1. Explain how you would model 5 x 2/3
2. When you multiply 2/3 by a fraction less than one, how does the product compare to the factors? Explain.
3. There is 5/6 of an apple pie left from dinner. Tomorrow, Victor plans to eat 1/6 of the pie that was left. How much of the whole pie will he eat tomorrow?
A. 1/36
B. 5/36
C. 1/3
D. 2/3
4. Matt made the model below to help him solve his math problem. Which of the expressions could he have been working out? (Yes, I made the model which emojis.)
Blue Heart: Green Square
Yellow Heart: Yellow Square
Broken Heart: Blank Square
A. 3/12 x 3/4
B. 3/4 x 3
C. 3/12 x 3/12
D. 1/3 x 3/4
5. If an angle measures 100 degrees, through what fraction of a circle does the angle turn?
A. 1/100
B. 1/4
C. 100/360
D. 1/2
Final answer:
To model 5 x 2/3, think of having 5 groups of 2/3 each. Multiplying 2/3 by a fraction less than one yields a smaller product. Victor will eat 5/36 of the whole apple pie, and an angle of 100 degrees represents 100/360 of a full circle.
Explanation:
To model 5 x 2/3, you can visualize having 5 groups of something, with each group containing 2/3 of that item. For example, if you have 5 pies, and you take 2/3 out of each pie, you would have a total of (5 x 2/3 = 10/3) pies.
When you multiply 2/3 by a fraction less than one, the product is smaller than the original fraction of 2/3 because you're effectively taking a portion of a portion, which reduces the overall size.
For the apple pie scenario, Victor plans to eat 1/6 of the 5/6 of a pie that is left, so the amount he will eat is (5/6 x 1/6 = 5/36) of the whole pie, which means the correct answer is Option B, 5/36.
Without the visual model provided, it is challenging to determine exactly which expressions Matt could have been working out. However, if you can provide the model, the answer would depend on the relationship between the hearts, squares, and the blank squares in Matt's model.
An angle of 100 degrees represents 100/360 or roughly 5/18 of a full circle since a full circle has 360 degrees. Therefore, the answer is Option C, 100/360.
12% of 72 is what number?
Answer:
x = 8.64
Step-by-step explanation:
12% of 72 = (12/100) * 72/x
= 0.12 * 72
x = 8.64
8.64 is 12% of 72. Determining any kind of percentage will not be a challenge for anybody if the above procedure is followed step by step.
(I think you are in the same county like me. Is it Dadeschools in Miami. Oh and the the Chapter is Chapter 2 Lesson 3 "The Percent Proportion" right?....)
You must be a 12 Grader by now...
Jamal is planting seeds for garden nursery.he plants 9 seeds In each container.if Jamal has 296 seeds to plant ,about how many containers will use?
estimate then find the product 48x38
-5 1/3 divided by 2 3/4 in fraction form
$4.30 markup, 40% discount, 6% tax
Jordan has 4/5 as many DVDs as Joseph. If Jordan has 56 DVDs, then how many does joseph have?
A family is tracking its spending habits. Over the past year, the grocery bill has ranged from $110 to $170.
Suppose you were going to plot these points on a coordinate grid.
(a) What is a good scale to use for the y-axis? Explain your reasoning.
(b) What is a good interval to use for the y-axis? Explain your reasoning.
Answer:
A. $10
B. 12 points
Step-by-step explanation:
Let, the x-axis represents the number of months and y-axis represents the money for the grocery.
Now, as we have the range of the grocery bills from $110 to $170.
Thus, taking the scale of $10 on y-axis will give us 7 intervals in which the changes in the grocery bills can be viewed.
Hence, a scale of $10 is a good scale.
Further, as y-axis represents the number of months. Thus, taking 12 months will be sufficient to plot the graph and show the changes in the grocery bills.
Hence, 12 points representing months are sufficient.
3p-4=8and 2p=4 is it equivalent
Chris wants to leave a 15% tip on the price of the food, calculated before sales tax. What is the maximum cost of food the group can order and not go over $63? Help Please
A certain TV can be purchased from the manufacturer for $160. A certain online retailer has a standard markup of 30%, and a certain superstore has a standard markup of 40%.
(a) What is the price of the TV when purchased online? What is the price of the TV when purchased at the superstore?
(b) What is the difference between the prices in Part (a)? How does this relate to the difference in the markup?
Answer:
The price of the TV purchased online is $208
The price of the TV purchased at the superstore is $224
Explanation
To solve this, we are going to use the markup formula solved for price:
[tex]Price=markup*cost+cost[/tex]
where
[tex]markup[/tex] is expressed in decimal form
- For the online retailer:
We know that the the TV can be purchased from the manufacturer for $160, so [tex]cost=160[/tex]. We also know that its markup is 30%; to express the markup as a decimal, we just need to divide it by 100%, so [tex]markup=\frac{30}{100} =0.3[/tex]. Now we can replace the values in our formula to find the price of the TV at the online retailer:
[tex]Price=markup*cost+cost[/tex]
[tex]Price=0.3*160+160[/tex]
[tex]Price=48+160[/tex]
[tex]Price=208[/tex]
The price of the TV purchased online is $208
- For the superstore:
The cost is the same, so [tex]cost=160[/tex]. The markup this time is 40%, so [tex]markup=\frac{40}{100}=0.4[/tex]. Let's replace the values to find the price:
[tex]Price=0.4*160+160[/tex]
[tex]Price=64+160[/tex]
[tex]Price=224[/tex]
The price of the TV purchased at the superstore is $224
(b)Answer
The difference between the prices is $16
The difference relates to the markup in two ways:
- When the markup increases 10% (from 30% to 40%), the price of the TV increases by $16.
- When the markup increases 10% (from 30% to 40%), the price of the TV increases 7.7%.
Explanation
To find the difference of our prices, we just need to subtract the price of the TV purchased at the superstore from the price of the TV purchased online:
$224 - $208 = $16
Now, to find how much the cost increased when the markup increases from 30% to 40%, we are going to divide the result of the difference of the two prices by the price of the TV at the online retailer, and then multiply by 100%:
[tex]\frac{16}{208} *100=7.69[/tex]
Which rounds to 7.7%
We can conclude that when the markup increases 10% (from 30% to 40%), the price of the TV increases 7.7%.
We can also conclude that when the markup increases 10% (from 30% to 40%), the price of the TV increases by $16.
Answer:
a) The price online of the TV is 208$
And in the superstore, it is 224$
b) The difference between the prices is $16.
208 - 224 = 16
The market difference is related as follows:
When the markup increases by 10% (from 30% to 40%), the price of the TV increases by $16.
which parachute has a slower descent a red parachute that was 10 feet in 4 seconds or a blue parachute that falls 1
2 feet in 6 seconds
19.25 X 0.12=
please show work
Lilah completed the division problem below.
7.84 divided by 2
Select True or False for each statement.
A. The first step of the division is to multiply 7.84 and 2 by 10
B. The quotient will be a whole number.
C. The quotient multiplied by 2 will equal 7.84
D. The first digit of the quotient will be in the ones place.
E. The quotient will have two decimal places.
350 yards to 420 yards
The range from 350 yards to 420 yards is of 70 yards.
To understand the range from 350 yards to 420 yards, it is important to recognize that this involves simple subtraction and addition within a specific interval. The interval is calculated as follows:
The lower limit: 350 yardsThe upper limit: 420 yardsThe range between these two distances is:
Lower Limit: 350 yardsUpper Limit: 420 yardsTo find the difference, which represents the span or range between these two points, simply subtract the smaller number from the larger number:
420 yards - 350 yards = 70 yards
Thus, the range between 350 yards and 420 yards is a total of 70 yards.
Dominic, Ralf and Peter have just eaten a HUGE Christmas meal. Dominic now weighs half as much as Ralf, and Peter weighs three times as much as Dominic. Together they weigh 720 pounds. How much does Dominic weigh?
which is a solution of the inequality y < x - 8
A solution to the inequality 'y < x - 8' is any point where the y-value is less than the x-value minus 8. An example solution is the point (10, 1). To find all solutions, one would graph the boundary line y = x - 8 and shade the region below it, without including the line itself.
Explanation:The question 'which is a solution of the inequality y < x - 8' falls within the subject of Mathematics, specifically under the topic of inequalities in algebra. A solution to this inequality is any ordered pair (x, y) where the y-value is less than the x-value minus 8. For example, if x is 10, then y must be less than 2 to satisfy the inequality, such as the point (10, 1).
