Given n(J) = 255, n(K) = 186 and n(J ∪ K) = 429, find n(J ∩ K).

There were 733 general tickets sold and 255 reserved tickets.

Let the general admission = g

Let the reserved seats = r

Therefore, the appropriate equation will be:

g + r = 988

4g + 6.5r = 4589.50

From equation i r = 988 - g

4g + 6.5r = 4589.50

4g + 6.5(988 - g) = 4589.50

4g + 6422 - 6.5g = 4589.50

6.5g - 4g = 6422 - 4589.50

2.5g = 1832.50

g = 1832.50/2.5

g = 733

Since g + r = 988

r = 988 - 733

r = 255

Therefore, there were 733 general tickets sold and 255 reserved tickets.

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System of equations modeling the given conditions:

x + y = 94

x - y = 36

Solving:

In order to use substitution, you have to isolate one of the variables in either of the equations

Using the second equation and isolating the variable x:

x - y = 36

x = 36 + y

then you can substitute x back into the first equation

36 + y + y = 94

36 + 2y = 94

2y = 58

y = 29

and then substitute 29 for y into either one of the equations

x + 29 = 94

x = 65

The answer is (2) 2f-5=86; I hope- :\

Answer:

Results of the Assembly elections in five States are indeed a shot in the arm for the Bharatiya Janata Party (BJP), which won in all four States where it was in power. The Hindu editorial captures the broad trends that emerge out of these results. Prime Minister Narendra Modi has said these results have sealed the outcome of the 2024 Lok Sabha elections too in the BJP’s favour. He said people have rejected caste and dynastic politics.

Answer:

[tex]\sf p =\sqrt{\dfrac{q+3}{5}}[/tex]

Step-by-step explanation:

To find p in terms of q, we have to isolate p.

[tex]\sf \sqrt{(5p^2 - 1)^2}-2 = q\\\\[/tex]

 5p² - 1 - 2 = q

      5p² - 3 = q

Add 3 to both sides,

              5p² = q + 3

Divide both sides by 5,

                [tex]\sf p^2 = \dfrac{q+3}{5}\\\\\text{Take square root,}\\\\p =\sqrt{\dfrac{q+3}{5}}[/tex]

From the graph of the piecewise function, we have that:

a) The range of the function is (-∞,7).

b) The vertical asymptote is of x = 2, and the horizontal asymptotes are y = -1 and y = -2.

c) The end behavior of the function is described as follows: As x -> -∞, y -> -2 and as x -> ∞, y -> -1.

A piecewise function is a function that has different definitions, depending on the input.

For this problem, the definitions of the function are given as follows:

The graph of the function is given at the end of the answer.

The range of the function is the set that contains all the output values of the function, and in a graph, this is the values of y.

Hence:

The range of the function is (-∞,7).

The asymptotes of the functions are the values of x for which the function is not defined. In this problem, the function is not defined for x = 2, hence the vertical asymptote is of x = 2.

The horizontal asymptotes are the values of the function when it goes to infinity, hence they are y = -2 and y = -1.

The end behavior is given by the limits of the function as it goes to infinity, being closely related to the horizontal asympotes.

Hence:

As x -> -∞, y -> -2 and as x -> ∞, y -> -1.

Please ignore the (60,1) point plotted on the graph, it should be (60,-1).

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The interval in which the function has positive average rate of change is x > √3

The function is given as

f(x) = x^3 - 9x

Differentiate the above function to determine the average rate of change

So, we have

f'(x) = 3x^2 - 9

Set the function to greater than 0

So, we have

3x^2 - 9 > 0

Add 9 to both sides

3x^2 > 9

Divide by 3

x^2 > 3

Take the square root of both sides

x > √3

Hence, the interval in which the function has positive average rate of change is x > √3

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The slope of the equation is -7. Then the slope of the perpendicular line will be 1/7.

Let the equation of the line be y = mx + c. Then the equation of the perpendicular line that is perpendicular to the line y = mx + c is given as y = -(1/m) + d. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given as,

y = - 7x

The slope of the equation is -7. Then the slope of the perpendicular line will be

⇒ -(1/(-7))

⇒ 1/7

The slope of the equation is -7. Then the slope of the perpendicular line will be 1/7.

