Exam scores in a large class are normally distributed with a mean of 60
and standard deviation of 10. The teacher decides to boost the scores by
multiplying everyone's score by 1.2
The model for the new scores will be:

Answer:

Undercoverage

Step-by-step explanation:

Using a local telephone book to select a simple random sample could introduce UNDERCOVERAGE bias.

I hope it helps! Have a great day!

The probability that more than the expected number of Sikh youths wear a turban in a random sample of five is 0.3671 (rounded to 4 decimal places).

a. Using the binomial distribution formula, we can determine the likelihood that two out of a random sample of five Sikh teenagers are turban-wearing:

\(P(X = 2) = (5 pick 2) (5 choose 2) * (0.75)^3 * (0.25)^2\)

"X" indicates the proportion of Sikh adolescents who wear turbans, "5 choose 2" indicates the number of possible methods to select 2 Sikhs from a group of 5, and "0.75" and "0.25" indicate the likelihoods that a Sikh youngster will not be wearing a turban and will be wearing one, respectively.

This expression can be made simpler by using a calculator to become:

P(X = 2) = 10 * 0.421875 * 0.0625 = 0.2659

Hence, 0.2659 percent chance exists that two out of every five Sikh youngsters in a random sample will be turban-wearing (rounded to 4 decimal places).

Using the complement rule, we can determine the likelihood that two or more of a random sample of five Sikh teenagers are wearing turbans:

P(X >= 2) = 1 - P(X 2)

where X is the proportion of young Sikhs who are turban-wearing.

P(X 2) is the likelihood that fewer than 2 of five Sikh teenagers chosen at random will be turban-wearing.

This can be calculated as:

P(X 2) equals P(X = 0) plus P(X = 1).

P(X = 0) = (5 select 0) * (0.75) * (5 select 0) * (0.25) * 0 = 0.2373

P(X = 1) = (5 select 1) * (0.75) * (4 select 1) * (0.25) * 1 = 0.3956

P(X 2) = 0.2373 + 0.3956 = 0.6329 as a result.

We can then compute P(X >= 2) = 1 - 0.6329 = 0.3671 using the complement rule.

Consequently, there is a 0.3671 percent chance that two or more of five Sikh teenagers chosen at random will be turban-wearing (rounded to 4 decimal places).

c. The following formula can be used to determine how many Sikh teenagers in a random sample of five are likely to wear a turban:

E(X) = n * p = 5 * 0.25 = 1.25

Using the cumulative binomial distribution function, we can determine the likelihood that more Sikh teenagers than predicted in a random sample of five wear turbans:

P(X > 1) = 1 - P(X <= 1)

P(X = 1) equals P(X = 0) plus P(X = 1).

P(X = 0) = (5 select 0) * (0.75) * (5 select 0) * (0.25) * 0 = 0.2373

P(X = 1) = (5 select 1) * (0.75) * (4 select 1) * (0.25) * 1 = 0.3956

Therefore,

P(X <= 1) = 0.2373 + 0.3956 = 0.6329

The complement rule can then be used to determine:

P(X > 1)

P(X > 1) = 1 - 0.6329 = 0.3671

Hence, in a random sample of five Sikh adolescents, the likelihood that there are more turban-wearing Sikh youths than expected is 0.3671. (rounded to 4 decimal places).

d. To determine the likelihood that more than predicted will occur.

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Answer: B: 85 °

Step-by-step explanation: I'm pretty sure that the triangle adds up up 360 degrees. When you add the 2 points together you get 275 and 360 minus 275 is equal to 85. Im not sure this is right, but im pretty sure

Answer:

r7

Step-by-step explanation:

\(\sqrt{((-6)-(-5))^2 +(9-2)^2}=5\sqrt{2} \approx 7.071\)

By using the concept of population standard deviation and sample standard deviation, it can be inferred that

2nd and 4th option  is correct

What is standard deviation?

At first, it is important to know about variance.

Variance is the sum of the square of deviation from the mean.

On taking the square root of the variance, standard deviation is obtained.

Here, the cases are

1) Population standard deviation \((\sigma)\) is known

2) Population standard deviation \((\sigma)\) is unknown

3) Sample standard deviation (s) is known

4) Sample standard deviation (s) is unknown

Now,

Formula for z

z = \(\frac{x - \mu}{\sigma}\) , \(\mu\) is the population mean, \(\sigma\) is the population standard deviation

Formula for t

t = \(\frac{x - \mu}{s}\) ,  s is the sample standard deviation

So if  Population standard deviation \((\sigma)\) is known and Sample standard deviation (s) is unknown, z table is used

If Population standard deviation \((\sigma)\) is unknown and Sample standard deviation (s) is known, t table is used

So 2nd and 4th option is correct

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Complete Question

The complete Question has been attached here

Answer: The first one can be an independent variable and the second one can be an dependent variable......

