Identify the sequence graphed below and the average rate of change from n = 1 to n = 3. (5 points)

coordinate plane showing the point 1, 8, point 2, 4, point 4, 1, and point 5, .5
an = 8(one half)n − 1; average rate of change is −3
an = 10(one half)n − 1; average rate of change is 3
an = 8(one half)n − 1; average rate of change is 3
an = 10(one half)n − 1; average rate of change is −3

The standard deviation is the positive square root of the sample variance.

Standard deviation is a measure of the spread or dispersion of a set of data from its mean (average) value. It tells us how much the individual values in a dataset deviate from the average value. In other words, it indicates the extent to which the data points are spread out or clustered around the mean.

The formula for standard deviation is the square root of the variance, which is calculated by finding the average of the squared differences between each data point and the mean. The standard deviation is expressed in the same units as the original data and is denoted by the symbol "σ" for the population standard deviation or "s" for the sample standard deviation.

A small standard deviation indicates that the data points are clustered around the mean, while a large standard deviation indicates that the data points are spread out over a wider range. The standard deviation can be used to determine the range of values within which the majority of the data points lie. For example, if the standard deviation is 2, then about 68% of the data points will be within 2 standard deviations of the mean.

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The surface areas of the given cylinders are 94.5 in²,150.72 in², 100.48 in², 200.96 in² and 314 in²

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.

Given are cylinders, we need to find the surface area of them,

The surface area of a cylinder  = 2πr(h+r), where r and h are radius and height of the cylinder,

1) Height = 2 in and radius = 3 in

Surface area = 2·3.14·3·(3+2) = 94.5 in²

2) Height = 5 in and radius = 3 in

Surface area = 2·3.14·3(5+3) = 150.72 in²

3) Height = 6 in and radius = 2 in

Surface area = 2·3.14·2(6+2) = 100.48 in²

4) Height = 4 in and radius = 4 in

Surface area = 2·3.14·4(4+4) = 200.96 in²

5) Height = 4 in and radius = 4 in

Surface area = 2·3.14·5(5+5) = 314 in²

Hence, the surface areas of the given cylinders are 94.5 in²,150.72 in², 100.48 in², 200.96 in² and 314 in²

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The radius of circle is 41.5.

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The total cost of the ticket is 125.35 dollars.

A ticket to an all day concert is priced at $115, plus an additional 9% sales tax.

The statements that describes how to find the total cost of the ticket can be represented as follows:

sale tax = 9% of 115

sale tax = 9  / 100 × 115

sale tax = 1035 / 100

sale tax = 10.35 dollars

Therefore,

total cost = 10.35 + 115

total cost = 125.35 dollars

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Answer:

∠ 2 = 40°

Step-by-step explanation:

complementary angles sum to 90° , that is

∠ 1 + ∠ 2 = 90°

50° + ∠ 2 = 90° ( subtract 50° from both sides )

∠ 2 = 40°

The numerical value of y in the function y = 8 - 2x when x equals 8 is -8.

A function is simply a relationship that maps one input to one output.

Given the function in the question;

y = 8 - 2x

To determine the value of y, replace all occurrences of x in the function with 8 and simplify.

y = 8 - 2x

Plug in x = 8

y = 8 - 2( 8 )

y = 8 - 16

y = -8

Therefore, the value of y is -8.

Option B) -8 is the correct answer.

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Answer:

Step-by-step explanation:

we can determine the maximum height using the expression given after finding the value of time at which the object reaches the maximum height. In order to find the time at which the object reaches the maximum height we need to use one of the UAM formulas.

and the compatible UAM formula is: vf=vi+at, we use UAM formula because the object is uniformly accelerating due to gravitational force.

vf=vi+at, at the point where the object reaches the maximum height its velocity will be zero so vf=0 and vi=29.4m/s.

given

a=-9.8m/s^2

vf=0

vi=29.4m/s

t=?

0=29.4-(9.8)t

-29.4= -9.8t

t= 29.4/9.8

t=3 seconds, it takes 3 seconds to reach the maximum height starting from a height of 30m.

h=30+29.4(3)-4.9(3)^2

h=30+88.2-44.1

h=118.2-44.1

h=74.1 m

Answer:

Part A
x + y = 150

Part B
7x + 5y = 850

Part C
Solution is x = 50, y = 100

there are 50 adult tickets and 100 student tickets sold

Step-by-step explanation:

Let x = number of adult tickets and y= number of student tickets

We have the following equation

x + y = 150        (1)   =>total number of tickets

7x + 5y = 850   (2)  > total cost of x adult and y student tickets

Multiply (1) x 5:

5x + 5y = 750    (3)

Subtract (2) - (3)

7x + 5y - (5x + 5y) = 850 - 750

7x - 5x + 5y - 5y = 100
2x = 100

x = 50

y = 150 - 50 = 100

The constant c that satisfies the condition of probability mass function of the random variable are 1/55, 1/30, 1/56

(a) For f(x) to be a probability mass function, it must satisfy the following conditions:

1. f(x) ≥ 0 for all x

2. Σf(x) = 1, where the sum is taken over all possible values of X

Here, x can take values 1, 2, 3, 4

So, Σf(x) = f(1) + f(2) + f(3) + f(4) = c + 4c + 9c + 16c = 30c

For Σf(x) = 1, we need 30c = 1. So, c = 1/30.

