true/false. when the population variance is not known (i.e., must be estimated from data), we use a z-statistic instead of a t-statistic for our hypothesis tests.

To show that the properties of a probability distribution for a discrete random variable are satisfied, we need to verify that the probability distribution function (PDF) satisfies, The PDF must be non-negative for all values of the random variable and The sum of the probabilities for all possible values of the random variable must be equal to 1.

Let X be a discrete random variable taking values x1, x2, ..., xn, and let P(X) be the probability distribution function for X, such that P(X = xi) = pi for all i.

The PDF must be non-negative for all values of the random variable. This means that for any value xi of the random variable, the probability pi must be greater than or equal to zero. That is,

pi ≥ 0 for all i.

This property ensures that probabilities are never negative, which is a necessary condition for a valid probability distribution.

The sum of the probabilities for all possible values of the random variable must be equal to 1. That is,

∑ pi = 1 for all i.

This property ensures that the total probability of all possible outcomes is equal to 1, which is a necessary condition for a valid probability distribution.

Therefore, if the PDF satisfies these two properties, we can conclude that it represents a valid probability distribution for the given discrete random variable.

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Sally will supply 3 quilts at $500.00 per quilt according to the market supply schedule she constructed.

The market supply schedule only takes into account the price per quilt and the quantity supplied per month. Other factors such as production costs, availability of raw materials, competition, and changes in technology are not taken into account in this supply schedule.

a. If Sally purchases a new sewing machine that helps her produce quilts in less time, her production efficiency will increase. This will enable her to produce more quilts in a shorter period of time, which will result in an increase in the supply of quilts.

b. If Sally anticipates an increase in prices for quilts in three months, she may increase the quantity supplied per month in order to take advantage of the higher prices. This may result in a temporary increase in the supply of quilts.

Lastly, c. If there are twice as many quilt suppliers as there were one year ago, Sally will likely face increased competition. This may result in a decrease in sales for Sally and a decrease in the price of quilts. In order to remain competitive, Sally may need to reduce the quantity supplied per month or find ways to differentiate her quilts from those of her competitors.

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See full question below

Part One

Sally Thomas is an entrepreneur. She makes hand-made quilts and sells them at craft shows and at her home studio. Below is a market supply schedule she constructed. Answer the questions that appear below it.

Price per quilt

Quantity Supplied Per Month

$300.00

1

$400.00

2

$500.00

3

$600.00

4

$700.00

5

1. How many quilts will Sally supply at $500.00 per quilt?

3

2. Are any other factors besides price taken into account with the market supply schedule she has constructed?

Supply

3. Several situations are listed below that Sally has encountered in her business. Explain how each of these situations might alter the supply of quilts. a. Sally purchases a new sewing machine that helps her produce quilts in less time.

Sally will be able to produce more quilts in less time, increasing the supply of quilts.

b. Sally anticipates an increase in prices for quilts in three months.

Sally will increase the quantity supplied per month for three months.

c. There are twice as many quilt suppliers as there were one year ago.

Sally will likely experience a decrease in sales which in turn will result in a decrease of supply and price.

Answer:

Step-by-step explanation:

To find the number of students who studied in the library or cafeteria (including both), we need to add the number of students who studied in the library and the number of students who studied in the cafeteria, but we need to subtract the number of students who studied in both the library and cafeteria to avoid counting them twice.

So, the number of students who studied in library or cafeteria is:

170 + 135 - 76 = 229

Therefore, 229 students studied in the library or cafeteria (including both).

Solving the system of equations, it is found that a viable time that the trains are side by side is given by:

15 seconds

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the equations are:

[tex]y=14t^2[/tex]

[tex]y=130t+1200[/tex]

They will be side by side when:

[tex]14t^2=130t+1200[/tex]

[tex]14t^2-130t-1200=0[/tex]

It's solution is a quadratic function with coefficients a = 14, b = -130, c = -1200, hence:

[tex]\Delta=(-130)^2-4(14)(-1200)=84100[/tex]

[tex]x_1=\dfrac{130+\sqrt{84100} }{28}=1.5[/tex]

[tex]x_2=\dfrac{130-\sqrt{84100} }{28}=-5.71[/tex]

Time is a non-negative measure, hence 15 seconds is correct.

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The quadratic function, x2 + 14x + 49 f, would have 7 as the lone zero.

Any subset of a Cartesian product is a relation.

For instance, a subset of is known as a "binary relation from A to B," and in specifically, a subset of is known as a "relation on A."

These ordered pairs (a,b) with first components from A and second components from B make up a binary relation from A to B.

