It was found that the mean length of 100 diodes (LED) produced by a company
was 20.05 mm with a standard deviation of 0.02mm. Find the probability that a diode
selected at random would have a length less than 20.01mm
Using the normal distribution, it is found that there is a 0.0228 = 2.28% probability that a diode selected at random would have a length less than 20.01mm.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem, we have that:
The mean is of [tex]\mu = 20.05[/tex].The standard deviation is of [tex]\sigma = 0.02[/tex].The probability that a diode selected at random would have a length less than 20.01mm is the p-value of Z when X = 20.01, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20.01 - 20.05}{0.02}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228.
0.0228 = 2.28% probability that a diode selected at random would have a length less than 20.01mm.
More can be learned about the normal distribution at https://brainly.com/question/24663213
[tex]\rm \lim \limits_{n \to \infty } {n}^{ - \frac{1}{2} ( \frac{n + 1}{n} )} (1 \times {2}^{2} \times {3}^{2} \times \dots \times {n}^{n} {)}^{ \frac{1}{ {n}^{2} } } [/tex]
[tex]\rule{200pt}{2pt}[/tex]
[tex] \rm I= \sum \limits_{k = 1}^{98} \int_{k}^{k + 1} \frac{k + 1}{x (x+ 1)} \: dx, then \\ [/tex] [tex] \rm[A] \phantom{gg}I>log_e99 \\ \\ \rm [B] \phantom{gg}I < log_e99 \\ \\ \rm[C] \phantom{hffgg} I < \frac{49}{50} \\ \\ \rm[D] \phantom{gfffg} I > \frac{49}{50} \\ [/tex]
Using the exp-log technique,
[tex]\displaystyle \lim_{n\to\infty} \frac{\left(1 \times 2^2 \times 3^3 \times \cdots \times n^n\right)^{\frac1{n^2}}}{n^{\frac{n+1}{2n}}}[/tex]
[tex]\displaystyle = \exp\left(\lim_{n\to\infty} \frac{\ln\left(\prod\limits_{k=1}^n k^k\right)}{n^2} - \frac{n+1}{2n} \ln(n)\right)\right)[/tex]
[tex]\displaystyle = \exp\left(\lim_{n\to\infty} \frac{\sum\limits_{k=1}^n k\ln(k)}{n^2} - \frac{n+1}{2n} \ln(n)\right)\right)[/tex]
We have ln(k) = ln(k/n) + ln(n), and so we can rewrite the limand as
[tex]\displaystyle = \exp\left(\lim_{n\to\infty} \left(\frac1n \sum\limits_{k=1}^n \frac kn \ln\left(\frac kn\right) + \frac{\ln(n)}{n^2} \sum_{k=1}^n 1 - \frac{n+1}{2n} \ln(n)\right)\right)[/tex]
Then the first sum converges to a definite integral,
[tex]\displaystyle \lim_{n\to\infty} \frac1n \sum_{k=1}^n \frac kn \ln\left(\frac kn\right) = \int_0^1 x \ln(x) \, dx = -\frac14[/tex]
while the remaining terms vanish since
[tex]\displaystyle \frac{\ln(n)}{n^2} \sum_{k=1}^n 1 = \frac{\ln(n)}{n^2} \times \frac{n(n+1)}2 = \frac{n+1}{2n}\ln(n)[/tex]
So the limit is [tex]\boxed{e^{-1/4}}[/tex].
Since
[tex]\dfrac1{x(x+1)} = \dfrac1x - \dfrac1{x+1}[/tex]
it's easy to show that the integral reduces to
[tex]\displaystyle \int_k^{k+1} \frac{k+1}{x(x+1)} \, dx = (k+1) \ln\left(\dfrac{(k+1)^2}{k(k+2)}\right)[/tex]
so we can write the sum as
[tex]I = \displaystyle \sum_{k=1}^{98} \int_k^{k+1} \frac{k+1}{x(x+1)} \, dx = \sum_{k=2}^{99} k \ln\left(\frac{k^2}{k^2-1}\right)[/tex]
We have k²/(k² - 1) > 1 for all k, so that ln(k²/(k² - 1)) > ln(1) = 0. We can see the first 3 terms of the sum already exceed 1 > 49/50, so (D) is true.
