Suppose Elena has $5 and sells pens for $1.50 each. Her goal is to save $20 to buy a t-shirt. She does not spend any money while she is saving money.

Let p represent the number of pens Elena sells. Write an expression for how much money she saves in total after selling p pens.



Write an equation using your answer from question 1, showing that she saves exactly $20.



Solve the equation you wrote from question 2. What do you notice about your value for p?





What if Elena wants to have some money left over? Write an inequality using your expression from question 1 to show this.



Write down other values for p where Elena would have money left over.



Write an inequality using p, to describe the values of p where she would be able to buy the tshirt and still have money left over.

The computer response time is a crucial application of the gamma and exponential distribution. The proportion of computers studied that will have a response time less than 3 seconds is 0.6321 or 63.21%.

If a study of 200 computers shows that the response time in seconds has an exponential distribution with a mean of 3 seconds, then the probability that the response time exceeds 5 seconds and the proportion of the computers studied will have a response time less than 3 seconds can be calculated as follows:The mean of the exponential distribution is equal to the reciprocal of the rate parameter, λ, i.e.,E(X) = λ-1 Given, the mean response time, E(X) = 3 seconds.The mean of the exponential distribution, E(X) = λ-1= 3 seconds. Therefore,λ = 1/3. The probability that the response time exceeds 5 seconds can be calculated as:P(X > 5) = e -λx= e -(1/3) (5)= 0.0498 The probability that the response time exceeds 5 seconds is 0.0498 or 4.98%.The proportion of computers studied that will have a response time less than 3 seconds can be calculated as:P(X < 3) = 1 - P(X > 3)= 1 - e -λx= 1 - e -(1/3) (3)= 1 - e -1= 1 - 0.3679= 0.6321 or 63.21%.

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The general solution of the given trignometric function tan3x . 1/tan24° - 1 = 0​ is x = nπ/3 + 2π/45.

Trigonometry is a field of mathematics that deals with correlations between angles and length ratios (from the Ancient Greek v (trgnon) "triangle" and v (métron) "measure").

The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

While Indian mathematicians produced the earliest tables of values for trigonometric ratios (also known as trigonometric functions), such as sine, the Greeks concentrated on chord calculation.

Trigonometry has been used historically in fields like geodesy, surveying, celestial mechanics, and navigation.

So, we have the function:

tan3x . 1/tan24° - 1 = 0​

Now, solve as follows:

tan3x . 1/tan24° - 1 = 0​

tan3x - tan24° = 0

tan3x = tan24°

tan3x = tan(24π/180)

3x = nπ + 2π/15

x = nπ/3 + 2π/45

Therefore, the general solution of the given trignometric function tan3x . 1/tan24° - 1 = 0​ is x = nπ/3 + 2π/45.

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Answer:

$31.45

Step-by-step explanation:

If something was reduced by 15 percent its the same as .85x or 85% of the original price. 37*.85 = $31.45

Answer:

0. 25 25/100

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the width to length ratio is 2 to 3, then for every 2 inches in the width, there are 3 inches in the length.

a. For 2 inches in the width, there are 3 inches in the length.

b. For 4 inches in the width, there are 6 inches in the length.

c. For 6 inches in the width, there are 9 inches in the length.

d. For 8 inches in the width, there are 12 inches in the length.

The length of the rectangle is 12 inches.

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that;

Width to length ratio = 2 to 3

Now,

Since the width to length ratio is 2 to 3, we can express the width as 2x and the length as 3x, where x is some constant. Then, we can use the given information to solve for x.

a. For every 2 inches in the width, there are 3 inches in the length.

This means that:

2x = 2 inches

3x = 3 inches

Solving for x, we get:

x = 1 inch

Then, we can find the length by multiplying x by the length factor:

3x = 3 inches

Therefore, the length of the rectangle is 3 inches.

b. For every 4 inches in the width, there are 6 inches in the length.

