Suppose that the population of some state in 2010 was P=40 million and its annual percentage rate of continuous growth is R = 1.03%. (a) Write the formula f(x)=Pex, where r is in decimal notation, that models the population in millions x years after 2010. (b) Estimate the population in 2021. (a) f(x)= (Use integers or decimals for any numbers in the expression.)

Answer:

16,700

Step-by-step explanation:

38,428

_

21,728

=

16,700

The correct statements are:

The triangle and trapezoid area formulas have 1/2.

The parallelogram and rectangle formulas are both the same.

In the trapezoid formula, the bases are added.

A triangle is a polygon with three sides and three vertices. A triangle's angles add up to 180 degrees.

Area of a triangle = 1/2 x base x height

A trapezium is a quadrilateral that is convex. A trapezium is made up of at least two parallel sides. Area of a trapezium = 1/2  x (sum of the lengths of the parallel sides) x height

A rectangle is a quadrilateral in two dimensions with four right angles. Area of a rectangle = length x width

A parallelogram is a quadrilateral with two parallel sides. The opposite sides equal in length

Area of a parallelogram = base x height

Hence, the correct statements are options (A), (B), and (D).

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The question seems to be incomplete the correct question would be:

A neighborhood was given a vacant lot in the shape of a rectangle on which to build a park. The neighborhood is

considering how to split up the area. Which statements about the formulas for finding areas are true? Check all that

apply.

A. The triangle and trapezoid area formulas have 1/2.

B. The parallelogram and rectangle formulas are both the same.

C. In the parallelogram formula, the bases are added.

D. In the trapezoid formula, the bases are added.

E. In the triangle formula, the sides are added, then multiplied by 1/2​

Answer:

[-4,2]

Step-by-step explanation:

From the given options, the SUM of Squared Deviations is not directly provided. However, the SUM of Squared Deviations can be calculated using the dataset. The SUM of Squared Deviations measures the dispersion or variability of a dataset by summing the squares of the differences between each data point and the mean of the dataset.

To calculate the SUM of Squared Deviations, we need the individual data points and the mean of the dataset. Once we have these values, we can follow these steps:

1. Calculate the mean of the dataset by summing all the data points and dividing by the total number of data points.

2. For each data point, subtract the mean and square the result.

3. Sum up all the squared values obtained from the previous step.

Based on the information provided, the specific dataset necessary to calculate the SUM of Squared Deviations is not given. Therefore, it is not possible to determine the exact value from the options provided (80, 88, 83, 89). The calculation requires the actual data values to derive an accurate result.

It's important to note that the SUM of Squared Deviations is a statistical measure used to quantify the dispersion or spread of a dataset. Without the dataset, it is not possible to calculate this measure accurately.

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The change in profit (ΔP) when the number of units (Δx) increases by 5, based on the given marginal profit function, is -18331.50

To find the change in profit (ΔP) when the number of units (Δx) increases by 5.

we need to evaluate the marginal profit function and multiply it by Δx.

The marginal profit function is given by dP/dx = 12.1(60 - 3x).

We are given the value of x as 121, so we can substitute it into the marginal profit function to find the marginal profit at that point.

dP/dx = 12.1(60 - 3(121))

= 12.1(60 - 363)

= 12.1(-303)

= -3666.3

Now, we can calculate the change in profit (ΔP) by multiplying the marginal profit by Δx, which is 5 in this case.

ΔP = dP/dx×Δx

= -3666.3 × 5

= -18331.5

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We need to find the inverse of the function gof (x). First we need to find the composite function gof (x) which is given by:

\(g(f(x)) = g(3x - 6)\)

= \((1/3)(3x - 6) + 1\)

= x - 1 + 1

= x

Thus,

gof (x) = x.

Now we need to find the inverse of the function gof (x) to obtain

\((gof)^-1 (x).\)

We have gof (x) = x

which implies\((gof)^-1 (x)\)

= gof (x)^-1

= x^-1

= 1/x,

x ≠ 0

Therefore,

\((gof)^-1 (x) = 1/x\)

which is option (3) (x+1) since 1/x can be written as 1/(x+1-1), where (x+1-1) is the denominator of 1/x.

Hence, the correct option is (3).

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To find (g(f))^-1 (x), substitute the expression for f(x) into g(x) and simplify. The composition of g(f) is x and its inverse is also x. Therefore, (g(f))^-1 (x) equals x.

To find (g(f))^-1 (x), we need to first find the composition of g(f) and then find its inverse. Start by substituting the expression for f(x) into g(x): g(f(x)) = g(3x-6) = \frac{1}{3}(3x-6) + 1 = x - 1 + 1 = x. So, g(f(x)) = x. Now, to find the inverse of g(f), we switch the x and y variables and solve for y: y = x. Therefore, (g(f))^-1 (x) = x.

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The maximum Number of  scholars in each row is 12. This means that the  scholars can be arranged in rows with an equal number of  scholars, and each row can have a  outside of 12  scholars.

To find the maximum number of  scholars in each row, we need to determine the  topmost common divisor( GCD) of the total number of  scholars in each section. The GCD represents the largest number that divides all the given  figures unevenly.  

Given that there are 24, 36, and 60  scholars in the three sections, we can calculate the GCD as follows    Step 1 List the  high factors of each number  24 =  23 * 31  36 =  22 * 32  60 =  22 * 31 * 51    

Step 2 Identify the common  high factors among the three  figures  Common  high factors 22 * 31    Step 3 Multiply the common  high factors to find the GCD  GCD =  22 * 31 =  4 * 3 =  12  

 thus, the maximum number of  scholars in each row is 12. This means that the  scholars can be arranged in rows with an equal number of  scholars, and each row can have a  outside of 12  scholars.

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Answer:

0.251

Step-by-step explanation:

for a normal distribution question, we need to use the z-score formula for finding the area (probability).

use the z-score formula to convert the values.

z = (X - υ) / σ

where X is the test statistic, υ is the mean, σ is the standard deviation.

z = (4 - 5) / 1.5

= -0.67

in the z-table, find -0.6 down the side column and 0.07 on the top row. the number in the table where these two meet is 0.25143. this is the area to the left of z = -0.67. this is what we want for this question since we want an orange that weighs less than 4oz.

that means that the probability is 0.251 to nearest thousandth

The amount you must deposit every year if your goal is for the present value of your savings to be equal to $4,462 is $279.28.

Let the amount you need to deposit every year = P

Thus, the amount of money you will have after 10 years at an interest rate of 9% per annum = $4462

Using the formula of present value,

PV = FV/(1 + r)n

Where,

PV = present value of your savings

FV = future value of your savings

r = rate of interest

n = time period of saving

Substituting the given values,

4462 = FV/(1 + 0.09)10

Now, to find FV, we will have to multiply P by the sum of the present value of an annuity of $1 at an interest rate of 9% for ten years. This sum can be found using the formula,

A = [r(1 + r)n]/[(1 + r)n - 1]

A = [0.09(1 + 0.09)10]/[(1 + 0.09)10 - 1]

A = 0.09 × 6.4177443

A = 0.577596989

A = 0.58 (rounded to two decimal places)

Thus,

FV = P × A = P × 0.58 = 0.58 P

Therefore,

4462 = 0.58 P × (1 + 0.09)10

Simplifying the above equation, we get,

4462 / [(1 + 0.09)10 × 0.58] = P

P ≈ 279.28

Therefore, the amount you need to deposit every year is $279.28 (rounded to two decimal places).Hence, the required answer is $279.28.

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The mean of the number of hours spent watching television is 15.75

The mean absolute deviation of the number of hours spent watching television is 6.625.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

(10 +  11 + 22 + 7 + 17 + 17 + 20 + 31 + 0 + 12 + 19 + 23) / 12 = 189/12 = 15.75

Mean absolute deviation is the average of the sum of the absolute difference between the numbers and the mean.

