AP Macroeconomics students were given an exam on a particular topic. Each week, they were tested with a comparable exam on the same topic and the average score for the class was measured. The function M (t) = 80 – 20log(t + 1) models the average score for the class after t weeks. How many weeks will it take for the average score of the class to equal 60?

A. 8 weeks
B. 9 weeks
C. 10 weeks
D. 11 weeks

Answer:

Step-by-step explanation:

The formula is the same almost as the previous question you posted.

You want to find the major arc. That's almost the whole circle. If it was the whole circle,  the formula would be 2 * pi * r

But we only want a part of it. Just how big is the angle we use in the formula?

A circle has 360 degrees to go around it. We've cut out a slice of it that is 30 degrees.

The remaining part is 360 - 30 = 330

Arc length = angle / 360  * 2 * pi * r

r = 3 m

Arc length = 330 / 360 * 2 * pi * 3

Arc length = 0.9167 * 6 * 3.14

Arc length = 17.27

   Sum of an arithmetic sequence is defined by the formula,

[tex]T_n=\frac{n}{2}[2a+(n-1)d][/tex]

Total length of the wooden boards will be [tex]14\frac{1}{6}[/tex] feet.

    It's given in the question,

Since, 1 inch = [tex]\frac{1}{12}[/tex] feet

Therefore, [tex]4[/tex] inch = [tex]\frac{4}{12}[/tex] feet

                             = [tex]\frac{1}{3}[/tex] feet

So, each stair is [tex]\frac{1}{3}[/tex] feet shorter than one below.

Now the sequence formed will be,

[tex]\frac{7}{2},[\frac{7}{2}-\frac{1}{3}],[\frac{7}{2}-\frac{2}{3}],......\frac{13}{6}[/tex]

[tex]\frac{21}{6},\frac{19}{6},\frac{17}{6}....\frac{13}{6}[/tex]

It's an Arithmetic sequence with common difference 'd' = [tex]-\frac{1}{3}[/tex] and first term 'a' = [tex]\frac{7}{2}[/tex] and nth term [tex]T_n=\frac{13}{6}[/tex]

If there are 'n' stairs, expression for the for the top stair of the arithmetic sequence will be,

[tex]T_n=a+(n-1)d[/tex]

[tex]\frac{13}{6}=\frac{21}{6}+(n-1)(-\frac{1}{3})[/tex]

[tex]\frac{13}{6}-\frac{21}{6}=-(n-1)\frac{1}{3}[/tex]

[tex]\frac{8}{6}=(n-1)\frac{1}{3}[/tex]

[tex]\frac{4}{3}=(n-1)\frac{1}{3}[/tex]

[tex](n-1)=4[/tex]

[tex]n=5[/tex]

Therefore, there are 5 stairs.

Now total length of the wooden boards = Sum of 5 terms of the sequence

                                                                    = [tex]\frac{n}{2}[2a+(n-1)(d)][/tex]

                                                                    = [tex]\frac{5}{2}[2(\frac{21}{6})+(5-1)(-\frac{1}{3})][/tex]

                                                                    = [tex]\frac{5}{2}[\frac{21}{3}-\frac{4}{3}][/tex]

                                                                    = [tex]\frac{17}{3}\times \frac{5}{2}[/tex]

                                                                    = [tex]\frac{85}{6}[/tex]

                                                                    = [tex]14\frac{1}{6}[/tex] ft

    Therefore, total length of the wooden boards will be [tex]14\frac{1}{6}[/tex] ft.

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Answer:

The Heaviest fish weigh 15.3(lb)

Step-by-step explanation:

14.9 +12.5+11.6+11.2+x/5=13.1

50.2+x/5=13.1

65/5=13

65.5/5=13.1

65.5 -50.2 = 15.3

Answer:

multiplicative inverse of 1/2 is 2

Answer:

30 feet

Step-by-step explanation:

I just took the quiz :)

Answer:

21cm

Step-by-step explanation:

for every 1m, it is 6cm on the paper. thus, your answer would be 3.5÷1 which is 3.5

then multiply 3.5 by 6 which is 21

Recall that the volume of a cube equals (side)^3. We can create an equation to model this.

