For the following set of problems, perform the necessary calculations. Show your work.
A) Consider the following set of scores and calculate the sum of scores (∑X) and the mean (M): 8 2 5 7 12 9 11 3 6
B) If you are presented with a sample of n = 12 scores that has a mean of M = 8, what would be the value of ΣX (sum of scores)?
C) If you are presented with a sample of n = 6 scores and you know that five of the scores are each above the mean by one point, where would the sixth score have to be located relative to the mean? Why? Hint: Think of the sea saw.
D) If you are presented with a sample with a mean of M = 8 that has ΣX=56, how many scores are in the sample?
E) You are presented with two samples. One sample of n = 10 scores had a mean of M = 8, and the second sample of n = 5 scores has a mean of M = 2. If the data from the two samples are combined, what is the mean for the combined sample? Hint: Find the sum of scores for each sample first in order to compute the mean for the combined sample.

The  value which we convert from 118 kilograms to pounds is equal to ( 260.15 ) pounds ( round upto two decimals ).

Convert 118 kilograms to pounds using standard relation  :

1 kilograms is equivalent to  2.20462 pounds

To covert 118 kilograms to pounds we have :

⇒ 118 kilograms = ( 118 × 2.20462  ) pounds

⇒ 118 kilograms =  ( 260.145 ) pounds

⇒ 118 kilograms =  ( 260.15 ) pounds ( round upto two decimals )

Therefore, converted relation between kilograms to pounds is given by :

118 kilograms =  ( 260.15 ) pounds ( round upto two decimals ).

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Answer:

A. –8.6, –5.0, –1.4, 2.2, 5.8, …

C. 5, 1, –3, –7, –11, …

D. –3, 3, 9, 15, 21, …

Step-by-step explanation:

If a sequence is an arithmetic sequence, the difference between any two terms must be the same for all terms.

This is known as the common difference

The correct choices are:
A : Common Difference = 3.6

C. Common difference = -4

D. Common difference = 6

To convert 80 kilograms (kg) to pounds (lb), Use the conversion factor that represents the relationship between kilograms and pounds, which is 1 kg = 2.20462 lb.

Now, to convert 80 kg to lb, multiply 80 by the conversion factor:

80 kg x (2.20462 lb / 1 kg) = 176.3696 lb

Therefore, 80 kilograms is equal to 176.3696 pounds (rounded to four decimal places). The complete mathematical expression for this conversion is:

80 kg x (2.20462 lb / 1 kg) = 176.3696 lb

A conversion factor is a mathematical expression that expresses the relationship between two units of measurement. It is used to convert measurements between units.

Conversion factors are commonly used to convert measurements between different units of measurement in math, science, and engineering. They are a useful tool for performing calculations and comparing data in various units.

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The values in the composite functions are (u o w)(2) is 7 and (w o u)(2) is 3

A composite function is a function that results from the combination of two or more functions. To form a composite function, the output of one function is used as the input of another function. The composite function can be represented by a single formula or equation, which combines the individual functions.

Let's say we have two functions f(x) and g(x). The composite function f(g(x)) is formed by using the output of the function g(x) as the input of the function f(x). In other words, we first apply g(x) to x, and then we apply f(x) to the result. The resulting composite function is written as f(g(x)).

In the problem given;

u(x) = x² + 3

w(x) = √(x + 2)

a.

(u o w)(2) = 7

b.

(w o u)(2) = 3

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A sample's null hypothesis indicates that no statistical relationship exists in a set of provided single observed variables. The null hypothesis is rejected for both parts A and B of the question.

A sample's null hypothesis indicates that no statistical relationship exists in a set of provided single observed variables.

Part A: The conclusion to be reached at the 5% level of significance-

The p value for the z score in the right tailed or upper test can be obtained from the z table, which is,

p-value=0.125=0.125

The p value of 0.125 is greater than the significance level of 0.06. As a result, the effect is not significant, and the null hypothesis cannot be rejected.

Part B: If the alternative hypothesis is Ha: p 0.6, the conclusion to reach at the 5% level is-

The unequal sign 2-test is carried out here. The p value for the 2-test is as follows:

The p-value is 0.25=0.25.

In this case, the p value of 0.25 is greater than the significance level of 0.05. As a result, the effect is not significant, and the null hypothesis cannot be rejected.

As a result, the null hypothesis fails to be rejected for both parts A and B of the question.

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The expression f - 5(2f – 3) is equivalent to two other expressions, option (a) -11f-3 and option (b) -11f + 15.

In mathematics, an expression is a combination of symbols, operated on by certain mathematical operations to create a numerical value or a function.

To understand why this is the case, let's break down the expression.

The first part of the expression is just the variable f, so that is unchanged. The second part involves the multiplication of -5 and (2f – 3).

To evaluate this part, we need to use the order of operations. First, we multiply -5 and 2f and get -10f.

Then, we subtract 3 from this result and get -11f.

Therefore, the expression f - 5(2f – 3) is equivalent to -11f-3 and -11f + 15.

