The level of cholesterol in the blood for all men aged 20 to 34 follows a Normal distribution with mean 188 milligrams per deciliter (mg/dl) and standard deviation 41 mg/dl. For 14 - year - old boys, blood cholesterol levels follow a Normal distribution with mean170mg/dl and standard deviation 30 mg/dl. Now suppose we select independent SRS of 25 men aged 20 to 34 and 36 boys aged 14 and calculate the sample mean heights xM - xB. Describe the shape, center, and spread of the sampling distribution xM - xB. Find the probability of getting a difference in sample means xM - xB that's less than0 mg/dl. Show your work. Should we be surprised if the sample mean cholesterol for the 14 - year - olds exceeds the sample mean for the men?

The x‐intercept is x = −5, and the graph approaches a vertical asymptote at x = −6. Then the correct option is A.

The collection includes all locations on the surface of the shape (x, f(x)) that make up a function of f's graph. We may alternatively say that the graph of f is the curve of y = f. (x). As a result, the diagram of an equation is a particular instance of the graphs of functions.

The x-intercept is at (-5, 0). Then the value of the abscissa is given as,

x = -5

The graph begins in the third quadrant near the line x = - 6. Then the equation x = - 6 represents the asymptote.

The x‐intercept is x = −5, and the graph approaches a vertical asymptote at x = −6. Then the correct option is A.

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False. The histogram shows the frequency of house values, not the values themselves.

The histogram in the question does not show the actual values of house values in a certain city. It instead shows the frequency of house values. The histogram has the house values on the x-axis and the frequency of house values on the y-axis. The frequencies are shown as bars and the height of each bar represents the number of houses with that value. The mean and standard deviation mentioned in the question are statistical measures of the actual house values in the city. The mean is the average of all the house values in the city and the standard deviation is a measure of the variation in the house values. Therefore, the statement that the histogram shows the distribution of house values in a certain city with the mean of $403,000 and the standard deviation of $278,000 is false.

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The cost at Pickwick Books is $5.75 and the cost at Dickens Books is $5.50, so the books are cheapre in Dickens Books.

We know that the equation:

C = 5.75*b

Repersents the cost for b books at Pickwick Books.

Then the cost of each book there is $5.75

We also know that at Dickens Books, a customer can buy 3 used books for $16.50, then the cost of each book there is given by:

C = $16.50/3 = $5.50

So the books are cheaper, by $0.25, in Dickens Books.

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Answer:

100.2

Step-by-step explanation:if its the lateral height of 4 it has to 420

The answers include the following:

The total frequency is 22 +  16 + 18 + 22 + 9 + 13 + 6 + 3 + 1 = 110

We have given the frequency table

Number:          0       1    2     3      4     5    6    7   8  

Frequency:       22   16   18   22   9    13    6    3    1

Number:          0            1          2         3          4           5          6       7        8  

Frequency:  22/110    16/110   18/110   22/110  9/110    13/110  6/110  3/110  1/110

Probability  P (x ≥ 7 ) =  3/110 + 1/110 = 4/110 = 2/55

P (x = 3 ) = 22/110 = 11/55

P (x < 4) = 22/110 + 18/110 + 16/110 + 22/110 = 78/110 = 39/55

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The initial height of the rocket is 24 metres, the rocket hit the ground in 0.88 seconds and the height of the rocket after 4 seconds is 24 metres.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The initial height of the rocket is given by the value of h when t = 0:

h(t)=-4t² + 16t + 24

h(0)=-4(0)² + 16(0) + 24

h(0)=24

So the initial height of the rocket is 24 metres.

The rocket will hit the ground when its height is 0 metres, so we can set h = 0 in the equation and solve for t:

0 = -4t²+ 16t + 24

-4t² + 16t + 24 = 0

t=-0.88 seconds

So the rocket will hit the ground after approximately 0.88 seconds.

