what is the greatest common factor of 18 and 45

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.

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

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.

The number of nights studies in a month is 20.

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.

Learn more about fractions here:

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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.

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:

Therefore, 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.

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.

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.

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...

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.

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 range between these two distances is:

To 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.

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.

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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