a) A box contains 50 diodes of which 10 are known to be bad. A diode is selected at random. What...




a) A box contains 50 diodes of which 10 are known to be bad. A diode is selected at random. What is the probabil ity that it is bad?

b) If the first diode drawn from the box was good, what is the probability that a: second diode drawn wi ll be good?

c) If two diodes are drawn from the box what is the probability that they are both good?









Answers

Answer 1

Final answer:

a) The probability of selecting a bad diode is 0.2 (20%). b) If the first diode is good, the probability of the second diode being good is 0.816 (81.6%). c) The probability that both diodes are good is 0.6326 (63.26%).

Explanation:

a) Probability that the diode is bad:

There are 50 diodes in total, with 10 known to be bad. The probability of selecting a bad diode is calculated by dividing the number of bad diodes by the total number of diodes: 10/50 = 1/5 = 0.2 or 20%.

b) Probability of second diode being good:

If the first diode drawn is good, there will be 49 diodes left, with 9 being bad. The probability of selecting a good diode as the second one is 40/49 = 0.816 or 81.6%.

c) Probability that both diodes are good:

If two diodes are drawn, there will be 48 diodes left, with 9 being bad. The probability of selecting a good diode for the first draw is 40/50 and for the second draw is 39/49. Therefore, the probability of both diodes being good is (40/50) * (39/49) = 0.6326 or 63.26%.

Answer 2
Final answer:

The probability of selecting a bad diode from the box of 50 is 0.2. If a good diode is selected first, the probability of selecting another good diode is 39/49. The probability of selecting two good diodes consecutively is approximately 0.6367.

Explanation:

The question deals with the concept of probability within a discrete random variable scenario. Specifically, it requires calculating the probabilities of selecting good and bad diodes from a batch with a known distribution of working and defective parts.

a) The probability that a randomly selected diode is bad is the number of bad diodes divided by the total number of diodes. Therefore, it is 10/50 or 1/5 or 0.2.b) If the first diode drawn is good, we have 49 diodes left with 10 bad still among them. The probability that a second diode drawn will be good is the number of remaining good diodes divided by the total remaining diodes, which is 39/49.c) To find the probability that both diodes are good when two are drawn without replacement, we multiply the probability of drawing one good diode by the probability of drawing a second good diode (having already drawn one good). This gives us (40/50) * (39/49), which simplifies to 0.8 * 0.7959 or approximately 0.6367.


Related Questions

The right triangle ABC shown below is inscribed inside a parabola. Point B is also the maximum point of the parabola (vertex) and point C is the x intercept of the parabola. If the equation of the parabola is given by y = -x2 + 4x + C, find C so that the area of the triangle ABC is equal to 32 square units.

Answers

I am not sure how to do that because you can not combine like terms

Bao and Calvin use 6 lemons to make ever 4auarts of lemonade. They want to make 12 quarts of lemonade. How many lemons do they need?

Answers

They are going to need 18 lemons

The graph of a sinusoidal function intersects its midline at (0,5) and then has a maximum point at (\pi,6)

Write the formula of the function, where x is entered in radians.

f(x)=

Answers

First, let's use the given information to determine the function's amplitude, midline, and period. 

Then, we should determine whether to use a sine or a cosine function, based on the point where x=0.

Finally, we should determine the parameters of the function's formula by considering all the above.
     
                      Determining the amplitude, midline, and period 

The midline intersection is at y=5 so this is the midline. 

The maximum point is 1 unit above the midline, so the amplitude is 1. 

The maximum point is π units to the right of the midline intersection, so the period is 4 * π.
 
                                                 Determining the type of function to use 

Since the graph intersects its midline at x=0, we should use thesine function and not the cosine function. 

This means there's no horizontal shift, so the function is of the form -

a sin(bx)+d

Since the midline intersection at x=0 is followed by a maximumpoint, we know that a > 0.

The amplitude is 1, so |a| = 1. Since a >0 we can conclude that a=1. 

The midline is y=5, so d=5. 

