Subsets and Sets HELP
Attached is the photo reference

Answer:

39

Step-by-step explanation:

1. (2(4)-5)(2(4)+5)

2.(3)(13)

3.39

Answer:

Step-by-step explanation:

This is a difference of squares question. You should 64 = 25 = 39 Let's see if that happens.

Difference of squares

(2x - y) ( 2x + y) = 4x^2 - y^2

4(4)^2 - (5)^2

64 - 25 = 39

Now do the question exactly as it is written.

(2*4 - -5)(2*4 + -5)

(8 +5)(8 - 5)

3 * 13

39

They really do give the same answer.

Answer:

A mutually exclusive event is when there are two events that can occur, such as flipping a coin, either it will be a head or a tail. Hence, both the events here are mutually exclusive.

An independent event is termed as an event that occurs without being affected by other events. The happening of one event has nothing to do with the happening of the other and there is no cause-effect between the two.

Answer:

2/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

There are 10 even numbers from 1 to 20

2 4 6 8 10 12 14 16 18 20

There 20 possible choices.

P(Even) = 10 /20 = 1/2

Answer:

6x^2-23x+20

Step-by-step explanation:

i think the expanded form of that equation is equal to it.

(3x-4)(2x-5)

3x(2x-5)-4(2x-5)

6x^2-15x-8x+20

6x^2-23x+20

I hope this helps and sorry if it's wrong

(a) The n-th partial sum of the infinite series,

[tex]\displaystyle\sum_{n=0}^\infty\frac5{4^n}[/tex]

is

[tex]S_n = \displaystyle\sum_{k=0}^n\frac5{4^k} = 5\left(1+\frac14+\frac1{4^2}+\cdots+\frac1{4^n}\right)[/tex]

Multiplying both sides by 1/4 gives

[tex]\dfrac14S_n = \displaystyle\sum_{k=0}^n\frac5{4^k} = 5\left(\frac14+\frac1{4^2}+\frac1{4^3}+\cdots+\frac1{4^{n+1}}\right)[/tex]

Subtract this from [tex]S_n[/tex] and solve for [tex]S_n[/tex] :

[tex]S_n-\dfrac14S_n = 5\left(1-\dfrac1{4^{n+1}}\right)[/tex]

[tex]\dfrac34 S_n = 5\left(1-\dfrac1{4^{n+1}}\right)[/tex]

[tex]S_n = \dfrac{20}3\left(1-\dfrac1{4^{n+1}}\right)[/tex]

(your solution is also correct)

(b) The infinite sum is equal to the limit of the n-th partial sum:

[tex]\displaystyle\sum_{n=0}^\infty \frac5{4^n} = \lim_{n\to\infty} \boxed{\sum_{k=0}^n \frac5{4^k}}[/tex]

and the sum indeed converges to 20/3.

Answer:

Amount of members = 9

then we multiply the different probabilities of the trustess which is 4, so we do 9 x 4= 36

Step-by-step explanation:

So there are 36 different ways

answer: 36 different ways

Answer:

The sum of the probabilities of all possible outcomes is not 1, which means that a probability distribution is not given.

Step-by-step explanation:

We are given these following probabilities:

[tex]P(X = 0) = 0.6591[/tex]

[tex]P(X = 1) = 0.2872[/tex]

[tex]P(X = 2) = 0.0503[/tex]

[tex]P(X = 3) = 0.0044[/tex]

[tex]P(X = 4) = 0.0015[/tex]

Determine whether a probability distribution is given.

We have to see if the sum of the probabilities of all possible outcomes is 1. So

[tex]0.6591 + 0.2872 + 0.0503 + 0.0044 + 0.0015 = 1.0025[/tex]

The sum of the probabilities of all possible outcomes is not 1, which means that a probability distribution is not given.

Answer:

[tex]S.E = 0.108[/tex]

Step-by-step explanation:

From the question we are told that:

Mean age [tex]\=x=5.5[/tex]

standard deviation [tex]\sigma= 0.7 years.[/tex]

Sample size [tex]n=43[/tex]

Generally the equation for Standard error is mathematically given by

[tex]S.E= \sigma \bar x[/tex]

[tex]S.E= \frac{\sigma}{\sqrt n}[/tex]

[tex]S.E= \frac{0.7}{\sqrt 43}[/tex]

[tex]S.E = 0.108[/tex]

Answer:

39

Step-by-step explanation:

5 + 15 + 12 + 7 = 39

Answer:

39

Step-by-step explanation:

5 + 15 = 20, 12 + 7 = 19, 20 + 19 = 39.

Answer:

12

Step-by-step explanation:

arrange the numbers in ascending order and cross out from either side till you have a middle line

FINAL ANSWER:

12

Step-by-step explanation:

Median is the middle number in the data set.

so first of ... we need to arrange the group of numbers from lower to greater.

