Calculate each value requested for the following scores: 16, 23, 8, 25, 11, 20, and 10 a. sigma x b. [sigma x]^2 c. sigma x^2 d. n sigma x^2

Answer:

do you have like any picture of a graph?

The two consecutive odd integers are 9 and 11. 1/8 plus 1/11 equals 12/35.

The sum of the reciprocals of two consecutive odd integers is 12/35.

1/x + 1/(x+2) = 12/35

(x+2)/(x*35) + (x/35) = 12/35

x + 2 + x = 12

2x = 10

x = 5

5 and 7 are the next two odd numbers.

The sum of the reciprocals of two consecutive odd integers is 12/35. To find the two integers, we need to solve for x. Since the two integers are consecutive and odd, the equation

1/x + 1/(x+2) = 12/35

can be used to find x. We can then multiply both sides of the equation by x*35 and simplify it to (x+2)/(x*35) + (x/35) = 12/35.

By subtracting x/35 from both sides and then adding 2 to both sides, we can get the equation

x + 2 + x = 12.

By solving the equation 2x = 10, we find that x = 5. This means that the two consecutive odd integers are 5 and 7. This can also be verified by checking that 1/5 + 1/7 is equal to 12/35.

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Mean height of the students in the class = 65.7 inches

The mean height of all 12 students in the class is 66.0 inches.

So the Total height of 12 students in the class = 66 × 12

                                                                              = 792 inches

As Danielle's height = 62.1 inches

So the total height of 13 students = 792 + 62.1

                                                        = 854.1 inches

Mean of all 13 students in the class = 854.1 / 13

                                                            = 65.7 inches

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The complete question:

Mr. Zuro finds the mean height of all 12 students in his class to be 66.0 inches. Just as Mr. Zuro finishes explaining how to get the mean, Danielle walks in late. Danielle is 62.1 inches tall. What is the mean of the 13 students in the class?

To find the nonpermissible replacement for y in the expression;

The nonpermissible replacement for y is the replacement for y at which the denominator of the expression is zero. (when the denomenator is zero, the final value can not be determined).

For the given expression, the denomenator is;

For y to be nonpermissible, the denometor must be equal to zero.

To get y, add 1 to both sides.

At y =1, the expression becomes;

Therefore, the nonpermissible replacement for y in the given expression is;

21

Step-by-step explanation:

=4x+5

=4*4+5

=16+5

=21

The value of function f(x) = 4x + 5 when x = 4 is 21 the answer is 21.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

f(x) =  4x + 5

Plug x = 4

f(4) = 4(4) + 5

f(4) = 16 + 5

f(4) = 21

Thus, the value of function f(x) = 4x + 5 when x = 4 is 21 the answer is 21.

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The strongest correlation is - 0.89 that is option B

To gauge how closely two variables are related to one another, correlation coefficients are used. The most common correlation coefficient is Pearson's, though there are other varieties as well. The correlation coefficient known as Pearson's is frequently applied in linear regression. Correlation coefficients typically fall between -1.00 and +1.00. The strongest correlation is taken into account when the value is closest to +1 or -1, according to the rule of correlation coefficients.

A positive correlation coefficient means that the two variables directly affect one other's values. There is no association between the two variables, according to a zero correlation coefficient and when the correlation coefficient is negative, it means that the values of the two variables are inversely related.

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Answer:

empirical and topical

Step-by-step explanation:

starting points (empirical, topical) common grounds you locate between yourself and your composite audience that will allow you to build conviction toward your conclusion. Empirical Starting points: Dealing in certainty, concrete evidence.

Answer:

i think the ratio for the first is 1:5 and the other is 1:1

Step-by-step explanation:

have a nice day

Answer:

20

Step-by-step explanation:

Given:

Lisa is checking out at the bookstore.

Each book (b) costs $1.50 and she has a $5 off coupon she can use.

She wants to spend $25 or less in the bookstore.

Solve:

Since there is a $5 off coupon..

$1.5b - $5.00<=$25.00

$1.5b<= $30.00

$1.5b/1.5 = $30.00/1.5

b=20

Lisa can buy 20 book.

