut 1/6 of the grass and Aayush cut 1/3 of the grass. Which statement is true?
(1 point)
Responses
a. Together the boys didn’t even cut half of the yard.
b. The boys cut almost the whole yard.
c. The boys cut exactly half of the yard.
d. Together the boys cut three-fourths of the yard.
To find the total amount of grass cut by both boys, we need to add the fractions 1/6 and 1/3.
First, we find a common denominator for 1/6 and 1/3, which is 6.
Next, we convert the fractions to have the same denominator:
1/6 = 1/6 * 1/1 = 1/6 * 2/2 = 2/12
1/3 = 1/3 * 2/2 = 2/6
Now, we can add the fractions:
2/12 + 2/6 = 4/12 + 8/12 = 12/12
The boys together cut 12/12, which is equivalent to the whole yard (1 whole).
Therefore, the statement "The boys cut almost the whole yard." (b) is true.
The Sweet Surprise Bake Shop sold slices of cake at the arts festival last weekend. Each cake was cut into eight slices. They sold 2 1/4
chocolate cakes, 2 1/2
red velvet cakes, 3/4
of a carrot cake and 3 1/2
sugar cream cakes.
Which statement tells the total number of cakes they sold and explains how the total can be calculated?
(1 point)
-
To calculate the total number of cakes sold, we need to add the number of each type of cake sold together.
2 1/4 chocolate cakes can be represented as a mixed number: 2 + 1/4 = 2 1/4 (or 9/4)
2 1/2 red velvet cakes can also be represented as a mixed number: 2 + 1/2 = 2 1/2 (or 5/2)
3/4 of a carrot cake can be represented as a fraction: 3/4
3 1/2 sugar cream cakes can be represented as a mixed number: 3 + 1/2 = 3 1/2 (or 7/2)
To find the total number of cakes sold, we add these quantities together:
2 1/4 + 2 1/2 + 3/4 + 3 1/2 = 9 + 5/4 + 3/4 + 7/2
We can convert the mixed numbers to improper fractions:
9 + 5/4 + 3/4 + 7/2 = 9 + 5/4 + 3/4 + 14/4
Next, we add the fractions with a common denominator:
9 + 5/4 + 3/4 + 14/4 = 9 + (5 + 3 + 14)/4 = 9 + 22/4
Finally, we simplify the fraction:
9 + 22/4 = 9 + 11/2 = 18/2 + 11/2 = 29/2
So, the total number of cakes sold is 29/2, which can also be expressed as 14 1/2.
Therefore, the statement that tells the total number of cakes sold is: "They sold a total of 14 1/2 cakes, which can be calculated by adding the quantities of each type of cake sold."
The Sweet Surprise Bake Shop sold slices of cake at the arts festival last weekend. Each cake was cut into eight slices. They sold 2 1/4
chocolate cakes, 2 1/2
red velvet cakes, 3/4
of a carrot cake and 3 1/2
sugar cream cakes.
Which statement tells the total number of cakes they sold and explains how the total can be calculated?
(1 point)
A. First, find the least common multiple and change only the denominators: 2 1/4 + 2 1/4 + 3/4 + 3 1/4 = 764
. Next, simplify: 7 6/4 = 8 1/2
.
B. First, change the fractions to make denominators common, and then add: 2 1/4 + 2 2/4 + 3/4 + 3 2/4 = 7 8/4
. Next, simplify: 7 8/4 = 9
.
C. First, add across the numerators and denominators: 1/4 + 1/2 + 3/4 + 1/2 = 6 1/2
. Next, add whole numbers: 2 + 2 + 3 = 7. Then combine, 7 6/12= 7/12
.
D. First, change the numerators to 3 to make them common, and then add: 2 3/4 + 2 3/2 + 3/4 + 3 3/4= 7 12/14
. Next, simplify: 7 12/14=7 6/7
.
.
. . . . . .
. [ a n s w e r ] . . .
.
The correct statement that tells the total number of cakes they sold and explains how the total can be calculated is:
B. First, change the fractions to make denominators common, and then add: 2 1/4 + 2 2/4 + 3/4 + 3 2/4 = 7 8/4. Next, simplify: 7 8/4 = 9.
Explanation:
In this statement, we correctly add the quantities of each type of cake sold after adjusting the fractions to have a common denominator of 4. By doing so, we can add the whole numbers (2 + 2 + 3) and the fractions (1/4 + 2/4 + 3/4 + 2/4) separately. This yields 9 as the total number of cakes sold.
Mrs. Taylor is crocheting a blanket for her daughter. She made 3/8
of the blanket green, 1/4
of the blanket blue, and the rest of the blanket was yellow. Which fraction represents the yellow part of the blanket?
A. 5/8
B. 3/4
C. 1/2
D. 3/8
. . . [ a n s w e r ] . . .
To find the fraction that represents the yellow part of the blanket, we can subtract the fractions representing the green and blue parts from 1 (or the whole).
Given that 3/8 of the blanket is green and 1/4 of the blanket is blue, we can represent the yellow part as 1 - (3/8 + 1/4).
To simplify this, we need to find a common denominator for 8 and 4, which is 8.
Now we can rewrite 1 as 8/8.
Therefore, 1 - (3/8 + 1/4) = 8/8 - (3/8 + 2/8) = 8/8 - 5/8 = 3/8.
Hence, the correct answer is:
D. 3/8
For Aliyah’s graduation party, her mom made her a chocolate cake. Her siblings ate 1/4
of the cake, and her friends ate 2/3 of the cake. How much of the cake was left?
(1 point)
A. 1/12
B. 5/6
C.1/2
D. 3/4
To find out how much of the cake is left, we need to subtract the fractions representing the portions eaten by Aliyah's siblings and friends from 1 (or the whole cake).
Given that Aliyah's siblings ate 1/4 of the cake and her friends ate 2/3 of the cake, we can represent the remaining cake as 1 - (1/4 + 2/3).
To find a common denominator for 4 and 3, we can use 12.
Now we can rewrite 1 as 12/12.
Therefore, 1 - (1/4 + 2/3) = 12/12 - (3/12 + 8/12) = 12/12 - 11/12 = 1/12.
Hence, the correct answer is:
A. 1/12
-84 - (-45) = / / / / / /
To simplify the expression -84 - (-45), we can rewrite it as -84 + 45.
When we add a negative number, it is equivalent to subtracting the positive number.
So, -84 + 45 can be calculated as (-84) + (+45) which gives us -39.
Therefore, -84 - (-45) = -39.
QUESTION 14:
In the Manchester Building, the elevation of the basement floor is -16 ft. The elevation of the roof is 37 feet. What is the distance from the basement floor to the roof? (Hint: Draw a picture or a number line.)(1 point)
Responses
A 53
B -21
C 21
D -53
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
QUESTION 15:
-8.5 - (-3.7) = / / /??
A 4.8
B -4.8
C 12.2
D -12.2
For Question 14, to find the distance from the basement floor to the roof, we need to calculate the difference between the elevations of the roof and the basement floor.
Given that the elevation of the basement floor is -16 ft and the elevation of the roof is 37 ft, we can find the difference by subtracting -16 from 37.
37 - (-16) can be calculated as 37 + 16 which gives us 53.
Therefore, the distance from the basement floor to the roof is 53 ft.
The correct answer is:
A) 53.
-------------------------------------------------------
For Question 15, to solve -8.5 - (-3.7), we need to change the subtraction of a negative number to addition.
-8.5 - (-3.7) can be rewritten as -8.5 + 3.7.
Adding the two numbers, we have:
-8.5 + 3.7 = -4.8.
Therefore, -8.5 - (-3.7) equals -4.8.
The correct answer is:
B) -4.8.
~`Question 16`~
~ - - -. . . . . . . . .. o o o. . . . * . . `
~ 25 - ( - 80 ) =
a. 105
b. -55
c. 115
d. 565
~ question 17 ~
-18.5 - 17.5 = ?
a. -36
b. -1
c. 36
d. 1
~ questions 18 ~''
What is the change in temperature between −20°F and 30°F?
- my answer : -50 ]]]]
A. 10 °F
B. -50 °F
C. -10 °F
D. 50 °F
QUESTION 19- - - - - - - - -
The temperature was −5°F this morning. If the temperature dropped 8°F, what is the temperature now?
{MY ANSWER IS -13}
A 3 °F
B -13 °F
C -3 °F
D 13 °F
`
QUESTION 20.
A Navy submarine is 650 feet below sea level. If it ascends 200 feet, which integer represents its new position?(1 point)
Responses
A. 850
B. 450
C. -450
D. -850
QUESTIONS 21:
John threw a rock into a lake from a bridge 124 feet above the river's surface. The rock sinks 81 feet below the river’s surface. What is the distance between the elevations? (Hint: Draw a picture or use a number line.)(1 point)
Responses
205 feet
43 feet
-43 feet
-205 feet
Question 16:
To solve 25 - (-80), we can change the subtraction of a negative number to addition.
25 - (-80) can be rewritten as 25 + 80.
Adding the two numbers, we have:
25 + 80 = 105.
Therefore, 25 - (-80) equals 105.
The correct answer is:
a) 105.
Question 17:
To solve -18.5 - 17.5, we simply subtract the two numbers.
-18.5 - 17.5 = -36.
Therefore, the result is -36.
The correct answer is:
a) -36.
Question 18:
To find the change in temperature between -20°F and 30°F, we subtract the initial temperature (-20°F) from the final temperature (30°F).
30°F - (-20°F) = 30°F + 20°F = 50°F.
Therefore, the change in temperature is 50°F.
The correct answer is:
D) 50°F.
Question 19:
To find the new temperature after a drop of 8°F from -5°F, we subtract the drop from the initial temperature.
-5°F - 8°F = -13°F.
Therefore, the new temperature is -13°F.
The correct answer is:
B) -13°F.
Question 20:
Starting 650 feet below sea level, if the submarine ascends 200 feet, we calculate this by adding the ascent to the starting depth.
650 feet + 200 feet = 850 feet.
Therefore, the new position is 850 feet.
The correct answer is:
A) 850.
Question 21:
To find the distance between the elevations of the bridge and the river's surface, we need to subtract the depth below the surface from the height above the surface.
124 feet - 81 feet = 43 feet.
Therefore, the distance between the elevations is 43 feet.
The correct answer is:
b) 43 feet.