A function is a relation that links every item in a set X to a single item in a different set Y. (possibly the same set).

A graph, which is the collection of all ordered pairs (x, f (x)), serves as the sole representation of a function.

As you can see from these definitions, every function is a relation from X to Y, but not vice versa .

(x - 7)(x - 7)

⇒ (x - 7)²

⇒ x² + 7²+ 2 × 7 × x

⇒ x² + 49 + 14x

⇒ x² + 14x + 49

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The statements below describe the graph of y > mx, where m > 0

The inequality is given as:

y > mx

Where m > 0

The inequality symbol implies that:

The condition m > 0 implies that:

Next, we assume that:

m = 5

So, we have:

y > 5x

See attachment for the graph of y > 5x

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The variance of a sample is equal to n - 1 degrees of freedom, the appropriate chi-square distribution for a sample of n observations taken from a normal population is n - 1 degrees of freedom.

The appropriate chi-square distribution for a sample of n observations taken from a normal population is n - 1 degrees of freedom. This is because the chi-square distribution measures the variance of a population, which is the squared sum of the differences between the observed values and the expected values. Since the expected value for a sample of n observations is equal to the mean of the population, the variance of the sample is equal to the sum of the squared differences between the observed values and the mean of the population. This gives us the formula for the chi-square distribution:

Chi Square = [tex](Sum of (Observed - Mean)^2) / (Mean)[/tex]

For a sample of n observations, the mean is equal to the sum of the observations divided by n, so we can rewrite the formula as follows:

Chi Square = [tex](Sum of (Observed - (Sum of Observations/n))^2) / (Sum of Observations/n)[/tex]

Since the sum of the observations is a constant, we can move it to the other side of the equation, giving us:

We can simplify this equation further by noting that the sum of the [tex](Observed - (Sum of Observations/n))^2[/tex] terms is equal to the variance of the sample. This gives us the final equation:

Chi Square = Variance / (Sum of Observations/n)

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The 95% confidence interval for the proportion in the adult population who would say “Yes” of asked is 0.51 and 0.57.

To find the 95% confidence interval for the proportion in the adult population who would say "Yes," we can use the following formula

CI = p ± z × sqrt((p × (1 - p)) / n)

where

p = proportion of the sample who answered "Yes"

z = the z-score corresponding to the desired level of confidence (in this case, 95% corresponds to a z-score of 1.96)

n = sample size

Plugging in the values given in the question, we get

p = 0.54

z = 1.96

n = 1019

CI = 0.54 ± 1.96 × sqrt((0.54 × (1 - 0.54)) / 1019)

CI = 0.54 ± 0.030

CI = (0.51, 0.57)

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I have solved the question in general, as the given question is incomplete,

The complete question is:

Overall, 54% of the sample (550 of 1019 people) answered “Yes.” Find a 95% confidence interval for the proportion in the adult population who would say “Yes” if asked.?

Step-by-step explanation:

B) 20:23

C) 6,0375

hope this helps

Answer:

The width of the frame is 10 inches.

5x7 = 35

80-35 = 45

45/7 = 6.4

5 + 6.4 = 11.4

11.4 rounded down = 11

11 - 5 = 10

Width of the frame = 10 inches

The correct sampling technique for the given case is C. Simple random sampling

Each person in a population has an equal probability of being chosen to be a member of specific sample when using simple random sampling as a statistical sampling technique. With this technique, a random sample is picked at random from a wider population, giving each person a fair chance of being chosen. This indicates that there is no bias in selection process and that any person or object in overall population has same likelihood of getting chosen.

Simple random sampling is frequently employed in research investigations because it is an easy-to-use and objective sampling technique. Given that 100 names were randomly chosen from a list of all registered voters, simple random sampling is appropriate sampling technique in this particular case.

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Answer:

See explanation below

Step-by-step explanation:

1. 12x - 18 = 6(2x -3)

2. 15x + 25 = 5(3x + 5)

3. 14x + 21 = 7(2x + 3)

4. 5x - 5 = 5(x - 1)

5. 12x - 30 = 6(2x - 5)

6. 10x + 8 = 2(5x + 4)

7. 27x + 18 = 9(3x + 2)

8. 4x - 20 = 4(x - 5)

9. 20x + 30 = 10(2x + 3)

10. 4(x + 5) = 4x + 20

11. 3(x - 2) = 3x - 6

12. 5(2x + 4) = 10x + 20

13. 5(x - 1) = 5x - 5

14. 1/2(10x + 12) = 5x + 6

15. 4(2x + 4) = 8x + 16

16. 2(5x - 2) = 10x - 4

17. 2(x - 8) = 2x - 16

18. 4(2x + 1) = 8x + 4

Answer:

Step-by-step explanation:

8.35 times 105 is 876.75

1.6 times 10 is 16

  Hope this helps

The cardinality of set from the given vein diagram is found as 2.

