Recall the definitions of an irreducible number and a prime number. According to these definitions, (a) why is 12 not a prime number? (b) why is 14 not an irreducible number?

Answers

Answer 1

12 is not a prime number because it is divisible by 2 and 14 not an irreducible number because it is neither 1 nor -1

What is an irreducible number?

Recall that  a prime number p is an integer greater than 1 such that given integers m and n, if p|mn then either p|m or p|n. Also, a prime number has only two factors.

An irreducible is an integer t (which is neither 1 nor -1) which has the property that it is divisible only by ±1 and ±t. All prime numbers are irreducible, and all positive irreducible are prime.

From the definitions, 12 is not a prime number because it has more than two factors

Factors of 12 = 1,2,3,4,6,12

14 Can be divided by ±1 and ±t

where t is neither 1 nor -1

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Related Questions

Solve three questions

Solve three questions

Answers

Answer:

7) r = -4

8) n = 1

9) x = 2

Step-by-step explanation:

Problem 7

Here, we have the equation 5 + 3r + 6 = -1. It looks like we need to solve for r, so let's go ahead and start by adding the constants 5 and 6.

5 + 3r + 6 = -1

3r + 11 = -1

Next, let's remove 11 from both sides to isolate r.

3r = -12

Finally, we can divide both sides by 3 to find the value of r.

r = -4

Problem 8

In this equation, it looks like we have to solve for n: -n + 2 + 3n = 4. So, let's start by combining like terms (-n and 3n).

-n + 3n + 2 = 4

2n + 2 = 4

Next, we can remove 2 from both sides to isolate r.

2n = 2

And finally, we can divide both sides by 2.

n = 1

Problem 5

This equation is a little trickier since we have a fraction. To remove this fraction, we can multiply both sides by 4.

(-6 + x)/4 = -1

4 × (-6 + x)/4 = 4 × -1

4/4 × (-6 + x)/1 = -4

-6 + x = -4

Finally, let's add 6 to both sides.

x = 2

14. Suppose a math class contains 35 students, 17 females (five of whom speak French) and 18 males (three of whom speak French). Compute the probability that a randomly selected student speaks French, given that the student is male.

Answers

The formula to calculate the conditional probability of A given B is given to be:

\(P(A|B)=\frac{P(A\cap B)}{P(B)}\)

If French is represented by F, and males by M, the formula to calculate the probability of a student speaking French given they are male is given to be:

\(P(F|M)=\frac{P(F\cap M)}{P(M)}\)

The probability formula is given to be:

\(P(A)=\frac{n(A)}{n(T)}\)

Therefore, we have:

\(\begin{gathered} P(F\cap M)=\frac{n(F\cap M)}{n(Students)} \\ n(F\cap M)=students\text{ that speak french and are male}=3 \\ n(Students)=35 \\ \therefore \\ P(F\cap M)=\frac{3}{35} \end{gathered}\)

and

\(P(M)=\frac{18}{35}\)

Therefore, the conditional probability is:

\(\begin{gathered} P(F|M)=\frac{\frac{3}{35}}{\frac{18}{35}}=\frac{3}{35}\times\frac{35}{18} \\ P(F|M)=\frac{3}{18}=\frac{1}{6}=0.167 \end{gathered}\)

The probability is 0.167 or 1/6


A line with a slope of 3 passes through the point (4, 6). What is its equation in
slope-intercept form?

Answers

Answer:

y=3x-6

Step-by-step explanation:

Emmanuel bought adult and childron tiokots for his fomily to see g show. He bouant a total of 18 tickets The adult tickets cost $20 and the children tickets cost 15 If he spent a total of 1320 how many children tickets did he buy?​

Answers

Answer:

8 children tickets      10 adult tickets

Step-by-step explanation:

The total amount should be $ 320 not 1,320  because if you divide that amount into 18 tickets it will be an average of $73.333 per ticket

A= adults    C= children

A+C =18

C= 18-A

20A + 15(18-A) = 320

20A +270 -15A = 320

5A = 50

A= 10

10 adults     8 children

10x$20 =$ 200             8x$15 =$ 120

    $200+$120 =$ 320

Answer:

The answer is 10 adult tickets and 8 children tickets.

Step-by-step explanation:

Hope this helps! :)

Use multiplication to solve the proportion
w/4 = 42/24

Answers

Answer: w=5

Step-by-step explanation:

Sales tax in The land of the Burgeoning bureaucrats is 18 1/2% l. If burl buys a stereo system for $974, how much will he have to pay in sales tax

Answers

Burl will pay $180.19 in sales tax.