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Answer:

You will translate A up until it is equal with A', then you will reflect the figure over the line of symmetry that will be half way between line segments CD and C'D'

Step-by-step explanation:

I am not sure if the polygon is drawn on a coordinate plane.  I cannot see any horizontal or vertical lines to tell you exactly how many units to move up.

The cutoff score is  mathematically given as

x_n=70.32 (cutoff)

This is further explained below.

Generally, the equation for is  mathematically given as

[tex]&P\left(X > x_0\right)=0.15 \Rightarrow P\left(X < x_0\right)=0.85 \\[/tex]

[tex]&\Rightarrow P\left(\frac{X-\mu}{\sigma} < \frac{x_0-\mu}{\sigma}\right)=0.85 \\[/tex]

[tex]&\Rightarrow P\left(Z < \frac{x_0-\mu}{\sigma}\right)=0.85 \\\\&\Rightarrow \frac{x_0-\mu}{\sigma}=\text { invNorm }(0.85) \\\\&\Rightarrow x_0=\mu+\sigma \times \text { invNorm }(0.85)[/tex]

Use z-table to get inv Norm() = 1.04

x_0=62+8 *(1.04)=70.32

In conclusion, Top 15% are above x_n=70.32 (cutoff)

Clearly this is 85th percentile

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Answer: (FINDING THE PRODUCT)

Exact form:

-3/16

Decimal form:

-0.1875

Step-by-step explanation:

<3

Answer:

13/40

Please mark my answer as the brainliest, that would mean a lot to me

Step-by-step explanation:

5/8 - 3/10

50/80 - 24/80

26/80

13/40

Answer:

6.8%

Step-by-step explanation:

[tex]\frac{21447.20}{315400}[/tex]  When you divide this, you get 0.068.  This is in decimal form.  To change to a percent move the decimal to places to the right 6.8%

Answer:

the length of her garden will have to be 5.5ft

22÷4=5.5

Answer: -119 feet relative to the surface of the water.

Step-by-step explanation:

Shark Depth ( x ) + Distance from Shark and Diver ( 38 ) = Divers position (-157)
x = -119

The diver is at -157 feet relative to the surface. The shark is swimming 38 feet above the diver, making its position -119 feet relative to the surface.

Given that,

Diver's depth: -157 feet (relative to the surface of the water)

Shark's position: 38 feet above the diver

The question asks for the position of the shark relative to the surface of the water.

The position of the shark can be determined by adding the distance above the diver to the depth of the diver.

So, the position of the shark would be:

-157 feet (diver's depth) + 38 feet (distance above the diver) = -119 feet relative to the surface of the water.

Hence,

The shark is located at -119 feet relative to the surface of the water.

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Answer:

example of compound interest with solution

Answer:

78 dollars

Step-by-step explanation:

9.75 multiplied by 8 is 78.

There is a real number whose product with every real number equals zero

a. Some real number has the property that its product with every real number equals 0.

b. There is a real number a such that the product of á and any real equals zero.

c. There is a real number á with the property that for every real number b, the product of a and b equals zero.

The billboard is not tall enough as the height is 27.5ft which is  less than 30ft.

The comparison of two quantities having the same units is called as Ratio.

ratio between quantity a and b is  represented by a:b .

In the given question

The bill board should have at least 30ft height.

Height of lady = 5 ft 6 inches

                        =5.5 ft     ...( as 6inch=0.5ft )

If the height of the lady is 5.5ft shadow length = 7 feet

Since the units of height of lady and length of shadow is same .

hence ratio can be used ,

also given that length of billboard = 35 ft.

Let the height of the bill board = x ft

The above situation can be represented using ratio as

(height of lady) / (length of shadow of lady)=(height of billboard)/( length of billboard shadow)

Substituting the values we get

5.5/7=x/35

On solving further we get

(5.5/7)*35=x

5.5*5=x

x=27.5

The height of the billboard is 27.5 ft  .

Since , it is given that the height of the bill board should be at least 30ft tall , and the height of the billboard is 27.5ft.

Therefore , the billboard is not tall enough as the height is less than 30ft.

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There is a 96.37% probability that the company will find 2 or more defective products.

There is a 2.08% probability that the company will find 4 or more defective products.

There is a 0.02% probability that the company will find 5 or more defective products. So company will give profit.

