Professor Isaac Asimov was one of the most prolific writers of all time. Prior to his death, he wrote nearly 500 books during a 40-year career. In fact, as his career progressed, he became even more productive in terms of the number of books written within a given period of time. The data given in increments of 100:
Number of books, x: 100 200 300 400 500
Time in months, y: 237 350 419 465 507
a. Assume that the number of books x and the time in months y are linearly related. Find the least-squares line relating y to x.
b. Plot the time as a function of the number of books written using a scatterplot, and graph the least-squares line on the same paper. Does this seem to provide a good fit to the data points?
c. Construct the ANOVA table for the linear regression.

Answer:

2/π

h(x) is concave up on the intervals (-∞, -1/√3) and (1/√3, ∞).

h(x) is concave down on the interval (-1/√3, 1/√3).

Step-by-step explanation:

f(x) = sin x

The average value of a function between x=a and x=b is:

avg = 1/(b−a) ∫ₐᵇ f(x) dx

avg = 1/(π−0) ∫₀ᵖⁱ sin x dx

avg = 1/π (-cos x) |₀ᵖⁱ

avg = 1/π (-cos π − (-cos 0))

avg = 1/π (1 + 1)

avg = 2/π

h(x) = x⁴/12 − x²/6

Find the second derivative.

h'(x) = x³/3 − x/3

h"(x) = x² − ⅓

Factor using difference of squares.

h"(x) = (x − 1/√3) (x + 1/√3)

h"(x) = 0 when x = ±1/√3.  Evaluate the sign of h"(x) in each interval.

-∞ < x < -1/√3, h"(x) > 0.

-1/√3 < x < 1/√3, h"(x) < 0.

1/√3 < x < ∞, h"(x) > 0.

h(x) is concave up on the intervals (-∞, -1/√3) and (1/√3, ∞).

h(x) is concave down on the interval (-1/√3, 1/√3).

Answer:

2/π

h(x) is concave up on the intervals (-∞, -1/√3) and (1/√3, ∞).

h(x) is concave down on the interval (-1/√3, 1/√3).

Step-by-step explanation:

Answer:

$ 50

Step-by-step explanation:

Original price = Sale price + discount

= 40 + 25% of 40

= 40 + 0.25 * 40

= 40 + 10

Original price =  $50

Answer:

6 and 8

Step-by-step explanation:

The hypotenuse of a 30°-60°-90° triangle measures 10 inches.

To find the length of one of the legs, we use the idea of Pythagorean Triples.

Pythagorean Triples are any set of three numbers that satisfies the Pythagorean Theorem. Some common examples are:

Note that in a Pythagorean Triple,

In our given triangle, the Hypotenuse=10 Inches

Consider the Pythagorean Triple 3,4, and 5

Therefore, 6 and 8 could be the length of a leg of the 30°-60°-90° triangle.

Answer:

32

Step-by-step explanation:

g(x) = 4x² - 3x + 7

g(3) = 4(3)² - 3(3) + 7

g(3) = 4(9) - 9 + 7

g(3) = 36 - 9 + 7

g(3) = 25 + 7

g(3) = 32

Answer:

Step-by-step explanation:

-6x + 6y = -12

6x + 6y = -36

12y = -48

y = -4

3x - 12 = -18

3x = -6

x = -2

(-2, -4)

Step-by-step explanation:

wait sorry that was wrong

Answer:

5.2

Step-by-step explanation:

The answer is 5.2 pounds of meat. To find this just divide the number of people by what the information you have about servings. 13/5=2.6(number of sets), then you multiply that by how many pounds are in each set.

Answer: C you pay fee fewer upfront cost

Step-by-step explanation:

Answer:6.25

Step-by-step explanation:

First one (on the left) is 2) associative property because we are regrouping terms or re-associating them based on the parenthesis. Think of the parenthesis like a tent or a house that separates off the stuff outside. First 27 and 36 are grouped, then we move the parenthesis so that 52 and 27 are grouped now.

Second one (on the right) is 1) commutative. The commutative multiplication property says we can multiply two numbers in any order. For example, 4*9 = 36 and 9*4 = 36. The 4 and 9 swap places. In this problem, the 3 and 4x swap places. The use of parenthesis isn't necessary, though it is sometimes used to imply multiplication.

Answer:

1) Associative property

2) Commutative property

Step-by-step explanation:

BECAUUUUSE ;

[tex]4 \div \frac{1}{5} = 20 \\ \frac{4}{1} \div \frac{1}{5} = 20 \\ \frac{4}{1} \times \frac{5}{1} = 20 \\ \frac{20}{1} = 20[/tex]

Answer:Because the divide sign change to multiplication sign, and when this happens denominator in the right hand side will become numerator,while the formal numerator will become denominator.

Step-by-step explanation:

4 ➗ 1/5

4 x 5/1=20

Answer:

Have them 4 by 5.

Step-by-step explanation:

If you she but 5 chairs in a row, then 3 on the side of the chairs. That would create a backward "L" type of shape.

For example, (The "o" is a chair)

OOOOO

O

O

O

As you see the the top are the 5 chairs, then side are are the 4 chairs.

Then, you will do the exact same thing  but on the opposite side.

Here is the next example.

OOOOOO

O            O

O            O

O            O

OOOOOO

Basically, arranging the chairs 4x5, it would make a rectangle.

Answer: (-4,-18)

Step-by-step explanation: If you use desmos you can graph the equation to find the vertex.

The vertex of the graph of function f(x) =  x² + 8x - 2 is (-4, -18)

In a quadratic function, the vertex of the graph refers to the highest or lowest possible outcome of the function. In a graph, the vertex is the highest or lowest point on the parabola,

Given that:

f(x) = x² + 8x - 2

where;

By using the vertex formula to find the x-value;

[tex]\mathbf{x = \dfrac{-b}{2a}}[/tex]

[tex]\mathbf{x = \dfrac{-8}{2(1)}}[/tex]

x = -4

So,

y = (-4)² + 8(-4) - 2

y = 16 -32 -2

y = -18

Therefore, the vertex of the graph of function f(x) =  x² + 8x - 2 is (-4, -18)

Learn more about the vertex of the graph function here:

https://brainly.com/question/1305555

#SPJ2

Answer:

yes

Step-by-step explanation:

yes

Answer: y=10x+25

y=10(7)+25

=70+25

=$95

Step-by-step explanation:

Answer:

76

Step-by-step explanation:

First get the equation into the form

ax^2 +bx+c =0

3x^2-10x+2=-2+2

3x^2-10x+2 =0

The discriminant is

b^2 -4ac  where a=3  b = -10 c =2

(-10)^2 - 4(3)(2)

100 - 24

76

Answer:

A.

Step-by-step explanation:

tan x= 6/8

usually tan θ = perpendicular / base

So,

we get perpendicular = 6, base = 8

Now using Pythagorean Theorem to find hypotenuse

hyp² = base² + Perp²

hyp² = 8² + 6²

hyp²= 64 + 36

hyp²=100

Taking sq root on both sides

hypotenuse = 10

Now

sin θ = Perpendicular / Hyp

sin x = 6 / 10

Now

cos θ = base / Hyp

cos x = 8 / 10

Answer:

It is 4

Step-by-step explanation: To find the area you multiply the numbers.

Answer:

10

Step-by-step explanation:

3+2 = 5

5x2 (Because only half cups)

= 10

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached images below to see the step by step explanation to the question above.

Answer:

Step-by-step explanation:

amplitude of oscillation a = 12 / 2 = 6 inches.

time period T = 2 s

b = angular frequency = 2π / T

= 2π / 2

= π

so putting the values in the equation

d = a cos ( b t )

d = 6 cos ( π t )

Answer:

there are two more questions and the answers are 0.5 is the least positive amount of the pendulum and 4.243=y when x=4.25

Step-by-step explanation:

Answer:

⅜ x + ¹/₁₂ sin(6x) + ¹/₉₆ sin(12x) + C

Step-by-step explanation:

∫ cos⁴(3x) dx

Use power reduction formula:

⅛ ∫ (3 + 4cos(6x) + cos(12x)) dx

⅜ ∫ dx + ½ ∫ cos(6x) dx + ⅛ ∫ cos(12x) dx

⅜ ∫ dx + ¹/₁₂ ∫ 6 cos(6x) dx + ¹/₉₆ ∫ 12 cos(12x) dx

⅜ x + ¹/₁₂ sin(6x) + ¹/₉₆ sin(12x) + C

Answer:

A: -2

B: -10

Step-by-step explanation:

A: the slope of line b is -2

B: Point: (-6,2)

So x= -6 and y = 2

Putting in slope intercept formula for finding b

y=mx+b

2=(-2)(-6)+b

2= 12 + b

b = 2-12

b= -10

The y-intercept of line b is -10

Answer:16/15 or 1 1/15

Step-by-step explanation:

4/5 ➗ 3/4

4/5 x 4/3

(4 x 4) ➗ (5 x 3)

16 ➗ 15=16/15 or 1 1/15

Answer:

  see the attachments

Step-by-step explanation:

An inequality without the "or equal to" case is graphed with an open circle at its boundary point. If the "or equal to" case is included, then the dot at the boundary is filled in (a solid dot). The number line is shaded to the left or right of the boundary point, depending on whether the set being graphed includes values less than or greater than the boundary value. Usually, a line extending indefinitely will have an arrow on its end. (Not here, because the program used doesn't easily support drawing arrows.)

__

a. The boundary point at x=7.75 has an open circle, and the shading of the number line extends indefinitely to the right from there.

__

b. The boundary point at x=2.5 is a solid dot, and the shading extends indefinitely to the left.

Answer:

Step-by-step explanation:

From the given information,

The ten observation data on october  snow cover for Eurasia  during the years is 6.5, 12.0, 14.9, 10.0, 10.7, 7.9, 21.9, 12.5, 14.5, 9.2

What would you report as a representative, or typical, value of October snow cover for this period, and what prompted your choice?

For the given data, 21.9 is an outlier, so trimmed mean would be good choice for the researcher,

Remove the smallest and the largest values to compute the trimmed mean

[tex]\bar x = \frac{12.0+14.9+10.0+10.7+7.9+12.5+14.5+9.2}{8} \\\\=\frac{91.7}{8} \\\\=11.465[/tex]

Answer:

4) 64 cubic inches

Step-by-step explanation:

8x8 = 64

Answer: 136°

Step-by-step explanation:

In this angle relationship, it is a supplementary angles. because the parallel lines are separated by a line, the 2 angles make 180°.

180°=44°+x°

x=136°

Answer:

Length is 3 meters and the Width is 5 meters

Step-by-step explanation:

L*W=15

L=2W-7

(2W-7)W=15

[tex]2W^{2} -7W=15\\2W^{2} -7W-15=0[/tex]

(2W+3)(W-5)=0, don't use (2W+3)=0, because it gives you a negative dimension.

W=5, L=3