Identify the domain and range of the relation. Write your answers as lists of numbers.
((-4,-4), (1, 3), (0, 5), (3, 9)}

The solutions are;

1. U = {a, d, e, i, l, n, o, p, y}

2. E ∪ I = {a, d, e, i, l, n, o, p, y}

3. E ∩ I = { }

4. J' = {a, d, e, l}

5. I ∪ J = {p, i, n, a, o, y}

6.( J ∩ I ) ∪ E = {d, o, l, e, p, i, n, y}

7. E' = {a, i, n, p, y}

8. I' ∪ J = {d, e, l, o, p, i, n, y}

9. (E ∩ I) ∩ (I ∪ J) = { }

10. (J ∪ I)' = {d, e, l}

What is Union of the set?

Union of two or more set is the set containing all the elements of the given set.

Here, U is the universal set, which is the set of all elements of the three given sets.

And, Three sets are;

⇒ E = {d, o, I, e},     I = {p, i, n, a, y},     J = {p, i, n, o, y}

Now, We find the universal set as;

1. U = {{a, d, e, i, l, n, o, p, y}

2. And, E ∪ I =  {d, o, I, e} ∪ {p, i, n, a, y}

                = {a, d, e, i, l, n, o, p, y}

Hence, E ∪ I = {a, d, e, i, l, n, o, p, y}

3.  E ∩ I =  {d, o, I, e} ∩ {p, i, n, a, y}

Since, It cannot contain any common elements.

So, Intersection of E and I is null set.

Hence, E ∩ I = { }

4. Since, J' = U - J

J' = {a, d, e, i, l, n, o, p, y} - {p, i, n, o, y}

J' = {a, d, e, l}

Hence, J' = {a, d, e, l}

5. I ∪ J = {p, i, n, a, y} ∪ {p, i, n, o, y}

           = {p, i, n, a, o, y}

Hence,  I ∪ J = {p, i, n, a, o, y}

6. ( J ∩ I ) ∪ E = ({p, i, n, o, y} ∩ {p, i, n, a, y}) ∪ {d, o, I, e}

                     = {p, i, n, y} ∪ {d, o, I, e}

                     = {d, o, l, e, p, i, n, y}

Hence, ( J ∩ I ) ∪ E = {d, o, l, e, p, i, n, y}

7.  E' = U - E

       = {a, d, e, i, l, n, o, p, y} - {d, o, I, e}

       = {a, i, n, p, y}

Hence, E' = {a, i, n, p, y}

8.  I' ∪ J = (U - I) ∪ J

            = ( {a, d, e, i, l, n, o, p, y} - {p, i, n, a, y}) ∪ {p, i, n, o, y}

            = {d, e, l, o} ∪ {p, i, n, o, y}

            =  {d, e, l, o, p, i, n, y}

Hence, I' ∪ J = {d, e, l, o, p, i, n, y}

9. (E ∩ I) ∩ (I ∪ J) = ( {d, o, I, e} ∩ {p, i, n, a, y}) ∩ ({p, i, n, a, y} ∪ {p, i, n, o, y})

                          = { } ∩ {p, i, n, a, o, y}

                          = { }

Hence,  (E ∩ I) ∩ (I ∪ J) = { }

10. (J ∪ I)' = U - (J ∪ I)

              = {a, d, e, i, l, n, o, p, y} - ({p, i, n, a, y} ∪ {p, i, n, o, y})

              = {a, d, e, i, l, n, o, p, y} - {p, i, n, a, o, y}

              =  {d, e, l}

Hence,  (J ∪ I)' = {d, e, l}

So, The solutions are;

1. U = {a, d, e, i, l, n, o, p, y}

2. E ∪ I = {a, d, e, i, l, n, o, p, y}

3. E ∩ I = { }

4. J' = {a, d, e, l}

5. I ∪ J = {p, i, n, a, o, y}

6.( J ∩ I ) ∪ E = {d, o, l, e, p, i, n, y}

7. E' = {a, i, n, p, y}

8. I' ∪ J = {d, e, l, o, p, i, n, y}

9. (E ∩ I) ∩ (I ∪ J) = { }

10. (J ∪ I)' = {d, e, l}

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Going by the stemplot, a correct comparison to make between eastern and western states’ expenditures is The eastern states have, on average, a higher per-pupil expenditure than the western states.

Reading a stemplot requires looking at the stem first which is the number in the middle. Then combine this with the leaf to find the actual number. For instance, a stem of 7 and a leaf of 6 in the attached photo is $76,000.

From the attached photo, we see that the Eastern states have more numbers of per-pupil expenditure which means that on average, they have a higher per-pupil expenditure than the western states.

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Answer: $239.74 :)

Step-by-step explanation:231.75 for Karen, mom, and dad's rafting, plus 7.99 for the water bottle=239.74 USD

Answer: 16, 17, and 18.

Step-by-step explanation: What I'll do I'll just let explain how to solve it and that will instantly solve your question!

The first case of business to make things easier would be to try and put this on a linear equation so...

Let the first integer be x.

Then the next consecutive two integers will be x + 1 and x + 2

x + (x + 1) + (x + 2) = 51 [Sum of the 3 consecutive integers is 51]

-> 3x + 3 = 51

-> 3x = 51 - 3

-> 3x = 48

-> x = 48/3

-> x = 16,

Thus, x + 1 = 17, x + 2 = 18

Therefore, the three consecutive integers are 16, 17, and 18.

Hope it helps ^^

Using simultaneous equations in two variables we get that the cost of laminate is $ 0.65 per sq. feet and the cost of carpet is $ 4.12 per sq. feet.

Equations in algebra that involve two or more variables simultaneously, such as x and y, are referred to as simultaneous equations. The equations are referred to as simultaneous equations since they are solved simultaneously. There are countless possible solutions to just these equations.

A set of finite equations for which common solutions are sought makes up a system of equations, often known as an equation system.

Let the cost per sq feet of laminate be x and the cost per sq feet of carpet be y.

Now it is given that the cost of 750 sq feet of laminate and 525 square foot of carpet is $2717.25

∴ 750x+525y=2717.25

Again  the cost of 100 sq feet of laminate and 75 square foot of carpet is $374.75

∴ 100x + 75 y = 374.15

Now we solve the pair of simultaneous equations to find the value of x and y:

Multiplying the second equation by 7 and subtracting from the first we get:

750x + 525y =  2717.25

600x + 575 y = 2619.05

150x = 98.20

or, x = 0.654...

Substituting this  value in the first equation we get:

y= 4.115...

Therefore the solution of the simultaneous equation is:

x = $ 0.65 and y = $ 4.12

Therefore  the cost of laminate is $ 0.65 per sq. feet and the cost of carpet is $ 4.12 per sq. feet.

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Answer:

7. 123

8. 38

10. 65

11. 113

The required measure for the supplementary angles EB is calculated as 126°.

Given that,
Two supplementary angles are given ZA and ZB.
ZA = 2x - 20 ; ZB = 3x + 15

To determine the measure of ZB.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The sum of the supplementary angle is 180°.
ZA + ZB = 180°
2x - 20 + 3x + 15 = 180
5x - 5 = 180
5x = 180 + 5
5x = 185
x = 37
Now,
the measure of angle,
ZB = 3x + 15
ZB = 3 * 37 + 15
ZB = 126°

Thus, the required measure of the angle EB is 126°.

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Answer:

Step-by-step explanation:

5

2

−9x−10

Calculate 5 to the power of 2 and get 25.

25−9x−10

1

Calculate 10 to the power of 1 and get 10.

25−9x−10

Subtract 10 from 25 to get 15.

