What is the greatest common factor of 15 and 20?

Answer: The answer is A- Function 1, because its rate of change is 2.

Answer:

93 students

Step-by-step explanation:

We need to calculate the 30% of 310 students.

We can calculate with a direct rule of 3. If the 100% is 310 students, how many students are the 30%?

[tex]100 -\!\!\!-\!\!\!- \text{310 students}\\ 30 -\!\!\!-\!\!\!- \text{x students}[/tex]

We use the formula of the direct rule of 3:

[tex]x = \frac {30 * 310}{100} \\ \\ x = \frac {9,300}{100}\\[/tex]

x = 93

93 students play an instrument at Southside Middle School.

The manager purchased 13 coffee mugs.

To find the number of coffee mugs purchased, we can set up a system of equations. Let's say the number of coffee mugs is represented by x and the number of key chains is represented by y. We have two pieces of information:

1. The total number of items purchased is 21: x + y = 21

2. The total cost of the purchase is $132.50: 8.50x + 2.75y = 132.50

Now we can solve this system of equations to find the value of x, which represents the number of coffee mugs:

Multiplying the first equation by 8.50, we get: 8.50x + 8.50y = 178.50

Subtracting the second equation from this new equation, we get: 8.50x + 8.50y - 8.50x - 2.75y = 178.50 - 132.50

Simplifying, we have: 5.75y = 46

Dividing both sides of the equation by 5.75, we find: y = 8

Substituting this value into the first equation, we can solve for x: x + 8 = 21

x = 13

Therefore, the manager purchased 13 coffee mugs.

20000-5000=15000

15000/1250=12

it will take 12 hours

Solution: The  figure 1 shows the graph of the volume of water in the pool over the time from when the hose is placed into the pool until it is full.

Explanation:

It is given that the capacity of the pool is 20,000 gallon and initial water in the pool is 5000 gallons. The remaining capacity of the pool is 15,000 gallons.

The water in the pool increased at the rate of 1250 gallons per hour.

[tex]\frac{15000}{1250}=12[/tex]

So tank will be full after 12 hours.

The initial water in the pool is 5000 gallons and water in the pool increased at the rate of 1250 gallons per hour. So, the volume of water in the pool is described by the equation [tex]V=5000+1250t[/tex].

First we find the value of volume function in different value of t, then plot these points in a coordinate plane and join them with a straight line.

Hence, the coordinate table and graph of the volume function is given below.

Each length of the track practice will be 1.67 kilometers.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Marc is running 5 kilometers at track practice.

And, He decide to break the run into 3 equal lengths.

Now,

Since, Marc is running 5 kilometers at track practice.

And, He decide to break the run into 3 equal lengths

So, The length of each track practice = 5 / 3

                                                          = 1.67 kilometer

Thus, Each length of the track practice will be 1.67 kilometers.

Learn more about the divide visit:

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The money was in the account for 6 years.

To find the number of years the money was in the account, we can use the formula for simple interest: I = P * r * t, where I is the interest earned, P is the principal (initial amount), r is the interest rate, and t is the time in years. We are given that Deshawn earned $4485 in interest and the interest rate is 11.5%. Let's plug in these values and solve for t:

4485 = 6500 * 0.115 * t

Simplifying the equation gives us:

t = 4485 / (6500 * 0.115) ≈ 6.1337

Rounding to the nearest whole year, we can conclude that the money was in the account for 6 years.

Answer:

The rule representing the function is [tex]f(x)=(x+3)^2[/tex].

Step-by-step explanation:

We are given,

The ordered pairs for the function are (1, 16), (2, 25), (3, 36), (4, 49), and (5, 64).

It is required to find the rule representing the function.

Now, we see that,

[tex]16=(1+3)^2[/tex]

[tex]25=(2+3)^2[/tex]

[tex]36=(3+3)^2[/tex]

[tex]49=(4+3)^2[/tex]

[tex]64=(5+3)^2[/tex]

From the pattern,we get the function is [tex]f(x)=(x+3)^2[/tex].

Hence, the rule representing the function is [tex]f(x)=(x+3)^2[/tex].

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.