Answer:
P(X< 40) = 0.014367
Step-by-step explanation:
From the given information:
Suppose X denotes the strength of each steel strand & X follows the lognormal distribution with a mean value [tex]\mu_x[/tex] = 50 kips & coefficient of variation CV = 10%
Using the formula for the coefficient of variation CV
[tex]cv = \dfrac{\sigma_x}{\mu_x}[/tex]
[tex]0.10 = \dfrac{\sigma_x}{50}[/tex]
[tex]\sigma_x = 50 (0.10)[/tex]
[tex]\sigma_x = 5[/tex]
By applying the mean and mean & variance from the lognormal distribution, we have:
[tex]\dfrac{\sigma_x^2}{\mu_x}= \dfrac{\{exp(2 \mu + \sigma^2)\} (exp(\sigma^2))-1}{exp( \mu + \dfrac{\sigma^2}{2} \}}[/tex]
[tex]\dfrac{5^2}{50}= \dfrac{\{exp(2( \mu + \dfrac{\sigma^2}{2})) \} (exp(\sigma^2))-1}{exp( \mu + \dfrac{\sigma^2}{2} \}}[/tex]
[tex]\dfrac{5^2}{50}= exp \{ 2 ( \mu + \dfrac{\sigma^2}{2}) - ( \mu + \dfrac{\sigma^2}{2}) \} \{ ( exp ( \sigma^2))-1 \}[/tex]
[tex]\dfrac{5^2}{50}=exp \{(\mu + \dfrac{\sigma^2}{2}) \} {(exp (\sigma^2))-1 \}[/tex]
[tex]\dfrac{5^2}{50}=50 \{ (exp (\sigma^2 )) -1 \}[/tex]
[tex]\dfrac{25}{50 \times 50 }= ( exp (\sigma^2 )) -1[/tex]
[tex]exp( \sigma^2) = \dfrac{25}{50 \times 50}+ 1[/tex]
[tex]exp( \sigma^2) = (\dfrac{25+2500}{2500 })[/tex]
[tex]exp( \sigma^2) =1.01[/tex]
[tex]\sigma^2 = In (1.01)[/tex]
[tex]\mathbf {\sigma^2 = 0.00995}[/tex]
However, the next process is to replace the value of [tex]\sigma^2[/tex] into the logman distributions mean.
[tex]\mu_x = exp ( \mu + \dfrac{\sigma^2}{2})[/tex]
[tex]50 = exp ( \mu + \dfrac{\sigma^2}{2})[/tex]
[tex]50 = exp ( \mu + \dfrac{0.00995}{2})[/tex]
[tex]In(50) = ( \mu + \dfrac{0.00995}{2})[/tex]
3.912023 = μ +0.004975
μ = 3.907048
Now, we know our mean to be 3.907048 and the variance to be 0.00995.
Therefore, the probability that the weakest strand will have a strength of fewer than 40 kips can be computed as follows:
P(X< 40) = P(In(x) < In(40))
[tex]P(X<40) = P(\dfrac{In(x) - \mu}{\sigma} < \dfrac{In(40) - \mu}{\sigma})[/tex]
since;
[tex]\sigma^2 = 0.00995 \\ \\ \sigma = \sqrt{0.00995} \\ \\ \sigma = 0.0998[/tex]
[tex]P(X<40) = P(Z < \dfrac{In(40) - 3.907048}{0.0998})[/tex]
P(X< 40) = P(Z < -2.18712)
Using the Excel formula =(=NORMDIST (-2.18712)
P(X< 40) = 0.014367
Which is the distance between the points M ( -21, -7)and N ( -5, -7)
Answer:
16
Step-by-step explanation:
becasue from -21 to -5 it's 16 units (-21 - -5= 16).
Mofor bought 12 Avocados for $18. How many avocados can Stefan buy if he has $6
Answer:
4
Step-by-step explanation
Stefan can buy 4 apple with $6 because the apples are $1.50 each
If f(x) = (4784), what is 13)?
Answer:
f(x)=4784
f(13)= 0 because there is x value on the right hand side
Let V(t) represent the values of a bank account, in thousands dollars, t years after the account is opened at the bank. Determine whether each statement below is true
Complete question is;
Let V(t) represent the value of a bank account, in thousands of dollars, t years after the account is opened at the bank. Determine whether each statement below is true. Select True or False for each statement.
