POSSIBLE POINTS
A town has a population of 12,300 and grows at a rate of 3.5% per year. What will the population be after 6 years? Round your answer to the nearest
whole number

Answer:

6

Step-by-step explanation:

Answer:

The temperature at 11:00 a.m. is 14 °F

Step-by-step explanation:

Let us list the information in the question

→ The temperature at 7:00 a.m. is - 7 °F

→ The temperature increases 21 °F during 4 hours

→ We need to find the temperature at 11:00 a.m.

∵ The temperature increases 21 °F during 4 hours

∵ The time 4 hours after 7: 00 a.m. is 11:00 a.m.

→ That means add 21 °F to - 7 °F to find the temperature at 11:00 a.m.

∴ The temperature at 11:00 a.m. = -7 °F + 21 °F

∴ The temperature at 11:00 a.m. = 14 °F

The temperature at 11:00 a.m. is 14 °F

Answer:

x=0

Step-by-step explanation:

if

h(x)= -5x+3

h(x)= 3

then

-5x+3 = 3

solve for x

-5x=0

x=0

The man should swim the entire distance at 2 miles per hour because the minimum walking speed that would make it quicker to walk the entire distance is infinity, which is not practical.

Let's assume the distance the man needs to travel is d miles. If the man swims at 2 miles per hour, he can swim the distance in d/2 hours. If he walks at a speed of x miles per hour, he can walk the distance in d/x hours. Therefore, the total time T it takes to travel the distance using swimming and walking is:

T = d/2 + d/x = d(1/2 + 1/x)

We want to find the walking speed x that minimizes the total time T. To do this, we can take the derivative of T with respect to x and set it equal to zero:

d(T)/dx = -d/2x^2 + d/x^2 = d/x^2(1/2 - 1) = -d/2x^2

Setting d(T)/dx = 0, we get:

d/2x^2 = 0

Solving for x, we get:

x = infinity

This means that the minimum walking speed for which it is quickest to walk the entire distance is infinity, which is not a practical solution. Therefore, the man should swim the entire distance at 2 miles per hour.

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Answer:

Follows are the solution to this question:

Step-by-step explanation:

\(95 \% \\) the confidence level for z:

\(\alpha = 1 - 95 \% \\\\\)

   \(= 1 - 0.95 \\\\ = 0.05\)

\(\to \frac{\alpha}{2} = \frac{0.05}{2} = 0.025\\\\\\to Z \ \frac{\alpha}{2} = Z_{0.025} = 1.96\)

Calculating the Margin of error:

\(E = Z\ \frac{\alpha}{2} \times ( \frac{\sigma}{\sqrt{n}})\)

   \(= 1.96 \times ( \frac{5000}{\sqrt{\sqrt{100}}})\\\\= 980\)

The population means estimate a 95 % confidence interval is:

\(\to \bar{x} \frac{+}{-} E\\\\ = \$ 90000 \frac{+}{-} 980\)

The given non-homogeneous differential equation can be written as:

- y''(t) + a*y'(t) + b*y(t) + c*y'(t) + d*y(t) = 3*e^t + t^2*cos(at)

To solve this differential equation, we first consider the corresponding homogeneous equation:

- y''(t) + a*y'(t) + b*y(t) + c*y'(t) + d*y(t) = 0

The solutions to the homogeneous equation can be found by assuming a solution of the form y(t) = e^(rt). Substituting this into the equation gives the characteristic equation:

r^2 + (a+c)*r + (b+d) = 0

The roots of the characteristic equation can be found using the quadratic formula:

r = (-b-c ± sqrt((a+c)^2 - 4(b+d))) / 2

Let the roots be denoted as r1 and r2.

If the roots are real and distinct (r1 ≠ r2), then the general solution to the homogeneous equation is:

y(t) = A*e^(r1*t) + B*e^(r2*t)

where A and B are constants determined by initial conditions.

Next, we find a particular solution to the non-homogeneous equation. Since the right-hand side contains terms of the form e^t and t^2*cos(at), we can assume a particular solution of the form:

y_p(t) = Ae^t + B*t^2*cos(at) + C*t^2*sin(at)

where A, B, and C are constants to be determined.

Substituting this particular solution into the non-homogeneous equation, we can solve for the values of A, B, and C.

Once the particular solution is found, the general solution to the non-homogeneous equation is given by the sum of the general solution to the homogeneous equation and the particular solution:

y(t) = y_h(t) + y_p(t)

where y_h(t) represents the general solution to the homogeneous equation and y_p(t) represents the particular solution to the non-homogeneous equation.