The height of the rocket after 4 seconds is given by:

h(4)== -4(4)²+ 16(4) + 24

=-64+64+24

=24

So the height of the rocket after 4 seconds is 24 metres.

Hence, the initial height of the rocket is 24 metres, the rocket hit the ground in 0.88 seconds and the height of the rocket after 4 seconds is 24 metres.

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Neither the addition property of equality nor the subtraction property of equality can be demonstrated by themselves. They are properties that must be satisfied by the operations of addition and subtraction respectively, in order for equality to hold.

The addition property of equality states that if two quantities are equal.

(a = b), then their sum with any other quantity (c) will also be equal (a + c = b + c). The subtraction property of equality states that if two quantities are equal (a = b), then their difference with any other quantity (c) will also be equal (a - c = b).

In other words, both properties say that when two quantities are equal, then the result of adding or subtracting the same quantity from both will also result in equal quantities.

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The compound inequality that has no solution, according to the query, is B.

Rule 1: When the same quantity is applied to or subtracted on both sides, an inequality sign does not change. Rule 2: Once both ends are duplicated or halved by a positive value, the inequality sign does not change.

[A] 3x + 4 < x - 8 and -5x + 4 > 3x - 10

Solving for x, we get:

3x + 4 < x - 8 => 2x > 12 => x > 6

-5x + 4 > 3x - 10 => 2x < 14 => x < 7

The correct solution to x is 6 < x < 7, which is the overlapping answer.

Since this two inequalities don't have any common solutions, when we solve all of the 2 inequality in [B], we find there is no solution.

In the actual number system, the equation 4x - 6 ≤ 5x + 6 can be resolved as -x ≥ 12, with no answer.

-3x - 2 > 2x + 8 can be solved as -5x > 10, which has no solution in the real number system.

[C] -4x-3 ≤ 2x +9 and -3x+2> - 2x + 5

Solving for x, we get:

-4x - 3 ≤ 2x + 9 => -6x ≤ 12 => x ≥ -2

-3x + 2 > -2x + 5 => -x > 3 => x < -3

which is an empty set and has no solution.

[D] 4(x + 1) ≥ 3(x + 2) and -3(x - 1) < 5(x + 2)

Solving for x, we get:

4(x + 1) ≥ 3(x + 2) => x ≥ -3

-3(x - 1) < 5(x + 2) => x > -2

The overlapping solution for x is x > -2 and x ≥ -3, which is a valid solution of x > -2.

Therefore, B has no solution.

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64.8 miles will be the distance travelled by Anthony.

Two or more expressions with an Equal sign is called as Equation.

Given that Anthony bikes a 16.2-mile long trail.

If Anthony bikes it 4 times we need to find how far Anthony traveled.

By means of multiplication we find the distance traveled by Anthony.

Multiplication is a method of finding the product of two or more numbers

Now multiply 16.2 with 4

16.2×4

64.8 miles

Hence, 64.8 miles will be the distance travelled by Anthony.

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Considering the definition of parallel line, the correct answer is the second option: if the slope of line a is -4, then the slope of a line parallel to it is -4.

A linear equation o line can be expressed in the form y = mx + b

where

Parallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope "m" and different y-intercepts "b".

If the slope of line a is -4, then the slope of a line parallel to it is -4 because two lines are parallel have the same slope "m".

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Answer:25.5

Step-by-step explanation:

64.5+90=154

180-154=25.5

The solution to the two functions f(x) = 3ˣ and g(x) = -x + 4 is, 1

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

The number of visitors increases exponentially as the temperature increases, and this situation is represented by the function

f(x) = 3ˣ

The number of people who leave the park early depending on the change in temperature, and it is represented by

g(x) = −x + 4

the solution of both the graphs = ?

the intersection of the two curves of graphs of the functions is the solution,

Basically, it represent that,

both function have same value for particular value of x,

So,

when both functions have same value that will be our solution,

f(x) = 3ˣ

g(x) = −x + 4

It can be seen in the graph that both the functions intersects at x = 1,

f(1) = 3

g(1) = −1 + 4 = 3

Hence, the solution is 1

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The required set of numbers includes is given as {-3, -2, 2, 3}. Option B is correct.

