1. Suppose A = { 1, 3, 5, 7, 9, 11 , 13} and B = {2, 3, 5, 7, 11, 13}. Find the value of A U B . 

2. suppose c: {prime numbers less than or equal to 20}. find n(C)

3. Suppose A = { 2, 3, 4, 5, 6, 7, 9, 12} , B = {2, 12, x, 9} and B is a subset of A. What possible values could x have?

help ​

Answers

Answer 1

Problem 1

Answer:  {1, 2, 3, 5, 7, 9, 11, 13}

-----------------------

Explanation:

The notation A U B means we're applying a union between A and B. This will form a larger set in which items from A or B are thrown into A U B. Think of "union" as in getting married, and person A's stuff is combined with person B's stuff to form a larger set. Any duplicates are tossed. It's often helpful to sort from smallest to largest.

==========================================================

Problem 2

Answer:  8

-----------------------

Explanation:

Set C is defined as the set of prime numbers less than or equal to 20. The roster form is C = {2,3,5,7,11,13,17,19} which basically lists every item that fits the description earlier. Note how the value 1 is not prime, so it's not in the set C.

From here, we simply count out the values in set C to find there are 8 values. Therefore, n(C) = 8.

============================================================

Problem 3

Answer:   3, 4, 5, 6, 7

-----------------------

Explanation:

Let's consider a real world example of set vs subset. Consider the set of all animals and consider the subset of all dogs. Let's say

A = all animals

B = all dogs

We can see that set A is clearly larger than B. Also, any member of set B is also in set A, but not the other way around. In other words, if something is a dog, then they are also an animal. However, this doesn't work the other way around. For instance, we could have a cat in set A that wouldn't be in set B.

Let's return to the problem at hand. Since B is a subset of A, this must mean everything in B = {2,12,x,9} is found in set A. Sure enough, the 2, 12 and 9 are all in set A. The x must also be a value in set A so we could have

x = 3

x = 4

x = 5

x = 6

x = 7

as our possible answers. I'm not listing x = 2, x = 9 or x = 12 as they have been taken care of. I'm assuming that your teacher wants {2,12,x,9} to list unique items (ie it's after the duplicates are tossed out).


Related Questions

x^{4} - 5x^(2) + 2x + 3 < 0

Answers

the Answer is irrational number

Find the measure of the missing angles.
100°
b =
C=

Answers

Answer:

<b = 80

<c = 80

Step-by-step explanation:

<b and 100 form a straight line so they add to 180

<b +100 =180

<b = 180-100

<b = 80

angles b and c are vertical angles and vertical angles are equal

<c = <b = 80

A furniture store is having a sale on sofas and you're going to buy one. The advertisers know that buyers get to the store and that 1 out of 5 buyers change to a more expensive sofa than the one in the sale advertisement. Let X be the cost of the sofa. What is the average cost of a sofa if the advertised sofa is $250 and the more expensive sofa is $450

Answers

Answer:

$290

Step-by-step explanation:

We are told that 1 out of 5 buyers change to a more expensive sofa than the one in the sale advertisement.

Now we are told that the advertised sofa is $250 and the more expensive sofa is $450.

Thus;

P(x) for expensive sofa = 1/5

P(x) for sofa in sale advertisement = 4/5

Thus, expected value is;

E(X) = (1/5)450 + (4/5)250

E(x) = 90 + 200

E(x) = $290

Answer:

The average cost of a sofa = [tex]\$290[/tex]

Step-by-step explanation:

Cost of advertised sofa = [tex]\$250[/tex]

Cost of more expensive sofa = [tex]\$450[/tex]

So, the average cost of sofa,

[tex]E(x) = (450*\frac{1}{5})+ (250*\frac{4}{5})\\\\E(x) = 90 + 200\\\\E(x) = 290[/tex]

Hence,

The average cost of a sofa = [tex]\$290[/tex]

For more information, visit

https://www.bartleby.com/questions-and-answers/question-13-a-furniture-store-is-having-a-sale-on-sofas-and-youre-going-to-buy-one.-the-advertisers-/61410cf1-5b19-4491-9893-42336374e48e