To solve the given non-homogeneous differential equation, we need to find the roots of the characteristic equation and determine the general solution to the homogeneous equation. Then, we find a particular solution by assuming a form that matches the right-hand side of the equation and solve for the constants. Finally, the general solution is obtained by adding the general solution to the homogeneous equation and the particular solution.

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Answer:

The measure of each interior angle of a regular polygon with 7 sides is about 128.6.

Step-by-step explanation:

hope this helps

The expression for the inverse function f⁽⁻¹⁾(X) is f⁽⁻¹⁾(X) = (12X² - 2)/3, where f(X) = (√(3x+2))/4.

To find the inverse function f⁽⁻¹⁾(X), we need to solve for X in terms of f⁽⁻¹⁾(X) in the equation:

f(X) = (sqrt(3x+2))/4

Start by replacing f(X) with Y:

Y = (sqrt(3x+2))/4

Swap X and Y:

X = (sqrt(3y+2))/4

Solve for Y:

4X = sqrt(3y+2)

(4X)² = 3y + 2

12X² - 2 = 3y

y = (12X² - 2)/3

Replace y with f⁽⁻¹⁾(X):

f⁽⁻¹⁾(X) = (12X² - 2)/3

Therefore, the expression for f⁽⁻¹⁾(X) is:

f⁽⁻¹⁾(X) = (12X² - 2)/3.)/3.

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Collect 250 or more more votes using an SRS.

You must carefully consider how you will choose a sample that is representative of the group as a whole if you want to make accurate conclusions from your data. It is referred to as a sampling method. You can use one of the following two main sampling techniques in your study:

Random selection is a key component of probability sampling, which enables you to draw robust statistical conclusions about the entire group.

Non-probability sampling entails non-random selection based on practicality or other factors, making it simple to gather data.

A simple random sample, also known as an SRS, is a subset of people (also known as a sample) picked at random from a larger group of people (also known as a population) with an equal probability. It is a method of choosing a sample at random.

explanation :

As everyone is aware, inferential statistics has the property of objectivity, which means that a statistic is an objective estimator of a population parameter. The confidence intervals adhere to this characteristic as well. Our sample mean is used in the computation of our confidence interval since we believe that the genuine population mean is somewhat close to it.

Confidence interval typically accounts for random error; relatively little systematic error is accounted for (i.e, bias). If we expand the sample size, we can eventually lower the bias in the confidence interval. Bias becomes zero when n equals infinity.

Therefore, employing an SRS to collect 250 more votes or more would be necessary to offset the issue.

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Answer: 4:1

Step-by-step explanation:

Divide by two to get in simplest form.

80 ÷ 2 = 40

20 ÷ 2 = 10

Make a ration with 40 and 10.

40:10

Make 40:10 simpler by dividing by 10.

40 ÷ 10 = 4

10 ÷ 10 = 1

Make 4 and 1 into a ration.

4:1

Answer:

4 : 1

Step-by-step explanation:

Given the ratio

80 : 20 ← divide both parts by 20

= 4 : 1 ← in simplest form

The correct statement is B. For all b, the equation Ax=b has a solution.

Since the columns of A are linearly independent, then the matrix A has full rank, and its column space is equal to the entire vector space in which it resides. This means that for any given vector b, we can find a linear combination of the columns of A that is equal to b, and therefore the equation Ax=b has a solution for all b.

Option A is incorrect, as there may be certain b vectors for which Ax=b has a solution.

Option C is incorrect, as the equation Ax=b may have a solution even when A has fewer columns than rows.

Option D is incorrect, as we can determine whether or not the equation Ax=b has a solution for all b by checking the rank of A.

Option E is incorrect, as the equation Ax=b may have a solution even when A has more columns than rows.

Option F is incorrect, as a square matrix may or may not have linearly independent columns, and therefore may or may not have a solution for all b.

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Answer:

Volume= area of cross section*height

so, volume of prism = A*h

The correct answer is option D

3(c) - 2 represents the total cost of three dance tickets at a cost of c each, less a one-time $2 discount.

         y = mx+b, where m is the slope and b is the y-intercept.

Based on the question. We have the parameters listed below.

The total cost of three dance tickets is 3c (at c for each)

One-time offer = $2

Because discounts are always subtracted from the total cost,

the equation represents,

the total cost of three dance tickets at a cost of c each, less a one-time discount $2

=  3(c) - 2

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The coordinates of the fourth point are given as follows:

(-2, 3).

