Use the diagram to estimate the perimeter, rounding each number to the nearest thousand.
18,167 cm/
43,812 cm
39,412 cm
O 102, 000 centimeters
O 103, 000 centimeters
O 100, 000 centimeters
O 101, 000 centimeters

The regular polygon has 20 sides.

The regular pentagon is a regular polygon with five sides

The regular decagon is a regular decagon with ten sides

The angle sum around a point adds to 360 degrees.

Each interior angle of the square is 90 degrees

Each interior angle of the regular pentagon is 108 degrees.

The Interior angle of our unknown polygon is 360 - 108 - 90 = 162 degrees.

A quick calculation shows us that the exterior angle of this polygon is 18 degrees.

The sum of the external angles of any regular polygon is 360 degrees

Divide 360 by 18 and you get 20 times.

Thus our unknown polygon has 20 sides.

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The doubling time is approximately 83 years. This means that it will take approximately 83 years for the squirrel population to double from its initial size of 450 squirrels.

What is an exponential function?

An exponential function is a function in which the variable appears in the exponent. Exponential functions have the form y = ab^x, where a and b are constants and x is the variable. The constant b is called the base of the exponential function.

The given information states that the squirrel population P(t) follows a logistic growth model with a growth constant k = 0.8 yr-1 and a carrying capacity of 1800 squirrels. The formula for the squirrel population P(t) can be found using the logistic growth model:

P(t) = K / (1 + (K/P0 - 1) * e^(-kt))

where P0 is the initial population of squirrels, K is the carrying capacity, and t is time in years.

Substituting the given values into the formula, we get:

P(t) = 1800 / (1 + (1800/450 - 1) * e^(-0.8t))

Simplifying the equation, we get:

P(t) = 1800 / (1 + 3e^(-0.8t))

This is the formula for the squirrel population P(t).

To find the doubling time (the time it takes for the squirrel population to double), we need to find the time t at which the squirrel population reaches twice the initial population of 450 squirrels. This can be represented by the equation:

2 * 450 = 1800 / (1 + 3e^(-0.8t))

Solving for t, we get:

0.8t = ln(3)

t = ln(3) / 0.8

Hence, the doubling time is approximately 83 years. This means that it will take approximately 83 years for the squirrel population to double from its initial size of 450 squirrels.

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Answer: 3m+4=6m is the false equation

Step-by-step explanation:

Substitute 5 into the 4 equations to find whether they are true or false

3(5)+4=6(5)

15+4=30

19[tex]\neq[/tex]30 False

-5(5-7)=10

-5(-2)=10

10=10 true

17=4(5)-3

17=20-3

17=17 True

5+9=14

14=14 True

3m+4=6m is the false equation

The simplified expression is  c²a³ - 3[tex]a^4[/tex]c +  a²bc² - a³bc  - 3[tex]a^4[/tex]b+ 4ab²c² - 22a²b²c + 36a³b + 12a³b² / (-2bc-6ab- 3a²)(a² + 2ab)(ac - 3a²).

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

c +6b/(-2bc-6ab- 3a²) + 2b/(a² + 2ab) - b/(ac - 3a²)

Now, simplifying

(c+ 6b) (a² + 2ab)(ac - 3a²) + 2b(-2bc-6ab- 3a²)(ac - 3a²)- b (-2bc-6ab- 3a²)(a² + 2ab) / (-2bc-6ab- 3a²)(a² + 2ab)(ac - 3a²)

= ca² + abc + 6a²b + ab² (ac - 3a²) + (4b²c - 12ab² - 6a²b)(ac - 3a²) - ( -2b²c - 6ab² - 3a²b)(a² + 2ab) / (-2bc-6ab- 3a²)(a² + 2ab)(ac - 3a²)

= c²a³ - 3[tex]a^4[/tex]c + a²bc² - 3a³bc + 6a³bc - 18[tex]a^4[/tex]b + 4ab²c² - 12a²b²c - 12 a²b²c+ 36a³b - 6a³bc + 18[tex]a^4[/tex]b + 2a²b²c +  4a³bc + 6a³b² + 12a²b³  - 3[tex]a^4[/tex]b + 6a³b² / (-2bc-6ab- 3a²)(a² + 2ab)(ac - 3a²)

= c²a³ - 3[tex]a^4[/tex]c +  a²bc² - a³bc  - 3[tex]a^4[/tex]b+ 4ab²c² - 22a²b²c + 36a³b + 12a³b² / (-2bc-6ab- 3a²)(a² + 2ab)(ac - 3a²)

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The charge for cutting a board into 8 equal pieces is $1.2

Equate charges for cutting board : Number of equal pieces

0.60 : 4 = x : 8

0.60/4 = x / 8

cross product

0.60 × 8 = 4 × x

4.8 = 4x

divide both sides by 4

x = 4.8 / 4

x = 1.2

Therefore, it will cost $1.2 for cutting a board into 8 equal pieces.