16, 12, 10, 15, 7, 9, 16 ⇒ 7, 9, 10, 12, 15, 16, 16

Now that we have arranged the numbers from least to greatest all we need to do is to find the middle number of the data set (data set? they are the group of numbers)

Ok, so what you want to do here is to just count the numbers until you get to the middle number of the data set...

7, 9, 10, 12, 15, 16, 16

the median in the given data set is 12.

I hope this helps you!!! Let me know if my answer is incorrect or not...

HAVE A GREAT DAY AND GOD BLESS YOU ;)!!!

Answer:

The motion is centered about (0,1)

Step-by-step explanation:

x = 3sint ---- (1)

y = 1 + cos(t) ----- (2)

x^2 = 9 *sin(t)*sin(t)  

hence; (x^2)/9 = sin(t)*sin(t) ---- (3)

y-1 = cos(t)  

hence; (y-1)^2 = cos(t) * cos(t)  ---- (4)

adding  equation 3 and 4

(x^2)/9 + ( y - 1 )^2 = 1

The motion is centered about (0,1)

Answer:

B 3360

Step-by-step explanation:

Area of Rectangle = Length X Width

120 X 28

= 3360 cm

Answered by Gauthmath

Answer:

y = 7x - 140

The slope is 7

The y-intersept is -140

= (7, -140)

Step-by-step explanation:

y + 14 = 7(x - 18)

y + 14 = 7x - 126

y =7x - 126 - 14

y = 7x - 140

Answer:

The image shows the graph of y = 2 tan x.

Answer:

Area of ΔPQR is 28 units²

Step-by-step explanation:

-P is the point with coordinates ( 0, y-intercept for line x-2y+2 =0)

-rearrange the equation in the point-slope form y=mx+b  to find the y coordinate of the point P( 0, b)

x-2y+2 = 0, subtract x and 2 from both sides

-2y = -x-2, divide by -2 both sides

y= (1/2)x +1 so b=1 and P (0, 1)

-Q  is the point with coordinates ( 0, y-intercept for line 3x+y -15 =0)

-rearrange the equation in the point-slope form y=mx+b  to find the y coordinate of the point Q( 0, b)

3x +y -15 =0, subtract 3x and add 15 to both sides

y= -3x +15 so b=15 and Q(0,15)

-R is the intersection of the two lines so is the solution of the system of equations y= (1/2)x +1 and y= -3x +15

(1/2)x +1 =  -3x +15, add 3x and subtract1

(1/2) x+3x = 15-1, combine like terms

(7/2)x = 14 , multiply both sides by 2

7x = 28, divide both sides by 7

x= 4

y= (1/2)x +1 = (4/2) +1 =3 so R(4,3)

- the area of ΔPQR is (base *height)/2

base= 15-1= 14

height = 4

A= (14*4)/2 = 14*2 = 28

Answer:

x = 12 m and y = 22 m

Step-by-step explanation:

Total area = 264 [tex]m^2[/tex]

∴ xy = 264

 [tex]$y=\frac{264}{x}$[/tex]     ............(1)

Cost function = [tex]C(x,y) = 2 x (15.60) + 2y(15.60) + 2x(13)[/tex]

                          [tex]C(x,y) = 57.2 x + 31.2y[/tex]

Therefore, using (1),

[tex]$C(x) = 57.2x+31.2 \left(\frac{264}{x} \right)$[/tex]

[tex]$C(x) = 57.2x+\frac{8236.8}{x} \right)$[/tex]

So, cost C(x) minimum where C'(x) = 0

[tex]$C'(x) = 57.2 - \frac{8236.8}{x^2}=0$[/tex]

[tex]$x^2=\frac{8236.8}{57.2}$[/tex]

[tex]$x^2=144$[/tex]

[tex]$x=12$[/tex] m

Therefore, [tex]$y=\frac{264}{x}$[/tex]

                      [tex]$=\frac{264}{12}$[/tex]

                      = 22 m

So the dimensions are  x = 12 m and y = 22 m.

[tex] \sf Q) \: {3}^{3} + {4}^{2} = {?}[/tex]

[tex] \sf \to \: {3}^{3} + {4}^{2} [/tex]

[tex] \sf \to \: 27 + 16= 43 [/tex]

Thus, the value is 43.

Michael = 210 / 3.5 = 60 miles per hour

Jordan = 330/ 6 =55 miles per hour

Jordan drove 5 miles per hour slower than michael

9514 1404 393

Answer:

   5/9 m/min

Step-by-step explanation:

The depth of the water is 2/5 of the depth of the trough, so the width of the surface will be 2/5 of the width of the trough:

  2/5 × 2 m = 4/5 m

Then the surface area of the water is ...

  A = LW = (18 m)(4/5 m) = 14.4 m²

The rate of change of height multiplied by the area gives the rate of change of volume:

  8 m³/min = (14.4 m²)(h')

  h' = (8 m³/min)/(14.4 m²) = 5/9 m/min

Answer:

a. (9, 2)

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the function is not given. So, I will make an assumption.

A quadratic function is represented as:

[tex]f(x) = ax^2 + bx + c[/tex]

If [tex]a > 0[/tex], then the function has a minimum x value

E.g. [tex]f(x) = 4x^2 - 5x + 8[/tex] ------ [tex]4 > 0[/tex]

Else, then the function has a maximum x value

E.g. [tex]f(x)= -4x^2 -5x + 8[/tex] ---- [tex]-4 < 0[/tex]

The maximum or minimum x value is calculated using:

[tex]x = -\frac{b}{2a}[/tex]

For instance, the maximum of [tex]f(x)= -4x^2 -5x + 8[/tex] is:

[tex]x = -\frac{-5}{2*-4}[/tex]

[tex]x = -\frac{5}{8}[/tex]

So, the maximum of the function is:

[tex]f(x)= -4x^2 -5x + 8[/tex]

[tex]f(-\frac{5}{8}) = -4 * (-\frac{5}{8})^2 - 5 *(-\frac{5}{8}) +8[/tex]

[tex]f(-\frac{5}{8}) = 9.5625[/tex]

Answer: [tex]405.7\ ft[/tex]

Step-by-step explanation:

Given

After 11 sec, diver is 69 feet below sea level

after 28 s , it is 195 feet

rate of traveling

[tex]\Rightarrow u=\dfrac{195-69}{28}\\\\\Rightarrow u=4.53\ ft/s[/tex]

after 1.5 minutes, that is 90 s, diver must have traveled

[tex]\Rightarrow d=4.53\times 90\\\Rightarrow d=407.7\ ft[/tex]

Answer:

7299 feet

Step-by-step explanation:

At 11 second the depth is 69 feet

At 28 seconds the depth is 195 feet  

Let the initial velocity at the time t = 0 is u.

Use second equation of motion

[tex]s = u t +0.5 at^2\\\\69 =11 u + 0.5 a\times 11\times 11\\\\69 = 11 u + 60.5 a..... (1)\\\\195 = u (28 -11) +0.5 a\times (28-11)^2\\\\195 = 17 u + 144.5 a .....(2)[/tex]

By soling (1) and (2)

a = 1.73 m/s^2, u = 3.25 m/s

So, the distance in 1.5 minutes is

h = 3.25 x 1.5 x 60 + 0.5 x 1.73 x 1.5 x 1.5 x 60 x 60

h = 292.5 + 7006.5 = 7299 ft

Given:

The given expression is:

[tex]3.5\times 10^{-2}+2.3\times 10^{-2}[/tex]

To find:

The simplified form of the given expression.

Solution:

We have,

[tex]3.5\times 10^{-2}+2.3\times 10^{-2}[/tex]

It can be written as:

[tex]=(3.5+2.3)\times 10^{-2}[/tex]

[tex]=5.8\times 10^{-2}[/tex]

Therefore, the simplified form of the given expression is [tex]5.8\times 10^{-2}[/tex].

Answer:

Step-by-step explanation:

This is the combination of 2 out of 20:

We have to find,

The number of ways in which he can choose two students.

Now the 2 out of 20 combination is,

→ 20C2

→ 20!/18!2!

→ 20 × 19/2

→ 10 × 19

→ 190 ways

Hence, there are 190 ways.

Answer:

The standard error for the new sample size is of 23.4.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Interpretation:

From this, we can gather that the standard error is inversely proportional to the square root of the sample size, that is, for example, if the sample size is multiplied by 4, the standard error is divided by the square root of 4, which is 2.

Standard error of 52.4, sample size multiplied by 5. What is the standard error for the new sample size?

The standard error of 52.4 divided by the square root of 5. So

[tex]s = \frac{52.4}{\sqrt{5}} = 23.4[/tex]

The standard error for the new sample size is of 23.4.

Answer:

81 pi cm^2

or approximately 254.34 cm^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

A = pi (9)^2

A = 81 pi

Using 3.14 as an approximation for pi

A = 81 (3.14)

A =254.34 cm^2

Answer:

81pi cm^2

Step-by-step explanation:

formula : pi*r^2

pi*9^2

pi*81

Answer:

1640

Step-by-step explanation:

Take the total amount and divide by the amount for one

Make sure to write 6 cent in dollar form (.06)

98.41 / .06

1640.1666

Round down since we need to buy whole bottles

1640

Answer:

20

22

24

Step-by-step explanation:

To determine the maximum number of runners that Manuel could make take the amount of cloth and divide by 3/4

18 ÷ 3/4

Copy dot flip

18 * 4/3

18/3 *4

6*4

24

He can make less than or equal to 24

Answer:

20, 22, 24

Step-by-step explanation: