Simplify: (3²-4)/5
A. 1
B. 1.25
C. 1/5
D. 5​

Answer:

The probability is  

Step-by-step explanation:

From the question we are told that

   The amount of time is uniform probability distribution between 21 and 38 minutes.

  Given that the amount of time is uniformly distributed then  the probability that a randomly selected car will require less than 25 minutes to service is mathematically evaluated as

=>      

Answer:

36 9/16 ft^3

Step-by-step explanation:

volume = length * width * height

volume = 3 3/4 ft * 3 ft * 3 1/4 ft

Change all mixed numerals to fractions.

volume = 15/4 * 3/1 * 13/4 ft^3

volume = 585/16 ft^3

volume = 36 9/16 ft^3

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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Answer:

y-3 = 2/9 (x-8)

Step-by-step explanation:

Answer:

The probability of finding a sample mean less than 18 hours is 0.0082

Step-by-step explanation:

To find the probability of finding a sample mean less than 18 hours, we need to calculate the z-score of this sample mean 18. And the probability of finding a sample mean less than 18 hours is P(z<z(18)).

Z-score can be calculated as follows:

z(18)= where

• X is the sample mean (18 hours)

• M is the average hours dentists spend per week on fillings (20 hours)

• s is the standard deviation (10 hours)

• N is the sample size (144)

Putting the numbers, we get:

z(18)=

Using z- table we can find that P(z<z(18)) = 0.0082

Final answer:

Based on given mean & standard deviation, by using principles of Central Limit Theorem and Z-score calculation, the probability of finding a sample mean less than 18 hours is approximately 0.0082 or 0.82%.

Explanation:

This question is about the probability of a specific sample mean in statistics, based on provided mean and standard deviation values. It requires the principle of the Central Limit Theorem which states that means of samples taken from a population are normally distributed irrespective of the population's distribution.

To answer this question, we first need to calculate the standard error (SE), which is the standard deviation divided by the square root of the sample size (n). In this case, SE = 10/sqrt(144) = 10/12 = 0.83 (rounded to 2 decimal places).

Next, we calculate the Z score, which tells us how many standard deviations an element is from the mean. So, Z = (Sample Mean - Population Mean) / SE = (18 - 20) / 0.83 = -2.4 (rounded to one decimal place).

Using the Z score table (also known as a standard normal distribution table), we find that the probability of a Z value of -2.4 or less is approximately 0.0082. Thus, the probability of finding a sample mean less than 18 hours is 0.0082, or 0.82% when expressed as a percentage.

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