Which scenarios use the correct mean, population (μ), or sample (x) to represent the calculation? Check all that apply.



A café owner wants to determine the average pay per week for all his employees. The mean should be calculated using population (μ).



A scientist wants to determine how nitrogen levels affect the average height of some of the bean sprouts grown in his greenhouse. The mean should be calculated using population (μ).



A psychology student surveys Dr. Kohl’s 10 a.m. English students about the number of hours they spend studying each week. The mean should be calculated using sample (x).



A cattle rancher weighs each of his cattle every six months. He calculates the average weight. The mean should be calculated using population (μ).



A running shoe distributor wants to know the average monthly inventory of a particular brand of shoe. He compiles the data from all the stores. The mean

Answer:

x(a-b-c)+y(-a+b-c)

Step-by-step explanation:

To find the expected value of the game, we need to calculate the expected value of the random variable X, which represents the image value of bills.Therefore, the expected value of the game to you is $16.50.

The probability distribution of X can be filled in as follows:

x   | $1   | $5   | $10  | $50

P(X) | 1/4  | 1/4  | 1/4  | 1/4

The probabilities are equal because each bill has an equal chance of being drawn.

To calculate the expected value, we multiply each value of X by its corresponding probability and sum them up:

E(X) = (1/4 * $1) + (1/4 * $5) + (1/4 * $10) + (1/4 * $50)

    = $0.25 + $1.25 + $2.5 + $12.5

    = $16.5

Therefore, the expected value of the game to you is $16.50.

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Expanding (2+t)⁴ using Pascal's Triangle gives the result 16 + 32t + 24t² + 8t³ + t⁴.

To expand (2+t)⁴ using Pascal's Triangle, we can utilize the binomial theorem. The fourth row of Pascal's Triangle is 1 4 6 4 1.

These numbers represent the coefficients of each term in the expansion. The general formula for expanding a binomial raised to the power of n is:

(2+t)⁴ = 1*(2)⁴*(t)⁰ + 4*(2)³*(t)¹ + 6*(2)²*(t)² + 4*(2)¹*(t)³ + 1*(2)⁰*(t)⁴

= 1*(16)(1) + 4(8)(t) + 6(4)(t)² + 4(2)(t)³ + 1(1)*(t)⁴

= 16 + 32t + 24t² + 8t³ + t⁴

Simplifying this expression gives the expanded form of (2+t)⁴. In this case, it is 16 + 32t + 24t² + 8t³ + t⁴.

Each term is obtained by multiplying the corresponding coefficient from Pascal's Triangle with the appropriate powers of 2 and t.

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Answer:

15x

Step-by-step explanation:

Answer:

16a - 6b + 6

Step-by-step explanation:

5a + 5b - 5 + 11a - 11b + 11 = 5a + 11a + 5b - 11b - 5 + 11 = 16a - 6b + 6

Answer:

609638400

Step-by-step explanation:

Answer:

609638400

Step-by-step explanation:

Each row must alternate boys and girls, so every row is either BGBGB or GBGBG, where B denotes a boy and G denotes a girl. Since there are 8 girls and 7 boys, the teacher must have two rows of GBGBG and one row of BGBGB. There are three ways to choose this row, and once this is done, every seat is reserved for either a girl or a boy. There are 8! ways to arrange the girls in their seats, and 7! ways to arrange the boys, so the total number of seating arrangements is 3 * 7! * 8!

The percentage of error of the gun speed will be 0.20%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

A radar gun measured the speed of a base ball at 103 but the baseball was going 102.8. Then the percentage of error is given as,

P = [(103 - 102.8) / 102.8] x 100

P = (0.2 / 102.8) x 100

P = 0.20%

The percentage of error of the gun speed will be 0.20%.

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The evaluated definite integrals using right Riemann sums are:

a) ∫[0, 2] (2x + 1)dx = 9.

b) ∫[3, 7] (4x + 6)dx is divergent.

c) ∫[1, 5] (1 - x)dx = 4.

d) ∫[0, 2] (x^2 - 1)dx = 2.

To evaluate the definite integrals using right Riemann sums, we partition the interval into subintervals and approximate the area under the curve using the right endpoints of each subinterval.

a) ∫[0, 2] (2x + 1)dx:

Let's partition the interval [0, 2] into n subintervals of equal width. The width of each subinterval is Δx = (2 - 0) / n = 2/n.

The right endpoints of the subintervals are: x1 = 2/n, x2 = 4/n, x3 = 6/n, ..., xn = 2. The right Riemann sum is given by: R_n = Σ[(2x + 1) * Δx] from i = 1 to n.

