Use differences to find a pattern in the sequence.
2,9,22,45,82,137,214

Assuming that the pattern​ continues, the eighth term should be.

If the spin lands on the space where the contestant wins nothing, then x = 0.

If the spin lands on a space where the contestant wins $1, then x = -1 + 1 = 0. If the spin lands on a space where the contestant wins $4, then x = -2 + 4 = 2.

The expected value of x can be calculated as follows:

E(x) = (333/555) × 0 + (111/555) × (-2 + 1) + (111/555) × (-2 + 4) = (111/555) * 2 = 0.4.

So, on average, the player's net gain per spin is 40 cents.

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Answer:

Step-by-step explanation: 21

The sum of all the paintable integers is 757.

Note that it is impossible for any of h,t,u to be 1, since then each picket will have been painted one time, and then some will be painted more than once.

h cannot be 2, or that will result in painting the third picket twice. If h=3, then t may not equal anything not divisible by 3, and the same for u. Now for the fourth and fifth pickets to be painted, t and u must be 3 as well. This configuration works, so 333 is paintable.

If h is 4, then t must be even. The same for u, except that it can't be 2 mod 4. Thus u is 0 mod 4 and t is 2 mod 4. Since this is all mod 4, t must be 2, and u must be 4, in order for 5,6 to be paintable. Thus 424 is paintable.

h cannot be greater than 4, since if that were the case then the answer would be greater than 999, which would be impossible for the AIME.

Therefore, the sum of all paintable numbers is 757.

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The domain restriction for f(x)/g(x) is x ≠ 0 or -3

The domain of a function is the set of all input values (or "independent variable") for which the function is defined and produces a valid output (or "dependent variable").

In other words, it is the set of all valid input values for which the function will produce a real output and not give an error or undefined result.

But the domain restriction is the set of values that are not allowed as input for the function.

f(x)/g(x) = (x+26)/(14x²+42x)

In order to find the Domain restriction for f(x)/g(x), equate the denominator g(x) to zero and solve for x. That is:

14x²+42x = 0

14x(x + 3) = 0

14x = 0 or x + 3 = 0

x = 0 or x = -3

Thus, the Domain restriction is x ≠ 0 or -3

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Answer: 83 inches

Step-by-step explanation:

1. 12 inches = 1 foot

2. 12x6=72 inches

3. 72+11=83 inches

The type of observational study in the following scenario is considered as prospective study.

A prospective study, also known as a prospective cohort study, is a type of longitudinal study in which researchers follow and watch a group of individuals across time to collect data and track the development of outcomes. A prospective study is one that follows participants over time to see if certain outcomes, like the onset of a disease, occur and then compares those instances to any known or suspected risk or protective factors (s). It is common practice to follow a group of people, or a "cohort," for an extended period of time as part of the study. In this scenario, the researcher wants to learn how closeness to a traumatic event might effect healing time by conducting interviews with victims and witnesses over the next 10 years. Hence, it fits the criteria for a prospective observational study.

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Answer:

Part 1

(a) There were 2798 patients who only had the protein for Lyme.

Part 2

(b) There were 2516 patients who only had the normal protein.

Part 3

(c) It is not specified in the given information how many patients had none of the proteins. It is only specified that 1538 had the protein for normal patients, CFS, and post-treatment Lyme disease; 1884 had the protein for CFS and Lyme; 408 had the protein for CFS only; 2602 had the protein for CFS; 1731 had the normal protein as well as the one for Lyme; 2798 had the protein for Lyme; 2516 had the normal protein. Based on this information, it is not possible to know how many patients had none of the proteins.

Answer: There are no patients who had none of the proteins.

Step-by-step explanation: Part 1

(a) There were 408 patients who only had the protein for Lyme.

This information can be inferred from the data given: 1884 had the protein for CFS and Lyme, and 2798 had the protein for Lyme. If we subtract 1884 from 2798, we get 914 which is the number of patients who only had the protein for Lyme.

Part 2

(b) There were 2516 patients who only had the normal protein.

This information can be inferred from the data given: 1538 had the protein for normal patients, CFS, and post-treatment Lyme disease, 1884 had the protein for CFS and Lyme, and 2602 had the protein for CFS. If we add 1538, 1884 and 2602, we get 6124, then if we subtract 6124 from the total number of patients (3991) we get 2516 patients who only had the normal protein.

Part 3

(c) There were 0 patients who had none of the proteins.

This information can be inferred from the data given: 1538 had the protein for normal patients, CFS, and post-treatment Lyme disease, 1884 had the protein for CFS and Lyme, 408 had the protein for CFS only, 2602 had the protein for CFS, 1731 had the normal protein as well as the one for Lyme, 2798 had the protein for Lyme, and 2516 had the normal protein. All patients have at least one protein, therefore there are no patients who had none of the proteins.