Think about set A. The set A is said to be finite and so its cardinality is same to the amount of elements n if it includes precisely n items, where n  ≥  0. |A| stands for the cardinality of such a set A.

It turns out that there are two kinds of infinite sets that we need to determine between since one form is much "bigger" than the other. Particularly, one type is referred to as countable and the other as uncountable.

From the given figure

Set A = {8 , 8, 3, 6}

Compliment of Set B (elements not present in set B):

Set [tex]B^{c}[/tex] = {8, 8, 6(pink), 3(white)}

Thus,

(A∩ [tex]B^{c}[/tex] ) = {8, 8} (present in both set)

n (A∩ [tex]B^{c}[/tex] ) = 2 (cardinal number)

Thus, the cardinality of the set from the given vein diagram is found as 2.

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Answer:

Step-by-step explanation:

D is it

The returned value would be 70 which is the missing value in the data set. Hence, option D is correct. We have some X values; we called these numeric inputs and some Y value that we are trying to predict.

This set of data would yield a result of 70 if a median imputer were run on it. In regression, we have some X values that are referred to as independent variables and some Y values that are referred to as dependent variables (this is the variable we are trying to predict). Several Y values are possible, but they are uncommon.

Learning a function that can predict Y given X is the fundamental concept behind a regression. Depending on the data, the function may be linear or non-linear.

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Complete question is:

Imagine X in the below is a missing value. If I were to run a median imputer on this set of data. What would the returned value be? 50 , 60 , 70 , 80 , 100 , 60 , 5000 , x (It's okay to have to look up how to do this!)

50

An error

80

70

100

The basic idea of a regression is very simple. We have some X values, we called these ______ and some Y value (this is the variable we are trying to _______.

We could have multiple Y values, but that is not but that is not re-ordered ordinals intercepts features numeric inputs.

The correct answer is C. This is not a probability model because the sum of the probabilities is not 1.Therefore, the sum of the probabilities must be equal to 1 for a set of probabilities to be considered a probability model.

Probability is a measure of the probability of an event, expressed as a number between 0 and 1.

For example, the probability of rolling a 6 on a fair six-sided die is 1/6 or approximately 0.17.

In order for a set of probabilities to represent a probability model, the sum of all the probabilities must be equal to 1. This ensures that there is a 100% chance that one of the possible outcomes will occur.

If the sum of the probabilities is less than 1, then there is a possibility that none of the outcomes will occur.

If the sum of the probabilities is greater than 1, then there is a possibility that more than one outcome will occur, which is not possible in a probability model.

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The values for a and b such that f(t) = a + logb(t) are,

a = log(1/log(49))

b = 49

Therefor

We can start by simplifying the expression for f(t)

f(t) = log49(t7)

f(t) = log(t7)/log(49) [Using the change of base formula]

Now we can rewrite f(t) as:

f(t) = log(t)/log(b) + a [Using the logarithmic properties log(ab) = log(a) + log(b)]

Comparing this expression with f(t) = a + logb(t), we can see that:

a = log(1/log(49)) [since log(b) = 1/log(49)]

b = t

Therefore, we have

f(t) = log(t7)/log(49) = log(t)/log(b) + log(1/log(49))

= log(t)/log(49) + log(1/log(49))

= log(1/log(49)) + log(t)/log(49)

So, a = log(1/log(49)) and b = 49.

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For Victor to have enough money to purchase the new iPhone 14 Pro Max, he will need to work for roughly 12 weeks.

An expression is made up of a number, a variable, or a combination of a number, a variable, and operation symbols. An equation is created by joining two expressions with an equal sign. For illustration: When you add 8 and 3, you get 11.

a) Here is the equation for Victor's savings account:

V(w) = 50w + 500

Slope (m) = 50

Y-intercept (b) = 500

b) The slope (m = 50) represents the rate at which Victor is saving money per week. For every week that he works as a tutor, he saves $50. The y-intercept (b = 500) represents the initial amount of money that Victor had saved up before he started working as a tutor.