Expanding the sum, we have:

R_n = [(2(2/n) + 1) * (2/n)] + [(2(4/n) + 1) * (2/n)] + ... + [(2(2) + 1) * (2/n)]

= [4/n + 1] * (2/n) + [8/n + 1] * (2/n) + ... + [5] * (2/n)

= 2[4/n + 1 + 8/n + 1 + ... + 5] * (2/n)

= 2[(4 + 8 + ... + 5n)/n + n] * (2/n)

R_n = 2[(n/2)(4 + 5n)/n + n] * (2/n)

= (4 + 5n + 2n) * (4/n)

= (9n + 4) * (4/n)

Taking the limit as n approaches infinity, we have:

∫[0, 2] (2x + 1)dx = Lim(n->∞) (9n + 4) * (4/n)

= Lim(n->∞) 9 + (4/n)

= 9.

Therefore, ∫[0, 2] (2x + 1)dx = 9.

b) ∫[3, 7] (4x + 6)dx:

The right Riemann sum is given by: R_n = Σ[(4x + 6) * Δx] from i = 1 to n.

Expanding the sum and simplifying, we find:

R_n = 4[(3 + 4n/n) + (3 + 4(2n)/n) + ... + (3 + 4(n)/n)] * (4/n)

= 4[(3 + 4 + ... + (3 + 4n))/n] * (4/n)

= 4[(3n + 4(1 + 2 + ... + n))/n] * (4/n)

= 4[(3n + 4(n(n+1)/2))/n] * (4/n)

= 4[(3n + 2n(n+1))/n] * (4/n)

= 4[3 + 2(n+1)] * (4/n)

= 4[6 + 2n] * (4/n)

= 8 + 8n

Taking the limit as n approaches infinity, we have:

∫[3, 7] (4x + 6)dx = Lim(n->∞) (8 + 8n)

= Lim(n->∞) 8n

= ∞.

Therefore, ∫[3, 7] (4x + 6)dx is divergent.

c) ∫[1, 5] (1 - x)dx:

Using the same approach, we have:

R_n = [(1 - 1/n) * (4/n)] + [(1 - 2/n) * (4/n)] + ... + [(1 - n/n) * (4/n)]

= [(1 + 1 + ... + (n-1))/n] * (4/n)

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

= (4(n-1))/n^2

Taking the limit as n approaches infinity, we have:

∫[1, 5] (1 - x)dx = Lim(n->∞) (4(n-1))/n^2

= Lim(n->∞) (4 - 4/n)

= 4.

Therefore, ∫[1, 5] (1 - x)dx = 4.

d) ∫[0, 2] (x^2 - 1)dx:

Using the same approach, we have:

R_n = [(0^2 - 1/n) * (2/n)] + [(1^2 - 2/n) * (2/n)] + ... + [(2^2 - n/n) * (2/n)]

= [(0^2 + 1^2 + ... + (n-1)^2)/n] * (2/n)

= [(0^2 + 1^2 + ... + (n-1)^2)/n] * (2/n)

= [(0 + 1 + 4 + ... + (n-1)^2)/n] * (2/n)

= [(n(n-1)(2n-1))/6n] * (2/n)

= [(n-1)(2n-1)]/3n

Taking the limit as n approaches infinity, we have:

∫[0, 2] (x^2 - 1)dx = Lim(n->∞) [(n-1)(2n-1)]/3n

= Lim(n->∞) (2n^2 - 3n + 1)/3n

= Lim(n->∞) (2n^2/n - 3n/n + 1/n)

= Lim(n->∞) (2 - 3/n + 1/n)

= 2.

Therefore, ∫[0, 2] (x^2 - 1)dx = 2.

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Francisco teaches group lessons to all of the violin and viola students at the Scott School of Music. All of his classes have the same number of students.

What is the greatest number of students he can have in each class We can determine the greatest number of students that Francisco can teach in each class by finding the greatest common factor (GCF) of the total number of violin and viola students at the school.

Suppose there are a total of m violin students and n viola students. Then the total number of students at the school is m + n. Let's find the GCF of m and n in order to determine the greatest number of students Francisco can teach in each class.

GCF of m and n will give us the number of students that can be divided equally among all the classes. Following the steps to find GCF :

Step 1 :List down all factors of m and n

Step 2 :Identify the common factors of both m and n

Step 3 :Find the largest common factor m and n. We find the factors of m and n below: Suppose m = 36 and n = 72.Therefore, the greatest common factor of m and n is 36.So, the greatest number of students that Francisco can teach in each class is 36.