~lenvy~

Answer:

41

Step-by-step explanation:

The derivative of the function g(x) = (x² - x + 1\()^1^0\) * (tan(x))³ is g'(x) = 10(x² - x + 1)⁹ * (2x - 1) * (tan(x))³ + 3(x² - x + 1\()^1^0\) * (tan(x))² * sec²(x).

To find the derivative of the given function g(x), we can apply the product rule and the chain rule. Let's break down the function into its constituent parts: f(x) = (x² - x + 1\()^1^0\) and h(x) = (tan(x))³.

Using the product rule, the derivative of g(x) can be calculated as g'(x) = f'(x) * h(x) + f(x) * h'(x).

First, let's find f'(x). We have f(x) = (x² - x + 1\()^1^0\), which is a composite function. Applying the chain rule, f'(x) = 10(x² - x + 1\()^9\) * (2x - 1).

Next, let's determine h'(x). We have h(x) = (tan(x))³. Applying the chain rule, h'(x) = 3(tan(x))² * sec²(x).

Now, we substitute these derivatives back into the product rule formula:

g'(x) = f'(x) * h(x) + f(x) * h'(x)

       = 10(x² - x + 1)² * (2x - 1) * (tan(x))³ + 3(x² - x + 1\()^1^0\)* (tan(x))² * sec²(x).

In summary, the derivative of the function g(x) = (x² - x + 1\()^1^0\) * (tan(x))³ is g'(x) = 10(x² - x + 1)⁹  * (2x - 1) * (tan(x))³ + 3(x² - x + 1\()^1^0\) * (tan(x))² * sec²(x).

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Approximately 2 half-lives have passed since the material containing potassium-40 (K-40) was formed.

Here we know that,

Initial mass of potassium-40 (K-40) = 6 grams

Current mass of potassium-40 (K-40) = 1.5 grams

The relationship between the number of half-lives and the remaining amount of a radioactive substance can be expressed using the formula:

Remaining amount = Initial amount × (1/2)^(number of half-lives)

Let's solve the equation for the number of half-lives. We can rearrange the formula to solve for the number of half-lives as follows:

(number of half-lives) = log(base 1/2) (remaining amount / initial amount)

Substituting the given values:

(number of half-lives) = log(base 1/2) (1.5 grams / 6 grams)

Using the logarithmic properties, we can rewrite the equation as:

(number of half-lives) = log(base 1/2) (1.5) - log(base 1/2) (6)

To simplify further, we can use the change of base formula to convert the logarithm to a base 10 logarithm:

(number of half-lives) = log(1.5) / log(1/2) - log(6) / log(1/2)

Evaluating the logarithms:

(number of half-lives) = 0.1761 / (-0.3010) - 0.7782 / (-0.3010)

(number of half-lives) = -0.5847 - (-2.5814)

(number of half-lives) = -0.5847 + 2.5814

(number of half-lives) = 1.9967

Since the number of half-lives must be a whole number, we can conclude that approximately 2 half-lives have passed since the material containing potassium-40 (K-40) was formed.

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The 90% confidence interval is: (2.51, 3.22)

It is a boundary of values which is eventually to comprise a population value with a certain degree of confidence. It is usually shown as a percentage whereby a population means lies within the upper and lower limit of the provided confidence interval.

We have the following information :

The level of significance is calculated as:

\(\alpha =1-c\\\\\alpha =1-0.90\\\\\alpha =0.10\)

The degrees of freedom for the case is:

df = n - 1

df = 15 - 1

df = 14

The 90% confidence interval is calculated as:

=x(bar) ±\(t_\frac{\alpha }{2}\), df \(\frac{s}{\sqrt{n} }\)

= 2.86 ±\(t_\frac{0.10 }{2}\), 14 \(\frac{0.78}{\sqrt{15} }\)

= 2.86 ± 1.761 × \(\frac{0.78}{\sqrt{15} }\)

= 2.86 ± 0.3547

= (2.51, 3.22)

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2x^2-3x+1 - Algebraic Expression

x^3-2x^2=x Algebraic Equation

x^2-5x+6=0 Algebraic Equation

5x+20 Algebraic Expression

y=-2x+3 Algebraic Equation

-x-5 Algebraic Expression

Hope it helps you! :)

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Please mark Brainliest if this answer is helpful!

