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A population has a mean μ=135 and a standard deviation Ï=28.

The mean of the sampling distribution of sample means is equal to the population mean, that is 135.

The standard deviation of the sampling distribution of sample means can be calculated by using the formula

SE = Ï /[tex]\sqrt{n}[/tex]

Where Ï is the population standard deviation and n is the sample size.

By putting the given values we get

SE = 28 / [tex]\sqrt{57}[/tex] = 3.7

Hence, the mean of the sampling distribution of sample means is 135, and the standard deviation is 3.7.

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Answer:

y= 7/3x -7

Step-by-step explanation:

Slope is 7/3 (rise/run or up seven over 3) and when you continue the graph the line will eventually hit your y-intercept at -7

Therefore, the temperature at the summit of the 3,000-foot mountain on a sunny day is estimated to be 10.8 F°.

In mathematics, an equation is a statement that indicates the equality of two expressions. An equation typically contains one or more variables, which are placeholders for unknown values or quantities. The variables can take on different values, and the goal is often to find the values that satisfy the equation.

Here,

Let's start by calculating the rate of change of temperature with respect to elevation:

=-5.4 F° / 1,000 ft

This means that for every 1,000-foot increase in elevation, the temperature will decrease by 5.4 F°.

Next, we can calculate how much the temperature will decrease from the base of the mountain to the summit:

3,000 ft / 1,000 ft = 3

This means that the elevation difference between the base of the mountain and the summit is 3,000 - 0 = 3,000 ft.

So, the temperature decrease from the base to the summit is:

-5.4 F° / 1,000 ft * 3,000 ft = -16.2 F°

This means that the temperature at the summit will be:

27 F° - 16.2 F° = 10.8 F°

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Here he formula for v is:

v = √(2gh)

What is meant by the term formula?

A formula is a mathematical relationship or rule that is expressed using symbols and mathematical operations. It is used to represent a relationship between quantities or to calculate a value based on given variables or inputs. Formulas are often used in various branches of mathematics, science, and engineering.

According to the given information

To change the subject of the formula mgh = (1/2)mv² to v, we need to isolate v on one side of the equation.

First, we can multiply both sides of the equation by 2 to eliminate the fraction:

2mgh = mv²

Next, we can divide both sides of the equation by m:

(2mgh) / m = v²

Simplifying the left side, we get:

2gh = v²

Finally, we can take the square root of both sides of the equation to solve for v:

v = √(2gh)

Therefore, the formula for v is:

v = √(2gh)

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The statement " Time plots are special scatterplots where the explanatory variable, x, is a measure of time" is true because time plots are scatterplots where the x-axis represents time, and they are commonly used to visualize trends and patterns in time series data.

A time plot is a type of scatterplot where the x-axis represents time and the y-axis represents a response variable. Time plots are useful for displaying data that change over time and can reveal trends, patterns, and seasonality in the data. They are commonly used in fields such as economics, finance, and social sciences to analyze time series data.

By visualizing data over time, time plots can help to identify relationships, outliers, and potential forecasting models. Overall, time plots are a powerful tool for analyzing and understanding trends and patterns in time series data.

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The given question is incomplete, the complete question is:

Time plots are special scatterplots where the explanatory variable, x, is a measure of time. True or false

Answer: Let's call the time it takes for Mrs. Cunningham to overtake Mr. Cunningham "t".

In that time, Mr. Cunningham will have traveled for 4 more hours than Mrs. Cunningham, so he will have traveled 4 + t hours.

We can set up an equation to represent the distance each person traveled:

distance = rate x time

For Mr. Cunningham:

distance = 46 mph x (4 + t) hours

For Mrs. Cunningham:

distance = 62 mph x t hours

Since they end up at the same place, their distances must be equal:

46 mph x (4 + t) = 62 mph x t

Simplifying this equation:

184 + 46t = 62t

16t = 184

t = 11.5

Therefore, it will take Mrs. Cunningham 11.5 hours to overtake Mr. Cunningham.

Step-by-step explanation:

According to the above, we have to add the surface area of each face. So, the surface area of this solid would be 127.

To calculate the surface area of the composite solid we have to perform the following procedure:

Sides (a) area

Sides (b) area

Face (c) area

Base area

4 * 7 = 28

Total surface area

To calculate the total surface area we have to add the value of each face as shown below:

According to the above, the surface area of this solid would be 127.