This means that:

2x = 4 inches

3x = 6 inches

Solving for x, we get:

x = 2 inches

Then, we can find the length by multiplying x by the length factor:

3x = 6 inches

Therefore, the length of the rectangle is 6 inches.

c. For every 6 inches in the width, there are 9 inches in the length.

This means that:

2x = 6 inches

3x = 9 inches

Solving for x, we get:

x = 3 inches

Then, we can find the length by multiplying x by the length factor:

3x = 9 inches

Therefore, the length of the rectangle is 9 inches.

d. For every 8 inches in the width, there are 12 inches in the length.

This means that:

2x = 8 inches

3x = 12 inches

Solving for x, we get:

x = 4 inches

Then, we can find the length by multiplying x by the length factor:

3x = 12 inches

Therefore, by the given ratio the answer will be 12 inches.

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The value of m∠B is 212 - 24x.

The totality of the angles in a quadrilateral is always amount to 360°. This is a primary property of all quadrilaterals, irrespective of their shape or size.

As a result, irrespective of the shape say if you are dealing with a square, rectangle, parallelogram, trapezoid, or any other type of quadrilateral, the totality of the angles will always be sum to 360°.

To determine the value of m∠B, one can employ the notion that the sum of the angles in a quadrilateral is 360°.

Thus,

m∠A + m∠B + m∠C + m∠D = 360

Substituting the given values, we get:

(16x)° + m∠B + (8x+20)° + 128° = 360

Simplifying and solving for m∠B, we get:

m∠B = 360 - (16x)° - (8x+20)° - 128°

m∠B = 212 - 24x

Therefore, the value of m∠B is 212 - 24x.

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As per the volume, the dimension of an Extra Large Box is 3.78 feet.

Let's call the length of one side of the cube "s". Since the volume of the cube is given as 512 cubic feet, we can set up an equation to relate the volume to the length of one side:

Volume of cube = s³ = 512 cubic feet

To solve for "s", we can take the cube root of both sides of the equation:

s = ∛512

We can simplify this expression by finding the prime factorization of 512:

512 = 2⁹

Therefore, we can rewrite the expression for "s" as:

s = ∛2⁹

Using the properties of exponents, we know that the cube root of 2^9 is the same as 2 raised to the power of (1/3) times 9:

s = [tex]2^{1/3} \times 9^{1/3}[/tex]

We can simplify this expression further by recognizing that 9 is a perfect cube, and its cube root is 3:

s = [tex]2^{1/3} \times 3[/tex]

Therefore, the length of one side of the cube-shaped box is:

s = [tex]2^{1/3} \times 3[/tex] feet

Since all sides of the cube are equal in length, the dimensions of the box are:

Length = Width = Height = [tex]2^{1/3} \times 3[/tex] feet = 3.78 feet.

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Complete Question:

Head Stevedore loads Extra Large Boxes, also in the shape of perfect cubes. The volume of each box is 512 cubic feet. What are the dimension of an Extra Large Box?

Considering the Markov chain with transition matrix, the chain does have stationary distribution which exhibits State 1 is transient and the stationary distribution is (2/9, 4/9, 8/27, 16/81, 32/729).

(a) Yes, the chain has a stationary distribution. To find it, we need to solve the system of equations π = πP, where π   is the vector of probabilities for each state and P is the transition matrix. This gives us:

π_{1} = π(1/2)

π_{2} = π(1/3) + π(2/2)

π_{3}= π(2/4) + π(3/2)

π_{4} = π(3/5) + π(4/2)

π_{5}= π4/5

We also have the normalization condition π1 + π2 + π3 + π4 + π5 = 1.

Solving this system of equations, we get:

π_{1} = 10/97

π_{2} = 30/97

π_{3}= 40/97

π_{4} = 14/97

π_{5}= 3/97

So the stationary distribution is (10/97, 30/97, 40/97, 14/97, 3/97).

(b) State 1 is transient, and all other states are recurrent.

(c) Yes, the chain still has a stationary distribution. We need to solve the system of equations  π = Pπ, where P is the new transition matrix. This gives us:

π_{1} = π(1/2)

π_{2} = π(1/3) + π(2/2)

π_{3}= π(2/4) + π(3/2)

π_{4} = π(3/5) + π(4/2)

π_{5}= π4/5

We also have the normalization condition π1 + π2 + π3 + π4 + π5 = 1.