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The exact answer to the definite integral ∫16^1^3/π of x dx using the fundamental theorem is 8/π^2.

The fundamental theorem of calculus states that if f(x) is a continuous function on the interval [a, b] and F(x) is an antiderivative of f(x), then:

∫a^bf(x)dx = F(b) - F(a)

To use the fundamental theorem to evaluate the definite integral ∫16^1^3/π of x dx, we need to find an antiderivative of x. The antiderivative of x is x^2/2 + C, where C is an arbitrary constant.

Therefore, the definite integral ∫16^1^3/π of x dx can be written as:

∫16^1^3/π x dx = (x^2/2 + C) |16^1^3/π

Evaluating this expression gives us:

(3/π)^2/2 + C - (1/π)^2/2 + C = (9/π^2 - 1/π^2)/2 + 2C

Since C is an arbitrary constant, it cancels out when we take the difference between the upper and lower limits of integration. Therefore, the definite integral ∫16^1^3/π of x dx is equal to:

(9/π^2 - 1/π^2)/2 = 8/π^2

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With regards to the function model then the true statement as per first and second derivatives is: (C) dw/dt = 1/100 W  (70 - W),

When, W = 10 then dw/dt = 6

When W = 35 then d²w/d²t = 0

where the point influx occurs, the weight of the carrying capacity is half

Therefore, 35 = a/2

Then the carrying capacity (a) = 35 x 2

a = 70

A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable. Calculus's core tool is the derivative. It is a crucial idea that is incredibly helpful in a variety of contexts: in daily life, the derivative can inform you how fast you are driving or assist you in predicting stock market changes; in machine learning, derivatives are crucial for function optimization.

Therefore, with regards to the function model then the true statement as per first and second derivatives is: (C) dw/dt = 1/100 W  (70 - W), because the carrying capacity is 70 and the rate of change of the weight is 6 grams per hour when the weight is 10 grams.

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Answer:  [tex]5.8\times 10^4[/tex]

Reason:

Place the decimal point between the 5 and the 8. So we have the value 5.8

To get back to 58000, we need to move the decimal point 4 spots to the right. This is why we have 4 as the exponent over 10.

All scientific notation values are of the form [tex]a \times 10^b[/tex]

where [tex]1 \le a < 10[/tex] or [tex]-10 < a \le 1[/tex]

The b value is an integer.

The value of x in the equation, 3/4x + 6 - 1/4x = 2/4x + 9, is: x = -2.

Solving an equation involves finding the value of the variable in the equation. The value, when plugged into the equation would make it true.

The equation given is, 3/4x + 6 - 1/4x = 2/4x + 9, to solve for the value of x, follow the steps below:

3/4x + 6 - 1/4x = 2/4x + 9 [given]

Combine like terms:

3/4x - 2/4x - 1/4x = 9 - 6

(3 - 2 - 1)/4x = 3

-6/4x = 3

Simplify

-3/2x = 3

Multiply both sides by -2/3:

-3/2x × -2/3 = 3 × -2/3

x = -6/3

x = -2

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Answer:

6*3 + 6*2

6*5

6(3+2)

Step-by-step explanation:

All of these equations lead to the same answer which is 30.

The two diagrams are basically the same but they are just separated apart. When you look for the area of both diagrams, it leads to the same answer.

Answer:

Step6x3 = 18. And. 2x6 = 12. Then you add the amounts, 18+12 = 30-by-step explanation:

6 + 12^2

12 squared would be 12 to the second power

since the directions say "the sum"

you would use addition to add 6 and 12^2

Answer:

D

Step-by-step explanation:

6^(4+0) = 6^4

6^(-10) : 6^4

6^(-10-4)

6^(-14)

1/6^(14)

We reject null hypothesis when hypothesis test, draw conclusions at significance level 0.08.

Given that,

Consider an NFL team that says the average weight of its defensive players is 315 pounds. A opposing team believes that their defensive players' average weight is lower than the 315 pounds they state. Consider that they take 15 defensive players as a sample and discover that the average weight of the players is 300 pounds, with an 8-pound sample standard deviation.

