The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
2, 6, 10,..
Find the 41st term.

Answer:

Step-by-step explanation:

Since there are 360 degrees in a circle the area of the shaded region = 80/360 * area of the circle.

This = 80/360 * 81 π

= 2/9 * 81 π

= 18 π

Answer:

Area = 18π  cm²

Step-by-step explanation:

The shaded region is a sector of a circle with radius 9 cm.

[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}[/tex]

From inspection of the give diagram:

Substitute the values into the formula for area of a sector:

[tex]\implies A=\left(\dfrac{80^{\circ}}{360^{\circ}}\right) \pi \cdot 9^2[/tex]

[tex]\implies A=\dfrac{2}{9} \pi \cdot 81[/tex]

[tex]\implies A=\dfrac{162}{9} \pi[/tex]

[tex]\implies A=18 \pi\;\; \f cm^2[/tex]

Therefore, the area of the shaded region is 18π cm².

the correlation coefficient of X and Y is Cov ( X, Y ) = 1/2

X = Number of heads in the first 20 flips

Y = Number of heads in the last 20 flips

Given that X and Y are binomial variables hence

P( probability ) = 1/2

Find Cov( X; Y )

xi = result of the ith flip ∴ X = x1 + x2 + x3 + x4+....x20

yj = result of the  jth flip ∴ Y = y3 + y4 + y5 + y6+ ....x20

covariance of  xi and yi = 1/2 * 1/2 = 1/4   when i = j  and it is = 0 when i ≠ j

hence Cov( X; Y ) can be expressed as

Cov( X; Y ) = ∑^4 ∑^6 ∴ Cov( Xi , Yj ) = 2/4 = 1/2  (  given that i = j )  

Hence he correlation coefficient of X and Y is Cov ( X, Y ) = 1/2

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The margin of error round to the nearest tenth will be 1.8.

The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.

The margin of error is given as

[tex]\rm ME = z\times \sqrt{\dfrac{\sigma ^2}{n}}[/tex]

The z-value for the 99% confidence will be 2.576. Then the margin of error is calculated as,

ME = 2.576 × √[(6.3)² / 82]

ME = 2.576 × √0.4840

ME = 2.576 × 0.6957

ME = 1.8

The margin of error round to the nearest tenth will be 1.8.

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Using the expression 5t + 16, the height of the tree after 7 years it was planted is: 51 inches.

To evaluate implies that we find the value of the expression by plugging in the value of the variable and simplify accordingly.

Given that t represents the number of years after a tree is planted, and the expression, 5t + 16 represents the approximate height of the tree, to find its height after 7 years, substitute t for 7 into the expression and evaluate:

5(7) + 16

35 + 16

= 51

Thus, the height of the tree after 7 years it was planted is: 51 inches.

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The slope of the line passing through the point (-6, 0) and (0, 3) is 0.5

An equation is an expression showing the relationship between numbers and variables.

The slope intercept form of a straight line is:

y = mx + b

Where m is the slope and b is the y intercept.

The standard form of a straight line is:

Ax + By = C

Where A, B and C are constants

The line shown in the graph passes through the point (-6, 0) and (0, 3). Hence:

Slope = (3 - 0)/(0 - (-6)) = 3/6 = 0.5

The slope is 0.5

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Answer:

center: [tex](6, -3)[/tex]

distance from center:

connect: [tex](16, -3), (6, -9), (-4, -3), (6, 3)[/tex]

Step-by-step explanation:

An ellipse has two forms, although they're essentially the same:

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

and

[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex]

Where a > b, and if the "a^2" is under the [tex](x-h)^2[/tex] then that means the ellipse has a horizontal major axis, but in general the value below this numerator relates to the length of the horizontal axis. Now if "a^2" is under the [tex](y-k)^2[/tex] then that means the ellipse has a vertical major axis, but in general the value below this numerator relates to the length of the vertical axis.