MAD =  1/n ∑ l x - m(x) l

(|10 - 15.75) + |11 - 15.75| + |22 - 15.75| + |7 - 15.75| + |17 - 15.75|+ |17 - 15.75| + |20 - 15.75| + |31 - 15.75| + |0 - 15.75| + |12 - 15.75| + |19 - 15.75| + |23 - 15.75|

= (5.75 + 6.75 + 6.25 + 8.75 + 1.25 + 1.25 + 4.25 + 15.25 + 15.75 + 3.75 + 3.25 + 7.25) / 12 = 6.625

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Answer:

12

Step-by-step explanation:

Step 1: plug 2 into x

–3(2) + 1.5 + 2.5(2) – 4.5 + 8(2)

Step 2: simplify

-6 + 1.5 + 5 - 4.5 + 16

Step 3: add all the numbers

-6 + 1.5 + 5 - 4.5 + 16 = 12

Answer:

12

Step-by-step explanation:

-3(2)+1.5+2.5(2)-4.5+8(2)

-6+1.5+5-4.5+16

-6+6.5-4.5+16

-6+6.5+11.5

-6+18

12

Answer:

they are reciprecants of eachother

Answer:

D. is not right triangle

Step-by-step explanation:

10²+ 49² = 2501 ≠ 50²

None of the statements a, b, c, or d can be determined to be true based solely on x ⇒ y and y ⇒ z.

Given that x ⇒ y and y ⇒ z, we can determine the valid implication between x and z.

To evaluate the possible truth values, let's consider the following cases:

If x is true and y is true:

Since x ⇒ y, the implication holds.

If y ⇒ z, the implication holds.

Therefore, z can be true in this case.

If x is true and y is false:

Since x ⇒ y, the implication does not hold.

The truth value of y ⇒ z is not relevant in this case.

Therefore, we cannot determine the truth value of z.

If x is false:

Since x ⇒ y, the implication holds vacuously, regardless of the truth value of y.

The truth value of y ⇒ z is not relevant in this case.

Therefore, we cannot determine the truth value of z.

Based on the above analysis, we cannot definitively conclude the truth value of z from the given information. Therefore, none of the statements a, b, c, or d can be determined to be true based solely on x ⇒ y and y ⇒ z.

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Answer:

B. 15x+7

Step-by-step explanation:

8x + 7

+ =15x +7

7x - 9

Answer:

I think its would be d

Step-by-step explanation:

the distributive property

Answer:

It D. yigigihihijojjvjhjbhhjhj

Step-by-step explanation:

\( { - z}^{6} \\ z = - 3\)

\( - {( - 3)}^{6} \\ = - 1 \times ( - 3 \times - 3 \times - 3 \times - 3 \times - 3 \times - 3)\)

= -1 × 729

= -729

To determine the shape of the distribution based on the given set of data, we can examine its skewness.

Skewness is a measure of the asymmetry of a distribution. If the distribution is symmetric, it means that the data is evenly distributed around the central point, and the left and right tails are of equal length.

On the other hand, if the distribution is positively skewed, it indicates that the right tail is longer or more spread out compared to the left tail. Conversely, if the distribution is negatively skewed, the left tail is longer or more spread out than the right tail.

Now, let's look at the data: 5, 54, 33, 12, 31, 5.

To determine the shape of the distribution, we can calculate the skewness. However, since one of the values in the data, "5A," is not clearly defined, it is not possible to accurately calculate the skewness and determine the shape of the distribution.

Please provide a valid value for the sixth observation, and I'll be happy to assist you further in determining the shape of the distribution.

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Answer:XDDXXDXD

DXDXXDXDDXDXDXDXXDDXDEDXXDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

Step-by-XDDXDXDXstep explanation:

seria tu cacá XDXDXDXDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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The answer doesn't exist for lim x → 0 tan−1(ln(x)).

To find the limit of the function as x approaches 0, lim(x→0) arctan(ln(x)), we need to analyze the behavior of the function near x = 0.

