\( {( \frac{5}{3} )}^{2n + 1} {( \frac{5}{3} )}^{5} = ({ \frac{5}{3} )}^{n + 2} \)
Pls include steps...
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Answer:

<CBA

Step-by-step explanation:

trust:)))))))))))))

Answer:

y=4/3x +7

Step-by-step explanation:

4x - 3y = -21

Move 4x to the other side

-3y = -21 -4x

Next divide the other side by -3

y= 7 +4/3x

Move numbers around

y = 4/3x + 7

f(x) = 4800 * 1.5^x is the equation to model the relationship between the number of weeks, x, and the number of site visits.

It is said that the number of visits increased by a factor of 1.5 each week, which means it multiplied by 1.5 every week.

So the equation can be modeled as:

f(x) = 4800 * 1.5^x

Where x is the number of weeks and f(x) is the number of site visits.

Note that this equation is only valid for the number of weeks after the new marketing plan has been launched, since before that the number of visits was 4,800.

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Answer:

$0.61 per battery

Step-by-step explanation:

8/13

Answer:

2x+19

Step-by-step explanation:

5x+14-(3x-5)

2x+14+5

2x+19

The correct answer of the exponential function to represent the amount of money in the account after x number of years is y = 300(1.005)^x.

The exponential function to represent the amount of money in the account after x number of years when Santi invested $300 in an account that earned 0.5% interest is given by the formula: y = ab^x, where "a" represents the initial amount of investment, "b" represents the growth factor, and "x" represents the time period.

In this problem, Santi invested $300 which is the initial investment.

The account earned 0.5% interest, which is equivalent to 0.005 in decimal form.

Therefore, the growth factor is 1 + 0.005 = 1.005.

Using the formula for exponential functions, we can write: y = ab^x where a = $300 and b = 1.005

Therefore, y = 300(1.005)^x

Therefore, the exponential function to represent the amount of money in the account after x number of years is y = 300(1.005)^x.

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it is not possible to move one of the poles to s = -10 by adjusting the value of K. The given transfer function and controller configuration result in two poles at s = -2, and these poles cannot be moved to s = -10.

The transfer function of the plant is \( G(s) = \frac{1}{(s+2)^2} \), and we want to determine the value of K in the PD-controller \( D_c(s) = K(s+7) \) that will move one of the poles to s = -10.

To find the location of the poles in the closed-loop system, we multiply the transfer function of the plant G(s) by the transfer function of the controller Dc(s). The resulting transfer function is \( G_c(s) = G(s) \cdot D_c(s) = \frac{K}{(s+2)^2}(s+7) \).

The poles of the closed-loop system are the values of s that make the denominator of \( G_c(s) \) equal to zero. In this case, the denominator is \((s+2)^2\). Since the denominator is squared, there will always be two poles located at s = -2 in the closed-loop system.

If the desired pole location is s = -10, a different control configuration or plant transfer function would be required.

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Based on this data, for every inch in height, the arm span increases by 1.1 inches.

Here, we have,

I put the height of people on the x-axis because this is what I am trying to correlate the arm span to. I put the arm span on the y-axis because it is dependent on height.

I used point (60,61) and (70,72) to draw the line of best fit and to get the equation. First, to get the slope I would use the slope formula of m = 72-61/70-60 or 11/10 to get a slope of approximately 1.1. Then I used (60,61) to get the rest of the equation by plugging it in: y-61 = 1.1(x -60). This becomes y-61 = 1.1x - 66. Add 61 to both sides and the final equation is y = 1.1x – 5.

The slope represents the rate of change arm span based on height. The y intercept is the arm span.

Using points (66,68) and points (70,72) I plug each into the equation y=1.1x-5 to figure each out based on the difference from the actual points and get .4 for (66,68) and 0 for point (70,72) so I would say, based on .4 and 0 for these two points that this is a good line of best fit.

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

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complete question:

There are many measurements of the human body that are positively correlated. For example, the length of one's forearm (measured from elbow to wrist) is approximately the same length as the foot (measured from heel to toe). They are positively correlated because, as one measurement increases, so does the other measurement.

The total number of copper (Cu) atoms in each face-centered cubic (FCC) unit cell is  7 atoms.