(b) Here, x can take values 1, 2, 3,...,10

For Σf(x) = 1, we need c(1+2+3+...+10) = c(55) = 1. So, c = 1/55.

(c) Here, x can take values 1, 2, 3,...

For Σf(x) = 1, we need c(14+142+143+...) = c(14)(1+2+3+...) = c(14)∞ = 1. So, c = 1/(14∞).

(d) Here, x can take values 0, 1, 2, 3

For Σf(x) = 1, we need c(12+22+32+42) = c(1+4+9+16) = c(30) = 1. So, c = 1/30.

(e) Here, x can take values 1, 2, 3,...,n

For Σf(x) = 1, we need c(1+2+3+...+n) = c(n(n+1)/2) = 1. So, c = 2/(n(n+1)).

(f) Here, x can take values 0, 1, 2, 3

For Σf(x) = 1, we need c(12×3+22×4+32×5+42×6) = c(56) = 1. So, c = 1/56.

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A scientific calculator is typically used for pre-calculus.

This type of calculator is designed to handle more advanced mathematical functions, such as trigonometry, logarithms, and exponents, which are commonly used in pre-calculus.

It is important to have a scientific calculator for pre-calculus because it allows you to easily solve more complex equations and perform calculations quickly and accurately.

Additionally, many scientific calculators have graphing capabilities, which can be useful for visualizing equations and understanding how they behave. Overall, a scientific calculator is an essential tool for pre-calculus and can help you succeed in the course.

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Answer:

Step-by-step explanation:

Ans:n^th=2n-1

we are going to use the formula of arithmetic sequence.

We need to find the first term of the sequence which is 1 and find the difference between any two number.

Then simply multiply the different by (n-1)

Finally add the result with first term which is 1.

Answer:

a What does it mean for a manufacturer’s warranty and an extended warranty to overlap? both warranties cover the same period.

Step-by-step explanation:

Answer:

Let's say the number of sweets that Amol has is A.

According to the problem, the number of sweets that Gemma has is 6 times the number of sweets that Amol has. Therefore, Gemma has 6A sweets.

The number of sweets that Harry has is half the number of sweets that Gemma has. Therefore, Harry has 1/2 * 6A = 3A sweets.

So the ratio of the number of sweets that Amol, Gemma, and Harry have respectively is:

A : 6A : 3A

Simplifying this ratio by dividing each term by A, we get:

1 : 6 : 3

Therefore, the ratio of the number of sweets that Amol has to the number of sweets that Gemma has to the number of sweets that Harry has is 1:6:3

To calculate the mathematical value of 20, you would use the  : 20 x 1 = 20. This means that 20 multiplied by 1 is equal to 20. Therefore, the value of 20 in ASL is equal to 20.

ASL stands for American Sign Language. It is the visual language used by the deaf and hard of hearing communities to communicate. In ASL, the sign for the number 20 is done by holding up both hands with the palms facing out and fingers spread apart. The hands are then moved together in a circular motion with the fingers crossed at the end. This sign is also used to represent the mathematical concept of multiplication. To express the value of 20 in ASL, you would sign the number 20 by making the above mentioned sign, and then sign the word "equals". To calculate the mathematical value of 20, you would use the formula: 20 x 1 = 20. This means that 20 multiplied by 1 is equal to 20. Therefore, the value of 20 in ASL is equal to 20.

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Han's strategy is correct, as V = πr²h is the exact formula for the volume of a cylinder of radius r and height h.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

This is the exact formula used by Han, hence the strategy is correct.

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The required highest common factor of 25, 75, and 150 is 25.

The highest common factor (HCF) of two or more numbers is the largest number that divides all of the numbers exactly.

To find the HCF of 25, 75, and 150, we can first find the prime factorization of each number and then look for the common factors.

Prime factorization of 25,  25 = 5²

Prime factorization of 75:, 75 =  5² × 3

Prime factorization of 150,  150 = 2 × 3² × 5²

The largest factor that all three numbers have in common is 5², which is 25.

So, the HCF of 25, 75, and 150 is 25.

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Answer:

x = 9

Step-by-step explanation:

if three or more parallel lines are intersected by two or more transversals, the parallel lines divide the transversals proportionally , that is

[tex]\frac{3}{x}[/tex] = [tex]\frac{2.5}{7.5}[/tex] = [tex]\frac{1}{3}[/tex] ( cross- multiply )

x = 3 × 3 = 9

There are 2.20462 pounds in one kilogram.

Therefore, to convert 73.5 kilograms to pounds, you would multiply 73.5 by 2.20462.

The calculation is as follows:

73.5 kg * 2.20462 pounds/kg = 162.04101 pounds

So, there are approximately 162.04101 pounds in 73.5 kilograms.

By the definition conversion of units means the conversion between different units and the measurements of the same quantity done by either the process of multiplication or division.

