suppose you are using the inclusion-exclusion principle to compute the number of elements in the union of four sets. each set has 15 elements. the pair-wise intersections have 5 elements each. the three-way intersections have 2 elements each. there is only one element in the intersection of all four sets. what is the size of the union?

Answer:

(3x−5)(3x+1)

Step-by-step explanation:

Evaluate

9x2−12x−5

Rewrite the expression

9x2+3x−15x−5

Factor out 3x from the expression

3x(3x+1)−15x−5

Factor out −5 from the expression

3x(3x+1)−5(3x+1)

Solution

(3x−5)(3x+1)

Answer:

(3x - 5)(3x + 1)

Step-by-step explanation:

1. Add the numbers

9x² - 12x - 5 + 0

9x² -12x - 5

2. Use the sum-product pattern

9x² - 12x - 5 + 0

9x² + 3x - 15x - 5

3. Common factor from the two pairs

9x² + 3x - 15x - 5

3x(3x + 1) - 5(3x + 1)

4. Rewrite in factored form

3x(3x + 1) - 5(3x + 1)

(3x - 5)(3x + 1)

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m∠W = 33.8° , using inverse trignometric ratio.

What do you mean by inverse trignometric functions?

The sine, cosine, tangent, cotangent, secant, and cosecant functions are the fundamental trigonometric functions. Inverse trigonometric functions are just the inverse functions of these functions. They can also be referred to as cyclometric functions, antitrigonometric functions, or arcus functions. Trigonometry's inverse functions are used to find the angle for any trigonometric ratio.

It is given that VU = 2 units and VW = 3 units and VUW is a right angle triangle , right angled at V.

Using the ratio of tanW,

As we know tanA = P/B where P is the perpendicular and B is the base

In the given triangle VUW,

tanW = VU/VW = 2/3

W = [tex]tan^{-1}[/tex](2/3) = [tex]tan^{-1}[/tex](0.67) = 33.8 degree

Therefore, m∠W = 33.8°

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The value of fraction 1/2 multiplied by 3/4 is 3/8 by multiplication of fractions.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. A fraction only informs us of the number of components that make up the total. The slash that is inserted between the two numbers identifies a fraction. The numerator is the highest number, while the denominator is the lowest number. 1/2, for instance, is a fraction. A fraction is a number that is a component of a whole.

Here,

1/2 of 3/4

=1/2*3/4

=3/8

By using fractional multiplication, the result of 1/2 times 3/4 is 3/8.

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Answer:The x-intercept is

(-3/2)

The y-intercept is

(0,-3)

Step-by-step explanation:

to find the x and y intercept you have to make x and y equal zero then solve.

finding x

2x+0=-3

2x/2=-3/2

x=-3/2

finding y

2(0)+y=-3

-2        -2

y= -5

The required equation of the line is y = (7/4)x + 2.

A linear equation is defined as an equation in which the highest power of the variable is always one.

The given coordinate of the point on the line is ; (-4, -5) and the slope is 7/4

Let the required equation of the line is

⇒ y - y₁ = m [x -x₁]

x₁ = -4, y₁ = -5 and m = 7/4

Substitute values in the equation, we get

y - (-5)= (7/4)(x - (-4))

y + 5 = (7/4)(x + 4)

y + 5 = (7/4)x + (7/4)4

y = (7/4)x + 7 - 5

y = (7/4)x + 2

Therefore, the required equation of the line is y = (7/4)x + 2.

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Answer: the answer is 8.70.

Step-by-step explanation:

Since were rounding to the 2 decimal places(hundredths) we can immediately drop the 5. since 2 is not greater than 5 we do not round to 8.71. So, the answer is 8.70!

Answer:

33 Hours.

Step-by-step explanation:

Their hourly receipts are $23, and their hourly operating costs are $5. So you would subtract the hourly receipts from the hourly operating costs.

23 - 5 = 18

Then you would take the new number and divide the money spent on equipment by the money earned an hour.

