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Lesechka [4]
3 years ago
8

We will flip a balanced coin 3 times and for each toss, record whether we get a Head or a Tail. Write all possible outcomes of t

his experiment to find the probability that we get exactly 1 tail.
a. 2/3
b. 1/8
c. 1/3
d. 3/8
Mathematics
1 answer:
Mandarinka [93]3 years ago
4 0

Answer: A- 2/3

Step-by-step explanation:

Possible outcomes when a coin is tossed 3 times is 1/2 + 1/2+ 1/2= 3/2

Probability of getting exactly one tail=

3/2x=1

x=1÷3/2

=1 ×2/3

=2/3

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What is the answer and show the work for 600299-510345=
scZoUnD [109]

Answer:

89954

Step-by-step explanation:

Sorry. I wish i could show my work, but I can upload my picture work. I will post that here when my computer is working again.

6 0
3 years ago
Jane’s cell phone plan is $40 each month plus $0.15 per minute for each minute over 200 minutes of call time. Janes cell phone b
san4es73 [151]

Answer:

The equation is 40+0.15m = 58.00 whose solution is m =120\:minutes.

Step-by-step explanation:

Let us call m the number of minutes the phone is used over 200 minutes, then we have

\boxed{40+0.15m = 58.00} <em>(this says monthly bill of $40 plus the cost of phone usage over 200 minutes must equal $58 )</em>

This equation can be used to solve for  m u as follows:

0.15m = 58-40

m = \dfrac{18}{0.15}

\boxed{m = 120\:minutes}

8 0
3 years ago
The hypotenuse of a right triangle is 50 and the short leg is 30, find the projection of the leg onto the hypotenuse
gladu [14]
Consider the attached figure. All the triangles shown are similar, so

CB/CA = CD/CB
30/50 = projection/30
projection = 30^2/50
projection = 18

6 0
3 years ago
Solve: (2x - 3)^2 = -4
Wewaii [24]

Answer:

No real solutions;

x=i+1.5

Step-by-step explanation:

The easiest method to solve an algebraic equation is to use inverse operations. This applies to the given equation;

(2x-3)^2=-4\\

- Take the square root of both sides

\sqrt{}                

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

As one can see, the right side is a negative number. However, one cannot take the square root of a negative number and get a real result. Therefore, one must use imaginary numbers. Remember, the imaginary unit (i) represents (\sqrt{-1}).

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

2x-3=2i

- Add (3) to undo the (-3)

+3          

2x=2i+3

- Divide by (2) to remove the coefficient of (2x)

÷2           ÷

x=\frac{2i+3}{2}

Simplify,

x=i+1.5

6 0
3 years ago
Trainees must complete a specific task in less than 2 minutes.Consider the probability density function below for the time ittak
grigory [225]

Answer:

1) P(X<1) = 0.5850

2) P(X>1) = 0.41500

3) P(0.68 < X < 1) = 0.0013

4) E(X) = 0.8867 minute

5) E(X²) = 1.1064

6) Var(X) = 0.3202

Step-by-step explanation:

Probability density function = f(x) = 0.67 - 0.17x (for 0 < x < 2)

1) The probability a trainee will complete the task inless than 1 minutes is given as P(X<1)

And,

P(X<1) = 1 - P(X≥1)

P(X≥1) = ∫²₁ f(x) dx = ∫²₁ (0.67 - 0.17x) dx = [0.67x - 0.085x²]²₁ = [0.67(2) - 0.085(2²)] - [0.67(1) - 0.085(1²)] = (1) - (0.585) = 0.415

P(X<1) = 1 - P(X≥1) = 1 - 0.415 = 0.5850

2) The probability that a trainee will complete the task inmore than 1 minutes is given as P(X>1)

And

P(X>1) = 1 - P(X≤1)

P(X≤1) = ∫¹₀ f(x) dx = ∫¹₀ (0.67 - 0.17x) dx = [0.67x - 0.085x²]¹₀ = (0.67(1) - 0.085(1²)) = 0.67 - 0.085 = 0.585

P(X>1) = 1 - P(X≤1) = 1 - 0.585 = 0.4150

3) The probability it will take a trainee between 0.68minutes and 1 minutes to complete the task. P(0.68 < X < 1)

P(0.68 < X < 1) = P(X<1) - P(X>0.68)

P(X<1) = 0.5850 (from question number 1)

P(X>0.68) = 1 - P(X≤0.68)

P(X≤0.68) = ∫⁰•⁶⁸₀ f(x) dx = ∫⁰•⁶⁸₀ (0.67 - 0.17x) dx = [0.67x - 0.085x²]⁰•⁶⁸₀ = (0.67(0.68) - 0.085(0.68²)) = 0.4556 - 0.039304 = 0.416296 = 0.4163

P(X>0.68) = 1 - P(X≤0.68) = 1 - 0.4163 = 0.5837

P(0.68 < X < 1) = P(X<1) - P(X>0.68) = 0.585 - 0.5837 = 0.001296 = 0.0013 to 4d.p

4) Expected value = E(X) = Σ xᵢpᵢ = ∫²₀ x f(x) dx (that is, a sum of all the products of possible values and their respective probabilities)

∫²₀ x f(x) = ∫²₀ x(0.67 - 0.17x) = ∫²₀ (0.67x - 0.17x²) dx = [0.335x² - 0.0567x³]²₀ = [0.335(2²) - 0.0567(2³)] = 1.34 - 0.4533 = 0.8867 minute.

E(X) = ∫²₀ x f(x) = 0.8867 minute

5) E(X²) = Σ xᵢ²pᵢ = ∫²₀ x² f(x)

∫²₀ x² f(x) = ∫²₀ x²(0.67 - 0.17x) = ∫²₀ (0.67x² - 0.17x³) dx = [0.2233x³ - 0.0425x⁴]²₀ = [0.2233(2)³ - 0.0425(2)⁴] = 1.7864 - 0.68 = 1.1064

6) Variance = Var(X) = Σx²p − μ²

where μ = E(X) = 0.8867 minute

Σx²p = ∫²₀ x² f(x) = 1.1064

Var(X) = 1.1064 - 0.8867² = 0.3202

5 0
2 years ago
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