There are only two possible outcomes for each product: either it is defective or it is not. The binomial distribution is used to answer this question because each product's defect probability is independent of all other products.

Binomial probability distribution

The probability of precisely x successes on n repeated trials is known as the binomial probability.

[tex]P_x = \;^nC_r.p^x.q^{n-x}[/tex]

Where,

Px = binomial probability,

 [tex]\;^nC_r =[/tex] number of combination

p = probability of success on a single trial

q = probability of failure on a single trial = (1 - p)

n = number of trials

x = number of times for a specific outcome within n trials

So, from question,

1) The probability that, 2 or fewer defective products is;

P(X≤2) = P(X=0) +  P(X=1)+ P(X=2) -----------------(1)

So,

[tex]P_x = \;^nC_r.p^x.q^{n-x}[/tex]

P(X=0) = [tex]\;^{20}C_0.p^0.q^{20-0}[/tex] =  [tex]\; 1.(1-p)^{20-0}[/tex] = (1-0.037)²⁰ = (0.963)²⁰ =  0.4704

P(X=1) = [tex]\;^{20}C_1.p^1.q^{20-1}[/tex] =  [tex]\; 20.(0.037).(0.963)^{19}[/tex]  = 0.3614

P(X=2) = [tex]\;^{20}C_2.p^2.q^{20-2}[/tex] =  [tex]\;190\times(0.037)^2\times(0.963)^{18}[/tex] = 0.1319

Now, putting the all values in equation (1)

P(X≤2) = P(X=0) +  P(X=1)+ P(X=2) -----------------(1)

           = 0.4704 + 0.3614 + 0.1319

P(X≤2) = 0.9637 = 96.37%

There is a 96.37% probability that the company will find 2 or more defective products.

2)

1.23% are defective means p = 0.0123

The probability that find 4 or more defective products are;

 P(X≤4) = 1 - P(X< 4) -----------(2)

 P(X< 4) = P(X=0) + P(X=1)+ P(X=2) + P(X=3)-----------------(3)

So,

P(X=0) =  = [tex]\;^{20}C_0.p^0.q^{20-0}[/tex] =  [tex]\; (0.9877)^{20}[/tex] = 0.7807

P(X=1) = [tex]\;^{20}C_1.p^1.(1-p)^{20-1}[/tex] =  [tex]20\times (0.0123)\times (0.9877)^{19}[/tex] = 0.1944

P(X=2) = [tex]\;^{20}C_2.p^2.(1-p)^{20-2}[/tex] =  [tex]190\times (0.0123)^2\times (0.9877)^{18}[/tex] = 0.0024

P(X=3) = [tex]\;^{20}C_3.p^3.(1-p)^{20-3}[/tex] =  [tex]1140\times (0.0123)^3\times (0.9877)^{18}[/tex] = 0.0017

So,

P(X< 4) = 0.7807+0.1944+0.0024+0.0017 =0.9792

 P(X≤4) = 1 - P(X< 4) = 1 - 0.9792 = 0.0208 = 2.08%

There is a 2.08% probability that the company will find 4 or more defective products.

3)

1.28% are defective means p = 0.0128

The probability that find 5 or more defective products are;

 P(X≤5) = 1 - P(X< 5) -----------(4)

 P(X< 5) = P(X=0) + P(X=1)+ P(X=2) + P(X=3)+ P(X=4)-----------------(5)

So,

P(X=0) =  = [tex]\;^{20}C_0.p^0.q^{20-0}[/tex] =  [tex]\; (0.9872)^{20}[/tex] = 0.7728

P(X=1) = [tex]\;^{20}C_1.p^1.(1-p)^{20-1}[/tex] =  [tex]20\times (0.0128)\times (0.9872)^{19}[/tex] = 0.2004

P(X=2) = [tex]\;^{20}C_2.p^2.(1-p)^{20-2}[/tex] =  [tex]190\times (0.0128)^2\times (0.9872)^{18}[/tex] = 0.0246

P(X=3) = [tex]\;^{20}C_3.p^3.(1-p)^{20-3}[/tex] =  [tex]1140\times (0.0128)^3\times (0.9872)^{18}[/tex] = 0.0019

P(X=4) = [tex]\;^{20}C_4.p^4.(1-p)^{20-4}[/tex] =  [tex]4845 \times (0.0128)^3\times (0.9872)^{18}[/tex] = 0.0001

So,

  P(X< 5) = 0.7728+0.2004+0.0246+0.0019+0.0001 = 0.9998

  P(X≤5) = 1 - P(X< 5) = 1 - 0.9998 = 0.0002 = 0.02%

There is a 0.02% probability that the company will find 5 or more defective products. So company will give profit.

