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The average rate of change of the function over the interval x = 0 to x = 4 is: 61/400.

Average rate of change = f(b) - f(a) / b - a

Given the function, f(x) = 2x - 1 / 3x + 5.

a = 0, f(a) = 2x - 1 / 3x + 5 = 2(0) - 1 / 3(0) + 5 = -1/5

b = 4, f(b) = 2x - 1 / 3x + 5 = 2(4) - 1 / 3(4) + 5 = 7/17

Average rate of change = 7/17 - (-1/5) / 4 - 0 = 61/400

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Answer:

Step-by-step explanation:

1. Circumference: 2(3.14)(4.2) = 26.38 in.

  Area: πr² = 3.14(4.2)² = 55.39 in.²

2. Circumference: 2(3.14)(1) = 6.28 m.

   Area: πr² = 3.14(1)² = 3.14 m.²

Hope this helps!

Answer:

3/8 cup of oil

Step-by-step explanation:

divide 1/4 by 2 to get how many are needed for 1/3 cup of water, and times 3 to find one cup of water.

Answer:

If this is your question: john and jack divided there math homework.John solved twice as many problems as jack plus 1 more problem how many problems did each boy solve if there are 28 assigned problems?

Answer:

John: 19

Jack: 9

Step-by-step explanation:

Hope it helps! God bless!

Answer:

4.8 years

Step-by-step explanation:

10 800 = 8000 e^(i t)        i = decimal interest per year     t = years

10800/8000 = e^(.0625 t)      ln both sides

.300 = .0625 t

t = 4.8 years

Answer:

8

Step-by-step explanation:

Concepts

The formula to find the slope of a line given two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. These points represent the x- and y-coordinates of the points.

Application

To find the slope of these points, we need to take two points and use the aforementioned formula. Let's take (0, 8), and (1, 16).

Solution

Therefore, the slope is 8.

Answer:

slope = 8

Step-by-step explanation:

Take 2 points from the given table:

[tex]\textsf{let}\:(x_1,y_1)=(0,8)[/tex]

[tex]\textsf{let}\:(x_2,y_2)=(-1,0)[/tex]

Use the slope formula to find the slope:

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-8}{-1-0}=\dfrac{-8}{-1}=8[/tex]

The probability of getting black crayons is 0.3, blue crayons 0.2, red crayons  0.25, yellow crayons 0.15, and white crayons 0.1.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

A box contains 6 black crayons, 4 blue crayons, 5 red crayons,3 yellow crayons, and 2 white crayons.

One crayon is chosen at random.

The total number of crayons = 20

The probability of getting black crayons

= 6/20

= 0.3

The probability of getting blue crayons

= 4/20

= 0.2

The probability of getting red crayons

= 5/20

= 0.25

The probability of getting yellow crayons

= 3/20

= 0.15

The probability of getting white crayons

= 2/20

= 0.1

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Answer:207

Step-by-step explanation:

First divide 72/8 to find how many photos the scanner scans per minute which is 9

Then you multiply 9 by 23 = 207

Answer:

19.00 x h + 25.00 =

What you make in a day if you work for h hours.

Step-by-step explanation:

You automatically make $25.00 when you show up.

So the equation is asking for how many hours. If you get $19 per hour

then it would be $19.00 x h (how many hours you worked) + $25.00.

Example:

If you worked for 5 hours and one day, then the equation would be

19.00 x 5= 95

95 + 25 (for showing up that day) = 120

So if you worked 5 hours for one day you would make 120

(This was just an example to further explain how the equation worked)

Hope this helped!

Have a great day!!

Answer: As a fraction it is 1/5 but as a percent 20%

Step-by-step explanation:

this is because 12/60=1/5 or 20%

answer is 20%

heres why

ok so if there is 60 balls all together out of all the color and you want to get a blue ball but the blue has less balls out of all the other colored balls so there is would be a less percent of getting a ball of that color out of 100%

you would need to take the blue color of balls and put in a fraction with the amount of balls together

so that would be 12/60

you half 12/60 and you would need to get the percent which is 20% so you have a 20% of getting a blue colored ball

Answer:1,024

Step-by-step explanation:

    We will use the formula hint it gives:

[tex]\displaystyle {1^{st}\;term} * \text{common ratio}\,^{(\text{desired term -1})}[/tex]

[tex]-1 * -4^{6-1}[/tex]

[tex]-1 * -4^{5}[/tex]

[tex]-1*-1,024[/tex]

[tex]1,024[/tex]

    The 6th term in the sequence is 1,024.

Answer:

114 laps

Step-by-step explanation:

Multiply 200 x 57% :

Answer:

x=-10

Step-by-step explanation:

2x²-7x=0+30

2x²-7x=30

4x-7x=30

-3x=30

x=-10

Answer:

Step-by-step explanation:

(2x + 5)(x - 6) = 0

2x + 5 = 0

x = -5/2

x - 6 = 0

x = 6

Answer:

0, 2/5, 1/6,-3/4,-7/10

Step-by-step explanation:

this is just what i think i didint understand the no spaces or no commas or negatives thing but here you go i hope its right

Answer:

normal

Step-by-step explanation:

Dot Product of Vectors

As the dot product of the vectors equals 0, the vectors are normal.

Answer:

1/15

Step-by-step explanation:

Total = 6 bottles

1 orange and apple

Without replacement:

P(orange and apple) = 1/6 x 1/5 = 1/15

Answer: Probability = 1/15

Answer:

[tex]\frac{31x-159}{168y}[/tex]

Step-by-step explanation:

[tex]\frac{x-4}{7y}[/tex] - [tex]\frac{x+7}{8y}[/tex] + [tex]\frac{x+3}{6y}[/tex]

the LCD of the denominators is 168y , then

[tex]\frac{24(x-4)-21(x+7)+28(x+3)}{168y}[/tex] ← distribute and simplify numerator

= [tex]\frac{24x-96-21y-147+28x+84}{168y}[/tex]

= [tex]\frac{31x-159}{168y}[/tex]

Answer:

[tex]\frac{31x - 159}{168y}[/tex]

Step-by-step explanation:

First we need to find a common denominator between 7y, 8y, and 6y. And the smallest common denominator is 336y, which I got by multiplying 7*8*6 and since they all share y, we can just keep the y without multiplying it.

Now, we need to multiply each fraction by the correct number on the top and bottom to reach 336. When we do this, we get [tex]\frac{x-4}{7y} (\frac{48}{48} ) - \frac{x+7}{8y}(\frac{42}{42}) + \frac{x+3}{6y}(\frac{56}{56})[/tex]. OMG. Well, now we need to expand the numerators...[tex]\frac{48x - 192}{336y} - \frac{42x + 294}{336y} + \frac{56x + 168}{336y} = \frac{62x - 318}{336y}[/tex]. Another OMG. But now we need to simplify...so we get [tex]\frac{31x - 159}{168y}[/tex]. Done.

Hope this helps! :)

Answer:

y = - 3x² + 6x + 9

Step-by-step explanation:

given the zeros of a parabola x = a , x = b , then the factors are

(x - a) , (x - b)

here the zeros are x = - 1 and x = 3 , then

factors are (x + 1) and (x - 3)

the equation of the parabola is then the product of the factors, that is

y = a(x + 1)(x - 3) ← a is a multiplier

to find a substitute the point (0, 9 ) into the equation

9 = a(0 + 1)(0 - 3) = a(1)(- 3) = - 3a ( divide both sides by - 3 )

- 3 = a

then equation is

y = - 3(x + 1)(x - 3) ← expand factors using FOIL

  = - 3(x² - 2x - 3) ← distribute parenthesis by - 3

y = - 3x² + 6x + 9

[tex]\sqrt[n]{3}[/tex] is 216−−−√3 radical: Yes because of the √

A radical in mathematics can be defined as the square root of a number. It can also be said to be the opposite of exponent.

The symbol of a radical is √ also known as the square root.