Sets are an orderly collection of items in mathematics that can be expressed in set-builder or roster form.

Here,
Integers are whole numbers, both positive and negative, including zero. For example -4, -3, -2, -1, 0, 1, 2, 3, 4, etc. They are used to represent whole quantities and are a basic type of number in mathematics.

Thus, from the options set of numbers includes is given as {-3, -2, 2, 3}. Option B is correct.

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The points are evenly distributed above and below the line, which provides the best explanation for why the graph displays a line of best fit.

A statistical tool that shows the relationship between two variables is a regression line. It is employed specifically when a change in one (the dependent variable) is dependent on a change in the value of the other (the independent variable).

Given the graph,

for the line of best fit, A graph's nodes are connected by a mathematical concept known as the line of greatest fit. It is a kind of linear regression that uses scatter data to determine how to best define the relationship between the dots.

A change in the value of X causes a change in the value of the equation, which is written as Y on X.

X on Y is the equation, and the deviation of the Y variable determines how the X variable changes.

The graph shows a line of greatest fit because the spots are equally spaced above and below the line.

Hence the points are drawn uniformly above and below the line, thus the best explanation is that the graph displays a line of best fit.

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The correct statement regarding the probabilities is given as follows:

Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2).

A probability is obtained with the division of the number of desired outcomes by the number of total outcomes in the context of a problem.

The probabilities for each player are given as follows:

Hence the correct statement is given by the last option among those presented in this problem.

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The probability of the time being 2.25 minutes is 0.9, and the probability of the time being 0.75 minutes is 0.1.

(a) p(x ≤ 2.25) = P(x = 0) + P(x = 0.5) + P(x = 1) + P(x = 1.5) + P(x = 2) + P(x = 2.5) = 0.1 + 0.2 + 0.3 + 0.2 + 0.1 + 0.1 = 0.9

(b) P(x = 0.75) = 0.1

The probability mass function is a function of discrete random variables that provides a probability for each value of the random variable. In this case, the random variable is the time in minutes (rounded to the nearest half minute) for a blood sample to be taken, and the probability mass function provides the probability of the time being a certain value. For example, the probability of the time being 2.25 minutes is 0.9, and the probability of the time being 0.75 minutes is 0.1.

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True. The proposition "for all x in set Z, either P(x) or Q(x) if and only if for all x in set Z, either P(x) or Q(x)" is a tautology. This means that the statement is always true, regardless of what predicates P(x) and Q(x) are.

The logical connective "if and only if" (written as "iff") is used to express that the two statements are logically equivalent. The symbol "V" represents the logical operator "or".

The tautology states that if either P(x) or Q(x) is true for some x in set Z, then the other statement, either P(x) or Q(x), must also be true. It follows that if either P(x) or Q(x) is false, then the other statement must also be false.

This implies that the two statements are logically equivalent and that one statement can be substituted for the other without affecting the truth value of the overall proposition.

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The slope of QR is 1/8.

The length of QR is 8.06 unit.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:

The points Q (7, 6), R(-1,5), S(-5, -2), and T(3, -1) form a quadrilateral.

A quadrilateral in geometry is a four-sided polygon with four edges and four corners.

The slope of QR,

= (5 - 6)/(-1-7)

= 1/8.

The length of QR = √{(5 - 6)² + (-1-7)²} = 8.06 unit.

Therefore, 1/8 is the slope and 8.06 unit is the length.

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The volume of the solid is 17.5 . In general, finding the volume of a solid of revolution involves finding the volume of each infinitesimal cylindrical shell.