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Answer:

I don't know there's no figure

Step-by-step explanation:

I don't have any clue is the answer because their is no figure so stop being umb and show me the pic lo ser

Answer: (-1.5, 0)

Step-by-step explanation:

Use the midpoint formula, [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]. Plug in the points into the equation to get [tex](\frac{-5+2}{2},\frac{5-5}{2})[/tex] = (-1.5, 0)

To find the mean of a set of numbers, we find their sum and divide it by the number of terms there are.

We're given:

The sum of (a + 1) + (a + 4) + (a + 7) + (a + 8) + (a + 10) divided by 5 (because there are 5 numbers) is 12. Write this as an equation:

[tex]12=\dfrac{(a + 1) + (a + 4) + (a + 7) + (a + 8) + (a + 10)}{5}[/tex]

Simplify:

[tex]12=\dfrac{a + 1 + a + 4 + a + 7 + a + 8 + a + 10}{5}\\\\12=\dfrac{5a + 30}{5}\\\\12=a +6\\a=6[/tex]

a = 6

1.  'x' = -18/4

2. 'x' = -4/3

The equations are Not Equivalent.

An equation between two variables that gives a straight line when plotted on a graph. Or we can say,

A linear equation is defined as an equation that is written in the form of Ax+By=C. It is the combination of two variables and a constant value present in them.  

We have given

(x/3) - 2 = (5x/3) + 3

(5x/3) - (x/3) = -2 - 3

4x/3 = -6

  4x = -6 × 3

    x = -18/4

In first equation we got the value of x is -18/4.

Two systems of linear equations are equivalent if and only if they have the same set of solutions.  

To determine the equivalent of linear equation,

First, we need to find the value of "x" for each equation. If "x" is the same for both equations, then they are equivalent. If "x" is different then the equations are not equivalent.

We have equation

x(x + 1) = (x + 2)²

x² + x = x² + 4 + 4x        

(We have solved  (x + 2)² by using algebraic identity (a + b)² = a² + b² + 2ab.)

  4x - x = x²- x² - 4

       3x = -4  

         x = -4/3

In the second equation we got the value of x is -4/3.

Hence, as we can see it clearly that the value of x is not same in both equations so this is Not Equivalent.

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The meeting point of the diagonal is the interior of the quadrilateral which  is  Point O.

Here is the quadrilateral PQRS you can find it is given below.

In this image you can see that a quadrilateral has four sides which is PQRS and two diagonals which is PR and QS,

then both diagonals intersects interior of quadrilateral each other at Point O.

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Answer:

x = 84

Step-by-step explanation:

-12(x+12) + 1177 = 10 + 15

-12x - 144 + 1177 = 25

1033 = 25 + 12x

1008 = 12x

x = 84

Answer:

x+20

Step-by-step explanation:

because ist correct

A relation that does not have the function property of each and every input having exactly one output.

A function is defined as a relation between  a group  of inputs having one output each. In simple words, a function may be a  relationship between inputs where each input is related to exactly one output. Every function  features a  domain and range. A function is usually  denoted by f(x) where x is the input.

The types of functions can be broadly classified into four types.  supported  Element: One to one Function, many  to at least one  function, onto function, one  to at least one  and onto function, into function.

A function  may be a  relation between a set of inputs (called the domain) and a permissible set of outputs (called the codomain),  such  each input is related to exactly one output.

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The slope of  P=(-4,-1) Q=(-3,-3) is -2.

Given,

 P=(-4,-1)

Q=(-3,-3)

The  slope  between two points   P=(x₁, y₁)

Q=(x₂ ,y₂)

slope = (y₂-y₁)/(x₂-x₁)

So slope between  P=(-4,-1)   Q=(-3,-3) is

 [(-3)-(-1) ]/ [(-3)-(-4)]

=-2/1

=-2

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two separate locations on a line is calculated using the slope of a line formula.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.

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