Therefore, the correct options are both (a) and (b).

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Complete Question:

Which expressions are equivalent to - f - 5(2f – 3)?

Choose all answers that apply:

a) -11f-3

b)-11f + 15

c) None of the above​

We can convert fps to mph by using the relation, one mph = 1.18 fps.

One fps means one foot per second and one mph means one mile per hour. Foot and mile are the units of distance and second and hour are the units or time.

We have to convert fps to mph.

As per the standard unit conversion rates, we know,

One mile = 5280 foot.

Also, one hour = 3600 seconds.

So, if we want to convert, we should write,

= mph

= 4280/3600

= 1.18 fps.

So, now we have a standard relation that says, one mph is equal to 1.18 fps.

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The distance between two points in a coordinate plane can be found by the formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

To calculate the distance between two points in a coordinate plane, you can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.

For example, if you want to find the distance between the points (2, 3) and (5, 7), you would plug in the values as follows:

d = sqrt((5 - 2)^2 + (7 - 3)^2)

d = sqrt(3^2 + 4^2)

d = sqrt(9 + 16)

d = sqrt(25)

d = 5

Therefore, the distance between two points is d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

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The value of 80 as fraction is 80/1.

To make 80 as a fraction, we need to place it over a denominator. The denominator can be any number as long as it is not equal to zero.

To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor (GCF), which is 10 in this case.

Therefore, the fraction 80 can be written as 80/1 or simplified as 8/1. This means that 80 is equivalent to 8 wholes or 8 times the unit.

In summary, 80 as a fraction is 80/1 or 8/1 when simplified.

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Answer:

360 miles

Step-by-step explanation:

To calculate how far a freight train travels in 4.5 hours, you need to know the train's average speed. Once you know the average speed, you can use the following equation to calculate the distance traveled: Distance = Speed x Time. So, if the freight train is traveling at an average speed of 80 miles per hour, it will have traveled a total of 360 miles in 4.5 hours.

I'm positive the answer is 1, 7, 13, and 91

One acre is equal to 43,560 square feet. To convert acres to square feet, you can multiply the number of acres by 43,560.

For example, if you want to convert 6 acres to square feet, you can multiply 6 by 43,560:

6 acres x 43,560 square feet/acre = 261,360square feet

So, 6 acres is equal to 261,360square feet.

Acres and feet are area and length measurement units, respectively. There is no direct conversion between acres and feet because they measure different things. However, you can convert acres to square feet using a conversion factor.

Please keep in mind that this conversion only applies to area measurements. If you need to convert linear measurements from acres to feet, you'll need more information about the area's shape and dimensions.

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Answer: 56

Step-by-step explanation: Since we know both triangles are similar, we want to first find the scale factor between the two triangles, knowing side UP and side PQ are corresponding we can find that 84/60 or in simplified terms, 7/5 is the scale factor. Now we know that side VP and side PR are corresponding so 40 x 7/5 gives us 56 which is side PR. Hope this helped! :)

The solution for the given system of equations as required to be determined is such that; it has infinitely many solutions.

It follows from the task content that;

y = (2/3)x + 5 and -2x + 3y = 15.

Also, by substitution, we have that;

-2x + 3 ( (2/3)x + 5 ) = 15

-2x + 2x + 15 = 15

15 = 15.

Consequently; it follows that the system of equations given has infinitely many solutions as the equations are coinciding equations and form coinciding lines when graphed.

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The number of dimples per square centimeter are on the surface of a golf ball is 0.17, the correct option is A.

Suppose that radius of the considered sphere is of 'r' units.

Then, its surface area S would be:

[tex]S = 4\pi r^2 \: \rm unit^2[/tex]

We are given that;

The circumference= 13.408cm

Number of dimples = 336

Now,

2pi*r= 13.408

r= 13.408/2*3.14

r=2.13

Surface area= 4*pi*r^2

=4*3.14*2.13*2.13

=56.98

336dimple=56.98cm^2

1dimple=56.39/336

=0.167

Therefore, by the area of sphere the answer will be 0.170.

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To solve for y, isolate y on one side of the equation by performing inverse operations, and simplify the expression as much as possible.

To solve for y online, input the equation into an equation solver or a mathematical software tool, and select the "solve for y" option. This will allow you to isolate the variable y and solve for it algebraically. There are many online equation solvers and mathematical software tools available that can perform this task quickly and easily. Simply input the equation, select "solve for y," and the tool will generate the solution set for the equation in terms of y.

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The probability that a continuous random variable will be equal to any specific value is zero. This is because the probability of an individual value for a continuous random variable is represented by the area under the probability density function (PDF) at that particular value, and the area of a single point is zero.

Answer:

C

Step-by-step explanation:

To make it easy, if there are 3 yellow, 2 green, and 8 total, just find the equation that has the fraction result of 5/8.

The domain of the equation y = -16x^2 + 1700 is the set of all real numbers.

