HURRY PLS I NEED IT
What is the purpose of apportionment? (its ideal, value, or vision)

∫[4, 6] f(x) dx = ∫[4, 6] (18x - 3) dx = [9x^2 - 3x] evaluated from 4 to 6 = (9(6)^2 - 3(6)) - (9(4)^2 - 3(4)).

∫[0, 2] f(x) dx = ∫[0, 2] (18x - 3) dx = [9x^2 - 3x] evaluated from 0 to 2 = (9(2)^2 - 3(2)) - (9(0)^2 - 3(0)).

E(x) = ∫[0, ∞] x f(x) dx = ∫[0, ∞] x(18x - 3) dx = [3x^3 - (3/2)x^2] evaluated from 0 to ∞ = lim(a→∞) [(3a^3 - (3/2)a^2) - (3(0)^3 - (3/2)(0)^2)].

a) To find the probability that the television set lasts between 4 and 6 years, we need to calculate the integral of the density function f(x) over the interval [4, 6]. Since the density function is given by f(x) = 18x - 3 for 0 ≤ x < 3 and 0 for x ≥ 3, we have:

∫[4, 6] f(x) dx = ∫[4, 6] (18x - 3) dx = [9x^2 - 3x] evaluated from 4 to 6 = (9(6)^2 - 3(6)) - (9(4)^2 - 3(4)).

b) To find the probability that the television set lasts at least 5 years, we need to calculate the integral of the density function f(x) over the interval [5, ∞). However, since the density function is zero for x ≥ 3, the integral over this interval is zero.

c) To find the probability that the television set lasts less than 2 years, we need to calculate the integral of the density function f(x) over the interval [0, 2]. Since the density function is given by f(x) = 18x - 3 for 0 ≤ x < 3 and 0 for x ≥ 3, the integral becomes:

∫[0, 2] f(x) dx = ∫[0, 2] (18x - 3) dx = [9x^2 - 3x] evaluated from 0 to 2 = (9(2)^2 - 3(2)) - (9(0)^2 - 3(0)).

d) To find the probability that the television set lasts exactly 4.18 years, we need to evaluate the density function f(x) at x = 4.18. Plugging in the value of x into the density function, we get f(4.18) = 18(4.18) - 3.

e) To find the expected value of the number of years that the television set lasts, we need to calculate the integral of xf(x) over the entire range of x, which is [0, ∞). The expected value is given by:

E(x) = ∫[0, ∞] x f(x) dx = ∫[0, ∞] x(18x - 3) dx = [3x^3 - (3/2)x^2] evaluated from 0 to ∞ = lim(a→∞) [(3a^3 - (3/2)a^2) - (3(0)^3 - (3/2)(0)^2)].

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The missing side length BE can be found by using the proportion of corresponding side lengths in similar triangles. We can set up the proportion AB/AD = BE/DF and solve for BE.

To find the missing side length in similar triangles, we can use the fact that corresponding side lengths are proportional. In other words, if two triangles are similar, then the ratio of any corresponding side lengths will be the same.

This allows us to set up a proportion with the known side lengths and the missing side length, and solve for the missing side.

For example, in the given problem, we have two similar triangles ABC and ADEF, with corresponding side lengths AB and AD, BC and DE, and AC and DF. We are given the values of AB, BC, AD, and DF, but we need to find the value of BE. We can set up the proportion AB/AD = BE/DF, which tells us that the ratio of AB to AD is equal to the ratio of BE to DF. We can then cross-multiply to get AB x DF = BE x AD, and solve for BE by dividing both sides by AD.

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4.875.............................

Answer:

D

Step-by-step explanation:

divide 3/4 and we will get: 0.75 x 650 then we solve 0.75 x 650 and we will get: 4.875

The probability that the coin will show tails and the cube will show a three, four, or six is 1/4.

The probability of two independent events occurring, we multiply their individual probabilities.

Let's start by determining the probability of the coin showing tails.

