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The average rates of change of a function f(x) and g(x) are their slopes

The average rate of change of the function f(x) is always less than the average rate of change of the function g(x)

The average rate of change of a function f(x) over the interval [a,b] is calculated as:

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

The average rates of change of the functions over the intervals are:

A. 0 ≤ x ≤ 3

[tex]m_1 = \frac{f(3) - f(0)}{3 - 0} = \frac{5 * 3 - 5 *0}{3 - 0} = 5[/tex] ---- f(x)

[tex]m_2 = \frac{g(3) - g(0)}{3 - 0} = \frac{25 * 3 - 25 *0}{3 - 0} = 25[/tex] --- g(x)

B. 0 ≤ x ≤ 2

[tex]m_1 = \frac{f(2) - f(0)}{2 - 0} = \frac{5 * 2 - 5 *0}{2 - 0} = 5[/tex] ---- f(x)

[tex]m_2 = \frac{g(2) - g(0)}{2 - 0} = \frac{25 * 2 - 25 *0}{2 - 0} = 25[/tex] --- g(x)

C. 3 ≤ x ≤ 6

[tex]m_1 = \frac{f(6) - f(3)}{6 - 3} = \frac{5 * 6 - 5 *3}{6 - 3} = 5[/tex] ---- f(x)

[tex]m_2 = \frac{g(6) - g(3)}{6 - 3} = \frac{25 * 6 - 25 *3}{6 - 3} = 25[/tex] --- g(x)

D. 1 ≤ x ≤ 2

[tex]m_1 = \frac{f(2) - f(1)}{2 - 1} = \frac{5 * 2 - 5 *1}{2 - 1} = 5[/tex] ---- f(x)

[tex]m_2 = \frac{g(2) - g(1)}{2 - 1} = \frac{25 * 2 - 25 *1}{2 - 1} = 25[/tex] --- g(x)

From the above computation, we can see that:

The average rate of change of the function f(x) = 5x is always less than the average rate of change of the function g(x) = 25x

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Answer:

  (c)  $80

Step-by-step explanation:

Each discounted price corresponds to the original price multiplied by a factor related to the discount. For a discount fraction of 'd', the multiplier is (1 -d).

This means you can use any of the lines in the table to find the original price.

  5% disount: (1 -5%)·p = $76 . . . . where p is the original price

     p = $76/0.95 = $80 . . . . . . . the original price

  10% discount: (1 -10%)·p = $72

     p = $72/0.90 = $80

  25% discount: (1 -25%)·p = $60

     p = $60/0.75 = $80

_____

Additional comment

The table values for 5% and 10% differ by 5% and $4. That means 5% of the original price is $4. There are two things you can do with this:

Step-by-step explanation:

Given:

32^(1/6)

To Find:

Convert to Radical form 32^(1/6)?

Solution:

here, given that- 321/6

Since, we know that - If n is a positive integer

that x and a is a real number or a factor, then

an = Vu?

=

now, using this rule to convert 321/6 to a radical,

where a=32, x=1 and n=6

√32

Hence,

Exact form:

32

Decimal Form:

2

Answer:

In geometry, a vertex form is a point where two or more curves, lines, or edges meet.

Step-by-step explanation:

this equation is stander form

Answer:

271.2 meters

Step-by-step explanation:

See attached image.

The value of [tex]cot\theta[/tex] when [tex]tan\theta =\frac{11}{60}[/tex] comes to be [tex]\frac{60}{11}[/tex].

Given that trigonometric ratio:

[tex]tan\theta = \frac{11}{60}[/tex]

The tangent of an angle is the ratio of the opposite side(to that angle) to the adjacent side(to that angle).

So, for the given problem

Opposite side to [tex]\theta[/tex] = 11

Adjacent side to [tex]\theta[/tex] = 60

So, [tex]cot \theta =\frac{AdjacentSide }{OppositeSide}[/tex]

[tex]cot\theta =\frac{60}{11}[/tex]

Therefore, the value of [tex]cot\theta[/tex] when [tex]tan\theta =\frac{11}{60}[/tex] comes to be [tex]\frac{60}{11}[/tex].

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Answer:

60/11 is correct (option c)

Step-by-step explanation:

I just took the test

Answer:

Runner A is more consistent as all of the dots are close to the line unlike Runner B or C

The total amount accrued, principal plus interest, with compound interest on a principal of $500.00 at a rate of 8% per year compounded 1 times per year over 16 years is $1,712.97.

Given Data

A = P + I where

P (principal) = $500.00

I (interest) = $1,212.97

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 8/100

r = 0.08 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 500.00(1 + 0.08/1)^(1)(16)

A = 500.00(1 + 0.08)6(16)

A = $1,712.97

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Answer: 81

Step-by-step explanation:

90% is the same as 0.9

We can multiply .9 by 90 to see how many students are enrolled in health

0.9×90=81.0

Answer:

[tex]\huge\boxed{\sf 81\ students }[/tex]

Step-by-step explanation:

Total students = 90

Enrolled in health:

= 90 % of 90

[Key: "of" means "to multiply" and "%" means "out of hundred"]

[tex]\displaystyle = \frac{90}{100} \times 90\\\\= 9 \times 9\\\\= 81[/tex]

So, 81 students are enrolled in health.

[tex]\rule[225]{225}{2}[/tex]

Probability helps us to know the chances of an event occurring. The probability distribution of a girl child being born can be drawn as given below.

The probability helps us to know the chances of an event occurring.

[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

As it is given to us that the possible genders of the children,

S = {BB, BG, GB, GG},

And we know that the probability of a girl child can be found using the formula of probability, now, finding the probability of the girl child,

A.) The probability that there is no girl child born,

[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\\\\[/tex]

[tex]\rm P(X=0)=\dfrac{\text{Outcomes in which no girl child is born}}{\text{All the possible values}}[/tex]

[tex]\rm P(X=0)=\dfrac{1}{4} = 0.25[/tex]

B.) The probability that there is one girl child is born,

[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\\\\[/tex]

[tex]\rm P(X=1)=\dfrac{\text{Outcomes in which one girl child is born}}{\text{All the possible values}}[/tex]

[tex]\rm P(X=1)=\dfrac{2}{4} = 0.5[/tex]

C.) The probability that there is two girl child is born,

[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\\\\[/tex]

[tex]\rm P(X=2)=\dfrac{\text{Outcomes in which two girl child is born}}{\text{All the possible values}}[/tex]

[tex]\rm P(X=2)=\dfrac{1}{4} = 0.25[/tex]

The probability distribution of a girl child being born can be drawn as given below.

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Answer:A

Step-by-step explanation:

Answer:

42°

Step-by-step explanation:

∠NML = ∠ZYX =88°

Angles in a triangle add up to 180 so ∠ZXY =

180 - (50+88)

180-138

42

∠ZXY = 42°

Answer:

42.25π cm²

Step-by-step explanation:

To find the area of the circle, first find its radius.

Formulas needed

Given: circumference= 13π cm

2πr= 13π

Divide both sides by 2π:

[tex]r = \frac{13}{2} [/tex]

r= 6.5 cm

Now, we can find the area by substituting r= 6.5 into the area of circle formula.

Area of circle

= πr²

= π(6.5)²

= 42.25π cm²

Answer:

0.018

Step-by-step explanation

6,100,9a-mo,0.018

Answer:

A: (x-4) squared

B: x+2

C: 9

D: 14

E: 7

F: 2

Step-by-step explanation:

A: This is because x^2 - 8x + 16 factored is (x-4) squared

B: Square root of something squared will remove the square root

C: Minus the variable x and 2 from the right side

D: Factor

E/F: These numbers make the right side become zero

The composite figure can be decomposed to two semicircles and a rectangle so as to find the area.

Area is the amount of space occupied by a two dimensional shape or object.

The area of a composite figure can be decomposed to smaller figures so as to find the area.

The composite figure can be decomposed to two semicircles and a rectangle so as to find the area.

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Answer:

A. as two semicircles and a rectangle

Step-by-step explanation:

i did it

Step-by-step explanation:

y+2=3(x-7)

y+2=3x-21

y=3x-21-2

y= 3x-23

Slope is 3

Answer:

Slope intercept form;

y = mx + b

Where y is the independent variable, and x is the dependent variable, 'm' represents the slope and 'b' represents the y intercept.