The period is 4π so b = 2π / 4π = 1/2 simplified. 

[tex]f(x) = 1 sin ( \dfrac{1}{2}x)+5[/tex]   = Solution 

Answer:

f(x)=1sin(1/2x)+5

Step-by-step explanation:

A beluga whale is 5 yards and 3 inches long, and a gray whale is 15 yards and 5 inches long. What is the difference in length between the two whales?

Answers

Answer:

Difference in length between two whales is 362 inches or 10 yards and 2 inches.

Step-by-step explanation:

Lets convert the values to inches:

1 yard = 36 inches

Length of a beluga whale in inches:

5 yards = [tex]5*36[/tex] inches = [tex]180[/tex] inches

Therefore total length of a beluga whale = 180 inches + 3 inches

                                                                     =183 inches

Length of a gray whale in inches:

15 yards = [tex]15*36[/tex] inches = [tex]540[/tex] inches

Therefore total length of a beluga whale = 540 inches + 5 inches

                                                                     =545 inches

Difference in length between two whales = 545 inches - 183 inches

                                                                      = 362 inches

To represent this in yards and inches we can divide the value by 36.

[tex]\frac{362}{36} =10.06[/tex] yards

=10 yards and 2 inches

Difference in length between two whales is 10 yards and 2 inches.




Beatrice invests $1,440 in an account that pays 3 percent simple interest. How much more could she have earned over a 4-year period if the interest had compounded annually?

$7.93

$31.73

$17.61

$28.37

$21.28






Answers

Final answer:

To calculate the compound interest, use the formula A = P(1 + r/n)^(n*t), where A is the future amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. Beatrice could have earned $419.38 more over a 4-year period with compounded interest.

Explanation:

To calculate the compound interest, we can use the formula: A = P(1 + r/n)^(n*t), where A is the future amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, Beatrice invests $1,440 at an interest rate of 3% for 4 years.

Using the formula, the future amount with compound interest would be: A = 1440 * (1 + 0.03/1)^(1*4) = $1576.18.

To find the difference in earnings, we subtract the future amount with simple interest from the future amount with compound interest: $1576.18 - $1156.80 = $419.38. Therefore, Beatrice could have earned $419.38 more over a 4-year period with compounded interest.

If a circular property has a diameter of 50' and costs $120 per square foot, what is the cost of the property?

Answers

find area
area=pir^2
d/2=r=50/2=25

A=pi25^2
a=pi625
aprox pi=3.141592
a=1963.495
that is how many square feet
multiply that by 120
1963.495 times 120=$235,619.4
Final answer:

To calculate the cost of a circular property with a diameter of 50', determine the area using the formula π * r^2, and then multiply by the cost per square foot. The total cost of the property comes to $235,619.40.

Explanation:

The question asks us to calculate the cost of a property with a circular shape having a diameter of 50'. To begin with, we will find the area of the circular property by using the formula for the area of a circle, A = π * r2, where π (pi) is approximately 3.14159, and r is the radius of the circle. Since the diameter is given as 50', the radius (r) would be half of that, which is 25'. Therefore, the area (A) of the property is 3.14159 * (25')2 = 3.14159 * 625 = 1963.495 square feet.

Now, if the cost is $120 per square foot, we multiply the area by this cost to find the total price of the property. So, the total cost is 1963.495 square feet * $120/square foot = $235,619.40.

Therefore, the cost of the property is $235,619.40.

how to simplify fractions

Answers

Firstly, find a common factor. 

Once you find that, divide both the numerator and denominator by that/those number (s) and you will have a simplified version of your original fraction. 

Keep doing so until you have fully simplified. 

Hope this helps!

Hello There!

To simplify fractions, divide both the numerator "top number" and the denominator "bottom number" until you can't go any lower.

EXAMPLE

[tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex]

You divide the numerator and the denominator both by 4 which gives you the fraction [tex]\frac{1}{2}[/tex]

one day a corn stalk was 0.85m tall. A tomato plant was0.850m. A carrot top was 0.085m.Which plant was the shortest?