Since it is a fair coin, there are two equally likely outcomes: heads or tails.

The probability of the coin showing tails is 1/2.

Next, we consider the number cube.

It is a standard six-sided die, and we want to find the probability of rolling a three, four, or six.

Out of the six possible outcomes (numbers 1 to 6), three of them satisfy our condition (3, 4, and 6).

The probability of rolling a three, four, or six is 3/6 or 1/2.

Now, we can find the probability of both events occurring by multiplying the probabilities together:

P(Tails and 3, 4, or 6) = P(Tails) × P(3, 4, or 6)

= 1/2 × 1/2

= 1/4

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Answer:

the length is 12 and the width is 9.

Step-by-step explanation:

The first step is always to assign letters to the variables.  We can call length L and width W.

Since all units are in cm, unit conversion is unnecessary.

Next, set up some equations.  L=2W-6 because of the first sentence of the problem.  Length times width equals area, so L*W=108.

Now that there are two equations and two variables, the next step is to solve the system.  I'm going to solve it by plugging in the right side of the first equation in for L in the second equation.  This gives me (2W-6)*W=108.  Distributing the W gives me 2W^2-6W=108, or W^2-3W-54=0.  Using the quadratic formula, I get that W=9.  Using the first equation, L=2*9-6=12.  So the length is 12 and the width is 9.

Answer:

Step-by-step explanation:

3x - 2y = 18

x -int

3x - 2(0) = 18

3x = 18

x = 6

(6,0)

3(0) - 2y = 18

-2y = 18

y = -9

(0, -9)

As per the given function, the equation of tangent line is y - e = e(x -1)

The term tangent line in math referred as a function y=f(x) can be calculate the slope by taking derivative m=f′(x) then at a given point (x1,y1) equation of tangent line is given by the formula y−y1=m(x−x1)

Here we have given the expression y = eˣ/x

Now, we have to calculate the tangent line for the given function,

Let us consider, Slope of the tangent line is written as,

=> m = dy/dx

Now, we have written it as,

=> dy/dx = eˣ/x

then the equation is equate with the slope, then  we get,

=> m = eˣ/x

When we put the value of x as 1, then we get

=> m = e

Here we know that the point value is (1, e)

Therefore, the equation of the tangent line is written as,

=> y - e = e(x -1)

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The range of x are;

1. x < -30

2. x > 8

3. x > 15

4. x < -2

A relationship between two expressions or values that are not equal to each other is called 'inequality.

1. -130 > 50x +20

-130-20> 50x

-150 > 50x

-150/50 > x

-30 > x

x < -30

2. -8(x-3) < -40

-8x +24< -40

collect like terms

-8x < -64

x > -64/-8

x > 8

3. 2x - 22 > 8

collect like terms

2x > 30

divide both sides by 2

x > 30/2

x > 15

4. -35 < -5(x+9)

-35 < -5x -45

collect like terms

10 < -5x

-2 > x

x < -2

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Answer:

Time goes down to 16.47 min

Step-by-step explanation:

Formula

Time to melt = k / Temperature      (I doubt it is this simple)

Givens

Temp = 70

Time = 20

k  =

Solution

20 = k / 70             Multiply both sides by 70

20*70 = k

k = 1400

Problem

What happens when Temp = 85?

Time = k / Temp

Time = 1400 / 85

Time = 16.47 Min

The chain rule is a formula used in calculus to find the derivative of a composition of functions. It is an important tool for solving problems in many areas of mathematics and science.

The chain rule formula can be stated as follows:

If y = f(g(x)), then the derivative of y with respect to x is given by:

dy/dx = (df/dg) * (dg/dx)

In other words, the derivative of y with respect to x is equal to the derivative of f with respect to g, multiplied by the derivative of g with respect to x.

Here, f and g are functions of x, and y is a function of g. The chain rule formula tells us how to find the derivative of y with respect to x, by taking into account the effect of both f and g on the function y.

The chain rule can be extended to more complex compositions of functions, by applying the formula repeatedly. For example, if y = f(g(h(x))), then the chain rule can be applied twice, as follows:

dy/dx = (df/dg) * (dg/dh) * (dh/dx)

This formula tells us how to find the derivative of y with respect to x, by taking into account the effects of all three functions f, g, and h on the function y.

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Based on the information provided, a) if X has a binomial distribution, n = 5 and p = 0.256. b) X can take values in the range of 0 to 5. c) The values of P(x) for x = 0, 1, 2, 3, 4 , 5 are 0.228, 0.392, 0.269, 0.093, 0.016, and  0.011 respectively. d) mean = 1.28 and standard deviation = 0.995.

a) If X has a binomial distribution n represents the number of tickets bought which is 5 and p represents the probability of winning a prize after taking a single ticket which is 0.256.

b) X can take values in the range of 0 to 5, which indicates the possible number of won tickets. Hence, x = 0, 1, 2, 3, 4, 5. c)

Using the binomial distribution formula, P (x) = nCx*p^x*(1 – p)^(n-x). Hence,

P(0) = 5C0*(0.256)^0*(1 – 0.256)^)(5-0) = 0.228

P(1) = 5C1*(0.256)^1*(1 – 0.256)^)(5-1) = 0.392

P(2) = 5C2*(0.256)^2*(1 – 0.256)^)(5-2) = 0.269

P(3) = 5C3*(0.256)^3*(1 – 0.256)^)(5-3) = 0.093

P(4) = 5C4*(0.256)^4*(1 – 0.256)^)(5-4) = 0.016

P(5) = 5C5*(0.256)^5*(1 – 0.256)^)(5-5) = 0.011

d) The mean and standard deviation of the distribution is given by:

mean = n*p = 5*0.256 = 1.28

standard deviation = √np(1 – p) = √5(0.256)(1 – 0.256) = 0.995

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Answer:

B 9

Step-by-step explanation:

We have 6 green socks, 18 purple socks, and 12 orange socks.

Adding more purple sock means 6 green socks, 18+x purple socks, and 12 orange socks.

We have a  probability of 60% of getting a purple sock.

P( purple) = number of purple socks / total

.60 = (18+x) / (6+18+x+12)

.60 = (18+x) / (36+x)

Multiply each side by 36+x

21.6 +.6x = 18+x

Subtract 18 from each side

3.6x +.6x = x

Subtract .6x from each side

3.6x = .4x

Divide each side by .4

9 =x

Jamal added 9 purple socks

Answer:

Step-by-step explanation:

first you have to make this an improper fraction my multiplying -3 by 11 then add the product of that to 6 and put it all over 11

\(-3\frac{6}{11}\) → \(-\frac{39}{11}\)

once you get this you have to do the reciprocal of this to get them to equal 1

\(-\frac{39}{11}\) → \(-\frac{11}{39}\)

then multiply the number by the reciprocal

\(-\frac{39}{11}* -\frac{11}{39}=\frac{429}{429}=1\)

Answer:

X = (1 - 6^2) / (2•6^6)

Step-by-step explanation:

Step 1: Subtract 6^2 from both sides:

6^2+2•6^3x - 6^2 = 1 - 6^2

Step 2: Divide both sides by 2•6^3:

(6^2+2•6^3x - 6^2) / (2•6^3) = (1 - 6^2) / (2•6^3)

Step 3: Simplify:

6^3x / (2•6^3) = (1 - 6^2) / (2•6^3)

Step 4: Divide both sides by 6^3:

x / (2•6^3) = (1 - 6^2) / (2•6^3) / (6^3)

Step 5: Simplify:

x = (1 - 6^2) / (2•6^3•6^3)

Step 6: Simplify further:

x = (1 - 6^2) / (2•6^6)

Explantion

In this equation, the goal is to solve for x. To do this, 6^2 was first subtracted from both sides of the equation. Then, both sides were divided by 2•6^3. This simplified the equation to x / (2•6^3) = (1 - 6^2) / (2•6^3). Then, both sides were divided by 6^3, which simplified the equation to x = (1 - 6^2) / (2•6^6). Therefore, x = (1 - 6^2) / (2•6^6).

To find the critical points of the function f(x,y)= x² + 18y² + 96x - 18y subject to the constraint 6x - 18y = 30, we can use the method of Lagrange multipliers.



Solving these equations simultaneously, we get:

x = -9, y = 1/2, λ = 7/4

Therefore, the critical point of the function is (-9, 1/2).
To find the critical points of the function f(x, y) = x² + 18y² + 9, subject to the constraint 6x - 18y = 30, using the method of Lagrange multipliers, follow these steps:

Step 1: Define the function and constraint.
Function: f(x, y) = x² + 18y² + 9
Constraint: g(x, y) = 6x - 18y - 30 = 0

Step 2: Set up the Lagrange multiplier equation.
∇f(x, y) = λ∇g(x, y)

Step 3: Compute the gradient of the function and the constraint.
∇f(x, y) = (df/dx, df/dy) = (2x, 36y)
∇g(x, y) = (dg/dx, dg/dy) = (6, -18)

Step 4: Set up the system of equations.
2x = λ(6)         (1)
36y = λ(-18)      (2)
6x - 18y - 30 = 0  (3)

Step 5: Solve the system of equations.
From (1): x = 3λ
From (2): y = -2λ
Plug x and y values from (1) and (2) into (3):
6(3λ) - 18(-2λ) - 30 = 0
18λ + 36λ - 30 = 0
54λ = 30
λ = 30/54 = 5/9

Step 6: Find the critical points.
x = 3λ = 3(5/9) = 5
y = -2λ = -2(5/9) = -10/9

The critical point of the function f(x, y) subject to the given constraint is (5, -10/9).

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The museum is submitting proposals to several foundations in the hope to gain(Option D) funds to build a tropical butterfly conservatory.

Sentence correction or sentence improvement is a type of grammatical practice where a sentence is given with a word or a phrase that requires grammatical changes or improvement.

Now, here, "to gain" is idiomatically incorrect over here. Thus, Option D is the part in the sentence where there is a fault and a correction needs to be made.

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Answer:

11 hours

Step-by-step explanation:

We first want to find the unit rate, mi/hr:  520 mi / 8 hr = 65 mi/hr.

We know that distance is the product of rate and time or d=rt

Thus, we have 715 = 65t, where t = 11 hours

It would take Deandre approximately 10.93 hours to drive 715 miles at the same rate he drove 520 miles in 8 hours.

To find out how long it would take Deandre to drive 715 miles at the same rate, we can use the concept of "distance equals rate multiplied by time" (d = rt).

We already know the distance (d) and rate (r) from the first scenario:

Distance (d) = 520 miles

Time (t) = 8 hours

Now, we need to find the time (t) for the second scenario when the distance is 715 miles.

Let's set up the equation using the same rate (r):

d = rt

For the second scenario:

Distance (d) = 715 miles

Rate (r) = Same rate as before

Time (t) = Unknown (what we want to find)

The equation becomes:

715 = r * t

Now, to find the time (t), we can rearrange the equation:

t = 715 / r

We know that the rate (r) is the same as in the first scenario, which is 520 miles in 8 hours. So, we can substitute r into the equation:

t = 715 / (520/8)

Now, divide 715 by (520/8):

t = 715 / (520/8) ≈ 10.93

Therefore, it would take Deandre approximately 10.93 hours to drive 715 miles at the same rate he drove 520 miles in 8 hours.

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Answer:

5. (2,-6)

6.no solution

7.(1,4)

8.(8,-2)

9.(-1,5)

10.

11.(-2,-9)

12.(-2,0)

Step-by-step explanation:

Answer: -3/14

Step-by-step explanation:

The end of the plank is sliding along the ground at a rate of approximately -0.08 m/s when it is 1.4 meters from the wall of the building. The negative sign indicates that the end of the plank is sliding in the opposite direction.

To find how fast the end of the plank is sliding along the ground, we can use related rates. Let's consider the position of the end of the plank as it moves along the ground.

Let x be the distance between the end of the plank and the wall of the building, and y be the distance between the end of the plank and the ground. We are given that dx/dt = 0.26 m/s, the rate at which the worker pulls the rope.

We can use the Pythagorean theorem to relate x and y:

x² + y² = 5²

Differentiating both sides of the equation with respect to time, we get:

2x(dx/dt) + 2y(dy/dt) = 0

At the given moment when x = 1.4 m, we can substitute this value into the equation above and solve for dy/dt, which represents the rate at which the end of the plank is sliding along the ground.

2(1.4)(0.26) + 2y(dy/dt) = 0

2(0.364) + 2y(dy/dt) = 0

0.728 + 2y(dy/dt) = 0

2y(dy/dt) = -0.728

dy/dt = -0.728 / (2y)

To find y, we can use the Pythagorean theorem:

x² + y² = 5²

(1.4)² + y² = 5²

1.96 + y² = 25

y² = 23.04

y = √23.04 ≈ 4.8 m

Substituting y = 4.8 m into the equation for dy/dt, we have:

dy/dt = -0.728 / (2 * 4.8) ≈ -0.0757 m/s

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Answer:

x= 416

Step-by-step explanation:

Hope this helps.

Sample 1: Mean=10.01, Standard deviation=13.90 Sample 2: Mean

=11.43, Standard deviation

=14.10

Sample size of 1st year = n1

= 1012Mean of 1st year sample

= X1 = 10.01Standard deviation of 1st year sample

= s1

= 13.90Sample size of 2nd year

= n2

= 1012Mean of 2nd year sample

= X2

= 11.43

Standard deviation of 2nd year sample = s2

= 14.10 Let us assume a significance level of α = 0.05, which implies that the critical region consists of 2.5% in both tails (since it is a two-tailed test).

Therefore, we do not have sufficient evidence to conclude that the mean number of hours per week spent on the Internet differs between 2010 and another year.

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Station A is at a distance of 28.83 miles from the storm

Sine rule is used to show the relationship between the sides of a triangle as well as their opposite angles. It is given by:

\(\frac{a}{sin(A)}= \frac{b}{sin(B)}=\frac{c}{sin(C)}\)

From the diagram:

Also:

Hence:

b = distance station A from the storm, c = AB = 27 miles

Using sine rule:

\(\frac{c}{sin(C)} =\frac{b}{sin(B)} \\\\\frac{27}{sin(27)}=\frac{b}{sin(29)} \\\\b=28.83\ miles \\\)

Station A is at a distance of 28.83 miles from the storm

Step-by-step explanation:

Looking at the graph, if you plot the point (-1,-4) you'll see that the point is on the area(red one, in the graph I attached) the graph covers, you can also put x=-1 and y=-1 to check if it's true or not

The user is prompted to enter the values of `x1`, `y1`, `x2`, and `y2`. After that, we have calculated the length and width of the rectangle

To complete the given question in C code,

we need to find the length and the width of the rectangle.

After that, we can multiply the length by the width to find the area of the rectangle. Here is the complete C code to solve the given question:```
#include
int main()
{
   int x1, y1, x2, y2;
   int length, width, area;
   
   print f("Enter the value of x1: ");
   scan f("%d", &x1);
   print  f("Enter the value of y1: ");
   scan f("%d", &y1);
   print f("Enter the value of x2: ");
   scan f("%d", &x2);
   print f("Enter the value of y2: ");
   scan f("%d", &y2);
   
   length = x2 - x1;
   width = y2 - y1;
   area = length * width;
   
   printf("Length = %d\n", length);
   printf("Width = %d\n", width);
   printf("Area = %d\n", area);
   
   return 0;
}```In the above code, we have declared four variables `x1`, `y1`, `x2`, and `y2` to store the coordinates of the two opposite vertices of the rectangle.

We have also declared three variables `length`, `width`, and `area` to store the length, width, and area of the rectangle respectively.

The user is prompted to enter the values of `x1`, `y1`, `x2`, and `y2`. After that, we have calculated the length and width of the rectangle using the following formulas:

`length = x2 - x1` and `width = y2 - y1`.

Finally,

we have calculated the area of the rectangle by multiplying the length and width of the rectangle.

The output of the above code is as follows:```
Enter the value of x1: 1
Enter the value of y1: 2
Enter the value of x2: 5
Enter the value of y2: 6
Length = 4
Width = 4
Area = 16```Thus, the length of the rectangle is 4, the width of the rectangle is 4, and the area of the rectangle is 16.

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The example matrix decomposition practice problems are LU Decomposition and QR Decomposition

Matrix decomposition is the process of breaking down a complex matrix into simpler components. It is a fundamental concept in linear algebra and is used extensively in various fields such as engineering, physics, and computer science. Matrix decomposition involves expressing a matrix as a product of two or more matrices that are easier to handle and manipulate. In this article, we will provide example matrix decomposition practice problems to help high school students understand this concept better.

LU decomposition involves expressing a matrix as a product of two matrices, one lower triangular matrix (L) and one upper triangular matrix (U). The process involves reducing the original matrix to row echelon form and then back-substituting to get the lower and upper triangular matrices.

QR decomposition involves expressing a matrix as a product of two matrices, one orthogonal matrix (Q) and one upper triangular matrix (R). The process involves applying the Gram-Schmidt process to the columns of the matrix.

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Learn how to decompose matrices into LU and QR forms with step-by-step example problems.

Example 1:

Decompose the matrix A into LU form:

A = [2, 4; 3, 8]

Step 1: Find L and U using Gaussian elimination:

[2, 4; 3, 8] ≈ [1, 2; 0, 1] × [2, 4; 0, 2]

Step 2: Write the final decomposition:

A = [1, 2; 0, 1] × [2, 0; 0, 2]

Example 2:

Decompose the matrix B into QR form:

B = [1, 2; -2, -4]

Step 1: Find Q and R using the Gram-Schmidt process:

[1, 2; -2, -4] = [1/sqrt(5), 2/sqrt(5); -2/sqrt(5), -4/sqrt(5) ] × [sqrt(5), 0; 0, sqrt(5)]

Step 2: Write the final decomposition:

B = [1/sqrt(5), 2/sqrt(5); -2/sqrt(5), -4/sqrt(5) ] × [sqrt(5), 0; 0, sqrt(5)]

In conclusion, A = [1, 2; 0, 1] × [2, 0; 0, 2] and B = [1/sqrt(5), 2/sqrt(5); -2/sqrt(5), -4/sqrt(5) ] × [sqrt(5), 0; 0, sqrt(5)]

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the statement that is true is that the second variety of tomatoes had a higher weight and a higher variability compared to the first variety.

This can be inferred from the mean weight of the second variety being 3.4 ounces and the mean weight of the first variety being 1.3 ounces. Additionally, the mean absolute deviation for the second variety is 1.67 ounces, which is higher than the mean absolute deviation for the first variety which is 0.53 ounces.

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Answer:

C, both plans will work for achieving the goal.

Step-by-step explanation:

For plan A, you must multiply 7.20 by 9, then multiply the product by 8. The answer is 526.4 This means that plan A will work, and more than the original goal will be saved up.

For plan B, you must multiply 6.50 by 15, then multiply the product by 6. The answer is 585. This is more than the original goal, so plan B would work as well.

This means that C is correct, because both plans will work for achieving the goal.

Answer:

C

Step-by-step explanation:

Edged 2022

Answer:

it is 18 mile

Step-by-step explanation:

12mile = 60 min

x = 90 min

we cris cross the equation and

we found x=18 mile