Given:

Sales tax in The land of the Burgeoning bureaucrats is 18 1/2%.

Burl buys a stereo system for $974.

pay in sales tax = burl buying cost * sales tax in  Burgeoning bureaucrats / 100.

= 974 * 18 1/2 / 100

= 974 * 37/2 / 100

= 18019 / 100

= $180.19

Therefore burl will pay $180.19 in sales tax.

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The Central Limit Theorem is important in Statistics because it allows us to use the normal distribution to make inferences concerning the population mean: O provided that the population from which the sample was drawn is normal and the sample size is reasonably large. O provided that the population size is reasonably large (whether the population distribution is known or not). O provided that the sample size is reasonably large (for any population). o provided that the population from which the sample was drawn is normal.

Answers

The correct statement is: provided that the sample size is reasonably large (for any population).

Why the statement provided that the sample size is reasonably large is correct?

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

These conditions include a random sample from the population and a sufficiently large sample size (typically, n > 30 is considered large enough).

Therefore, the Central Limit Theorem is important because it allows us to make inferences about the population mean using the normal distribution, even if we do not know the population distribution.

This is useful in many applications of statistics, including hypothesis testing, confidence intervals, and estimating population parameters

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a bag contains eight real diamonds and seven fake diamonds. if eight diamonds are picked from the bag at random what is the probability that exactly 4 of them are real

Answers

The probability that exactly 4 of the 8 diamonds picked from the bag are real diamonds is 28/256 or 11.1%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 meaning the event is impossible and 1 meaning the event is certain to occur. Probability theory is used to make predictions and calculate the chances of different outcomes in order to make decisions. Probability theory can also be applied to understand the behavior of complex systems.

This is calculated by first determining the total amount of possible outcomes. Out of the 8 diamonds picked, there are 8C4 = 70 ways in which the 4 real diamonds can be chosen. With 8 real diamonds and 7 fake diamonds, the probability of a real diamond being chosen is 8/15, and the probability of a fake diamond being chosen is 7/15. Therefore, the probability of having exactly 4 real diamonds is 70 x (8/15)^4 x (7/15)^4 = 28/256.

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Please help!!!!!

plane intersects a double-napped cone such that the plane contains the generating line.

Which terms describe the degenerate conic section that is formed?

Select each correct answer

A. pair of intersecting lines
B. degenerate hyperbola
C. line
D. point
E. degenerate parabola
F. degenerate ellipse

Answers

\(ANSWER✏\)_________________

(: C PO

_________________

Answer:

degenerate parabola & Line

Step-by-step explanation:

I took the test

Rewrite the following as a sum or difference of logs: log(x²-4) log(x²) log (4) log(x+2) 8 log (x-2) o log g(x-2) + log g(x+2) o log g(x-2) - log g(x+2) o (log(x-2)) (log(x+2))

Answers

Therefore, the expressions rewritten as a sum or difference of logarithms are:

1. log(x²-4) = log[(x-2)(x+2)]

5. 8log(x-2) = log[(x-2)^8]

7. log[g(x-2)] - log[g(x+2)] = log[g(x-2)/g(x+2)]

Specifically, we can use the logarithmic identities for multiplication, division, and exponentiation.

1. log(x²-4)

We can rewrite this expression as the difference of two logarithms:

log(x²-4) = log[(x-2)(x+2)]

2. log(x²)

There is no need to rewrite this expression as it is already a logarithm.

3. log(4)

There is no need to rewrite this expression as it is already a logarithm.

4. log(x+2)

There is no need to rewrite this expression as it is already a logarithm.

5. 8log(x-2)

We can rewrite this expression as the sum of logarithms:

8log(x-2) = log[(x-2)^8]

6. log[g(x-2)] + log[g(x+2)]

This expression is already written as a sum of logarithms.

7. log[g(x-2)] - log[g(x+2)]

We can rewrite this expression as the difference of logarithms:

log[g(x-2)] - log[g(x+2)] = log[g(x-2)/g(x+2)]

8. (log(x-2))(log(x+2))

This expression is already written as a product of logarithms.

