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Kryger [21]
3 years ago
15

Jamal hiked on two trails. The first trail was 7 1/3 miles long, and the second trail was 1 9/11 times as long as the first trai

l. How many miles did Jamal hike? Enter your answer as a mixed number in simplest form.
Mathematics
1 answer:
algol [13]3 years ago
7 0

9514 1404 393

Answer:

  20 2/3 miles

Step-by-step explanation:

Altogether Jamal hiked 1 + 1 9/11 times the length of the first trail:

  (2 9/11)(7 1/3) = (31/11)(22/3) = 62/3 = 20 2/3

Jamal hiked 20 2/3 miles.

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Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.1
svet-max [94.6K]

Answer:

a) 0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

b) 0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

Mean of 8.0 ounces and a standard deviation of 1.1 ounces.

This means that \mu = 8, \sigma = 1.1

(a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces?

n = 5 means that s = \frac{1.1}{\sqrt{5}} = 0.4919

This probability is the pvalue of Z when X = 9.3. So

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

By the Central Limit Theorem

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

Z = \frac{9.3 - 8}{0.4919}

Z = 2.64

Z = 2.64 has a pvalue of 0.9959

0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.0 ounces?

n = 6 means that s = \frac{1.1}{\sqrt{6}} = 0.4491

This probability is 1 subtracted by the pvalue of Z when X = 9. So

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

Z = \frac{9 - 8}{0.4491}

Z = 2.23

Z = 2.23 has a pvalue of 0.9871

1 - 0.9871 = 0.0129

0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

8 0
3 years ago
Marylou buys a package of 500 jewels to decorate 4 different pairs of jeans. She uses the same number of jewels on each pair of
patriot [66]
500 divided by 4 = 125 so 
125 jewels on each pair of jeans

4 0
3 years ago
−3(3x−4)=2x+23 <br><br> helppppppppp
Assoli18 [71]

Answer:

The correct answer is -1

4 0
3 years ago
Read 2 more answers
Plz HElp, Worth 30 pts, Will give branliest...
Yanka [14]

Answer:

The answer is 15 21/40

Step-by-step explanation:

If you convert 8 1/8 to 8 5/40 then convert

7 2/5 to 7 16/40 then add the wholes 7 + 8 = 15

and then add the actual fractions 5/40 + 16/40 = 21/40

then add the whole and the fraction 15 + 21/40 youll end

up with 15 21/40 so that is the awnser PS I’m in 5th grade age 10

6 0
3 years ago
Given:
Natali [406]

Answer:

\overline{PM}\cong\overline{ON}:, Segment subtended by the same angle on two adjacent parallel lines are congruent

Step-by-step explanation:

Statement,                                              Reason

MNOP is a parallelogram:,                     Given

\overline{PM}\left |  \right |\overline{ON}:,                                               Opposite sides of a parallelogram

∠PMO ≅ ∠MON:,                                    Alternate Int. ∠s Thm.

\overline{MN}\left |  \right |\overline{PO}:,                                               Opposite sides of a parallelogram

∠POM ≅ ∠NMO:,                                    Alternate Int. ∠s Thm.

OM ≅ OM:,                                               Reflexive property

\overline{PM}\cong\overline{ON}:,                                               Segment subtended by the same                                                                                                                              angle and on two adjacent parallel lines are congruent

4 0
3 years ago
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