Sampling distribution. a quarterback threw 1 interception in his first game, 2 interceptions in his second game, 5 in terceptions in his third game, and then he retired. consider the values of 1, 2, and 5 to be a population. assume that samples of size 2 are randomly selected (with replacement) from the population
a. list the 9 different possible samples and find the mean of each sample
b. what is the mean of the sample means from part a?
c. is the mean of the sampling distribution from part t equal to the mean of the population of the three listed values? are those means always equal?

So, on solving the provided question, we can say that the equations will be y=2x; y=2x +2; y=2x+4; y=2x+6

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equations will be

y=2x

y=2x +2

y=2x+4

y=2x+6

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The correct question is

Review the scatter plot.

Select the equation which best represents the linear model, the line of best fit. Responses

y=2x

y=2x +2

y=2x+4

y=2x+6

When Alonzo splits 3/4 pounds of candy among 4 people the unit rate in pounds per person is 3/16 pounds per person

The ratio of two measures, with one as the second of the item, is known as unit rate.

For the problem where Alonzo have to split 3/4 pounds of candy, the  unit rate is solved by division.

In this case, Alonzo will divide each the 3/4 pounds by 4 to get a value of which is the unit rate

The unit rate of candy in pounds per person

= 3/4 pounds / 4 persons

= 3/16 pounds per person

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Step-by-step explanation:

82=−3(−4a+3)−5

Step 1: Simplify both sides of the equation.

82=−3(−4a+3)−5

82=(−3)(−4a)+(−3)(3)+−5 (Distribute)

82=12a+−9+−5

82=(12a)+(−9+−5) (Combine Like Terms)

82=12a+−14

82=12a−14

Step 2: Flip the equation.

12a−14=82

Step 3: Add 14 to both sides.

12a−14+14=82+14

12a=96

Step 4: Divide both sides by 12.

[tex]\frac{12a}{12} = \frac{96}{12}[/tex]

a=8

A
____
M = 10
5x10 = 50

The horizontal line test is a procedure that can be used to determine if a function is a one-to-one function. This means that, for every y-value in the function, there is only one distinctive x-value.

The purpose of the horizontal line test is to decide whether or not a given function is one-to-one considering its graph. A function from one set to another is a relation between the two sets in which each element of the first set is assigned to a single element in the second.  In other words, a function f is one-to-one

                           [tex]f(x_{1}) = f(x_{2})[/tex]  ⇒ [tex]x_{1} = x_{2}[/tex]

for every [tex]x_{1} , x_{2}[/tex] n the domain of f.

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Answer:

x=138

Step-by-step explanation:

A triangle's angles equal to 180

104+34=138

180-138=42

X and 42 are a liner pair so they equal 180

138+42=180

x=138

The first equation is based on the fact that Devon is 34 years older than his son Milan:

d = m + 34 (1)

The second equation is based on the fact that the sum of their ages is 44:

d + m = 44 (2)

An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two parts, separated by an equals sign (=). For example, the equation 2x + 3 = 7 is a statement that the expression 2x + 3 is equal to the expression 7. The expressions on either side of the equals sign are often referred to as the left-hand side (LHS) and the right-hand side (RHS) of the equation. Equations can be used to model and describe a wide range of real-world situations, including physical phenomena, financial models, and scientific relationships. Equations can be simple or complex, involving one or more variables and a variety of mathematical operations. Equations can be solved to find the value of the variable(s) that make the equation true.

We can use the information provided to write a system of equations to describe the situation.

The first equation is based on the fact that Devon is 34 years older than his son Milan:

d = m + 34 (1)

The second equation is based on the fact that the sum of their ages is 44:

d + m = 44 (2)

To find how old is Devon we can use either of the equation. Let's use equation (1)

d = m + 34

We know that Milan is x years old, We can substitute that in equation (1)

d = x + 34

So, Devon is 34 years older than Milan.

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The equation of the graph is y=x+1.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The two points from the graph are (1,2) and (2, 4).

m=2/2=1

We have to find the y intercept.

2=1(1)+b

b=1

The slope intercept form is y=x+1

Hence, the equation of the graph is y=x+1.

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The probability that they share the same color is 7/15.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The likelihood that an event will occur increases with its probability.

A straightforward illustration is tossing a fair (impartial) coin.

The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half (which may also be.

According to our question-

Then n(S)= number of ways of drawing 2 balls out of (6+4)=10

Let E= event of getting both balls of same color

Then, n(E)= no of ways (2 balls out of six) or (2 balls out of 4)

= 6C 2​+ 4c2

∴P(E)= n(S)/n(E)= 45/21= 15/7

7/15

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​

​

Answer:

.6 km

Step-by-step explanation:

We need to convert meters to kilometers.

1000 meters is 1 km.

600 meters * 1 km/ 1000m

600/1000  km

.6 km

Answer:

Step-by-step explanation:

The race course is 600 meters long. What is the length of the race in kilometers?

1000 meters = 1 Kilometer

so

600 : 1000 =

0.6 Km

A division is to separate into two or more equal parts, areas, classes, categories, groups, or divisions.

In another word, the meaning of divide is to distribute the whole thing to a group in equal parts or make equal parts. The symbol used to represent divide or division is ÷, slash (/), or a horizontal line ( _ ).

There are four important terms used in the division operation:

dividend, divisor, quotient, and remainder.

The formula to calculate the division of two numbers is:

Dividend ÷ Divisor = Quotient + Remainder.

Here,

The dividend is the number, which is divided

The divisor is the number, which divides the number into equal parts

The quotient is the result of the division operation

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The expression by subtracting 6 from −16, which gives us: q - 6 = -22.

What is expression?

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, *, /) that represent a mathematical relationship or value.

The problem is asking us to find the value of q − 6 when q is equal to −16. To do this, we need to substitute −16 for q in the expression q − 6, which gives us:

q - 6 = (-16) - 6

We then simplify the expression by subtracting 6 from −16, which gives us:

q - 6 = -22

So, the value of q − 6 when q = −16 is −22. This means that if we had a number line and plotted −16 on it, then moved 6 units to the left, we would land on the number −22.

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To use substitution to determine which value of x makes the equation true, we must first have an equation to substitute the values from the set {4, 8, 10} into.

If we don't have an equation, we can't use substitution.

It would be helpful if you could provide an equation to solve with the set {4, 8, 10}

The  breakdown is as follows:

A: The entire green box represents the overall chemical equation.

B: The blue box represents the reactant, which is 2H2O (water)

C: The arrow represents the chemical reaction or the process of breaking down the reactant into the products.

D: The pink box represents the products, which are 2H2 (hydrogen) and O2 (oxygen)

So the chemical equation is 2 H2O --> 2 H2 + O2

The entire green box represents the chemical equation, the blue box represents the reactant (water) and the pink box represents the products (hydrogen and oxygen) and the arrow represents the chemical reaction.

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Therefore ,opposing angles are those that are equal. All of the opposing sides are equal and parallel to one another. Quadrilateral , there are perpendicular divisions.

The two-dimensional shape known as a quadrilateral has four corners, four vertices, or four angles. The two most frequent shapes are convex and concave. Trapezoids, parallelograms, rectangles, rhombuses, and squares are only a few of the many subgroups of convex quadrilaterals.

Here,

example

An object is a quadrilateral if it has four sides, even if they are not all equal. Numerous objects, such as a tabletop, newspaper, photograph, door, baseball diamond, etc., are examples of this.

The trapezoid is one type of quadrilateral that is more challenging to locate in the actual world than others. Quadrilaterals come in a wide variety of sizes and shapes.

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Susie AnnaMarie spent 6 hours cutting grass

Let a represent the number of hours Susie AnnaMarie spent cutting grass

Let b represent the number of hours Susie AnnaMarie spent tutoring

a + b = 14..........equation 1

12a + 14b= 184.........equation 2

From equation 1

a + b= 14

a= 14-b

Substitute 14-b for a in equation 2

12(14-b) + 14b= 184

168 - 12b + 14b= 184

168 + 2b= 184

2b=  184-168

2b= 16

b= 16/2

b= 8

Substitute 8 for b in equation 1

a + b= 14

a + 8= 14

a= 14-8

a= 6

Hence Susie AnnaMarie spent 6 hours cutting the grass

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Therefore , the solution to the given problem of circle comes out to be  

572 yard^2.

