Aaron rolls a die 40 times. On 25 of those rolls, he has a 3. Michelle rolls a die 80 times. On 40 of those rolls, she has a 6. Which statement is TRUE about the experimental and theoretical probabilities?
A) The theoretical probability for rolling a 3 is the same as for rolling a 6.
B) The theoretical probability for rolling a 3 is greater than for rolling a 6.
C) The experimental probability for Aaron's tries is the same as Michelle's tries.
D) The experimental probability for Aaron's tries is less than the experimental probability for Michelle's tries.

Answer:

Step-by-step explanation:

[tex]\dfrac x{x+2}-\dfrac4{x-2}=1\qquad\qquad\qquad x\ne2\ \wedge\ x\ne-2\\\\\\ \dfrac {x(x-2)}{(x+2)(x-2)}-\dfrac{4(x+2)}{(x-2)(x+2)}=1\\\\\\ \dfrac {x^2-2x-4x-8}{x^2-4}=1\\\\ \\\dfrac {x^2-6x-8}{x^2-4}=1\quad\iff\quad x^2-6x-8=x^2-4\\\\x^2-6x-8=x^2-4\\\\-6x-8=-4\\\\-6x=4\\\\x=-\frac46\\\\x=-\frac23[/tex]

The solution to the equation is x = -2/3.

Two or more expressions with an equal sign are defined as an equation.

The given equation is  [tex]\frac{x}{x+2}-\frac{4}{x-2}=1[/tex].

Solve the equation as follows:
[tex]\frac{x}{x+2}-\frac{4}{x-2}=1\\\\\frac{x(x-2)-4(x+2)}{(x+2)(x-2)}=1\\\\\frac{x^2-2x-4x-8}{x^2-4}=1\\\\x^2-6x-8= x^2-4\\\\-6x = 8-4\\\\6x = -4\\\\x=-\frac{2}{3}[/tex]

Hence, the solution to the equation is x = -2/3.

Learn more about equations here:

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Answer:

15 CM

Step-by-step explanation:

Both sides are same length proven by the same angles making botrh sides 15 cm

Answer:

It will be 0.5 repeating so 0.555 because the 5 is repeating

9514 1404 393

Answer:

  0.56

Step-by-step explanation:

5/9 is the repeating decimal fraction 0.55555...

Rounded to the nearest hundredth, it is ...

  5/9 ≈ 0.56

Answer:

1. 30

2. x<-72

3. 7b=63

4. x=3.2

5. 1/10

Step-by-step explanation:

1. Substitute a for 10

2(150/10)

2*15

30

2. Think of it like a normal equation

x/4<-18

x<-18*4

x<-72

3. 7b=63

4. 2.5x=8

x=3.2

5. 1/5*1/2= 1/10

Answer:

the square root of a number is when you take a mole number and multiply it by itself in order to create a bigger number therefore some square roots would be 5 times 5 equals 25 therefore 5 is the square root of 25 so on and so forth

Answer:

516 cm squared

Step-by-step explanation:

To find the surface area of a rectangular prism such as this, is basically just like finding the OUTSIDE surfaces. We are looking for the "perimeter" of a 3D shape.

How do we do it?

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]Savings = \$500[/tex]

[tex]Withdrawal = \$12[/tex] weekly

Required

The question is incomplete as the linear function or table or graph of Melissa's plan is not given.

The available details can only be used to solve the function of the given individual

Let the number of weeks be w.

So: the amount left in w weeks is:

[tex]Amount = Savings - Withdrawal * w[/tex]

[tex]Amount = 500- 12* w[/tex]

[tex]Amount = 500- 12w[/tex]

Represent as a function

[tex]f(w)= 500- 12w[/tex]

To solve the amount left at the end of a certain week (say week 5), simply substitute 5 for w in [tex]f(w)= 500- 12w[/tex]

[tex]f(5) = 500 - 12 * 5[/tex]

[tex]f(5) = 440[/tex]

Answer:

it is two because one apple plus one apple equals two

it is 2

Answer:

[tex]y = 12.001 + 7.63 = 19.631[/tex]

Hope it helps

Answer: The answer is 0.8

Step-by-step explanation: Every gram is 0.001 of a kilogram

Answer:

The slope is 2

Answer:

60 = 45 + t

Step-by-step explanation:

Answer:

Range: [1, ∞)

Step-by-step explanation:

[tex]f(x)=2(x+3)^2+1[/tex]

Range: [1, ∞)

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

Explanation:

We'll plug x = -10 into each equation shown. If we get y = 4 as an output, then it is one of the answers.

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

A)

y = -x^2 + 6

y = -(-10)^2 + 6

y = -100 + 6

y = -94

We don't get y = 4, so we cross choice A off the list.

The point (-10,4) is not on y = -x^2+6. Instead, the point (-10,-94) is.

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

B)

y = (-1/2)*x - 1

y = (-1/2)*(-10) - 1

y = 5 - 1

y = 4

We can see that x = -10 leads to y = 4. The point (x,y) = (-10,4) is on the line. Choice B is one of the answers.

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

C)

y = (-1/10)*x - 3

y = (-1/10)*(-10) - 3

y = 1 - 3

y = -2

Choice C is not one of the answers since we want y = 4 as an output. So we can cross choice C off the list.

The point (-10,-2) is on the line instead of (-10,4)

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

D)

y = (1/10)x + 5

y = (1/10)*(-10) + 5

y = -1 + 5

y = 4

Choice D is one of the answers

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

E)

y = (1/5)*x^2 - 16

y = (1/5)*(-10)^2 - 16

y = (1/5)*(100) - 16

y = 20 - 16

y = 4

Choice E is one of the answers

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

An alternative method is to graph each equation and see if (-10,4) is on the curve or not. See the diagram below. Only choices B, D and E have (-10,4) on their respective curves.

Answer:

Step-by-step explanation:

ummm what there is no question!

Answer:

y = 8.49

Step-by-step explanation:

cos 45 = 6/y

0.7071 = 6/y

y = 8.49

Answer:

2x+30

Step-by-step explanation:

Answer:

U=-50

Step-by-step explanation:

Answer:3

Step-by-step explanation:

Answer:

2q=8

q=4

Step-by-step explanation:

hope that helped you

Answer:

8q + 1 = 6q + 9

2q + 1 = 9

2q = 8

q = 4

Answer:

27

Step-by-step explanation:

you can do cross multiplication

90/100 = x/30

100x=2700

x=27

Answer:

C

Step-by-step explanation:

A linear equation cannot have a variable as a denominator. So that makes C a non - linear equation. Also, if you graph C, it is NOT a straight line.  

Answer:

2/3

Step-by-step explanation:

Two points on this line are (0, -3) and (6, 1).

Going from the first to the second, we see a change in x of 6 units and a change in y of 4 units.  The slope of the line is thus m  = rise / run  =  4/6 = 2/3

Answer: 2 − 8x

Step-by-step explanation: