Given any two events, e1 and e2, what does the probability p(e1 ∪ e2) represent?

Based on the calculations, the dimensions of the rectangle are

The diagonal of a rectangle can be defined as a line segment that connects any two (2) of its non-adjacent vertices together while dividing the rectangle into two (2) equal parts.

Mathematically, the length of diagonals of a rectangle can be calculated by using this formula:

d = √(l² + w²)

Where:

Since the ratio of the length to the width is 12:5, we have:

Width, w = 5l/12

Substituting the given parameters into the formula, we have;

169 = √(l² + (5l/12)²)

169² = l² + (5l/12)²

169² = l² + (25l²/144)

Length, L = 156 meters.

For the width, we have:

Width, w = 5l/12

Width, w = 5(156)/12

Width, w = 65 meters.

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Answer:

Step-by-step explanation: P(x 3), Q(7, -1) and PQ= 5 .

To Find :

The possible value of x.​

Solution :

We know, distance between two points in coordinate plane is given by :

Therefore, the possible value of x are 10 and 4.

The first integer is 5.

The second integer  is 10.

If an integer is higher than zero, it is positive; if it is lower than zero, it is negative. Zero can be either positive or negative. Since a b and c d, then a + c b + d, the ordering of integers is consistent with algebraic operations.

One integer is twice the other

so,

If one integer is x then

The other will be 2x.

Their product :

2x * x = 50

2x² = 50

x² = 50/2

x² = 25

x = √25

x = 5

the first integer is 5.

the second integer is 2x = 2 x 5

                                        = 10.

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In the given diagram, the value of the dashed side of rhombus OABC is 5

From the question, we are to determine the length of the dashed line (OA), in rhombus OABC

In the diagram, we can observe that the length of OA is the distance between point A and the origin (O).

Using the formula for calculating distance between two points,

d =√[(x₂-x₁)² + (y₂-y₁)²]

In the diagram,

The coordinate of the origin is (0, 0)

The coordinate of point A is (3, 4)

Thus,

x₁ = 0

x₂ = 3

y₁ = 0

y₂ = 4

Putting the parameters into the formula, we get

OA =√[(3-0)² + (4-0)²]

OA =√(3² + 4²)

OA =√(9+16)

∴ OA =√25

OA = 5

Hence, in the given diagram, the value of the dashed side of rhombus OABC is 5

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Answer: (-4, 0) and (4, 8)

Step-by-step explanation:

Looking at the graph, we can see where the line passes the parabola and can tell the solutions are (-4, 0) and (4, 8)

Answer: 10xy-12+15x-8y=(5x-4)*(2y+3).

Step-by-step explanation:

[tex]10xy-12+15x-8y=(10xy-8y)+(15x-12)=\\=2y*(5x-4)+3*(5x-4)=(5x-4)*(2y+3).[/tex]

The standard deviation of the x distribution is 0.2.

According to the statement

we have given that the the sample n is 64 and we have to find the standard deviation of the given sample.

So, For this purpose, we know that the

The standard deviation of the sample is the standard deviation of population divided by the square root of the length of the sample.

In this problem, we have that the value of alpha is

[tex]\alpha = 1.6[/tex]

Suppose that for aluminum alloy sheets of a particular type,

If X is the sample mean Young's modulus for a random sample of n = 64 sheets, and the standard deviation of the X distribution is given by

[tex]s = \frac{\alpha}{\sqrt{64} }[/tex]

then solve it then the standard deviation

s =  {1.6} / {8 }

s = 0.2

So, The standard deviation of the x distribution is 0.2.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Given that Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and 1.6 GPa, respectively.

a. If X is the sample mean Young's modulus for a random sample of n = 64 sheets, the sampling distribution of X centered at 70 GPa, and the standard deviation of the X distribution is given by

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Step-by-step explanation:

log 6 = log (2×3) = log 2 + log 3 = 0.3010+0.4771

=0.7781

Answer:

[tex]\sf \log_{10}6=0.7781[/tex]

Step-by-step explanation:

Given:

[tex]\sf \log_{10} 2 = 0.3010[/tex]

[tex]\sf \log_{10} 3 = 0.4771[/tex]

To find log₁₀ 6, first rewrite 6 as 3 · 2:

[tex]\sf \implies \log_{10}6=\log_{10}(3 \cdot 2)[/tex]

[tex]\textsf{Apply the log product law}: \quad \log_axy=\log_ax + \log_ay[/tex]

[tex]\implies \sf \log_{10}(3 \cdot 2)=\log_{10}3+\log_{10}2[/tex]

Substituting the given values for log₁₀ 3 and log₁₀ 2:

[tex]\begin{aligned} \sf \implies \log_{10}3+\log_{10}2 & = \sf 0.4771+0.3010\\ & = \sf 0.7781 \end{aligned}[/tex]

Therefore:

[tex]\sf \log_{10}6=0.7781[/tex]

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Answer:

$63.36

Step-by-step explanation:

The home audio system costs $264 wholesale.

The system's price had been increased by 60 percent at the electronics retailer.

Consequently, the increased cost is 60/100x264=$158.40.

The audio system's total cost is now $422.40 (264 + 158.40).

Given that Lori received a commission of = 15% on $422.40, her commission is now (15/100) x 422.40

= $63.36

The number of ways there are to move from (0, 0) to (7, 7) in the coordinate plane with movements of only one unit right or one unit up accordingly is; 49 while that such that y =x is; 7.

It follows from the task content that the movement intended on the coordinate plane is; from (0, 0) to (7, 7).

The number of ways to move such that movements of only one unit right or one unit up is; 7 × 7 = 49.

The number of ways for which y= x is therefore is; 7 as the movement is diagonal.

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Answer:

An arc of a circumference or of a circle mostly is a portion of the circumference. The length of an arc for all intents and purposes is simply the length of this portion of the circumference in a definitely major way. The circumference itself can particularly be considered an arc that goes around the circle in a fairly major way.

Answer:

11/6 + -2/5 +-13/10?

11/6 + (-2/5) + (-13/10)

43/30 - 13/10

2/15

The equation for the variable 'c' is c = d(q² + 1)/(q² - 1). By using simple arithmetic operations on the original equation, the required equation can be obtained.

An equation is a relationship between two expressions given by a mathematical statement.

There are different types of equations. They are linear equations, quadratic, polynomial, etc.

The given equation is

q = √((c + d)/(c - d))

Squaring on both, root gets canceled out

⇒ q² = (c + d)/(c - d)

⇒ q²(c - d) = (c + d)

⇒ cq² - dq² = c + d

Separating like terms  aside,

cq² - c = d + dq²

⇒ c(q² - 1) = d(q² + 1)

⇒ c = d(q² + 1)/(q² - 1)

Therefore, the required equation is c = d(q² + 1)/(q² - 1).

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For a pair of sample x and y values, the residual exists as the distinction between the observed sample value of y and the y value that exists indicated by utilizing the regression equation.

In regression analysis, the distinction between the observed value of the dependent variable and the predicted value exists named the residual.

A regression equation exists utilized in stats to estimate what relationship if any, exists between sets of data.

For a pair of sample x and y values, the residual exists as the distinction between the observed sample value of y and the y value that exists indicated by utilizing the regression equation.

Residual = observed y - predicted y.

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Answer:

5%

Step-by-step explanation:

price after discount :

9 600 - 9 600×40%

= 5760

Original price (price without profit) :

let x be the original price of the device.

x + x × 20% = 5760

Then

x = (5 760×100)÷120

  = 4 800

Original price increased by 30% :

4 800 + 4 800×30%

= 6 240

the discount needed to increase the profit by 10% :

[(9 600-6 240)÷9 600]×100

= 35%

Then

to increase the profit by 10% ,we have to reduce

the percent of discount to :

40% - 35%

= 5%

The terms through degree four of the Maclaurin series is [tex]f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....[/tex].