1728 in^3 = (side)^3

We can get the cube root of both sides.

12 in = side

Each side is 12 inches long.

Answer:

7.5, 27, 51

Step-by-step explanation:

19.5 + 24 + 7.5 = 19.5 + 7.5 + 24 = 27 + 24 = 51

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

5(1+2x)= 5 +10x =10x + 5

Answer:

Yes, they are eqivelant.

Step-by-step explanation:

5(1+2x) and 10x+5

The first step is to set them equal to each other, to see if they are equivelent.

5(1+2x) = 10x+5

Distribute the 5 to both terms in the parentheses by multiplying.

5(1) + 5(2x) = 10x +5

5 + 10x = 10x +5

The communative property of addition proves that these are equal.

The answer is "[tex]\bold{x^3-4x^2-29x-24, y=x-3,\ and\ x=2}[/tex]" and following are the complete solution to the given parts:

For point A)[tex]\to \bold{f(x)=(x-8)(x+1)(x+3)=(x^2-7x-8)(x-8)=(x^3-4x^2-29x-24)}[/tex]For point B)

[tex]\to \bold{x^2-x-2=(x-2)(x+1)}\\\\\to \bold{g(x)=\frac{(x-8)(x+1)(x+3)}{(x-2)(x+1)}}[/tex]

When  [tex]x \neq -1[/tex] then  

[tex]\to \bold{g(x)=\frac{(x-8)(x+3)}{x-2}}\\\\\to \bold{\lim_{n \to \infty} \frac{g(x)}{x}}[/tex]

So  

For point C)

It is discontinuity when a [tex]\bold{x=2}[/tex] that is a vertical asymptote.

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Answer:

Part A:

x^3 - 4x^2 - 29x -24

(x + 1)(x - 8)(x + 3)

Part B.

(x + 1)(x - 8)(x + 3) / x^2 - x - 2= (x + 3)(x - 8) / x - 2

g(x)=  (x + 3)(x - 8) / x - 2= y= x - 3

Part C.

x=2.

Step-by-step explanation:

See images for more information, it wouldn't let me post it.

Answer:

[tex]x=y-4[/tex]

Step-by-step explanation:

Solve for x by simplifying two sides of the equation then isolating the variable.

Hope this helps!

Answer:

Negative five is in fact a rational number.

Step-by-step explanation:

Rational numbers can either be negative or positive. An irrational number would be pi (3.14159 etc.)

Answer:

9 ft = 9 × 12 = 108 in

ratio is 1:108

Step-by-step explanation:

Answer:

B. 2

it is the only odd prime number

Answer:

35• 43 m square is correct answer

Answer:

[tex]f(x)=3x^{2} -40fx[/tex] i think

Step-by-step explanation:

hi <3

i'm not sure of which method you will have been taught but i'll try to explain the method i was shown.

so, you need to multiply the coefficient of x^2 by the last value

3 x -12 = -36

now, you need to find two values that multiply to make -36 but add to make 5.

9 and 4 would work. it would have to be positive 9 and negative 4, as these would subtract to give the 5 that you need

now we have:

(x - 4)(x + 9)

however, we need to achieve the 3 from somewhere so it needs to be divided somewhere

9 is divisible by 3 so you can divide it there. as 4 cannot divide by 3, you would move the 3 up to be the coefficient.

thus, your final answer would be:

(3x - 4)(x + 3)

hope this helps :)

Answer:

it's gonna be 3(X*2 + 4X - 4)

Step-by-step explanation:

Just factor out 3 from the expression

Answer:

This equation has no solution.

Answer:

Ashley

Step-by-step explanation:

Ashley:

12n (n=5) = 60+2u (u=10)=80

4 quarters equal a dollar

$1.80

Beto:

10n (n=5)= 50+ 4u (u=10) = 90

3 quarters equal .75

$1.65

Answer:

C. take 10% of $46

Step-by-step explanation:

I took it on edge

You can use the same technique I showed in another one of your questions (24467305).

