part 2. (6 points) normal distributions the normal distribution curve to the right displays the distribution of grades given to managers based on management performance at ford. of the large population of ford managers, 10% were given a grades, 80% were given b grades, and 10% were given c grades. a’s were given to those who scored 380 or higher and c’s were given to those who scored 160 or lower. a. (2 point) what are the z scores associated with the 10th and 90th percentiles from the standard normal distribution? recall that a z-score is value from the standard normal distribution and represents the number of standard deviations a value is away from its mean. b. (2 point) from part a, you should have two values - the z-scores associated with the 10th and 90th percentiles. using these two values and the mathematical definitions of a z-score, calculate the mean and standard deviation of the performance scores? show work. c. (2 point) suppose the company adds grades d and f so there are 5 categories to grade performance. if they want to give a’s only to those in the top 3%, what performance score must a manager exceed to get an a?

For any probability distribution, the expected value: 1. represents the location/center of the distribution.

In Mathematics and statistics, an expected value is sometimes referred to as the long-term mean (average) of a discrete random variable, E(X) and it can be calculated by taking the weighted average of all the outcomes of the discrete random variable with respect to their probabilities.

For instance, in a game of dice, the total number of outcomes (expected values) is generally equal to six (6). This ultimately implies that, the probability of rolling each number is p(x) = 1/6.

In conclusion, the location or center of distribution is represented by the expected value in any probability distribution.

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The equation of motion of an object moving back and forth on a spring with mass is represented by the formula given below;x′′(t)+k/mx(t)=0x(0)= initial displacement in meters

x′(0)= initial velocity in m/s

We are to find the initial conditions and the equation of motion of an object moving back and forth on a spring with mass (m). The constant k, in the formula above, is determined by the displacement and force. Hence, k = 220 N/mUsing the formula for the equation of motion, we can determine the position function of the object To solve the above differential equation, we assume a solution of the form;x(t) = Acos(wt + Ø) where A, w and Ø are constants and; w = sqrt(k/m) = sqrt(220/55) = 2 rad/sx′(t) = -Awsin(wt + Ø)Taking the first derivative of the position function gives.

Substituting in the initial conditions gives;

A = 2.2362 and

Ø = -1.1072x

(t)= 2.2362cos

(2t - 1.1072)x

(0) = 1.6852m

(approximated to four decimal places)x′(0) = -2.2362sin(-1.1072) = 2.2247 m/s (approximated to four decimal places)Thus, the initial conditions are;x(0)= 1.6852m (approximated to four decimal places)x′(0) = 2.2247m/s (approximated to four decimal places)And the equation of motion is;x(t) = 2.2362cos(2t - 1.1072)

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Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

A number's  root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as  or as 3 x 3.

Here,

If an equation have 2 roots , it means it is a quadratic function

If D=0, a quadratic function has two roots that are equal.

D (discriminant) = 0

=>b24ac=0 is required for a polynomial function to have equal roots.

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

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Answer:

The expressions a(8x+7) and 4x + 3.5 are equivalent

Therefore, according to the above problem the equation is :---

\(a(8x + 7) = (4x + 3.5) \\ 8ax + 7a = 4x + 3.5\)

By comparing the term, we get

\(8ax = 4x \\ 8a = 4 \\ a = \frac{4}{8} \\ \boxed{a = \frac{1}{2} }\)

and,

\(7a = 3.5 \\ a = \frac{3.5}{7} \\ \boxed{a = \frac{1}{2} }\)

Answer:

The expressions a(8\(x\) + 7) and 4x + 3.5 are equivalent

Step-by-step explanation:

a(8x+7)=4x+3.5

8ax+7a=4x+3.5

let keep a=1/2

8/2x+7/2=4x+3.5

4x+3.5=4x+3.5

so no is or value of a=1.5

Answer:

  a = 1/2

Step-by-step explanation:

You want the solution to 3 +0.5(4a +8) = 9 −2a.

It usually works well to start by simplifying the equation. That is, you eliminate parentheses, combine like terms.

  3 +0.5(4a) +0.5(8) = 9 -2a

  3 + 2a +4 = 9 -2a

  7 +4a = 9 . . . . . . . . . add 2a

  4a = 2 . . . . . . . . . subtract 7

  a = 0.5 . . . . . . divide by 4

The value of a is 1/2.

__

Additional comment

The attached calculator output shows this value of 'a' satisfies the equation.

Answer:

15

Step-by-step explanation:

he can read 30 pages in 10 minutes, which means 15 pages in 5 minutes  =15, 15 plus 30 = 45

30 pages in 10 minutes

15 pages in 5 minutes

The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

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The confidence interval for the proportion of students supporting the fee increase: (0.5827, 0.6539)

What is Interval?