In maths, conversion is referred as the process of changing the value of one form to another for example inches to millimeters, or liters to gallons.

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The required algebraic expression for the verbal expression is 3w.

From the question, we have the following parameters that can be used in our computation:

3 times as many wins as last season

If we let "w" be the number of wins last season, then "3 times as many wins as last season" can be expressed as:

3w

Hence, the algebraic expression for "3 times as many wins as last season" is 3w.

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The name of the relationship is b. Alternate interior angles.

Alternate interior angles are two angles that are located on opposite sides of a transversal line, but within the same two lines. When two lines are cut by a transversal line, the alternate interior angles are always congruent, meaning that they have the same measure.

In this case, angles ∠1 and ∠4 are alternate interior angles. Alternate interior angles are formed when two parallel lines are cut by a transversal line. When this happens, corresponding angles are formed on the same side of the transversal.

The alternate interior angles are the two angles that are on opposite sides of the transversal. These angles are also congruent, meaning that they have the same measure.

To summarize, alternate interior angles are two angles that are located on opposite sides of a transversal line and within the same two lines. In this case, angles ∠1 and ∠4 are alternate interior angles, meaning that they have the same measure.

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Answer:

They are not equivalent expressions

Step-by-step explanation:

Let's expand each expression and see if they are the same
6(-b + 8) = 6 x (-b) + 6 x 8 = -6b + 48

2(-3b + 4) = 2 x (-3b) + 2 x 4 = -6b + 8

So while the terms -b are the same, the constants are different

Hence the two expressions are not equivalent

The present value of the payment is: $25,015.42

Now, According to the question;

An annuity is series of equal annual payments or receipts made for a certain number of years.

A delayed annuity is that which the first cash flow occurs at a time later than year one.

A standard annuity is that which the first cash flow occurs a year from now.

An advanced annuity is that which first cash flow  occurs immediately or now.

$5,100 per where the first payment occurs in year 6 and end 20 years from today is an example of a delayed annuity.

Present Value = A ×( 1 - (1+r)^(-n))/r

                       = 5,100 × ( 1 - (1+0.079)^(-11))/0.079

                      = 36,586.01

Present Value = Future Value × (1 + r)^(-n)

Present Value = $ 36,586.01  × (1+0.079)^(-5)

Present value = $25,015.42

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Answer:

Step-by-step explanation:

3(x−3)=6

Divide both sides by 3.

x−3=

3

6

​

Divide 6 by 3 to get 2.

x−3=2

Add 3 to both sides.

x=2+3

Add 2 and 3 to get 5.

x=5

Answer:

A. 24 math problems

B. 20 tests

Step-by-step explanation:

A.

We know

1 hour = 60 minutes

Jaxon completed 12 math problems in 30 minutes

30 mins = 12 math problems

60 mins = 12 x 2 = 24 math problems

So, he finishes 24 math problems in an hour.

B.

We know

1 hour = 60 minutes

Mrs. Maven corrected 5 tests every 15 minutes.

15 mins = 5 tests corrected

60 mins = 5 x 4 = 20 tests corrected

So, she grades 20 tests every hour.

These are some of the main sources of error that can contribute to the margin of error in a survey or study.

The margin of error in a statistical survey or study is a measure of the uncertainty or variability in the results.

Here,
The margin of error reflects the potential difference between the sample estimate and the true population value. The margin of error is calculated by taking into account various sources of errors, including,

Sampling error: Sampling error arises from the fact that the sample is only a subset of the population and thus may not perfectly represent the population. The larger the sample size, the smaller the sampling error.

Other various sources are non-response error, Coverage error, Measurement error, Response bias, Weighting error, and  Model error.

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To convert kilometers per hour (kph) to miles per hour (mph), we use the following formula: mph = kph x 0.621371. This is because there are 0.621371 miles in a kilometer.

To calculate the value of 130 kph in mph, we can simply plug the value into the formula: mph = 130 x 0.621371 = 80.78 mph. Therefore, the value of 130 kph in mph is 80.78 mph. To further understand how this conversion works, we can break down the calculation into its basic components. First, we divide 130 by 1. That gives us 130. Then, we multiply 130 by 0.621371, which gives us the result of 80.78. Therefore, the value of 130 kph in mph is 80.78 mph. The above formula and calculation can be used to convert any value from kph to mph. All we need to do is plug the kph value into the formula and we will get the equivalent mph value. It is important to note that the conversion from kph to mph is not exact, as there are slight variations in the exact value of a kilometer. However, this formula provides a good approximation and is accurate enough for most purposes.

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The solution is,

The average of the data set is 275

The range is given as 300.

The range can be described as the distance that lies between the maximum and the minimum value in a data set.

here, we have,

to solve for the average distance of electric cars:

The average would be a summation of the data under the electric vehicle divided by the total number of data in the table

given that,

We have ,

250 + 250 + 250 + 400 + 300 + 300 + 350 + 100 / 8

= 2200 / 8

= 275

now,

we get,

= 400 - 100

= 300

Hence, The solution is,

The average of the data set is 275

The range is given as 300.

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Answer:

ABBBB

Step-by-step explanation: