I WILL GIVE YOU BRAINLIEST!
In 1990 the population of the Midwest was about 60 million. During the 1990s, the population of this area increased an average of 0.4 million a year. Write an equation for the word problem

Answer:

2\(x^3\) - 7\(x^2\) + 8x -3

Step-by-step explanation:

To multiply a binomial (2 terms) by a trinomial (3 terms):

Multiply the first term of the binomial by the each term of the trinomial.

Multiply the second term of the binomial by each term of the trinomial.

Combine the expressions and simplify.

(2x-3)*(\(x^2\)-2x+1)

(2x * \(x^2\)) + (2x * -2x) + (2x * 1)

(2\(x^3\)) + (-4\(x^2\)) + (2x)

(2x-3) * (\(x^2\)-2x+1)

(-3 * \(x^2\)) + (-3 * -2x) + (-3 * 1)

(-3\(x^2\)) + (6x) + (-3)

[2\(x^3\) + -4\(x^2\) + 2x] + [-3\(x^2\) + 6x + -3]

2\(x^3\) - 7\(x^2\) + 8x -3

give me brainliest please

Answer:

10feet

Step-by-step explanation:

Calculate the length from the base of the stair to the walls of the house.

We have the ladder extend 2 feet beyond the edge of the roof so 28-2=26feet

Let x is the length from the base of the stair to the wall of the house

(26)²=(24)²+x²

x²=(26)²-(24)²=676-576=100

x=√100=10feet

So the length from the base of the stair to the wall of the house is 10 feet.

Answer:

-I

Step-by-step explanation:

To find the volume of the solid obtained by rotating the region bounded by the graphs of y = x, y = 3 - x, and the x-axis about the x-axis, we can use the method of cylindrical shells.

First, let's determine the limits of integration. The region is bounded by the graphs of y = x and y = 3 - x. To find the x-values at which these curves intersect, we set them equal to each other:

x = 3 - x

2x = 3

x = 3/2

So, the limits of integration are x = 0 to x = 3/2.

Now, let's consider a small vertical strip within this region with thickness dx. The height of the strip is given by the difference between the two curves: h = (3 - x) - x = 3 - 2x. The length of the strip is the circumference of the resulting cylindrical shell, which is given by 2πx. The width or thickness of the shell is dx.

The volume of each cylindrical shell is then given by dV = 2πx(3 - 2x)dx.

To find the total volume, we integrate this expression with respect to x over the interval [0, 3/2]:

V = ∫(0 to 3/2) 2πx(3 - 2x)dx.

Evaluating this integral will give us the volume of the solid obtained by rotating the region about the x-axis.

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Answer:

hello!!

i like ur pfp! :)

Answer:

ill suck ya wang

Step-by-step explanation:5$ and ill suck yo wang to do your homework

Answer:

It is C.

Step-by-step explanation:

If you multiply 2 times 2 you get 4. Then multiply 4 by 5 and you get 20.

Therefore, it is C.

Answer:

565

Step-by-step explanation:

18-53=-35

-35+6=-29

18-2=16

16+-29=-13

-13+578=565

Could I please have BRAINLIEST?

This problem involves permutation since we are dealing with different ways that the colors of the 7 balls can be arranged distinctly. The equation of permutation is described as

There are 7 balls in this problem, hence, n = 7. Also, 7 colors are selected at each process of arranging them by color, hence, r = 7. Substitute it on the equation above and compute, we get

The expression above can be simplified as

Answer: E. 5040

the eigenvalues λn are given by \(\lambda n = n^2 = (4k)^2 = 16k^2\), and the corresponding eigenfunctions yn(x) are given by yn(x) = A sin(4kx), where k is an integer.

What is eigenvalues?

Eigenvalues are essential in linear algebra and are closely related to square matrices. An eigenvalue is a scalar value that describes how a matrix affects a vector along a particular direction.

The given boundary-value problem is y'' + λy = 0, with the boundary conditions y(0) = 0 and y(π/4) = 0. To find the eigenvalues and eigenfunctions, we can assume a solution of the form y(x) = A sin(nx), where A is a constant and n is a positive integer representing the eigenvalue.

Substituting this solution into the differential equation, we have:

y'' + λy = -A \(n^2\) sin(nx) + λA sin(nx) = 0

This equation holds for all x if and only if the coefficient of sin(nx) is zero. Thus, we obtain:

A \(n^2\) + λA = 0

Simplifying this equation, we have:

λ = \(n^2\)

So, the eigenvalues λn are given by λn = \(n^2\), where n is a positive integer.