We have to create a suitable hypothesis test, draw conclusions at significance level 0.08, and then. Suppose that the weights are evenly distributed.

We know that,

Weights are normally distributed.

We are given μ = 315 , n= 15 , x = 300, s = 8, α = 0.08

The hypothesis are :

H₀ : μ = 315   v/s  H₁ : μ ≠ 315

The test statistic is given by,

z=x-μ/σ/√15

=300-315/8/√15

=-7.26

The critical value = z(α)  = z(0.04) = -1.75 and z(1-α)  = z(1-0.04)  = 1.75

Here calculated value of z > critical value of z

Therefore, we reject null hypothesis when hypothesis test, draw conclusions at significance level 0.08.

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The money left is $5000 - $2000 = $3000 will be earned through an internship.

To subtract in mathematics is to take something away from a group or a number of objects.

In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.

As per the given,

Money earned in award = $2000

Money had at the end of saving account = $5000

Money earned by internship = $5000 - $2000 = $3000

Hence "$3000 of the remaining $5000 will be earned through an internship".

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The table with constant of proportionality between x and y is table A

We should be able to know that constant of proportionality shows a type of relationship between two variables that shows a constant relationship or same ratio.

The given fraction is 8/5

Rewrite 8/5 as a ratio of two numbers

8:5

Constant of proportionality is written as

y=k/x

Making k the subject, k=y/x

Where k is a constant.

From table A,

The constant  (K) is 4/1 = 4:1

Now multiply 4*8=32

8*1=5

Therefore 32/5 is a proportion of 8/5

Also using the constant k=10

⇒10:1   Then 10*8=80

And 1*5=5

⇒ 80/5=16

Also in the last constant K=11, we have 11:1

⇒[tex]\frac{11*8}{1*5}[/tex] =88/5

In conclusion option A gives the table that has constant of proportionality to 8/5

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The dimensions we will tell the shop to use are ⇒ Volume =  10 x 10 x 5 foot

The surface area of the box = [tex]225[/tex] [tex]ft^{2}[/tex]

Weight of the metal = 1125 kg

According to the question,

Given value = [tex]500[/tex] [tex]ft^{3}[/tex] tanks is to be built which has to be a square-based rectangle steel holding tank.

For this, we have to know the total surface area of the box,

Surface area (A) = 4 x sides of the rectangle + square base -- equation 1

Let's take the width of the square base = p

And let height = h

Since we know that,

Rectangle sides = p x h

Square base ⇒ p x p = [tex]p^{2}[/tex]

Substituting these values in equation 1,

Surface area ( A ) = 4 x ( p x h ) + [tex]p^{2}[/tex] ---- equation 2

The formula for calculating the volume of the box,

V = p x p x h

V = [tex]p^{2}[/tex] x h --- equation 3

Referring to the question that the value of the volume is already given such that volume = [tex]500[/tex] [tex]ft^{3}[/tex]

So, V = [tex]500[/tex] [tex]ft^{3}[/tex]

Putting the value of V in equation 3,

500 = [tex]p^{2}[/tex] x h

h = [tex]\frac{500}{p^{2} }[/tex] ---- equation 4

Substituting the value of h from equation 4 to equation 2,

A = 4 x ( p x [tex]\frac{500}{p^{2} }[/tex] ) + [tex]p^{2}[/tex]

⇒ A = [tex]\frac{2000}{P}[/tex] + [tex]p^{2}[/tex]

We will be taking the derivative of the above equation,

⇒ A' = - [tex]\frac{2000}{p^{2} }[/tex] + 2p

Now we will be minimizing A,

⇒ 0 = - [tex]\frac{2000}{p^{2} }[/tex] + 2[tex]p[/tex]

⇒ [tex]\frac{2000}{p^{2} }[/tex] = 2[tex]p[/tex]

⇒ 2000 = 2[tex]p^{3}[/tex]

⇒ 1000 = [tex]p^{3}[/tex]

⇒ p = [tex]\sqrt[3]{1000}[/tex]

⇒ p = 10 foot

Substituting the value of p in equation 4,

⇒ h = [tex]\frac{500}{10^{2} }[/tex]

⇒ h = [tex]\frac{500}{100}[/tex]

⇒ h = 5 foot

Substituting values in the area of the square box,

A = 4 x (10 x 5) + [tex]5^{2}[/tex]

A = 200 + 25

A = 225 [tex]ft^{2}[/tex]

The weight of the metal,

⇒ weight = A x weight per square foot

⇒ weight = 225 x 5

⇒ weight = 1125 kg

Therefore, The dimensions we will tell the shop to use are ⇒ Volume =  10 x 10 x 5 feet

The surface area of the box = 225 [tex]ft^{2}[/tex]

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The quadrilateral abcd is a parallelogram because the slopes of opposite sides are equal.

In the given figure we have a quadrilateral  ABCD with A (-2,-2) , B(-3,4), C(2,2)

and D(3,-4).

We know that when the slope of two lines are equal then they are parallel.

In the given figure, Slope of BC= Slope of AD =

⇒ BC and AD are parallel .

Also, Slope of CD= Slope of BA =-6

⇒ CD and BA are parallel .

ABCD is a parallelogram because both pairs of opposite sides are parallel.

Hence, the correct reason for the given space is "slopes of opposite sides are equal"

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Answer:

Step-by-step explanation:

what is your question?

The answer is false. The covariance statistic gauges how closely two variables are related to one another.

a connection between two quantitative variables in which the corresponding values of the second variable tend to rise when the value of the first variable tends to rise (or fall) (or decrease).

The direction of the link between two variables is measured by covariance. A positive covariance indicates that both variables frequently exhibit high or low values together. While two variables have a negative covariance, they are often low when one is high.

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Answer:

y = -4/3x + 10

Step-by-step explanation:

A line with a slope of -4 over 3 that passes through the point (6,2) can be written in slope-intercept form as:

y = (-4/3)x + b

To find the value of b, we can plug in the coordinates of the given point (6,2) into the equation and solve for b:

2 = (-4/3)(6) + b

2 = -8 + b

b = 10

Therefore, the equation of the line in slope-intercept form is:

y = (-4/3)x + 10

Answer:

Step-by-step explanation:

If a sample mean is 32, the range of possible values that best describes an estimate for the population mean is most likely (30, 38).

The sample mean is a statistic that is used to estimate the population mean. In general, the sample mean is a good estimate of the population mean, but it is not always perfectly accurate. There is always some degree of uncertainty or variability associated with any estimate, and this is especially true when the sample size is small.

One way to quantify this uncertainty is to use a confidence interval, which is a range of values that is likely to contain the population mean with a certain level of confidence. For example, a 95% confidence interval is a range of values that is likely to contain the population mean with 95% confidence.

In this case, if a sample mean is 32, a 95% confidence interval for the population mean would likely be a range of values centered around 32 and extending approximately 2 standard errors in either direction. For a sample mean of 32, a range of values extending 2 standard errors in either direction would be approximately (30, 38). Therefore, the range of possible values that best describes an estimate for the population mean is most likely (30, 38).

If a sample mean is 32, (30, 38) is most likely the range of possible values that best describes an estimate for the population mean. the correct option is option D.

Range serves as a statistical measure of dispersion in mathematics, or how widely spaced a particular data collection is from smallest to biggest. The range in a piece of data is the distinction between the highest and lowest number. The confidence interval of 95% for the population mean in this scenario, assuming the sample mean is 32, is likely to include a range of values centred around 32.

Extending around 2 standard errors in each direction. A range of results spanning two standard deviations in either way would result in around (30, 38) for a sample mean of 32. Thus, the range of potential values that most accurately captures an estimate of the population mean is (30, 38).

Therefore, the correct option is option D.

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For the study about cholestrol levels of people was taken by medical researcher.

a) Null and Alternative hypothesis for study is

H₀ : μd ≥0

Hₐ : μd <0

where μd --> average

b) The value of t-statistic is 3.78118

c) The critical value for t-test is - 2.015.

d) We fail to reject null hypothesis, H₀

e) There is sufficient evidence to support the claim of researcher that cholesterol level decreases on average.

The above table represents the patients and their cholesterol levels before and after they showed the film about the effect of high cholesterol levels. The "d" column shows the difference in their cholesterol levels.

Singnificance level, α =0.05

∑d = 122, n = 6 , ∑d² = 3348

Xd -bar = 122/6 = 20.33

Standard deviations, σ = √(∑d² - ∑d/n)/(n-1)

σ = √(3348 - 20.33)/5 = 13.170

a) The Null and Alternative hypothesis are

H₀ : μd ≥0

Hₐ : μd <0

b) test- statistic,

t - value = (Xd-bar - μd)/σ /√n

=> t = (20.33 - 0)/13.17/√6

=> t = 20.33/5.37662

=> t = 3.78118

c) degree of freedom, df = n-1 = 5

The critical t-value for a given confidence level c and sample size n is obtained by computing the quantity tα/2 for t-distribution with (n-1) degrees of freedom.