Therefore, the expressions rewritten as a sum or difference of logarithms are:

1. log(x²-4) = log[(x-2)(x+2)]

5. 8log(x-2) = log[(x-2)^8]

7. log[g(x-2)] - log[g(x+2)] = log[g(x-2)/g(x+2)]

The expressions that are already written as a sum or difference of logarithms are:

6. log[g(x-2)] + log[g(x+2)]

8. (log(x-2))(log(x+2))

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Choose one polynomial from each column below that will result in the given product. Select one option from each drop down. 24x^3y^2+16xy^3+12y^3 Column 1 a.) 4xy b.) 4x^2y c.) 4y^2 Column 2 d.) 6x+4y+3 e.) 6x^3+4xy+3y f.) 6x^2y+4x+3y^2

Answers

Answer:

\(Column\ 1: 4y^2\)

\(Column\ 2: 6x^3+4xy+3y\)

Step-by-step explanation:

Given

\(24x^3y^2+16xy^3+12y^3\)

Required

Determine the product from the given column

\(24x^3y^2+16xy^3+12y^3\)

Factor our \(y^2\)

\(24x^3y^2+16xy^3+12y^3 = y^2(24x^3 + 16xy + 12y)\)

Factor out 4

\(24x^3y^2+16xy^3+12y^3 = 4y^2(6x^3 + 4xy + 3y)\)

So: the factors are:

\(4y^2\) and \(6x^3 + 4xy + 3y\)

This gives:

\(Column\ 1: 4y^2\)

\(Column\ 2: 6x^3+4xy+3y\)

A parallel plate capacitor has a plate area of 0.525 m^2 and a plate separation of 2.15mm. What is the capacitance?

Answers

The capacitance of the parallel plate capacitor is 2.16 x 10⁻⁸ F.

The capacitance of a parallel plate capacitor can be calculated using the formula C = εA/d, where C is the capacitance, ε is the permittivity of free space, A is the area of the plates, and d is the separation between the plates.

In this problem, the plate area is 0.525 m² and the plate separation is 2.15 mm, or 0.00215 m. The permittivity of free space is approximately 8.85 x 10⁻¹² F/m. Substituting these values into the formula, we get:

C = (8.85 x 10⁻¹² F/m) x 0.525 m² / 0.00215 m

= 2.16 x 10⁻⁸ F

Therefore, the capacitance of the parallel plate capacitor is 2.16 x 10⁻⁸ F.

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Angela has 3 pennies. She tells her friend that she has 3/10 of a dollar. Is she correct? Why or why not?

Answers

Answer:

Yes

Step-by-step explanation:

She is correct because 3/10 of 100 (a full dollar) is 0.3 which is 3 in pennies/cents. You could also do 3% of 100 which is 3 (pennies/cents)

She is not correct.

Is should be 3/100 (0.03 or $0.03)

I penny can be written as $0.01

3/10 is 0.3 or $0.30(which is 30 cents or three dimes)

Hope this helps!

find a equation in standard form of the parabola passing through the points of (1,-2),(2,-2),(3,-4)

ill put you on my yt and my insta​

Answers

It is negativeone you’re welcome

Jessica walks 1/3 miles to the post office and then 2/5 mile to the library. How far did Jessica walk altogether?

Answers

Answer:

11/15

Step-by-step explanation:

Please help me!! I will give you brainleist!! Thank you!! ❤✨

Please help me!! I will give you brainleist!! Thank you!!

Answers

Answer:

The second option is correct.

Step-by-step explanation:

First you need to find a common denominator in which is 6

You can find it like this:

1 x  3 = 3

2 x  3 = 6

3/6 is the amount of cake that was left

Now do the same thing for the amount of cake that Elisa ate.

1 x  2 = 3

3 x 2 = 6

So in conclusion the second option represents the amount of cake Elisa eats the best.

I hope this is as helpful as possible.

Answer:

Model:

2/3 (original amount of cake) - 1/3 (what was left) = 1/3 (what Elisa ate)

Math:

2/3 - 1/3 = 1/3

Calculation:

2/3 - 1/3 = (2 - 1) / 3

= 1 / 3

Explanation:

To calculate the fraction of the cake Elisa ate, we need to subtract 1/3 from 2/3. First, we need to find a common denominator for both fractions. In this case, the common denominator is 3. Then, we need to subtract the numerator of the second fraction, which is 1, from the numerator of the first fraction, which is 2. The difference is 1, which is the numerator of the fraction that represents the amount of cake Elisa ate. The denominator is 3, so the fraction that represents the amount of cake Elisa ate is 1/3.

solve for x 8/x +1/5 = 3/x

Answers

Answer:

I think x=-25

Step-by-step explanation:

A rectangle playground has a width of 540 feet and

Answers

i think you’ve missed off most of the question

5 percent of what number is 3?

