What is the average rate of change between the points (3, 9) and (5, 15)?

The distance from Durham to Cary on the second map is 75 km

The scale of the first map:

1 cm = 2 km

The scale of the second map:

1 cm = 5 km

Map scale: A distance on a map and its corresponding distance on the planet are related by a scale. The equivalent of a map scale can be expressed, typically using different units. or visually, using a bar scale.

Distance from Durham to Cary = 15 cm

Distance from Durham to Cary on the second map = Scale of the second map * Distance from Durham to Cary

= 5*15

= 75 km

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The formula for y in terms of x is y = [tex]\frac{16}{25} x^{3}[/tex]

Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.

Given that,

Y is inversely proportional to a³ When a = 2, y = 10

A is directly proportional to x when x = 4, a = 20

If y is inversely proportional to a³

[tex]\frac{y}{x^{3} }[/tex]∝1

y = [tex]\frac{k}{a^{3} }[/tex], where k is the proportionality constant

Given, a=2, y=10, then 10 = [tex]\frac{k}{2^{3} }[/tex]

k = 10 × 2³

k = 80

Substituting k = 80 back into the formula;

y = [tex]\frac{80}{a^{3} }[/tex]............. 1

Similarly, if a is directly proportional to x, then a ∝ x i.e a = kx

If x=4, a=20 then;

20 = 4k

k = [tex]\frac{20}{4}[/tex]

k = 5

Substituting k = 5 back into the formula;

a = 5x ....... 2

Substitute equation 2 into 1;

y = [tex]\frac{80}{a^{3} }[/tex]

y = [tex]\frac{80}{5x^{3} }[/tex]

y = [tex]\frac{80}{125x^{3} }[/tex]

y = [tex]\frac{16}{25x^{3} }[/tex]

Therefore, the formula for y in terms of x is y = [tex]\frac{16}{25} x^{3}[/tex]

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There are 2 numbers between 7 and 5 and 3 numbers between 5 and 2

TO KNOW HOW MANY WHOLE NUMBERS THERE ARE BETWEEN 121 AMD 176 WE CAN SIMPLY GET THEIR DIFFERENCE.

THE DIFFERENCE IS THE NUMBER OF WHOLE NUMBERS INBETWEEN 121 AND 176.

[tex] = 176 - 121 \\ = 55[/tex]

THERE ARE 55 WHOLE NUMBERS BETWEEN 121 AND 176.

Answer:

54

Step-by-step explanation:

Whole numbers are 0,1,2,3,...  Following that pattern forever.

Take a simpler example.  How many whole numbers between 2 and 5?  It would be just 3 numbers; 3 and 4.  

We could subtract 5-2 to get 3 and then subtract 1 more to get the answer of 3

What if I wanted to know the number of whole numbers between 3 and 7?

The numbers would be 4,5,6.

7-3 = 4 and then subtract 1 more to get the answer that there are 3 whole numbers between 3 and 7.

176 - 121 = 55 take one more away to get 54

For an equivalent expression for [tex]18^{-7}\\[/tex] * [tex]18^5\\[/tex] it is option 4 that is correct that means the equivalent expression can be seen as [tex]\frac{1}{18} ^{2}[/tex].

Expressions that can be considered are equivalent do the same thing even when they have distinct appearances. When we get to enter the same value(s) for the same variable, two algebraic expressions that are equivalent have the same value (s).

Calculating the equivalent expression,

[tex]18^{-7}\\[/tex] * [tex]18^5\\[/tex]

= [tex]18^{-7+5}[/tex]

=[tex]18^{-2}[/tex]

=  [tex]\frac{1}{18} ^{2}[/tex]

An expression that can be considered equivalent to another phrase but then differs in appearance is the one that has the same value or worth. In algebra, we can say 2(2x – 3y + 6) is equal to 4x -6y + 12 as an example of an equivalent expression.

When two expressions can be reduced to a single thread expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. You can also determine whether two expressions are equivalent.

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7x + 49 rewritten using common factor is 7(x + 7)

A common factor is a whole number which is a factor of two or more numbers.

In other words, common factors of two or more numbers are a number which divides each of the given numbers exactly.