To find the corresponding eigenfunctions yn(x), we substitute the eigenvalues back into the assumed solution:

yn(x) = A sin(nx)

Now, applying the boundary conditions, we have:

y(0) = A sin(0) = 0, which implies A = 0 (since sin(0) = 0)

y(π/4) = A sin(nπ/4) = 0

For the second boundary condition to be satisfied, we need sin(nπ/4) = 0, which occurs when nπ/4 is an integer multiple of π (i.e., nπ/4 = kπ, where k is an integer). This gives us:

n = 4k, where k is an integer

Therefore, the eigenvalues λn are given by \(\lambda n = n^2 = (4k)^2 = 16k^2\), and the corresponding eigenfunctions yn(x) are given by yn(x) = A sin(4kx), where k is an integer.

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Answer:

0.064

Step-by-step explanation:

ezy very very very ezy

The evaluations of the composite functions expressions and operations are presented as follows;

1. (f + g)(x) = 2·x² + 7·x + 3

(f - g)(x) = 7·x + 21

(f · g)(x) = x⁴ + 7·x³ + 3·x² - 63·x - 108

(f/g)(x) = f(x)/g(x) = (x² + 7·x + 12)/(x² - 9)

2. (f + x)(x) = 3·x - 2

(f - g)(x) = x + 4

(f · g)(x) = f(x) × g(x) = (2·x + 1) × (x - 3) = x⁴ + 7·x³ + 3·x² - 63·x - 108

(f/g)(x) = (2·x + 1)/(x - 3)

3. f[h(-9)] = 25

4. h[f(4)] = 20

5. g[h(-2)] = 10

6. The composite function that converts inches into miles is; n/63360

Composite function is a function that is applied to the result of another function.

Part 1: Operations of Functions

1. f(x) = x² + 7·x + 12 and g(x) = x² - 9, therefore;

(f + g)(x) = f(x) + g(x) = (x² + 7·x + 12) + (x² - 9) = 2·x² + 7·x + 3

(f - g)(x) = f(x) - g(x) = (x² + 7·x + 12) - (x² - 9) = 7·x + 21

(f · g)(x) = f(x) × g(x) = (x² + 7·x + 12) × (x² - 9) = x⁴ + 7·x³ + 3·x² - 63·x - 108

(f/g)(x) = f(x)/(g(x)) = (x² + 7·x + 12)/(x² - 9)

2. f(x) = 2·x + 1 and g(x) = x - 3

(f + g)(x) = f(x) + g(x) = 2·x + 1 + (x - 3) = 3·x - 2

(f - g)(x) = f(x) - g(x) = 2·x + 1 - (x - 3) = x + 4

(f · g)(x) = f(x) × g(x) = (2·x + 1)·(x - 3) = 2·x² - x - 3

(f/g)(x) = f(x)/(g(x)) = (2·x + 1)/(x - 3)

Part 2; 3. f(x) = x², g(x) = 5·x, and h(x) = x + 4

f[h(-9)] = (h(-9))² = (-9 + 4)² = 25

4. f(x) = x², g(x) = 5·x, and h(x) = x + 4

h[f(4)] = (f(4) + 4) = (16 + 4) = 20

5. f(x) = x², g(x) = 5·x, and h(x) = x + 4

g[h(-2)] = (h(-2) × 5) = (-2 + 4) × 5 = 10

6. The formula F = n/12 converts n inches into feet f, and m = f/5280 converts feet to miles m.

Let F(N) represent the function that converts inches to feet and let G(F) represent the function that converts feet to miles. Then the composition function that converts inches to miles is G(F(N))

G(F(N)) = G(n/12) = (n/12)×(1/5280) = n/63360

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Answer:

Step-by-step explanation:

0.5 ×10^5=5/10×10^5=5×10^4=50,000

To calculate the final price, we need to consider the sale discount and the sales tax rate. Here's the breakdown:

1. Calculate the discounted price:

$450.00 * (1 - 15%) = $450.00 * 0.85 = $382.50

2. Calculate the sales tax amount:

$382.50 * 8.25% = $31.56

3. Add the sales tax to the discounted price to find the total amount paid:

$382.50 + $31.56 = $414.06

Therefore, you would end up paying $414.06 to buy the TV after the discount and sales tax.