To visualize this, you would graph the line y = x - 8 and then shade the region below this line on a coordinate plane. The shaded region represents all the points where the y-coordinate is less than the x-coordinate minus 8, thus showing all the potential solutions to the inequality. Points on the boundary line are not included since the inequality is strictly less than, not less than or equal to.
Coach brown bought 6 basketballs for $16 each and 6 footballs for $24 each. The expression 6× 16+6×24 gives the total cost in dollars of the basketballs and footballs. Use the distributive property to write the expression another way. Then evaluate.
Nadia charges $6.50 an hour for babysitting. She babysits 16.50 hours the first week of the month and 22 hours the second week of the month.Suppose Nadia raises her rate by $0.65 an hour. How many hours would she need to work to earn the same amount of money she made in the first two weeks of the month?
Mr.Mason's height is at most 4 inches mire than twice his daughters height Mr.Mason's height is 70 inches.
Can someone help me out here . Thanks!
Kathleen studied 2/3 of the night's in the month. If the month has 30 days, how many nights did she study?
The number of nights studies in a month is 20.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Number of nights in a month = 30
The number of nights studied in a month.
= 2/3 x 20
= 2 x 10
= 20
Thus,
The number of nights is 20.
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A bakery used 475 pounds of apples to make 1000 apple tarts. each jar contains the same amount of apples. how many pounds of apples are used in each tart.
f(x)=x^2-x-1 , average rate of change of f over interval -1 greater than or equal to x less than or equal to 1
The average rate of change of the function f(x)=x^2-x-1 over the interval from -1 to 1 is calculated as the change in the function's values over the change in x, which results in -1.
Explanation:The average rate of change of a function f(x) over a given interval [a, b] is defined as the change in f(x) divided by the change in x. It is equal to the value of the function at point b minus the value of the function at point a, divided by (b-a).
For the function f(x)=x^2-x-1, we are given the interval from -1 to 1. In this case, a=-1 and b=1.
So first calculate f(a) and f(b), i.e., f(-1) = (-1)^2 -(-1)-1 = 1, and f(1) = (1)^2 -(1)-1 = -1.
Then, plug these values into the average rate of change formula, which gives us (-1-1) / (1 - (-1)) = -2 / 2 = -1. So the average rate of change of the function f over the interval from -1 to 1 is -1.
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list all of the factors of 72
A bathtub holds about 2 hectoliters of water. If 25 liters of water are let down the drain, how many liters of water are still in the bathtub?
Chelsea earns $30 per day plus $5 for every sale that she makes at her job. On thursday ,she wants to earn at least $60
What is another way to write 300+20+5
Gina hiked down a canyon and stopped each time she descended ½ mile to rest. She hiked a total of 4 sections. What is her overall change in elevation?
Yolanda and her 3 brothers shared a box of 156 toy dinosaurs. About how many Dino's did each child get?
Yolanda and her 3 brothers are sharing 156 toy dinosaurs. By dividing 156 by the total number of children, which is 4, we find that each child gets 39 toy dinosaurs.
Explanation:The question requires us to divide a certain number of items, specifically toy dinosaurs, equally among a group of children. Yolanda and her 3 brothers share a total of 156 toy dinosaurs. To find out how many dinosaurs each child gets, we need to perform a simple division operation.
Since there are 4 children in total (Yolanda plus her 3 brothers), we divide the total number of toy dinosaurs by 4:
156 toy dinosaurs ÷ 4 children = 39 toy dinosaurs per childTherefore, each child would receive approximately 39 toy dinosaurs.
Final answer:
To determine how many toy dinosaurs each child receives, divide 156 (the total number of dinosaurs) by 4 (the number of children), resulting in 39 dinosaurs per child.
Explanation:
The subject of this question is Mathematics, and it belongs to the Middle School grade level. The question involves dividing a set of items equally among a group of children, which is a basic arithmetic problem.
Yolanda and her 3 brothers together make a group of 4 children. To find out how many toy dinosaurs each child gets, we divide the total number of toy dinosaurs by the number of children:
Total number of toy dinosaurs: 156
Number of children: 4
Number of dinosaurs per child = 156 ÷ 4
= 39
So, each child would receive approximately 39 toy dinosaurs.