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3 years ago

The product of 4 and the sum of a number and 12 is at most 16

Mathematics

1 answer:

Vadim26 [7]3 years ago

8 0

    4(x + 12) ≤ 16
4(x) + 4(12) ≤ 16
   4x + 48 ≤ 16
   - 48 - 48
   4x ≤ 32
      4 4
   x ≤ 8

Solution Set: (8, ∞)

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jane loves animals. She has an equal number of beetles, birds and spiders as pets. Apart from human legs, there is a total of 27

kherson [118]

Answer:

16.875 spiders

Step-by-step explanation:

Given

Let

$B = Beetles$

$C = Birds$

$S = Spiders$

So, we have:

$B = C = S$ --- equal amounts

$6B + 2C + 8S = 270$ --- the legs

Required

The number of spider

Since she has an equal amount of B, C and S;

The expression can be written as:

$6B + 2C + 8S = 270$

$6S + 2S + 8S = 270$

$16S = 270$

Solve for S

$S = \frac{270}{16}$

$S = 16.875$

<em>The result of the solution does not represent real life situation because it it is not possible to have a fraction number of spider</em>

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3 years ago

Factor the Trimonial y to the second +3y-54

Molodets [167]

See the answer below.

6 0

3 years ago

1.Famous basketball player Michael Jordan had a free throw percentage of 0.83. (He made 83% of his free throw shots.) Assume tha

MissTica

Michael Jordan's Freethrow, the population of the 6 countries and the distribution of the uninsured drivers are illustrations of probabilities

<h3>1. Michael Jordan Freethrow</h3>

The given parameter is:

p = 83% -- the percentage of free throws he made

<u>Probability that he misses his 6th throw </u>

The probability that he misses his 6th throw is:

P = P(He made the first 5 throws) * P(He lost the 6th)

This gives

P = (83%)^5 * (1 - 83%)^1

P = 0.0670

<u>Expected number of miss</u>

The expected number till he misses the first free throw is:

E(x) = np

This gives

E(x) = 6 * 83%

E(x) = 4.98

Approximate

E(x) = 5

Hence, the probability that he misses his 6th throw is 0.0670 and the expected number till he misses the first free throw is 5

<h3>2. Country Populations</h3>

The given parameters are:

Average population = 268.35 million

Standard deviation = 370.43 million

<u>The z-scores for the United States, Egypt, and Mexico</u>

This is calculated as:

z = (x - $\mu$ )/ $\sigma$

So, we have:

US = (332 million - 268.35 million)/ 370.43 million

US = 0.17

Egypt = (104 million - 268.35 million)/ 370.43 million

Egypt = -0.44

Mexico = (128 million - 268.35 million)/ 370.43 million

Mexico = -0.38

<u>The countries from the smallest to the largest </u>

By comparing the z-score of the countries, the order of the countries are:

Egypt, Japan, Mexico, Brazil, United States and India

The countries are ranked that way because the higher the z-score, the higher the population

<h3>3. Uninsured drivers</h3>

The given parameter is:

p = 12.6% -- the percentage of uninsured drivers

<u>Probability that exactly 5 drivers of 30 are uninsured</u>

This is calculated as:

P(x) = nCx * p^x * (1 - p)^(n-x)

So, we have:

P(5) = 30C5 * (12.6%)^5 * (1 - 12.6%)^(30-5)

Evaluate the product

P(5) = 0.1561

<u>Probability that the next uninsured driver is the 7th</u>

This is calculated as:

P = P(First 6 are insured) * P(7th is unisured)

This gives

P = (1 - 12.6%)^6 * (12.6%)^1

P = 0.0562

The probability that exactly 5 drivers of 30 are uninsured is 0.1561, and the probability that the next uninsured driver is the 7th is 0.0562