What is the probability of rolling a 5 on a fair number cube 5 times in a row?

Answer:

Since [tex]P(A)P(B) \neq P(A \cap B)[/tex], these two events are not independent.

Step-by-step explanation:

Independent events:

Two events, A and B, are independent if:

[tex]P(A \cap B) = P(A)*P(B)[/tex]

In this question:

Event A: Male

Event B: Independent

Probability of male:

20 + 15 + 17 = 52 out of (20 + 15 + 17 + 18 + 12 + 7) = 89.

So

[tex]P(A) = \frac{52}{89}[/tex]

Probability of favoring independent:

20 + 18 = 38 out of 89. So

[tex]P(B) = \frac{38}{89}[/tex]

Probability of male and favoring independent:

20 out of 89. So

[tex]P(A \cap B) = \frac{20}{89}[/tex]

Test if they are independent:

[tex]P(A)P(B) = \frac{52}{89}*\frac{38}{89} = \frac{52*38}{89*89} = 0.24946[/tex]

[tex]P(A \cap B) = \frac{20}{89} = 0.22472[/tex]

Since [tex]P(A)P(B) \neq P(A \cap B)[/tex], these two events are not independent.

answer:

h

Step-by-step explanation:

if there is more blues and green cards than purple there is a lower chance of getting purple

Answer:

[tex]K)~\frac{3}{16+x}[/tex]

Step-by-step explanation:

[tex]green~ cards=4[/tex]

[tex]blue ~cards=9[/tex]

[tex]purple~ cards=3[/tex]

[tex]pink ~cards=x[/tex]

[tex]total:-[/tex] 4×9×3×x

→ [tex]16+x[/tex]

[tex]p(x)=\frac{3}{16+x}[/tex]

[tex]Answer:K[/tex]

[tex]------------[/tex]

hope it helps...

have a great day!!

Answer:

the average no of customers in the system is 0.9

Step-by-step explanation:

Given that

The average number of arrivals is 6 per minute

And, the average service rate of a single server is 10 minutes

We need to find out the average no of customers in the system

So,

Lq = rho^2 / 1 ÷ rho

= (6 ÷ 10)^2 ÷ (1 - 6 ÷ 10)

= 36 ÷ 100  ×  10 ÷ 4

= 0.9

Hence, the average no of customers in the system is 0.9

The simple interest for principal of 640 and rate of 3% and time of 2 years is $3.84

The Simple interest the end of 2 years is calculated using the simple interest formula

The formula is stated as

Simple interest = Principal *  time *  rate / 100

In the problem the give data include

principal = $640

rate= 3%

time = 2 years

plugging in the values

Simple interest = Principal *  time *  rate / 100

Simple interest = 640 * 2 * 3 /100

Simple interest = 3840 / 100

Simple interest = $3.84

The simple interest  is $3.84

Learn more on simple interest at:

https://brainly.com/question/29785550

#SPJ1

Answer:

The equation of the line is: [tex]y = 0.6x + 0.6[/tex]

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept.

Two points:

We have these following two points in this exercise:

x = -6, y = -3, so (-6,-3)

x = 4, y = 3, so (4,3)

Finding the slope:

Given two points, the slope is given by the change in y divided by the change in x.

Change in y: 3 - (-3) = 3 + 3 = 6

Change in x: 4 - (-6) = 4 + 6 = 10

So

[tex]m = \frac{6}{10} = 0.6[/tex]

Then

[tex]y = 0.6x + b[/tex]

Finding b:

We replace one of the points in the equation to find b. I will use (4,3).

[tex]y = 0.6x + b[/tex]

[tex]3 = 0.6*4 + b[/tex]

[tex]2.4 + b = 3[/tex]

[tex]b = 0.6[/tex]

The equation of the line is: [tex]y = 0.6x + 0.6[/tex]

The value of the principal investment would be = $12,500.75

A principal investment is defined as the capital amount of money that is being deposited into an account with the purpose of receiving interest for a particular period of time.

The years of investment (t) = 9 years

The annual interest rate (r) = 3.9% = 3.9/100= 0.039

The total worth of the investment (A) = $17,757.16

Then, solve the equation for P

P = A / ert

P = 17,757.16 / e(0.039*9)

P = $12,500.75

Therefore, the principal amount that is needed which can be compounded continuously to get the total amount given = $12,500.75

Learn more about simple interest here:

https://brainly.com/question/25793394

#SPJ1

Answer:

E 16 cm

5cm + 5cm = 10cm

3cm + 3cm = 6cm

10cm + 6cm

= 16 cm

5×3=15 so 15 is your answer

Answer:

A

Step-by-step explanation:

its just a definition

Answer:

A

Step-by-step explanation:

The x and y coordinates are both positive. The clue of how to solve this is just to look at the x and y axis.

If x>0 (x is positive) then you are going right from (0,0).

If y >0 (y is positive) then you are going up.

Which quadrant does that?

Use an example

(4,2)

What quadrant are you in? If you said 1, you are correct. So the answer is A.

Answer:

90

Step-by-step explanation:

A regular quadrilateral is a square.

The sum of the exterior angles of a polygon is always

360 degrees

Therefore a quadrilateral has four exterior angles making the individual exterior angles

360 over 4=90 degrees

Hope this helps plz like and brainly :D

much would be appreciated <3

Solution :

Along the edge [tex]$C_1$[/tex]

The parametric equation for [tex]$C_1$[/tex] is given :

[tex]$x_1(t) = 9t , y_2(t) = 0 \ \ for \ \ 0 \leq t \leq 1$[/tex]

Along edge [tex]$C_2$[/tex]

The curve here is a quarter circle with the radius 9. Therefore, the parametric equation with the domain [tex]$0 \leq t \leq 1 $[/tex] is then given by :

[tex]$x_2(t) = 9 \cos \left(\frac{\pi }{2}t\right)$[/tex]

[tex]$y_2(t) = 9 \sin \left(\frac{\pi }{2}t\right)$[/tex]

Along edge [tex]$C_3$[/tex]

The parametric equation for [tex]$C_3$[/tex] is :

[tex]$x_1(t) = 0, \ \ \ y_2(t) = 9t \ \ \ for \ 0 \leq t \leq 1$[/tex]

Now,

x = 9t, ⇒ dx = 9 dt

y = 0, ⇒ dy = 0

[tex]$\int_{C_{1}}y^2 x dx + x^2 y dy = \int_0^1 (0)(0)+(0)(0) = 0$[/tex]

And

[tex]$x(t) = 9 \cos \left(\frac{\pi}{2}t\right) \Rightarrow dx = -\frac{7 \pi}{2} \sin \left(\frac{\pi}{2}t\right)$[/tex]

[tex]$y(t) = 9 \sin \left(\frac{\pi}{2}t\right) \Rightarrow dy = -\frac{7 \pi}{2} \cos \left(\frac{\pi}{2}t\right)$[/tex]

Then :

[tex]$\int_{C_1} y^2 x dx + x^2 y dy$[/tex]

[tex]$=\int_0^1 \left[\left( 9 \sin \frac{\pi}{2}t\right)^2\left(9 \cos \frac{\pi}{2}t\right)\left(-\frac{7 \pi}{2} \sin \frac{\pi}{2}t dt\right) + \left( 9 \cos \frac{\pi}{2}t\right)^2\left(9 \sin \frac{\pi}{2}t\right)\left(\frac{7 \pi}{2} \cos \frac{\pi}{2}t dt\right) \right]$[/tex]

[tex]$=\left[-9^4\ \frac{\cos^4\left(\frac{\pi}{2}t\right)}{\frac{\pi}{2}} -9^4\ \frac{\sin^4\left(\frac{\pi}{2}t\right)}{\frac{\pi}{2}} \right]_0^1$[/tex]

= 0

And

x = 0,  ⇒ dx = 0

y = 9 t,  ⇒ dy = 9 dt

[tex]$\int_{C_3} y^2 x dx + x^2 y dy = \int_0^1 (0)(0)+(0)(0) = 0$[/tex]

Therefore,

[tex]$ \oint y^2xdx +x^2ydy = \int_{C_1} y^2 x dx + x^2 x dx+ \int_{C_2} y^2 x dx + x^2 x dx+ \int_{C_3} y^2 x dx + x^2 x dx $[/tex]

                        = 0 + 0 + 0

Applying the Green's theorem

[tex]$x^2 +y^2 = 81 \Rightarrow x \pm \sqrt{81-y^2}$[/tex]

[tex]$\int_C P dx + Q dy = \int \int_R\left(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}\right) dx dy $[/tex]

Here,

[tex]$P(x,y) = y^2x \Rightarrow \frac{\partial P}{\partial y} = 2xy$[/tex]

[tex]$Q(x,y) = x^2y \Rightarrow \frac{\partial Q}{\partial x} = 2xy$[/tex]

[tex]$\left(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y} \right) = 2xy - 2xy = 0$[/tex]

Therefore,

[tex]$\oint_Cy^2xdx+x^2ydy = \int_0^9 \int_0^{\sqrt{81-y^2}}0 \ dx dy$[/tex]

                            [tex]$= \int_0^9 0\ dy = 0$[/tex]

The vector field F is = [tex]$y^2 x \hat i+x^2 y \hat j$[/tex]  is conservative.