The standard deviation of is equal to the standard deviation multiplied by, and the anticipated value of is equal to the mean.

The mean, which is the average of the random variable, is equal to the expected value of. It is determined by summing up all of the random variable's values and dividing the total number of values in the set. The result of multiplying the standard deviation by is the standard deviation of. By taking the square root of the variance, the standard deviation—a measurement of the range of data points from the mean—is created. By dividing the total of the squares of the deviations between each data point and the mean, the variance is computed.

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The answers include the following below:

The Simon effect refers to the finding that people are faster and more accurate when responding to stimuli that occur in the same relative location as the response.

An appropriate  task demonstrating the auditory version of the Simon effect will be putting the hands close to or far from the loudspeakers and noting how fast they react to the stimuli.

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The words that can be changed into mathematical or arithmetic operators are

More = +, of  = *, if=Condition.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.

The four basic arithmetic operations in Maths, for all real numbers, are:

Addition (Finding the Sum; ‘+’)

Subtraction (Finding the difference;  ‘-’)

Multiplication (Finding the product; ‘×’ )

Division (Finding the quotient; ‘÷’)

Now,

we can change

More = +, of  = *, if=Condition as only these makes sense according to mathematics actions.

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Answer:

D.[tex]\sqrt[32]{2}[/tex]

I think this is right becuse V=l*w*h which is 64=4*4*4

Answer:

Step-by-step explanation:

the answer is : 4,8,6,6,6

= 6

The experimental probability that the puppy would be named lemon or linus is 13/50. Option D

The experimental probability that the pupply would be named lemon or linus can be solved by

P(A) + P(B)

where P (A) is probability of lemon

P(B) is probability of linus

The total value in the frequency table is given as 10 + 13 + 3 + 14 + 10 = 50

P(A) = 3 / 50

P(B) = 10 / 50

The probability = 3/50 + 10/50

solve using the lcm method of solving fractions. There is a common denominator

3  + 10 / 50

= 13 / 50

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The solution for the given differential equation is  [tex]\frac{dy}{dx} = 12C_1e^{12x} = 12y[/tex].

We have given a differential equation:

[tex]\frac{d}{dx}(C_1e^{12x})[/tex]

since C1 is a constant,

=[tex]C_1\frac{d}{dx} (e^{12x})[/tex]

we know that [tex]\frac{d}{dx} (e^{ax}) = e^{ax}\frac{d}{dx} (ax)[/tex]

= [tex]C_1e^{12x}(12) = 12C_1e^{12x}[/tex]

Therefore, [tex]\frac{d}{dx}(C_1e^{12x}) = 12C_1e^{12x}[/tex]

Now, let y = [tex]C_1e^{12x}[/tex]

Therefore, [tex]\frac{dy}{dx} = 12C_1e^{12x} = 12y[/tex]

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The complete question is:

Fill in the blank. The symbol C represents a constant. [tex]\frac{d}{dx}C_1e^{12x}[/tex]= ____ Write this result as a linear first-order differential equation that is free of the symbol C1 and has the form dy/dx = f(x, y).

The equation of a circle whose center is at the origin and passes through (7, 8) is x² + y² = 113

Circle is a round geometry whose all points constitute form a path having a constant distance (radius) from a fixed point (center of the circle).

The standard form for the equation of a circle is (x − h)² + (y − k)² = r², where (h,k) is the center of the circle, and r is the radius.

Center = (h,k) = (0,0)

Point = (7,8)

Now we input those values into the equation:

(x − h)² + (y − k)² = r²

(x − 0)² + (y − 0)² = r²

x² + y² = r²

Next, we have to determine the radius. It can be done by applying Pythagoras' Theorem. Look at the picture:

x² + y² = r²

7² + 8² = r²

49 + 64 = r²

113 = r²

Then we go back to the previous equation, and we get:

x² + y² = r²

x² + y² = 113

Thus, the equation of a circle whose center is at the origin and passes through (7, 8) is x² + y² = 113

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The coordinates of the midpoint of the segment whose endpoints are H (-2, 4) and K (2, –3) is (0,1/2)

Suppose we've two endpoints of a line segment as:

A(p,q), and B(m,n)

Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:

x = [tex]\dfrac{p+m}{2}[/tex]

and y =[tex]\dfrac{q+n}{2}[/tex]

Given;

The endpoints= H (-2, 4), K (2, –3)

X coordinate of midpoint;

-2+2/2=0

Y coordinate of midpoint;

4-3/2=1/2

Therefore, the midpoint will be (0,1/2)

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Answer:

k-m+1

if you have 36 and 78 for example, you would do 78-36 to find how many numbers there are plus one. so, the answer is k-m+1

Jane typed all the natural numbers between m and k (where k>m), which implies she wrote all the positive integers between m and k, inclusive. Jane would have written the numbers 5, 6, 7, 8, 9, and 10 if m was 5 and k was 10.

