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3 years ago

An animal shelter has two purebred Labradors among the 81 dogs available for adoption. It is also known that 7/9 of the

Mathematics

1 answer:

insens350 [35]3 years ago

3 0

Answer:

Their are 18 number of purebreds

Step-by-step explanation:

An animal shelter has 2 purebred Labradors among the 81 dogs available for adoption. It is known that 7/9 of the dogs are mongrels .The number of purebreds can be computed below.

The number of purebreds Labrador available for adoption = 2 purebred

The total number of dogs = 81 dogs

7/9 of the dogs are mongrels. This means 7/9 × 81 = 567/9 = 63

The number of mongrels = 63

The number of purebreds = 81 - 63 = 18

Their are 18 number of purebreds

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Daniel [21]

Using the normal distribution, the percentages are given as follows:

a) 9.18%.

b) 97.72%.

c) 50%.

d) 4.27%.

e) 0.13%.

f) 59.29%.

g) 2.46%.

h) 50%.

i) 50%.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

For this problem, the mean and the standard deviation are given as follows:

$\mu = 247, \sigma = 60$

For item a, the proportion is the p-value of Z when Z = 167, hence:

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

Z = (167 - 247)/60

Z = -1.33.

Z = -1.33 has a p-value of 0.0918.

Hence the percentage is of 9.18%.

For item b, the proportion is the p-value of Z when Z = 367, hence:

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

Z = (367 - 247)/60

Z = 2.

Z = 2 has a p-value of 0.9772.

Hence the percentage is of 97.72%.

For item c, the proportion is one subtracted by the p-value of Z when X = 247, hence:

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

Z = (247 - 247)/60

Z = 0

Z = 0 has a p-value of 0.5.

Hence the percentage is of 50%.

For item d, the proportion is one subtracted by the p-value of Z when X = 350, hence:

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

Z = (350 - 247)/60

Z = 1.72

Z = 1.72 has a p-value of 0.9573.

1 - 0.9573 = 0.0427.

Hence the percentage is of 4.27%.

For item e, the proportion is the p-value of Z when Z = 67, hence:

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

Z = (67 - 247)/60

Z = -3.

Z = -3 has a p-value of 0.0013.

Hence the percentage is of 0.13%.

For item f, the proportion is the p-value of Z when X = 300 subtracted by the p-value of Z when X = 200, hence:

X = 300:

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

Z = (300 - 247)/60

Z = 0.88.

Z = 0.88 has a p-value of 0.8106.

X = 200:

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

Z = (200 - 247)/60

Z = -0.78.

Z = -0.78 has a p-value of 0.2177.

0.8106 - 0.2177 = 0.5929.

Hence the percentage is 59.29%.

For item g, the proportion is the p-value of Z when X = 400 subtracted by the p-value of Z when X = 360, hence:

X = 400:

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

Z = (400 - 247)/60

Z = 2.55.

Z = 2.55 has a p-value of 0.9946.

X = 360:

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

Z = (360 - 247)/60

Z = 1.88.

Z = 1.88 has a p-value of 0.97.

0.9946 - 0.97 = 0.0246

Hence the percentage is 2.46%.

For items h and i, the distribution is symmetric, hence median = mean and the percentages are of 50%.

More can be learned about the normal distribution at brainly.com/question/24808124

#SPJ1

4 0

1 year ago

Which number line represents the solution set for the inequality 3(8-4x) < 6(x-5) ?

viktelen [127]

Answer:

Second number line(from top to bottom).

Step-by-step explanation:

We are given the following inequality:

$3(8 - 4x) < 6(x - 5)$

It is solved similarly to an equality, so:

$24 - 12x < 6x - 30$

$-18x < -54$

Multiplying by -1, the signal changes from < to >. So

$18x > 54$

$x > \frac{54}{18}$

$x > 3$

Thus the correct answer is given by the second number line.

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3 years ago