Please help explanation if possible

Answers

Answer:

length = 48 feet , width = 32 feet

Step-by-step explanation:

Using

2W + 2L = 160 with W = L - 16 , then

2(L - 16) + 2L = 160 ← distribute and simplify left side

2L - 32 + 2L = 160

4L - 32 = 160 ( add 32 to both sides )

4L = 192 ( divide both sides by 4 )

L = 48

Substitute L = 48 into W = L - 16

W = 48 - 16 = 32

Thus length = 48 feet and width = 32 feet

Answer:

l = 48 cm

w =  32 cm

Step-by-step explanation:

length = l

Width w= l - 16

Perimeter = 160 ft

2*(l + w) = 160

2*(l + l -16) = 160

2*(2l - 16) = 160

Use distributive property

2*2l - 2*16 = 160

4l - 32 = 160  {add 32 to both sides}

4l = 160 + 32

4l = 192            {Divide both sides by 4}

l = 192/4

l = 48 cm

W = 48 - 16 = 32 cm

A typist can type 4800 words per hour. How many words can she type in 1 minute?
(Using direct proportion)​

Answers

Answer: 80

1 hour= 60mins

So to know how many words can she type in 1 min, we do the math "4800 : 60"

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!

Answers

Answer:

1071.79 yd³

Step-by-step explanation:

radius r = 16/2 = 8 yd

height = 16 yd

volume = (1/3)×πr²h

= (1/3)×3.14×8²×16

= 1071.79 yd³ (rounded to the nearest tenth)

You put $5000 in an investment account with interest compounded
continuously. Calculate the approximate annual interest needed for the
account to grow to $10,000 after 20 years.

Answers

Answer:

3.465 %

Step-by-step explanation:

10000 = 5000 [tex]e^{20r}[/tex]

2= [tex]e^{20r}[/tex]

ln(2) = 20r ln(e)

r = ln(2)/20

r = 0.03465

Find the surface area of the triangular prism

Answers

Front: 12 square centimeters
1/2 x 6 x 4 = 12

Back: 12 square centimeters
1/2 x 6 x 4 = 12

Right: 15 square centimeters
3 x 5 = 15

Left: 15 square centimeters
3 x 5 = 15

TOTAL: 54 square centimeters

The surface area is the added areas of each face of a 3D figure.
Formulas I’ve used:
Area of a parallelogram:
A = bh

Area of a triangle:
A = 1/2bh

HELP ME PLEASE.
find the perimeter,area and T.S.A of the following solids​

Answers

Answer:

I think the perimeter is 50cm the solids is 600cm³

Step-by-step explanation:

Perimeter: (5×10)=50cm

Solids: divided with 2box(A box & B box)

Abox: 5cm x 5cm x 12cm

=300cm³

Bbox: 5cm x 12cm x 5cm

=300cm³

Solids:(Abox +Bbox) 300cm³ + 300cm³

=600cm³

I think, I'm sorry if it's wrong

Once upon a time, there was a former whose family raised pigs and chickens. One morning, the farmer's wife looked into the barnyard and told her husband that she counted 24 heads and 80 feet. How many chickens are in the yard? How many pigs are in the yard?

Answers

Using a system of equations, it is found that:

There are 8 chickens in the yard.There are 16 pigs in the yard.

-----------------------------------------

This question is solved using a system of equations. I am going to say that:

x is the number of chickens.y is the number of pigs.

-----------------------------------------

A chicken has 1 head, as do a pig.There are 24 heads.

Thus:

[tex]x + y = 24 \rightarrow y = 24 - x[/tex]

-----------------------------------------

A chicken has 2 feet.A pig has 4 feet.In total, there are 80 feet.

Thus:

[tex]2x + 4y = 80[/tex]

-----------------------------------------

Number of chicken:

Since [tex]y = 24 - x[/tex]

[tex]2x + 4y = 80[/tex]

[tex]2x + 4(24 - x) = 80[/tex]

[tex]2x + 96 - 4x = 80[/tex]

[tex]2x = 16[/tex]

[tex]x = \frac{16}{2}[/tex]

[tex]x = 8[/tex]

There are 8 chickens in the yard.