Natural numbers are positive integers (1, 2, 3, and so on) that can be counted and ordered. They are the most fundamental sort of number in mathematics and are frequently referred to as counting numbers. Natural numbers begin with one and continue forever; however, they do not include negative numbers, fractions, or decimals.

Natural numbers are the foundation of many mathematical ideas and are used to express the quantities of things in a collection. Natural numbers, for example, are used to define the number of sides of a polygon, the dimensions of a matrix, and the length of a number line. They are also used to indicate how much time has elapsed.

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The value of x in the given polygon is 31 degrees.

An exterior angle is an angle created by the expansion of the neighboring side and one of the sides of a closed shape construction, such as a polygon. Regardless of the number of sides in the polygons, the sum of the measures of the outside angles is equal to 360 degrees.

The sum of the exterior angle of any polygon is 360 degrees.

So,

360 = 57 + 41 + 82 +x + 62 + 87

360 = x + 329

x = 31

Hence, the value of x in the given polygon is 31.

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Answer:

X/4=3/6

Start off by cross multiplying the tops and bottoms, so X/4=3/6 turns into 6X=12. Now divide by 6 on both sides.

6X=12      X=2

Answer:

2

Step-by-step explanation:

Cross Multiple and Divide

X. 3

----. = ----

4. 6

So what you want to do is multiply diagonally:

(6)(X) = 6X

(3)(4) = 12

Now that we have our two answers, we put an equal sign between them.

6X = 12

Now to get X alone. Since it's being multiplied by 6, you want to do the opposite and divide.

So remember to divide on both sides to get rid of the 6.

6X divided by 6 is just X.

12 divided by 6 is 2

We got our answers, put the equal sign in-between

X = 2

That since exact value of sin(A-β) depends on the cos(-β) value, which we miss, we are not able to determine the value.

To determine (A-β), we can use trigonometric identities.

Tan(A) = 3/4 and sin() = 4/5 in Quadrant III.

The identification can be used for:

tan(A) = cos/sin(A) (A)

Sin(A) in this instance equals 3/4. * cos(A) (A)

We can adopt a different guise.

(A-sin) = sin (A)

(cos) - (cos (A)

Sin(β), so sin(A-) = (3/4 * cos(A)) (sin()) - cos()) (cos(A))

sin(A-β) = (3/4) - (4/5) * (sin(A) * (cos(A) * cos())

We can now apply the double angle formula.

cos(2A) = sin2 + cos2(A) (A)

Therefore, cos(A) = (1 - sin(A)2), and sin(A-) = (3/4) * (± √(1 - (3/4)^2) * cos(β)) - (4/5) * (3/4)

sin(A-β) = (3/4) * (± √(1 - (9/16)) * cos(β)) - (3/5)

The formula for sin(A-) is (3/4) * ((7/16) * cos()) - (3/5)

That since exact value of sin(A-) depends on the cos(-) value, which we miss, we are not able to determine the value.

Therefore, using the equation given, it is impossible to figure out the precise value of (A-β).

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The Complete statement is : The location of proton in the atom is inside nucleus , has a charge of +1 elementary charge and the approximate mass of proton is 1.00727647 amu .

The Protons are the positively charged particles, the electrons are negatively charged particles and the neutrons have no charge.

In an atom there are equal number of protons and number of electrons . Thus the atom is electrically neutral in nature. The charge of the  proton is equal and opposite of an electron. So , proton has a unit positive charge.

The Protons are found inside the nucleus of atom , the proton carries the elementary charge of  1.00727647 amu (atomic mass units) , the charge on the proton is +1 .

The given question is incomplete , the complete question is

Answer the following questions about the Proton ,

The location of proton in the atom is  ______ , has a charge of ______ elementary charge and the approximate mass of proton is _____ amu .

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The medians and IQRs of two distributions can be compared to determine how the distributions differ. If the medians and IQRs are the same, the distributions are similar. If the medians and IQRs are different, the distributions are not the same.

a. The medians and IQRs of distributions (1) and (2) are the same; both have a median of 6 and an IQR of 4.

b. The medians and IQRs of distributions (1) and (2) are the same; both have a median of 6 and an IQR of 2.c. The medians and IQRs of distributions (1) and (2) are different; distribution (1) has a median of 3 and an IQR of 2, while distribution (2) has a median of 8 and an IQR of 2.

d. The medians and IQRs of distributions (1) and (2) are different; distribution (1) has a median of 50 and an IQR of 50, while distribution (2) has a median of 500 and an IQR of 400.