Answer:

40 Balcony/15 floor

Step-by-step explanation:

A and C are out instantly cause the amount of tickets sold doesnt equal 55 and B is out cause 50x5=250 and 5x10=50 which totals to 300 not 350

Answer:

78

Step-by-step explanation:

a + 8b = 6 + 8 x 9 = 6 + 72 = 78

Answer: 78

Step-by-step explanation:

value of a=6

value of b=9

a+8b= 6+8*9

as the 8 will be multiplied by 9

6+8*9= 6+72

6+72 = 78

Answer:

Step-by-step explanation:

B im pretty sure hope its right

Answer:

Rounding to tenths

E: 56.8 %

F: 48.8 %

G: 44.9 %

H: 50.4 %

Step-by-step explanation:

Hope this helps!

Answer:

50.4 percent is f

Step-by-step explanation:

and the steps is calculate it

Answer: -3√3

Step-by-step explanation: Factor out the square roots from each term

2√54 -> 6√6

√27 -> 3√3

3√24 -> 6√6

The equation becomes 6√6 - 3√3 - 6√6

By combining like terms we can eliminate 6√6

This leaves us with -3√3 as the simplified solution

Answer:

-3√3

Step-by-step explanation:

do the hcf method to get all the values outside

hcf of 54= 2, 3, 3, 3

hcf of 27 = 3, 3, 3

hcf of 24 = 2,2,3,3

2✓2×3×3×3 - √3,3,3 - 3√2,2,3,3

take out the common factor and multiply it with the value we have outside leave it if it doesnt have a number

2×3√2×3 - 3✓3 -3×2×3

6√6 - 3√3 - 3×2×3

6×3 - 3√3 - 3×2×3

18-18 - 3✓3

-3√3

Answer:

D) ASA

Step-by-step explanation:

Answer:

3 is 20% of 15

Step-by-step explanation:

Answer:

-85º

Step-by-step explanation:

275 - 360 = -85

9514 1404 393

Answer:

  56.8 in

Step-by-step explanation:

The side length (s) can be found using the Pythagorean theorem. The short leg of the right triangle is 17/2 = 8.5 inches.

  8.5^2 + 18^2 = s^2

  s = √396.25 ≈ 19.906 . . . inches

Then the perimeter is ...

  2 × 19.9 in + 17 in = 56.8 in

Answer:

56.8

Step-by-step explanation:

Answer:

3t^3-2t^2

Step-by-step explanation:

Multiply the terms inside the parenthesis by the term outside.

In this case its t.

Answer:

y=x-2

Step-by-step explanation:

I graphed the equations on desmos and saw which one had those ordered pairs on the line.

Answer:

Step-by-step explanation:

8.4

Answer:

$8.4

Step-by-step explanation:

[tex]3.36*2.5[/tex]

Answer:

m = 2

Step-by-step explanation:

[tex]\frac{13-5}{6-2}=\frac{8}{4} =\boxed{2}[/tex]

Hope this helps.

Answer:

1. 29. Solve for the variable and graph the solution on a number line: –2x < –10 30. Solve for the variable and graph the solution on a number line: 9 + c > –2 31. Solve for the variable and graph the solution

2.  v – 4 ≥ 3 (6 + 2v

3. The last term, "the constant", is -5 Step-1 : Multiply the coefficient of the first term by the constant 4 • -5 = -20 Step-2 : Find two factors of -20 whose sum equals the coefficient of the middle term, which is -8

4.The first term is, 4p 2 its coefficient is 4 . The middle term is, -8p its coefficient is -8 . The last term, "the constant", is -5 Step-1 : Multiply the coefficient of the first term by the constant 4 • -5 = -20

Step-by-step explanation:

the rest is up to you, and u better say thanks and give me brainliest this took ages to explain

Answer:

1

Step-by-step explanation:

9 - 3  ÷ 1/3 + 1

first do division

3 ÷ 1/3 = 9

9 - 9 + 1 = 1