Suppose an investigator takes a random sample of n = 50 birth weights from several teaching hospitals located in an inner-city neighborhood. In her random sample, the sample mean is y¯ = 3.15 kg and the standard deviation is 250 grams. (a) Calculate a 95% confidence interval for the population mean birth weight in these hospitals. (b) The typical weight of a baby at birth for the US population is 3.25 kg. The investigator suspects that the birth weights of babies in these teaching hospitals is different than 3.25 grams, but she is not sure if it is smaller (from malnutrition) or larger (because of obesity prevalence in mothers giving birth at these hospitals). Carry out the hypothesis test that she would conduct.

The probability density function will be expressed as f_M(x) = n * x^(n-1) and cumulative density function is f_Z(z) = n * (1-z)^(n-1).

To find the probability density function of M, we need to find the probability that M takes on a particular value x, which is equal to the probability that all of the random variables U1, ..., Un are less than or equal to x. Since the Ui are independent, this probability is equal to the product of the individual probabilities that each Ui is less than or equal to x. Since each Ui has a uniform distribution over [0, 1], the probability that Ui is less than or equal to x is simply x. Therefore, the probability that M takes on a particular value x is equal to x^n.

This means that the probability density function of M is given by:

f_M(x) = n * x^(n-1)

for x in the range [0, 1].

For the second part of the question, we want to find the cumulative distribution function (c.d.f.) and probability density function (p.d.f.) of Z = min(U1, ..., Un). We can find the c.d.f. of Z by finding the probability that Z is less than or equal to a particular value z. This is equal to the probability that all of the random variables U1, ..., Un are greater than or equal to z. Since the Ui are independent, this probability is equal to the product of the individual probabilities that each Ui is greater than or equal to z. Since each Ui has a uniform distribution over [0, 1], the probability that Ui is greater than or equal to z is simply 1-z. Therefore, the probability that Z is less than or equal to z is equal to (1-z)^n.

This means that the cumulative distribution function of Z is given by:

F_Z(z) = (1-z)^n

for z in the range [0, 1].

To find the probability density function of Z, we can differentiate the cumulative distribution function with respect to z. This gives us:

f_Z(z) = n * (1-z)^(n-1)

for z in the range [0, 1].

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Point E does not follow the trend with respect to the other data and is probably an outlier. The value of the car is much higher than other cars with similar miles driven.

"Information available from the question",

In the question:

In a study to determine whether miles driven is a good predictor of trade-in value, 11 cars of the same age, make, model, and condition were randomly selected. The following scatterplot shows trade-in value and mileage for those cars.

Five of the points are labeled A, B, C, D, and E, respectively.

E $6,500+ А $6,000 B $5,500+ $5,000+ $4,500+ Value $4,000 + + 50 60 70 80 90 100 Miles Driven

To find the which point is the most influential with respect to a regression of trade-in value versus miles driven?

Now, According to the question:

According to the points of labeled:

The correct answer is :

To see the figure.

Hence, Point E does not follow the trend with respect to the other data and is probably an outlier. The value of the car is much higher than other cars with similar miles driven.

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1.35 as a fraction in simplest form is written as 27/20.

A fraction, which is expressed in the form p/q, where p and q are both integers, denotes a portion of a whole.

To convert 1.35 to a fraction, do the following:

Write the decimal number split by 1 first as follows:

1.35/1

Since the numerator has two digits after the decimal point, we must multiply the numerator and denominator by 102 to get 100, removing the decimal point.

1.35 × 100/ 1 × 100 = 135/100

Because 135 and 100 have 5 in common, we may simplify the fraction to show the same amount: 135 5/100 5 = 27/20.

We can also phrase 1.35 as an improper fraction since the numerator exceeds the denominator.

Therefore, 1.35 as a fraction in simplest form is written as 27/20.

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Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.

The correct option is (B).

Now, According to the question:

Stratified sampling design divides the given population into small sub-groups called strata. The members of each strata share some common features and at any particular time, a sample is randomly selected from each stratum which is then compared to the entire population. During random sampling, a number proportional to the stratum size is selected from all strata. The randomly selected samples from each strata are then combined to form a common random sample.

Considering that the editor wants to adopt stratified sampling, option B fits (Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.)

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The complete question is this:

A newspaper editor wants to investigate whether residents of the city support a proposal to build a new high school football stadium. The editor hires a polling firm to conduct a survey and requests that a sample of 500 residents be selected using a stratified sampling design based on voting districts within the city. Which of the following methods will achieve the desired sampling design?

(A) Send a survey to all city residents and use the first 500 returned surveys for the sample.

(B) Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.

(C) Select one voting district at random, and then select a random sample of 500 from the selected voting district.

(D) Alphabetize a list of all city residents, and then select the first 500 residents on the list, classifying those selected by voting district.

(E) Select the first 500 city residents who attend the next high school football game.

The confidence interval for the task of organizing the poll for the upcoming elections be,

(222.117 , 257.883)

Given, You have been given the task of organizing a poll regarding an upcoming election.

The object is to estimate the proportion of the country that will vote to keep the current government in power.

You have been told to collect a sample and find a 95% confidence interval for the proportion.

This interval is allowed to have a margin of error of 3%. A preliminary investigation suggests that the proportion of people that will vote to keep the current government is 0.74.

We have to find the confidence interval,

Subtract 1 from your sample size. 10 – 1 = 9.

Subtract the confidence level from 1, then divide by two.

(1 – .95) / 2 = .025

For 9 degrees of freedom df and α = 0.025, margin of error is 2.262.

Divide your sample standard deviation by the square root of your sample size.

25 / √(10) = 7.90569415

Now, Multiply 2.262 × 7.90569415 = 17.8826802

For the lower end of the range

240 – 17.8826802 = 222.117

For the upper end of the range

240 + 17.8826802 = 257.883

Hence, the confidence interval be (222.117 , 257.883)

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The relative price of ingredient A is 158, ingredient B is 131.1 and ingredient C is 96.

In the given question we have to compute the price relatives for the three ingredients A, B and C.

Now finding the relative price using the formula.

Relative Price(RP) = Ending Cost(E)/Beginning Cost(B) *100

Now from the given table;

Ingredient Beginning(B)      Ending(E)            E/B                 E/B*100

A                     2.50                3.95                    1.58                   158

B                     8.75                9.90                    1.131                   131.1

C                     0.99                0.95                    0.96                   96

Hence, the relative price of ingredient A is 158, ingredient B is 131.1 and ingredient C is 96.

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The right question is

A chemical company produces a special industrial chemical that is a blend of three chemical ingredients. The beginning-year cost per pound, the ending-year cost per pound, and the blend proportions follow. (Round your answers to the nearest integer.)

                    Cost per Pound ($)

Ingredient Beginning Ending Quantity (pounds) per 100

                                                                     Pounds of Product

A                     2.50            3.95                   25

B                     8.75            9.90                   15

C                     0.99            0.95                   70

Compute the price relatives for the three ingredients.

Item Price Relative

A

B

C

The volume of cylinder is 84.82 cubic feet

In this question, we have been given for a cylinder the diameter equals 3 feet and the length equals 12 feet.

We need to find  the volume of a cylinder.

From given data,

diameter d = 3 feet

So, radius r = d/2

                r = 1.5 ft

length of cylinder (h) = 12 ft

The formula for the  volume of a cylinder is,

V = π * r² * h

V = π * 1.5² * 12

V = π * 2.25 * 12

V = 84.82 cubic feet

Therefore, the volume of cylinder with the diameter equals 3 feet and the length equals 12 feet is 84.82 cubic feet

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The area of the entire floor is: C. 140 square feet.

The entire floor of the building given is composed of a trapezoid, rectangle, and a triangle.

Therefore, the area of the entire floor = area of the trapezoid + area of the rectangle + area of the triangle.

The formula are:

Area of entire floor = 1/2(a + b)h + (l × w) + 1/2(b)(h)

The variables are:

Base (a) = 4 ft

Base (b) = 8 ft

Height of trapezoid (h) = 6 ft

Length of rectangle (l) = 10 ft

Width of rectangle (w) = 8 ft

Base of triangle = 6 ft

Height of triangle (h) = 8 ft

Area of entire floor = 1/2(4 + 8)6 + (10 × 8) + 1/2(6)(8)

Area of entire floor = 36 + 80 + 24 = 140 square feet.

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Answer:

0.9475

Hope this Helps!

if a decimal number is divisible by 3 if and only if the sum of its digits is divisible by three is evident and proved below.

