The width of kevin's yard is three times the width of his garage, increased by 12 feet. What expression describes the width of kevin's yard if g represents the width of his garage?
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Answer:
The expression that describes the width of Kevin’s yard is (3g + 12) feet
Step-by-step explanation:
This is an expression problem.
From the question, we are made to know that the width of the yard is 3 times the width of the garage increased by 12 feet.
Now, we are told that the width of the garage is g feet and we want to find the width of the yard.
The width of the yard will be g feet * 3 + 12
Mathematically that would be 3g + 12 feet
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Answer:
the probability that a randomly selected item is non-defective is approximately 96.3%.
Step-by-step explanation:
This involves finding the probability of an item being non-defective for each machine and then combining these probabilities based on the machine's contribution to the total production.
Let's calculate it step by step:
Probability that an item from Machine A is non-defective:
The probability of a defective item from Machine A is 3%, so the probability of a non-defective item from Machine A is 100% - 3% = 97%.
Probability that an item from Machine B is non-defective:
The probability of a defective item from Machine B is 4%, so the probability of a non-defective item from Machine B is 100% - 4% = 96%.
Probability that an item from Machine C is non-defective:
The probability of a defective item from Machine C is 5%, so the probability of a non-defective item from Machine C is 100% - 5% = 95%.
Now, we need to consider the contribution of each machine to the total production:
Machine A produces 50% of the items.
Machine B produces 30% of the items.
Machine C produces 20% of the items.
To find the overall probability that a randomly selected item is non-defective, we'll use a weighted average:
Probability (Non-Defective) = (Probability from A * Fraction from A) + (Probability from B * Fraction from B) + (Probability from C * Fraction from C)
Probability (Non-Defective) = (97% * 50%) + (96% * 30%) + (95% * 20%)
Now, calculate the weighted average:
Probability (Non-Defective) = (0.97 * 0.50) + (0.96 * 0.30) + (0.95 * 0.20)
Probability (Non-Defective) = 0.485 + 0.288 + 0.19
Probability (Non-Defective) = 0.963
So, the probability that a randomly selected item is non-defective is approximately 96.3%.
The probability that an item randomly selected from the production of machines A, B, and C is non-defective is 0.963 or 96.3%.
The question is about calculating the probability of an item being non-defective in a factory production environment. Here is how you can find the solution:
- Determine the probability that an item is produced by each machine and it isn't defective.
- Machine A: Probability = 0.50 (proportion of total items) x 0.97 (proportion of non-defective items) = 0.485
- Machine B: Probability= 0.30 x 0.96 = 0.288
- Machine C: Probability = 0.20 x 0.95 = 0.19
- Add the probabilities from each machine. This is valid because the events are mutually exclusive; an item can only be produced by one machine. Therefore, the total probability that an item randomly selected is non-defective is: 0.485 + 0.288 + 0.19 = 0.963 or 96.3%.
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Final answer:
To determine the total number of people surveyed when given the number who preferred swimming and the percentage they represent, you set up an equation based on the percentage and then solve for the total. With this data, 40 people were surveyed.
Explanation:
The question pertains to the mathematical concept of percentages. You mention that 27.5 percent of the surveyed population favored swimming and this equaled to 11 people. To calculate the total number of people surveyed, we let the total number be 'x'. Therefore, the mathematical equation, based on the provided data, becomes 27.5% of 'x' = 11. In mathematical terms, it can be written as 0.275x = 11. For finding 'x', divide both sides of the equation by 0.275. Thus 'x' = 11 / 0.275 = 40. Therefore, based on the given percentages and data, it's inferred that a total of 40 people were surveyed.
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Answer:
The probability that a typical customer buys both gasoline and groceries, P(Ga n Gr) = 0.1955
Step-by-step explanation:
Let the probability that a customer guys groceries be represented by P(Gr) and that of buying gasoline be P(Ga)
Given
P(Gr) = 0.76
P(Ga) = 0.23
P(Gr|Ga) = 0.85
For mutually exclusive events,
P(B|A) = (P(B n A))/P(A)
P(Gr|Ga) = (P(Gr n Ga))/P(Ga)
P(Gr n Ga) = P(Gr|Ga) × P(Ga)
P(Gr n Ga) = 0.85 × 0.23 = 0.1955
Hope this Helps!!!!
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? + 5 = 3 × 9
? + 5 = 27
? = 27 - 5
? = 22
The number is 22
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For a pentagon, there are 5 corners, and you want to choose 2 holes to stitch between, so it's a combination of 5 holes taken 2 at a time.
The combination formula is:
C(n, k) = n! / (k!(n-k)!)
Where:
- n is the total number of items to choose from (in this case, 5 holes).
- k is the number of items to choose (in this case, 2 holes).
C(5, 2) = 5! / (2!(5-2)!)
Now, calculate the combinations:
C(5, 2) = 5! / (2!(3!))
C(5, 2) = (5 * 4 * 3!) / (2! * 3!)
Now, simplify:
C(5, 2) = (5 * 4) / (2!)
C(5, 2) = (20) / (2)
C(5, 2) = 10
So, Trey would need to make 10 different stitches to stitch a piece of thread across every possible pair of non-adjacent holes in the pentagonal button.