(c)To find out how many weeks Victor will have to work to buy the new iPhone 14 Pro Max, we need to set up an equation where the amount of money he has saved up (V(w)) is equal to the price of the phone ($1099). Therefore, we can write:

50w + 500 = 1099

Subtracting 500 from both sides, we get:

50w = 599

Dividing both sides by 50, we get:

w = 11.98

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The distance Jamie will run is equal to half of the rate in kilometers per hour, the equation is d = r (1/2)

Speed is a scalar number that represents the rate of movement of an item. It is described as the distance covered in a certain amount of time, regardless of direction. In contrast, velocity is a vector quantity that accounts for both speed and direction. It is characterised as the pace at which an item shifts in a certain direction. In physics, the idea of velocity is crucial since it aids in explaining how an object's location varies over time and is used to compute other crucial variables like acceleration and momentum.

The distance is calculated using the given formula:

Distance = rate (time)

Given that, the time is 1/2 hour thus:

d = r (1/2)

Thus, the distance Jamie will run is equal to half of the rate in kilometers per hour, and the equation is d = r (1/2).

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Therefore, A, B, C, and F are the proper responses as the congruence theories or postulates based on the data.

Having three straight sides and three angles where they intersect, a triangle is a closed, two-dimensional shape. It is one of the fundamental geometric shapes and has a number of characteristics that can be used to study and resolve issues that pertain to it. The triangle inequality theory states that the sum of a triangle's interior angles is always 180 degrees, and that the longest side is always the side across from the largest angle. Triangles can be used to solve a wide range of mathematical issues in a variety of disciplines and can be categorised based on the length of their sides and the measurement of their angles.

given

We can use the following congruence theories or postulates based on the data in the diagram:

A. ASA

B. AAS

C. LL (corresponding angles hypothesis)

F. SAS

Therefore, A, B, C, and F are the proper responses as the congruence theories or postulates based on the data.

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The value of a is 2.

the vertex form of the graph : y = 2 ( x + 1 )² - 9,

the standard form of the graph : y = 2x² + 4x - 7,

the factored form of the graph : y = 2 ( x + 1) ( x + 1 ) - 9.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The equation of the parabola in vertex form:

The vertex v is at v ( -1, -9 ) this is equivalent to v ( h, k )

the equation of parabola in vertex form is y = a ( x- h )² + k

y = a ( x - (-1) )² + (-9)

substituting point ( -3, -5 ) from the graph we have:

-5 = a ( -3 + 1 )² - 9

-5 = 2a - 9

a = 2

substituting the known values to y = a ( x- h ) + k

y = 2 ( x + 1 )² - 9

the equation of the parabola in factored form

y = 2 ( x + 1) ( x + 1 ) - 9

the equation of the parabola in standard form

y = 2 ( x + 1) ( x + 1 ) - 9

y = 2 ( x² + 2x + 1 ) - 9

y = 2x² + 4x - 7

Hence, the value of a is 2

the vertex form of the graph : y = 2 ( x + 1 )² - 9

the standard form of the graph : y = 2x² + 4x - 7

the factored form of the graph : y = 2 ( x + 1) ( x + 1 ) - 9

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if we  that Abby spent 50% of her time on School, 30% on Work, and 20% on Sleep, we can estimate that she spent:

100% - (50% + 30% + 20%) = 100% - 100% = 0% on Other.

If Abby divided her time into four categories (School, Work, Other, and Sleep), the percentage she spent on Other would be 100% less the sum of the percentages she spent on School, Work, and Sleep.

So, assuming Abby spending 50% of her time at school, 30% at work, and 20% sleeping, we can estimate she spent:

On Other, 100% - (50% + 30% + 20%) = 100% - 100% = 0%.

However, this is just a guess based on assumptions about how Abby spent her time. It's difficult to provide a more accurate estimate without more information.

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The real estate tax on Brianna Wallen's home is $37,934.83.

Property owners, including homeowners, are subject to a tax based on the assessed value of their properties. It is often collected by local governments and used to pay for amenities like public transportation, roads, and security.

The assessed value of the property and the tax rate are used to determine the amount of property tax due. The assessed value of a property is its worth as established by a government assessor and may be based on a number of variables, including recent sales prices of nearby properties, the price to replace the property, and the property's condition.

The tax is calculated using the given formula:

Tax = (Assessment Rate x Market Value) x (Tax Rate / 1000)

Substituting the given values we have:

Tax = (0.29 x $438,300) x (81.16 / 1000)

Tax = $37,934.83

Hence, the real estate tax on Brianna Wallen's home is $37,934.83.

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Answer:

You need to know that the ratio of their sides are congruent

Answer:

Step-by-step explanation:

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).