In this question,

The function is f(x) = [tex]\frac{sin(x)}{1-x}[/tex]

The general form of Maclaurin series is

[tex]\sum \limits^\infty_{k:0} \frac{f^{k}(0) }{k!}(x-0)^{k} = f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} +\frac{f'''(0)}{3!}x^{3}+......[/tex]

To find the Maclaurin series, let us split the terms as

[tex]f(x)=sin(x)(\frac{1}{1-x} )[/tex] ------- (1)

Now, consider f(x) =  sin(x)

Then, the derivatives of f(x) with respect to x, we get

f'(x) = cos(x), f'(0) = 1

f''(x) = -sin(x), f'(0) = 0

f'''(x) = -cos(x), f'(0) = -1

[tex]f^{iv}(x)[/tex] = cos(x), f'(0) = 0

Maclaurin series for sin(x) becomes,

[tex]f(x) = 0 +\frac{1}{1!}x +0+(-\frac{1}{3!} )x^{3} +....[/tex]

⇒ [tex]f(x)=x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+.....[/tex]

Now, consider [tex]f(x) = (1-x)^{-1}[/tex]

Then, the derivatives of f(x) with respect to x, we get

[tex]f'(x) = (1-x)^{-2}, f'(0) = 1[/tex]

[tex]f''(x) = 2(1-x)^{-3}, f''(0) = 2[/tex]

[tex]f'''(x) = 6(1-x)^{-4}, f'''(0) = 6[/tex]

[tex]f^{iv} (x) = 24(1-x)^{-5}, f^{iv}(0) = 24[/tex]

Maclaurin series for (1-x)^-1 becomes,

[tex]f(x) = 1 +\frac{1}{1!}x +\frac{2}{2!}x^{2} +(\frac{6}{3!} )x^{3} +....[/tex]

⇒ [tex]f(x)=1+x+x^{2} +x^{3} +......[/tex]

Thus the Maclaurin series for [tex]f(x)=sin(x)(\frac{1}{1-x} )[/tex] is

⇒ [tex]f(x)=(x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+..... )(1+x+x^{2} +x^{3} +......)[/tex]

⇒ [tex]f(x)=x+x^{2} +x^{3} - \frac{x^{3} }{6} +x^{4}-\frac{x^{4} }{6} +.....[/tex]

⇒ [tex]f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....[/tex]

Hence we can conclude that the terms through degree four of the Maclaurin series is [tex]f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....[/tex].

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Answer:

0 < r < 1

Step-by-step explanation:

That every sequence gets multiplied by a number less than 1 but more than 0

The law is

Common ratio or r must lies in between 0 and 1

It means

r is in (0,1)

The formula is

[tex]\boxed{\sf S_{\infty}=\dfrac{a}{1-r}}[/tex]

The store will break even after selling 35 books.

To find  what is the break-even point for this bookstore:

Given:

Let, n be the number of books.

Total costs = 12n + 105

The selling price of each book = $15

Total revenue = 15n

For breaking even, costs = revenue.

Therefore, the store will break even after selling 35 books.

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The equation be 38 + 2x - (64 - 2x) = 0 then the value of x = 6.5.

To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.

Let the day be x

38 + 2x - (64 - 2x) = 0

Subtract 38 from both sides

38 + 2x - (64 - 2x) - 38 = 0 - 38

Simplifying the above equation, we get

2x - (64 - 2 x) = -38

Expanding the above equation, 2x - (64 - 2x) = 4x - 64

4x - 64 = -38

Add 64 to both sides

4x - 64 + 64 = -38 + 64

Simplify

4x = 26

Divide both sides by 4

[tex]$\frac{4 x}{4}=\frac{26}{4}[/tex]

Simplifying the equation

[tex]$x=\frac{13}{2}[/tex]

The value of x = 6.5.

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Answer:

Step-by-step explanation:

The expression is:

Find its value when n = 3, substitute n with 3 in the expression:

The matching answer choice is B.

Answer:

Step-by-step explanation:

Add the segment LX, parallel to QP.

Recall the properties of midsegment:

We have:

Find the length of LX:

Since QP ║ LX ║ NM, the segment NM is the midsegment of ΔPLX.

Find the length of NM:

Answer:

no

Step-by-step explanation:

In a function, each "x" value [input] must have only one corresponding "y" value.

We know that points are written as (x, y)

Our points: {(3,-2), (1, 2), (-1,-4), (-1, 2)}

We can see that the x-input of -1 has two y-outputs, so this is therefore not a function

hope this helps! have a lovely day :)

Answer:

w = -11

Step-by-step explanation:

[tex]\sqrt{3 - 2w} = w + 6[/tex]

[tex](\sqrt{3 - 2w})^2 = (w + 6)^2[/tex]

[tex] 3 - 2w = w^2 + 12w + 36 [/tex]

[tex] w^2 + 14w + 33 = 0 [/tex]

[tex] (w + 11)(w + 3) = 0 [/tex]

[tex] w + 11 = 0 [/tex]   or   [tex] w + 3 = 0 [/tex]

[tex] w = -11 [/tex]   or   [tex] w = -3 [/tex]

When you square both sides of an equation, you must check all solutions for extraneous solutions.

