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3 years ago

The width of a field is 3 miles less than the length. The square mileage of the plot is 18 miles squared. Find the dimensions.

1 answer:

6 0

LW = A
L(L - 3) = 18
L^2 - 3L - 18 = 0
(L - 6) (L + 3) = 0
L could be 6 or -3 ( -3 cannot be a length of a side of a rectangle since it’s negative.)
So L = 6 and W= 3

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4 years ago

The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean 1263 and a stan

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Answer:

(a) The 29th percentile for the number of chocolate chips in a bag is 1198.65.

(b) The number of chocolate chips in a bag that make up the middle 95% of bags are [1146, 1380].

Step-by-step explanation:

Let the random variable X represent the number of chocolate chips in a bag of chocolate chip cookies.

The random variable X is normally distributed with mean, μ = 1263 and a standard deviation, σ = 117.

(a)

Compute the 29th percentile for the number of chocolate chips in a bag as follows:

P (X < x) = 0.29

⇒ P (Z < z) = 0.29

The value of z for the above probability is, z = -0.55.

Compute the value of x as follows:

$z=\frac{x-\mu}{\sogma}\\-0.55=\frac{x-1263}{117}\\x=1263-(117\times 0.55)\\x=1198.65$

Thus, the 29th percentile for the number of chocolate chips in a bag is 1198.65.

(b)

According to the Empirical rule 95% of the normally distributed data lies within 2 standard deviations of the mean.

P (μ - σ < X < μ + σ) = 0.95

P (1263 - 117 < X < 1263 + 117) = 0.95

P (1146 < X < 1380) = 0.95

Thus, the number of chocolate chips in a bag that make up the middle 95% of bags are [1146, 1380].

(c)

The inter-quartile range of the normal distribution is:

IQR = 1.349 σ

Compute the inter-quartile range of the number of chocolate chips in a bag of chocolate chip cookies as follows:

IQR = 1.349 σ

= 1.349 × 117

= 157.833

Thus, the inter-quartile range of the number of chocolate chips in a bag of chocolate chip cookies is 157.83.

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3 years ago