\(\frac{1}{2} | 261-161|\)The area of the quadrilateral whose vertices are A(1,1)B(7,−3),C(12,2) and D(7,21) is 49 square units

To find the area of the quadrilateral with vertices A(1, 1), B(7, -3), C(12, 2), and D(7, 21), you can follow these steps:

1. Divide the quadrilateral into two triangles: Triangle 1 (A, B, C) and Triangle 2 (A, C, D).

2. Calculate the area of each triangle using the   determinant method for the coordinates.

For Triangle 1 (A, B, C):
Area =   \(\frac{1}{2} | (1(-3)+7(2)+12(1) )- (-3(2)+1(12)+7(1)|\)
Area =\(\frac{1}{2} | (-3+14+12) - (-6+112+7)|\)
Area = \(\frac{1}{2} | (23-13)|\)
Area =\(\frac{1}{2} (10)\)

Area = 5 square units

For Triangle 2 (A, C, D):
Area =  \(\frac{1}{2} | (1(2)+12(21)+7(1))- (2(1)+21(7)+1(12)|\)
Area = \(\frac{1}{2} | (2+252+7)- (2+147+12)|\)
Area = \(\frac{1}{2} | 261-161|\)
Area = \(\frac{1}{2} (100)\)

Area = 44 square units

3. Add the areas of the two triangles to get the area of the quadrilateral:

Area of quadrilateral = Area of Triangle 1 + Area of Triangle 2 = 5 + 44 = 49 square units.

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Answer:

Step-by-step explanation:

Y=-2/3x-2

I cant truly graph it but the coordinates would be (0,-2) (3,-4) (6,-6) (9,-8)

The scale of measurement for the type of car(sedan, SUV,​ convertible, etc) is D. Nominal.

The scale of measurement is a way to categorize and describe the type of data collected in a study. In the case of the type of car, the data collected is categorical, meaning it falls into a specific category without any order or ranking. The categories don't have any meaningful mathematical relationships between them. This type of data is best described by the nominal scale of measurement.

It's important to understand the scale of measurement for a variable because it determines the type of statistical analysis that can be performed on the data.

Nominal data can be summarized using frequency tables and percentages, but more advanced statistical techniques like regression or correlation cannot be performed.

In conclusion, the type of car is a nominal variable, and it's important to identify the scale of measurement of a variable as it affects the type of analysis that can be performed on the data.

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Answer

The fundamental theorem of algebra is true with quadratic equation x^2-12x+12=-20 with zeros of 4 or 8.

A quadratic equation is an equation with the highest power of unknown to be 2. It is given in the form Ax^2+ Bx+ C= 0

 finding the roots or zeros of the equation x^2-12x+12=-20 can be done by factorization method;

we equate the equation to zero by bringing -20 to the LHS .

x^2-12x+12+20=0

x^2-12x+ 32 = 0

 find the factors of +32 that their sum will give -12

x^2-8x-4x+32=0

grouping the above equation

(x^2-8x)(-4x+32)= 0

x(x-8)-4( x-8)= 0

(x-4))(x-8) = 0

for the equation above to be true.

x-4=0 or x-8 = 0

: x=4 or x=8.

In conclusion, the algebra theorem is obeyed because the zeros of the equation are real numbers

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The probability of drawing 2 aces and 3 kings from a standard 52-card deck is 0.000002. To find the probability of drawing 2 aces and 3 kings, we need to first find the number of ways to choose 2 aces and 3 kings from the deck.

The total number of ways to choose 5 cards from a deck of 52 cards is given by the combination formula:

To find the probability of drawing 2 aces and 3 kings, we need to first find the number of ways to choose 2 aces and 3 kings from the deck. There are 4 aces and 4 kings in the deck, so the number of ways to choose 2 aces from 4 aces and 3 kings from 4 kings is given by:

Next, we need to find the number of ways to choose the remaining cards from the deck. There are 44 cards that are not aces or kings, so the number of ways to choose 5 cards from these 44 cards is given by:

Therefore, the total number of ways to draw 2 aces and 3 kings and 5 cards from the deck is:

Finally, the probability of drawing 2 aces and 3 kings from a standard 52-card deck is:

Therefore, the probability of drawing 2 aces and 3 kings from a standard 52-card deck is 0.000002.

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Answer:

20

Step-by-step explanation:

because 4.6 + 5.4 = 10

then you need to multiply 2 to 10 so its 20

Answer:

the answer is 20 meters

Step-by-step explanation:

The perimeter is 20 meters

The graph of the function f(x) = −15|x−40|+8 will be a piecewise linear function.

Graph explain: What is it?

A graph is defined as a mathematical structure that connects a collection of points to express a specific function. A pairwise relationship between the objects is established using it. The edges that connect the graph's vertices (also known as nodes) are its vertices (lines).

It will be a V-shape, with the vertex at x = 40 and y = 8.

On the left side of the vertex, the function will be decreasing, representing Tyra moving away from home.

On the right side of the vertex, the function will be increasing, representing Tyra moving towards home.

The vertex at x = 40 and y = 8 represents the point in time where Tyra reaches her furthest distance from home (8 miles) and then begins to head back towards home.