Check w = -11.

[tex]\sqrt{3 - 2w} = w + 6[/tex]

[tex] \sqrt{3 - 2(-11)} = -11 + 6 [/tex]

[tex] \sqrt{3 + 22} = -5 [/tex]

[tex] \sqrt{25} = -5 [/tex]

[tex] 5 = -5 [/tex]

This is a false statement, so the solution w = -11 is extraneous since it does not satisfy the original equation.

Check w = -3.

[tex]\sqrt{3 - 2w} = w + 6[/tex]

[tex] \sqrt{3 - 2(-3)} = -3 + 6 [/tex]

[tex] \sqrt{3 + 6} = 3 [/tex]

[tex] \sqrt{9} = 3 [/tex]

[tex] 3 = 3 [/tex]

This is a true statement, so the solution w = -3 is valid.

Answer: w = -11

Answer:

Step-by-step explanation:

15 rows adding 4 additional seats to each. Once at end add all seats in rows together for the final answer.

1-25

2-29

3-33

4-37

5-41

6-45

7-49

8-53

9-57

10-61

11-65

12-69

13-73

14-77

15-81

Add all togther. 25+29+33+37+41+45+49+53+57+61+65+69+73+77+81=795

So there are 795 seating capacity.

We subtract 5 from both sides of the inequality.

Multiply both sides by 2/3.

Therefore, the correct option is alternative "A".

We would think that it is option B, but the only difference is that it changes the direction of the sign.

Answer:  [A]: " b < 8 " .
_____

Step-by-step explanation:

Given:
Find the solution to:   " 3/2b + 5 < 17 " ; and choose from the answer choices.

So; we have:  

 (3/2)b + 5 < 17  ;

 Now, subtract "5" from each side of this inequality:
 (3/2)b + 5 − 5  <  17 − 5  ;

   To get:
  (3/2)b  <  12 ;

Now, let's multiply Each Side of this inequality by "2" ;

 to get rid of the fraction:

    "  2*(3/2)b  <   12*2 "  ;

{Note: " [tex]2 *\frac{3}{2}=\frac{2}{1}*\frac{3}{2}[/tex] " } ;

Note:  To simplify:  " [tex]\frac{2}{1} * \frac{3}{2}[/tex] " ;
   Note the "2" in the denominator in the "first term" ;  

   And:  The "2" in the denominator in the "second term" ;

      Both "cancel out" to "1" ;  since:  "[ 2 / 2 = 2÷2 = 1 ]" ;

   And:  we have:  " [tex]\frac{1}{1}*\frac{3}{1}= 1 *3 = 3[/tex] " };

_____
and rewrite:
   " 3b < 24 "  ;

Now, divide Each side of the inequality by "3" ;

 to isolate "b" on one side of the inequality;

and to solve for "x" ;
_____
 " 3b/3 < 24/3 " ;

 to get:

_____

   " b < 8 " ; which corresponds to the correct answer:

Answer choice:  [A]:  " b < 8 " .
_____

Hope this is helpful to you! Best wishes!
_____

Using derivatives, it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval:

(-15,-10).

It is given by the derivative at x = x0, that is:

[tex]m = f^{\prime}(x_0)[/tex].

In this problem, the function is:

[tex]f(x) = 0.2x^2 + 5x - 12[/tex]

Hence the derivative is:

[tex]f^{\prime}(x) = 0.4x + 5[/tex]

For a slope of -1, we have that:

0.4x + 5 = -1

0.4x = -6

x = -15.

For a slope of 1, we have that:

0.4x + 5 = 1.

0.4x = -4

x = -10

Hence the interval is:

(-15,-10).

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Answer:

B. 20x⁹

Step-by-step explanation:

A monomial is a polynomial with just one term.

Example: 3x²

A. 11x - 9

INCORRECT, this has two terms 11x and 9

B. 20x⁹

CORRECT, this only has one term!

C. 20x⁹ - 7x

INCORRECT, this has two terms 20x⁹ and 7x

D.9/x

INCORRECT, this is not a polynomial

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