Numerical computation of the sum suggests I < ln(99), but I have yet to come up with an analytical solution for this bound...
HELP PLEASE ITS DUE TODAY
Answer:
easy peasyyyyy.
1 17/24
Step-by-step explanation:
Answer:
1 17/24
Step-by-step explanation:
we have to make both denominators of the fractions the same. in order to do this you have to basically increase the fraction and make it 20/24. Do the same thing to 7/8 and get 21/24. Now we can add them together 20/24 + 21/24 = 41/24 = 1 17/24
mark me as brainliest
Two consecutive odd integers have a sum of 92
I need really good support in this!
Answer:
○ D. [tex]\displaystyle -8, -3, 1, 5[/tex]
Explanation:
The greatest negative quantity will ALWAYS be the least. That is all there is to it. ♂️
I am joyous to assist you at any time.
Pls help me
Question 2 Part C (5 points): Mrs. Hinson is replacing her rectangular driveway with pavers. The area of her driveway is 64m² - 9n² square units. Mrs. Hinson needs to find the dimensions of her driveway so she knows how many pavers to buy.
Help Mrs. Hinson by factoring the area completely. To receive full credit, you must show all work.
WORK:
ANSWER: The dimensions are...
Let's factor out
[tex]\\ \rm\Rrightarrow 64m^2-9n^2[/tex]
[tex]\\ \rm\Rrightarrow (8m)^2-(3n)^2[/tex]
Use the identity
(a+b)(a-b)=a^2-b^2[tex]\\ \rm\Rrightarrow (8m-3n)(8m+3n)[/tex]
Done
3( x + 2 ) = 2( 2 - x )
Answer:
x=2
Step-by-step explanation:
3x+6=4-2x
3x+2x=6+4
5x=10
x=10/5
x=2
Find the slope of the line that passes between the points (4,3/8) and (6,7/8)
Answer:
1
Step-by-step explanation:
1. Plug the points into the slope formula:
[tex]\frac{\frac{7}{8} - \frac{3}{8}}{6 - 4}[/tex]
2. Simplify.
[tex]\frac{4}{8}[/tex] ÷ [tex]\frac{2}{1}[/tex] = 1
Determine the absolute value. Type the numerical answer only. -l12l
Answer:
-12
cause l12l is 12 then u add the negative sign.
Step-by-step explanation:
What is the range of the following relation? {(2, 3), (-4, 1), (5, -2), (0, 0)}
due in soon hours
Answer:
range is {-2, 0, 1, 3}
Step-by-step explanation:
Range is all the y's. Those are the second number in each ordered pair. I put them smallest to biggest, but it doesn't have to be. All the y-numbers in the set brackets should work for correct.
How do you do these two questions?
Step-by-step explanation:
(a) ∫₋ₒₒ°° f(x) dx
We can split this into three integrals:
= ∫₋ₒₒ⁻¹ f(x) dx + ∫₋₁¹ f(x) dx + ∫₁°° f(x) dx
Since the function is even (symmetrical about the y-axis), we can further simplify this as:
= ∫₋₁¹ f(x) dx + 2 ∫₁°° f(x) dx
The first integral is finite, so it converges.
For the second integral, we can use comparison test.
g(x) = e^(-½ x) is greater than f(x) = e^(-½ x²) for all x greater than 1.
We can show that g(x) converges:
∫₁°° e^(-½ x) dx = -2 e^(-½ x) |₁°° = -2 e^(-∞) − -2 e^(-½) = 0 + 2e^(-½).
Therefore, the smaller function f(x) also converges.