Let n be a decimal number.

Assume n is divisible by 3.

lets consider n in terms of its digits as

n = d_1 * 10^(m-1) + d_2 * 10^(m-2) + ... + d_m * 10^0

where m is the number of digits in n and d_1, d_2, ..., d_m are its digits.

Substituting n = 3k into the above equation, we get

3k = d_1 * 10^(m-1) + d_2 * 10^(m-2) + ... + d_m * 10^0

Subtracting 3k from both sides of the equation, we get

0 = d_1 * 10^(m-1) + d_2 * 10^(m-2) + ... + d_m * 10^0 - 3k

Adding 3k to both sides of the equation, we get

3k = d_1 * 10^(m-1) + d

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If a priority mail package has a maximum combined length and girth of 171 inches and is rectangular in shape with a square cross section, the maximum volume allowed is 925.

Given that,

The combined length and girth of a priority mail package cannot exceed 171 inches, according to postal standards.

We have to find calculate the size of the largest volume, cylindrical container that can be sent via priority mail.

We know that,

Let

Length= Breadth =x

Height=y

Volume can be written as

V=x²y

Now,

Combined length and girth is

7x+y=171

y=171-7x

V(x)=x²(171-7x)

V(x)=171x²-7x³

Differentiating with respect to x.

V'(x)=343x-21x²

The maximum value

V'(x)=0

343x-21x²=0

7x(49-3x)=0

x=0

and

49-3x=0

3x=49

x=49/3

Once again differentiating with respect to x.

V''(x)=343-42x

V''(x)=343-42(0)=343>0(min)

V''(x)=343-42(49/3)=-343<0(max)

The maximum volume is

Vmax=V(49/3)=(49/3)(171-7(49/3))

Vmax=925

Therefore, If a priority mail package has a maximum combined length and girth of 171 inches and is rectangular in shape with a square cross section, the maximum volume allowed is 925.

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The ways the assignments can be assigned to the students with the condition is 66 ways

From the question, we have the following parameters that can be used in our computation:

Total number of questions, n = 12

Total numbers of students, r = 2

The number of ways the assignments can be assigned to the students is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 12 and r = 2

Substitute the known values in the above equation

Total = ¹²C₂

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 12!/10! * 2!

Evaluate

Total = 66

Hence, the number of ways is 66

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Answer:

[tex]\begin{aligned}\textsf{1.} \quad \textsf{As}\;\; &x \rightarrow - \infty,\;\;f(x) \rightarrow + \infty\\ \textsf{As}\;\; &x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty \end{aligned}[/tex]

[tex]\begin{aligned}\textsf{2.} \quad \textsf{As}\;\; &x \rightarrow - \infty,\;\;f(x) \rightarrow - \infty\\ \textsf{As}\;\; &x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty \end{aligned}[/tex]

[tex]\begin{aligned}\textsf{3.} \quad \textsf{As}\;\; &x \rightarrow - \infty,\;\;f(x) \rightarrow - \infty\\ \textsf{As}\;\; &x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty \end{aligned}[/tex]

Step-by-step explanation:

Root Multiplicity

Odd multiplicity → the graph will cross the x-axis at the root.

Even multiplicity → the graph will touch the x-axis at the root (but will not cross the x-axis).

Given function:

[tex]p(x)= \dfrac{2}{3}(3x - 6)(x + 2)(x - 3)^2[/tex]

Therefore:

End behaviors:

[tex]\textsf{As}\;\; x \rightarrow - \infty,\;\;f(x) \rightarrow + \infty[/tex]

[tex]\textsf{As}\;\; x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty[/tex]

The x-intercepts of a function are when f(x)=0.  

Therefore, the x-intercepts are:

Therefore, the graph of the given function has 3 turning points.

Given function:

[tex]p(x)=(x - 3)^2 (x + 2) (2x + 7)^2[/tex]

Therefore:

End behaviors:

[tex]\textsf{As}\;\; x \rightarrow - \infty,\;\;f(x) \rightarrow -\infty[/tex]

[tex]\textsf{As}\;\; x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty[/tex]

The x-intercepts of a function are when f(x)=0.  Therefore, the x-intercepts are:

Therefore, the graph of the given function has 4 turning points.