15−9x

Answer:

x = -1, y = 1

Step-by-step explanation:

Solve the following system:

{y = 3 x + 4 | (equation 1)

y = x + 2 | (equation 2)

Express the system in standard form:

{-(3 x) + y = 4 | (equation 1)

-x + y = 2 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

{-(3 x) + y = 4 | (equation 1)

0 x + (2 y)/3 = 2/3 | (equation 2)

Multiply equation 2 by 3/2:

{-(3 x) + y = 4 | (equation 1)

0 x + y = 1 | (equation 2)

Subtract equation 2 from equation 1:

{-(3 x) + 0 y = 3 | (equation 1)

0 x + y = 1 | (equation 2)

Divide equation 1 by -3:

{x + 0 y = -1 | (equation 1)

0 x + y = 1 | (equation 2)

Collect results:

Answer: {x = -1, y = 1

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

                             ( -∞ , ∞ )

Set-Builder Notation:

                                  { x | x ∈ R }

The range is the set of all valid  y  values. Use the graph to find the range.

Interval Notation:

                               ( -∞ , ∞ )

Set-Builder Notation:

                                 { y | y ∈ R }

Determine the domain and range.

Domain:  ( −∞ , ∞ ), { x | x ∈ R }

Range:  ( −∞ , ∞ ), { y | y ∈ R }

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P(AUB|C)=P(A|C) + P(B|C) - P(AnB|C) is the correct answer.

From distributive law we have,

P((AUB)nC)=P(AnC) + P(BnC)-P(AnBnC)

Dividing both sides by P(C)

P((AUB)nC)/P(C)=P(AnC)/P(C) + P(BnC)/P(C) - P(AnBnC)/P(C)

P(AUB|C)=P(A|C) + P(B|C) - P(AnB|C)

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Step-by-step explanation:

what form should the equation have ?

I assume slope-intercept

y = ax + b

"a" being the slope, "b" being the y-intercept (the y value when x = 0).

but since we have the slope and a point, we can start with the point-slope form and transform it :

y - y1 = a(x - x1)

"a" is again the slope, (x1, y1) is the point.

so,

y - 7 = -5/3 × (x - -3) = -5/3 × (x + 3) = -5x/3 - 5

and therefore

y = -5x/3 + 2

Answer:

w=5

Step-by-step explanation:

3(w-2)=9

3w-6=9

w=5

Answer:

w = 5

Step-by-step explanation:

The equation is 3(w - 2) = 9
1st : Distribute 3 to w and -2
    Should equal 3w and -6
2nd : Add 6 on both sides
    Should equal 3w = 15
3rd : Divide 3 on both sides
    Should equal w = 5

Hope this helps!
--Blu

answer: 7,602

explanation: 2×3×7×181

Answer:7602

Step-by-step explanation:First line up the numbers vertically and match the places from the right like this.

181

942

* ​____

​

Now multiply the first number with the 1 st  digit in 2 nd

 number to get intermediate results. That is Multiply 181 with 2. Write the result 362 at the end leaving 0 spaces to the right like this.

181

42

*​_____

362

​

Now multiply the first number with the 2nd digit in 2nd

 number to get intermediate results. That is Multiply 181 with 4. Write the result 724 at the end leaving 1 spaces to the right like this.

181

42

*______

362

724

​______-

Now add the intermediate results to get final answer.

181

42

*_____

362

724

______

​7602

​

Answer:

Step-by-step explanation:

Midpoint coordinates(x, y)  of 2 points (x1, y1) and (x2, y2) are given by
x = (x1 + x2)/2

y = (y1 + y2)/2

So in this situation

x = (8 + 0)/2 = 8/2 = 4

y = (10 + 5)/2 = 15/2 = 7.5

Midpoint is at (4, 7.5)

Check the graph attached

The number 102 in the sequence will be closest to 100.

A sequence in which each next term gets increased or decreased from the preceding by a constant value is called an arithmetic progression.

The difference of any two consecutive terms in an arithmetic progression is called the common difference of the AP (arithmetic progression).

Here each terms increases by 8. So, the common difference d is 8.

The first term is given to be 38.

So our sequence will be,

38, 46, 54, 62,...

nth term in an AP can be calculated by using the formula,

aₙ = a₁ + (n-1)d

To find the term nearest to 100,

100 = 32 + (n-1)8

68/8 = (n-1)

9.5 = n

But the value of n can not be a non-integer,

So the term nearest to 100 will be 9th or 10th term.

a₉ = a₁ + (9-1)d

a₉ = 8 + (8 x 8)

a₉ = 94

and,

a₁₀ = a₁ + (10-1)d

a₁₀ = 8 + (9 x 8)

a₁₀ = 102.

We can see,

a₁₀ = 102 is closest to 100.

Hence, 10th term is closest to 100.

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Answer:

-3/2

Step-by-step explanation:

Slope:

Rise: The difference between the y -coordinates of the two points is called the rise.

Run: The difference between the x-coordinates of the same two points is called the run.

First plot two points on the line.

(0, 6 )  and (4 , 0)

Rise = 6 - 0 = 6

Run = 0 - 4 = -4

[tex]\sf \boxed{Slope = \dfrac{Rise}{Run}}[/tex]

          [tex]\sf =\dfrac{6}{-4}\\\\=\dfrac{-3}{2}[/tex]

The expression is completely simplified to give 13√7

Surds are defined as square root values that cannot be further decreases to integers or whole numbers.

Another name for surds are irrational numbers.

Given the surd forms;

5√28 + √63

Now, let's find the factors of the value 28 with perfect squares.

√28 = √4 × 7

The factors of 63 with perfect squares

√63 = √9 × 7

Now, let's substitute the values

5√4 × 7 + √9 × 7

Find the perfect squares

5 × 2√7 + 3√7

Multiply through

10√7 + 3√7

Since the values have common roots, add the coefficient and keep the root the same.

We have;

13√7

Thus, the expression is completely simplified to give 13√7

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Answer: 19

Step-by-step explanation:

Answer:

Step-by-step explanation:

If 8 panes cost 1880

then 1 pane cost 1880 divided by 8

1 pane = $ 235

3 pane = $235 x 3

            = $ 705

$1715 + $705 = $ 2420

Answer:

Step-by-step explanation:

The range of the function is the set of all y- values.

The range on the graph can be determined by minimum and maximum points if the graph is continuous.

Looking at the given graph we observe:

The range is:

Answer:

152 =x

Step-by-step explanation:

180 - 152= 28

180-28= 152

The probability mass function of the binomial distribution is given by:

B. [tex]\frac{n!}{x!(n-x)!} \times p^{x} \times (1-p)^{n-x}[/tex]

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Hence, considering the combination formula, the probability mass function of the binomial distribution is given by:

B. [tex]\frac{n!}{x!(n-x)!} \times p^{x} \times (1-p)^{n-x}[/tex]

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Answer: x=7

Step-by-step explanation: (3x−2)=19

Add 2 to both sides.

3x=19+2

Add 19 and 2 to get 21.

3x=21

Divide both sides by 3.

x= [tex]\frac{21}{3}[/tex]

​

Divide 21 by 3 to get 7.

x=7

(2)  3x-2

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of [tex]ax^{2}[/tex]

 is [tex]nax^{n-1}[/tex]

.

[tex]3x^{1-1}[/tex]

Subtract 1 from 1.

[tex]3x^{0}[/tex]

For any term t except 0, [tex]t^{0}[/tex] =1.

3×1

For any term t, t×1=t and 1t=t.

answer=3

Answer:

(8,-14)

Step-by-step explanation:

mid piont is (4,-5) So let us consider that S(x,y)

Now,

from mid point formula,

[tex]4 = \frac{x + 0}{2} \\ x = 8[/tex]

[tex] - 5 = \frac{y + 4}{2} \\ - 10 = y + 4 \\ y = - 10 - 4 \\ y = - 14[/tex]

Answer: use a picture math thing

Step-by-step explanation:0.0038 x 105=0.399 so move the decimal point over 1 then it should look like 0.038 x 10.5=0.399 then repeat.

Answer:

16.8

Step-by-step explanation:

84 / 5 = 16.8

Answer:

17 points(Rough estimate)

Step-by-step explanation:

Using long division,

[tex]5|84\\5 \times 1 = 5\\8 - 5 = 3\\\mathrm{Drop~4~onto~3~to~get~34}\\5 \times 6 = 30\\34 - 30 = 4[/tex]

Round 16 to nearest ones place

[tex]\mathrm 16 = 17[/tex]

Therefore,

You scored ≈ 17 points per game out of 5 games.

if you need the exact value, it's 16.8

Any concerns, let me know. Have a good day!

The growth factor for the annual rate of change +0.1 % is 1.001.

A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.

With the function displayed to the right, you may represent exponential growth or decay.

A(x) = a( 1 + r)ˣ

Where A is the amount after x time periods, a is the initial amount, x is the number of time periods, and r is the rate of change.

Now, we have the annual rate of change as:

r = + 0.1% = + 0.1 / 100 = + 0.001

From the function A(x) = a( 1 + r)ˣ , the corresponding factor is 1 + r.

So, let B = 1 + r

B = 1 + r

B = 1 + (+0.001)

B = 1.001

Now, the value of B is greater than 1 therefore, the corresponding growth factor is 1.001.

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The four ways are :

A cylinder is a 3-dimentional solid shape . It has two parallel bases which are joined by the curved surface. The cylinder has 2 circular bases one on the top and other at bottom and a curved region between them.

Important formulas of cylinder:

Base area of cylinder =  π r²

Surface area of cylinder = 2 π r( r+ h)

Volume of cylinder = π r² h

where,  h defines height and r defines the radius

According to ques ,  [tex]h= k\frac{V}{r^{2} }[/tex]

The four ways are :

1. when the value of volume V is quadrupled

  i.e. V = 4V

  then, h = [tex]k\frac{4V}{r^{2} }[/tex] = 4 ([tex]k\frac{V}{r^{2} }[/tex]) = 4h

2. when the value of radius (r) is halved

 i.e. r = r/2

  then , h =  [tex]k \frac{V}{(\frac{r}{2} )^{2} }[/tex] = [tex]k\frac{4V}{r^{2} }[/tex] = 4 ([tex]k\frac{V}{r^{2} }[/tex]) = 4h

3. when the value of V is enlarged 16 times and the value of r is doubled

  i.e. V= 16 V and r =2r

  then, h =  [tex]k \frac{16 V}{(2r)^{2}}[/tex] = [tex]k\frac{4V}{r^{2} }[/tex] = 4 ([tex]k\frac{V}{r^{2} }[/tex]) = 4h

4. If the values of V and r are quartered

    i.e. V= V /4 and r =r/4

      then, h = [tex]k \frac{(\frac{V}{4} ) }{(\frac{r}{4} )^{2} }[/tex] =  [tex]k \frac{16 V}{(4r^{2})}[/tex] = [tex]k\frac{4V}{r^{2} }[/tex] = 4 ([tex]k\frac{V}{r^{2} }[/tex]) = 4h

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The probability that the next type of stir fry ordered is shrimp is 0.28.

Given that, the frequency table provided summarizes yesterday's orders at Sizzlin' Skillets.

A frequency distribution table displays the frequency of each data set in an organized way. It helps us to find patterns in the data and also enables us to analyze the data using measures of central tendency and variance. The first step that a mathematician does with the collected data is to organize it in the form of a frequency distribution table. All the calculations and statistical tests and analyses come later.

The given frequency table is

Type of stir fry         Number of orders

Vegetable                       333

Chicken                           666

Pork                                 222

Beef                                 222

Shrimp                             555

As we know, probability of an event = Number of favourable outcomes / Total number of outcomes

Here, the number of favourable outcomes = 555

The total number of outcomes = 333+666+222+222+555 = 1998

So, the probability of getting shrimp = 555/1998

=0.277≈0.28

Therefore, the probability that the next type of stir fry ordered is shrimp is 0.28.

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