MATHEMATICS COLLEGE

The floor of a shed given on the right has an area of 44 square feet . The floor is in the shape of a rectangle whose length is 3 less than twice the width. Find the length and width of the floor of the shed.

Answers

Answer 1

Answer:

Answer:

The length and width of the floor of the shed are 8 feet and 5.5 feet, respectively.

Step-by-step explanation:

Given that the shape of the shed is a rectangle, the expression for the area is:

$A = w \cdot l$

Where $w$ and $l$ are the width and length of the shed, measured in feet. In addition, the statement shows that $l = 2\cdot w - 3\,ft$ . Then, the equation of area is expanded by replacing length:

$A = w\cdot (2\cdot w - 3)$

$A = 2\cdot w^(2) - 3\cdot w$

If $A = 44\,ft^(2)$ , then, a second-order polynomial is formed:

$2\cdot w^(2)-3\cdot w - 44 = 0$

The roots of this equation are found via General Equation for Second-Order Polynomials:

$w_(1) = (11)/(2)\,ft$ and $w_(2) = -4\,ft$

Only the first roots is a physically reasonable solution. Then, the length of the shed is:

$l = 2\cdot \left((11)/(2)\,ft \right)-3\,ft$

$l = 8\,ft$

The length and width of the floor of the shed are 8 feet and 5.5 feet, respectively.

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Follow these steps to prove the given quadrilateral is a parallelogram 1. determine the slope of AB

Which of the following is the correct factorization of the polynomial below? 8x3 + 64y3 A. (4x + 4y) (2x+8y) B. (2x + 4y)(4x2 - 8xy + 16y2) C. (4x + 2y)(4x2 - 2xy + 16y?) D. The polynomial is irreducible.

Answers

Answer:

B. (2x+4y)(4x2-8xy+16y2)

Step-by-step explanation:

hope this helps!

Estimate the total budget in millions of dollars.

Answers

it C 40 million your welcome.

If x1, x2, . . . , xn are independent and identically distributed random variables having uniform distributions over (0, 1), find (a) e[max(x1, . . . , xn)]; (b) e[min(x1, . . . , xn)].

Answers

Denote by $X_((n))$ the maximum order statistic, with $X_((n))=\max\{X_1,\ldots,X_n\}$ , and similarly denote by $X_((1))$ the minimum order statistic. Then the CDF for $X_((n))$ is

$F_{X_((n))}(x)=\mathbb P(X_((n))\le x)$

In order for there to be some $x$ that exceeds the value of $X_((n))$ , it must be true that $x$ exceeds the value of all the $X_i$ , so the above is equivalent to the joint probability

$F_{X_((n))}(x)=\mathbb P(X_1\le x,\ldots,X_n\le x)$

and since the $X_i$ are i.i.d., we have

$F_{X_((n))}(x)=\mathbb P(X_1\le x)\cdots\mathbb P(X_n\le x)=\mathbb P(X_1\le x)^n$
$\implies F_{X_((n))}(x)=F_X(x)^n$

where $X\sim\mathrm{Unif}(0,1)$ . We have

$F_X(x)=\begin{cases}0&\text{for }x<0\nx&\text{for }0\le x\le1\n1&\text{for }x>1\end{cases}$

and so

$F_{X_((n))}(x)=\begin{cases}0&\text{for }x<0\nx^n&\text{for }0\le x\le1\n1&\text{for }x>1\end{cases}$
$\implies f_{X_((n))}(x)=\begin{cases}nx^(n-1)&\text{for }0<x<1\n0&\text{otherwise}\end{cases}$
$\implies\mathbb E[X_((n))]=\displaystyle\int_0^1xnx^(n-1)\,\mathrm dx=n\int_0^1x^n\,\mathrm dx=\frac n{n+1}$

Using similar reasoning, we can find the CDF for $X_((1))$ . We have

$F_{X_((1))}(x)=\mathbb P(X_((1))\le x)=1-\mathbb P(X_((1))>x)$
$F_{X_((1))}(x)=1-\mathbb P(X_1>x,\ldots,X_n>x)=1-\mathbb P(X_1>x)^n$
$F_{X_((1))}(x)=1-(1-\mathbb P(X\le x))^n=1-(1-F_X(x))^n$
$\implies F_{X_((1))}(x)=\begin{cases}0&\text{for }x<0\n1-(1-x)^n&\text{for }0\le x\le1\n1&\text{for }x>1\end{cases}$
$\implies f_{X_((1))}(x)=\begin{cases}n(1-x)^(n-1)&\text{for }0<x<1\n0&\text{otherwise}\end{cases}$
$\implies\mathbb E[X_((1))]=\displaystyle\int_0^1xn(1-x)^(n-1)\,\mathrm dx=\frac1{n+1}$

Final answer:

The expected values of the maximum and minimum of independent and identically distributed (iid) uniform random variables, x1, x2, ..., xn, are given by E[max(x1, ..., xn)] = n / (n + 1) and E[min(x1, ..., xn)] = 1 / (n + 1) respectively.

Explanation:

In mathematics, particularly in probability theory and statistics, the question is related to independent and identically distributed (iid) random variables with a uniform distribution. The expected value or mean (E) of the maximum (max) and minimum (min) of these random variables is sought.

(a) The expected value of the max of 'n' iid uniform random variables, x1, x2, ..., xn, is calculated by integrating the nth power of x from 0 to 1. It can be found via the equation E[max(x1, ..., xn)] = n / (n + 1).

(b) Similarly, the expected value of the min of 'n' iid uniform random variables is acquired by doing (1 / (n + 1)). Hence, E[min(x1, ..., xn)] = 1 / (n + 1).

By understanding these, you could visualize the various outcomes of the random variables and their distributions, demonstrating how likely each outcome could occur.

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10 POINTS Solve for x:
2x-7=5x+13

x = -20/3
x = -7
x = 22/3

Answers

The answer is X= -20/3 :)

Subtract 2x to both sides and subtract 13 from both sides

-20 = 3x

Divide 3 from both sides to isolate x

-20/3=x

First do 5x - 2x and you get 3x.
Now the equation is -7 = 3x + 13.
Next do -7 - 13 and you get -20.
The final step is to do -20 divided by 3 and you get -20/3.

The answer is x = -20/3

At a given time, the length, L, of the shadow of an object varies directlyas the height of the object, H. If the shadow is 27 ft when the height of
the object is 12 ft, what is the height of the object if the shadow is 18 ft?

Answers

Answer:

8 ft

Step-by-step explanation:

Use the direct variation equation, y = kx, where k is a constant.

Change the equation to fit the variables: L = kH

Plug in the given length of the shadow and the height of the object, then solve for k:

L = kH

27 = k(12)

2.25 = k

So, the equation is L = 2.25H

Then, plug in 18 as L, and solve for H:

L = 2.25H

18 = 2.25H

8 = H

So, when the shadow is 18 feet, the height of the object is 8 ft

Final answer:

Using the concept of direct variation, we find that the constant of variation is 2.25. Subsequent substitution in the equation reveals that the object's height when the shadow is 18ft is 8ft.

Explanation:

The question involves the concept of direct variation in mathematics. In direct variation, two quantities increase or decrease together to keep their ratio constant. This concept is given by the equation Y = kX, where Y and X are the quantities and k is a constant.

In our situation, the length of the shadow (L) varies directly with the object's height (H), i.e., L = kt. We are given that L=27ft when H=12ft, we can find the constant k by solving the equation 27ft = k * 12ft. This will get us k = 27ft/12ft = 2.25.

Now, we can determine the object's height if the shadow is 18ft. By substituting the values into the equation, we get 18ft = k * H. Substituting the value of k (2.25) will yield H = 18ft /2.25 = 8ft. Hence, the object's height when the shadow is 18ft is 8ft.

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8(13 + 2y)Which expression is equivalent to the expression above?
13 + 16y
B
16 + 104y
C
104 + 16y
D.
104 + 2y

Answers

It’s answer C. You multiply 8 & 13, which will give you 104. Then, multiply 8 & 2y, which will also give you 16y.

Answer:

Step-by-step explanation:

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