Solving this system of equations, we get:

π_{1} = 2/9

π_{2}  = 4/9

π_{3} = 8/27

π_{4} = 16/81

π_{5}  = 32/729

So the stationary distribution is (2/9, 4/9, 8/27, 16/81, 32/729)

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Answer:

b = 12.12 (or) 7 sqrt 3

Step-by-step explanation:

a^2 + b^2 = c^2

7^2 + b^2 = 14^2

49 + b^2 = 196

-49 -49

b^2 = 147

b = sqrt 147

decimal form:

b = 12.12

exact form:

b = 7 sqrt 3

By answering the presented question, we may conclude that Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

To simplify the expression,

[tex]a(b+c) = ab + ac\\9(4/3m-5-2/3m+2) = 9(4/3m - 2/3m - 5 + 2)\\= 9(2/3m - 3)\\= 6m - 27[/tex]

Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.

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Answer:

We can use similar triangles to solve this problem. Let's call the length of the kite's line "x". Then, we can set up a proportion:

(length of kite) / (length of shadow) = (height of kite) / (length of shadow)

x / 9 = 10 / 9

To solve for x, we can cross-multiply and simplify:

x = 90 / 9

x = 10

Therefore, the length of the kite's line is 10 feet.

Step-by-step explanation:

The probability of producing the genotype AABBCC in a cross AaBbCc × AaBbCc is 1/64.

A Punnett square is a grid used to forecast the likelihood of an offspring of a mating between two parents with known genotypes. The grid consists of four boxes or cells with one parent's gamete genotype listed along the top, and the other parent's gamete genotype listed down the side.

To determine what proportion of their offspring will possess a certain genotype or phenotypic characteristic, the gamete genotypes are combined using the grid.

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To summarize, a perfectly egalitarian society has a Gini index of 0, and a perfectly totalitarian society has a Gini index of 1.

The Gini index (G) measures how much the income distribution differs from absolute equality.

On the other hand, a perfectly totalitarian society (where a single person receives all the income) will have a Gini index of 1. This means that there is a huge inequality between individuals, with the single person receiving all of the income.

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Answer:

Volume = length x width x height

Step-by-step explanation:

A rectangular prism is a three-dimensional solid object with six faces, where each face is a rectangle. The shape of a rectangular prism is defined by its length, width, and height. The volume of a rectangular prism is the amount of space it occupies and can be calculated by multiplying its length, width, and height. The formula for the volume of a rectangular prism is:

Volume = length x width x height

Understanding the shape of a rectangular prism and its formula for volume is essential in various fields, such as architecture, engineering, and physics, where it is necessary to calculate the volume of objects for design and analysis purposes.

If you multiply that is how u get volume

Given, X has a uniform distribution on the interval (-1,1]. We are to determine the incorrect statement among the following:

Statement 5: The variance of a uniform distribution is (b-a)^2/12. Here, a=-1 and b=1. Hence, Var(X) = (1-(-1))^2/12 = 1/3. This statement is correct .Therefore, the incorrect statement is P(X ≤ 0.5) = 0.5.

Statement 1: f(x) = 0.5 for -1 < x ≤ 1Statement 2: P(X ≤ 0.5) = 0.5Statement 3: P(X ≤ 1) = 1Statement 4: E[X] = 0Statement 5: Var(X) = 1/3Let's check each statement one by one:

Statement 1: The probability density function (PDF) of a uniform distribution is f(x) = 1/(b-a) for a < x ≤ b. Here, a=-1 and b=1. Hence, f(x) = 1/(1-(-1)) = 0.5 for -1 < x ≤ 1. This statement is correct.

Statement 2: The cumulative distribution function (CDF) of a uniform distribution is F(x) = (x-a)/(b-a) for a < x ≤ b. Here, a=-1 and b=1. Hence, [tex]P(X ≤ 0.5) = F(0.5) = (0.5-(-1))/(1-(-1)) = 0.75[/tex], which is not equal to 0.5. Therefore, this statement is incorrect.