(b) The width of the intervals is:
Δx = (3 − -3) / 6 = 1
Evaluating the function at the beginning and end of each interval:
f(-3) = e^(-9/2)
f(-2) = e^(-2)
f(-1) = e^(-1/2)
f(0) = 1
f(1) = e^(-1/2)
f(2) = e^(-2)
f(3) = e^(-9/2)
Apply Simpson's rule:
S = Δx/3 [f(-3) + 4f(-2) + 2f(-1) + 4f(0) + 2f(1) + 4f(2) + f(3)]
S ≈ 2.5103
A regular Pyramid is formed from 3 right triangles as shown below use the information given in the figure to find the length of RT.
Answer:
The length of BD is 65 units.
Step-by-step explanation:
ΔADC is a right angle triangle, we will use the Pythagorus Theorem to find the length CD.
Formula of the Pythagorus Theorem :
⇒ a² + b² = c²
⇒ AD² + CD² = AC²
The value of AD is 54 and the value of AC is 90:
54² + CD² = 90²
Solve for CD:
54² + CD² = 90²
CD² = 90² - 54²
CD² = 5184
CD = √5184
CD = 72
ΔADC is also a right angle triangle, we will use the Pythagorus Theorem to find the length BD.
Formula of the Pythagorus Theorem :
⇒ a² + b² = c²
⇒ BD² + CD² = BC²
The value of CD is 72 and the value of BC is 97:
BD² + 72² = 97²
Solve for BD:
BD² = 97² - 72²
BD² = 4225
BD = √4225
BD = 65
Suppose a cubic polynomial, f, has two rational roots c and d and one irrational
root which is a conjugate pair a + vb, where a and b are rational numbers.
Does f have rational coefficients? Explain.
Answer:
what is force ? write its S.I unit
x^4y^2 - 6xyz + 9z^2=
Answer:
(xy+3z) 2 (The two is small just saying)
Step-by-step explanation:
Step 1:
(((x2) • (y2)) + 6xyz) + 32z2
Step 2:
2.1 Factoring x2y2 + 6xyz + 9z2
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (xy + 3z)•(xy + 3z)
Step 3:
2.2 x2y2 +6xyz +9z2 is a perfect square
It factors into (xy+3z)•(xy+3z)
which is another way of writing (xy+3z)2
Jim earns a regular hourly rate of five dollars and a premium hourly rate of six dollars he worked 45 hours last week what is his gross pay
Name
8.2 Using Parallelograms in Proofs
1. Given: Parallelogram ABCD
DE I AB
BFI DC
с
Prove: DE 2 BF
A
E
B
Answer:
Step-by-step explanation:
1) Parallelogram ABCD, [tex]\overline{DE} \perp \overline{AB}, \overline{BF} \perp \overline{DC}[/tex] (given)
2) [tex]\angle DAE \cong \angle FCB[/tex] (opposite angles of a parallelogram are congruent)
3) [tex]\angle AED[/tex] and [tex]\angle BFC[/tex] are right angles (perpendicular lines form right angles)
4) [tex]\angle AED \cong \angle BFC[/tex] (all right angles are congruent)
5) [tex]\overline{AD} \cong \overline{BC}[/tex] (opposite sides of a parallelogram are congruent)
6) [tex]\triangle AED \cong \triangle CFB[/tex] (AAS)
7) [tex]\overline{DE} \cong \overline{BF}[/tex] (CPCTC)
if you answer all i will give you brainliest answer! help asap, school starts in 10
Answer:
1. 20% increase
2. 40% decrease
3. 50% increase
4. 75% decrease
5. 54.5% decrease
6. 150% increase
Step-by-step explanation:
Hope this helps!!
You have listed a property. The seller told you that he must net at least $14,000 after all the fees and expenses are paid. You estimate the seller's closing cost to be $3,500, and he must payoff an existing loan of $108,750. In addition, you are going to charge 7 percent commission on the sale. What is the LEAST amount that the property can sell for to return the seller's desired net?