For example the common factor of 24 and 36 are 1, 2, 3, 4, 6 and 12.

Therefore,

rewriting 7x + 49 using common factors is as follows:

7x + 49 = 7(x + 7 )

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Answer: 28.87 seconds

Step-by-step explanation:

Check attached image for explaination

The relationship between the distance that Justin runs, in kilometers, and the running time, in hours, is equal to d = (17 / 2) · t.

In this problem we find that the distance that Justin runs (d), in kilometers, is directly proportional to the running time (t), in hours. That is:

d ∝ t

d = k · t

Where:

If we know that d = 17 km and t = 2 h, then the relationship between distance and time is described below:

k = 17 km / 2 h

k = 17 / 2 km / h

d = (17 / 2) · t

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The function that represents the vertical stretch by a factor of 3 of f(x) is given as follows:

g(x) = 3x - 21.

Vertical stretches or compression to the graph of a function f(x) are applied by the multiplication of a constant a to the function, as follows:

g(x) = a x f(x).

Then the value of the constant determines if it is an stretch or a compression.

For this problem, we want a vertical stretch with a factor of 3, then the constant is given as follows:

a = 3.

Then the definition of function g(x) is given by:

g(x) = 3f(x)

g(x) = 3(x - 7)

g(x) = 3x - 21.

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The school uses a total of 23,080 pieces of paper in one year.

To calculate the total number of pieces of paper used by the school we use addition. We also use subtraction to find the pieces of blue paper and yellow paper.

As the pieces of blue paper are 3580 fewer than white paper, we find the pieces of blue paper by subtracting 3580 from 11,280.

blue paper = 11280 - 3580 = 7700

As the pieces of yellow paper are 3600 fewer than blue paper, we subtract 3600 from the total number of pieces of blue paper.

Yellow paper = 7700 - 3600 = 4100

Now, the total number of pieces can be found by the addition of white, blue, and yellow pieces of paper.

Total pieces = White papers + Blue papers + Yellow papers

Total pieces = 11,280 + 7700 + 4100

Total pieces = 23,080

Therefore, 23,080 pieces of paper were used by the school in one year.

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The expression represented by 50 added to half of a number, c is 50 + c/2

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

50 added to half of a number, c

half of a number, c means divide c by 2

So, we have

50 added to half of a number, c  => 50 added to c/2

Added to means +

So, we have

50 added to half of a number, c  => 50 + c/2

Hence, the expression represented by the statement is  50 + c/2

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Answer:

4 * 5 * 6 = 120  possible meals can we order.

Step-by-step explanation:

given that-

If you go to a restaurant and there are 4 choices for main dishes, 5 choices for sides, and 6 choices for drinks

4 * 5 * 6 = 120 combinations or Ways to Order

we can order the main dish in 4 different ways. Then, we can choices for sides in 5 different ways and the drinks in 6 different ways.

(The outcome of the selection of the first does not influence the second or third)

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the probability that at least 5 will do their homework on time in a class of 50 students is 0.1

How do you calculate probability?

Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes. Probability and odds are different concepts. Odds are the probability that something happens divided by the probability that it doesn't happen.

the probability that a randomly chosen student in a statistics class submits his/her homework on time is 0.06.

each student does homework independently.

in a statistics class of 50 students, what is the probability that at least 5 will do their homework on time?

probability = event occur/ total number of outcomes

                 = 5/50= 1/10=0.1

thus the probability becomes 0.1

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The relationship is that number sense can be used to solve area models or partial products.

Number sense refers to a set of important numerical skills. It includes the capacity to comprehend numbers and concepts such as more and less. Some people have a better sense of numbers than others.

Number sense is a set of abilities that enable humans to work with numbers. These abilities are essential for performing math as well as many other jobs.

In this case, partial products model of multiplication. This is a model which breaks numbers down into their factors. or place values in order to make multiplication easier. This depicts number sense.

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Answer:

A- 2/4

simplified-1/2

B- 3/5

C- 4/9

D-3/3 which=1

so basically D is 1

hope this helped

please mark as brainliest and have a good day!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Margaret invests $3,500 in a savings account that offers 5% simple interest per annum. So interest she will get after 8 years is

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

Given that :  Margaret invests $3,500 in a savings account that offers 5% simple interest per annum.