Key features of the graph in the context of the situation:

The vertex at x = 40 and y = 8 represents the point in time where Tyra reaches her furthest distance from home (8 miles) and then begins to head back towards home.

The left side of the vertex represents the time period when Tyra is moving away from home, and the right side represents the time period when Tyra is moving towards home.

The slope of the graph on the left side of the vertex is negative, indicating that Tyra is moving away from home at a decreasing rate, while the slope of the graph on the right side of the vertex is positive, indicating that Tyra is moving towards home at an increasing rate.

The y-intercept is at 8, which means Tyra starts 8 miles away from home.

The graph is symmetric about the y-axis because for every time x on the left side of the vertex, there is a corresponding time on the right side of the vertex.

The graph is not a function because for every x value, there are two y values, one for when Tyra is moving away from home and one for when Tyra is moving towards home.

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A skewed right distribution is most likely to result in the mean being substantially smaller than the median.

The mean and median are measures of central tendency used to describe the center of a distribution. In a skewed right distribution, the tail of the distribution extends towards the right, indicating a larger number of smaller values and a few extremely large values. This distribution shape is also known as positively skewed.

When a distribution is skewed right, the mean is typically pulled towards the larger values in the tail, making it larger than the median. However, there are scenarios where the mean can be substantially smaller than the median in a skewed right distribution.

This occurs when there are extremely large values in the tail that significantly affect the mean, but the bulk of the distribution remains concentrated on the smaller side. As a result, the mean can be pulled downward, making it smaller than the median.

On the other hand, in a symmetric distribution or a skewed left distribution (negatively skewed), where the tail extends towards the left with a larger number of larger values and a few extremely small values, it is less likely for the mean to be substantially smaller than the median. In these cases, the mean is typically closer to or larger than the median.

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Answer:

x = 14

Step-by-step explanation:

15² = x² + 6²

225 = x² + 36

189 = x²

√189 = x

x = 13.7

x = 14

Answer:

2/3

Step-by-step expl anation:

The table is an illustration of a quadratic regression model

The function that best models the data is y = -60.4x^2 +348.1x -334.2

To determine the function that models the data, we make use of a graphing calculator.

Using the graphing calculator, we have the following calculation summary

a = -60.4

b = 348.1

c = -334.2

A quadratic regression model is represented as:

y = ax^2 + bx + c

So, we have:

y = -60.4x^2 +348.1x -334.2

Hence, the function that best models the data is y = -60.4x^2 +348.1x -334.2

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By taking the quotients between the areas, we see that:

First we need to find the areas of the 3 shapes.

For the triangle, the area is:

T = 3*5/2 = 7.5

For the blue square, the area is:

S = 3*3 = 9

For the rectangle, the area is:

R = 10*6 = 60

Now, what is the probability that a random point lies on the triangle or in the square?

It is equal to the quotient between the areas of the two shapes and the total area of the rectangle, this is:

P= (7.5 + 9)/60 = 0.275

b) The area of the rectangle that is not the square is:

A = 60 - 9 = 51

Then the probability of not landing on the square is:

P' = 51/60 = 0.85

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The speed of the plane is the rate of change of distance over time

The speed of the plane should be 453.65 mph southwest

The speed of the wind is given as:

\(\mathbf{S_w = 38.7mph}\)

The expected speed of the plane is:

\(\mathbf{S_s = 452mph}\)

So, the actual speed is calculated using the following Pythagoras theorem

\(\mathbf{S_{sw}^2 = S_w^2 + S_s^2}\)

This gives

\(\mathbf{S_{sw}^2 = 38.7^2 + 452^2}\)

\(\mathbf{S_{sw}^2 = 205801.69}\)

Take square roots of both sides

\(\mathbf{S_{sw} = 453.65}\)

Hence, the speed of the plane should be 453.65 mph southwest

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The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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A cylindrical object is 3.13 cm in diameter and 8.94 cm long and weighs 60.0 g. The density of the cylindrical object is 0.849 g/cm^3.

To calculate the density, we first need to find the volume of the cylindrical object. The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius (half of the diameter) and h is the height (length) of the cylinder.

Given that the diameter is 3.13 cm, the radius is half of that, which is 3.13/2 = 1.565 cm. The length of the cylinder is 8.94 cm.

Using the values obtained, we can calculate the volume: V = π * (1.565 cm)^2 * 8.94 cm = 70.672 cm^3.

The density is calculated by dividing the weight (mass) of the object by its volume. In this case, the weight is given as 60.0 g. Therefore, the density is: Density = 60.0 g / 70.672 cm^3 = 0.849 g/cm^3.

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