Answer:
wow
Step-by-step explanation:
Answer with step-by-step explanation:
Step 1: $14,00 - $3,500 + $108,570 = $10,500 + $108,750 = $119,250
Step 2: 7% of $119,250 = $8,347.50
Step 3: $119,250 + $8,347.5 = $127.597.50
Hope this was helpful! (brainliest please)
what are the 3 linear equations and how they different
x2-x-6=0, then x is
Answer:
A is the answers for the question
Step-by-step explanation:
please mark me as brainlest
[tex]\underline{\underline{\large\bf{Solution:-}}}\\[/tex]
[tex]\longrightarrow[/tex]Given is a quadratic equation which can be solved by splitting the middle term.
[tex]\leadsto[/tex]For this we have to look at factors of the constant term . Since here constant term term is- 6 so splitted middle term should have product equal to -6
[tex]\begin{gathered}\\\implies\quad \sf x^2-x-6=0 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf x^2-3x+2x-6=0 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf x(x-3)+2(x-3)=0 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf (x-3)(x+2) =0 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf (x-3) =0 \quad or \quad (x+2) =0\\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf x=3 \quad or \quad x= -2\\\\\end{gathered} [/tex]
[tex]\quad\therefore\: \sf x \:is \: \:3 \:or -2 [/tex]
The greatest common factor of 2M to the fifth power and 32M to the fourth power
So 2 is the GCF for the coefficient. The variables are m4 and m5 . 4 is the greatest shared power, and so the GCF for that is m4
brainliest please if correct
Emma spent $60.20 on 5 dozen bagels and a gallon of iced tea. The price of the gallon of iced tea was $5.25. The following equation can be used to find d, the price of each dozen of bagels. 5d + 5.25 = 60.2 What was the price of each dozen of bagels?
23.23 - 5.25 = 17.98
d = 17.98 ÷ 2
d = 8.99
The answer is B. $8.99
Jacoby says that they
need to save $293.75
per week.
CARD 10:
The Hudson family is saving for a
family vacation to Disney World.
They determine that the trip will
cost $3,200. Mr. and Mrs.
Hudson have already set aside
$1,500 for the trip. If they leave
in 16 weeks, then how much
will they need to save
each week?
Janelle says that they
need to save $106.25
per week
Grade 7 lesson 5 terminating and repeating decimals quiz
Answer:
I need more context.
Step-by-step explanation:
PLEASE HELP I WILL GIVE BRAINLIEST
Answer:
V=72
Step-by-step explanation:
4x6=24
24x3=72
WxBxH=V
B=6
W=3
H=4
Can someone help me with my homework need to divide fractions
Answer:
yeah sure
Step-by-step explanation:
write an equation that you can use to determine the number of hours for which it would cost $270 to hire brian then solve the equation
Answer:
How do you write an equation for problem solving?Here are some steps to follow:Understand the problem. Understand all the words used in stating the problem. Understand what you are asked to find. ... Translate the problem to an equation. Assign a variable (or variables) to represent the unknown. ... Carry out the plan and solve the problem.
Step-by-step explanation:
Suppose heights of seasonal pine saplings have an unknown distribution with mean 291 and standard deviation 14 millimeters. A sample of size n=55 is randomly taken from the population and the mean is taken. Using the Central Limit Theorem for Means, what is the standard deviation for the sample mean distribution?
Answer:
1.89
Step-by-step explanation:
The center al limit theorem for means states that the standard deviation of the normal distribution of sample means is equal to the original distribution’s standard deviation divided by the square root of the sample size. the original standard deviation is 14 and the sample size is 55.
Which equation is true for x = 1.8?
Answer:
I found the full question online, the answer is 5.4 = 3.6 + x
1ST ONE TO ANSWER THIS QUESTION GETS BRAINLIEST
Find the area of this polygon
Answer:
162 units^2
Explanation:
Separate the polygon into a rectangle and triangle, and then use the equations of area for those shapes to find the area.