HOW TO DETERMINE THE ANSWER?

The average rate of change of the function f(x) on the interval −9≤x≤1 is of:

r = -0.2.

The average rate of change of a function is obtained by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given by the equation presented as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

Over the interval −9≤x≤1, the bounds of the interval are given as follows:

a = -9, b = 1.

From the graph shown by the image presented at the end of the answer, the numeric value of the function at each of these bounds is given as follows:

Hence the average rate of change of the function on the interval is calculated as follows:

r = (1 - 3)/(1 - (-9)) = -2/10 = -0.2.

The graph is shown by the image at the end of the answer.

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Answer:

40/9

Step-by-step explanation:

The chicken breast being brought at store B is more expensive than store A as it costs $5.01 more per pound.

Given,

Violet was comparing the price of chicken breast at two stores.

The equation which represents the total cost, in dollars and cents, y, that it costs for x pounds of the chicken breast at Super grocery B is:

y = 11.38x

whereas at store A the chicken breast of 3 pounds costs $19.11.

we are asked to determine how expensive is it per pound to buy chicken breast at store B than store A.

⇒ at store B the total cost is:

y = 11.38x

check the total cost of 3 pounds of chicken breast at store B:

⇒ y = 11.38(3)

since x represents the number of pounds.

⇒ y = $34.14

at store the chicken breast of 3 pounds costs $19.11

⇒ cost difference at both stores for simillar quantity:

⇒ 34.14 - 19.11

= 15.03

The cost of chicken per pound = 15.03/3

= $5.01

Hence the chicken breast at store B is $5.01 more expensive per pound than the chicken breast at store A.

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Answer:

if what I think you want is the number of bachelor degrees from from 1970 to 2014 for both men and women is then:

men: 617.6

women: 940.8

Step-by-step explanation:

from 1970 to 2014 it is 44 years so we plug 44 into x for both equations

Men:

y = 3.9(44) + 446

y = 171.6 + 446

y = 617.6

Women:

y = 14.2(44) + 316

y = 624.8 + 316

y = 940.8

The annual rainfall in 2016 is 336 mm.

Let the annual rainfall in 2016 be 100x mm.

Now it is given that rainfall in 2017 is 25% more than rainfall in 2016.

So. rainfall in 2017 is = 100x + 100x*(25/100) = 100x+25x = 125x mm

Also given that the amount of rainfall in 2017 = 420 mm.

According to question the suitable equation is,

125x = 420

x = 420/125

x = 3.36

Hence the rainfall in 2016 is = 100x = 100*3.36 = 336 mm.

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Answer: Yes

Step-by-step explanation:

Yes, it is because if you multiply 2 and 5, you get 10. 2 and 5 LCM is also 10. If you check 2 and five multiples you see this is also proved true.

2 - 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 ...

5 - 5, 10, 15, 20 ...

Let the present age of student be x

Present of teacher will be 4x

After 20 years,

Age of student = x + 20

Age of teacher = 4x + 20

According to the given condition after 20 years,

x + 20 = (4x + 20)/2

x + 20 = 2x + 10

2x - x = 20 - 10

x = 10

So student's present age is 10 years while teacher's is 4 x 10 i.e 40 years.

Hope This Helps You!

Answer:

28

Step-by-step explanation:

Translate words into math -- "warmer" means +, "is" means =

So  D + 50 = 78
D = 78 - 50

D = 28

The ratio of cranberry juice to apple juice to orange juice in the fruit punch is  = 1 : 2 : 3

Let the total quantity of juice is 60 ml .

Now the apple juice is 1/3 of 60 = 20 ml

The orange juice is 1/2 of 60 = 30 ml

Therefore cranberry juice = 60 -(20+30) ml = 10 ml

Now the ratio of cranberry juice to apple juice to orange juice

= 10 : 20 : 30

= 1 : 2 : 3

We can exactly find out how much of one simple quantity is included in the other by simply comparing two amounts of the same units. Ratios can be divided into two smaller groups.