The length of the major axis is defined as 2a and the minor axis as 2b, but the distance from the center to the end points will be half of this, so either "a" or "b" depending on which axis the end point is on.

The other thing to note is that (h, k) is the center of the ellipse.

We're given the equation: [tex]\frac{(x-6)^2}{36}+\frac{(y+3)^2}{100}=1[/tex], in this case the bigger value is under the (y+3)^2, so we know that we will have a horizontal major axis. Since the denominator's represent the square of "a" and "b" we first have to take the square root of them. So the following is true:

[tex]a=\sqrt{100}=10\\b=\sqrt{36}=6[/tex]

The "a" gives us the distance from the center to the end point on the major axis while the "b" gives us the distance from the center to the end point on the minor axis, so the distance from the center to the end point on the minor axis is 6 and for the major axis it's 10.

We also know the center is at (6, -3) by looking at the signs and what is being added/subtracted from the x and y values in the equation. We can use this to calculate the end points since the end points on the horizontal major axis can be calculated as: [tex](6\pm10, -3)[/tex] and the end points on the vertical major axis can be calculated as: [tex](6, -3\pm 6)[/tex], which gives us four points: [tex](16, -3), (6, -9), (-4, -3), (6, 3)[/tex] which we can connect to draw a graph.

Answer:

[tex]\textsf{The center of the ellipse is $\boxed{(6,-3)}$}\;.[/tex]

[tex]\textsf{The endpoints of the major axis are $\boxed{10}$ units from the center}\;.[/tex]

[tex]\textsf{The endpoints of the minor axis are $\boxed{6}$ units from the center}\;.[/tex]

[tex]\textsf{To graph the ellipse, connect $\boxed{(12,-3),(6,-13),(0,-3), \;\textsf{and}\; (6,7)}$ with a smooth curve}\;.[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.2 cm}\underline{General equation of an ellipse}\\\\$\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$\\\\where:\\\phantom{ww}$\bullet$ $(h,k)$ is the center\\ \phantom{ww}$\bullet$ $a$ and $b$ are the radii.\\ \phantom{ww}$\bullet$ $(h\pm a,k)$ and $(h,k\pm b)$ are the vertices.\\ \end{minipage}}[/tex]

Given equation:

[tex]\dfrac{(x-6)^2}{36}+\dfrac{(y+3)^2}{100}=1[/tex]

As b > a, the given ellipse is vertical.

The major axis is the longest diameter and the minor axis is the shortest diameter, therefore:

Determine the values of h and k:

[tex](x-h)=(x-6) \implies h=6[/tex]

[tex](y-k)=(y+3) \implies k=-3[/tex]

Therefore, the center of the ellipse is:

Calculate the values of a and b:

[tex]a^2=36 \implies a=6[/tex]

[tex]b^2=100 \implies b=10[/tex]

As the major axis is 2b, then the major radius is b.

Therefore, the endpoints of the major axis are "b" units from the center, so they are 10 units from the center.

As the minor axis is 2a, then the minor radius is a.

Therefore, the endpoints of the minor axis are "a" units from the center, so they are 6 units from the center.

To graph the ellipse, connect the vertices and co-vertices with a smooth curve.

The sequence from least to greatest is d) √65 < |-7.82| < 7.2/3.

To calculate this, we first need to find the square root of 65, or √65. This can be done using the formula √a = b, where a is the number to be square rooted and b is the result of the square root. In this case, a = 65, so we calculate √65 = 8.062257748. Next, we need to find the absolute value of -7.82, which is |-7.82| = 7.82. . To calculate this, the absolute value formula is used, which is |x| = |x|. Finally, 7.2/3 is the greatest of the three numbers. To calculate this, first convert 7.2/3 to a decimal by dividing it by 3. Then divide 7.2 by the result to get the final answer.Finally, we find 7.2/3, which is equal to 2.4. Therefore, the sequence from least to greatest is √65 < |-7.82| < 7.2/3, or 8.062257748 < 7.82 < 2.4.