To find the domain of the equation y = -16x^2 + 1700, we need to determine the set of all real numbers for which the equation is defined.

Since the equation is a quadratic equation, it is defined for all real values of x. There are no restrictions on the values of x that can be plugged into the equation.

Therefore, the domain of the equation y = -16x^2 + 1700 is the set of all the real numbers.

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The apex predator in the given triangle is the animal at the highest point, Beluga whale. Option 2 is the correct answer.

An apex (plural apices) is the vertex in geometry that is essentially the "highest" of the form to which it belongs. The phrase is frequently used to describe the vertex that is opposite from a "base." The word comes from a Latin root that means "summit, peak, tip, top, or extreme end."

the point (vertex) of an item that is furthest distant from its base.

The apex predator in the given triangle is the animal at the highest point, Beluga whale.

Hence, Option 2 is the correct answer.

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Option B is the correct option.

A 10-year-old youngster is having his physical evaluated by the nurse right now. The nurse records that the child weighed 80 pounds during the previous year's checkup. The child's current weight should be around 86 pounds based on growth typical for this age group.

As per the data given in the above question are as bellow,

According to average growth for a 10-year-old boy,

the expected weight gain per year is around 5 to 7 pounds.

Assuming a steady growth rate,

the expected current weight of the child would be:

=80 pounds (last year's weight) + 6 pounds (average weight gain for a 10-year-old boy)

= 86 pounds

Therefore, the expected current weight of the child would be around 86 pounds, which is closest to option B) 85 pounds.

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Answer:

1% of $500 = $5

Total Saving from $500 to $ 860

[tex] = \frac{860}{5} = 172 \\ [/tex]

Now percentage of growth :-

[tex] \frac{172}{500} \times 100 \\ \\ \frac{17200}{500 } = 34.4[/tex]

Hence, the rate of change Sergio savings = 34.4%

375 different combinations of pizza Allie and his friends can create.

What is a combination?

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.

The vegetable toppings are mushrooms, broccoli, green peppers, olives, and onions.

Here, n=5 r=1

So, C(n, r) = 5!/1!(5-1)!

= 5

The meat toppings are pepperoni, salami, sausage, chicken, and ground beef.

Here, n=5 r=1

So, C(n, r) = 5!/1!(5-1)!

= 5

They can pick thick, hand-tossed, or deep-dish crust.

Here, n=3 r=1

So, C(n, r) = 3!/1!(3-1)!

= 3

They can also pick garlic, tomato, ranch, pesto, or barbecue sauce.

Here, n=5 r=1

So, C(n, r) = 5!/1!(5-1)!

= 5

Number of ways = 5×5×3×5

= 375

Hence, in 375 ways they can choose pizza.

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The expected value of the game is $16.50.

First we need to multiply the amount you can win by the probability of winning it, then add up all the products.

Let's call the expected value "E":

E = (0.20 x $60) + (0.15 x $30) + (0.25 x $0) + (0.40 x $0)

E = $12 + $4.50 + $0 + $0

E = $16.50

Therefore, the expected value of the game is $16.50.

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the equation of the line will be 5y = 7x -7. Option c is correct.

A linear equation is an algebraic equation of the form y = mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, a linear equation that passes through the points (5,0) and (0, -7)

The slope-intercept form of the equation of a line

y=mx+b,

where m is the slope

b is the y-intercept

since, slope = (y - y')/(x -x')

In our case,

slope = (-7 -0)/(0-5)

slope = 7/5

b = -7

thus,

the equation of the line will be:

y = 7/5x -7

multiply by 5 on both sides

5y = 7x -7

Therefore, the equation of the line will be 5y = 7x -7.

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The value of conversion from Celsius to Fahrenheit for the value 31 Celsius is equal to 87.8 Fahrenheit.

Standard measuring  units for the temperature is known as Celsius and  Fahrenheit.

Formula used to convert the temperature from Celsius to Fahrenheit is written as

°F = 9 /5 ( ° C ) + 32.

Convert 31 Celsius  to Fahrenheit by substituting the given value in the above formula :

= 9 /5 ( 31° ) + 32

= (1/5) (279° ) + 32

= 55.8°  + 32

= 87.8°F

Therefore, the values after conversion for the 31Celsius to Fahrenheit is given by 87.8 Fahrenheit.

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Answer:

The step which is used is to construct the altitude from the incentre  to a side of triangle and label the intersection point.

Step-by-step explanation:

Given point d is is the center of inscribed circle.

To construct the inscribed circle of abc we have several steps of construction

Step 1: First step is to construct the incenter with the help of angle bisectors of two base vertices.

Here given d center of inscribed circle that means the incenter given.

Step 2: After incenter, draw a line perpendicular to one side of triangle that passes through incenter and the label the point of intersection.

This is very important step because after labelling measure the radius(same as the distance between the incenter and labelled point) and draw the circle.  

Hence, after incenter The next step is to construct the altitude from the incentre  to a side of triangle and label the intersection point.

Step 2 is used draw inscribed circle when incenter already given.