Each point in the plane that is a certain distance from some other point forms a circle (center). Thus, it is an curve composed of spots that are spaced apart from one another in the plane. Additionally, at every angle, it is axis of rotation symmetric about the center. The closed, two-dimensional plane of a circle has every pair of points uniformly separated from the "center." With tracing a path through the circle, one can create a line of circular symmetry. Additionally, at every angle, it is radially symmetric about the center.

Here,

area=pi times

radius2 area=3.14 times 13.52

=>3.14 times diameter=2radius dameter/2

=>radius d=27 27/2=radius.

The answer, 182.25=572.265,

Area is 572 yards.

Therefore , the solution to the given problem of circle comes out to be  

572 yard^2.

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The 4 types of problem-solving method are-

Problem solving involves defining a problem, figuring out its root cause, locating, ranking, and choosing potential solutions, as well as putting those solutions into action. the procedure for solving issues.

Clarifying:

Ideating:

Developing:

Implementing:

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The probability of all 6 locations being in water is 0.9994.

The probability of a single location being in water is 0.71. When finding the probability of 6 locations all being in water, we can use the binomial probability formula:

P(x=6) = (n!/(x!(n-x)!)(p^x)(q^(n-x))

where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure.

Plugging in the values, we get:

P(x=6) = (6!/(6!(6-6)!)(0.71^6)(0.29^(6-6))

P(x=6) = 0.9994

Therefore, the probability of all 6 locations being in water is 0.9994.

The probability of all 6 locations being in water is 0.9994.

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If both variables tend to deviate in the same direction (both go above their means or below their means at the same time), then the covariance will be positive.

What Is Covariance?

The direction of the link between the returns on two assets is measured by covariance. Asset returns move together when the covariance is positive, and inversely when the covariance is negative.

It is calculated by analyzing at-return surprises (standard deviations from the expected return) or multiplying the correlation between the two random variables by the standard deviation of each variable.

Types of Covariance:-

This link is determined by a covariance value, either positive or negative.

Covariance Calculated:-

Covariance = Σ[tex][ ( Return_{abc} - Average_{abc} ) * ( Return_{abc} - Average_{abc} ) ][/tex]÷ [ Sample Size - 1 ].

Therefore, the both variables tend to deviate in the same direction, then the covariance will be positive.

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Answer:

35

Step-by-step explanation:

The dimensions of the paint, obtained by factoring the polynomial function for the area of the tray, 42·x + 135·x + 108 are as follows;

(a) The width of the tray = 6·x + 9

(b) Area of the square paint compartment is 9 in²

(c) The width of the edges is 12 inches

The factors of a polynomial are other polynomials of lesser degree, that when multiplied together, produces the polynomial which is factored.

The area of the paint tray = 42·x² + 135·x + 108 in²

The dimensions of the square paint compartment are the same

Space along the edge of the tray = 2 × space between the squares

(a) The length of the tray obtained from the diagram in the question = 7·x + 12 inches

Using an online tool, we get;

42·x² + 135·x + 108 = 3·(2·x + 3)·(7·x + 12)

The area of a rectangle = Length × Width

Therefore, the width of the tray = The area ÷ The length

Width = (42·x² + 135·x + 108)/(7·x + 12) = 3·(2·x + 3)

(b) Let s represent the side length of each square paint compartment, we get;

Width of four compartments + 3 spaces between compartments = (7·x + 12) - 2 × 2·x

Width of four compartments + 3 spaces between compartments = 4·s + 3·x

4·s + 3·x = (7·x + 12) - 2 × 2·x = 3·x + 12

4·s = 3·x + 12 - 3·x = 12

s = 12/4 = 3

s = 3

The side length of each square = 3 inches

The area of each square paint compartment = s²

s² = 3² = 9

(c) Where the width = 45 inches, we get;

3·(2·x + 3) = 45

2·x + 3 = 45/3 = 15

2·x + 3 = 15

2·x = 15 - 3 = 12

x = 12/2 = 6

x = 6

The width of the edges of the tray = 2·x

2·x = 2 × 6 = 12

The width of the edges of the tray = 12 inches

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The change in profit for each owner is -$22.00c

You should be aware that change in profit in this regard talks about how much money each partner is going to loose over what he or she gains initially

The given parameters that will help us to understand the question are

This implies that the 100 dollars will be shared among the five partners in this way

110/5 = 22.00

In conclusion each partner gets a change in profit of $22.00

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The formula for the image of a point (x, y) after a transformation is (x', y'), where: x' = a*x + b*y + e  , y' = c*x + d*y + f  , a, b, c, d, e, and f are constants that depend on the type of transformation being applied.