1. Consider the domain of the function. The natural logarithm ln(x) is only defined for x > 0, so we cannot evaluate the function at x = 0. However, we can still analyze the limit as x approaches 0 from the right.

2. As x approaches 0 from the right (x → 0+), the natural logarithm ln(x) approaches negative infinity (ln(x) → -∞).

3. The arctan function is continuous and has horizontal asymptotes at y = -π/2 and y = π/2. When its argument approaches negative infinity (ln(x) → -∞), the arctan function approaches its horizontal asymptote at y = -π/2.

Therefore, the limit of the function as x approaches 0 from the right is -π/2: lim(x→0+) arctan(ln(x)) = -π/2.

Since the function is not defined for x ≤ 0, the limit as x approaches 0 does not exist. Your answer is DNE (does not exist).

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Answer:

See below picture.

Explanation:

y=2 has a y-intercept of 2, so we start graphing there. with most equations, we would follow the slope starting from that point, but y=2 doesn't have a slope. The 2 stays going all the way "across" for all x-values. I used demos to graph.

True. If the derivative (dy/dx) of a function f(x) is zero at a particular value of x, then the slope of the tangent line at that point is also zero, which means it is a horizontal line.

A tangent line is a straight line with the same slope as the curve it touches at a single point on a curve. A local approximation of the curve close to the point of contact is provided. Finding the slope of the curve at a given location, which is determined by the derivative of the curve at that position, is necessary to determine the equation of a tangent line to a curve at that point. The equation of the tangent line is then written using the point-slope form of a line. Calculus relies on tangent lines to help students comprehend how functions and their derivatives behave.

This is because the derivative represents the rate of change (slope) of the function at any given point, and if it is zero, then the function is not changing (not curving) at that point.

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The amount Thabang will receive if they decided to share their money according to hour is 380, 50 cents pieces of the container.

We know that Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents.

We also know that Thabang worked three hours and Nidhu worked for two hours.

Therefore, let the number of 50 cents coins in the container be "x".

We know that the total number of coins in the container is 600, so we can write, x + 220 = 600

Solving for x, we get,

x = 600 - 220

x = 380

Therefore, there are 380, 50 cents pieces in the container. The amount Thabang will receive if they decided to share their money according to hour is 380, 50 cents pieces of the container.

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Complete question: Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents. Thabang and his friend Nidhu share a job of cleaning a neighbor's yard and they were paid R400. Thabang worked three hours and Nidhu worked for two hours. Determine the amount Thabang will receive if they decided to share their money according to hours.​

Answer:

x=1

Step-by-step explanation:

Distribute 5/8 to x and -1/3 which will result you in 5/8x - 5/24

The equation now looks like this:

5/8x - 5/24= 5/12

Move -5/24 to the other side by adding 5/24 on both sides

5/8x - 5/24 + 5/24 = 5/12+5/24

(Multiply 2 and 5/12 on both the numerator and denominator which will result you to 10/12 add 5/24 which is 15/24)

Result:

5/8x=15/24

Multiply by 8/5 on both sides:

x=1

Answer:

(1.5, -4)

Step-by-step explanation:

( -1, -5) and (4, -3)

\((\frac{-1+4}{2} ,\frac{-5-3}{2} )\\\\(\frac{3}{2} ,\frac{-8}{2} )\\\\(1.5,-4)\)

The percent of sales tax was 6.8%.

Tax is a form of government imposed financial obligation which is required to be paid by individuals or businesses within a given jurisdiction. Tax is usually calculated as a percentage of income or profit and is used to fund public services such as education, health care, infrastructure, and other public goods. Generally, taxes are progressive, meaning that tax rates increase as income increases.

Step 1: Subtract the cost of the computer from the total cost including sales tax.

1,337.50 - 1,250 = 87.50

Step 2: Find the amount of sales tax paid by dividing the amount of sales tax by the cost of the computer.

87.50 / 1,250 = 0.07

Step 3: Convert the decimal to a percent by multiplying it by 100.

0.07 x 100 = 7%

So ,The percent of sales tax was 7%.

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