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Answer:

Step-by-step explanation:

2x

The equation which shows the relationship between x and y is A: y = 2x.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

Alisha's soccer team is having a bake sale.

Alisha decides to bring chocolate chip cookies to sell.

There is a proportional relationship between the number of cookies Alisha sells, x, and the total cost (in dollars), y.

Proportional relationships are relationships for which the equations are of the form y = kx, where k is a constant.

Alisha sells 6 cookies for $12.00.

That is, total cost, y = 12 when the number of cookies, x = 6.

The equation becomes,

12 = 6k

k = 12/6 = 2

Required equation is y = 2x.

Hence the required equation is y = 2x.

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If the inflation rate is 180%, the average prices will double in less than one year.

This is because inflation measures the increase in the prices of goods and services over a period of time. Therefore, the formula for calculating how many years it will take for average prices to double at a given inflation rate is:Years to double = 70/inflation rate

In this case, the inflation rate is 180%.

Therefore:Years to double = 70/180%

Years to double = 0.389 years

This means that average prices will double in approximately 4.67 months (0.389 years multiplied by 12 months per year).

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Answer:

Insert the table

Step-by-step explanation:

There is no table above

Answer:

biggafigure a

mnn

Step-by-step explanation:

Answer:

No, it doesn't

Step-by-step explanation:

2+5=7

The two smaller lengths of a triangle cannot be equal to or less than the third side.

Angles 6 and 8 are adjacent, they are Linear pair οf angles.

Linear pair οf angles are fοrmed when twο lines intersect each οther at a single pοint. The angles are said tο be linear if they are adjacent tο each οther after the intersectiοn οf the twο lines. The sum οf angles οf a linear pair is always equal tο 180°. Such angles are alsο knοwn as supplementary angles.

Angles 1 and 4 are not adjacent, they are vertically opposite.

Angles 5 and 8 are not adjacent, they are vertically opposite.

Angles 6 and 8 are adjacent, they are Linear pair οf angles

Angles 1 and 5 are corresponding exterior angle, so the are not linear pair.

Thus, Angles 6 and 8 are adjacent, they are Linear pair οf angles

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The matching of the first row of expressions with the second row of expressions are;

1) 2√(3x²y) → x√(12y)

2) 2x√(6xy²) → y√(24x³)

3) 2y√(2x⁴) → x²√(8y²)

4) 3x²√(2y⁴) → xy√(18x²y²)

1) 2√(3x²y)

This can be broken down into the expression;

2x√(3y)

2) 2x√(6xy²)

This can broken down into;

2xy√(6x)

3) 2y√(2x⁴)

This can be simplified into;

2x²y√2

4) 3x²√(2y⁴)

This can be simplified into;

3x²y²√2

The second row of expressions are simplified as;

xy√(18x²y²)

= 3x²y²√2

x√(12y)

= 2x√3y

x²√(8y²)

= 2x²y√2

y√(24x³)

= 2xy√6x

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Answer:

the one you have selected is correct

Step-by-step explanation:

Answer:

Principal is $1000

Step-by-step explanation:

• From the formular of simple interest:

\(s.i = principal \times rate \times time\)

• substitute and find the principal:

\(100 = p \times \frac{2}{100} \times 5 \\ \\ 0.1p = 100 \\ \\ = { \underline{ \: \:1000 \: \: dollars \: \: }}\)

Answer:

The answer is in the picture

The required number of pieces Demarco does to the rest of the fabric is 4.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

here,
Demarco has a piece of frabric 6yd long. He uses a piece 3yd long.
Piece left = 6 - 3 = 3yd

Now, he cuts the rest into 3/4 long.
= length of rest piece/length of each piece
= 3 / [3/4]
= 4 pieces

Thus, the required number of pieces Demarco does to the rest of the fabric is 4.

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The probability of a patient scoring above 192 on the endurance test is approximately 40.90%. A patient at the 80th percentile receives a score of approximately 208.2.

a. To find the probability that a patient will score above 192, we need to use the Z-score formula. The Z-score measures the number of standard deviations a data point is from the mean. In this case, the formula is Z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation.

First, calculate the Z-score: Z = (192 - 185) / 30 = 7/30 ≈ 0.23.

Next, we need to find the probability of scoring above this Z-score. Using a Z-table or a calculator, we find that the probability is approximately 0.4090, or 40.90%.

b. To find the score that corresponds to the 80th percentile, we need to find the Z-score that has an area of 0.80 to the left. Using the Z-table or a calculator, we find that the Z-score is approximately 0.84.