α = 0.05 , α/2 = 0.25 , df = 5

t(₀.₂₅, ₅) = - 2.015

d) Decision: As we seen t-value= 3.781 and t-critical value = - 2.015

so, t -value > critical value. Therefore, we fail to reject null hypothesis.

e) Conclusion: There is sufficient evidence to claim that the cholesterol level decrease on average.

Hence, we got all required answers.

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Complete question:

Cholesterol Levels A medical researcher wishes to see if he can lower the cholesterol levels through diet in 6 people by showing a film about the effects of high cholesterol levels. The data are shown. At =α0.05 , did the cholesterol level decrease on average? Use the P -value method and tables. Patient 1 2 3 4 5 6 Before 250 219 218 224 209 223 After 216 203 192 190 207 213 State the hypotheses and identify the claim with the correct hypothesis. H0 : ▼(Choose one) H1 : ▼(Choose one) This hypothesis test is a ▼(Choose one) test. Compute the test value. Always round t score values to three decimal places. t= Find the interval for the P -value. The correct interval is Make the decision. ▼(Choose one) the null hypothesis. Summarize the results. There is ▼(Choose one) that the mean heights are different

Although part of your question is missing, you might be referring to this full question: Write an expression that describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. –1, 0, 1, 2, ...

The expression that describes the given sequence is: aₙ = –2 + n

This is an arithmetic sequence. Arithmetic sequence is a sequence of numbers in which every term (except the first term) is provided by adding a constant number to the previous term.

An arithmetic sequence can be defined by an explicit formula in which aₙ = d (n – 1) + c, where d is the common difference between consecutive terms, and c = a₁.

In this case, the given sequence is –1, 0, 1, 2, ...

This is an arithmetic sequence with common difference.

Because of:

0 – (–1) = 1

1 – 0 = 1

2 – 1 = 1 …

Then, a₁ = –1

Now, substitute the value of a₁ = –1, d = 1 into the formula.

aₙ = d (n – 1) + c

aₙ = 1 (n – 1) + (–1)

aₙ = n + (–2)

aₙ = –2 + n

Hence, the expression that describes the given sequence is: aₙ = –2 + n.

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The ordered pair for the vertices for r(90°, s)(QRST) include the following:

Q' = (-5, 1)

R' = (-3, -1)

S' = (0, 0)

T' = (-3, -2)

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

Note: The point S represents the center (origin) of this geometric figure.

By applying a rotation of 90° counterclockwise to the vertices for r, the coordinates of the vertices of the image point r' are as follows:

(x, y)                               →            (-y, x)

Ordered pair Q  = (1, 5) → Ordered pair Q' = (-5, 1)

Ordered pair R = (-1, 3) → Ordered pair R' = (-3, -1)

Ordered pair S = (0, 0) → Ordered pair S' = (0, 0)

Ordered pair T = (-2, 3) → Ordered pair T' = (-3, -2)

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According to the statement above, The Hamden board of education called every tenth person on the registration list. The sample is not randomly chosen (FALSE)

Given that the statement doesn't tell us anything about the way they choose the sample, it is reasonable to conclude that this is a randomly chosen. They called every tenth person on the registration list until the number of people was 40.

The sample should be larger to give more reliable information (TRUE)

We did not have to use mathematics to determine that you would need more information to get a conclusion. You must increase the sample, that is, the sample must be larger to give a reliable information.

The sample size is too large to make inferences (False)

This is explained in the previous item. If the sample should be lager is because the size is not too large.

The sample size is too small to represent the population (TRUE

This is true because 40 voters represent barely 0.5% of the entire list. This list has 7300 voters, so getting the conclusion from this sample doesn't provide with a strong conclusion.

The sample size is too small and will show larger variation. (FALSE)

Although the sample size is too small, the sample size not necessarily will show variation. In fact, it is possible that it does not show any variation and most of the people feel well about building a new media center for the middle school but it doesn't mean that the whole community does.

The sample is invalid because it randomly chooses voters. (FALSE)

It is false because in probability studies the sample is chosen randomly, so you get conclusions about the whole population always taking samples that represent the population as a whole.