The rule for a reflection over the x-axis is given as follows:

(x,y) -> (x, -y).

Meaning that the x-coordinate remains constant, while the y-coordinate has the signal exchanged.

Points D, C, C' and a fourth point become the vertices of a rectangle, hence the fourth vertex is:

D'.

Vertex D has the coordinates given as follows:

D(-2,-3).

Hence the coordinates of vertex D' are given as follows:

(-2,3).

(keep x-coordinate constant, exchange the sign of the y-coordinate).

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Step-by-step explanation:

b = 42

c = 138

plz mark my answer as brainlist plzzzz if you find it useful .

30% Chance to land on yellow

You gotta add all the colors and then divide the percent you want (in this case the number of times on yellow) and divide it by the total

Answer:

-3

Step-by-step explanation:

- 9/4 X 4/3

-9 X 1/3 =

-3

I hope this helps! If it does could you please mark me brainliest?

Depreciation is the accountant's estimate of the cost of a capital asset used in the production process, which is allocated over its useful life based on the benefits it generates.

Depreciation is a concept in accounting that recognizes the gradual reduction in value or usefulness of a capital asset over time. When a company purchases a capital asset, such as machinery, equipment, or vehicles, it incurs a cost that is expected to be spread over the asset's useful life. This cost is allocated as an expense called depreciation. The purpose of depreciation is to match the cost of the asset with the benefits it produces during its useful life. The estimation of depreciation involves considering factors like the initial cost of the asset, its expected useful life, and its residual value (the estimated value at the end of its useful life). By spreading the cost of the asset over its useful life, depreciation helps in accurately reflecting the consumption of the asset's value in the production process and provides a more accurate representation of the company's financial performance.

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If an independent variable in a multiple linear regression model is an exact linear combination of other independent variables, the model suffers from the perfect collinearity. Correct answer is A.

Perfect collinearity is the problem caused when two variables are in association linearly. When two variables are correlated to each other, then the collinearity is formed. When these are highly correlated ,  perfect collinearity is formed.

Perfect collinearity causes severe problem when present in the dataset. They cannot produce estimates in regression model by causing to defect in the least squares.

We can reduce this effect , by dropping few variables in the dataset which shows the exact linearly possible relation with other variables. We need to make sure that regression model fits into the dataset.

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Complete question is:

If an independent variable in a multiple linear regression model is an exact linear combination of other independent variables, the model suffers from the problem of

a) perfect collinearity

b) homoskedasticity

c) heteroskedasticity

d) multicollinearity

The mean of the sample (D) none of these alternatives is correct.

Therefore, the mean of the sample (D) none of these alternatives is correct.

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The correct question is given below:

The mean of the sample

a. is always smaller than the mean of the population from which the sample was taken

b. can never be zero

c. can never be negative

d. None of these alternatives is correct.

Answer:

D

Step-by-step explanation:

180 degrees in a triangle

102+(x+6)+(x+15)=180

remove parenthesis and combine like terms

123+2x=180

subtract 123 from both sides

2x=57

divide

x=28.5

substitute x for its actual value

28.5+6

angle A= 34.5

28.5+15

angle B= 43.5

The answer is that we cannot verify the similarity of triangles △PQR and △STU based on the given information. The missing ratios QR/TU and PR/SU cannot be determined without additional data or measurements. Only the ratio PQ/ST can be determined, which is equal to 4. Therefore, we do not have enough information to conclude that △PQR and △STU are similar triangles.

To verify that the triangles △PQR and △STU are similar, we can compare the ratios of their corresponding sides.

We have:

QR/TU = ?

PR/SU = ?

PQ/ST = 52/13 = ?

To find the missing values, we can use the property of similar triangles that states the corresponding sides of similar triangles are proportional.

Let's find the missing values one by one:

1. QR/TU:

We don't have enough information to determine the value of QR/TU. It is not possible to establish a ratio without additional data or measurements.

2. PR/SU:

Similarly, we cannot determine the value of PR/SU without more information or measurements.

3. PQ/ST:

Given PQ/ST = 52/13, we can simplify the ratio:

PQ/ST = (4*13)/(1*13) = 4/1 = 4.

Therefore, PQ/ST = 4.

Since we were unable to determine the values of QR/TU and PR/SU, we cannot conclude that △PQR and △STU are similar triangles based on the given information.