Answer:

Distance, d, could be a(n) independent variable because it affects the amount of time that someone has traveled.

Distance, d, could also be a(n) dependent variable because it is affected by the speed traveled.

Step-by-step explanation:

Both can be dependent or independent variables depending on what result we are looking for. If one tries to know distance covered then distance is dependent variable and speed is independent variable.

So distance is an independent variable of the inverse of the function of motion as a function of time.

So we can conclude that the "Independent variable" is Time in hours or time traveled and the "Dependent variable" is Distance in miles or speed traveled.

To find the values of c and a that satisfy the equations f(-2) = 16/5 and f(2) = 1/80 for the function f(x) = ca^x, we can substitute the given x-values into the function and set them equal to the corresponding y-values. By solving these equations simultaneously, we can determine the values of c and a.

Let's substitute x = -2 and x = 2 into the function f(x) = ca^x and set them equal to the given y-values:

For x = -2: f(-2) = ca^(-2) = 16/5

For x = 2: f(2) = ca^2 = 1/80

Now we have a system of equations:

ca^(-2) = 16/5     --(1)

ca^2 = 1/80         --(2)

To solve this system, we can divide equation (2) by equation (1):

(ca^2) / (ca^(-2)) = (1/80) / (16/5)

a^(2-(-2)) = (1/80) / (16/5)

a^4 = 1/80 * 5/16

a^4 = 1/256

Taking the fourth root of both sides, we find:

a = ± (1/4)

Now we can substitute the value of a into either equation (1) or (2) to solve for c. Let's use equation (1):

c(1/4)^(-2) = 16/5

c(1/4)^2 = 16/5

c(1/16) = 16/5

c = (16/5) * 16

c = 256/5

Therefore, the values of c and a that satisfy the given equations are c = 256/5 and a = ± (1/4).

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Answer:

  (x, y) = (-1, 5)

Step-by-step explanation:

You want to solve this system of equations by substitution.

The idea of substitution means we want to replace an expression in one equation for an equivalent expression based on the other equation.

Here, the second equation gives an expression equivalent to "y", so we can use that expression in place of y in the first equation:

  5x +2(-2x +3) = 5 . . . . . . . . (-2x+3) substitutes for y

  x +6 = 5 . . . . . . . . . . simplify

  x = -1 . . . . . . . . . subtract 6

  y = -2(-1) +3 = 5 . . . . . use the second equation to find y

The solution is (x, y) = (-1, 5).

__

Additional comment

Choosing substitution as the solution method often works well if one of the equations gives an expression for one of the variables, or if it can be solved easily for one of the variables. The "y=" equation is a good candidate for providing an expression that can be substituted for y.

Any equation that has one of the variables with a coefficient of +1 or -1 is also a good candidate for providing a substitution expression.

  4x -y = 3   ⇒   y = 4x -3 . . . . . for example

The attached graph confirms the solution above.

The minimum value of x + 4y is 5, attained when x = 10 and y = 5. To solve the linear programming problem using the simplex method, we first convert the given problem into standard form by introducing slack variables

The problem can be written as follows:

Minimize z = x + 4y

subject to:

2x + 5y - s1 = 35

-3x + 5y - s2 = 2

8x + 3y + s3 = 94

-9x + 7y + s4 = 49

x, y, s1, s2, s3, s4 ≥ 0

The initial tableau is constructed using these equations. The simplex method involves iteratively improving the solution until an optimal solution is reached. In each iteration, the pivot element is selected to perform row operations.

After applying the simplex method, we find that the minimum value of the objective function z (x + 4y) is 5, which is attained when x = 10 and y = 5. This means that for x = 10 and y = 5, the objective function is minimized and satisfies all the given constraints.

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Using the inverse relation for the cubic root, we conclude that the correct option is the third one.

This is kinda a trivial question, as that is the definition of a root.

Actually, for any root we will have:

\(\sqrt[n]{x} = x^{1/n}\)

Now, using the inverse relation, we know that:

(∛x)^3 = x

Then:

(∛4)^3

Now, remember that:

(a^n)^m = a^(n*m)

Using that property, we can write like in option 3.

(4^(1/3))^3 = 4^( (1/3)*3) = 4^1 = 4

Then we can see that:

(∛4)^3  = (4^(1/3))^3

This means that ∛4 = 4^(1/3)

Then the correct option is the third one.

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a) Yes, It does. The scatterplot support the newspaper report about number of semesters and starting salary.

b) The value is relatively low, indicating that there are other factors that also contribute to starting salary.

c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables.

a) The scatterplot appears to show a positive association between the number of semesters needed to complete an academic program and the starting salary in the first year of a job. As the number of semesters increases, the starting salary generally increases as well. Therefore, the scatterplot supports the newspaper report.

b) The coefficient of determination, or R-squared value, represents the proportion of the variation in the dependent variable (starting salary) that is explained by the independent variable (number of semesters). A value of 0.335 means that 33.5% of the variation in starting salary is explained by the number of semesters. This value is relatively low, indicating that there are other factors that also contribute to starting salary.

c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables. A value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no correlation. The correlation coefficient for this data is not provided in the problem, so it is not possible to determine it. Without the correlation coefficient, it is not possible to interpret the strength and direction of the association between number of semesters and starting salary.

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Answer:

85

Step-by-step explanation:

x:y

8:10

68:y

divide 68 by 8 u get 8.5 and the times it by 10

so y equals 85

9 pounds of hamburger meat will be needed by Brian.

We are given value for one unit. The calculation is required for more than one units, hence, multiplication will be performed.

As per the given information, amount of hamburger meat required for one person is = 3/4 pound

Amount of hamburger meat required for 12 people = (3/4) × 12

Performing division to find the amount of hamburger meat required for 12 people

Amount of hamburger meat required for 12 people = 3 × 3

Performing multiplication to find the amount of hamburger meat required for 12 people

Amount of hamburger meat required for 12 people = 9 pounds

Therefore, Brain needs to buy 9 pounds of hamburger meat.

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Answer:

  yes

Step-by-step explanation:

You want a graph of P = 125 +50W.

The given equation is in slope-intercept form. The independent variable is W, and the dependent variable is P.

Usually, the independent variable is graphed on the horizontal axis, which you have done.

The dependent variable is graphed on the vertical axis, which you have done.

The axes are correctly labeled and graduated.

The "y-intercept" (P value) when the independent variable is zero is the constant in the equation, 125. You have correctly shown that on the graph.

The slope of the line is the coefficient of the independent variable (W) in the equation. You have correctly shown that P increases by 50 when W increases by 1.

Yes, you properly graphed the equation.

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Answer:10:05

Step-by-step explanation:

subtract 45 from 50!

Answer:

She started the test at 10:05 am

Step-by-step explanation:

Take the end time and subtract the time of the test

10:50-45 = 10:05

She started the test at 10:05 am

The probability distribution of X is 0.5, 0.25, 0.25, and 0.125. Mean value ∑ X × P (X) = 1.875. Standard Deviation of X = 1.0533

a) For a fair coin,

P(H) = P(T) = 0.5

Outcome  X                            Probability

T                  1                                  0.5

HT              2                       0.5×0.5 = 0.25

HHT          3                       0.5×0.5×0.5 = 0.125

HHHT          4                           0.5×0.5×0.5×0.5 = 0.0625

HHHH          4                           0.5×0.5×0.5×0.5 = 0.0625

So, probability distribution of X is

X P(X)

1 0.5

2 0.25

3 0.125

4 0.0625+0.0625 = 0.125

b)

X     P(X)    X×P(X)         X2×P(X)

1     0.5     0.5          0.5

2     0.25      0.5               1

3     0.125    0.375         1.125

4     0.125       0.5            2

sum 1     E(X) = 1.87

c) Variance = E(X²) - E(X)²

= 4.625 - 1.875²

= 1.1094

Standard Deviation of X = √ Variance

= √1.1094

= 1.0533

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Answer:

11

Step-by-step explanation:

(8y + 5) - 2z

y = 3, z = 9

Let's plug in the given values.

(8(3) + 5) - 2(9)

First let's multiply.

(24 + 5) - 18

Now simplify within the parentheses.

29 - 18

Subtract.

11

This is your answer.

Hope this helps!

Since we have a unique value of x and y, it shows that the system of the equation is consistent and independent.

Given the system of equation expressed as:

3x + y = 3

x - 2y = 4

Solve simultaneosly;

3x + y = 3 ............. 1 * 1

x - 2y = 4 ...............2 * 3

_________________________

3x + y = 3

3x - 6y = 12

Subtract

y-(6y) = 3 - 12

7y = -9

y = -9/7

Substitute y = -9/7 into the equation to get x

x - 2y = 4

x - 2(-9/7) = 4

x + 18/7 = 4

x = 4 -  18/7

x = 3/7

Since we have a unique value of x and y, it shows that the system of the equation is consistent and independent.

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With the thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters.

a) 40% of the flanges exceeds 1.01 millimeters.

b) 1.04 millimeters is the thickness that is exceeded by 90% of the flanges.

c) The mean of flange thickness is 1 millimeters and the variance of flange thickness is 0.01 millimeters^2.

a) To determine the proportion of flanges that exceeds 1.01 millimeters, we need to find the area under the probability density function (pdf) of the thickness that is greater than 1.01 millimeters.

Let's call the random variable X representing the thickness of the flange. The pdf of X is uniform, so it has constant value over the interval [0.95, 1.05]. Therefore, the proportion of flanges that exceeds 1.01 millimeters can be found as follows:

P(X > 1.01) = (1.05 - 1.01) / (1.05 - 0.95) = (1.05 - 1.01) / 0.1 = 0.04 / 0.1 = 0.4

So, 40% of the flanges exceed 1.01 millimeters.

b) To find the thickness that is exceeded by 90% of the flanges, we need to solve for X in the following equation:

P(X > X) = 0.9

Substituting the values for the pdf, we get:

(X - 0.95) / (1.05 - 0.95) = 0.9

Solving for X, we get:

X = 0.95 + 0.9 * (1.05 - 0.95) = 0.95 + 0.9 * 0.1 = 0.95 + 0.09 = 1.04

So, 1.04 millimeters is the thickness that is exceeded by 90% of the flanges.

c) The mean of X can be calculated as follows:

Mean = (0.95 + 1.05) / 2 = 1

The variance of X can be calculated as follows:

Variance = (1.05 - 0.95)^2 / 12 = 0.01

So, the mean and variance of flange thickness are:

Mean = 1 millimeters

Variance = 0.01 millimeters^2

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Answer:

.2 Cm

Step-by-step explanation:

The overall shapes of the distributions are symmetric  and right skewed

In statistics, a distribution is considered symmetric if the right and left halves of the distribution are mirror images of each other.

In this case, the overall shape of the distribution is symmetric

From the dot plot, we have the following readings

0,3,4,5,5,6,6,7,7,8,8

Using a graphing tool, we have

Mean absolute deviation = 1.79

A right-skewed distribution is a type of probability distribution where the majority of the data values are clustered on the left side of the distribution, while a few large values extend out to the right side.

In this case, the overall shape of the distribution is right skewed

From the histogram, the true statement about the distribution is that the distribution has an outlier

The datapoints for the last question are not given

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The equation of the function, g(x) from the task content is; g(x) = -x/25 + 203/25.

From observation of the function, f(x), it follows that the slope of f(x) is 25. Hence, it follows that the slope of g(x) is; -1/25 since both functions are perpendicular to each other.

Therefore, the equation for g(x) is;

-1/25 = (y-8)/(x-3)

25y -200 = -x +3

Hence, y = -x/25 + 203/25.

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The probability of rolling two dice and getting a sum of 7 is 1/6.

The probability is the ratio of the number of favorable outcomes to the total outcomes in that sample space. Probability of an event P(E) = (Number of favorable outcomes) ÷ (Sample space).

Sample space for rolling a pair of dice we have:

=> S {(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)}

n(S) = 36

Let A = sum of numbers is 7 = { (1, 6)(2, 5)(3, 4) (4, 3) (5, 2) (6, 1)}

n(A) = 6

P (Sum of numbers is 7) = n(A) / n(S)

= 6/36 = 1/6

Therefore, the probability of rolling two dice and getting a sum of 7 is 1/6.

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Answer:

∠ 1 = 50°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

140° is an exterior angle of the triangle, thus

90° + ∠ 1 = 140° ( subtract 90° from both sides )

∠ 1 = 50°

Answer:

50 degrees

Step-by-step explanation:

To find the measure of angle 1, you must first find the other unknown angle in the triangle. You can find this through supplementary angles. The bottom angle as well as 140 must be equal to 180 because they are supplementary, so to find it solve 180-140, which is 40. Now two of the angles in the triangle are known, one is 40 and the other is 90 as shown by the square. You know that every angle equals 180 degrees, so to find angle 1 add the known angles and subtract that from 180. 180-(90+40), which equals 50. So m<1=50.

Answer:

1)x=5 y=4

2)y=2 x=5

3)y=12 x=3

Step-by-step explanation:

hope that helps!

Answer:

15 mph

Step-by-step explanation:

28mi=2  1/3

2   1/3 = 2 hrs 20min

110min

28/110=.254 mi per min

.25*60=15 mi per hrs

Answer:

33 students

Step-by-step explanation:

ratio = 6 : 5

if there are 3 more girl that boy

ratio 1 equal 3.

total ratio

6 + 5 = 11

total number of students

11 × 3 = 33