Here, we have,

In a face-centered cubic (FCC) unit cell, there are a total of 4 atoms.

Each corner of the unit cell contains 1/8th of an atom,

and since there are 8 corners in a cubic unit cell,

the total contribution from the corners is 8 * 1/8 = 1 atom.

Additionally, there is 1 atom located at the center of each face,

and since there are 6 faces in a cubic unit cell,

the contribution from the faces is 6 * 1 = 6 atoms.

Therefore, the total number of copper (Cu) atoms in each face-centered cubic (FCC) unit cell is 1 + 6 = 7 atoms.

Hence, 7 atoms of cu are present in each unit cell.

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Answer:

Step-by-step explanation:Okay so first you have to find out if -2 is your growth or y-axis.Your y-axis is when the line hits the up and down graph line.Your -2 is most likely your growth now you need to create a starting point it can be 10 for example then you would subtract 2 from it everytime you place a new dot like (0,10) and then (1,8) and so on.If u make a table the x will be on the left side this is where u will put the number 0,1,2,3.for everytime you make a dot on the graph.

Answer:

0.976 or 97.6%

Step-by-step explanation:

To calculate the frequency of the recessive allele, we need to use the information provided about the frequency of the dominant trait.

Let's assume that the particular dominant trait is determined by a single gene with two alleles: the dominant allele (A) and the recessive allele (a).

Given that 45 out of 1,000 babies are born with the dominant trait, we can infer that the remaining babies (1,000 - 45 = 955) do not have the dominant trait and can be considered as the recessive trait carriers.

The frequency of the recessive allele (q) can be calculated using the Hardy-Weinberg equation:

q = sqrt((Recessive individuals) / (Total individuals))

In this case, the total number of individuals is 1,000, and the number of recessive individuals is 955.

q = sqrt(955 / 1,000)

Using a calculator, we can find the value:

q ≈ 0.976

Therefore, the frequency of the recessive allele is approximately 0.976 or 97.6%.

Answer:

It is based on simple probability because there is only one possible answer each spin hope this helps :)

Step-by-step explanation:

Answer:

$1,073,741,824

Step-by-step explanation:

Every 12 years, the price increases by double. So, first we would need to find the difference of years between 2370 and 2046.

2370-2046=324

Divide this number by 12 to see how many times the number is doubled.

324/12=27

Continue this pattern of "every 12 years, the price increases by 2x" 27 times.

Ex: 2058-->$16

Ex: 2070-->$32

Ex: 2082-->$64

etc....

Yes, the responses x(t) and y(t) will oscillate if f(t) = us(t). The oscillation frequency can be computed using the equation:

ω = 2πf

Where ω is the radian oscillation frequency and f is the frequency in hertz. To find the frequency in hertz, we can use the equation:

f = 1/T

Where T is the period of the oscillation. The period can be found by examining the function f(t) and determining the time it takes for one complete oscillation. Once we have the period, we can plug it into the equation for frequency and then use that value to find the radian oscillation frequency.

As for how long it will take for the oscillations to disappear, this will depend on the damping factor of the system. If the damping factor is large, the oscillations will disappear quickly. If the damping factor is small, the oscillations will take longer to disappear. Without more information about the damping factor, it is difficult to estimate how long it will take for the oscillations to disappear.

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The required number of children and adults for sitting in the theater are 300 and 50 respectively.

A equation is supposed to be linear equation in two factors in the event that it is written as hatchet + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an a and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are straight equation in two factors.

Let be consider number of children be x and that of adults is y.

We have,

x + y = 350-------(1)

y = 350 - x

And 5x + 10y = 2000------------------(2)

Put value of y in equation (2)

5x + 10( 350 - x) = 2000

5x + 3500 - 10x = 2000

-5x = -1500

x = 300

Then

y = 350 - x = 350 - 300 = 50

Thus, There will be 300 children and 50 adults in the  theater .

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The value of  f(0) = 2 and f(-2) = -2 given the equation that we have in this image.