One is the part to the whole ratio; the other is the part to the part ratio. The exact relationship that is between the two distinct entities or groupings is only exactly depicted by the part-to-part ratio.

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The number of ways to split the integers, given the condition and using the Fundamental Counting Theorem, is of:

144.

It is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes considering all trials is calculated by the multiplication of the factorials as presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Given the condition that the greater number is at least 2 times the lesser number we have that the pairs are composed by one number between 1 and 7 and another number between 8 and 14.

Hence the pairs of each number are built as follows:

Hence the number of ways to split the numbers is:

2 x 3 x 4 x 3 x 2 = 144.

(the numbers were multiplied because of the Fundamental Counting Theorem).

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The value of g, for a  30-sided regular polygon has an angle measure represented as 6g° is calculated to be 28

The problem is solved using the formula for number of angles for n sided polygon

The formula is (n - 2)180

where n = number of sides

for 30-sided polygon the angles is solved as below

= (n - 2)180

= ( 30 - 2 ) * 180

= 28 * 180

= 5040

this is represented as 6g

each angle is measured 5040 / 30 = 168

6g = 168

g = 28

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Answer: 28

Step-by-step explanation: 168 is the whole polygon, so 6 times 28 is 168 therefore its correct, btw i also did the test

The equation of the line d that is parallel to line c is y = -5x + 4.

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, c has an equation y = -5x + 3. Line d is parallel to line c. Therefore, they have the same slopes. Parallel lines have the same slope.

Hence, let's find the equation of line d passing through (2, -6)

Let's find the y-intercept

-6 = -5(2) + b

-6  = -10 + b

b = -6 + 10

b = 4

Therefore, the equation of the line d is y = -5x + 4

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Answer:40%

Step-by-step explanation:

Answer: you prob fininshed 5,3

Step-by-step explanation:

also this is easy im srry for doing this

Answer:(-7, infinite down)

Step-by-step explanation: -7,-8,-9...

8 pants wil cost 192 u.m.

10 pants ----> 240u.m

8 pants  ----> x

In a rule of 3, whenever the x is located at the bottom right corner, you always have to multiply upwards and to the right, and then divide the resulting number by the number on the top left. This is the operation you need to make:

x= (8 x 240) / 10

x= 192

Check the attached image to get a better understanding of this process.

8 pants wil cost 192 u.m.

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Proportional quantities are divided into directly and inversely proportional.

Two magnitudes are said to be directly proportional

when we multiply one of them by a number, the other is multiplied by the same number, and when we divide one of them by a number, the other is divided by the same number.

Problem :

If 10 pants cost 240u.m, how much will 8 pants cost?

We have:

[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \\ \bold{ Assumption \: { \rightarrow} 10 \: pants \: \rightarrow 240 \: u.m\\\sf \: \: \: \: \: \: \: \: \: Question \rightarrow8 \: pants \rightarrow \: x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

As can be seen, the number of pants and the cost are magnitudes directly proportional, and therefore, we put the + sign below the pants and the - sign above.

Therefore we will have:

[tex]\boxed{ \bold{ \: x = \dfrac{240 * 8}{10} = 192 \: u.m} }[/tex]

So the 8 pants cost 192.

A real world situation that could be modeled by the expression, 300+7x is that Bob bought goods for $300 and then bought 6 pens that cost x dollar each.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both

In this case, Bob bought goods for $300 and then bought 6 pens that cost x dollar each. The total cost will be:

= 300 + (7 × x)

= 300 + 7x

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Answer:

30%

Step-by-step explanation:

130980-91686=39294

39294/130908=0.3

Answer: 168,609 ton

Hi, to answer this question, first we have to calculate the amount of the weight decrease by multiplying the original weight of the goods (240,870) by the percentage decrease in decimal form ( divided by 100)

Mathematically speaking:

240,870 (30/100) =72,261 ton

Finally we have to subtract that value to the original weight:

240,870-72,261 = 168,609 ton

Feel free to ask for more if needed or if you did not understand something.  