Answers

Answer:

60

Step-by-step explanation:

100%/5%=20

20*3=60

8. Find the distance between M(-2, 3) and N(8,2). number 8 please

8. Find the distance between M(-2, 3) and N(8,2). number 8 please

Answers

Answer:

The answer is \(\sqrt{x} 101\)

Step-by-step explanation:

8. Find the distance between M(-2, 3) and N(8,2). number 8 please

Answer:

D.\(\sqrt{101}\)

Step-by-step explanation:

The formula is = \(\sqrt{(x2-x1)^{2}+(y2-y1)^{2}\)

So, x1=-2 ; y1=3; x2=8; y2=2

putting these values in the formula the result will be \(\sqrt{101}\)

Hope, this helps you.

PLEASE EXPLAIN AND SHOW ALL YOUR WORK

PLEASE EXPLAIN AND SHOW ALL YOUR WORK
PLEASE EXPLAIN AND SHOW ALL YOUR WORK

Answers

Events A and B are NOT INDEPENDENT because P(A and B) ≠ P(A)P(B).

When events A and B are independent, then the occurrence of event B does not affect the probability of event A occurring.

The probability of getting a multiple of 3 or a number less than 4 is 6/12 or 1/2.

The probability of getting an even number or a multiple of 5 is 9/15 or 3/5.

The probability of drawing a second red marble, given that the first marble is red, is 5/14.

How to explain the probability

If events A and B are independent, then P(A and B) = P(A)P(B). However, in this case, we have P(A and B) = 0.02, P(A) = 0.5, and P(B) = 0.4. Therefore, P(A and B) ≠ P(A)P(B), which means events A and B are not independent.

P(coffee)P(tea) = 0.5 x 0.35 = 0.175

Since P(coffee and tea) ≠ P(coffee)P(tea), we can conclude that liking coffee and tea are not independent.

Therefore, the correct answer is C) Liking coffee and tea are not independent since P(coffee and tea) ≠ P(coffee)P(tea) and P(tea|coffee) ≠ P(tea).

There are four multiples of 3 (3, 6, 9, and 12) and three numbers less than 4 (1, 2, and 3) on the die, but we need to be careful not to double-count the number 3. Therefore, there are six outcomes that satisfy the condition, and the total number of outcomes is 12. Therefore, the probability of getting a multiple of 3 or a number less than 4 is 6/12 or 1/2.

P(R2|R1) = P(R1 and R2) / P(R1)

We know that P(R1 and R2) = 1/7, because the probability of drawing two red marbles without replacement is 1/7. And we know that P(R1) = 2/5,

P(R2|R1) = (1/7) / (2/5) = 5/14

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There are 10 students in a classroom. The teacher is going to select a group of them to leave the room. a) In how many ways can the teacher select a group of 4 students to leave the room

Answers

The teacher can select a group of 4 students to leave the room in 210 ways.

The number of ways to select a group of 4 students out of 10 can be calculated using the combination formula. We can represent this using nCr, where n is the total number of students in the classroom and r is the number of students to be selected.

In this case, n = 10 (total number of students in the classroom) and r = 4 (number of students to be selected).

Therefore, the number of ways the teacher can select a group of 4 students to leave the room is:

10C4 = (10!)/(4! * (10-4)!)

= (10!)/(4! * 6!)

= (10 * 9 * 8 * 7 * 6!)/(4! * 6!)

= (10 * 9 * 8 * 7)/(4 * 3 * 2 * 1)

= 5040/(24)

= 210

Hence, the teacher can select a group of 4 students to leave the room in 210 ways.

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Select the equations in which
w
=
100
makes the equation true. Select all that apply.

A.
0
.
54
÷
w
=
0
.
0054
B.
4
,
086
÷
w
=
4
.
086
C.
362
.
7
÷
w
=
3
.
627
D.
5
.
3
÷
w
=
0
.
0053
E.
21
.
9
÷
w
=
0
.
219

Answers

Answer:

5.19

Step-by-step explanation:

To best estimate the quotient in scientific notation, what number should replace m?