594 / 18 = 33

Hope this helps! :)

The transformations that would map triangle D''E''F'' onto triangle DEF are given by:

The transformations to map triangle DEF into triangle D''E''F'' is given by:

The dilation means that the coordinates of each vertex of the figure are multiplied by the scale factor.

The dilation from DEF to D'E'F' has a scale factor of 4, hence the inverse dilation will have a scale factor of:

1/4.

Then the inverse translation is applied, as follows:

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The Trigonometric function sin(A - B) = (3 - 2[tex]\sqrt{14}[/tex]) ÷ 12

The easiest way is to use the Pythagorean Identity to find both cos A and sin B. Then use the sum/difference angle identity for sine.

The trigonometric Pythagorean identity tells us that,

[tex]Sin^{2}[/tex]θ + [tex]cos^{2}[/tex]θ = 1

which follows directly from the geometric identity for right triangles and the fact that,

sinθ = y/r and cosθ = x/r

If r is the distance (x,y) is from the origin, then

[tex]x^{2}[/tex] + [tex]y^{2}[/tex] = [tex]r^{2}[/tex]

[tex](x/r)^{2}[/tex] + [tex](y/r)^{2}[/tex] = 1(divide both sides by [tex]r^{2}[/tex])

[tex]cos^{2}[/tex]θ +  [tex]Sin^{2}[/tex]θ  = 1

Anyway, if we know sin A (and which quadrant it ends in), we can solve for cos A and vice versa:

[tex]Sin^{2}[/tex]θ + [tex]cos^{2}[/tex]θ = 1

[tex](1/3)^{2}[/tex] +  [tex]cos^{2}[/tex]θ = 1

⇒ cos A = [tex]\sqrt{1-(1/3)^{2} }[/tex] = [tex]\frac{2\sqrt{2}}{3}[/tex]

cosθ is always negative in this quadrant.

Therefore,

cos A = -[tex]\frac{2\sqrt{2} }{3}[/tex]

Similar reasoning can be done with cos B = [tex]\frac{3}{4}[/tex] to show that sin B = -[tex]\frac{\sqrt{7} }{4}[/tex]

Now that we have all the necessary elements, we can use the sum/difference angle identity:

Sin(A-B) = sin A cos B - cos A sin B

= ( [tex]\frac{1}{3}[/tex] × [tex]\frac{3}{4}[/tex] ) - ( (-[tex]\frac{2\sqrt{2} }{3}[/tex] ) × (-[tex]\sqrt{7[/tex]/4) )

= (3 ÷ 12) - (2[tex]\sqrt{14}[/tex] ÷ 12)

= (3 - 2[tex]\sqrt{14}[/tex]) ÷ 12

We get sin(A - B) = (3 - 2[tex]\sqrt{14}[/tex]) ÷ 12

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[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{8.5})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{3.5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3.5}-\stackrel{y1}{8.5}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-2)}}} \implies \cfrac{-5}{0 +2}\implies -\cfrac{5}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8.5}=\stackrel{m}{- \cfrac{5}{2}}(x-\stackrel{x_1}{(-2)}) \implies y -8.5= -\cfrac{5}{2} (x +2) \\\\\\ y-8.5=-\cfrac{5}{2}x-5\implies y=-\cfrac{5}{2}x-5+8.5\implies {\Large \begin{array}{llll} y=-\cfrac{5}{2}x+3.5 \end{array}}[/tex]

Answer:

Either a or d

Step-by-step explanation:

Because they show the data correctly it is A trust me

Answer: Scatterplot A

Step-by-step explanation:

edGE 23

The probability of taking out a red sweet is; 1/3. The probability of taking out a green, blue or orange sweet is; 10/21

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We are given that there are 4 yellow, 3 blue, 5 green, 7 red and 2 orange sweets in my bag.