Step-by-step explanation:

Answer:

Let the girls be x

then, 5:4 = 5x and 4x

,

total stud.=36 so,

5x+4x=36

9x=36

x=36÷9

hence

x=4

now, boys = 5x=5×4=20

girls= 4x=4×4=16

so there are 16 girls

Answer: 35

Step-by-step explanation:

[tex]f(4)=7(4+2)-7\\\\f(4)=7(6)-7\\\\f(4)=7(5)\\\\f(4)=35[/tex]

Answer: All Are correct

Step-by-step explanation:

Look at graph, the vertex hits the origin, the parent function is on the top half of the graph (quads 1 and 2), both the left and right side have a slope of 1, and it is v shaped!

The time that would be taken for the money to double is 9 years.

Given that a compound interest has to do with the type of interest that is charged both on the principal and on the interest. We know that the principal is the money that was invested.

Let the principal be P and let the time taken be t. Let us now apply the formula;

A = P(1 + r)^n

Where A = 2P and r = 0.08

2P = P(1 + 0.08)^n

2P/P = (1.08)^n

2 = (1.08)^n

ln2 = nln1.08

n = ln2/ln1.08

n = 0.693/0.077

n = 9

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The equation that models the height of the plant H in terms of number of days is H = 1.875+0.125d and the height of the plant after 15 days is 3.75 inches.

According to the question,

We have the following information:

Initially the plant was 2 inches tall and it grew at an average rate of change of 0.125 inches per day.

2, 2.125, ...

Now, this series will become an arithmetic progression.

Formula to find the nth term:

an = a+(n-1)d

H = 2+(d-1)0.125

H = 1.875+0.125d

Now, the height after 15 days will be:

H = 1.875+0.125*15

H = 1.875+1.875

H = 3.75 inches

Hence, the equation that models the height of the plant H in terms of number of days is H = 1.875+0.125d and the height of the plant after 15 days is 3.75 inches.

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Answer:

[tex]250\pi[/tex] cm³

Step-by-step explanation:

If the radius is 20 cm, the diameter is 10 cm.

Thus, the volume is [tex]\pi(10^2)(25)=250\pi[/tex] cm³.

Answer:

The answer to the question is B or 8

Step-by-step explanation:

this is because ther is 3x meaning three time what ever the answer is and because 8x3=24 it is equal to 24 so 24 is less than or equal to 24 hence the corr6 answer is 8.

Answer:

the answer is 8

Answer:r

Step-by-step explanation:r

Answer:

Slope = -3/4, y-intercept = -4

Step-by-step explanation:

[tex]6x+8y=-32 \\ \\ 3x+4y=-16 \\ \\ 4y=-3x-16 \\ \\ y=-\frac{3}{4}x-4[/tex]

So, the slope is -3/4 and the y-intercept is -4.

Answer:

-30

Step-by-step explanation:

the order of multiplication doesn't matter

a*b*c = 5*-2*3 = -30

A 270° counterclockwise rotation about the origin is the different one

Rotation simply means turning

In order to answer this question, you need to know some rules about rotation. They are as follows:

1. If a point P, whose position vector is (x,y), is rotated 90° counterclockwise rotation about the origin, the position of the image P' is (-y, x)

2. If a point P, whose position vector is (x,y), is rotated  270° clockwise rotation about the origin, the position of the image P' is (-y, x). This is the same number 1

3. A 90° leftward rotation about the origin is the same as a 90° counterclockwise rotation about the origin. This is the same with number 1

4.  If a point P, whose position vector is (x,y), is rotated  270° counterclockwise rotation about the origin, the position of the image P' is (y, -x). This is different from the other three.

From the graph: A(1, 2), B(2, 4), C(4, 2)

Answer for the different question: A'(2, -1), B'(4, -2), C'(2, -4)

Answer for the same three question: A'(-2, 1), B'(-4, 2), C'(-2, 4)

Therefore, a 270° counterclockwise rotation about the origin is the different one. The 4th option is the answer

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