Answers

the carrot top is the smallest
The carrot with 0.085 meters is the shortest.

A repeated-measures study using a sample of n = 20 participants would produce a t statistic with df of what?

Answers

for this I suggested a go to this website https://quizlet.com/86562680/psy-201-ch-11-repeated-measures-flash-cards/

The t-statistic for a repeated-measures study with a sample of n = 20 participants would have df=19.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, For determine the degrees of freedom (df) for a repeated-measures study with a sample size of n = 20, we can use the formula:

⇒ df = n - 1

However, in a repeated-measures study, we are comparing two sets of measurements from the same participants.

This means that the difference scores between the two sets of measurements will be used to compute the t-statistic.

Now, For a paired t-test with a sample size of n=20, we would have;

⇒ n - 1 = 19

⇒ n = 20 degrees of freedom.

Therefore, the t-statistic for a repeated-measures study with a sample of n = 20 participants would have df=19.

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find the sum 1 + 4 + 16 + · · · + 65,536

Answers

65,536÷4
=16,384
----------
16,384÷4
=4,096
---------
4,096÷4
=1,024
---------
1,024÷4
=256
---------
256÷4
=64
--------
64÷4=16
16÷4=4
4÷4=1
there are 8 numbers
a(1-q^n)÷q-1=1(1-4^7)÷(1-4)=1-16384\-3=-16383\-3=5461

Final answer:

The sum of the series of powers of 2 from 1 to 65,536 is a geometric series, which can be calculated using the geometric series sum formula to find that the sum is 131,071.

Explanation:

The student is asking about the sum of a series of powers of 2, starting from 2⁰ (which is 1) up to 2¹⁶ (which is 65,536). This is a geometric series where each term is a power of 2, and the common ratio is 2. The sum of a geometric series can be found using the formula:

S = a₁(1 - rⁿ) / (1 - r), where S is the sum of the series, a1 is the first term, r is the common ratio, and n is the number of terms.

In this case, a₁ = 1 (first term), r = 2 (common ratio), and n = 17 (since the series starts at 2⁰ and ends at 2¹⁶, giving us 17 terms).

Plugging these values into the formula gives us:

S = 1(1 - 2¹⁷) / (1 - 2)

S = 1(1 - 131,072) / (-1)

S = 131,071

Therefore, the sum of the series is 131,071.

describe how to find the number of $4 train tickets you can buy with $32

Answers

32/4 you can buy 8 tickets

if you have $32 and you want to buy as many train tickets as possible, you could just mentally divide $32 by $4, which is 8 tickets. if the question is asking for an equation, you could create a quick one-step:

4x = 32

so, 4 dollars multiplied by x, the number of tickets, equals 32. then, again, divide 32 by 4 and see that you can buy 8 tickets.

if you have 18 1/4 pounds of crabs and you need to serve 30 people at a dinner. How much crab will each person receive?

Answers

18 1/4 divided by 30 equals 0.608333333

Each person would receive 0.6 pounds of crab.

A pizza shop offers nine toppings. No topping is used more than once. What is the probability that the toppings on a tree topping pizza are pepperoni, onions, and mushrooms?

Answers

Final answer:

The probability of selecting pepperoni, onions, and mushrooms from nine toppings for a pizza is 1/84, using the combination formula to calculate the total number of three-topping combinations.

Explanation:

To find the probability that a pizza has pepperoni, onions, and mushrooms as the toppings, we first have to determine the total number of ways we can select any three toppings from nine. This is given by the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items, and k is the number of items to choose.

In this case, n is 9 and k is 3. Thus, the total number of ways to choose any three toppings from nine is C(9, 3).

Since there is only one way to specifically get pepperoni, onions, and mushrooms together, the probability P is 1 divided by the total number of three-topping combinations, which simplifies to P = 1 / C(9, 3).

Therefore, P = 1 / (9! / (3!(9-3)!)) = 1 / (9! / (3!6!)) = 1 / (84) = 1/84. Thus, the probability is 1/84.