We are given;

y + 2 =3(x - 7)

So we rearrange this into slope intercept form.

y + 2 = 3(x - 7)

Simplify:

y + 2 = 3x - 21

Apply inverse operation of addition (subtraction).

-2           -2

y = 3x - 23

Answer:

(3 x 1) x 4 = 12

[tex]-\frac{62}{9}[/tex]

The properties of equality state that you are allowed to perform operations on an equation as long as the operations are done equally on both sides.

Solving the Equation

First, rewrite the equation

Next, apply the addition property of equality and add 17 to both sides

Finally, apply the division property of equality and divide both sides by -18

Then, simplify for the final answer (divide numerator and denominator by 2)

Answer:

don't know if this is the right way butttt i'm going to give it a shot

Step-by-step explanation:

Cost: I'm guessing this is for the rent for the shoes or is the total cost?

Bowler World: 5 + 1.1g = c | c + 1.1g = t {(this is the other option) probs not correct}

Lucky Spares: 3 + 1.5g = c | c + 1.5g = t

K so personally you should choose option 1 (for example: 5 + 1.1g = c), i have no idea how the proper format is supposed to be

either i hope this helps :)

Answer:

angle d = 106

Answer:

16 pencils and 17 glue sticks

Step-by-step explanation:

X=pencils

Y=glue sticks

X+Y=33

1.50X+2Y=58

times ten to get whole numbers

=15X+20Y=580

same for e1

=10X+10Y=330

15X+20Y=580

10X+10Y=330

elimination mthd

150X+200Y=5800

150X+150Y=4950

50Y= 850

Y=17

X+17=33

X=33-17

X=16

Answer:

1/5

Step-by-step explanation:

a=225

45/225=1/5

The formula for GP is Tn=ar^n-1

Answer: Here, this should help ya out :

With graphing lines and slopes use desmos graphing calulator dont worry, its safe ;)

Answer:

See below ↓

Step-by-step explanation:

Step 1 : Mark the y-intercept.

Step 2 : Draw the slope.

1/18

Step-by-step explanation:

[tex] \frac{1}{3} \times \frac{1}{6} = \frac{1}{18} [/tex]

Answer:

1/5

Step-by-step explanation:

16 out of the 20 times landed on heads, making 4/20 times it landed on tails.

16 divided by 20 is .8 which turns into 80%

100% - 80% = 20%

To simplify into a fraction:

80/100 is equivalent to 4/5 when divided by 20, leaving 1/5 to complete the fraction which later totals to 100%

Answer:

the answer is 1/2

Step-by-step explanation:

i just did it

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: ({4}^{2}) \star ( {2}^{9} ) = {2}^{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \: ({ {2}^{2}) }^{2} \star ( {2}^{9} ) = {2}^{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \: ({ {2}^{}) }^{4} \star ( {2}^{9} ) = {2}^{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \:2 {}^{4 + 9} = {2}^{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 4 + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 13[/tex]

hence, value of x is 13

[tex]➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖[/tex]

Answer:

x = 13

Step-by-step explanation:

[tex]\left(4^2\right)\left(2^9\right)=2^x[/tex]

[tex]\mathrm{multiply}[/tex]

[tex]4^2=16[/tex]

[tex]2^9=512[/tex]

[tex]16*512=8192[/tex]

[tex]8192=2^x[/tex]

[tex]\mathrm{Flip \;the \;equation}[/tex]

[tex]2x=8192[/tex]

[tex]log(2x)=log(8192)(Take \;log \;of\; both \;sides)[/tex]

[tex]x*(log(2))=log(8192)[/tex]

[tex]x=\frac{log(8192)}{log(2)}[/tex]

[tex]x=13[/tex]

[RevyBreeze]

Answer:

Step-by-step explanation:

X1=-4

Y1=7

X2=-3

Y2=6

(-2,0 ) X INTERCEPT

(0,-7)Y INTERCEPT OR B

M=6-7/-3+4

M=_1

Y=-1X+-7

The examples of geometric names include triangle, circle, square, rectangle, pentagon, etc.

Your information is incomplete as the shapes aren't given. Therefore, an overview will be given.

A geometric name is the name that is given to a shape. In this case, examples include  triangle, circle, square, rectangle, pentagon, etc.

Triangle has three sides. A square has four equal sides. A rectangle has opposite sides equal, etc

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