1. The formula for the image of a point (x, y) after a transformation is (x', y'), which means that the image of the point (x, y) will be another point (x', y') after the transformation.

2. The coordinates (x', y') of the resulting point are determined by constants a, b, c, d, e, and f, which depend on the type of transformation being applied.

3. The constants a, b, c, d, e, and f are used to calculate the coordinates of the resulting point using the following formulas:

x' = a*x + b*y + e

y' = c*x + d*y + f

4. In these formulas, x and y are the coordinates of the original point, and x' and y' are the coordinates of the resulting point. The constants a, b, c, d, e, and f are determined by the type of transformation being applied.

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Answer:

As it is a right angle triangle, you can find a by Pythagoras Theorem.

[tex] {a}^{2} + {51}^{2} = {60}^{2} \\ a = \sqrt{( {60}^{2} - {51}^{2} )} \\ a = 31.63 \: yd[/tex]

Given is the parabola opening down.

It increases up to vertex and then decreases in value.

The vertex is at (3, 4) so the intervals are:

Answer:

Increasing: (-∞, 3)

Decreasing: (3, ∞)

Step-by-step explanation:

A function is increasing when the slope is positive (y gets bigger as x gets bigger).

A function is decreasing when the slope is negative (y gets smaller as x gets bigger).

From inspection of the given parabola, the turning point is (3, 4).

The function is increasing as the curve approaches the turning point.

The function is decreasing as the curve approaches infinity after the turning point.

Therefore, the intervals where the function is increasing and decreasing are:

Note: x = 3 is not included in the intervals, as the curve is not increasing or decreasing when x = 3.  There is a turning point (stationary point) at x = 3 which means the slope is zero as this point. Therefore, the function is not increasing or decreasing when x = 3.

Constant variance is the assumption in regression analysis that the standard deviation and variance of the residuals are constant for all values ​​of the independent variables.

Constant variance is the assumption in regression analysis that the standard deviation and variance of the residuals are constant for all values ​​of the independent variables.

Homogeneity of variances means the assumption that the variances of the random variables are constant. This homoscedasticity (that is, constant variances) assumption can be tested using the same diagnostics used for linear regression models.

All data usually consist of the dependent variable and the independent variable itself. Constant variance is about many linear regression assumptions. For example, if you have 325 rows, there should be at least one variance, possibly a constant. The next question is how to compare variables with appropriate variances. The basic fact is that when plotting between a single value and a predicted value, the resulting variance should be constant for the prediction error value.

                                  Var(μ) = E(μ)² = constant

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The triangle is a perfect right angle triangle  since it satisfies the Pythagoras theorem .

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

According to the definition of a right triangle, a triangle is referred to as a right-angled triangle or simply a right triangle if one of the angles is a right angle (90°). Triangle ABC is a right triangle in the illustration, consisting of the base, altitude, and hypotenuse. Here, the hypotenuse is BC, the height is AC, and the base is AB. The significant side of a right triangle is the hypotenuse, which is the longest side and sits in opposition to the triangle's right angle.

By using pythagoras theorem

[tex]\sqrt{24\x^{2} + 7\x^{2} } = 25[/tex]

The triangle si a perfect right angle triangle  since it satisfies the Pythagoras theorem .

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Standard form is any positive or negative whole number more than or equal to 1 and less than 10.

When working with extremely large or small numbers, you may find that writing them in standard form, also known as standard index form, is the most convenient method. It is predicated on expressing magnitudes of numbers as powers of 10.

For example = 5.5 x 10²²

As the speed of light and the distances between galaxies can be extremely large, scientists typically employ standard form when dealing with these variables. Standard form can also be used to refer to extremely small scales, such as the size of bacteria or atoms.

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