The sample size is too small and can lead to false inferences (TRUE)

We can get false conclusions given that the sample size is too small. It's important to note that the sample size supports the conclusion of the study, so the sample must increase to have a reliable study.

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The probability is 0.7888.

Standard error of the mean [tex]$\sigma_{\bar{x}}=20$[/tex]

The population standard deviation (σ)=500

Standard deviation of [tex]$\bar{x}$[/tex] is given by:

[tex]\sigma_{\bar{x}} & =\frac{\sigma}{\sqrt{n}} \\\\\Rightarrow 20 & =\frac{500}{\sqrt{\mathrm{n}}} \\\\\Rightarrow n & =\left(\frac{500}{20}\right)^2 \\[/tex]=625

Probability that the point estimate [tex]$\bar{x}$[/tex] was within ±25 of the population mean is: [tex]$$p(\mu-25 < \bar{x} < \mu+25)$$[/tex]

At [tex]$\bar{x}[/tex]=μ-25, we have

[tex]z & =\frac{-25}{20} \\[/tex]=-1.25

Z=-1.25

At [tex]$\bar{x}[/tex]=μ+25, we have

[tex]z & =\frac{25}{20} \\[/tex]=1.25

Z=1.25

So the required probability is:

[tex]$$\begin{aligned}p(\mu-25 < \bar{x} < \mu+25) & =p(-1.25 < z < 1.25) \\& =p(z < 1.25)-p(z < -1.25) \\\end{aligned}$$[/tex]

                                     =0.8944-0.1056

                                     =0.7888

Therefore, probability that point estimate is within ±25 population mean is 0.7888.

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A researcher reports survey results by stating that the standard error of the mean is 20 . The population standard deviation is 500 . How large was the sample used in this survey

a. What is the probability that the point estimate was within ±25 of the population mean?

The value of b must be equal to -14, so that the function has at least one inflection point. Hence, option B is correct.

Expressions are mathematical operations that involve at least two terms connected by an operator and can be either integers, variables, or both. The operations with reflection coefficients are addition, subtraction, multiplication, and division. 

As per the instruction given in the question,

The given function,

f(x) = x⁴ + bx² + 1

Differentiate with respect to x,

f'(x) = 4x³ + 2xb

Again differentiate with respect to x,

f''(x) = 12x² + 2b

For inflection point, f''(x) = 0

12x² + 2b = 0

2b = -12x²

b = -6x²

x = √-b/6, x ∈ [1, 2]

Let's assume that b = -28

x = √-(-28)/6

x = √28/6

x = √14/3, here x ∉ [1, 2], hence it is incorrect.

If b = -14

x = √-(-14)/6

x = √14/6

x = √7/3 ≈ 1.82, here x ∈ [1, 2], hence it is correct.

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Answer:

Answer:

Below

Step-by-step explanation:

Domain is the set of values x can be for a function .....it looks like this one goes from -2 to 2 with asymptopes at these values:

-2< x < 2  

Range is the 'y' values a graph can have...this one goes from -1.5 -ish to 5.5 ish    

-1.5 <= y <= 5.5

Here is the graph with some lines on it:

To compare the sampling distribution, first I would simulate the machine by randomly generating n number of samples between 8 and 10 oz with a uniform distribution and calculate the 4th spread for each sample size. I would then repeat this experiment multiple times and take the average of the fourth spread values for each sample size to compare the sampling distributions.

To compare the sampling distributions of the fourth spread for sample sizes n = 5, 10, 20, and 30, I would simulate the machine by randomly generating samples between 8 and 10 oz with a uniform distribution. For each sample size, I would calculate the fourth spread for each sample and then repeat the experiment multiple times. Finally, I would take the average of the fourth spread values for each sample size to compare the sampling distributions. This way, I would be able to see how the fourth spread changes as the sample size changes. It would also allow me to see how the fourth spread is affected by the uniform distribution of the machine's output.

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The product of a,b and c from the fraction is 6/125

The product is the result of the multiplication of the numbers

From the given exponential fractions, we have

=(3x³y²/³)÷(125³*¹/³y³*¹/³

Simplifying the expression to have

(3x³y²/³)(125)(1)

⇒3/125x³y²/³

The expressed form is [tex]ax^{b} y^{c}[/tex]

a=3/125 b=3 c 2/3

Simplify further to have

⇒3/125*3/1*2/3

Simplify further to get your final answer as

=6/125

Therefore, the product of the fractional exponents is 6/125

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