A 46- inch piece of steel is cut into three pieces so that the second piece is twice as long ad the first piece , and the third piece is one inch more than six times the length of the first piece. Find the lengths of the pieces.
Answers
Final answer:
The first piece is 5 inches long, the second piece is 10 inches long, and the third piece is 31 inches long.
Explanation:
The problem involves a piece of steel that is 46 inches long and it is cut into three pieces. The wording of the problem gives us equations we can use to solve for lengths of the pieces. We're told:
- The second piece is twice as long as the first piece.
- The third piece is one inch more than six times the length of the first piece.
We can let x represent the length of the first piece. Then the length of the second piece is 2x, and the length of the third piece is 6x+1.
Because the three pieces together form the original 46-inch piece, we can set up this equation: x + 2x + 6x + 1 = 46, which simplify to 9x +1 = 46. Solving for x gives x = 5. Therefore, the lengths of the pieces are 5 inches, 10 inches (2 * 5), and 31 inches (6 * 5 + 1).
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A jar contained 8 balls: 6 red, 1 green and 1 blue. We randomly take a ball out of the jar. Once a ball is selected we do not put it back. We keep selecting balls until for the first time we get a blue one. We count the number of times we had to draw a ball, (including the last drawing) until we actually got the blue ball. How many elements are in the sample space for this experiment
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Answer:
p = 0.48
Step-by-step explanation:
A binomial experiment is and experiment with n trials, every trial is identical and independent and every trial has the same probability p of success and 1-p of fail.
Then, we have a binomial experiment of 16 trials. it means that every trial has the same conditions. So, if the probability of success on trial 9 is 0.48, the probability of success on trial 13 is also 0.48.
Answers
Step-by-step explanation:
What are the options to choose from?
Answers
Answer:
Sample size should be atleast 625
Step-by-step explanation:
Given that the Labor Bureau wants to estimate, at a 90% confidence level, the proportion of all households that receive welfare
Sample proportion = 17.5%
Let n be the sample size
Standard error of sample proportion=
Z critical for 90% = 1.645
Margin of error = 1.645 * std error
Since margin of error<0.025 we have
Final answer:
The sample size that would limit the margin of error to be within 0.025 of the population proportion is approximately 185.
Explanation:
To estimate the sample size needed to limit the margin of error within 0.025, we can use the formula for sample size in proportion estimation. The formula is:
n = (Z^2 * p * (1-p)) / (E^2)
Where:
n = sample size
Z = Z-score corresponding to the desired confidence level
p = preliminary sample proportion
E = margin of error
Given that the confidence level is 90%, the Z-score for a 90% confidence level is approximately 1.645. The preliminary sample proportion is 17.5% (or 0.175) and the margin of error is 0.025.
Substituting these values into the formula:
n = (1.645^2 * 0.175 * (1 - 0.175)) / (0.025^2)
Simplifying the equation:
n = 1.645^2 * 0.175 * 0.825 / 0.025^2
n ≈ 185.16
So, the sample size that would limit the margin of error to be within 0.025 of the population proportion is approximately 185, rounded up to the nearest whole number.
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