V(0) = 2 means that the value of the bank account when it is opened is $2000
V(5) = 2.2 means that 2.2 years after the bank account is opened, its value is $5000
V(10) – V(5) = 0.4 means that the bank account grows by $400 between 5 and 10 years after its opening
Answer:
Statement 1: True
Statement 2: False
Statement 3: False
Step-by-step explanation:
We are told that the function V(t) represents the value of a bank account, in thousands of dollars, t years after the account is opened at the bank.
This means that if V(10) = 50, it means that the bank account is valued after 10 years is $50,000
From this little explanation, it's clear that only statement 1 is correct.
i need help pls like now if you can pls help me!
Answer:
With what there is nothing there
Step-by-step explanation:
Please help!!!!!!!!!!!
Answer:
The ordered pair (15, 12) means that 15 pounds of beans cost $12.
Step-by-step explanation:
Ordered pairs are in the format of (x,y). The first number represents a point's position on the x-axis and the second represents a point's position on the y-axis. Also note that in this graph, the x-axis represents the weight of beans in pounds and the y-axis represents the cost of beans.
Knowing this, (15,12) means that 15 pounds of beans must cost $12.
Which set of mixed numbers has a difference less than 1?
use repeated subtraction to divide 93÷10
Answer:
9r3
Step-by-step explanation:
93-10=83-10=73-10=63-10=53-10=43-10=33-10=23-10=13-10=3
so 93÷10=9 remainder of 3
Factor completely 3x^2+ 2x -1.
O (3x + 1)(x - 1)
O (3x + 1)(x + 1)
O (3x - 1)(x + 1)
O (3x - 1)(x - 1)
Answer:
option C
Step-by-step explanation:
[tex]3x^2+2x-1\\\\=(3x+a)(x+b)\\\\(3b+a)=2\\\\ab=-1[/tex]
and here we think of b=1 and a=-1
so we have
[tex](3x-1)(x+1)[/tex]
Help plz:)))I’ll mark u Brainliest
If Sin theta=3/4,find the value of cos theta
Answer:
[tex]Cos \ \theta = \frac{\sqrt{7} }{4}[/tex]
Step-by-step explanation:
Given;
Sin θ = 3/4
To calculated Cos θ;
make a sketch of right-angled triangle with following sides;
opposite side = 3
hypotenuse side = 4
then, the adjacent side will be calculated from Pythagoras theorem;
let the adjacent side = b
b² = 4² - 3²
b² = 16 - 9
b² = 7
b = √7
Therefore, Cos θ is now calculated as;
Cos θ = adjacent / hypotenuse
Cos θ = √7/4
[tex]Cos \ \theta = \frac{\sqrt{7} }{4}[/tex]
Therefore, [tex]Cos \ \theta = \frac{\sqrt{7} }{4}[/tex]
Look at this graph:
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
What is the value of n in the equation below? a^n/a^3=a^9
3
6
12
27
Joanna is building 2 square planter boxes in her garden . Each box is 2 yard wide . What is the total perimeter of the boxes ?
Answer:
16 yards
Step-by-step explanation:
Square: all sides are equalSquare: 4 sides totalPerimeter of square: 2 + 2 + 2 + 22 + 2 + 2 + 2 = 8 yardsPerimeter of second box: 2 + 2 + 2 + 2 = 8 yardsPerimeters in total: 8 + 8 = 16 yardsI hope this helps!
Choose the rule to describe the transformation:
D(-3, -4), C(-3, -1), B(0, -4)
to
D '(3, -4), C '(3, -1), B '(0, -4)
a. reflection across the y-axis
b. reflection across y = -x
c. translation: (x,y)LaTeX: \longrightarrow⟶(x + 4, y)
d. reflection across y = x
Answer:
a. reflection across the y-axis
Find the value of 3(5. 10 + 2).
Answer:
the value is
Step-by-step explanation:
=3(5.10+2)
=3(7.1)
=21.3
Answer:
3(5. 10+2)
Step-by-step explanation:
3(5.12)
3(60)
180
86% percent of senators support a bill.
Is it true that m || n?
Your response should be at least 3 complete sentences. Be sure to include information about the slopes of the line and calculations. NO PLAGIARISM!!