- Your friend, \(GraceRosalia\)

*Just a teen who listens to music

Answer:

1. Expression

2. Equation

3. Equation

4. Expression

5. Equation

6. Expression

Step-by-step explanation:

Algebraic Equation is basically algebraic expression except there's one difference.

Algebraic Equation must always have = sign.

The = sign applies to all equations, no matter what equation it is.

Next is Algebraic Expression;

Algebraic Expression does not have =, <, ≠, >, ≤ and ≥.

To put it simply, algebraic expression is just terms there; no comparison between two.

Usually, algebraic expression refers to polynomial, square root, etc.

So now, you understand the difference between two?

1. 2x^2-3x+1 is algebraic expression because there is no comparison.

2. x^3-2x^2=x is algebraic equation because there is comparison between two expressions.

3. x^2-5x+6=0 is algebraic equation because there is comparison between one expression and a constant.

4. 5x+20 is algebraic expression because there is no comparison.

5. y = -2x+3 is algebraic equation because there is comparison between x-term and y-term.

6. -x-5 is algebraic expression because no comparison.

The length of the cable needed is 1360ft.

To find the length of the cable needed for the construction worker to attach from the tip of the Burj Khalifa to where he stands, we can use the concept of similar triangles.

Let's represent the length of the cable as "x."

According to the given information, the height of the construction worker is 6ft, and the length of his shadow is 3ft. Similarly, the height of the Burj Khalifa is 2720ft, and the length of its shadow is the unknown variable "x."

We can set up the following proportion based on the similar triangles formed by the construction worker and the Burj Khalifa:

(Length of construction worker's shadow) / (Height of construction worker) = (Length of Burj Khalifa's shadow) / (Height of Burj Khalifa)

Using the values given:

3ft / 6ft = x / 2720ft

Now, we can solve this proportion for "x":

(3/6) * 2720 = x

Simplifying:

(1/2) * 2720 = x

1360 = x

Therefore, the length of the cable needed is 1360ft.

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A construction worker, standing at the tip of the Burj Khalifa’s shadow, must attach a cable from the tip of the building to where he stands. The worker notices that his shadow is 3ft and the Burj Khalifa is 2720ft tall.

In the given question, the worker notices that his shadow is 3ft and the Burj Khalifa is 2720ft tall.

Therefore, the height of the construction worker can be found using the concept of similar triangles, which states that corresponding angles in similar triangles are equal.

Hence, height of the worker can be calculated as (height of the Burj Khalifa / length of its shadow) x length of worker’s shadow = (2720 / 3) x 6

             = 2720 x 2

             = 5440 feet.

Thus, the length of the cable needed will be the sum of the height of the Burj Khalifa and the height of the construction worker,

which is 2720 + 5440 = 8160 feet.

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The future value of an annuity of $500 per year for 12 years, with an interest rate of 5%, can be calculated using the future value of an ordinary annuity formula. The future value is approximately $7,005.53.

To calculate the future value of an annuity, we can use the formula:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the annuity,

P is the annual payment,

r is the interest rate per compounding period,

n is the number of compounding periods.

In this case, the annual payment is $500, the interest rate is 5% (or 0.05), and the number of years is 12. As the interest is compounded annually, the number of compounding periods is the same as the number of years.

Plugging the values into the formula:

FV = $500 * [(1 + 0.05)^12 - 1] / 0.05

= $500 * [1.05^12 - 1] / 0.05

≈ $500 * (1.795856 - 1) / 0.05

≈ $500 * 0.795856 / 0.05

≈ $399.928 / 0.05

≈ $7,998.56 / 100

≈ $7,005.53

Therefore, the future value of the annuity of $500 per year for 12 years, with a 5% interest rate, is approximately $7,005.53.

