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A 3 ft by 5 ft wooden board has three equally sized circles cut out of it. A penny will be randomly tossed onto the board. What is the probability the penny will fall through any of the holes?

Answers

Answer 1

Answer:

Pr = 15.71% ≈ 16%

Step-by-step explanation:

Let's begin by listing out the data given unto us, we have:

Length of board = 3 ft, Width of board = 5 ft,

Area of board = Length * Width = 3 * 5 = 15 ft²,

Diameter of each circle (d) = 1 ft; r = d ÷ 2

⇒ r = 1 ÷ 2 = 0.5 ft

Area of each circle = πr² = π * 0.5² = 0.785 ft²

Area of the three circles = 3πr² = 2.356 ft²

Probability = favourable outcome ÷ Total outcome

Probability of the penny falling into the hole = area of the three circles ÷ area of board

Pr = 2.356 ÷ 15 = 0.1571

Converting to percentage, we multiply by 100

Pr = 0.1571 * 100

Pr = 15.71% ≈ 16%

Therefore, the probability of the penny falling into the hole is 15.71% ≈ 16%

Related Questions

1. Consider the following hypotheses:H1 : ∃x (p(x) ∧ q(x)) H2 : ∀x (q(x) → r(x))Use rules of inference to prove that the following conclusion follows from these hypotheses:C : ∃x (p(x) ∧ r(x))Clearly label the inference rules used at every step of your proof.2. Consider the following hypotheses:H1 : ∀x (¬C(x) → ¬A(x)) H2 : ∀x (A(x) → ∀y B(y)) H3 : ∃x A(x)Use rules of inference to prove that the following conclusion follows from these hypotheses:C : ∃x (B(x) ∧ C(x))Clearly label the inference rules used at every step of your proof.3. Consider the following predicate quantified formula:∃x ∀y (P (x, y) ↔ ¬P (y, y))Prove the unsatisfiability of this formula using rules of inference.
An object weighs 1 pound on earth weighs about 1/15 pounds on Pluto. If a man weighs 240 pounds on earth how many pounds would he weigh on Pluto?
Choose the missing number. 36 x ____ = 7,200
|-9×+7|+8 is less than or equal to 9
12 times 10 to the 0 power equals 12 times one equals?

Parallel Lines and Angle Relationships#1 What is the value of y. Type your answer below. *

#2 If the m<4 is 110 degrees, what is m<1 ? (Give number value only.) *

#3 If e || f and a || b, what is the value of y. *
A) 87
B) 88
C) 91
D) 92

Answers

Answer:

1. y = 80°

2. m<1 = 70°

3. y = 92°

Step-by-step explanation:

1. Since lines c and b are parallel lines cut across by transversal a, therefore:

y = 80° (alternate exterior angles are congruent)

2. m<1 is the supplement of m<4, because the angle that forms a linear pair with <1, corresponds with <4.

Therefore: m<1 = 180° - 110° = 70°

3. First, find the value of x.

(x + 1)° + (x - 3)° = 180° (supplementary)

x + 1 + x - 3 = 180°

2x - 2 = 180°

2x = 180 + 2 (addition property of equality)

2x = 182

x = 182/2 (division property of equality)

x = 91

(x + 1)° = y° (alternate interior angles are congruent)

Substitute x = 91

91 + 1 = y

92° = y

Write the addition equation as a multiplication equation.
8 + 8 +8= 24

Answers

Answer:

3 × 8 = 24

3 × 8 is the multiplication equation.

Answer:

8x=24

Step-by-step explanation:

Please sayb this was helpful

Can anyine kindly help please?

Answers

Answer:

i think it might be C

Step-by-step explanation:

The sum of two consecutive integers is -39. List the two numbers from smallest to greatest

Answers

Answer:

-20, -19

Step-by-step explanation:

The average of the two numbers is -39/2 = -19.5. The smaller number is 0.5 less than this, -20, and the larger number is 0.5 more than -19.5, so is -19.

_____

Comment on the problem and solution

I find that working consecutive integer problems is often simplified by working with the average value of those integers:

the average of two consecutive odd integers is the even integer between them
the average of two consecutive even integers is the odd integer between them
the average of an odd number of integers of the same type (consecutive, consecutive odd, consecutive even) is the middle one
The average of an even number of consecutive integers is the "half" number between the middle two (as in this problem).

For the function y=ln(x-1)+2 which of the following statements is truea. the domain is all real numbers and the range is [2, infinity)
b. the domain is (-1, infintity} and the range is all real numbers
c. the domain is (1, infinity) and the range is [2, infinity)
d. the domain is (1, infinity) and the range is all real numbers

Answers

For the function $y = ln(x-1) + 2$ , statement d is true. The domain is (1, ∞) and the range is all real numbers.

A function is an expression or a rule establishing a relationship between two sets or two variables, where one is independent and another is dependent.

The set of values you input into the data as the independent variable is called the domain of the function.

The set of possible outputs of the function, the dependent variable, is called the codomain of the function.

The set of elements part of the dependent variable that actually comes out of the function as output is called the range of the function.

Given function, $y = ln(x-1) + 2$

The domain of the function is what you can put into x.

for ln(x-1) to be defined, x-1 > 0 implies that x > 1

Thus the domain of function becomes (1, ∞).

The range of the function is what you get as y.

if 1 < x < 2, 0 < x-1 < 1, ln(x-1) < 0, thus $y = ln(x-1) + 2$ will have a value y < 2, maybe even negative.

if x = 2, x-1 = 1, ln(x-1) = ln(1) = 0, making y = 2

if x > 2, x-1 > 3, ln(x-1) > 0, making y >2.

Thus the range of function becomes (-∞, ∞).

Learn more about function here

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#SPJ2

Answer:

d. the domain is (1, infinity) and the range is all real numbers

Step-by-step explanation:

The domain of a logarithmic function

$f(x)=\ln(x)$

is the set of all positive numbers

$D:\ x>0\Rightarrow x\in\mathbb{R}^+$

The range of a logarithmic function

$f(x)=\ln(x)$

is the set of all real numbers

$R:\ y\in\mathbb{R}$

We have:

$y=\ln(x-1)+2$

DOMAIN

$x-1>0$ add 1 to both sides

$x-1+1>0+1\n\nx>1$

$D:x>0\Rightarrow x\in(1,\ \infty)$

RANGE

$f(x)=\ln(x)\to f(x)+2=\ln(x)+2$

The graph shifted 2 units up. The range no change.

$R:\ y\in\mathbb{R}$

6.solve an inequality that represents the description and then solve Toni can carry up to 18 lb in her backpack.
Her lunch weighs 1 lb, her gym clothes weigh
2 lb, and her books (b) weigh 3 lb each. How
many books can she carry in her backpack?

Answers

Answer:

nothing

Step-by-step explanation:

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