In mathematics, an interval is expressed in numerical terms. All the numbers between two specific integers are referred to as an interval. All actual values between those two are included in this range. Any form of number you may imagine is a real number.

We have the following confidence interval of proportions for a sample of n people who were surveyed with a probability of success of π and a confidence interval 1 - α

π ± z\(\sqrt{\pi (1 - \pi )/n}\)

, where

Z stands for the z score with a p value of 1 - α/2

We have this in relation to the issue:

A price increase to pay for upgrades to the student recreation center was supported by 780 of the 1,280 students who were sampled. So

n = 1280, π = 780 / 1280

π = 0.6093

95 percent confidence level

Consequently α = 0.05, z is the Z value that has a p value of, thus

1 - 0.05/2 = 0.975

So, z = 1.96

The interval's lowest limit is:

= π - z\(\sqrt{\pi (1 - \pi )/n}\)

= 0.6093 - 1.96\(\sqrt{0.6093 * 0.3907/1280}\)

= 0.6093 - 1.96\(\sqrt{0.000185}\)

= 0.5827

This range's maximum value is:

= π + z\(\sqrt{\pi (1 - \pi )/n}\)

= 0.6093 + 1.96\(\sqrt{0.6093 * 0.3907/1280}\)

= 0.6093 + 1.96\(\sqrt{0.000185}\)

= 0.6359

For the percentage of students who favor the fee hike, the 95% confidence interval is (0.5827, 0.6539)

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Answer:

The margin of error corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is of 1.495 miligrams.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1-0.95}{2} = 0.025\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1-\alpha\).

So it is z with a pvalue of \(1-0.025 = 0.975\), so \(z = 1.96\)

Now, find the margin of error E as such

\(E = z*\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

In this question:

\(\sigma = 8, n = 110\). So

\(E = 1.96\frac{8}{\sqrt{110}} = 1.495\)

The margin of error corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is of 1.495 miligrams.

Answer:

Step-by-step explanation:

There is only one possible outcome where the first card is odd and the second card is even: {3,2}.

We are dealing with a shuffled deck of three cards: 2, 3, and 4. There are three possible outcomes when dealing one card, and two possible outcomes when dealing the second card (since one card has already been dealt). Therefore, there are a total of 3x2=6 possible outcomes when dealing two cards, and 3x2x1=6 possible outcomes when dealing all three cards.

(a) What is P(E2 | E1), the probability the second card is even given that the first card is even?

There are two ways the first card can be even: 2 or 4. If the first card is 2, there are two possible outcomes for the second card: 3 or 4. If the first card is 4, there is only one possible outcome for the second card: 2. Therefore, there are three possible outcomes where the first card is even and the second card is even: {2,3}, {2,4}, and {4,2}. The probability of the second card being even given that the first card is even is therefore:

P(E2 | E1) = number of outcomes where E1 and E2 occur / number of outcomes where E1 occurs

P(E2 | E1) = 2 / 3

(b) What is the conditional probability that the first two cards are even given that the third card is even?

There is only one way the third card can be even: 2. If the third card is 2, there are two possible outcomes for the first card: 2 or 4. If the third card is 2 and the first card is 2, there is only one possible outcome for the second card: 4. If the third card is 2 and the first card is 4, there are two possible outcomes for the second card: 2 or 3. Therefore, there are three possible outcomes where the third card is even and the first two cards are even: {2,4,2}, {2,2,4}, and {4,2,4}. The probability that the first two cards are even given that the third card is even is therefore:

P(E1E2 | E3) = number of outcomes where E1 and E2 and E3 occur / number of outcomes where E3 occurs

P(E1E2 | E3) = 3 / 6 = 0.5

(c) Let Oi represent the event that the ith card dealt is odd numbered. What is P(E2 | O1), the conditional probability that the second card is even given that the first card is odd?

If the first card is odd, there is only one possible outcome: 3. If the first card is 3, there is only one possible outcome for the second card: 2. Therefore, there is only one possible outcome where the first card is odd and the second card is even: {3,2}. The probability that the second card is even given that the first card is odd is therefore:

P(E2 | O1) = number of outcomes where O1 and E2 occur / number of outcomes where O1 occurs

P(E2 | O1) = 1 / 3

(d) What is the conditional probability that the second card is odd given that the first card is odd?

If the first card is odd, there is only one possible outcome: 3. If the first card is 3, there is only one possible outcome for the second card: 2. Therefore, there is only one possible outcome where the first card is odd and the second card is even: {3,2}. Therefore, the conditional probability that the second.

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Answer:

(-4 + sqrt11)/5

Step-by-step explanation:

-8 + sqrt(64-20)/10 = -4/5 + sqrt11/5

The statement about regression line that is true is "it indicates a linear relationship between dependent variable and independent variable(s)."