-----------------------------------------

Number of pigs:

[tex]y = 24 - x = 24 - 8 = 16[/tex]

There are 16 pigs in the yard.

A similar problem is given at https://brainly.com/question/24104709

I need help please help me

Answers

Answer:

I found x for you, right there.

Answer:  x is 12 and y is 5

Step-by-step explanation:

help me, asap, please

Answers

answer is 19

the explanation is in the attachment

#What is the value of the discriminant for the quadratic equation –3 = –x2 + 2x?

Discriminant = b2 – 4ac

–8
4
8
16

Answers

Answer:

16

Step-by-step explanation:

the quadratic equation –3 = –x2 + 2x can be changed into :

x²-2x-3= 0

a=1, b= -2 , and c = -3

so, the discriminant = (-2)²-4(1)(-3)

= 4 + 12 = 16

Find the surface area of the composite figure

Answers

Answer:

384 cm^2

Step-by-step explanation:

Start with the prism (I multiply by 2 because some of the surfaces are more of):

4×15×2=1206×15×2=1806×4=24

The Triangular Prism (I divide by 2 because it is a triangle shape on the sides):

3×4/2*2=123×6=186×5=30

The Last Step (adding everything):

120+180+24+12+18+30=384


Find the value of z
A.110
B.141
C.80
D.100

Answers

Answer:

Option A 110degree is the answer

Please Help !


Which of the following describes point D? (-4, 0) (0, -4) (0, 4) (4, 0)

Answers

Answer:

D(0 , 4)

Step-by-step explanation:

Point D is on the y axis. So, x-coordinate  = 0

y- coordinate is the vertical length from origin which is 4

Answer:

D(0 , 4)

Step-by-step explanation:

Given a dilation around the origin, what is the scale factor K?

D o, K = (2,4) → (3,6)

Answers

Answer:

It is 3/2, I got it right on my exam.

Step-by-step explanation:

Dilation is a transformation that allows you to resize an object. The dilation factor of the given point is 3/2.

What is dilation?

Dilation is a transformation that allows you to resize an object. Dilation is a technique for making items bigger or smaller. This transformation yields a picture that is identical to the original shape. However, there is a size discrepancy in the form.

Given the dilation of the k around the origin as K = (2,4) → (3,6), therefore, the point k is dilated 1 unit to the right and 2 units upwards.

Let the dilation factor be represented by a, then,

2 × a = 3

a = 3/2

Similarly for the y-axis,

4 × a = 6

a = 6/4 = 3/2

Hence, the dilation factor of the given point is 3/2.

Learn more about Dilation:

https://brainly.com/question/13176891

#SPJ2

[tex]|\frac{x+1}{x-1}+1|\ \textgreater \ \frac{x+1}{x-1}+1[/tex]

Answers

The inequality boils down to

|y| > y

By definition of absolute value, we have

• |y| = y if y ≥ 0

• |y| = -y if y < 0

So if y ≥ 0, we have

y > y

but this is a contradiction.

On the other hand, if y < 0, we have

-y > y   ==>   2y < 0   ==>   y < 0

and no contradiction.

Now replace y with (x + 1)/(x - 1) + 1. Then you're left with solving

(x + 1)/(x - 1) + 1 < 0

(x + 1 + x - 1)/(x - 1) < 0

2x/(x - 1) < 0

The left side is negative if either 2x > 0 and x - 1 < 0, or 2x < 0 and x - 1 > 0. The first case reduces to x > 0 and x < 1, or 0 < x < 1. In the second case, we get x < 0 and x > 1, but x cannot satisfy both conditions, so we throw this case out.

what is simplfiled for x^8 y^2 / x^3 y^9

Answers

Answer:

x^5/y^7

Step-by-step explanation:

x^8 y^2 / x^3 y^9

We know that a^b/ a^c = a^(b-c)

Simplify the x terms

x^8 / x^3 = x^(8-3) = x^5

Simplify the y terms

y^2 / y^9 = y^(2-9) = y^-7

We know a^-b = 1/a^b

y^-7 = 1/y^7

Put the terms back together

x^5/y^7

In the town of Rockville, 35 of the students in middle school participate in organized sports after school. If 14 of them play basketball, what fraction of the students play basketball?