In this case, we know that P = $10,000, r = 6.5% = 0.065, and we want to find t when A = $29,500. We also know that the interest is compounded annually, so n = 1.

Substituting these values into the formula, we get:

$29,500 = $10,000(1 + 0.065/1)^(1t)

Dividing both sides by $10,000, we get:

2.95 = (1.065)^t

Taking the natural logarithm of both sides, we get:

ln(2.95) = ln(1.065)^t

Using the property of logarithms that ln(a^b) = b ln(a), we can rewrite the right side as:

ln(2.95) = t ln(1.065)

Dividing both sides by ln(1.065), we get:

t = ln(2.95)/ln(1.065) ≈ 18.2

Therefore, the person must leave the money in the bank for about 18.2 years to reach $29,500. To the nearest tenth of a year, the answer is 18.2 years.

Answer:

x = 21

Step-by-step explanation:

Given the angle measurements of two angles, we can deduce that this is a 30-60-90 triangle. The formula for side lengths of this type of triangle is given by s → s√3 → 2s with s being the shortest side (the side opposite the 30° angle).

We are looking for the side length represented by s[tex]\sqrt{3}[/tex]. We can see that the hypotenuse is represented by 2s, so...

2s = 24

s = 12

The side length of the shortest side is 12. Therefore, we can say that

x = s  [tex]\sqrt{3}[/tex]

x = 12 * [tex]\sqrt{3}[/tex]

x = 20.785

The question asks for our answer to the nearest whole number, so

x = 21

the probability of the complement of (A ∪ B) is 0.3.

How to find and what is Morgan's law?

Since A and B are mutually exclusive, we have:

P(A ∩ B) = 0

The complement of (A ∪ B) is the set of outcomes that are not in A or B. So:

(A ∪ B)′ = A′ ∩ B′

Using De Morgan's law, we have:

A′ ∩ B′ = (A ∪ B)′

We can now use the formula for the probability of the complement:

P((A ∪ B)′) = 1 - P(A ∪ B)

Since A and B are mutually exclusive, we have:

P(A ∪ B) = P(A) + P(B)

So:

P((A ∪ B)′) = 1 - (P(A) + P(B))

Substituting the given probabilities, we get:

P((A ∪ B)′) = 1 - (0.2 + 0.5)

P((A ∪ B)′) = 1 - 0.7

P((A ∪ B)′) = 0.3

Therefore, the probability of the complement of (A ∪ B) is 0.3.

De Morgan's laws are a pair of fundamental laws in Boolean algebra and set theory that describe the relationship between the intersection and union of sets and their complements. The two laws are:

The complement of the union of two sets is equal to the intersection of their complements.

Symbolically: (A ∪ B)′ = A′ ∩ B′

The complement of the intersection of two sets is equal to the union of their complements.

Symbolically: (A ∩ B)′ = A′ ∪ B′

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If the probability distribution is f(x) = 2(1/3)ˣ for x = 1,2,3,... then the moment generating function is Mₓ(t) = [tex]\frac{2e^{t} }{3-e^{t} }[/tex].

The moment generating function (MGF) of a random variable is defined as a mathematical function that is used to determine expected values of the random variable.

It is a way to characterize the entire probability distribution of the random variable by generating a sequence of moments from the function.

The probability distribution is  f(x) = 2(1/3)ˣ for x = 1,2,3,... ;

The MGF will be ⇒ Mₓ(t) = [tex]\[ \sum_{x=1}^{\infty} e^{tx} .2(\frac{1}{3})^{x}[/tex]

⇒ [tex]2 \[ \sum_{x=1}^{\infty}(\frac{e^{t} }{3} )^{x}[/tex] ;

This expression [tex]\[ \sum_{x=1}^{\infty}(\frac{e^{t} }{3} )^{x}[/tex] represents an infinite geometric series.

So, [tex]\[ \sum_{x=1}^{\infty}(\frac{e^{t} }{3} )^{x}[/tex] = [tex]\frac{e^{t}/3 }{1-e^{t}/3 }[/tex] = [tex]\frac{e^{t} }{3-e^{t} }[/tex]

We get, Mₓ(t) = [tex]\frac{2e^{t} }{3-e^{t} }[/tex].

Therefore, the Moment generating Function for the given Probability Distribution is Mₓ(t) = [tex]\frac{2e^{t} }{3-e^{t} }[/tex].

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The given question is incomplete, the complete question is

Find the moment-generating function of the discrete random variable X that has the probability distribution f(x) = 2(1/3)ˣ for x = 1,2,3,....