In statistics, regression is a method of modeling the connection between a dependent variable (also known as a response variable) and one or more independent variables (also known as explanatory variables or predictors). It's also known as a linear regression model.

A regression model is established in order to identify the linear relationship between the dependent variable and one or more independent variables. The line of best fit is represented by the regression line in a simple linear regression model, which represents the relationship between the dependent variable and independent variable(s).

The line of best fit is determined by minimizing the sum of the squares of the residuals (errors). The objective of the regression model is to obtain a relationship between the dependent variable and the independent variable that explains the variance of the dependent variable based on the independent variable(s).

Hence, the correct option is: it indicates a linear relationship between dependent variable and independent variable(s).

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Answer:

5.09

There will be a dash over .09

Step-by-step explanation:

Answer:

Circumference of the edge is 12.56 yards

Step-by-step explanation:

\( { \rm{circumference = \pi d}} \\ { \rm{c = 3.14 \times 4}} \\ { \rm{c = 12.56 \: yards}}\)

Answer:

The numbers are 37 and 38.

Step-by-step explanation:

Forming the equation,

→ x + (x + 1) = 75

→ 2x + 1 = 75

Now the value of x will be,

→ 2x + 1 = 75

→ 2x = 75 - 1

→ x = 74/2

→ [ x = 37 ]

The another number will be,

→ x + 1

→ 37 + 1 = 38

Hence, numbers are 37, 38.

Option B : because the amount of money Tanner plans to spend on video games plus the amount of money he plans to spend on art supplies must add up to the $350 he saved.

Tanner saved $350 and plans to spend some of it on art supplies and some on video games. This means that the amount of money he spends on video games plus the amount of money he spends on art supplies must add up to $350.

Let a represent the amount of money Tanner plans to spend on art supplies. Then we have the following equation:

v + a = 350

Solving for a, we get:

a = 350 - v

This means that the amount of money Tanner plans to spend on art supplies is 350 minus the amount of money he plans to spend on video games.

Since Tanner cannot spend a negative amount of money on video games, v must be less than or equal to 350. Therefore, the correct inequality is v ≤ 350.

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Tanner saved $350 this summer. He plans to spend some of the money on art supplies and some on video games.

Let v represent the money, in dollars, Tanner plans to spend on video games. Which inequality models the story? explain?

A. v > 350________

B. v ≤ 350______

C. v <350________

D. v ≥ 350

The p-value for the test is approximately 0.2643. This indicates that there is a 26.43% chance of observing a sample proportion as extreme as 0.30 or greater, assuming the null hypothesis is true.

Since the p-value is greater than the significance level of 0.05, we do not have enough evidence to reject the null hypothesis. This means that we fail to find significant evidence that the current arrest rate is greater than the past arrest rate of 25%.

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\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \:Domain = [-9, -1]\)

\(\qquad \tt \rightarrow \:Range = [-1 , 3]\)

____________________________________

\( \large \tt Solution \: : \)

Domain = All possible values of x for which f(x) is defined

[ generally the extension of function in x - direction ]

Range = All possible values of f(x)

[ generally the extension of function in y - direction ]

\( \large\textsf{For the given graph : } \)

\(\qquad \tt \rightarrow \: domain = [ - 9, -1]\)

\(\qquad \tt \rightarrow \: range= [ -1,3]\)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

100 is the least number of sheets of each type he might buy given that reptile stickers come in sheets of 10 and fish stickers come in sheets of 25 and Antonio buys the same number of both types of stickers and he buys at least 100 of each type. This can be obtained by finding LCM(Least Common Multiple) of 10 and 25 and identifying the multiple nearest to 100.

Here in the question it is given that,

We have to find the least number of sheets of each type he might buy.

First we have to find the LCM(Least Common Multiple) of 10 and 25

10 = 2 × 5

25 = 5 × 5    

LCM(10,25) = 2 × 5 = 50  

But  he buys at least 100 of each type, then we recall the multiples of 18 to find the least number which is nearest to 100.

Multiples of 50 = 50, 100, 150,...

The number nearest to 100 is 100 itself.

Hence 100 is the least number of sheets of each type he might buy given that reptile stickers come in sheets of 10 and fish stickers come in sheets of 25 and Antonio buys the same number of both types of stickers and he buys at least 100 of each type.

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9514 1404 393

Answer:

  16

Step-by-step explanation:

Radii of the same circle are the same, so we have ...

  3x -2 = 4x -8

  6 = x . . . . . add 8-3x

  3x -2 = 3(6) -2 = 16 . . . . the radius of the circle

Answer:

pronoun

Step-by-step explanation:

Given:

The degree of the polynomial = 3

Leading coefficient = 1

Zeros of the polynomial are 5 and 4i.

To find:

The expanded form of the polynomial.

