Combine like terms to simplify. 5z + 3z

Suppose it is known that 60% of radio listeners at a particular college are smokers. A sample of 500 students from the college i

vladimir1956 [14]

Answer:

The probability that at least 280 of these students are smokers is 0.9664.

Step-by-step explanation:

Let the random variable X be defined as the number of students at a particular college who are smokers

The random variable X follows a Binomial distribution with parameters n = 500 and p = 0.60.

But the sample selected is too large and the probability of success is close to 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

1. np ≥ 10

2. n(1 - p) ≥ 10

Check the conditions as follows:

$np=500\times 0.60=300>10\\n(1-p)=500\times(1-0.60)=200>10$

Thus, a Normal approximation to binomial can be applied.

So,

$X\sim N(\mu=600, \sigma=\sqrt{120})$

Compute the probability that at least 280 of these students are smokers as follows:

Apply continuity correction:

P (X ≥ 280) = P (X > 280 + 0.50)

= P (X > 280.50)

$=P(\frac{X-\mu}{\sigma}>\frac{280-300}{\sqrt{120}}\\=P(Z>-1.83)\\=P(Z$

*Use a z-table for the probability.

Thus, the probability that at least 280 of these students are smokers is 0.9664.

8 0

2 years ago

Tom rented a truck for one day. There was a base fee of $16.99 , and there was an additional charge of 90 cents for each mile dr

12345 [234]

I believe the answer is 193mi

5 0

3 years ago

Perform the indicated operations. Reduce the answers to lowest terms .

kozerog [31]

Step-by-step explanation:

1. (2+4+1)/9 = 7/9

2. 2 1/3 + 2/3 = 2 + (1+2)/3 = 2 + 3/3 = 2+1 = 3

3. 1 1/5 + 2 3/5 = 1+2 + 1/5 + 3/5 = 3 + (1+3)/5 =

3 4/5

4. 5/6 + 2/10 + 1/5 = 5/6 + 1/5 + 1/5 = 5/6 + 2/5

= (5×5)/(6×5) + (2×6)/(5×6)

= 25/30 + 12/30

= (25+12)/30

= 37/30 = 1 7/30

5. 3 1/2 + 4 2/3

= 3+4 + 1/2 + 2/3

= 7 + (1×3)/(2×3) + (2×2)/(3×2)

= 7 + 3/6 + 4/6

= 7 + (3+4)/6 = 7 7/6 = 8 1/6

6. 9/13 - 5/13 = (9-5)/13 = 4/13

7. 7 6/8 - 5 2/8

= (7-5) + (6/8 - 2/8)

= 2 + 4/8

= 2 1/2

8. 2/3 - 3/7

= (2×7)/(3×7) - (3×3)/(7×3)

= 14/21 - 9/21 = (14-9)/21 = 5/21

9. 11 1/5 - 5 4/5

= 10 6/5 - 5 4/5

= (10-5) + (6/5 - 4/5)

= 5 + 2/5 = 5 2/5

10. 15 4/5 - 7 7/10

= (15-7) + (4/5 - 7/10)

= 8 + (4×2)/(5×2) - 7/10

= 8 + 8/10 - 7/10

= 8 + 1/10

= 8 1/10

6 0

2 years ago

Clare is paid $90 for 5 hours of work. At thos rate how many seconds does i take for her to earn 25 cents?

natka813 [3]

We are given

Clare is paid $90 for 5 hours of work

Total money paid =$90

total hours of work =5 hours

so, firstly we will find rate of work

rate of work = ( total money paid)/( total hours of work)

now, we can plug values

and we get

The rate of work is

$=\frac{90}{5}$

$=18$ $/ hour

now, we have to find time for amount paid is 25 cents

so, amount paid =25 cents

100 cents =1$

so, amount paid =$ 0.25

Since, the rate is constant

so, we can take same rate here

now, we can use formula

rate of work = ( total money paid)/( total hours of work)

now, we can plug values

$18=\frac{0.25}{T}$

now, we can solve for T

$T=\frac{0.25}{18}$ hour

since, T is in hours

so, we can change into seconds

1 hour =3600seconds

so, we can plug

$T=\frac{0.25}{18}\times 3600$ seconds

$T=50$ seconds......................Answer

6 0

3 years ago

2cos<img src="https://tex.z-dn.net/?f=2cos%5E%7B2%7D%20x-3cosx%2B1%3D0" id="TexFormula1" title="2cos^{2} x-3cosx+1=0" alt="2cos^

sattari [20]

Answer:

34

Step-by-step explanation:

7 0

3 years ago

Combine like terms to simplify. 5z + 3z - 1/2y+ 2y