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The amount of calories in fruit juice increases by 2.5 for every one gram of sugar. The calorie amount estimated by this model is 57 if there are zero grams of sugar.

Quantity of sugar=x ( in grams)      

The juice's calorie count=y

Estimate of y, which means it's the juice's estimated calorie count=ŷ

Rearranging the regression equation, we get: ŷ=57+2.5x

This has the mathematical formula y = mx+c, where m is the slope and c is the y-intercept.

Here m= 2.5 and c=57

We can get the rate of change from the slope. It specifically informs us of the increase in calories (y) that occurs every time sugar (x) increases. Whenever x increases by 1, y increases by 2.5.

The starting or initial number of calories is represented by the y-intercept 57. You begin with 57 calories if you have 0 grams of sugar, the least amount of sugar that is feasible. Plugging x = 0 into = 2.5x + 57 (you should get = 57) will show us this. Where the line crosses the y-axis can be seen as the y-intercept.

Therefore, The amount of calories in fruit juice increases by 2.5 for every one gram of sugar. The calorie amount estimated by this model is 57 if there are zero grams of sugar

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The line integral of xy dx + x^2 dy around the given rectangle is 0.

To evaluate the line integral ∮C (xy dx + x^2 dy) along the given rectangle C with vertices (0, 0), (5, 0), (5, 1), and (0, 1), we can break it down into four line integrals along each side of the rectangle and sum them up.

Along the bottom side:

Parametrize the line segment from (0, 0) to (5, 0) as r(t) = (t, 0), where t ranges from 0 to 5. The differential element along this line segment is dr = (dt, 0). Substituting these values into the line integral, we get:

∫[0,5] (t*0) dt = 0.

Along the right side:

Parametrize the line segment from (5, 0) to (5, 1) as r(t) = (5, t), where t ranges from 0 to 1. The differential element along this line segment is dr = (0, dt). Substituting these values into the line integral, we get:

∫[0,1] (5t0 + 25dt) = ∫[0,1] 25*dt = 25.

Along the top side:

Parametrize the line segment from (5, 1) to (0, 1) as r(t) = (5-t, 1), where t ranges from 0 to 5. The differential element along this line segment is dr = (-dt, 0). Substituting these values into the line integral, we get:

∫[0,5] ((5-t)*0 + (5-t)^2 * 0) dt = 0.

Along the left side:

Parametrize the line segment from (0, 1) to (0, 0) as r(t) = (0, 1-t), where t ranges from 0 to 1. The differential element along this line segment is dr = (0, -dt). Substituting these values into the line integral, we get:

∫[0,1] (0*(1-t) + 0) dt = 0.

Summing up all the line integrals, we have:

0 + 25 + 0 + 0 = 25.

Therefore, the line integral of xy dx + x^2 dy around the given rectangle is 25.

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To determine the mean and 90% confidence interval for the average fluoride concentration in the sample, we can follow these steps: The correct answer is 90% confidence interval = 0.791 to 0.817 mg/L

The first step is to calculate the mean of the data:

mean = (0.815 + 0.789 + 0.811 + 0.789 + 0.815) / 5 = 0.804 mg/L

The next step is to calculate the standard deviation of the data:

std_dev = sqrt((\(0.009^{2}\) + \(0.015^{2}\) + \(0.002^{2}\) + \(0.015^{2}\) + \(0.009^{2}\)) / 5) = 0.008 mg/L

The 90% confidence interval for the mean is calculated using the following formula:

mean ± t * std_dev / sqrt(n)

where t is the 90% critical value for the t-distribution with 4 degrees of freedom, which is 1.685.

90% confidence interval = 0.804 ± 1.685 * 0.008 / \(\sqrt{5}\) = 0.791 to 0.817 mg/L

The mean fluoride concentration in the sample is 0.804 mg/L. The 90% confidence interval for the mean is 0.791 to 0.817 mg/L.

Reporting:

The mean and the confidence interval should be reported to 3 significant figures, since the original data was given to 3 significant figures.

mean = 0.804 mg/L

90% confidence interval = 0.791 to 0.817 mg/L

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The matrix of \(t\) relative to the basis \(b'\) is \(A' = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\).