Statement 3: P(X ≤ 1) = F(1) = (1-(-1))/(1-(-1)) = 1. This statement is correct.

Statement 4: The expected value of a uniform distribution is (a+b)/2. Here, a=-1 and b=1. Hence,[tex]E[X] = (-1+1)/2 = 0.[/tex] This statement is correct.

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the probability of Jacinta selecting a green marble is 5/11. The total number of marbles in the bag is:

2 (blue) + 4 (red) + 5 (green) = 11

The probability of selecting a green marble can be found by dividing the number of green marbles by the total number of marbles:

P(selecting a green marble) = number of green marbles / total number of marbles

= 5 / 11

Therefore, the probability of Jacinta selecting a green marble is 5/11. Answer: 5/11.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

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Answer:

20%

Step-by-step explanation:0% of 4445=

ANSWER:
x=y/5
STEPS:
1. Divide each term in 5x=y

2. Simplify

----------------------
I hope this helped!! Much love <333

Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.

Average temperature is calculated as (Monday's temperature plus Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature)/Total days.

Temporary for Monday and Tuesday plus Temperatures for Wednesday and Thursday.

The sum of the temperatures for Monday, Tuesday, Wednesday, and Thursday is equal.

As stated, the 6.5 degree average for the days of Tuesday, Wednesday, Thursday, and Friday.

using the formula no.

Average temperature is equal to (Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature plus Friday's temperature)/Total days.

Thus, Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.

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the complete question is

Write a positive or negative number to represent each change in the high temperature.

1. Tuesday’s high temperature was 4 degrees less than Monday’s high temperature. ?

2. Wednesday’s high temperature was 3.5 degrees less than Tuesday’s high temperature. ?

3. Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature. ?

4. Friday’s high temperature was 2 degrees less than Thursday’s high temperature. ?

The value of x is 8/3 or 2.67 cm (rounded to two decimal places).

The problem at hand entails determining the value of a variable "x" in a right-angled triangle.

We can begin by applying the Pythagorean Theorem, which states that the square of the length of the hypotenuse in a right-angled triangle equals the sum of the squares of the lengths of the other two sides.

We have a right-angled triangle ABC in this case, with AC as the hypotenuse, AB as one of the other sides, and BC as the remaining side.

We know that AB equals 5 cm and BC equals x cm. We must locate AC.

The Pythagorean Theorem yields:

[tex]AC^2 = AB^2 + BC^2[/tex]

[tex]AC^2 = 5^2 + x^2[/tex]

[tex]AC^2 = 25 + x^2[/tex]

Also, we know that AC = 2x + 1. We get the following result when we plug this number into the above equation:

[tex](2x + 1)^2 = 25 + x^2[/tex]

[tex]4x^2 + 4x+ 1 = 25 + x^2[/tex]

[tex]3x^2 + 4x - 24 = 0[/tex]

The above quadratic equation can be factored as follows:

[tex](3x - 8)(x + 3) = 0[/tex]

As a result, either[tex]3x - 8 = 0 or x + 3 = 0.[/tex]

We get the following when we solve for x:

3x - 8 = 0

3x = 8

x = 8/3

or

x + 3 = 0

x = -3

We reject the second solution because length cannot be negative.

As a result, the value of x is 8/3 or 2.67 cm (rounded to two decimal places).

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A. The power of the two-tailed hypothesis test with α = .05 is 0.53.

B. The power of the one-tailed hypothesis test with α = .05 is 0.95.

A hypothesis test is used to make decisions about a population based on sample data. It involves specifying a null hypothesis, collecting data, and then assessing the data to either reject or accept the null hypothesis.

A. The power of the two-tailed hypothesis test is calculated using the formula:

Power=

1- β=1- (1-α)[tex]^{1/2}[/tex]

=1- (1-0.05)[tex]^{1/2}[/tex]

=0.525

=0.53

This means that the researcher has an 53% chance of correctly rejecting the null hypothesis that there has been no change in the IQ over the past 10 years.