Answers

Answer:

2/5

Step-by-step explanation:

The fraction that play basketball is the number that play basketball over the total

14/35

Divide the top and bottom by 7

2/5

4.5 X 6 - 1243
0 26
21
O
6
o
-10

Answers

Answer:

-1243

Step-by-step explanation:

4.5×6-1243

27-1243

=-1216

Yet another Calculus question...

This time, it's about integrals/antiderivatives. The question asks to find the value of [tex]\int\limits^6_0 {[g(x)+2]} \, dx[/tex]. Since the derivative of 2 is 0, can I directly find [tex]\int\limits^6_0 {g(x)} \, dx[/tex]? Thanks in advance!

Answers

Answer:

[tex]\displaystyle \int\limits^6_0 {[g(x) + 2]} \, dx = 32[/tex]

General Formulas and Concepts:

Calculus

Integration

Integrals

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int\limits^6_0 {g(x)} \, dx = 20[/tex]

[tex]\displaystyle \int\limits^6_0 {[g(x) + 2]} \, dx[/tex]

Step 2: Integrate

[Integral] Rewrite [Integration Property - Addition/Subtraction]:               [tex]\displaystyle \int\limits^6_0 {[g(x) + 2]} \, dx = \int\limits^6_0 {g(x)} \, dx + \int\limits^6_0 {2} \, dx[/tex][2nd Integral] Rewrite [Integration Property - Multiplied Constant]:         [tex]\displaystyle \int\limits^6_0 {[g(x) + 2]} \, dx = \int\limits^6_0 {g(x)} \, dx + 2\int\limits^6_0 {} \, dx[/tex][1st Integral] Substitute in value:                                                                   [tex]\displaystyle \int\limits^6_0 {[g(x) + 2]} \, dx = 20 + 2\int\limits^6_0 {} \, dx[/tex][Integral] Reverse Power Rule:                                                                     [tex]\displaystyle \int\limits^6_0 {[g(x) + 2]} \, dx = 20 + 2(x) \bigg| \limits^6_0[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:           [tex]\displaystyle \int\limits^6_0 {[g(x) + 2]} \, dx = 20 + 2(6)[/tex]Simplify:                                                                                                         [tex]\displaystyle \int\limits^6_0 {[g(x) + 2]} \, dx = 32[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer:

32

(I think I remember your other information correctly.)

Step-by-step explanation:

I think you said you were given

*Integral from x=-5 to x=0 of g was -14

*Integral from x=-5 to x=6 of g was 6

Asked to find integral( g(x) + 2 , from x=0 to x=6)

Yes this can be split into two integrals:

Integral(g(x), x=0 to x=6) + Integral(2, x=0 to x=6)

The last integral is easier... the antiderivative or 2 is 2x. So evaluate 2x as the limits and subtract. Always plug in the top limit first. 2(6)-2(0)=12-0=12

Let's start with the bigger interval from x=-5 to x=6 which was 6... and since we want to get rid of the interval from x=-5 to x=0 to find the integral of g from x=0 to 6, all we must do is do 6-(-14)=20.

Integral( g(x) + 2 , from x=0 to x=6)

=

Integral(g(x), x=0 to x=6) + Integral(2, x=0 to x=6)

=

20+12

=

32

help pls will give brainly

Answers

Answer:

Graph B

Step-by-step explanation:

Look at the first part of the function: 2-x , -7 ≤ x ≤ 5

If you put -7 in place of x you'll have:

2 - (-7) = 2 + 7 = 9

In the graph A, the point x = -7 have a y = 8, so cannot be the graph A. and it have to be graph B

Can someone please help me

Answers

Answer:

c

Step-by-step explanation:

come on ! you can literally see that in the chart.

how many parts of the gray 3/8 are covered by the gray 1/4 ?

2 parts = 2/8 are clearly covered by 1/4.

