Write an inequality for the following: all numbers less than 7 and greater than -7

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

3 years ago

What is the simplest form of ^4 sqrt 81x^8y^5

lara31 [8.8K]

ANSWER

$3 {x}^{2} y \sqrt[4]{y}$

EXPLANATION

We want to simplify:

$\sqrt[4]{81 {x}^{8} {y}^{5} }$

We can split the radical sign to obtain:

$\sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{5} }$

Or

$\sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4} \times y}$

$\sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y}$

$\sqrt[4]{ {3}^{4} } \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y}$

Recall that:

$\sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} }$

${3}^{4 \times \frac{1}{4} } \times {x}^{8 \times \frac{1}{4} } \times {y}^{4 \times \frac{1}{4} }\times \sqrt[4]{y}$

$3 {x}^{2} y \sqrt[4]{y}$

6 0

4 years ago

Read 2 more answers

Barbra buys-

zysi [14]

Answer:

No, Barbra is wrong as cost of 1 loaf of bread is £1.50 not $1.40.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

Barbara buys 3 boxes of eggs costing £1.20 each

1 jar of mayo costing £1.80

2 loaves of bread

she pays £10 note and gets £1.60 change

Barbara works out the cost of 1 loaf of bread as £1.40.

Is she correct? You MUST show your working out.

The explanation of the answer is now given as follows:

Total cost of 3 boxes of eggs = Number of boxes of eggs bought * Price per box of egg = 3 * £1.2 = £3.60

Cost of 1 jar of mayo = £1.80

Total amount spent = Note paid - Change collected = £10 - £1.60 = £8.40

Total cost of 2 loaves of bread = Total amount spent - Total cost of 3 boxes of eggs - Cost of 1 jar of mayo = £8.40 - £3.60 - £1.80 = £3.00

Cost of 1 loaf of bread = Total cost of 2 loaves of bread / 2 = £3.00 / 2 = £1.50

Therefore, Barbra is wrong as cost of 1 loaf of bread is £1.50 not $1.40.

8 0

3 years ago

Use the number line to complete the statements.A number line going from negative 10 to positive 10 in increments of 2.The opposi

g100num [7]

Answer:

-4 and 8

Step-by-step explanation:

When looking at the number line to get the opposite of a number take your number and count that many numbers on the opposite side of the 0 (zero).

So if your number is -4 count that many on the opposite side of the zero to get 4.

8 0

3 years ago

Ignore my answer on the top. Anyways please help!

Over [174]

Answer:

i think c but im not positive

Step-by-step explanation:

7 0

3 years ago