The total sweets = 4+3+5+7+2 = 21

1. the probability of taking out a red sweet is;

7/21 = (7:7)/(21:7)

= 1/3

2. The probability of taking out a green, blue or orange sweet is;

= (5+3+2)/21

= 10/21

Hence, The probability of taking out a red sweet is; 1/3. The probability of taking out a green, blue or orange sweet is; 10/21

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The time that would be needed for the trip is 2 hours.

It is important to note that the formula that can be used for calculating the time taken will be:

Time = Distance / Speed

where

Distance = 9 1/3

Speed = 4 2/3

Therefore time will be:

Time = Distance / Speed

= 9 1/3 ÷ 4 2/3

= 28/3 ÷ 14/3

= 28/3 × 3/14

= 2 hours

The time is 2 hours.

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There are 450 positive integers between 100 and 999 (both included) that are divisible by 3 or 4.

According to the question,

We have the following information:

Positive integers between 100 and 999 including both these integers which are divisible by 3 or 4

Now, the number of positive integers between 100 and 999 is (999-100+1) or 900.

Now, the numbers divisible by 3 will be in multiplication of 3.

So, number which are divisible by 3:

900/3 = 300

Now, the numbers divisible by 4 will be in multiplication of 4:

So, the numbers which are divisible by 4:

900/4 = 225

Now, there are also numbers in numbers divisible by which are divisible by 3. So, they are 1/3 of the numbers divisible by 4:

225/3

75

Now, total numbers divisible by 4:

225-75

150

Now, total numbers divisible by 3 or 4:

300+150

450

Hence, there are 450 positive integers between 100 and 999 (both included) that are divisible by 3 or 4.

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Answer:

$500

Step-by-step explanation:

400/40 = 10.  This gives us her hourly rate

50 x 10 = 500

Answer:

Exact Form:

7/8

Decimal Form:

0.875

The number of pounds of grapes is 24 sold and the number of pounds of apples sold is 30.

Given that,

Apples and grapes are sold at Arianys' farm stand. The price per pound for apples is $4 while the price per pound for grapes is $3.75. 64 pounds of apples and grapes were sold for a total profit of $251.75 for Arianys.

We have to find the number of the sold apples and pounds of grapes should be calculated.

a declaration that two mathematical expressions' values are equal (represented by the symbol =).

We get the equations as,

3.75x+4y=251.75

y=-0.93x+62.93---->equation(1)

x+y=64

y=-x+64------>equation (2)

We get the points as

For equation (1),

(0,62.93) and (67.66,0)

For equation (2),

(0, 64) and (64,0)

If we draw a graph we get 2 lines intersect at a point (24, 30).

Therefore, The number of pounds of grapes is 24 sold and the number of pounds of apples sold is 30.

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The equation of the line that passes through the point (18,-3) with slope -1 is y = -x+15.

According to the question,

We have the following information:

The line passes through the point (18,-3) with slope -1.

We know that the following formula is used to find the equation of the line passing through a point with the slope which is denoted by m:

(y-y') = m(x-x')

In this case, we have the following values:

m = -1

x' = 18 and y' = -3

Putting these values in the above formula:

y-(-3) = -1(x-18)

y+3 = -x+18

Subtracting 3 from both sides of the equation:

y = -x+18-3

y = -x+15

Hence, the equation of the line that passes through the point (18,-3) with slope -1 is y = -x+15.

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Answer:

535.50

Step-by-step explanation:

hope this helps :)

Answer:

535.50

Step-by-step explanation:

Hope this helps : )

The true statements are:

C. . A line segment consists of two endpoints and all the points between

D. A line has two endpoints.

A line segment is bounded by two distinct points on a line.

How to know which statement is true?

From the definition,.

Also, we know that through two points one and only one line can pass .

Therefore, A line has two endpoints.

So, option C and D are correct.

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Answer:

y - 1 =0 (x-2)

Step-by-step explanation:

We are given that a horizontal line which is passing through the point (2,1).

We have to find the equation in point -slope form of the line .