A furniture store received an order for 3,456 chairs. they can fit 9 chairs in a large shipping box. how many shipping boxes will they need to ship all of the chairs

Answers

This is simple :)
If 9 chairs can fit in one box, and you have 3,456 chairs, just divide how many chairs you have by how many can fit in the box in order to find how many boxes you will need.

3,456/9 = 384
384 boxes will be needed
Final answer:

To ship 3,456 chairs with each box holding 9 chairs, you will need a total of 385 boxes.

Explanation:

To find the number of shipping boxes needed, we need to divide the total number of chairs by the number of chairs that can fit in one box. So, with 3,456 chairs and the capacity of each box being 9 chairs, we use the formula:

Number of boxes = Total chairs / Chairs per box

This gives us:

Number of boxes = 3,456 / 9

This division results in 384 with a remainder of 0. Since you can't ship a fraction of a box, but you need a whole box even for a single chair, this means that you will need 385 boxes to ship all the chairs.

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Find two consecutive positive integers such that the sum of their squares is 421 .

Answers

We assume the two numbers are x and (x+1)
so x^2+(x+1)^2=421
x^2+(x^2+2x+1)=421
2x^2+2x-420=0
According to the formula of quadratic 
x=14 or-15
cuz we know the two numbers are integers
so x=14
therefore the other number is 15
To make sure that's correct
14^2+15^2=421

Hope that helps you!!


Law of cosines: a2 = b2 + c2 – 2bccos(A)

Which equation correctly uses the law of cosines to solve for y?
92 = y2 + 192 – 2(y)(19)cos(41°)
y2 = 92 + 192 – 2(y)(19)cos(41°)
92 = y2 + 192 – 2(9)(19)cos(41°)
y2 = 92 + 192 – 2(9)(19)cos(41°)

Answers

In this case,
a = y
b = 9
c = 19
So...
[tex]a^2 = b^2 + c^2 - 2bc*\cos(A)[/tex]
[tex]y^2 = 9^2 + 19^2 - 2*9*19*\cos(41^{\circ})[/tex]
which means the answer is choice D

an airline travels 135 miles in 15 minutes whats its speed in miles per hour

Answers

It is 540 miles because 15x4 is 60 and that is a full hour so you have to multiply 135x4 which is 540
135 miles in 15 minutes....135/15 = 9 miles per minute
1 hr = 60 minutes
so miles per hr would (9 x 60) = 540.....540 miles per hr

Your friend has a fabulous recipe for salsa, and he wants to start packing it up and selling it. He can rent the back room of a local restaurant any time he wants, complete with their equipment, for $100 per time. It costs him $2 a jar for the materials (ingredients for the salsa, jars, labels, cartons) and labor (you and a couple of friends of his) for each jar he makes. He can sell 12,000 jars of salsa each year (I told you it was a fabulous recipe!), with a constant demand (that is, it's not seasonal; it doesn't vary from week to week or month to month). It costs him $1 a year per jar to store the salsa in the warehouse he ships from. He wants to find the number of jars he should produce in each run in order to minimize his production and storage costs, assuming he'll produce 12,000 jars of salsa each year.

Your friend wants to find the number of jars he should produce in each run in order to minimize his production and storage costs, assuming he'll produce 12,000 jars of salsa each year.

Answers

each run costs him 100 dollars
he sells 12000 every year, so 12000*2=24000
and also, each jar cost 1 dollar to store, so an additional 12000
12000+24000=36000

so he wil defenitely spend 36000 on the salsa alone
the only dependent variable is how much he spends on the rent
he can minimize this by making all 12000 jars in 1 run (wow!)
resulting in a cost of $36100
that is minimum cost
you could just do it in your dorm room or your parents' house

The EOQ formula takes into account the demand, setup cost, and holding cost per unit is 154.91 by calculating the EOQ, that identify the batch size that results in the most cost-efficient production and storage.

Given that:

 demand is 12,000 jars, setup cost is $100 per run, and holding cost per unit is $1 per jar per year.