2/8 is what part of 3/8 ?

it is the same question as "2 is what part of 3" ?

is 2 a quarter (1/4) of 3 ? no, 1/4×3 = 3/4 and not 2.

is 2 one third (1/3) of 3 ? no, 1/3 of 3 = 1/3×3 = 1 and not 2.

is 2 two thirds (2/3) of 3 ? ah, 2/3 × 3 = 2. that is correct !

is 2 three quarters (3/4) of 3 ? no, 3/4×3 = 9/4 and not 2.

once you have the same denominator, you can easily compare the numerators and ignore the denominators for such problems.

Find angle CBA

pls help

Answers

Answer:

40

Step-by-step explanation:

u can draw a line at point c parallel to line ab

angle at d and lower part of c is interior angle so u can find the value at lower part of c that is 180-145=35

so point c 75-35=40 is upper part of point c

upper part of c and angle b is alternate angle so both angle are the same

angle cba is 40

Answer:

<CBA = 40°

Step-by-step explanation:

If AB is parallel to DE, you can make an irregular pentagon by continuing AB and drawing a line perpendicular to DE.  The sum of the interior angles of a pentagon is 540.  You can use this to solve for the supplement of <CBA, then subtract that from 180.  (I’m sure there’s an easier way, but I cant think of one right now).

540-90-90-145-75=x

140=x

<CBA=180-140= 40°

Instructions: Determine whether the
following polygons are similar. If yes, type
in the similarity statement and scale
factor. Pano, type 'None' in the blanks.
35
M
х
w -18
50°
63
63
10
10
50°
35 N
z
18
Similar: Yes
Similarity Statement:
Scale Factor:

Answers

Answer:

No, the above polynomials aren't similar as they don't have a constant scale factor

The following polygons given in the question are not similar .

What are similar polygons ?

Similar polygons are those polygon which have the similar shapes but with different size and dimensions.  Similar polygons have also the scaling factor ration equal.

How to identify whether the given polynomials are similar?

There are two polygons given in the question LMNO and WXYZ .

For both of the polygons, we are checking the adjacent sides of the polygons.

The value of LM = 35 but for the other polygon , its adjacent side WX = 18.

Similar LO = 63 and WZ = 10 .

Also the adjacent angles are not equal as ∠MNO = 50° and ∠ZWX = 50° .

Therefore, the polygons given have different scaling factor.

Thus, the following polygons given in the question are not similar .

To learn more about similar polygons, refer -

https://brainly.com/question/16058229

#SPJ2

Simplify: 5^(x+2)-4×5^x÷21×5^x​

Answers

Answer:

(1/21)(21×5^(x+2)-4×5^2x)

Step-by-step explanation:

5^(x+2)-4×5^x÷21×5^x

= 5^(x+2)-4×5^2x/21

= 1/21(21×5^(x+2)-4×5^2x)

Find the scale factor where the pre-image is the small triangle and the image is the large triangle.

Answers

Answer:

D

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to pre image

scale factor = [tex]\frac{18}{14}[/tex] = [tex]\frac{9}{7}[/tex] → D

1) Define onto function. 2) Find k if f.f(k) = 5 where f (k) = 2k – 1​

Answers

Answer:

3

Step-by-step explanation:

2k-1=5

>2k=5+1=6

>k=3

Answer:

1)

An onto function is a function where it's range is the term in that function.

[tex]{ \sf{if \: function \: is \: x \: to \: y}} \\ { \sf{then \: range \: of \: function \: is \: y}} \\ i.e \: \: f(x) = y[/tex]

It is given by formula:

[tex]{ \boxed{ \sf{ {x}^{y} - {}^{x} c _{1}(n - 1) {}^{y} + {}^{x} c _{2} (x - 2) {}^{y} + ..... {x}^{n} }}}[/tex]

2).

[tex]f(k) = 2k - 1 \\ but \: f(k) = 5 \\ 2k - 1 = 5 \\ 2k = 1 + 5 \\ 2k = 6 \\ k = 3[/tex]

Solve for x. Leave your answer in simplest radical form.

Answers

Answer:

sqrt 51

Step-by-step explanation:

You should use the pythagorean theorem, which states a^2+b^2=c^2. So the missing side length for the smaller triangle is sqrt{2^2+3^2}=sqrt{4+9}=sqrt{13}. And the side length x is sqrt{8^2-sqrt{13}^2}=sqrt{64-13}=sqrt{51}

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