S.I = [tex]\frac{(P)(R)(T)}{100}[/tex]

P = $3,500

R=5%

T=8 years

S.I = [tex]\frac{(P)(R)(T)}{100}[/tex]

S.I = [tex]\frac{(3500)(5)(8)}{100}[/tex]

S.I = 1400

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The numerical value of x is 2 as segment AB equals segment BC.

A midpoint is simply a point that divides a line segment into two equal halves.

Given the data in the question;

Given that B is the midpoint of segment AC, this means that segment AB is equal to segment BC.

Hence

Segment AB = Segment BC

4x + 5 = 13

Solve for x

Subtract 5 from both sides

4x + 5 - 5 = 13 -5

4x = 8

Divide both sides by 4

4x/4 = 8/4

x = 8/4

x = 2

Therefore, the value of x is 2.

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The given graph represents a non-linear function.

Take two points in the graph and calculate the slope:

Slope of (-2,1) and (0,2) = (2-1)/(0-(-2) = 1/2

Slope of (2,1) and (0,2) = (2-1)/(0-2) = 1/(-2)

As the slope of the given graph is variable, it is a non-linear function.

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The solution in the given interval is x =6

A "equal to" symbol on both sides of an equation is not necessarily necessary for it to be balanced. It may also refer to a connection when two things are "not equal to," i.e., where one is better or worse than the other. Any relationship between two numbers or other mathematical expressions that leads to an unfair comparison is referred to in mathematics as an inequality. Certain algebraic mathematical expressions are known as inequalities.

Equation is :

[tex]x^{3} +2x^{2} -41x -25 =17\\x^{3} +2x^{2} -41x -42\\Put x =-1\\-1^{3} -2(-1)^{2} -41(-1) -42=0\\So, (-1) is the solution of the given equation and (x+1) must divide the equation so,\\\frac{x^{3} +2x^{2} -41x -42}{(x+1)} =x^{2} +x-42\\So we can write \\(x+1)(x^{2} +x-42)=0\\(x+1)(x^{2} +7x-6x-42)=0\\(x+1)(x-6)(x+7)=0\\So the solution of the equation are\\x_{1} =-1\\x_{2} =+6\\x_{3} =-7\\[/tex]

We need to find the integer solution in the interval 0≤x≤10

So total no. of solution in the given interval is 1

The solution in the given interval is x =6

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Answer:

x = 1/2, y = 4

Step-by-step explanation:

2x + 3y = 13----------> 2x + 3y = 13

4x - y = -2------------> 12x - 3y = -6

-----------------

14x = 7

x = 1/2, y = 4

See below for the pseudocode and the flowchart is added as an attachment

Flowcharts and pseudocodes are used as prototypes of actual programs.

Area of circle

The pseudocode is as follows:

Perimeter of rectangle

The pseudocode is as follows:

Perimeter of square

The pseudocode is as follows:

See attachment for the flowcharts

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Step-by-step explanation:

The answer is 8+2x . This is the correct answer .

SOLUTION:

Step 1:

In this question, we have the following question:

A rock is dropped from a height of 10 feet. The height of the rock is modeled by the graph shown.

Part A



​​What is the height of the rock 0.5 seconds after being dropped? The height of the rock 0.5 seconds after being dropped is ........... feet

6 .

Step 2:

Part B



To the nearest tenth of a second, how many seconds after being dropped does the rock hit the ground?The rock hits the ground approximately ...............................seconds after being dropped.

0.8



Answer:

cost per day = 2.99(c)+20
sam's lessons cost $30.47 per day

Step-by-step explanation:

2.99 (price of clay used per pound) * c (pounds of clay used) + 20 (cost of lesson)
2.99(c)+20
since sam uses 3.5 pounds of clay per lesson that's 2.99(3.5)+20, which is equal to 30.47

Answer:

It's the 3rd one

Step-by-step explanation:

2x7=14 7x4=28 7x6=42

Answer:

The third table, since x/y = 7.