To determine the number of jars to produce in each run,  uses the Economic Order Quantity (EOQ) formula.

The Economic Order Quantity (EOQ) formula is given by:

EOQ =[tex]\sqrt{[/tex][(2 * Demand * Setup cost) / Holding cost per unit].

By substituting these values into the formula:

EQR = [tex]\sqrt{\frac{2\times1200\times10}{1} }[/tex]

On multiplying gives:

EQR = [tex]\sqrt{{24000}}[/tex]\

Take square root on both sides:

EQR = 154.91

The EOQ formula takes into account the demand, setup cost, and holding cost per unit is 154.91 by calculating the EOQ, that can identify the batch size that results in the most cost-efficient production and storage.

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The number of automobiles sold weekly at a certain dealership is a random variable with expected value 16 .Give an upper bound to the probability that
(a) next week's sales exceed 18;
(b )next week's sales exceed 25.
(c) Suppose that the variance of the number of automobiles sold weekly is 9. Give a lower bound to the probability that next week's sales are between 10 and 22 inclusively;
(d) give an upper bound to the probability that next week's sales exceed 18.

Answers

Final answer:

Using the properties of normally distributed random variables and Chebyshev's inequality, we can find the upper and lower bounds for the probability of next week's automobile sales, given the expected value and variance. These calculations involve finding the 'k' value, which is derived from subtracting the expected value from the target sales value, and then using this in the inequality.

Explanation:

The subject of this question is Probability in Mathematics, and this question is likely for a College level course. To bound the probability of a normally distributed random variable exceeding a given value, we can use Chebyshev's inequality: Pr(|X - μ| ≥ kσ) ≤ 1 / k2. Here, X represents the random variable (automobile sales), μ is its expected value (16 sales), and σ is its standard deviation (the square root of the variance).

To find an upper bound for the probability that next week's sales exceed 18, we calculate k as |18 - 16| and use the inequality to calculate the upper bound. The same method applies for finding an upper bound that next week's sales exceed 25. For the probability that next week's sales are between 10 and 22, we have two k-values (|10-16| and |22-16|), and we use both in the inequality to find the lower bound. The fourth part of the question appears to be a repeat of part (a).

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Suppose an Egyptian mummy is discovered in which the amount of carbon 14 is present is only about one third the amount found in living human beings. About how long did the egyptian die

Answers

Answer: 9035

Step-by-step explanation:

The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the diameter is 80 mm? Evaluate your answer numerically.

Answers

Well, if it is increasing at a fixed rate of 2 mm/s, then the volume would still be increasing at a rate of 2 mm/s when the diameter is 80 mm, if I understand your question correctly.

The diameter is 80 mm, the volume of the sphere is increasing at a rate of approximately 40211.2 mm³/s.

To find how fast the volume of the sphere is increasing, we can use the formula for the volume of a sphere:

[tex]\[ V = \frac{4}{3}\pi r^3 \][/tex]

Where V is the volume of the sphere and r is the radius.

Differentiating both sides of the equation with respect to time t, we get:

[tex]\[ \frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt} \][/tex]

Given:

- [tex]\( \frac{dr}{dt} = 2 \)[/tex] mm/s (rate at which the radius is increasing)

- [tex]\( r = \frac{d}{2} = \frac{80}{2} = 40 \)[/tex] mm (radius when the diameter is 80 mm)

Substitute these values into the formula:

[tex]\[ \frac{dV}{dt} = 4\pi (40)^2 (2) \][/tex]

[tex]\[ \frac{dV}{dt} = 4\pi (1600) (2) \][/tex]

[tex]\[ \frac{dV}{dt} = 12800\pi \][/tex]

Now, let's evaluate this numerically:

[tex]\[ \frac{dV}{dt} ≈ 12800 \times 3.14 \][/tex]

[tex]\[ \frac{dV}{dt} ≈ 40211.2 \text{ mm}^3/\text{s} \][/tex]

Therefore, when the diameter is 80 mm, the volume of the sphere is increasing at a rate of approximately 40211.2 mm³/s.

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