To find the volume of the solid obtained by rotating the region bounded by the curves y = x + 1, y = 0, x = 0, and x = 5 about the x-axis, we can use the method of cylindrical shells. The volume of the solid is given by the formula:

V = ∫ 2πrh dr

Where r is the radius of the cylindrical shell, h is the height of the shell, and dr is the incremental change in the radius as we move from one shell to the next. The radius of the cylindrical shell is equal to the distance from the line of rotation (in this case, the x-axis) to the point on the boundary curve that is vertically above the point where the shell intersects the x-axis.

In this case, the boundary curves are y = x + 1 and y = 0. For the interval 0 < x < 5, the height of the cylindrical shell is given by x + 1, and the radius of the shell is x. Therefore, the volume of the solid is given by:

V = ∫ 0 to 5 2π(x)(x + 1) dx = 17.5

The units of volume would be cubic units, determined by the units used for the variables x and π.

The choice of the method of integration, either by using disks/washers or cylindrical shells, depends on the geometry of the region being rotated and the axis of rotation.

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The standard deviation of the given variable is 0.95.

The standard deviation is a measure of the amount of variation or dispersion of a set of values. It is calculated as the square root of the variance. The variance is calculated by subtracting the mean from each data point and squaring the result. The variance is then divided by the number of data points. The standard deviation for the given table can be calculated as follows:

Mean = [tex](0 * 0.21) + (1 * 0.28) + (2 * 0.3) + (3 * 0.09) + (4 * 0.08) + (5 * 0.04) = 1.92[/tex]

Variance = [tex](0 - 1.92)2 * 0.21 + (1 - 1.92)2 * 0.28 + (2 - 1.92)2 * 0.3 + (3 - 1.92)2 * 0.09 + (4 - 1.92)2 * 0.08 + (5 - 1.92)2 * 0.04 = 0.907[/tex]

Standard Deviation = √0.907 = 0.95

Therefore, the standard deviation of the given variable is 0.95.

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The correct equation for the following sentence:

24 = 31.4n + (–8.4).

The correct option is C.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

A phrase:

Twenty-four is the same as 31.4 times a number plus negative 8.4.

Let the number is n.

The phrase can be expressed as,

24 = 31.4n + (–8.4).

Therefore, the expression is 24 = 31.4n + (–8.4).

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The time it will take Juan and Laura to meet each other is 25.88seconds

Velocity is the rate of change of velocity with time. It is a vector quantity and it is measured in meter per second. It can also be measured in Mikes per hour and so on.

Velocity = displacement /time

displacement = velocity × time

The total distance traveled = 220feet

220 = v1t + v2t

220 = (v1+v2) t

220 = ( 3.5 + 5) t

220 = 8.5 t

divide both sides by 8.5

220/8.5 = t

t = 25.88 seconds

therefore it will take Juan and Laura 25.88 seconds to meet each other

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Using percentages we know that 106 people stated they didn't think these questions seriously interrupted their ability to do their jobs.

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.

Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.

A% is a number that has neither dimensions nor a defined unit of measurement.

The percentage can be calculated by dividing the value by the total value and multiplying the result by 100.

(Value/Total Value)100% is the formula for calculating percentages.

So, the percentage of people who answered the questionnaire is 66%.

That will be,

= 400/100 * 66

= 264

Of the 264 respondents, 40% said that they did not feel that these questionnaires significantly disrupted their workday.

= 264/100 * 40

= 105.6

= 106

Therefore, using percentages we know that 106 people stated they didn't think these questions seriously interrupted their ability to do their jobs.

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The length of the other two sides are 4m and 5m

Using the Pythagorean theorem, we have that the square of the hypotenuse sides is equal to the sum of the squares of the other two sides of the triangle

This is represented as;

x² = y² + z²

From the information given, we have that;

z = 3m

x = x + 1

y = x

Substitute the values, we get

(x + 1)² = x² + 3²

Find the squares

(x + 1) ² = 9 + x²

expand the bracket

(x + 1) ( x + 1) - x² = 9

x² + x + x + 1 - x² = 9

collect like terms

2x = 8

x = 4

Then,

x + 1 = 5

x = 4

Hence, the values are 4m and 5m

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Nikhil has been with the company for 24 years, while Mae has been there for 4 years.