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Answer:

a=60 (12*5=60)

b=7 (45/9=5 5+2=7)

c=62

d=25 (11*5=55 55-30=25)

The coordinates for the image after the translation of EFG would be E'(-2, 3), F'(-4, 0), and G'(-1, -2).

To translate a point, you simply add or subtract the specified units from its x and y coordinates. In this case, you are asked to translate the points 3 units left and 1 unit down.

To translate 3 units left, subtract 3 from the x-coordinate, and to translate 1 unit down, subtract 1 from the y-coordinate.

For point E (1, 4):

E' = (1 - 3, 4 - 1) = (-2, 3)

For point F (-1, 1):

F' = (-1 - 3, 1 - 1) = (-4, 0)

For point G (2, -1):

G' = (2 - 3, -1 - 1) = (-1, -2)

The translated points are E'(-2, 3), F'(-4, 0), and G'(-1, -2).

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Answer:

(1/256)

Step-by-step explanation:

[tex](\frac{1}{4})^{4} = \frac{1^{4} }{4^{4} } = \frac{1}{256}[/tex]

Using laws of exponents I distributed the exponent to the fraction and solved.

Answer:

409 > 1.008

Step-by-step explanation:

409 is greater than 1.008

The average score of 100 students taking a statistics final was 70, with a standard deviation of 7. The test score esteem that isolates the beat 2.5% of normal distribution from the rest of the understudies is roughly 83.72.

To discover the test score esteem that isolates the best 2.5% of the understudies, we got to discover the z-score comparing to that rate utilizing the standard ordinary conveyance table.

z = (x - μ) / σ

To discover the z-score compared to the best 2.5%, we see up the region of the right-hand tail of the standard normal distribution table, which is 0.025. This compares to a z-score of roughly 1.96.

Presently ready to utilize the z-score equation to unravel for x:

1.96 = (x - 70) / 7 Increasing both sides by 7, we get:

x - 70 = 13.72

Including 70 to both sides, we get:

x = 83.72

Hence, the test score esteem that isolates the beat 2.5% of the understudies from the rest of the understudies is roughly 83.72.

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An equation that matches the table include the following: y = x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 5)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1.

At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

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The equation is linear and can be written in the slope intercept form as: y = -3x/5 + 6.

A linear equation is an algebraic equation that represents a straight line on a graph. It can be written in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept, which is the point where the line crosses the y-axis.

given the slope m = -3/5 and y intercept b = 6, we can write the equation as;

y = (-3/5)x + 6

y = -3x/5 + 6.

Therefore, the equation is linear and can be written in the slope intercept form as: y = -3x/5 + 6.

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(a) The simplified and correct expression is (6×7)-(5 +4) = 16

(b) The simplified and correct expression is (-2x²) + (24÷12)-4 = 2

a. 6×7-5 +4= 16

In this calculation, we need to use brackets to ensure the correct order of operations, which is typically remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division [from left to right], Addition and Subtraction [from left to right]).

Without brackets, the calculation would be evaluated as follows:

6×7-5 +4 = 42-5 +4 (applying multiplication first)

= 37 +4 (applying subtraction)

= 41 (applying addition)

However, the desired result is 16. To achieve this, we can use brackets to group the addition and subtraction operations together, like this:

(6×7)-(5 +4) = 42 - 9 (applying addition within the brackets first)

= 33 (applying subtraction)

b. -2x²+24÷12-4=2

Similarly, in this calculation, we need to use brackets to ensure the correct order of operations.

Without brackets, the calculation would be evaluated as follows:

-2x²+24÷12-4 = -2x²+2-4 (applying division first)

= -2x²-2 (applying addition and subtraction)

However, the desired result is 2. To achieve this, we can use brackets to group the division and subtraction operations together, like this:

-2x²+(24÷12)-4 = -2x²+2-4 (applying division within the brackets first)

= -2x²-2 (applying addition and subtraction)

By adding brackets to each calculation to ensure the desired order of operations, we arrive at the correct results of 16 and 2, respectively.

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The acceleration of this classroom table is equal to 1.5 meter per seconds square.

From Newton's Second Law of Motion, the force exerted on the classroom table is modeled or represented by this mathematical equation (formula):

F = ma

Where:

By making "acceleration" the subject of formula, we have the following:

Acceleration, a = force/mass

Acceleration, a = 36/24

Acceleration, a = 1.5 meter per seconds square.

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The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.

The given mass of  the metal is 611 g  and it is kept in a elevated cylinder that contains 25.1 mL of water,
Now, let us increase the water level to 56.7 mL. The metal  volume can be evaluated by subtracting the initial volume  from the final volume of water released by the metal.

Hence,
Metal volume = final volume - initial volume
= 56.7 mL - 25.1 mL
= 31.6 mL

Therefore,
Density = Mass / Volume
= 611 g/31.6 mL
= 19.3 g/cm³

The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.


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The probability that the cost will exceed $600 is approximately 0.057, or 5.7%. which is relatively small, so it is highly unlikely that the cost of conducting the test will exceed $600.

we need to use the information provided to calculate the probability that the test execution cost will exceed a certain value.

Let X be the cost of conducting a test to find three of her employees with positive signs of asbestos poisoning. From the information provided, we can see that:

E(X) = $550

Var(X) = $500

Using these values, we can standardize X to a standard normal distribution.

Z = (X - E(X)) / sqrt(Var(X))

= (X - $550) / square meters ($500)

Accepting that the costs take after an ordinary conveyance, able to utilize the standard ordinary conveyance to compute the likelihood that the fetched surpasses a certain esteem. For case, to find the likelihood that the taken toll surpasses $600, we are able to compute:

P(X > $600) = P(Z > ($600 - $550) / square meters ($500))

= P(Z > 1.58)

Using a standard normal table or calculator, we find that P(Z > 1.58) is approximately 0.057. hence, the probability that the cost will exceed $600 is approximately 0.057, or 5.7%.

This likelihood is generally little, so it is profoundly impossible that the fetch of conducting the test will surpass $600.

Be that as it may, the precise limit for what is considered exceedingly improbable may change depending on the setting and the particular criteria utilized. 

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The common ratio is -1/3 and the initial term is -4, then the formula is:

A(n) = -4*(-1/3)^(n - 1)

Remember that in a geometric sequence, to get the next term we need to multiply the previous term by the common ratio.

To get the common ratio, take the quotient between two consecutive terms.

We will get:

(4/3)/(-4) = -1/3

Then the n-th term of the geometric sequence is:

A(n) = -4*(-1/3)^(n - 1)

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Answer:

[tex](-4)\left(\frac{1}{3}\right)^{n-1}[/tex]

Step-by-step explanation:

The common ratio between any two terms in a geometric sequence is constant. Let this ratio be denoted by r. Then, we have:

[tex]r = \frac{\frac{4}{3}}{-4} = \frac{-\frac{4}{9}}{\frac{4}{3}} = \frac{\frac{4}{27}}{-\frac{4}{9}} = \frac{1}{3}[/tex]

Using this value of r, we can write the formula for the nth term an as:

[tex]an=[/tex][tex](-4)\left(\frac{1}{3}\right)^{n-1}[/tex]

The given piecewise function has a range of:

Range = {46, 48, 50, 52, 54, 56}.

The range of a function is the set of all possible output values, or the set of all y-coordinates that correspond to the x-coordinates in the domain of the function.

It is, in other words, the entire set of values that the function is capable of returning as its result.

From the given piecewise function, we can see that the y-coordinates of the function are limited to the values 46, 48, 50, 52, 54, and 56.

These values correspond to the y-intercepts of each of the line segments in the graph.

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The circle with equilateral triangle is constructed.

What is triangle?

A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.

Here we need to construct the circle  with center D.

Now we know that in equilateral triangle , side length of the all sides are equal.

Then, AB=BC=CA.

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The percentage of pens that are blue =18%

Let's assume that r represents the red pens, b represents the blue pens and g represents the green pens.

From the statements we can observe that the blue appears in both ratio.

The ratios are,

r:b=5:9 and b:g=1:4

Consider ratio b:g,

b:g

= 1:4

= (1×9) : (4×9)

=9:36

i.e., b:g = 9:36 and r:b = 5:9

So, we can conclude that, b=9, g=36, r=5

so, the total number of pens would be,

n = b + g + r

n = 9 + 36 + 5

n = 50

Now we need to find the percentage of pens that are blue.

Using percentage formula,

p = (b/n) × 100

p = (9/50) × 100

p = 18%

Hence, the percentage of blue pens are 18%.

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Answer:

The unit rate is 35 pages per minute.

Step-by-step explanation:

Divide 175 by 5, or 175/5  to get the unit rate, which is 35.

Yes, we can determine the probability of one thing happening before another based on their expected time to occur.