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The item would be the rental value of the home owned by the taxpayer. The correct option is D.

A taxpayer is a person or organization that is required to pay taxes. Modern taxpayers may have an identification number, which is a reference number issued by the government to individuals or businesses. The term "taxpayer" generally refers to someone who pays taxes.

A recurring payment made by a tenant to a landlord in exchange for the use of land, a building, an apartment, an office, or other property. a payment made by a lessee to an owner in exchange for the use of machinery, equipment, etc.

A taxpayer who wishes to file as head of household paid more than half the cost of keeping up their home will be the rental value of the home owned by the taxpayer.

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Histogram representing point estimator w labelled fourth bar as a population parameter is a true statement.

As given in the question,

The given graph represents the sampling distributions of two different point estimators,

Two point estimators are r and w represents same population parameters.

Two histogram each one with 7 bars:

Left histogram represents point estimator r and right histogram represents point estimator w.

Increase of the heights of the bars in both r and w histogram left to right.

Peak point is at fourth bar.

In point estimator r histogram : Third bar represents population parameter.

In point estimator w histogram : Fourth bar represents population parameter.

Here fourth bar represents the peak point.

Therefore, point estimator w histogram represents the population parameter is a true statement.

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The percentage of 12th graders preferring chicken wings is 30%.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

From the given information total number of 12th graders are,

(39 + 24 + 27)

= 90.

The number of 12th graders preferring chicken wings is 27.

Therefore, The percentage  bar for 12th graders shows for preferring chicken wings is,

= (27/90)×100%.

= 30%.

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The true statement about the sampling distributions is: Both will be approximately normal, and the mean for size 50 will be closer to 26.8 than the mean for size 4.

Thus, option (C) is correct.

According to the Central Limit Theorem, for a large enough sample size, the sampling distribution of the sample mean tends to follow a normal distribution, regardless of the shape of the population distribution.

Therefore, both sampling distributions of size 4 and size 50 will be normal.

Moreover, the mean of the sampling distribution of the sample mean will be equal to the population mean.

Since the population mean is given as 26.8 years, the mean for both size 4 and size 50 will be 26.8 years.

Thus, option (C) is correct.

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Answer:

-1/2

Step-by-step explanation:

use slope formula

it'd be:

\frac{5-7}{-1+5} =\frac{-2}{4} =\frac{x}{y} -1/2\\

An ordered array is an arrangement of numbers in a specific order, usually in increasing or decreasing order. 43, 73, 107, 158, 226, 305, 312

To rewrite the numbers in an ordered array: you need to arrange the numbers in either ascending or descending order. For example, the ordered array of the numbers in ascending order: 43 73 107 158 226 305 312

Note that it's important to read the instruction carefully when you have to order the numbers without using the factorial key on your calculator.

The factorial key on a calculator is typically represented by the symbol "!", and it is used to calculate the factorial of a number. The factorial of a number is the product of all the positive integers less than or equal to that number.

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The differential equation that represents the relationship is

     dT/dt = - k * ( T - T0 ) from the condtion - dT/dt ∝ ( T - T0 ).

Given:

The engine fluid temperature rate of change, dT/dt

- dT/dt ∝ ( T - T0 )   [proportional to the difference of the fluid's instantaneous temperature, T, and the fluid's original temperature, T0.]

The Differential Equation that represents the relationship.

The framework is already set, there is only one thing that changes the proportionality to an equation. And that is a proportionality constant.

Let's call it 'k'

Since this is a directly proportional set up, the constant 'k' will be multiplied to the term of ( T - T0 )

                            - dT/dt = k * ( T - T0 )

And to make this look like a typical equation, multiply both sides by a -1 to get:

                           ∴ dT/dt = - k * ( T - T0 )

As expected, this comes to represent the same thermodynamic effect you'd see in Newton's Law of Cooling; it is expected because most of all fluids exhibit this cooling effect when interacting with other fluids of differing temperatures.