B. The power of the one-tailed hypothesis test is calculated using the formula:

Power=

1- β=1- α

=1- 0.05

= 0.95

This means that the researcher has a 95% chance of correctly rejecting the null hypothesis that there has been no increase in the IQ over the past 10 years.

This is a higher power than the two-tailed test because the one-tailed test focuses on detecting an increase in the IQ, while the two-tailed test can detect both an increase or decrease in the IQ.

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The equation that models the shape of the monument is simply y = 25.

The equation that models the shape of the parabolic monument can be written in the form of a quadratic function, y = ax^2 + bx + c, where y is the height of the monument at a given distance x from the center of the base.

Since the monument has a height of 25 feet at the center of the base, we know that the vertex of the parabolic shape is located at (0, 25). Also, since the base width is 30 feet, the distance from the center of the base to either side is 15 feet.

Therefore, we can use the information about the vertex and the width to write the equation as y = -a(x-15)^2 + 25.

To determine the value of a, we need another point on the curve. Let's use one of the endpoints of the base, which is (15, 0). Plugging these values into the equation, we get:

0 = -a(15-15)^2 + 25

0 = 25

This is not possible, so we need to adjust the equation to fit the known points. We can rewrite the equation as y = a(x-15)^2 + 25, and solve for a using the other endpoint of the base, which is (-15, 0):

25 = a(-15-15)^2 + 25

0 = 900a

a = 0

This means that the equation that models the shape of the monument is simply y = 25.

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The exponential function that can model the revenue of a technology company whose starting value is $395,000 in 2010 at 1.2% annual growth is b) S(t)=395*(1.012)^(t).

An exponential function is a mathematical function that calculates the exponential growth or decay of a given data set.

An exponential function is defined by the formula f(x) = ab^x.

There are two kinds of exponential functions:

Starting value of the revenue in thousands of dollars = $395,000

Time measured in years after 2010 = t

Annual growth rate = 1.2%

Thus, the exponential function that mirrors the revenue growth is b) S(t)=395*(1.012)^(t).

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a) R(t)=395*e^((0.012t))

b) S(t)=395*(1.012)^(t)

Answer:

The simplified expression is sec^2a

Step-by-step explanation:

We can start by using the trigonometric identities:

cot^2 a + 1 = csc^2 a

tan^2 a + 1 = sec^2 a

Using these identities, we can rewrite the expression as:

(cos^2 a - cot^2 a)/(sin^2 a - tan^2 a)

= (cos^2 a - (csc^2 a - 1))/(sin^2 a - (sec^2 a - 1))

= (cos^2 a - csc^2 a + 1)/(sin^2 a - sec^2 a + 1)

Now we can use the identity:

sin^2 a + cos^2 a = 1

to rewrite the expression further:

= (1/sin^2 a - 1/sin^2 a cos^2 a)/(1/cos^2 a - 1/cos^2 a sin^2 a)

= (1 - cos^2 a)/(sin^2 a - sin^2 a cos^2 a)

= sin^2 a / sin^2 a (1 - cos^2 a)

= 1 / (1 - cos^2 a)

= sec^2 a

Therefore, the simplified expression is sec^2 a.

The probability that the diameter of a selected bearing is greater than 52 millimeters is 0.8413. This can be calculated using the formula for probability of a normal distribution:

P(x > 52) = 1 - P(x ≤ 52)

P(x ≤ 52) = (52 - 58) / 6 = -1

P(x > 52) = 1 - P(-1) = 1 - 0.1587 = 0.8413.

Therefore, the probability that the diameter of a selected bearing is greater than 52 millimeters is 0.8413.

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To conclude, the probability of the Acme Drug Company seeing a percent difference of -.13 or less if the true difference is 0 is quite low and is equal to 0.0934.

The probability that the Acme Drug Company would see a percent difference of -.13 or less if the true difference is 0 is quite low. This is because a difference of -.13 is a very small percentage in comparison to a true difference of 0.

Mathematically, the probability of this happening would be equal to the area under the standard normal distribution curve for values between -0.13 and 0. In other words, the probability that the Acme Drug Company would see a percent difference of -.13 or less if the true difference is 0 is equal to the area from the left tail of the standard normal distribution curve up to the mean (0) of the curve.

Using a standard normal distribution calculator, we can see that the probability of the Acme Drug Company seeing a percent difference of -.13 or less is 0.0934. This probability is extremely low and it is not likely that the Acme Drug Company would experience such a small percent difference.

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The probability that at least one of the males has red-green color blindness is 0.6057.

Number of males in a group, n = 7

Probability of red-green color blindness, p = 0.06

Probability of non-red-green color blindness, q = 0.94

P(at least one of them has red-green color blindness) = 1 - P(none of them has red-green color blindness)

Probability of none of the males in the group having red-green color blindness = P(X = 0)

Now, let us apply the Binomial Probability formula, which is:

P(X = x) = (nCx)pxq^n−x where n = 7, x = 0, p = 0.06, q = 0.94

P(X = 0) = (7C0)(0.06)0.94^(1 - 0.06)7-0

= 0.3943

Now, using the given formula:

P(at least one of them has red-green color blindness) = 1 - P(none of them has red-green color blindness)

P(at least one of them has red-green color blindness) = 1 - 0.3943

P(at least one of them has red-green color blindness) = 0.6057

Therefore, the probability that at least one of the males has red-green color blindness is 0.6057.

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Based on the information provided, the table that correctly displays the data is table III.

Note: The question is incomplete; below I attach the missing information:

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A quadratic function in standard form that passes through the points (-8,0), (-5,-3), and (-2,0) is equals to the f(x) = (1/3)( x² + 10x + 16).

A quadratic function is a polynomial function with one or more variables, the highest degree of the variable is two. It is also called the polynomial of degree 2. The form of quadratic function is

f(x) = ax² + bx + c ----(1)

is determined by three points and must be a≠ 0. That is for determining the f(x) we have to determine value of three values a, b, and c. Now, we have three ordered pairs (-8,0), (-5,-3), and (-2,0) and we have to determine quadratic function passing through these points. So, firstly, plug the coordinates of point ( -8,0), x = -8, y = f(x) = 0 in equation (1),

=> 0 = a(-8)² + b(-8) + c

=> 64a - 8b + c = 0 --(2)

Similarly, for second point ( -5,-3) , f(x) = -3, x = -5

=> - 3 = a(-5)² + (-5)b + c

=> 25a - 5b + c = -3 --(3)

Continue for third point (-2,0)

=> 0 = a(-2)² + b(-2) + c

=> 4a -2b + c = 0 --(4)

So, we have three equations and three values to determine.

Subtract equation (4) from (2)

=> 64 a - 8b + c - 4a + 2b -c = 0

=> 60a - 6b = 0

=> 10a - b = 0 --(5)

subtract equation (4) from (3)

=> 21a - 3b = -3 --(6)

from equation (4) and (5),

=> 3( 10a - b) - 21a + 3b = -(- 3)

=> 30a - 3b - 21a + 3b = 3

=> 9a = 3

=> a = 1/3

from (5) , b = 10a = 10/3

from (4), c = 2b - 4a = 20/3 - 4/3 = 16/3

So, f(x)= (1/3)( x² + 10x + 16)

Hence, required values are 1/3, 10/3, and 16/3.

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The ability of the normal distribution to approximate the binomial distribution under appropriate conditions justifies the use of the normal distribution for the sampling distribution of the proportion.

A sampling distribution is a statistical probability distribution derived from a larger number of samples gathered from a certain population. The sampling distribution of a particular population is the distribution of frequencies of a range of possible outcomes for a population statistic.

A population is the whole pool from which a statistical sample is selected in statistics. A population can be defined as a large group of people, things, events, medical visits, or measures. A population can thus be defined as an aggregate observation of persons linked by a common trait.

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