A coin has two sides: one side ("heads") is side A and the other ("tails") is side B. A coin is tossed into the air and the question is what are the chances, the "probability" if you want it to land on side A. The probability of an event occurring describes the number of chances that the event occurred. The total probability of hitting A before B is the sum: P(A before B) = p + rp + r² + r³p + r⁴p + … = p[1 + r + r² + r³ + r⁴ + … ] and this determines the result. Thus, it is possible to determine the probability of one thing happening before another, based on their expected time to occur.

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Step-by-step explanation:

Perimeter =  2 m + 2 * 7m

Perimeter = 2 ( m + 7m)

Perimeter = 2m + 14m

Perimeter = 16 m                          Pick any of them

Answer:

Step-by-step explan             456

the average rate of change over the interval (-1, 2] in the given function is 1.17.all three functions have the same average rate of change over the interval [1, 2], which is 2

A function is a mathematical rule that takes an input and produces an output. The average rate of change of a function over an interval is the average amount the output changes per unit change in the input over that interval.

For the function f(x) = 2x + 3:

Let x1 = -1 and x2 = 2

f(x1) = 2(-1) + 3 = 1

f(x2) = 2(2) + 3 = 7

The average rate of change is:

[f(x2) - f(x1)] / [x2 - x1] = [7 - 1] / [2 - (-1)] = 6 / 3 = 2

Therefore, the average rate of change of f(x) over the interval (-1, 2] is 2.

For the function g(x) = x^2 - 1:

Let x1 = -1 and x2 = 2

g(x1) = (-1)^2 - 1 = 0

g(x2) = 2^2 - 1 = 3

The average rate of change is:

[g(x2) - g(x1)] / [x2 - x1] = [3 - 0] / [2 - (-1)] = 3 / 3 = 1

Therefore, the average rate of change of g(x) over the interval (-1, 2] is 1.

For the function h(x) = 2^x + 1:

Let x1 = -1 and x2 = 2

h(x1) = 2^(-1) + 1 = 1.5

h(x2) = 2^2 + 1 = 5

The average rate of change is:

[h(x2) - h(x1)] / [x2 - x1] = [5 - 1.5] / [2 - (-1)] = 3.5 / 3 = 1.17 (rounded to 2 decimal places)

Therefore, the average rate of change of h(x) over the interval (-1, 2] is approximately 1.17.

b)To determine which function has the greatest average rate of change over the interval [1, 2], we need to calculate the average rate of change for each function over that interval and compare the results.

Let's assume the functions are f(x), g(x), and h(x).

The average rate of change for f(x) over the interval [1, 2] is:

[f(2) - f(1)] / [2 - 1] = (2(2) + 3 - 2(1) - 3) / 1 = 2

The average rate of change for g(x) over the interval [1, 2] is:

[g(2) - g(1)] / [2 - 1] = (2^2 - 1 - 1^2 + 1) / 1 = 2

The average rate of change for h(x) over the interval [1, 2] is:

[h(2) - h(1)] / [2 - 1] = (2^2 + 1 - 2^1 - 1) / 1 = 2

Therefore, all three functions have the same average rate of change over the interval [1, 2], which is 2.

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Answer:

b, c, d, f

Step-by-step explanation:

Which ordered pairs are solutions to the inequality?

 2x+3y≥−1?

a≥b means that A must be equal to or greater than B.

Let's do this the long, but easy way, by plugging it in!

(x,y)

a. (0,-1) -> -3≥-1 -> false

b. (5,-1)-> 7≥-1 -> true

c. (-2,1) -> -1≥-1 -> true

d. (0,1) -> 3≥-1 -> true

e. (-6,0) -> -12≥-1 - > false

f. (2,-1) -> 1≥-1 -> true

Let me know if it is incorrect!

- a friendly 8th grader :)

The side of the house which the ladder will reach now is equal to 14.2 feet.

In Mathematics and Geometry, Pythagorean's theorem is represented or modeled by the following mathematical equation:

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

In order to determine how far up the side of the house will the ladder reach, we would have to apply Pythagorean's theorem as follows;

21² + y² = 35²

y² = 1,225 - 441

y² = 784

y = √784

y = 28 feet.

Since Elijah grabs the ladder at its base and pulls it 4 feet farther from the house, we have:

New Length = 28 + 4 = 32 feet.

Therefore, the required length is given by;

Distance = √(35² - 32²)

Distance = 14.2 feet.

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