The median IQRs of two distributions can be compared to determine how the distributions differ. If the medians and IQRs are the same, the distributions are similar. If the medians and IQRs are different, the distributions are not the same.

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Answer: The statement given tells us that the Acme Company manufactures widgets and that the distribution of widget weights is bell-shaped. A bell-shaped distribution is also known as a normal distribution or a Gaussian distribution. This means that the majority of the data will cluster around the mean (average) value and the farther the data is from the mean, the less common it is.

The mean weight of the widgets is given as 51 ounces, which is the average weight of all the widgets manufactured by the company. The standard deviation is given as 10 ounces, which is a measure of how spread out the data is from the mean. A smaller standard deviation means that the data is more tightly clustered around the mean, while a larger standard deviation means that the data is more spread out.

This information allows us to make some predictions about the weights of the widgets. For example, we know that approximately 68% of the widgets will weigh between 41 ounces (mean - standard deviation) and 61 ounces (mean + standard deviation). Additionally, we know that approximately 95% of the widgets will weigh between 31 ounces (mean - 2standard deviation) and 71 ounces (mean + 2standard deviation) and 99.7% of the widgets will weigh between 21 ounces (mean - 3standard deviation) and 81 ounces (mean + 3standard deviation).

It is important to note that these predictions are based on the assumption that the distribution of widget weights is indeed bell-shaped. If that assumption is not true, these predictions may not be accurate.

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to use the graph to estimate the lower and upper quartiles of the lengths of the 16 fish that Jay measured.

The lower quartile is comprised of the 1/4 of the total number of fish that are the shortest. The graph shows that 4/16 of the fish are 10 inches or less, so the lower quartile is 10 inches.

The upper quartile is comprised of the 1/4 of the total number of fish that are the longest. The graph shows that 12/16 of the fish are 25 inches or less, so 4/16 of the fish are 25 inches or more. The upper quartile is 25 inches.

The lower and upper quartiles are 10 inches and 25 inches, respectively.

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The multifactor productivity for a given operation is 6.16 fees generated per dollar of input.

The Break Even Point, or the inflection point at which a corporation starts to make a profit, is the amount of output required for a company's revenue to equal its total costs.

First, we need to calculate the revenue generated per week:

Potential leads per week = 3 employees x 4,000 leads/employee/week = 12,000 leads/week

Actual sign-ups per week = 12,000 leads/week x 7% = 840 sign-ups/week

Revenue per week = 840 sign-ups/week x $90/sign-up = $75,600/week

Next, we need to calculate the input costs per week:

Labor cost per week = 3 employees x $18/hour x 40 hours/week/employee = $2,160/week

Material cost per week = $1,300/week

Overhead cost per week = $8,800/week

Total input cost per week = $2,160/week + $1,300/week + $8,800/week = $12,260/week

Finally, we can calculate the multifactor productivity:

Multifactor productivity = Revenue per week / Input cost per week = $75,600/week / $12,260/week = 6.16

So the multifactor productivity for this operation is 6.16 fees generated per dollar of input.

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The salesperson's gross earnings for a week, based on the informations, equals to $1,195.

An employees' gross pay is what they earn before taxes, benefits, and other payroll deductions are deducted from their pay. It is opposite of net pay, also known as take-home pay which is the amount left over after all withholdings are deducted.

Data

Weekly base salary of $600 on a quota of $4500.

On the next $2000, she receives a commission of 11 %.

On any additional sales, the commission rate is 15%.

Gross earning is computed as:

= Base salary + (First sales *11%) + (Additional sales*15%)

= $600 + ($2,000*11%) + ($2,500 * 15%)

= $1,195

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The graph shows a maximum wolf population size of 500 individuals, which occurred in 2017.

The graph depicts the magnitude of the wolf population in a certain location during the previous 25 years. The population size is shown to have changed over time, with the peak population count of 500 people happening in the year 2017. A population size of 450 people, which is a little less than the highest population level, was then reached in 2018. The year 2000 saw the lowest population size, with only 200 people living there. In 2017, there were 500 people in the population, which had grown considerably over the years. This suggests that over the past 25 years, the wolf population has been growing which occurred in 2017.

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The complete question is

based upon the data presented in the graph, which of the following best identifies the highest wolf population size which occurred in 2017?

The numbers for the first eight beads that are white are; 1, 5, 9, 13, 17, 21, 25, 29

step1

Arithmetic Sequence

We are told that she strings in this order;

Now, after the first white bead, the next white bead is the 5th bead in total.

This means the difference in interval between white beads is; 5 - 1 = 4 beads

Thus, the numbers for the first eight beads that are white are

1, (1 + 4), (1 + 4 + 4), (1 + 4 + 4 + 4)…..

Thus, we have;

1, 5, 9, 13, 17, 21, 25, 29

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