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MrMuchimi
3 years ago
6

Simplify the following expression, 2(k - 9) + 12

Mathematics
1 answer:
Phoenix [80]3 years ago
8 0

Answer:

2k - 6

Step-by-step explanation:

Distribute:

2k - 18 + 12

Add:

2k - 6

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the ratio of high school students who were homeschooled to those who attended other schools was three to seven. if there were 90
lina2011 [118]

Answer:

210 high schoolers as ratio becomes 90:210

Step-by-step explanation:

we can see that 3:7 can be multiplied if 3 x 3 = 9 then 7 x 3 =21 we just add the zero and find a 90:210 ratio

6 0
3 years ago
Susan is taking Western Civilization this semester on a pass/fail basis. The department teaching the course has a history of pas
Volgvan

Answer:

a. P(n) = 0.85 * (0.15)^(n-1)

b. P(n=1) = 0.85

c. P(n= 2) = 0.1275

d. P(n≥3) = 0.0225

e. Expected number of attempts is 1.176

Step-by-step explanation:

a.

Given

p = success = 85% = 0.85

q = failure = 1 - q = 1 - 0.85 = 0.15

The results of passing/failing takes a Bernoulli distribution

Since, there are independent trials

The number of trials until the first successful event occurs is given by

P(n = k) = p . (1 - p)^(k-1)

P(n = k) = p.q^(k-1)

This is so because it is a Bernoulli distribution and it is modeled by a geometric distribution.

Substitute 0.85 for p

P(n) = 0.85 * (0.15)^(n-1)

b.

Given

n = 1

Using P(n=1) = 0.85 * (0.15)^(n-1)

P(1) = 0.85 * 0.15^(1-1)

P(1) = 0.85 * 0.15°

P(1) = 0.85 * 1

P(1) = 0.85

Therefore, the probability that Susan passes on the first try is 0.85.

c.

n = 2

Using P(n=2) = 0.85 * (0.15)^(2-1)

P(2) = 0.85 * 0.15^(2-1)

P(2) = 0.85 * 0.15¹

P(2) = 0.85 * 0.15

P(2) = 0.1275

Therefore, the probability that Susan passes on the first try is 0.1275

d.

We'll make use of the probability of Susan passing the course after an infinite number of trials is 1.

i.e.

P(n=1) + P(n=2) + P(n=3) + P(n=4) + ......... = 1 --- This is then simplified to

P(n=1) + P(n=2) + P(n≥3) = 1

P(n≥3) = 1 - P(n=1) - P(n=2)

P(n≥3) = 1 - 0.85 - 0.1275

P(n≥3) = 0.0225

Therefore, the probability that Susan needs at least 3 attempts to pass is 0.0225

e.

In (a) above, we explained that the distribution is modeled by an exponential distribution.

The Expected Value for this is inverse of p, where p = 0.85

So, E(n) = 1/p

E(n) = 1/0.85

E(n) = 1.176470588235294

E(n) = 1.176 --- Approximated

Hence the Expected number of attempts is 1.176

7 0
3 years ago
Brooklyn Bridge is 5,985 ft long and 85 ft wide. What distance is one sixth of its length
I am Lyosha [343]

Answer:

The distance is 997.5 ft.

Step-by-step explanation:

Given:

Length of Brooklyn Bridge = 5,985 ft.

Width of Brooklyn Bridge = 85 ft.

We need to find the Distance

Distance = \frac{1}{6}\times lenght

Substituting the value of length to find distance we get;

Distance = \frac{1}{6}\times 5985 = 997.5 ft.

Hence Distance is 997.5 ft.

5 0
3 years ago
Michael buys some items at a grocery store.
tia_tia [17]

Answer:

B

Step-by-step explanation:

It's b my correct answer is b

8 0
2 years ago
Express 9/10 in simplest form.
mario62 [17]

Answer:

9/10 in simpliest form is 9/10

Step-by-step explanation:

In order to simplify a fraction there must be:

1. A number that will divide evenly into both the numerator and denominator so it can be reduced. No such number exists for 9 and 10.

or

2. The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number. 9 is not greater than 10.

9/10 as a decimal: 0.9

9/10 as a percent: 90%

5 0
3 years ago
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