MATHEMATICS COLLEGE

What is 3/5 times 1/6 in simplest form

Answers

Answer 1

Answer:

Answer:

It should be 1/10

Step-by-step explanation:

3*1 is 3

5*6 is 30

simplify and get 1/10

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Write the slope-intercept form of the equation of the line
2x + 3y = 18

Answers

Answer:

y=-2/3x+18

Step-by-step explanation:

Slope intercept form equals y=mx+b

Step 1 move 2x to the other side. 3y=-2x+18

Step 2 divide by 3. y=-2/3x+18

he amount of time people spend exercising in a given week follows a normal distribution with a mean of 3.8 hours per week and a standard deviation of 0.8 hours per week. i. Which of the following shows the shaded probability that a person picked at random exercises less than 2 hours per week? a. b. ii. What is the probability that a person picked at random exercises less than 2 hours per week? (round to 4 decimal places) iii. Which of the following shows the shaded probability that a person picked at random exercises between 2 and 4 hours per week? a. b. iv. What is the probability that a person picked at random exercises between 2 and 4 hours per week? (round to 4 decimal places)

Answers

Answer:

Step-by-step explanation:

Let X denote the amount of time spending exercise in a given week

Given that X normal (3.8, (0.8)²)

Thus we know that

$Z= (x-3.8)/(0.8) N(0,1)$

i)P [ amount of time less than two hour ]

= P[x < 2]

ii)

$P [x < 2]=P[(x-3.8)/(0.8) < (2-3.8)/(0.8) ]\n\n=P[z<-2.25]$

= P[z > 2.25] ∴ symmetric

= P[0 ≤ z ≤ ∞] - P[0 ≤ z ≤ 2.25]

= 0.5 - 0.48778

= 0.0122

iii)

P[2 < x < 4]

Answer:

i) Check attached image.

ii) P(x < 2) = 0.0122

iii) Check attached image.

iv) P(2 < x < 4) = 0.5865

Step-by-step explanation:

This is a normal distribution problem with

Mean = μ = 3.8 hours per week

Standard deviation = σ = 0.8 hours per week

i) The probability that a person picked at random exercises less than 2 hours per week on a shaded graph?

P(x < 2)

First of, we normalize/standardize the 2 hours per week

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (2.0 - 3.8)/0.80 = -2.25

The probability that someone picked at random exercises less than 2 hours weekly is shown in the attached image to this question.

P(x < 2) = P(z < -2.25)

ii) To determine the probability that someone picked at random exercises less than 2 hours weekly numerically

P(x < 2) = P(z < -2.25)

We'll use data from the normal probability table for these probabilities

P(x < 2) = P(z < -2.25) = 0.01222 = 0.0122 to 4 d.p

iii) The probability that a person picked at random exercises between 2 and 4 hours per week on a shaded graph?

P(2 < x < 4)

We then normalize or standardize 2 hours and 4 hours.

For 2 hours weekly,

z = -2.25

For 4 hours weekly,

z = (x - μ)/σ = (4.0 - 3.8)/0.80 = 0.25

The probability that someone picked at random exercises between 2 and 4 hours weekly is shown in the attached image to this question.

P(2 < x < 4) = P(-2.25 < z < 0.25)

iv) To determine the probability that a person picked at random exercises between 2 and 4 hours per week numerically

P(2 < x < 4) = P(-2.25 < z < 0.25)

We'll use data from the normal probability table for these probabilities

P(2 < x < 4) = P(-2.25 < z < 0.25)

= P(z < 0.25) - P(z < -2.25)

= 0.59871 - 0.01222 = 0.58649 = 0.5865

Hope this Helps!!!

If you flip three fair coins, what is the probability that you’ll get two tails and one head in any order?

Answers

Step-by-step explanation:

1/ 3 is the probability of getting one head

An arithmetic series contains n terms. Show that if t1 = a−b and tn = a+b then the value of Sn is independent of b.[Arithmetic Sequences]

Answers

Answer:

Sn is independent of b

Step-by-step explanation:

t1=a-b

tn=a+b

we know that nth term of arithmetic series is an=a1+(n-1)d

a+b=a-b+(n-1)d

⇒2b=(n-1)d-----------equation 1

formula for sum of n terms of arithmetic series

Sn= $(n)/(2)$ (2a1+(n-1)d)

⇒Sn= $(n)/(2)$ (2(a-b)+2b) (since (n-1)d=2b from equation 1)

⇒Sn= $(n)/(2)$ (2a)

therefore we can see that Sn is independent of b

The distribution of the annual incomes of a group of middle management employees approximated a normal distribution with a mean of $37,200 and a standard deviation of $800. About 68% of the incomes lie between what two incomes

Answers

Answer:

68% of the incomes lie between $36,400 and $38,000.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = $37,200

Standard Deviation, σ = $800

We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.

Empirical rule:

Almost all the data lies within three standard deviation of mean for a normally distributed data.
About 68% of data lies within one standard deviation of mean.
About 95% of data lies within two standard deviation of mean.
About 99.7% of data lies within three standard deviation of mean.

Thus, 68% of data lies within one standard deviation.

$\mu \pm \sigma\n=37200 \pm 800\n=(36400,38000)$

Thus, 68% of the incomes lie between $36,400 and $38,000.

Consider an unreliable communication channel that can successfully send a message with probability 1/2, or otherwise, the message is lost with probability 1/2. How many times do we need to transmit the message over this unreliable channel so that with probability 63/64 the message is received at least once? Explain your answer. Hint: treat this as a Bernoulli process with a probability of success 1/2. The question is equivalent to: how many times do you have to try until you get at least one success?

Answers

Answer:

6 times we need to transmit the message over this unreliable channel so that with probability 63/64.

Step-by-step explanation:

Consider the provided information.

Let x is the number of times massage received.

It is given that the probability of successfully is 1/2.

Thus p = 1/2 and q = 1/2

We want the number of times do we need to transmit the message over this unreliable channel so that with probability 63/64 the message is received at least once.

According to the binomial distribution:

$P(X=x)=(n!)/(r!(n-r)!)p^rq^(n-r)$