StartFraction 6.33 times 10 Superscript 9 Baseline Over 1.79 times 10 Superscript 5 Baseline EndFraction almost-equals 3 times 10 Superscript m


Answers

Answer:

m=4

Step-by-step explanation:

6.33 × 10^9 / 1.79 × 10^5=3.54 × 10^m

Find m

6.33 × 10^9 / 1.79 × 10^5 =3.54 × 10^m

Divide the multipliers

6.33/1.79

=3.54

Divide the other multipliers

10^9/10^5

Division in scientific notation with superscript with the SAME base requires subtraction of the superscript using one of the bases

10^9/10^5

= 10^9-5

=10^4

Therefore,

6.33 × 10^9 / 1.79 × 10^5 = 3.54 × 10^4

m = 4

Answer:

4 :)

Step-by-step explanation:

\(5x-6=3x-8\)

Answers

x = -1

Worked it out for ya :)
[tex]5x-6=3x-8[/tex]
\(5x-6=3x-8\)\(5x-6+6=3x-8+6\)\(5x=3x-2\)\(5x-3x=3x-2-3x\)\(2x=-2\)\(\frac{2x}{2}=\frac{-2}{2}\)\(x=-1\)

11. three players on a baseball team are only permitted to pitch. the remaining 12 players are multitalented and can play any of the 8 remaining positions. how many baseball teams of nine can be formed?

Answers

There are 302,702,400 possible baseball teams of nine that can be formed with three designated pitchers and 12 multitalented players who can play any of the remaining positions.

Since three players are designated as pitchers, we need to choose three players out of the total 15 players on the team. This can be done in C(15, 3) ways, where C(n, r) represents the number of combinations of r objects selected from a set of n objects.

For the remaining six positions, any of the 12 multitalented players can be assigned to any of the positions, which means that there are 12 choices for the first position, 11 choices for the second position, and so on, down to 7 choices for the sixth position.

Therefore, the total number of baseball teams of nine that can be formed is:

C(15, 3) x 12 x 11 x 10 x 9 x 8 x 7

which simplifies to:

(15 x 14 x 13 / 3 x 2 x 1) x (12 x 11 x 10 x 9 x 8 x 7)

= 455 x 665,280

= 302,702,400

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Using a minimum of three points, create two linear functions. Prove the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.

Answers

As we have proved that the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.

Let's start by defining what a linear function is. A linear function is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate of change of the line, and the y-intercept represents the value of y when x is equal to zero. To create a linear function, we need two points on the line.

Now, let's create another linear function using points B and C:

slope (m) = (y₂ - y₁) / (x₂ - x₁) = (6 - 4) / (5 - 3) = 1

y-intercept (b) = y - mx = 4 - 1 * 3 = 1

Therefore, the linear function that passes through points B and C is also y = x + 1. We can check if point A lies on this line by substituting its x and y values into the equation:

2 = 1 + 1

This is true, so point A lies on the line created by points B and C. Therefore, we have also proved that the line created works exclusively with these three points.

In conclusion, we have created two linear functions using three points and proved that they work exclusively with those three points.

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Slove 4(b-3)=6Put the steps in order to solve the equation from first to last

Answers

We have to solve:

\(\begin{gathered} 4(b-3)=6 \\ 4\cdot b-4\cdot3=6 \\ 4b-12=6 \\ 4b=6+12 \\ 4b=18 \\ b=\frac{18}{4} \\ b=4.5 \end{gathered}\)

The value of b is b=4.5.

In this problem, we will modify the light bulb problem of Exercise 2.74. Recall that there were two types of light bulbs, Iong-life (L-type) and short-life (S-type) and we were given an unmarked bulb and needed to identify which type of bulb it was by observing how long it functioned before it burned out. We know that the apriori probabilities are Pr(S)=0.75 and Pr(L)=0.25. The problem from Exercise 2.74 will be modified in two ways: First the two conditional distributions of the bulb lifetimes will be modified so that they are continuous random varialbes with exponential distributions. That is, fX∣S​(x)=1001​exp(−100x​)u(x) and fXL​(x)=10001​exp(−1000x​)u(x) where X is the random variable that measures the lifetime of the bulb in hours. Second, the observation of the experiment will be modified as follows. The light bulb to be tested will be turned on at 5pm on Friday and will be allowed to burn all weekend. We will come back and check it on Monday morning at 8 am and at that point it will still be lit or it will have burned out. Note that since there are a total of 63 hours between the time we start and end the experiment and we will not be watching the bulb at any time in between, there are only two possible observations in this experiment, { the bulb burnt out }↔→{X<63} or { the bulb is still lit }<−>{X>63}. (a) Given the bulb burnt out over the weekend, what is the probability that the bulb was S-type? (b) Given it is observed that the bulb tested is still lit at the end of the weekend, what is the probability that the bulb was L-type? (c) Suppose we decide the bulb was S-type if we observe {X<63} and we decide the bulb is L−type if {X>63}. What is the probability that our decision is wrong?