Given function:

[tex]p(x)=(x - 5)(x + 2)(x - 1)-30[/tex]

Therefore:

End behaviors:

[tex]\textsf{As}\;\; x \rightarrow - \infty,\;\;f(x) \rightarrow -\infty[/tex]

[tex]\textsf{As}\;\; x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty[/tex]

The graph has 2 turning points.

a) The line belongs to the plane.

b) The line does not belong to the plane.

The equation of a line has the format given as follows:

[tex]\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}[/tex]

The equation of a plane has the format given as follows:

Ax + By + Cz + D = 0.

The line will belong to the plane if these two conditions are satisfied:

In standard format, the line for item a is given as follows:

[tex]\frac{x - 1}{4} = \frac{y + 2}{9.5} = \frac{z - 3}{1}[/tex]

Then the conditions are tested as follows:

The two conditions are satisfied, hence the line belongs to the plane.

For item b, we have that:

(-2)(-6) + 1(8) - 5(-3) + 1 = 36.

First condition already not satisfied, hence the second does not need to be tested, meaning that the line does not belong to the plane.

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The angle with a positive sine and negative cosine among the options is [tex]\frac{3\pi }{4}[/tex]

What is an obtuse angle?

Obtuse angle is any angle greater than 90°: Straight angle is an angle measured equal to 180°: Zero angle is an angle measured equal to 0°: Complementary angles are angles whose measures have a sum equal to 90°:

All obtuse angles usually have positive sine and negative cosine.

Amongst all the options  [tex]\frac{3\pi }{4}[/tex] is the only obtuse angle . which if you convert to degrees

using π rad = 180 degrees, 3/4 x 180  you get  135°

In conclusion  [tex]\frac{3\pi }{4}[/tex] is the angle with a positive sine and negative cosine.

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Answer: D.) None of these

Step-by-step explanation: A polygon is regular when all angles are equal and all sides are equal (otherwise it is "irregular").

Answer:

Side h and side

(3,1),(4,-2),(-5,4),(4,-1),(-1,-2) match with the given coordinates of the graph thus option (B) will be correct.

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane.

As per the given coordinates,

The coordinate is the representation of horizontal and vertical distinctions.

The (3,1) is the point that is 3 grid right or horizontal and 1 unit up or vertical from the origin.

Hence "(3,1),(4,-2),(-5,4),(4,-1),(-1,-2) match with the given coordinates of the graph".

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The key phase that we see in our response is "Divide the numerator by the denominator" (option C).

A key phrase refers to a phrase that contains words that define the most important part of a text. A key phrase serves as a summary of a paragraph or larger text.

In this case, the key phrase would serve to establish what was the mathematical procedure that we carried out to solve a mathematical problem. According to the above, it can be inferred that the key phrase must contain the most precise information to describe this procedure.

Based on the above, the correct answer is "Divide the numerator by the denominator" because it exactly describes the procedure that was performed.

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x - y = -15 -3x + 3y = 45 (x, y) = the system of two linear equations using the method of elimination ( 5, 45).

x - y = -15

-3x + 3y = 45

written as

3x - 3y = -15

+3x + 3y = 45

6x = 30

x = 5

Substitute x = 5 into either of the linear equations to find y.

x - y = -15

5 - y = -15

y = 45

Therefore, the solution is (5, 45).

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The solved expression we get for 20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98 is the numbers 18.4, 34.2,31,55.2 and 11.76.

Given that,

Finding the expression that can be utilised to find

20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98.

From the Latin word "per centum," which means "by the hundred," the word "percentage" was borrowed. The denominator of percents is 100, making them fractions. In other words, it is the relationship between a part and a whole in which the value of the whole is consistently set to 100.

Take

20% of 92

Multiply 20%×92

=18.4

45% of 76

Multiply 45% ×76

=34.2

50% of 62

Multiply 50%×62

=31

60% of 92

Multiply 60%×92

=55.2

12% of 98

Multiply 12%×98

=11.76

Therefore,

The solved expression we get for 20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98 is the numbers 18.4, 34.2,31,55.2 and 11.76.

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Answer: 191.3

Step-by-step explanation:

In 2005: x=2005-1998=7

y=123.1(1.065)^7

= 191.3

The distance of the ball away from Amaya at Maximum height is; 18 feet

Given the projectile equation as;

y = -0.02(x - 18)² + 12 to model the horizontal distance of a ball from Amaya's position.