Solution:

According to the complex conjugate root theorem, if a+ib is a zero of a polynomial, then a-ib is also a zero of that polynomial.

Here, zeros of the polynomial are 5 and 4i. It means the third zero of the polynomial is -4i. So, the factors of the polynomial are \((x-5),(x-4i),(x+4i)\).

The required polynomial is the product of its all factor and a constant which is equal to the leading coefficient. Here, the constant is 1. So, the required polynomial is

\(P(x)=1(x-5)(x-4i)(x+4i)\)

\(P(x)=(x-5)(x^2-(4i)^2)\)

\(P(x)=(x-5)(x^2+16)\)             \([\because i^2=-1]\)

\(P(x)=(x-5)(x^2+16)\)

On further simplification, we get

\(P(x)=x^3+16x-5x^2-80\)

\(P(x)=x^3-5x^2+16x-80\)

Therefore, the required polynomial P is \(P(x)=x^3-5x^2+16x-80\).

The 99% confidence interval for the difference in the proportions of people from City A and City B who prefer New Spring soap is given by the lower limit and upper limit.

To calculate the confidence interval for the difference in proportions, we can use the formula for the confidence interval for the difference between two proportions:

p1 - p2 ± Z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)),

where p1 and p2 are the proportions of people from City A and City B who prefer New Spring soap, n1 and n2 are the sample sizes of City A and City B, and Z is the z-score corresponding to the desired level of confidence (in this case, 99%).

From the given information, we have p1 = 121/294 ≈ 0.412 and p2 = 149/409 ≈ 0.364. The sample sizes are n1 = 294 and n2 = 409.

We can substitute these values into the formula along with the z-score for a 99% confidence level (which corresponds to approximately 2.576) to calculate the confidence interval for the difference in proportions.

After performing the calculations, we find the lower limit and upper limit of the confidence interval, rounded to three decimal places.

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The derivatives of the expressions are as follows: a. f(x) = e + 5e²z e : f '(x) = 5e² eb. f (x) = e + 5e³ ea: f'(x) = 15e³ ec. f(x) = e + 10e² ez: f '(x) = 20e² z Therefore, the answer to the question "Match the expression with its derivative" is: Expression Derivativea.

\(f(x) = e +5e2z ef '(x) = 5e² eb. f (x) = e +5e³ eaf '(x) = 15e³ ec. f(x) = e +10e2 ezf '(x) = 20e² z\) The function's derivative, f '(x), is the rate of change of the function at a particular point x. The notation for the derivative is f'(x) or df/dx.

The fundamental theorem of calculus is the relationship between differentiation and integration. It establishes that the two operations are inverse operations.

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Answer:

20ft

Step-by-step explanation:

These two triangles are similar therefore you can do the ration of 5/12=x/48 and x=20

To find the second partial derivatives of the function \(f(x, y) = x \cdot y^{10} + x^2 + y^4\) at the point \(x_0 = (4, -1)\), we need to calculate the following derivatives:

1. \(\frac{{\partial^2 f}}{{\partial x^2}}\):

Taking the partial derivative of \(f\) with respect to \(x\) once gives: \(\frac{{\partial f}}{{\partial x}} = y^{10} + 2x\). Taking the partial derivative of this result with respect to \(x\) again yields: \(\frac{{\partial^2 f}}{{\partial x^2}} = 2\).

2. \(\frac{{\partial^4 f}}{{\partial y^4}}\):

Taking the partial derivative of \(f\) with respect to \(y\) once gives: \(\frac{{\partial f}}{{\partial y}} = 10xy^9 + 4y^3\). Taking the partial derivative of this result with respect to \(y\) three more times gives: \(\frac{{\partial^4 f}}{{\partial y^4}} = 90 \cdot 10! \cdot x + 24 \cdot 4! = 90! \cdot x + 96\).

Therefore, the second partial derivative \(\frac{{\partial^2 f}}{{\partial x^2}}\) is equal to 2, and the fourth partial derivative \(\frac{{\partial^4 f}}{{\partial y^4}}\) is equal to \(90! \cdot x + 96\).

In conclusion, the second partial derivative with respect to \(x\) is a constant, while the fourth partial derivative with respect to \(y\) depends on the value of \(x\).

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Since the probability that each airplane part passes inspection is 93%, the probability that all five of the next parts pass inspection is:

(0.93)^5 = 0.696

Use code with caution. Learn more

This is about a 70% chance that all five of the next parts will pass inspection.

However, it is important to note that this is just a probability. It is possible that all five parts will pass inspection, but it is also possible that none of them will pass inspection

Answer:

m= -2n-13

Step-by-step explanation:

1. Subract 1 from both sides

m=-2(n+6)-1

2. Mulitply n+6 by -2

m=-2n-12-1

3. m=-2n-13