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The probability that the average final exam grade of the sample is between 75 and 80 is approximately 0.294, or 29.4%.

To solve this problem, we need to calculate the z-scores for the lower and upper bounds of the average final exam grade range, and then use the z-scores to find the corresponding probabilities from the standard normal distribution.

First, let's calculate the z-score for the lower bound:

z1 = (75 - 81.2) / (6.95 / sqrt(42))

z1 = -6.2 / (6.95 / sqrt(42))

z1 ≈ -2.512

Next, let's calculate the z-score for the upper bound:

z2 = (80 - 81.2) / (6.95 / sqrt(42))

z2 = -1.2 / (6.95 / sqrt(42))

z2 ≈ -0.528

Now, we can use the z-scores to find the corresponding probabilities using a standard normal distribution table or a calculator.

The probability that the average final exam grade of the sample is between 75 and 80 is equal to the probability of having a z-score between z1 and z2.

P(z1 < Z < z2) = P(-2.512 < Z < -0.528)

By looking up the probabilities corresponding to these z-scores from a standard normal distribution table or using a calculator, we find:

P(-2.512 < Z < -0.528) ≈ 0.294

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Answer:

3t-10

Step-by-step explanation:

g(h(t))=g(t-4)

=3(t-4)+2

=3t-12+2

=3t-10

Answer:

The system of equations is y = x - 4 and y = x² - 6

Step-by-step explanation:

The graph has a linear equation represented by a line and a quadratic equation represented by a parabola

The form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept

The form of the quadratic equation is y = a(x - h)² + k, where (h, k) are the coordinates of its vertex point and a is the coefficient of x²

let us use the graph to find each equation

→ Equation the line

∵ The line passes through points (-1, -5) and (2, -2)

∵ m = \(\frac{y2-y1}{x2-x1}\)

∴ m = \(\frac{-2--5}{2--1}=\frac{-2+5}{2+1}=\frac{3}{3}\)

∴ m = 1

∵ The line intersected the y-axis at point (0, -4)

∵ b is the value of y at x = 0

∴ b = -4

→ Substitute the values of m and b in the form of the equation above

∴ y = (1)x + (-4)

∴ y = x - 4

→ Equation the parabola

∵ The vertex of the parabola is (0, -6)

∴ h = 0 and k = -6

→ Substitute them in the equation

∴ y = a(x - 0)² + -6

∴ y = ax² - 6

→ To find a choose any point on the parabola and substitute x and y

   by its coordinated

∵ The point (2, -2) lies on the parabola

∴ x = 2 and y = -2

∵ -2 = a(2)² - 6

∴ -2 = 4a - 6

→ Add 6 to both sides

∵ -2 + 6 = 4a - 6 + 6

∴ 4 = 4a

→ Divide both sides by 4

∴ 1 = a

∴ y = (1)x² - 6

∴ y = x² - 6

The system of equations is y = x - 4 and y = x² - 6

Answer:

sorry I dont see the eqation I would help I just need to look at it - sorry (>-<)

Step-by-step explanation:

An inverse does not exist for a parabola.

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics.

It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

An inverse does not exist for a parabola.

One definition of a parabola includes a line and a point (the focus) (the directrix).

The directrix is not the main focus.

The locus of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.

A right circular conical surface and a plane parallel to another plane that is tangential to the conical surface intersect to form a parabola, which is also known as a conic section.

Therefore, an inverse does not exist for a parabola.

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In the given right triangle, b= √3, A is 30°, and B is 60°.

Trigοnοmetric functiοns in mathematics relate the angles and sides οf a right triangle. They are typically used in geοmetry, physics, and engineering tο sοlve prοblems invοlving triangles and periοdic phenοmena. The fundamental trigοnοmetric functiοns are:

Sine (sin) is the ratiο οf a side's length tο an angle's length relative tο a triangle's hypοtenuse.

The ratiο οf a side's length tο an angle's length tο the triangle's hypotenuse is knοwn as the sine (cs) functiοn.

Tangent (tan) is the ratiο οf the length οf the side next tο an angle tο the length οf the side next tο the angle.

Using the Pythagorean theorem:

\(b^2 = c^2 - a^2\)

\(b^2 = 2^2 - 1^2\)

\(b^2 = 3\)

b = √3

Using the sine functiοn:

sin A = οppοsite/hypοtenuse

sin A = 1/2

A = 30°

Using the cοsine functiοn:

cοs B = adjacent/hypοtenuse

cοs B = 1/2

B = 60°

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