Option C is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 2 = 8 is an equation.

We have,

Number of years Nikhil worked =  x

Number of years Mae worked =  y

x = 6y ______(1)

x = 8 + 4y ______(2)

Substituting (1) in (2)

6y = 8 + 4y

Subtract 4y on both sides.

6y - 4y = 8

2y = 8

Divide 2 into both sides.

y = 4

Now,

x = 6y

x = 6 x 4

x = 24

Thus,

The number of years Nikhil worked is 24 years.

The number of years Mae worked 4 years.

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The shape of the distribution, is symmetric, is the best description of   statistics about scores.

What is standard deviation ?

The standard deviation is the positive square root of the variance of this data set. Variance of a data set is the sum of squared differences of the data values from its mean to the total count of data values.

The given data in the problem is;

Mean = 78%

Standard deviation = 4%

Min = 64

Median = 78

Q1 = 72

Q3 = 84

Max = 99

The condition for the symmetric distribution is found as;

Q2-Q1 = Q3 - Q2

From the data we have;

Q2-Q1 = 6

Q3 - Q2= 6

So that , both are equal

Hence, the condition of symmetry is followed.

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The amount of the down payment, considering the median house price, is given as follows:

$41,980.

The down payment is obtained applying the proportions in the context of this problem.

A proportion is applied because the down payment is obtained with the multiplication of the median house price by the fraction.

The parameters are given as follows:

Hence the down payment is obtained as follows:

1/5 x 209900 = $41,980.

The problem asks for the amount of the down payment, considering the median house price.

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Make that the target variable is in the numerator, not the denominator, of the rearrangement.

Variable

A variable is a placeholder sign for a varying quantity or other mathematical entity.

Move all other variables to the other side of the equation by applying the opposite function to them, keeping in mind to carry out that operation on both sides of the equation, in order to isolate a single variable when rearranging equations. Make that the target variable is in the numerator, not the denominator, of the rearrangement.

Move all other variables to the other side of the equation by applying the opposite function to them, keeping in mind to carry out that operation on both sides of the equation, in order to isolate a single variable when rearranging equations. Make that the target variable is in the numerator, not the denominator, of the rearrangement.

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Based on the result shown in the table below, a statement which is true include the following: A. exactly 1/5 of the students chose pizza as their favorite food.

In Mathematics, a fraction simply refers to a numerical quantity which is not expressed as a whole number. In order to determine the true statement, we would evaluate them as follows;

"Exactly 1/5 of the students chose pizza as their favorite food."

Total number of students that chose pizza = 6 + 4

Total number of students that chose pizza = 10 students.

Total number of students = 26 + 24

Total number of students = 50 students.

Therefore, the fraction of students that chose pizza as their favorite food is given by:

Fraction = 10/50

Fraction = 1/5.

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Complete Question:

Two classes were asked what was their favorite food at a local restaurant. The results are shown in the table below.

Which statement is true?

Exactly 1/5 of the students chose pizza as their favorite food.

Less than 25% of students chose tacos as their favorite food.

More students prefer French fries than prefer tacos.

Exactly 1/2 of students prefer either pizza or hamburgers.

Answer:

p = -6, 7    

Step-by-step explanation:

To find the solutions to the equation p^2 = p + 42, we are going to need to solve for p. So, let's do just that!

p^2 = p + 42     [Subtract p^2 from both sides]

0 = -p^2 + p + 42     [Factor out the -]

0 = - ( p^2 - p - 42 )     [Factor p^2 - p - 42]

0 = - ( p + 6 ) ( p - 7 )     [Set both pair of parentheses equal to 0}

p + 6 = 0          

p = -6  

p - 7 = 0

p = 7    

So, the solutions to the equation are p = -6, 7    

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