Partial fractions:

[tex]\dfrac2{(2n-1)(2n+1)} = \dfrac a{2n-1} + \dfrac b{2n+1} \\\\ \implies 2 = a(2n+1) + b(2n-1) = (2a+2b)n + a- b \\\\ \implies \begin{cases}2a+2b=0 \\ a-b = 2\end{cases} \implies a = 1, b=-1[/tex]

Then we have a telescoping sum,

[tex]S = \displaystyle \sum_{k=1}^n \frac 2{(2k-1)(2k+1)} \\\\ S = \sum_{k=1}^n \left(\frac1{2k-1} - \frac1{2k+1}\right) \\\\ S = 1-\frac13 + \frac13 - \frac15 + \cdots +\frac1{2n-3}-\frac1{2n-1}+\frac1{2n-1}-\frac1{2n+1} \\\\ S = 1 - \frac1{2n+1} = \boxed{\frac{2n}{2n+1}}[/tex]

(And in case you were actually interested in an infinite sum, we can see that this converges to 1 as n goes to ∞.)

Answer:

(3x - x) :v

Step-by-step explanation:

3x - 5 - x =134

2x - 5 = 134

2x = 139

x = 139/2

Answer:

I think the graph is the fourth choice

I hope I helped you^_^

  If a function 'f' is translated by 'k' units down, image function 'g' will be,

If the function 'g' gets shrink by a factor 'm', the new function 'k' will be,

  Following these rules image of the function 'f' given in the question will be g(x) = [tex]\frac{1}{3}x-1[/tex]

Function given in the question is,

  If the function f is translated by 3 units down, image function 'h' will be,

h(x) = f(x) -3

h(x) = x - 3

  If the image function is vertically shrink by a factor of k, equation of the image function will be,

g(x) = [tex]k[h(x)-3][/tex]

where, k = [tex]\frac{1}{3}[/tex],

g(x) = [tex]\frac{1}{3}}(x-3)[/tex]

      = [tex]\frac{1}{3}x-1[/tex]

    Therefore, image function will be [tex]g(x)=\frac{1}{3}x-1[/tex].

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Answer:

180-85=95

180-95=85

5x=85

x=17

For given figure, x = 17° and y = 95°

"It is a mathematical statement which consists of equal symbol between two mathematical expressions."

For given question,

We have been given ∠1 = 5x°, the measure of ∠2 = y°, and the measure of ∠3 = 85°

we know, the sum of all the angles on one side of a straight line is always 180°

So, we get two equations.

∠1 + ∠2 = 180°                   .....................(i)

and ∠2 + ∠3 = 180°            .....................(ii)

First we solve equation (ii) to find the value of ∠2

⇒ ∠2 + ∠3 = 180°

⇒ y + 85° = 180°

⇒ y = 95°

Now substitute this value of ∠2 in equation (i)

⇒ ∠1 + ∠2 = 180°

⇒ 5x° + y° = 180°

⇒ 5x° + 95° = 180°

⇒ 5x° = 85°

⇒ x = 17°

Therefore,  x = 17° and y = 95°

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#SPJ2

Answer: -10

Step-by-step explanation:

Formula for mid point is :

Mid point = ( (x1+x2)÷2 , (y1+y2)÷2) )

So, X1 = 4

X2 = X

Y1 = -2

Y2 = y

Now, use the formula

(-3,1) = ( (4 + x)÷2 , (-2+y)÷2) )

Now divide the sides for yourself to solve for midpoint for X and y separately

-3 = (4+x) ÷ 2 and 1 = (-2+y) ÷ 2

This is because 3 is the x coordinate of the mid point of A and B , so we equate it to (4+x) ÷ 2 because this expression basically gives us the x coordinate of mid point of A and B. So we already have the x coordinate of midpoint which is -3 so we can use this to find X coordinate of point B

So then we solve it by multiplying the 2 with -3 which gives -6

-6 = 4+X

Shift 4 on the other side and it will become negative 4

-6-4 = X

X = -10

Answer:

30 degree c

Step-by-step explanation: