In a study of the relationship between birth order and college success, an investigator found that 126 in a sample of 180 college graduates were firstborn or only children; in a sample of 100 nongraduates of comparable age and socioeconomic background, the number of firstborn or only children was 54. estimate the difference in the proportions of firstborn or only children for the two populations from which these samples were drawn. give a bound for the error of estimation.

let's solve for y :

Answer:

x=-2+y

Step-by-step explanation:

4=2y-2x

switch sides

2y-2x=4

subtrackt 2y from both sides

2y-2x-2y=4-2y

simplify

-2x=4-2y

divide both sides by -2

-2x/-2=4/2-2y/2

simplify

x=-2+y

To find the values of the cost function C(x) = 128√x² + 64000, we can substitute the production level x into the function.

a) The cost at the production level 1500:

Substitute x = 1500 into the cost function:

C(1500) = 128√(1500)² + 64000

        = 128√2250000 + 64000

        = 128 * 1500 + 64000

        = 192000 + 64000

        = 256000

Therefore, the cost at the production level 1500 is $256,000.

b) The average cost at the production level 1500:

The average cost is calculated by dividing the total cost by the production level.

Average Cost at x = C(x) / x

Average Cost at 1500 = C(1500) / 1500

Average Cost at 1500 = 256000 / 1500

Average Cost at 1500 ≈ 170.67

Therefore, the average cost at the production level 1500 is approximately $170.67.

c) The marginal cost at the production level 1500:

The marginal cost represents the rate of change of cost with respect to the production level, which can be found by taking the derivative of the cost function.

Marginal Cost at x = dC(x) / dx

Marginal Cost at 1500 = dC(1500) / dx

Differentiating the cost function:

dC(x) / dx = 128 * (1/2) * (2√x²) = 128√x

Substitute x = 1500 into the derivative:

Marginal Cost at 1500 = 128√1500

                     ≈ 128 * 38.73

                     ≈ $4,951.04

Therefore, the marginal cost at the production level 1500 is approximately $4,951.04.

In summary, the cost at the production level 1500 is $256,000, the average cost is approximately $170.67, and the marginal cost is approximately $4,951.04.

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a) No, the relation (a, b) ∈ R if a is taller than b does not form a poset on the set of all people in the world. b) Yes, the relation (a, b) ∈ R if a is not taller than b forms a poset on the set of all people in the world. c) Yes, the relation (a, b) ∈ R if a = b or a is an ancestor of b forms a poset on the set of all people in the world. d) No, the relation (a, b) ∈ R if a and b have a common friend does not form a poset on the set of all people in the world.

a) The relation (a, b) ∈ R if a is taller than b does not form a poset on the set of all people in the world. This is because the relation is not reflexive, as a person cannot be taller than themselves.

b) The relation (a, b) ∈ R if a is not taller than b does form a poset on the set of all people in the world. This relation is reflexive, antisymmetric, and transitive. Every person is not taller than themselves, and if a person is not taller than another person and that person is not taller than a third person, then the first person is also not taller than the third person.

c) The relation (a, b) ∈ R if a = b or a is an ancestor of b does form a poset on the set of all people in the world. This relation is reflexive, antisymmetric, and transitive. Every person is an ancestor of themselves, and if a person is an ancestor of another person and that person is an ancestor of a third person, then the first person is also an ancestor of the third person.

d) The relation (a, b) ∈ R if a and b have a common friend does not form a poset on the set of all people in the world. This relation is not antisymmetric, as two people can have a common friend without being equal to each other.

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Answer:

2.75 tsp

Step-by-step explanation:

1/4 divided by 0.75

Answer:

The median is 33.5

Step-by-step explanation:

In order to solve for a median it would either be the middle or it would be the average of the middle if there are even amount of numbers. First you would put them in order. 12 17 28 31 36 54 55 and 71. This would mean the the middle number would be 31 and 36. Since you can't have two medians you would find the average of the two so add 31 and 36 which would be equal to 67 then divide by 2 which would equal to 33.5.

The median of numbers 17, 12, 54, 36, 71, 28, 31, 55 is 33.5.

The median of a set of numbers is the middle value when the numbers are arranged in ascending or descending order.

To find the median of the given numbers, we first need to arrange them in ascending order:

12 17 28 31 36 54 55 71

Since there are an even number of numbers (8), the median will be the average of the two middle values, which are 31 and 36.

To find the average, we add the two numbers and divide by 2:

(31 + 36) / 2 = 67 / 2 = 33.5

Therefore, the median of the given numbers is 33.5.

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Answer:

(x + 1)(3x - 10)

Step-by-step explanation:

Given

3x² - 7x - 10

Consider the factors of the product of the x² term and the constant which sum to give the coefficient of the x- term.

product = 3 × - 10 = - 30 and sum = - 7

The factors are + 3 and - 10

Use these factors to split the x- term

3x² + 3x - 10x - 10 ( factor the first/second and third/fourth terms )

3x(x + 1) - 10(x + 1) ← factor out (x + 1) from each term

(x + 1)(3x - 10), thus

y = (x + 1)(3x - 10) ← in factored form

The polynomial function with real coefficients of a least possible degree having zero 2 of multiplicity 2, and zero i of single multiplicity is                   x⁴ - 4x³ + 5x²- 4x + 4 = 0. This can be obtained by finding factors and multiplying them.  

Given that zeroes, 2 of multiplicity 2, and i of single multiplicity, that is,       (x - 2), (x - i) and (x + i) are the factors of the polynomial.

Thus the polynomial can be written as  

(x - 2)²(x - i)(x + i) = 0 ((x - 2) is squared as multiplicity is 2)

(x² - 4x + 4)(x²-i²) = 0

(x² - 4x + 4)(x²+1) = 0

x⁴ - 4x³ + 4x² + x² - 4x + 4 = 0

⇒ x⁴ - 4x³ + 5x²- 4x + 4 = 0

Hence the polynomial function with real coefficients of a least possible degree having zero 2 of multiplicity 2, and zero i of single multiplicity is                   x⁴ - 4x³ + 5x²- 4x + 4 = 0.

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Answer:

9) 5.8

10) 27.9

11) 37.1

12) 16.8

Step-by-step explanation:

For this you need to know SOH (sine = opposite/adj) CAH (cos = adj/hypo) and TOA (tan = opp/adj).

For 9, you have one side 15 and one angle 21 degrees.  We can see that relative to the 21 degrees the side lengths, x and 15, are the Opposite and the Adjacent. So we label them "x=O" and "15=A". This means we have Tangent(21) = Opposite "x" /Adjacent "15"

We then evaluate tan21=x/15.

1) To get rid of the fraction multiply 15 on both sides to get 15*tan21=x.

2) Use a calculator to get the answer 5.8 (5.7579..)

For 10, it is the same process but with cosine. You have one side 19 and one angle 47 degrees. We can see that relative to the 21 degrees the side lengths, x and 19, are the Hypotenuse and the Adjacent. So we label them "x=H" and "19=A". This means we have Cosine(47) = Adjacent "19" / Hypotenuse "x"

We then evaluate cos47=19/x.

1) To get rid of the fraction multiply x on both sides to get x*cos47=19.

2) Divide by cos47 on both sides to isolate x. This will be x=47/cos21

3) Use a calculator to get the answer 27.9 (27.8593...)

For 11, refer to how I did question 9 on how it's tan68 = 15/x.

Then refer to question 10 on what to do if x is the denominator (isolate the x).

You should end up with x=15/tan68 which is 37.1 (37.1263...)

Finally for 12, it's the same but for sine (sin=opp/hyp).

You should get that the opp=15 and hypo=x.

That means sin63=15/x which is then x=15/sin63

Answer is 16.8 (16.834...)

we need to find the smaller of two negative, even consecutive integers whose product is 224.

Let's assume the smaller integer is x. Since the integers are consecutive, the larger integer would be x + 2. We are given that their product is 224, so we can set up the equation: x(x + 2) = 224

Expanding and rearranging the equation, we get: x^2 + 2x - 224 = 0

This is a quadratic equation. By factoring or using the quadratic formula, we find that the solutions are x = -16 and x = 14. Since we are looking for negative integers, the smaller integer is -16, which corresponds to option (c).

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Answer: b

Step-by-step explanation: death normally last 9 min and birth 9 sec

The correct equation is (a) because π/1 = C2/r2, \(C_2= 2\pi r\)

The complete question is added as an attachment

The given parameters are:

d1 = 1

d2 = 2r

The circumferences of the circles are calculated as:

C = πd

This gives

C1 = π * 1 = π

C2 = π * 2r = 2πr

So, we have:

C1 = π

C2 = 2πr

and

d1 = 1

d2 = 2r

Divide both equations

\(\frac{C_2}{d_1} = \frac{C_2}{d_2}\)

\(\frac{\pi}{1} = \frac{2\pi r}{2r}\)

This gives

\(\frac{\pi}{1} = \frac{C_2}{2r}\)

Hence, the correct equation is (a) because π/1 = C2/r2, \(C_2= 2\pi r\)

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Answer:

Its A

Step-by-step explanation:

The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

The two most important parts of a vehicle in preventing traction loss are the tires and the traction control system.

Tires: Tires are the primary point of contact between the vehicle and the road surface. The quality and condition of the tires greatly influence traction. Tires with good tread depth and appropriate tread pattern are essential for maintaining grip on the road. Tread depth helps to channel water, snow, or debris away from the tire, preventing hydroplaning or loss of traction. Additionally, tire pressure should be properly maintained to ensure even contact with the road. Choosing tires suitable for the specific driving conditions, such as all-season, winter, or performance tires, is crucial for optimal traction and handling.

Traction Control System: The traction control system is a vehicle safety feature that helps prevent the wheels from slipping or spinning on low-traction surfaces. It uses various sensors to monitor the speed and rotation of the wheels. If the system detects a loss of traction, it will automatically reduce engine power and apply braking force to the wheels that are slipping. By modulating power delivery and braking, the traction control system helps maintain traction and prevent wheel spin, especially in challenging conditions like slippery roads or during quick acceleration.

The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

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It aids in comprehending measurements when the data is scattered, standard deviation is significant. The standard deviation of the data will be higher the more evenly dispersed the data is.

Although the standard deviation is a frequently used statistic, it rarely receives the attention it merits. Although the mean and median are frequently mentioned in the news, they are rarely accompanied by any indication of how diverse the underlying data set was, so you only get a partial picture. In actuality, you might be overlooking the most captivating aspect of the tale.

What is Standard deviation?

A statistic known as the standard deviation is used to describe how volatile or dispersed a group of numerical values is. While a big standard deviation denotes that the values are scattered across a wider range, a low standard deviation indicates that the values tend to be close to the set mean.

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To find the magnitude of the vector B - A, we need to subtract the corresponding components of vector A from vector B and then calculate the magnitude of the resulting vector. the magnitude of vector B - A is approximately 12.93.

Vector B - A can be obtained by subtracting the x-component and y-component of vector A from the x-component and y-component of vector B, respectively.

The x-component of B - A is calculated as Bx - Ax, which is equal to (-5.1) - 7.6 = -12.7.

Similarly, the y-component of B - A is By - Ay, which is equal to (-6.8) - (-9.2) = 2.4.

Now, we have the x-component and y-component of vector B - A. To find the magnitude of this vector, we use the Pythagorean theorem:

Magnitude = sqrt((x-component)^2 + (y-component)^2) = sqrt((-12.7)^2 + (2.4)^2) = sqrt(161.29 + 5.76) = sqrt(167.05) ≈ 12.93.

Therefore, the magnitude of vector B - A is approximately 12.93.

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Answer:

Solution is in the photo

Whenever a sample is taken, the survey will reflect sampling error.

Option D is the correct answer.

We have,

Whenever a sample is taken, the survey will reflect sampling error.

Sampling error refers to the discrepancy or difference between the characteristics or values observed in a sample and the true characteristics or values of the entire population.

It arises due to the fact that a sample is only a subset of the population and may not perfectly represent the entire population.

Sampling error can occur due to various factors such as random sampling variation, non-response bias, sampling bias, and other sources of error in the sampling process.

It is important to consider and account for sampling errors when interpreting the results of a survey or study based on a sample.

Thus,

Whenever a sample is taken, the survey will reflect sampling error.

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(A) The original Value is $75.

(B) Students spends on Coffee shop is $ 2.5

(C) After 20 days, the value of gift card is $ 25

(D) In total 30 days is remaining value of the gift.

The given Equation is :

F(n) = -2.5n + 75

(A) The function of the original value, in dollar, of the gift card is

F(0) = -2.5 × 0 + 75

      = 75 dollars

(B) As given in the Question,

Since, n is the number of the days.

Therefore, based on the function, the student spend each day at the coffee shop is :

$2.5 is cost each days.

(C) The remaining value, in dollar, of the gift card after 20 day

   F(20) = -2.5 +75

            = -50 + 75

            = 25

Therefore, after 20 days the remaining value of gift card is $ 25

(D) Based on the given equation:

F(n) = 0

⇒ -2.5n +75 = 0

⇒ 2.5n = 75

⇒ n = 30 days.

Therefore, In total it will take 30 days until the remaining value of the gift.

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It will take 5 minutes to print a batch of newspapers if 20 printers are used.

What is proportionality?

Proportionality is a mathematical relationship between two variables, where one variable is a constant multiple of the other. In other words, two quantities are proportional if they maintain a constant ratio to each other, meaning that as one quantity increases or decreases, the other quantity changes in the same proportion.

We are given that the time it takes to print a batch of newspapers, m, is inversely proportional to the number of printers used, n, and the equation of proportionality is:

m = k/n

where k is a constant of proportionality. We are also given that when k = 100, the equation is satisfied. So we can substitute k = 100 into the equation to get:

m = 100/n

To find the time it will take to print a batch of newspapers if 20 printers are used, we can substitute n = 20 into the equation:

m = 100/20 = 5

So it will take 5 minutes to print a batch of newspapers if 20 printers are used. Rounded to 1 decimal place, the answer is 5.0 minutes.

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Answer:

approximately 71.50215

Step-by-step explanation:

The values of distance, velocity, and acceleration is s(3) = 25/3 feet, v(3) = 3.15 feet/min, and a(3) = -1/2 feet/min².

What is distance, velocity, and acceleration?

Distance: Distance is a measurement of how far apart two things or locations are, either quantitatively or occasionally qualitatively. Distance in physics or common language can refer to a physical length or an estimate based on other factors.

Velocity: An object's velocity is defined as its speed and direction of motion. A key idea in kinematics, the area of classical mechanics that studies how bodies move, is velocity. The definition of velocity requires both its magnitude and its direction because it is a physical vector quantity.

Acceleration: The rate of change in an object's velocity with respect to time is known as acceleration in mechanics. The vector quantity of accelerations. The direction of the net force that is acting on an object determines its acceleration.

As given graph,

S (1) = 2 feet

Now, evaluate the distance:

S(3) = No. of squares under the graph of 'q' up to t = 3 sec.

S(3) = S(1) + {S(2) -S(1)} +{S(3) -S(2)}

S(3) = 2 + 3 +3*(1/3)

S(3) = 2 + 3 + 10/3

S(3) = 25/3 feet.

Evaluate the velocity:

From the graph,

The velocity is V(3) = 3.15 feet/min.

Evaluate the acceleration:

a(3) = {V(2) - v(3)}/ Δt

a(3) = (2.5 - 3.5)/(4 - 2)

a(3) = -1/2 feet/min².

Hence, the values of distance, velocity, and acceleration is s(3) = 25/3 feet, v(3) = 3.15 feet/min, and a(3) = -1/2 feet/min².

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To show that the given parabolic velocity profile satisfies the appropriate boundary conditions, we need to verify that it satisfies the continuity and the no-slip conditions.

Continuity Condition: At the boundary y = δ, the velocity profile should be continuous. For y ≤ δ, we have u/U = 2 - (y/δ), and for y > δ, we have u/U = 1. Evaluating the velocity profile at y = δ, we get: u/U = 2 - (δ/δ) = 2 - 1 = 1. Therefore, the velocity profile is continuous at y = δ, satisfying the continuity condition. No-Slip Condition: At the solid surface y = 0, the velocity should be zero. For y ≤ δ, we have u/U = 2 - (y/δ), and when y = 0, we get: u/U = 2 - (0/δ) = 2 - 0 = 0.

Therefore, the velocity profile satisfies the no-slip condition at y = 0. Hence, the parabolic velocity profile u/U = 2 - (y/δ) for y ≤ δ, and u = U for y > δ satisfies the appropriate boundary conditions.

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The cost for children meal is $16 and the.cost for adult meal is $26.

Let cost of adult meal = a

Let cost of child meal = c

Lexi plans to have 63 adults and 59 children attend, so the total projected cost of her meals is $2,582.This will be:

63a + 59c = 2582 ...... i

Raymond has 63 adults and 93 children on her guest list, so he will pay the caterer $3,126. This will be;

63a + 93c = 3126 ...... ii

Collect both equations

63a + 59c = 2582 ...... i

63a + 93c = 3126 ...... ii

Subtract i from ii

34c = 544

Divide

c = 544 / 34

c = 16

The cost of children meal is $16.

From equation i, 63a + 59c = 2582

63a + 59(16) = 2582

63a + 944 = 2582

Collect like terms

63a = 2582 - 944

63a = 1638

a = 1638/63

a = 26

Adult meals is $26.

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Answer:

$47.76

Step-by-step explanation:

77 : 100 = x : 207.65

x = (207.65 * 77)/100

x = 159.8905

final price = 207.65 - 159.8905 = 47.7595= $47.76

Answer:

All real numbers Greater than or equal to 2.

Step-by-step explanation:

If x has a nonzero valve either positive or negative its square is always positive so we have a number greater than 2.

and if x has value 0 than its square is zero and we get 0 plus 2 equal to 2.

Hence answer is

All real numbers Greater than or equal to 2

Answer

Check Explanation

Explanation

A function is an expression that takes up each value of an independent variable (x) and gives a corresponding value of a dependent variable (y) without the same values of the independent variable (x) giving different values of the dependent variable (y).

So, if a given group of data shows the same values of x that give different values of y, that relation is not a function.

Hope this Helps!!!

Thus, the two factors of quadratic expressions found after factorization are 2 and 3.

Factorization is the technique of expressing a given statement as the product between two or more components. The sum of the greatest common factors of the integer coefficients and the same letters with the smallest powers yields the greatest common factor for two or more monomials.

Given quadratic expressions:

=  x² - 5x + 6

To factorize the expression, find the factors of 6 such that on addition it becomes -5.

= x² - 3x - 2x + 6

Taking x common from first two terms and -2 from last two terms.

= x(x -3) -2(x - 3)

Taking (x - 3) common.

= (x - 3)(x - 2)

x -3 = 0

x = 3

and, x - 2 = 0

x = 2

Thus, the two factors of quadratic expressions found after factorization are 2 and 3.

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Complete question:

Factorize quadratic expressions:  x² - 5x + 6

Step-by-step explanation:

Perhaps you entered your question incorrectly

maybe you meant

x^2 -x + 6     THIS factors to

(x-3)(x+2)     <=====if you multiply this out, you will see = x^2 -x+6

Are you familiar with the Quadratic Formula ?

   for this Quadrtatic     a = 1      b = -1      c = 6

    if you plug these numbers into the Quadratic Formula you get the roots:

            x = 3   and x = -2

       then you know the quadratic is   (x-3)(x+2)