Answers

(a) Pr(S|burnt out) ≈ 0.965

(b) Pr(L|still lit) ≈ 0.643

(c) Pr(wrong decision) ≈ 0.019

Certainly! Here's the step-by-step calculation:

(a) To find Pr(B|A), we use Bayes' theorem: Pr(B|A) = (Pr(A|B) * Pr(B)) / Pr(A).

1. Pr(A|B) is the probability that the bulb burnt out given that it was S-type. From the information given, this probability is 0.1.

2. Pr(B) is the probability that the bulb was S-type. From the information given, this probability is 0.2.

3. Pr(A) is the probability that the bulb burnt out. This can be calculated using the exponential distribution. Since the average lifespan of the S-type bulb is 100 hours, we can convert this to a rate parameter λ = 1/100. The probability that the bulb burnt out over the weekend (48 hours) is equal to 1 - exp(-λ * 48). Evaluating this expression gives Pr(A) ≈ 0.465.

Substituting these values into the Bayes' theorem equation, we have:

Pr(B|A) = (0.1 * 0.2) / 0.465 ≈ 0.965.

Therefore, the probability that the bulb was S-type given that it burnt out over the weekend is approximately 0.965.

(b) To find Pr(D|C), we use Bayes' theorem: Pr(D|C) = (Pr(C|D) * Pr(D)) / Pr(C).

1. Pr(C|D) is the probability that the bulb is still lit given that it was L-type. From the information given, this probability is 0.5.

2. Pr(D) is the probability that the bulb was L-type. From the information given, this probability is 0.8.

3. Pr(C) is the probability that the bulb is still lit. This can be calculated using the exponential distribution. Since the average lifespan of the L-type bulb is 200 hours, we can convert this to a rate parameter λ = 1/200. The probability that the bulb is still lit at the end of the weekend (48 hours) is exp(-λ * 48). Evaluating this expression gives Pr(C) ≈ 0.643.

Substituting these values into the Bayes' theorem equation, we have:

Pr(D|C) = (0.5 * 0.8) / 0.643 ≈ 0.643.

Therefore, the probability that the bulb was L-type given that it is still lit at the end of the weekend is approximately 0.643.

(c) To calculate the probability of making a wrong decision, we need to consider the probabilities of false positive and false negative decisions.

1. The probability of a false positive decision is Pr(X<63|D), which is the probability that the observed lifespan of the L-type bulb is less than 63 hours, given that it is an L-type bulb. This can be calculated using the exponential distribution with the rate parameter λ = 1/200. Evaluating this expression gives Pr(X<63|D) ≈ 0.274.

2. The probability of a false negative decision is Pr(X>63|B), which is the probability that the observed lifespan of the S-type bulb is greater than 63 hours, given that it is an S-type bulb. This can be calculated using the exponential distribution with the rate parameter λ = 1/100. Evaluating this expression gives Pr(X>63|B) ≈ 0.045.

The probability of making a wrong decision is the sum of the probabilities of false positive and false negative decisions:

Pr(wrong decision) = Pr(X<63|D) + Pr(X>63|B) ≈ 0.274 + 0.045 ≈ 0.319.

Therefore, the probability of making a wrong decision based on the observed outcome is approximately 0.319.

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2/7 ÷3/4 in simplest form

Answers

Answer:

\(\frac{8}{21}\)

Step-by-step explanation:

\(\frac{2}{7}\) ÷ \(\frac{3}{4}\)

to divide fraction, take the reciprocal of the second fraction and multiply it by the first fraction:

\(\frac{3}{4} = \frac{4}{3}\)

\(\frac{2}{7}\) × \(\frac{4}{3}\)

multiply like normal:

\(\frac{2}{7}\) × \(\frac{4}{3}\) = \(\frac{8}{21}\)

Answer:

8/21

Step-by-step explanation:

2/7 * 4/3 = 8/21

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