\(\textbf{To find the matrix of } t \textbf{ relative to the basis } b', \textbf{we have to follow some steps. The steps are described below:}\)

First, we have to find the images of basis vectors under the transformation \(t\). \(t(-1,1) = (-9,7)\) and \(t(1,-5) = (-37,43)\).

Represent the image vectors of the basis in the standard basis. We use these vectors as columns in the matrix of \(t\) in the basis \(b'\).

\((-9,7) = -9(1,0) + 7(0,1) = (-9,7) = -9(-1,1) + 7(1,-5)\)

\((-37,43) = -37(1,0) + 43(0,1) = (-37,43) = -37(-1,1) + 43(1,-5)\)

Hence, we can write the following equation: \(A[x]_{b'} = [x]_S\)

Where \(A[x]_{b'}\) is the main answer in the form of a matrix, and \([x]_S\) is the coordinate of \([x]_{b'}\) with respect to the standard basis.

Now, we will write the equations with the coordinates of the basis vectors of \(b'\).

\(A[1,0] = [-9, -37]\) and \(A[0,1] = [7, 43]\)

Now we will write the matrix of \(A\) as follows:

\(A = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\)

Thus, the matrix of \(t\) relative to the basis \(b'\) is \(A' = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\).

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dellana company tested 50 products for 75 hours each. during this time, it experienced four breakdowns. compute the number of failures per hour, 937.50 hours is the mean time between failures.

The span of time before something occurs or before a given time frame expires. We can utilise the current computers while waiting for the new ones to arrive next week.

Given that,

dellana company tested 50 products

time =75 hours

Thus, total products in hours

= 50 products × 75 hours each

= 3750 product hours

Also said that, 4 breakdowns in 3750 product hours,

so, (4/3750) = 1.067 × 10⁻³ = 0.001067 breakdowns per hour.

Also, an average of 0.001067 breakdowns per hour = λ

therefore, mean time between failures:

= 1/ λ

= 1/0.001067

= 937.50 hours

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The distance between point P and line l is

1. Distance = 2√2

2. Distance =0

3. Distance =6

4. Distance =1

5. Distance =√10

To find the distance between a point and a line, we can use the formula for the distance between a point and a line in the coordinate plane. The formula is:

Distance = |Ax + By + C| / √(A² + B²)

1. Line & contains points (0, -3) and (7, 4). Point P has coordinates (4,3).

The equation of the line is y = x - 3. We can rewrite it as x - y + 3 = 0.

So, Distance = |4 - 3 + 3| / √(1² + (-1)²)

= |4| / √2

= 4 / √2

= 2√2

2. Line & contains points (11, -1) and (-3, -11). Point P has coordinates (-1, 1).

The equation of the line is y = -2x - 1. We can rewrite it as 2x + y + 1 = 0.

So, Distance = |2(-1) + 1 + 1| / √(2² + 1²)

= |-2 + 2| / √5

= 0 / √5

= 0

3. Line & contains points (-2, 1) and (4, 1). Point P has coordinates (5, 7).

The equation of the line is y = 1.

So, Distance = |0(5) + 7 - 1| / √(0² + 1²)

= |6| / √1

= 6

4. Line & contains points (4, -1) and (4, 9). Point P has coordinates (1, 6).

The line is vertical, and its equation is x = 4.

so, Distance = |1 - 4 + 4| / √(1² + 0²)

= |-1| / √1

= 1

5. Line & contains points (1, 5) and (4, -4). Point P has coordinates (-1, 1).

The equation of the line is y = -3x + 8.

So, Distance = |3(-1) + 1 - 8| / √(3² + 1²)

= |-3 - 7| / √10

= |-10| / √10

= 10 / √10

= 10√10 / 10

= √10

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Answer:

y = 1/4 x - 31/4

Step-by-step explanation:

Slope (m) = 1/4

Point A (-1, -8)

y = mx + b

-8 = 1/4 (-1) + b

-8 + 1/4 = b

b = -32/4 + 1/4

b = -31/4

y = mx + b <-- this is a linear equation, continuing line, so there are infinite values for x and y. Therefore we don't have to plug the values of x and y in

y = 1/4 x + - 31/4

y = 1/4 x - 31/4

Option C. No, because the 100 adults were selected without replacement, the selections are dependent.

The binomial probability formula assumes that the trials are independent, meaning that the probability of success or failure for each trial remains the same regardless of the outcomes of previous trials. However, in this case, the 100 adults were selected without replacement, so the probability of being left-handed for each selection depends on the outcomes of previous selections. Therefore, the binomial probability formula cannot be used to find the probability in this situation. Instead, the hypergeometric distribution can be used to account for the dependence between selections.

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Complete question:

It is assumed that approximately 15% of adults in the U.S. are left-handed. Consider the probability that among 100 adults selected in the U.S., there are at least 30 who are left-handed. Given that the adults surveyed were selected without replacement, can the probability be found by using the binomial probability formula with x counting the number who are left-handed? Why or why not?

A. Yes, because the 100 adults represent less than 5% of the U.S. adult population, the trials can be treated as independent.

B. No, because the 30 adults represent more than 5% of the sample size, the trials are dependent.

C. No, because the 100 adults were selected without replacement, the selections are dependent.

D. No, because the probability of being right-handed is greater, x must count the number of right-handed adults.

Answer:

The answer is 3.2

Step-by-step explanation:

The original amount of the loan is approximately $6,605.45, and the balance after the 30th payment can be calculated using the remaining number of payments, interest rate, and the original loan amount

The original amount of the loan can be calculated using the monthly payment amount and the interest rate. The balance after the 30th payment can be determined by considering the remaining number of payments and the interest accrued on the loan.
To find the original amount of the loan, we need to calculate the present value (PV) using the monthly payment amount, interest rate, and the loan term. In this case, the loan term is five years, or 60 months, and the monthly payment is $200.38.
Using the formula for the present value of an ordinary annuity:
PV = PMT × [(1 - (1 + r)^(-n)) / r]
Where PMT is the monthly payment, r is the monthly interest rate, and n is the number of periods (number of months in this case).
First, we need to convert the annual interest rate to a monthly interest rate. The annual interest rate is 7.5%, so the monthly interest rate is 7.5% / 12 = 0.075 / 12 = 0.00625.
Next, we can substitute the values into the formula to find the present value (original amount of the loan):
PV = $200.38 × [(1 - (1 + 0.00625)^(-60)) / 0.00625]
  ≈ $200.38 × 32.9536
  ≈ $6,605.45
Therefore, the original amount of the loan is approximately $6,605.45.
To find the balance after the 30th payment, we need to consider the remaining number of payments and the interest accrued on the loan. Since each monthly payment reduces the loan balance, we need to calculate the remaining loan balance after 30 payments.
Using the formula for the remaining balance of a loan:
Balance = PV × (1 + r)^n - PMT × [(1 + r)^n - 1] / r
Where PV is the present value (original loan amount), r is the monthly interest rate, n is the remaining number of periods (remaining number of months), and PMT is the monthly payment.
Substituting the values into the formula:
Balance = $6,605.45 × (1 + 0.00625)^(60 - 30) - $200.38 × [(1 + 0.00625)^(60 - 30) - 1] / 0.00625
Calculating the expression will give the balance after the 30th payment.

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Answer:

a=0

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is decay, the rate of change is 49%

hope this helps!

The correct rate of change is B)49% decay.

What constant rate of change ?

    A rate of change is constant when, at any given point along the function, the ratio of the output to the input remains constant. The slope is another name for the rate of change that is constant. A linear function's rate of change will be constant.

Here the given function is ,

=> h(x)=38(0.51)x.

For any exponential function in which the base is less than 1, it will be an exponential decay situation.

In this problem, the base is 0.51.

Then,The amount that the base is less than 1  ( i.e. 1 - base) . It represents the rate of change in decimal ,

=> 1-0.51 = 0.49

Converting into percentage => 0.49 *100 = 49%

Therefore the correct option is B) 49% decay.

To learn more about rate of change in function

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