The function that we have here is given as

\(\frac{2x-2}{(x + 1)(x-1)}\)

We have to find the value of f(-2)

= 2(-2) - 2 / (-2 + 1) (-2 - 1)

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

= -6 / 3

= -2

Hence  f(-2) = -2

Next we have to find f(0)

2(0) - 2 / (0 + 1) (0 - 1)

= -2 / 1 * -1

= -2 / -1

= 2

Hence we can say that the value of  f(0) = 2 and f(-2) = -2 given the equation that we have in this image.

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Answer:

Table B has a constant proportionality between x and y of 0.6

Answer:

1. swimming, playing soccer, walking, running

2. skiing, walking, ?

3. hot weather

Answer: 0.00330033003

Answer:

x= 18.29

Step-by-step explanation:

- distribute then simplify- .75x + 12 = 2.5x - 20

- subtract .75x from each side- 12 = 1.75x - 20

- add 20 on each side- 32 = 1.75x

- divide each side by 1.75x- x= 18.29

not 100% sire if thats correct

\(0.75\left(x+16\right)=3-0.5\left(x-8\right)\)

\(0.75\left(x+16\right)\cdot \:100=3\cdot \:100-0.5\left(x-8\right)\cdot \:100\)

\(75\left(x+16\right)=300-50\left(x-8\right)\)

\(75x+1200=-50x+700\)

\(5x+1200-1200=-50x+700-1200\)

\(75x=-50x-500\)

\(75x+50x=-50x-500+50x\)

\(125x=-500\)

\(\frac{125x}{125}=\frac{-500}{125}\)

\(x=-4\)

From hypothesis testing, the test statistic value for two samples is 0.30. The p-value = 0.766> 0.05, null can't reject the null hypothesis. So, there is no evidence to support claim that a difference in population mean percentage increases for corporate revenue and CEO salary. So, option(A) is right one.

For comparing means of two population where population variance are unknown, then our hypothesis is \(H_0 :μ_1−μ_2 =ξ_0 \)

\(H_1 :μ_1−μ_2 ≠ξ_0\)

The test statistic for the given hypothesis is \(T= \frac{ (\bar x_{1} − \bar x_2) - ξ_0}{ \sqrt{\frac{ s²_1}{n_1} + \frac{ s²_2}{n_2}}}\)

\( s_ i = ∑_{j=1}^{n_i}\frac{ x_{ij} - \bar x_i}{ n_i - 1} \\ \)

Now, there are america's top chief executive officers. Let's consider A denotes be the CEO's annual percentage salary increase and B denote be the annual company percentage increase in revenue, in that same company. To test the different of population mean percentage increase in corporate revenue \((μ_B)\) and the population mean percentage increase in CEO salary \((μ_A)\). We need the hypothesis as : For A sample, \(n_1 = 8\)

sample mean \(\bar x_1 = \sum_{j = 1}^{n_1} x_{ij} = 16.13 \\ \)

Standard deviations, \(sd_1 = \sqrt{ \sum_{j = 1}^{8} \frac{ x_{1j} - \bar x_1}{n_1 - 1} } \\ \)

= 9.46

Similarly for B, \(n_2 = 8\)

sample mean \(\bar x_2 = \sum_{j = 1}^{n_2} x_{ij} = 17.28 \\ \)

standard deviations, \(sd_2 = \sqrt{ \sum_{j = 1}^{8} \frac{ x_{1j} - \bar x_2}{n_2- 1} } \\ \)

=11.8

d = \(\bar x_1 - \bar x_2 = 1.67\)

Therefore the test statistic :

\(T= \frac{ 1.67 - 0}{ \sqrt{\frac{ 9.41²}{8} + \frac{11.8² }{8}}}\)

= 0.30

degree of freedom, df = 8 + 8 - 2 = 14

Level of significance= 0.05

The above test statistic follows t-distribution with, so the critical value for t = 0.30 and degree of freedom 14 is equals to 0.766 > 0.05.

Based on obtained answers, we will fail to reject the null hypothesis because p-value is greater than the level of significance then we can says that the data is not statistically significant at level 0.05. Hence, we conclude that there is no enough evidence at the 5% level of significance to the claim that a difference in population mean percentage increases for corporate revenue and CEO salary.

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Complete question:

are america's top chief executive officers (ceos) really worth all that money? one way to answer this question is to look at row b, the annual company percentage increase in revenue, versus row a, the ceo's annual percentage salary increase in that same company. suppose a random sample of companies yielded the following data: b: percent increase for company 4 20 24 18 6 4 21 37 a: percent increase for ceo 17 14 21 14 -4 19 15 30 do these data indicate that the population mean percentage increase in corporate revenue (row b) is different from the population mean percentage increase in ceo salary? Use a 5% level of significance. Solve the problem using the critical region method of testing. (Let

d=B−A. Round your answers to three decimal places.)

test statistic = _____

critical value =

A: Fail to reject the null hypothesis, there is insufficient evidence to claim a difference in population mean percentage increases for corporate revenue and CEO salary.

B. Fail to reject the null hypothesis, there is sufficient evidence to claim a difference in population mean percentage increases for corporate revenue and CEO salary.

C. Reject the null hypothesis, there is insufficient evidence to claim a difference in population mean percentage increases for corporate revenue and CEO salary.

D. Reject the null hypothesis, there is sufficient evidence to claim a difference in population mean percentage increases for corporate revenue and CEO salary.

The solution to the system of equations is x = 8/3 and y = 41/43.

To find the solution for the given system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:

Given equations:

3x + 2y = 22 ---(1)

-x + 15y = 21 ---(2)

To eliminate one variable, we can multiply equation (2) by 3 and equation (1) by -1, then add the resulting equations:

-3x + 45y = 63 ---(3) (multiplying equation (2) by 3)

-3x - 2y = -22 ---(4) (multiplying equation (1) by -1)

Adding equations (3) and (4) eliminates the x variable:

43y = 41

Dividing both sides by 43 gives us:

y = 41/43

Now we can substitute this value of y into either equation (1) or (2). Let's use equation (1):

3x + 2(41/43) = 22

Multiplying both sides by 43 to eliminate the fraction:

129x + 82 = 946

Subtracting 82 from both sides:

129x = 864

Dividing both sides by 129:

x = 864/129

Simplifying:

x = 8/3

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Answer:

the correct answer is 2x+3

Step-by-step explanation:

because your adding the (x) factors together then your adding a negitive to a positive so you would get a lower number

Answer:

X = 4, Y = - 2

Step-by-step explanation:

2X - Y = 10 ( +Y)

2X = 10 + Y ( -10)

Y = 2X - 10

2X - 5Y = 18

2X - 5(2X - 10) = 18

2X - 10X + 50 = 18

50 - 8X = 18

50 - 18 = 8X

32 = 8X ( divide by 8)

X = 4

Y = 2(4) - 10

Y = - 2

Answer:

y = 4x + 16 (fourth answer choice)

Step-by-step explanation:

From the given equation we can immediately discern that the slope of these lines is 4 (as they are parallel).

Starting with the slope-intercept formula y = mx + b, we get:

32 = 4(4) + b, or 16 = b, or y = 4x + 16

In order for f(x) to be a linear function, determine the value of k in the data set.

x = {-7, -2, 2, 5}

f(x) = {-15, k, 3, 9}

The value of k is {-5}.

Given that to find the value of k in the data set such that the data set represents a linear function.

Linear Function is a straight line on the coordinate plane is represented by a linear function. The formula for a linear function is f(x) = mx + b, where m and b are real values.

Here, f(x) or y is the dependent variable, m is a slope of the line, x is the independent variable and b is the y-intercept.

Here,(x,f(x)) are {(-7,-15),(-2,k),(2,3),(5,9)}

The slope of the function,

(x, f(x)) = (2,3) and (5,9)

Slope formula is m=\(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\).

Slope m= \(\frac{9-3 }{5-2}\)

Slope m=\(\frac{6}{3}\)

Slope m=2.

Using the point slope form, determine the linear function's equation.

\(y-y_{1} =m(x-x_{1})\)

Here, \((x_{1},y_{1})=(-7,-15)\) and m=2

We get

y + 15 = 2 (x + 7)

y = 2x - 1

Now at x = -2 and f(x) = k

k = 2(-2) - 1

k = -4-1

k=-5

Therefore, the value of k is -5.

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