We want to find out how far away is the ball from Amaya when it is at its maximum​ height.

The model takes the form of a parabolic equation and as such, the maximum height is obtained at the Vertex :

The general vertex form of the equation of a parabola is;

y = a(x - h)² + k

With maximum height obtained at the Vertex (h, k)

From the model given, we can say that;

Coordinate at the Vertex : (h, k) = (18, 12)

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Complete question is;

Amaya is standing 30 ft from a volleyball net. The net is 8 ft high. Amaya serves the ball. The path of the ball is modeled by the equation y = -0.02(x - 18)² + 12​, where x is the​ ball's horizontal distance in feet from​ Amaya's position and y is the distance in feet from the ground to the ball. a. How far away is the ball from Amaya when it is at its maximum​ height?

The example of the commutative property of addition is option (D) 4 + 3 = 3 + 4

The commutative property of the addition states that changing the order of the numbers or the variable does not affect the result of sum

The commutative property of addition is

A + B = B + A

Here the position of the variable A and B are changed but still the result is same

From the given option

The example that shows the commutative property of  addition is

4 + 3 = 3 + 4

Here the position of the 3 and 4 changed, but the result will be

7 = 7

Therefore, the correct example is option D) 4 + 3 = 3 + 4

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The integer in the solution set that will make the equation true is (c) 3

From the question, we have the following parameters that can be used in our computation:

3p + 13 = 22

Subtract 13 from both sides of the expression

So, we have the following representation

3p = 9

Divide both sides of the equation by 3

p = 3

Hence, the solution is p = 3

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using the formula Upper Bound = X_Bar + (critical value * standard deviation/sqrt(n)) to calculate the upper bound of the interval. The result is an upper bound of 72.41.

The standard normal distribution table is used to calculate the critical value for this problem.

The critical value at 99% confidence level is 2.576.

The formula for the one-sided confidence interval is given by:

Upper Bound = X_Bar + (critical value * standard deviation/sqrt(n))Therefore, the one-sided 99% Confidence Interval for mu when n = 86, and X_Bar =71 is:

Upper Bound = 71 + (2.576 * 2/sqrt(86))

Upper Bound = 71 + (1.41)

Upper Bound = 72.41

The one-sided 99% Confidence Interval for mu when n = 86 and X_Bar =71 is calculated by using the standard normal distribution table to find the critical value of 2.576, and then using the formula Upper Bound = X_Bar + (critical value * standard deviation/sqrt(n)) to calculate the upper bound of the interval. The result is an upper bound of 72.41.

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The Ratio of Julia’s frogs to Rimma’s frogs will be 9:5

A ratio in mathematics demonstrates how many times one number is present in another.

For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

Ratio = [tex]\frac{1^{st} element}{2^{nd} d element}[/tex]

Let Rimma’s frog = x

So, Julia's frog =  [tex]\frac{2x}{5}[/tex]

Rimma gives  [tex]\frac{1}{2}[/tex] of her frog to Julia

Therefore, rimma left with  [tex]\frac{x}{2}[/tex]

Ratio = [tex]\frac{Julia's frog}{Rimma's frog}[/tex]

[tex]=\frac{\frac{2x}{5} +\frac{x}{2} }{\frac{x}{2} } \\=\frac{\frac{9x}{10} }{\frac{x}{2} }\\=\frac{9}{5}[/tex]

Therefore, ratio will be 9:5

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The equation to solve the width of rectangle created by John from 48 square centimetre tiles is w(w+2) = 48

and the greatest width in centimetres use for mosaic is 6 cm.

We have given that

John wants to create a mosaic of rectangular shape.

total area of tile(A) = 48 square centimetre

let l and w be length and width of rectangle

length of rectangle is 2 cm longer than width then length of rectangle (l) =( w+2) cm

Area oa rectangle (A) = l × w

=> (w+2) × w = 48

=> w²+ 2w = 48

which is quadratic equation , solve it

w² + 2w - 48 = 0

=> w² - 6w + 8w - 48 = 0

=> (w-6) (w+8) = 0

=> w = 6, -8

Hence, the required equation is w(w+2) = 48 and width of rectangle is 6cm.

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