Now, we can use the Z-score formula to find the corresponding score: X = Z * σ + μ. Plugging in the values, we get X = 0.84 * 30 + 185 = 208.2.

Therefore, a patient at the 80th percentile receives a score of approximately 208.2.

a. To find the probability of a patient scoring above 192 on the endurance test, we first calculate the Z-score. This allows us to standardize the score by measuring how many standard deviations it is from the mean. We then use a Z-table or calculator to find the probability corresponding to this Z-score, which is approximately 0.4090 or 40.90%.

b. To find the score at the 80th percentile, we first need to find the Z-score that corresponds to an area of 0.80 to the left. Using a Z-table or calculator, we find this Z-score to be approximately 0.84. We then use the Z-score formula to find the corresponding score, which is approximately 208.2.

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Answer:

its rather 3 or 5 its prob 3

Step-by-step explanation:

Solving quadratic equations by factorization can be challenging for grade 10 learners due to a variety of factors, including a lack of foundational knowledge, difficulty with mental math, and the need to remember multiple steps.

Learners need to have a strong understanding of the basics of algebra, including factoring and simplifying expressions. They also need to be able to identify the coefficients of the quadratic equation and use them to factorize it. Second, learners may struggle with the process of splitting the middle term, especially if the coefficients are large or if there are negative signs involved. This requires a strong knowledge of multiplication and addition, as well as mental math skills.

Learners may find it difficult to remember the steps involved in solving quadratic equations by factorization, especially if they are new to the concept. It is important for teachers to provide clear explanations and plenty of practice problems to help learners build their skills and confidence.

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Answer:

Equation B has no solution

Step-by-step explanation:

The reason it has no solution is because we are getting 2 answers for the same sum

We already have 4x -5y = 3

And also we are still having the same sum as equal to -3

This shows that we can not have a solution to the system

Answer:

Step-by-step explanation:

equation b it has no soulution

The expected value and the standard error for a labor participation rate in the company's sample is 0.0043

In the given question, the labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized.

The BLS reported in February 2012 that the labor force participation rate in the united states was 66.9% (calculate risk).

A marketing company asks 120 working-age people if they either have a job or are looking for a job, or the labor force.

We have to find the expected value and the standard error for a labor participation rate in the company's sample.

Working age people sample n = 120

The labor force participation rate in the United States was 66.9% = 0.669

The Expected value is μ = p = 0.669

The standard error:

SE = √p(1-p)/n

SE = √0.669(1-0.669)/120

SE = √0.669*0.331/120

SE = √0.2214/120

SE = √0.001845

SE = 0.043

Hence, the expected value and the standard error for a labor participation rate in the company's sample is 0.0043.

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Point A (1, 0) and point B (3/5, 4/5) both lie on the unit circle with center at the origin.

A circle is a geometric shape defined as the set of all points in a plane that are equidistant from a fixed point called the center. The distance between any point on the circle and the center is called the radius.

Center: The center is a fixed point in the plane from which all points on the circle are equidistant. It is denoted by the coordinates (h, k), where h represents the x-coordinate and k represents the y-coordinate of the center.

Radius: The radius is the distance between the center of the circle and any point on the circle. It is denoted by the letter "r". The radius is constant for all points on the circle.

Diameter: The diameter is a line segment passing through the center of the circle and with endpoints on the circle. It is twice the length of the radius, and it divides the circle into two equal halves.

In the xy-plane, the unit circle with center at the origin (0, 0) is defined by all the points that are at a distance of 1 unit from the origin.

Point A: (1, 0)

Point A lies on the x-axis and is 1 unit away from the origin. It represents a point on the unit circle.

Point B: (3/5, 4/5)

Point B lies on the unit circle but is not one of the standard points (such as (1, 0), (-1, 0), (0, 1), or (0, -1)). Instead, it represents a point on the unit circle with coordinates (3/5, 4/5). The x-coordinate of B is 3/5, and the y-coordinate is 4/5. The distance between point B and the origin (0, 0) is 1 unit, which satisfies the condition of being on the unit circle.

Therefore, point A (1, 0) and point B (3/5, 4/5) both lie on the unit circle with center at the origin.

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Answer:

(B) 42°

Step-by-step explanation:

The triangle LMN is inscribed in a semi-circle so therefore, if LM is the diameter, m∠LMN is 90°. Then, if one angle in ΔLMN is 90° and another is 48°, the third angle (∠NLM) will be 42° (The sum of the angles in a triangle is 180°).

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To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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Answer: