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ra1l [238]
3 years ago
9

Hagrid plans to put up new fencing around his rectangular garden. He wants the width of his new garden to be 6 less than the len

gth. The perimeter of the new garden will be 188 feet. Create and use an algebraic equation to find the dimensions (length and width) of Hagrid's new garden. Show your work!
Mathematics
1 answer:
Elanso [62]3 years ago
8 0

Answer:

Lenght=50 feet.

Width=44 feet.


Step-by-step explanation:

1.  He wants the width of his new garden to be 6 less than the length, this can be expressed as following:

W=L-6

Where W is the width L is the length.

2. The perimeter of a rectangle can be calculated with:

P=2L+2W

3. You know the perimeter, therefore, you can substitute W=L-6 into the equation of the perimeter and solve for the length:

2L+2(L-6)=188\\2L+2L-12=188\\4L=200\\L=50 (The length is 50 feet)

3. Then, the width is:

W=L-6

W=50-6=44 (The width is 44 feet)

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Answer:

19-\dfrac{28}{n} is the expression with value of 15 when n = 7.

Step-by-step explanation:

To find the expression whose value is 15, substitute the value of n = 7 in each given expression.

Expression 1:

43-5n

Substituting the value of n,

43-5\left(7\right)

Simplifying,

43-35=8

Since the value of the expression is 8 which is not equal 15.

Hence expression 43-5n does not have value of 15 when n = 7.

Expression 2:

3n-5

Substituting the value of n,

3\left(7\right)-5

Simplifying,

21-5=16

Since the value of the expression is 16 which is not equal 15.

Hence expression 3n-5 does not have value of 15 when n = 7.

Expression 3:

6n-28

Substituting the value of n,

6\left(7\right)-28

Simplifying,

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Since the value of the expression is 14 which is not equal 15.

Hence expression 6n-28 does not have value of 15 when n = 7.

Expression 4:

19-\dfrac{28}{n}

Substituting the value of n,

19-\dfrac{28}{7}

Simplifying,

19-4=15

Since the value of the expression is 15 which is equal 15.

Hence expression 19-\dfrac{28}{n} has the value of 15 when n = 7.

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Answer:

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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 normally distributed samples are 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:

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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.

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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.

In this question, we have that:

\mu = 8.4, \sigma = 1.8, n = 40, s = \frac{1.8}{\sqrt{40}} = 0.2846

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