We know that equation of horizontal line is given by

It means y does not vary with x therefore, Slope of line= Slope of horizontal line =0

Point- slope form equation of line

We have,

Substitute the values in the given formula

Then, we get the equation of horizontal line which is passing through the point (2,1) is given by

Hence, the equation of horizontal line which is passing through the point (2,1) is given by y - 1 =0 (x-2)

The perimeter of the square can be expressed as either S+S+S+S or  4×S

Perimeter is the distance around the edge of a shape. It can be found by adding up the side lengths of the shapes

Given: a square with a side length of S. Thus, the perimeter can be expressed as:

Perimeter = S + S + S + S = 4S

Since there are 4 equal sides each having a length of S. Thus, we can also write perimeter as:

Perimeter = 4 × S = 4S

Therefore, we can conclude the same expression are the same since they both have the same value of 4S

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Answer:

Step-by-step explanation:

$y = -16x^2 + 240x + 115$

$= -16x^2 + 240x + 120 - 5$

$= -16x^2 + 240x + 120 - 5x - 5x$

$= -16x^2 + 240x + 120 - 10x - 5x$

$= -16x^2 + 240x + 120 - 10x - 5x + x^2 - x^2$

$= -16x^2 + 240x + 120 - 10x - 5x + x^2 - x^2 + 2x - 2x$

$= -16x^2 + 240x + 120 - 10x - 5x + x^2 - x^2 + 2x - 2x + x -x$

$= -16x^2 + 240x + 120 - 10x - 5x + x^2 - x^2 + 2x - 2x + x -x + 3 - 3$

$= -16x^2 + 240x + 120 - 10x - 5x + x^2 - x^2 + 2x - 2x + x -x + 0

Answer:

180

Step-by-step explanation:

13 X 8 = 104 --> 104 + 76 = 180

8 * 10^9 is 8000000000

just 9 zeros to the 8

The area of the largest rectangle will be 3.

By using properties of similar triangles we can say that

[tex]\frac{EF}{FB} - \frac{AC}{CB}[/tex]

B / (3 - a) = 4/3

3b = 12 - 4a

4a = 12 - 3b

a = (12 - 3b) / 4

Now as we know area of a rectangle is length * width. let us find the area

A = l * w

A = b * ( (2 - 3b) / 4 )

A = 3b - 3[tex]b^{2}[/tex]/4

Now to find maximum value we will differentiate the area and put it equal to zero.

[tex]D^{1}[/tex] = 3 - 6b/4 = 0

6b/4 = 3

6b = 12

b = 2

and

a = (12 - 3b) / 4

a = 6/4

a = 3/2

So, area will be = 3/2 * 2

Therefore maximum are of the triangle will be 3.

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Answer:

a take 2 hour to plant so flower bulbs if they are working together how long should it takes to plant 150 bulb? solving the question

The numbers round to 56.8 when rounded to the nearest tenth are 56.809, 56.795, and 56.832 respectively.

What is rounding decimals?

The term "rounding decimals" describes the accurate rounding of decimal figures. To the nearest whole, tenth, or hundredth, we can round decimals.

The next place value on the right should be used to round a number to the closest tenth (the hundredths). Simply take away all the digits to the right if it's 4 or fewer. Remove all the digits to the right after adding 1 to the digit in the tenth position if the number is 5 or above.

We need to find the value that rounds to the nearest tenth which results in 56.8

Now, we check all options one by one and rounded them to the nearest tenth

56.85 = 56.9 (rounded to the nearest tenth)

56.809 = 56.8 (rounded to the nearest tenth)

56.749 = 56.7  (rounded to the nearest tenth)

56.08 = 56.1  (rounded to the nearest tenth)

56.795 = 56.8 (rounded to the nearest tenth)

56.832 = 56.8 (rounded to the nearest tenth)

56.72 = 56.7  (rounded to the nearest tenth)

Hence, the required answers are 56.809, 56.795, and 56.832.

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Answer:

102

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