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Serggg [28]
3 years ago
7

A 180 ft long board is cut into 3 pieces. The second piece of board is twice as long as the first. The third piece of board is s

ix times as long as the first. What is the length of the first piece of the board?
Mathematics
1 answer:
andrew11 [14]3 years ago
8 0
So, let's let w be the length of the first piece of the board.
(I was going to do l (small L) but it's too hard to see on computers)

second piece is 2w since it's twice the length of first.
third piece is 6w, since it's six times longer than the first.
and these three pieces were one one 180ft board, therefore, that means:
w + 2w + 6w = 180

now let's solve for w (length of first piece)!
w + 2w + 6w = 180
7w = 180
w = 180/7 ≈ 25.71ft

Therefore, the first piece of the board would be approximately 25.71ft.

You might be interested in
2. What is the sample proportion of heads in your sample of 40? Report this value to your teacher.
Alexeev081 [22]

Answer:

\frac{18}{40}=0.45

Though it may vary, it's going closer to 0.5 as long as we enlarge our sample.

Step-by-step explanation:

1) Since a coin has heads and tails, then a sample proportion of 40 we can simulate it using some applets.

2) Here are the most common outcomes, as long as we continue on flipping coins.

\frac{18}{40}=0.45

If we continue enlarging our sample (80, 120,160...) the probability goes closer to 0.5

This shows: the theoretical probability goes closer and closer to the experimental probability of heads and tails

S_{80}=0.503\\S_{120}=0.50

6 0
3 years ago
Assume the average height for American women is 64 inches with a standard deviation of 2 inches. A sorority on campus wonders if
satela [25.4K]

Answer:

a) s = 0.4

b) Z = 2.5

c) 99th percentile.

d) The larger sample size would lead to a smaller margin of error, which would lead to a higher z-score and a increased percentile.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Assume the average height for American women is 64 inches with a standard deviation of 2 inches

This means that \mu = 64, \sigma = 2

A) Calculate the standard error for the distribution of means.

Sample of 25 means that n = 25, so s = \frac{2}{\sqrt{25}} = 0.4.

B) Calculate the z statistic for the sorority group.

Sample mean of 65 means that X = 65.

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{0.4}

Z = \frac{65 - 64}{0.4}

Z = 2.5

C) What is the approximate percentile for this sample? Enter as a whole number.

Z = 2.5 has a p-value of 0.9938, so 0.99*100 = 99th percentile.

D) If the sorority actually had 36 members (still with an average of 65 inches), would you expect the percentile value to increase or decrease? why?

The larger sample size would lead to a smaller margin of error, which would lead to a higher z-score and a increased percentile.

3 0
2 years ago
What is the measure of ZWX?
GaryK [48]

Step-by-step explanation:

180°+63°

=243°

holp it help

5 0
2 years ago
4x + y > -6 order pair solution
slamgirl [31]
I guess it could be anything? because it says 4 times x + y is GREATER THAN -6
6 0
3 years ago
Bonnie purchased a 30 ounce package of chocalte chunk cookies for $2.40.What is the cost per ounce
Sladkaya [172]
.08 cents per ounce, because 2.40 ÷30 =.08
8 0
3 years ago
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