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3 years ago

12

Based on the data in the table, how many of the next 125 cards the student chooses could be expected to have a number shown on t

he card that is a multiple of 4?

2 answers:

Minchanka [31]3 years ago

6 0

Answer:

20

Step-by-step explanation:

Makovka662 [10]3 years ago

6 0

Answer:

20

Step-by-step explanation:

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Plz help I will mark you brainlist plz help

lakkis [162]

<u><em>Answer</em></u>

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<u><em>Step-by-step explanation:</em></u>

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8 0

3 years ago

Read 2 more answers

Drag each tile to the correct box. Not all tiles will be used.

Alina [70]

Answer:

3rd box, last box, 2nd box, 5th box in that order

Step-by-step explanation:

PEMDAS

7 0

3 years ago

Read 2 more answers

Let f(x) = 1/x^2 (a) Use the definition of the derivatve to find f'(x). (b) Find the equation of the tangent line at x=2

Verdich [7]

Answer:

(a) $f'(x)=-\frac{2}{x^3}$

(b) $y=-0.25x+0.75$

Step-by-step explanation:

The given function is

$f(x)=\frac{1}{x^2}$ .... (1)

According to the first principle of the derivative,

$f'(x)=lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{\frac{1}{(x+h)^2}-\frac{1}{x^2}}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{\frac{x^2-(x+h)^2}{x^2(x+h)^2}}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{x^2-x^2-2xh-h^2}{hx^2(x+h)^2}$

$f'(x)=lim_{h\rightarrow 0}\frac{-2xh-h^2}{hx^2(x+h)^2}$

$f'(x)=lim_{h\rightarrow 0}\frac{-h(2x+h)}{hx^2(x+h)^2}$

Cancel out common factors.

$f'(x)=lim_{h\rightarrow 0}\frac{-(2x+h)}{x^2(x+h)^2}$

By applying limit, we get

$f'(x)=\frac{-(2x+0)}{x^2(x+0)^2}$

$f'(x)=\frac{-2x)}{x^4}$

$f'(x)=\frac{-2)}{x^3}$ .... (2)

Therefore $f'(x)=-\frac{2}{x^3}$ .

(b)

Put x=2, to find the y-coordinate of point of tangency.

$f(x)=\frac{1}{2^2}=\frac{1}{4}=0.25$

The coordinates of point of tangency are (2,0.25).

The slope of tangent at x=2 is

$m=(\frac{dy}{dx})_{x=2}=f'(x)_{x=2}$

Substitute x=2 in equation 2.

$f'(2)=\frac{-2}{(2)^3}=\frac{-2}{8}=\frac{-1}{4}=-0.25$

The slope of the tangent line at x=2 is -0.25.

The slope of tangent is -0.25 and the tangent passes through the point (2,0.25).

Using point slope form the equation of tangent is

$y-y_1=m(x-x_1)$

$y-0.25=-0.25(x-2)$

$y-0.25=-0.25x+0.5$

$y=-0.25x+0.5+0.25$

$y=-0.25x+0.75$

Therefore the equation of the tangent line at x=2 is y=-0.25x+0.75.

5 0

3 years ago

Cathy sells an average of 32 pot holders each week.

Art [367]

Answer:

1500 pot holders

Step-by-step explanation:

32×48=1536 so it's about 1500 pot holders because 1536 it's closet to 1500

4 0

3 years ago

After 3 weeks, a plant is 8 centimeters tall. After 4 weeks, it has grown to 10 centimeters. Of the plant grows following an ari

Oliga [24]

Answer:

5

Step-by-step explanation:

4 0

3 years ago