Which equation represents a line passing through the points (0, 1) and (2, -3)?

The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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Answer:

x = 30, x = 5 and x = 9

Step-by-step explanation:

The diagonals of a square are perpendicular bisectors of each other, so

∠ AEB = 90° , then

3x = 90 ( divide both sides by 3 )

x = 30

---------------------------------------------------------

(9)

The 4 angles of a square are right and the diagonals bisect the angles, then

∠ BAC = 45° , so

9x = 45 ( divide both sides by 9 )

x = 5

-------------------------------------------------------

(10)

All sides are congruent , so

CD = AB , that is

3x - 5 = 2x + 4 ( subtract 2x from both sides )

x - 5 = 4 ( add 5 to both sides )

x = 9

To find a₂ and a₃ in a geometric sequence, we need to determine the common ratio (r) first.

In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio, denoted as "r." Given that a₁ = 3 and a₅ = 768, we can use these values to find the common ratio.

We can use the formula for the nth term of a geometric sequence: aₙ = a₁ * r^(n-1).

Substituting a₁ = 3 and a₅ = 768, we have:

a₅ = a₁ * r^(5-1)

768 = 3 * r^4

Now, we can solve for the common ratio, r, by dividing both sides of the equation by 3 and taking the fourth root:

r^4 = 768/3

r^4 = 256

r = ∛(256)

r = 4

Now that we have the common ratio, we can use it to find a₂ and a₃.

To find a₂, we use the formula a₂ = a₁ * r^(2-1):

a₂ = 3 * 4^(2-1)

a₂ = 3 * 4

a₂ = 12

To find a₃, we use the formula a₃ = a₁ * r^(3-1):

a₃ = 3 * 4^(3-1)

a₃ = 3 * 16

a₃ = 48

Therefore, a₂ = 12 and a₃ = 48 are the values for the second and third terms in the geometric sequence, respectively.

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Answer:

hi sh Sheet sh I monorailg Jericho improve Odom Ybor

The linear equation that models the value V of the computer t years since its purchase is V(t) = -700t + 3000

T do this, use the two given data points to write a linear equation in slope-intercept form

Thus,

V(t) = mt + b

where

m is the slope and

b is the y-intercept.

At t=0 (the time of purchase), the value of the computer is $3000

V(0) = m(0) + b

3000 = b

After 4 years, the value of the computer is $200

V(4) = m(4) + b

200 = 4m + 3000

Collect like terms

200-3000 =4m

Divide both side by 4

m=-2800/4

m = -700

b = 3000

Therefore, the linear equation that models the value V of the computer t years since its purchase is V(t) = -700t + 3000

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Answer:

The exterior angle is equal to 77°

Step-by-step explanation:

We know that all three angles of a triangle are equal to 180°. We also know that the exterior angle and its adjacent angle are equal to 180°.

1) We can find the angle adjacent to the exterior angle is 180-(3x+23), we can simplify this and get 157-3x for that angle.

2) We can create the equation 4x-15+2x-16+157-3x=180. After simplifying we get 3x+126=180.

3) To solve for x we can subtract 126 from both sides, 3x=54. We can divide 3 from both sides to isolate x, we get x=18.

4) Substitute the x value into the given term for the exterior angle, 3(18)+23

5) After simplifying you get 77

The correct answer is 100.48 degrees = 628π/1125 radians

Here is how to calculate 100.48 degrees to radians. The math to convert 100.48 degrees to radians, is as follows:

degrees in radians, we multiply degrees by π and divide by 180. The formula for conversion of degrees in radians: (degrees × π) ÷ 180 = radians. 100.48 degrees in our formula, we get 100.48 degrees in radians as follows:

(degrees × π) ÷ 180 = radians

(100.48 × π) ÷ 180 = 64251 0/4.4.

48 degrees = 628π/1125 radial

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The average student headcount for the spring terms is: 10700

A graph is a non-linear kind of data structure made up of nodes or vertices and edges. The edges connect any two nodes in the graph, and the nodes are also known as vertices. This graph has a set of vertices V= { 1,2,3,4,5} and a set of edges E= { (1,2),(1,3),(2,3),(2,4),(2,5),(3,5),(4,50 }.

We have the information:

From the graph,

Number of headcounts for spring '0.2 - 0.3' = 10900

Number of headcounts for spring '0.3 - 0.4' = 10500

Number of headcounts for spring '0.4 - 0.5' = 10700

The average student headcount for the spring terms is:

= 1/3 (10900 + 10500 + 10700)

= 10700

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For complete question, to see the attachment.

___________________________________________________

Total number of ice-creams sold / –

= No of ice-creams sold on Saturday + No of ice-creams sold on Sunday

= (8x + 16) + (7x – 9)

= 8x + 16 + 7x – 9

= 8x + 7x + 16 – 9

= 15x + 7 ( — Ans )

______________________________________________________

In a scenario where water in an open bowl evaporates at a rate proportional to the area of the water's surface, the depth of the water decreases at a constant rate, regardless of the bowl's shape.

Let's assume we have an open bowl filled with water. The rate of decrease in volume due to evaporation is directly proportional to the area of the water's surface. As water evaporates, the surface area decreases, causing the depth of the water to decrease as well.

To demonstrate that the depth decreases at a constant rate, we can consider two different time intervals. During the first time interval, let's say the water's surface area decreases by ΔA1, resulting in a corresponding decrease in depth by Δh1. In the second time interval, if the surface area decreases by ΔA2, the depth decreases by Δh2.

Since the rate of decrease in volume is proportional to the surface area, we can say that ΔV1/Δt = k1 * ΔA1 and ΔV2/Δt = k2 * ΔA2, where k1 and k2 are proportionality constants.

Since the depth is defined as the volume divided by the surface area, we have Δh1 = ΔV1 / ΔA1 and Δh2 = ΔV2 / ΔA2.

Combining these equations, we find that Δh1/Δt = k1 and Δh2/Δt = k2.

Therefore, we can conclude that the depth of the water decreases at a constant rate, regardless of the shape of the bowl, as long as the evaporation rate remains proportional to the surface area.

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The required scale factor between the building and toy model is given as 900.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
The area of the front side of the toy building is 1 square foot.
The real building's front side has an area of 900 square feet.
The real buildings as a dilation of the toy,
Scale factor = 900 /1
Scale factor = 900

Thus, the required scale factor between the building and the toy model is given as 900.

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Answer:

PEMDAS (Paranthesis (), Exponnets^2, Multiplication X, Division 1/2(or fractions, Addtion +, and Subtraction -

Step-by-step explanation:

Answer:

Where is the question?

If you were looking for order of operations, look at the image.

Answer:

60

Step-by-step explanation:

5+7= 12

12x5=60

(5 is blue)

Answer:

Okay, so:

sinA = 22.5/25.5

<A = 62* (correct)

cos C = 22.5/25.5 (correct)

tanA = 22.5/12.0 = 1.875 (correct)

sinC = 12.0/25.5

tan C = 12.0/22.5 = 0.53 (correct)

Step-by-step explanation:

I'll explain the wrong ones in the comments hold on-

Answer:

I believe the answer is function

Step-by-step explanation:

Answer:

733

Step-by-step explanation:

18 - √81 + 9 × 3⁴ - ( 3 - 2 + 9 ) ÷ 2

18 - 9 + 9 × 81 - ( 10 ) ÷ 2

(18 - 9) + (9 × 81) (-10 ÷ 2)

9 + 729 - 5

738 - 5

733

I hope this helps!

To solve this problem, we can use the principle of inclusion-exclusion. First, we can count the total number of arrangements of the letters in "tamely," which is 6! = 720.

Next, we can count the number of arrangements where t is before a, which is 5! (since we treat ta as a single unit) multiplied by the 2 ways to arrange the remaining letters, which is 2*4! = 48. Similarly, we can count the number of arrangements where a is before m or m is before e, which is also 48.

However, we have double-counted the arrangements where both t is before a and a is before m, or where both t is before a and m is before e, or where both a is before m and m is before e.

Each of these arrangements can be counted as 4! = 24. Therefore, the total number of arrangements that satisfy the conditions is 48+48+48-24-24-24+0 = 72. In summary, there are 72 arrangements of "tamely" with either t before a, or a before m, or m before e.

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Answer:

$1360

Step-by-step explanation:

Smith pays a monthly payment to the insurance company = $50

So in 12 months, he pays = 12 x 50

                                          = $ 600

Now subtracting a $ 2600 by the deduction of amount $300 , i.e. $2300.

Now multiplying it by 20 percent as the insurance company pays the 80% leaving Smith with 20%, to get $460.

Now adding $460 with $300, as these amount Smith paid and he got $760.

Now monthly payment = $760 + $600

                                      = $1360

Correct Answer: $1,840

The student should plan to use a two-means (unpaired) t distribution hypothesis test to compare the average GPAs of male and female undergraduates at her university.

The area of the shaded region in this problem is given as follows:

995.44 cm².

The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:

A = πr²

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, hence it's measure is given as follows:

r = 21 cm.

Then the area of the entire circle is given as follows:

A = π x 21²

A = 1385.44 cm².

The right triangle has two sides of length 39 cm and 20 cm, hence it's area is given as follows:

A = 0.5 x 39 x 10

A = 390 cm².

Then the area of the shaded region is given as follows:

1385.44 - 390 = 995.44 cm².

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Answer:

B, C

Step-by-step explanation:

Seeing as you said ASAP I thought I wouldn't spend time writing an explanation, but let me know if you do want one.

Answer:  B

Step-by-step explanation:each of the pairs of opposite angles made by two intersecting lines.

yes proper subset  is different from a regular subset. The empty set is a proper subset of every set except for the empty set

A proper subset of a set A is a subset of A that cannot be equal to A. In other words, if B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B.

Subset: If A and B are sets and every element of A is also an element of B, then:

A is a subset of B, denoted by A ⊆ B.

or equivalently, B is a superset of A, denoted by B ⊇ A.

Any set is considered to be a subset of itself. No set is a proper subset of itself. The empty set is a subset of every set. The empty set is a proper subset of every set except for the empty set.

For example, A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

A = {1, 2, 3} and B = {1, 2, 3}

Here, A is a subset of B, or we can say that B is the superset of A.

Proper Subset: If A is a subset of B, but A is not equal to B (that is, there exists at least one element of B which is not an element of A), then

A is also a proper (or strict) subset of B; this is written as A ⊊ B.

For example A = {1, 2, 3} and B = {1, 2, 3, 4}.

Clearly, A is not equal to B and element {4} belongs to set B but is absent in set A, so we have one element in set B which is not an element of set A. Thus, A can be called a proper subset of B.

Hence, a proper subset of a set A is a subset of A that is not equal to A. In other words, if B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B, thus the proper subset may or may not be the same.

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Answer:

12

Step-by-step explanation:

9/0.75 = 12

A good point estimate for the population proportion is 0.01714. Option D is correct.

A good point estimate to use for the population proportion to test the effectiveness of the flu vaccine can be calculated by dividing the number of people who got the flu (12) by the total number of participants in the study (700).

Point Estimate = Number of people who got the flu / Total number of participants

Point Estimate = 12 / 700

Using a calculator, the approximate value of the point estimate is 0.01714 (rounded to five decimal places).

Therefore, the good point estimate to use for the population proportion to test the effectiveness of the flu vaccine is 0.01714. Option D is correct.

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The central tendency of the data set is given by mean of the set and the value of mean is 12.6 .

Given,

Data set : 1,3,3,3,4,10,20,30,40 .

Here,

To calculate the central tendency of the data set firstly calculate the mean of the data set .

So,

Mean = Sum of all the observation in the data set / Number of observations in the data set

So,

Mean = 1+3+3+3+4+10+20+30+40/9

Mean = 114/9

Mean = 12 .6

Thus the mean of the data set is 12.6 .

Therefore mean represents the central tendency of the data correctly .

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Answer:

(2,-4)

Step-by-step explanation:

In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

2x+3y=−8,3x+y=2

To make 2x and 3x equal, multiply all terms on each side of the first equation by 3 and all terms on each side of the second by 2. Then simplify

6x+9y=−24,6x+2y=4

Add 6x to −6x. Terms 6x and −6x cancel out, leaving an equation with only one variable that can be solved, add 9y to −2y, add −24 to −4, and divide both sides by 7.

y=−4

Substitute −4 for y in 3x+y=2. Because the resulting equation contains only one variable, you can solve for x directly. Add 4 to both sides of the equation and divide both sides by 3.

x=2

Instead of attempting to remember each numeral individually, Wayne chooses to memorize the series of four ages. Wayne is employing a tactic known as "chunking."

In a "chunking" project, students rewrite the "portions" of a challenging material in their own words after breaking it down into more digestible chunks.

Thus, when instead of attempting to remember each numeral individually, Wayne chooses to memorize the series of four ages. Wayne is employing a tactic known as "chunking."

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