Radicals are really important in mathematics as they help us find the nth term of any number.

We can conclude by saying that 216−−−√3 is a  radical, because the radical sign is carried by 3.

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Julio's number is 3.

Algebra is a branch of mathematics that deals with symbols or variables and uses arithmetic operations (+, –, ×, ÷) to find the unknown quantities represented by these variables.

Let us consider the number is 'x'

Julio's number be,

-3(x-16)=69

x-16=-13

x= -13+16

x= 3

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Answer:

164 [tex]in^{2}[/tex]

Step-by-step explanation:

We find the areas of all the faces

30    [tex]in^{2}[/tex]

30[tex]in^{2}[/tex]

40[tex]in^{2}[/tex]

40[tex]in^{2}[/tex]

12[tex]in^{2}[/tex]

12[tex]in^{2}[/tex]

add them all up to get 164[tex]in^{2}[/tex]

:)

Answer:

3×9=27 the two numbers right to use is 2and7

Answer:

Hi! There are 3600 seconds in one hour.

Step-by-step explanation:

60 min. = one hour

60 seconds = one minute

:)

Expand the integrand:

[tex](2x - 3) (4x^2 + 1) = 8x^3 - 12x^2 + 2x - 3[/tex]

Then integrate using the power rule:

[tex]\displaystyle \int (8x^3-12x^2+2x-3) \, dx = 2x^4 - 4x^3 + x^2 - 3x + C[/tex]

By the fundamental theorem of calculus, the definite integral has a value of

[tex]\displaystyle \int_0^2 (2x-3)(4x^2+1) \, dx = \left(2x^4 - 4x^3 + x^2 - 3x\right)\bigg|_{x=2} - \left(2x^4 - 4x^3 + x^2 - 3x\right)\bigg|_{x=0}[/tex]

[tex]\displaystyle \int_0^2 (2x-3)(4x^2+1) \, dx = 32 - 32 + 4 - 6 = \boxed{-2}[/tex]

Answer:

D. 4/8

Step-by-step explanation:

To find probability, you simply divide what you are looking for over the total. In the word, ILLINOIS, you have 4 vowels, and 8 letters total, so the probability of finding a vowel would be 4/8.

The value of the definite integral corresponds to the total area of two triangles (see attached plot).

[tex]\displaystyle \int_{-4}^3 \left|\frac x2\right| \, dx = \dfrac12 \times 2 \times 4 + \dfrac12 \times 3 \times \dfrac32 = \boxed{\frac{25}4}[/tex]

Answer:

8

Step-by-step explanation:

Re-write the equation:

h(x) = x² * 2 - x² -7x

If X is equal to -8, then we can re-write the equation as:
h(-8) = (-8)² * 2 - (-8)² - 7(-8)

Following P.E.M.D.A.S. we must first solve for the exponents:

h(-8) = (64) * 2 - (64) - 7(-8)

Then we need to solve the multiplication.

h(-8) = (128) - (64) - (-56)

Now, we solve for the addition/subraction.

h(-8) = (128) - (120)

Lastly...

128 - 120 = 8

This means that if h(-8), then H = 8

I think?

Answer:48V/10

Step-by-step explanation:

I got it right from Khan Academy

To solve this problem, we have to understand and establish some basic mathematical facts on a cone.

The answer to this question are option b and c only.

This is a solid figure that has the base of a circle and the top is made up round triangle.

The formula of volume of a cone is given as

[tex]v = \frac{1}{3}\pi r^2 h[/tex]

where;

In the given question, the first fact given is if the radius doubles the diameter and that false.

[tex]diameter = 2 * radius[/tex]

If we have the value of the the radius, we can calculated the base area using area of a circle

[tex]area = \pi r^2[/tex]

The volume of a cone is actually one-third the volume of a cylinder

we can only calculate the volume of the cone is we have the value of the height of the cone.

The answer to this question are option b and c only.

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Answer:

B, C, D, E

Step-by-step explanation:

Got it wrong the first time.