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If ∠A and ∠B are acute angles such that cos A = cos B we have proved that ∠A = ∠B since AC = BC and angles opposite to equal sides of a triangle are equal.

Image outcome

An acute angle has a degree that is less than 90 degrees, i.e. less than a right angle. Acute angle degrees include 12°, 35°, 48°, 65°, 80°, and 89°. An acute angle triangle (also known as an acute-angled triangle) is a triangle with all of its internal angles being acute angles. Remember that an acute angle is one that is less than 90°. Because all three angles are less than 90°, ABC is an acute angle triangle or acute-angled triangle.

The sine function for the angle yields the ratio of the length of the opposing side to the length of the hypotenuse.

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Answer: 1. 8, 2. 1680

Step-by-step explanation:

1. area is length times width, so 6 times 7 is 30. To find the missing one just do 40 divided by 5, which equals 8.

2. to find the total area do length x width x length x width. so 5 x 6 x 7 x 8 which equals 1680.

No, you do not have to ratio test to find the radius of convergence if geometric test does into work,

when representing a function as a power series, it is not necessary to ratio test to find the radius of convergence if geometric test does into work. A geometric test does not always converge to the right value if it is used to find the radius of convergence of a function at a given point.

The radius of convergence is the distance between two points within a specified radius. If the geometry test fails, the convergence radius may not be found. To find the radius of convergence, use another test like a Venn diagram to see if there is a compatibility pattern.

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The value of x is 6, which can be calculated using triangle proportionality theorem.

From the figure, we have both triangles' corresponding sides proportionate to one another.

so, PR/ PR' = RQ/ RQ'

so, x/10 = 9/15

x = 6

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Answer: y is equal to 5

Solve for y :

x=0

y=2(0)+5

y=0+5

y=5

Hope this helped =)

-YinAhara

Answer: 3 players

Step-by-step explanation: Hello! You know that there are 31 players on the softball team, there are 8 cars in total for everyone to drive in, and there are 4 players in each car for the first 7 cars.  What you have to find out is how many players are traveling in the eighth car.  The first thing that you want to know is how many players are already in the cars.  You already know that 4 players are in each of the 7 cars.  To know how many players are in the 7 cars, multiply the 4 players by the 7 cars.  4 x 7 = 28.  28 players are in the first 7 cars.  You know that there are 31 players in total.  To find the number of players in the last car, subtract the number of players in the first 7 cars from the total amount of players.  31 - 28 = 3.  There are 3 players on the softball team in the eighth car.  Hope this helps!

The probability that a randomly selected box of the cereal contains less than 9.65 ounces of cereal is 0.4608.

The probability that a randomly selected box of the cereal contains less than 9.65 ounces of cereal is 0.4608.

P(x < 9.65) = P(Z < (9.65 - 9.70) / 0.03)

= P(Z < -0.17)

= 0.4608

The first step is to calculate the Z-score for 9.65 ounces. To calculate the Z-score, you subtract the mean (9.70 ounces) from the value (9.65 ounces) and then divide by the standard deviation (0.03 ounces). The Z-score in this case is -0.17. The next step is to use a Z-table to find the probability of a Z-score less than -0.17. The probability is 0.4608. Therefore, the probability that a randomly selected box of the cereal contains less than 9.65 ounces of cereal is 0.4608.

The probability that a randomly selected box of the cereal contains less than 9.65 ounces of cereal is 0.4608.

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Answer:

m = -1

Step-by-step explanation:

Slope = rise/run = [tex]\frac{-5-1}{7-1} = \frac{-6}{6} = -1[/tex]

Answer: the ratio is 1/2

Answer: 10,000 guests per hour

The dependent variable is the factor that is affected by the changes in the independent variable and is measured to observe the effects.

The dependent variable is the factor that is affected by the changes in the independent variable and is measured to observe the effects. This is the variable that is expected to change in response to changes in the independent variable. The dependent variable is the factor that is affected by the changes in the independent variable and it is measured to observe the effects of the changes in the independent variable. For example, in an experiment about plant growth, the dependent variable would be the height of the plant and the independent variable would be the amount of water added to the soil. By changing the amount of water, the height of the plant can be observed and measured to determine the effect of the water on the growth of the plant.

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Answer:

8142

Step-by-step explanation:

Answer: 354x23=8142

because if you brake 300+50+4 and multiply 300x23, 50x23, and 4x23, then you get 8142

The inequality that shows the amount Malek needs to reduce his monthly debt payments by to have a debt-to-income ratio of 35% is x ≤ $984.50.

Debt to income ratio is usually calculated as a percentage of the gross monthly debt payments divided by the gross monthly income.

Given that Malek has a biweekly gross income of $3115.00.

Monthly gross income of Malek = 2 × $3115.00 = $6230

Monthly debt payments is minimum of $3165.00

We need the debt to income ratio as 35%.

Let x be the monthly debt payment to get the ratio 35%.

x / 6230 = 0.35

x = 2180.5

$3165.00 - $2180.5 = 984.5

So the inequality is x ≤ $984.50

Hence the inequality showing the amount to be reduced to get the debt top income ratio as 35 % is x ≤ $984.50.

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Answer:

[tex]\frac{171}{20}[/tex] is equal to 8.55

Step-by-step explanation:

[tex]\frac{171}{20}[/tex] in decimal form is 8.55

[tex]\frac{17}{2}[/tex] in decimal form is 8.5

[tex]\frac{55}{8}[/tex] in decimal form is 6.875

[tex]\huge\text{Hey there!}[/tex]

[tex]\textbf{Let us say:}[/tex]

[tex]\mathsf{8.55 \rightarrow \dfrac{8.55}{1}}[/tex]

[tex]\textbf{This method should make this question easier to solve (in some cases}\\\textbf{of course)}[/tex]

[tex]\mathsf{8.55 \rightarrow \dfrac{8.55}{1}}[/tex]

[tex]\mathsf{= \dfrac{8.55}{1}\times\dfrac{100}{100}}[/tex]

[tex]\mathsf{= \dfrac{8.55\times100}{1\times100}}[/tex]

[tex]\mathsf{= \dfrac{855}{100}}[/tex]

[tex]\mathsf{= \dfrac{855\div5}{100\div5}}[/tex]

[tex]\mathsf{= \dfrac{151}{21}\rightarrow 8 \dfrac{11}{20}}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{Option\ A. \ \dfrac{171}{20}}}\huge\checkmark[/tex][tex]\textsf{What you have chosen as the answer to this question is correct}\ \heartsuit[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

11 pounds

Step-by-step explanation:

16 lbs - 5 lbs = 11 pounds

The PMF of the number of letters needed to draw to have seen both A and B is pmf(L=k) = $\frac{1}{26 \choose k-1}$ for k = 2, 3, ..., 26. Given that we have already drawn k many cards and neither A nor B have yet appeared, the probability that these two letters will be drawn consecutively is $\frac{2}{26-k}$.

(a) pmf(L=k) = $\frac{1}{26 \choose k-1}$ for k = 2, 3, ..., 26

(b) P(AB or BA | k cards already drawn) = $\frac{2}{26 - k}$

(a) Since the deck is shuffled randomly, we can assume that each of the 26 letters has an equal probability of being drawn. The probability of drawing A and B before any other letter is $\frac{1}{26 \choose k-1}$.

(b) The probability of drawing AB or BA is $\frac{2}{26-k}$, since there are two possible combinations and we have (26-k) cards left to draw.

The PMF of the number of letters needed to draw to have seen both A and B is pmf(L=k) = $\frac{1}{26 \choose k-1}$ for k = 2, 3, ..., 26. Given that we have already drawn k many cards and neither A nor B have yet appeared, the probability that these two letters will be drawn consecutively is $\frac{2}{26-k}$.

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