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3 years ago

9

In a race, Jane ran 3 minutes less than twice as many minutes as Mike ran. Write an expression to represent the number of minute

s Jane ran.
Use "n" as your variable

2 answers:

Otrada [13]3 years ago

5 0

Answer:

2n - 3

Step-by-step explanation:

Hope this helps!

a_sh-v [17]3 years ago

4 0

Answer:

n * 2 - 3

Step-by-step explanation:

Let's say n is the number of minutes Mike ran then the expression would be

n * 2 - 3

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Market-share-analysis company Net Applications monitors and reports on Internet browser usage. According to Net Applications, in

Alex_Xolod [135]

Answer:

a) 2.43% probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

b) 80.5% probability that at least 3 of the 20 Internet browser users use Chrome as their Internet browser.

c) 4.074

d) Variance 3.24, standard deviation 1.8

Step-by-step explanation:

For each internet browser user, there are only two possible outcomes. Either they use chrome, or they do not. They are chosen at random, which means that the probability of an user using chrome is independent from other users. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The variance of the binomial distribution is:

$V(X) = np(1-p)$

20.37% share of the browser market

This means that $p = 0.2037$

Group of 20 Internet browser users

This means that $n = 20$

(a) Compute the probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

This is $P(X = 8)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{20,8}.(0.2037)^{8}.(0.7963)^{12} = 0.0243$

2.43% probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

(b) Compute the probability that at least 3 of the 20 Internet browser users use Chrome as their Internet browser.

Either less than 3 users use Chrome, or at least 3 do. The sum of the probabilities of these events is decimal 1. So

$P(X < 3) + P(X \geq 3) = 1$

So

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{20,0}.(0.2037)^{0}.(0.7963)^{20} = 0.0105$

$P(X = 1) = C_{20,1}.(0.2037)^{1}.(0.7963)^{19} = 0.0538$

$P(X = 2) = C_{20,2}.(0.2037)^{2}.(0.7963)^{18} = 0.1307$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0105 + 0.0538 + 0.1307 = 0.195$

Finally

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.195 = 0.805$

80.5% probability that at least 3 of the 20 Internet browser users use Chrome as their Internet browser.

(c) For the sample of 20 Internet browser users, compute the expected number of Chrome users.

$E(X) = np = 20*0.2037 = 4.074$

(d) For the sample of 20 Internet browser users, compute the variance and standard deviation for the number of Chrome users.

$V(X) = np(1-p)$

$V(X) = 20*0.2037*0.7963 = 3.24$

The standard deviation is the square root of the variance. SO

$\sqrt{V(X)} = \sqrt{3.24} = 1.8$

8 0

3 years ago

Given the function defined in the table below, find the average rate of

AURORKA [14]

Answer:

Average rate of change = $\frac{2}{5}$

Step-by-step explanation:

Average rate of change of a function 'f' in the interval a ≤ x ≤ b is given by,

Average rate of change = $\frac{f(b)-f(a)}{b-a}$

We have to find the average rate of change in the interval 20 ≤ x ≤ 65

From the table attached,

f(65) = 32

f(20) = 14

Average rate of change = $\frac{32-14}{65-20}$

= $\frac{18}{45}$

= $\frac{2}{5}$

Therefore, average rate of change in the given interval is $\frac{2}{5}$ .

7 0

3 years ago

Which of the following multiplication problems would result in a negative product?

Alex_Xolod [135]

$(-3)(-4)(4) = 48$
$(-3)(-4)(-4) = -48$
$(3)(4)(-4) = -48$
$(3)(-4)(-4) = 48$

That means answers B and C will give you a negative answer!

8 0

4 years ago

The probability that a pupil in class has a calculator is 0.87 what is the probability that a pupil does not have a calculator?

lidiya [134]

Answer:

0.87 1.0

0.13

Step-by-step explanation:

0.13 dont have a calculator

8 0

3 years ago

If A and B are events with P(A)=0.7, P(A OR B)=0.77, and P(A AND B)=0.13, find P(B).

Rufina [12.5K]

Answer:

P(B) = 0.20

Step-by-step explanation:

For these events, which are not independent or mutually exclusive, the relation between the various probabilities is ...

P(A or B) = P(A) +P(B) -P(A and B)

Solving for P(B), we find ...

P(B) = P(A or B) +P(A and B) -P(A)

P(B) = 0.77 +0.13 -0.7 = 0.20

The probability of B is 0.20.

__

<em>Additional comment</em>

The formula applies to independent and mutually exclusive events, as well. For independent events, P(A and B) = P(A)·P(B). For mutually exclusive events, P(A and B) = 0.

5 0

2 years ago