Answer:
False
Step-by-step explanation:
Lines m and n are not parallel
See attached that shows vertical segment of 6 units, its longer than the distance between the lines on the right and its shorter on the left
Parallel lines should have same distance at any point between them
How can I find the area for a semi circle that is 11 inches tall, 4.8 inches wide and 3.7 feet long (if I’m not making to much sense, I have a reference photo here)
Answer:
195.36
Step-by-step explanation:
11 x 4.8 =52.8
52.8 x 3.7 = 195.36
A=195.36
A ball is drawn from a bag of 26 red and 12 yellow balls. The process is repeated 50 times, replacing each ball that is drawn. Which of the following statements about the distributions of counts and proportions is true?A. The count of drawing a yellow ball is not a binomial distribution.B. The count of drawing a red ball is a binomial distribution.C. The distribution of the count of drawing a red ball cannot be approximated with a normal distribution D. The distribution of the count of drawing a yellow ball from a sample size of 10 can be approacimated with a normal distribution.
Answer:
B. The count of drawing a red ball is a binomial distribution.
Step-by-step explanation:
The count of drawing a red ball can be gotten by binomial distribution because:
the chance of success; p = 26/50 and chance of no failure; q = 24/50
For example, If we want to find probability of getting 5 red balls out of 20 selections, we will use the binomial probability distribution formula;
P(X = 5) = C(20, 5) × p^(5) × q^(20 - 5)
This same procedure also applies if we want to get the probability of getting a number of yellow balls out of a number of selections from the bag.
Looking at the options, the best option that explains how it's binomial probability that works is option B
Answer:b
Step-by-step explanation:
Baseball hat for
$22.90 at 5% sales tax
Answer:I got $21.76
Step-by-step explanation:
;-;
the area of square Garden is 625 metre square find its length its perimeter and find the cost of fencing it with 5 round at Rs 25 per metre
Answer:
Length=25m
Parameter=100m
5 round cost RS 12500
Step-by-step explanation:
The area of a square
=x²
According to the question the equation is
x²=625
x=√625
x=25
The parameter is
25×4
100 meter
So
1 meter costs 25
100 " " 25×100
2500
1 round = 100 meter
So
5 round cost 2500×5
12500
Luna's bill for lunch at a restaurant was $11. She left a 20% tip. What was the amount of the tip?
Answer:
$2.20
Step-by-step explanation:
If you want to leave a 20% tip, multiply the cost by 0.20 to get the tip amount or multiply the cost by 1.20 to get the total including tip.
A hexagon ABCDEF is shown.
С-115
D
B
145
Angle CDE is twice the size of angle DEF.
Work out the size of angle CDE.
You must show all your working.
E
160°
+
F
Answer:
140
Step-by-step explanation:
115+165+140+90=510
180*4=720 (sum of interior angles of hexagon)
115+165+140+90+x+2x=720
why 2x because i kept ANGLE DEF as x and ANGLE CDE is twice so 2x
510+2x+x=720
3x=210
x=210/3
x=70
ANGLE DEF IS 70
so because ANGLE CDE IS TWICE ANGLE DEF thus 70*2=140
ANGLE CDE =140
The angle CDE is 140°.
What is a hexagon?
A hexagon can be defined as a closed two-dimensional polygon with six sides. Hexagon has 6 vertices and 6 angles.
According to the given problem,
We know,
Sum of the interior angles of a polygon is,
Sum = 180° (n - 2) where n is the number of sides,
Here n = 6 , then
Sum = 180° × 4 = 720°
Let ∠ DEF be x
Therefore ∠ CDE = 2x,
Sum the interior angles,
⇒ 160 + 90 + 145 + 115 + 2x + x = 720
⇒ 510 + 3x = 720 ( subtracting 510 from both sides )
⇒ 3x = 210 ( dividing both sides by 3 )
⇒ x = 70
∠ CDE = 2x
= 2 × 70
= 140°
Hence, we can conclude, in the hexagon, the angle CDE is 140°.
Learn more about hexagon here:
https://brainly.com/question/2001860
#SPJ2
please awnser asap asap
Answer:
d) 280
Step-by-step explanation:
40320/3=6720
8720/24=280
What is the surface area of an orange with a 3inch radius
Orange = sphere
S.A of sphere
= 4πr²
= 4 × π × r × r
[tex] = 4 \times \pi\times 3 \times 3[/tex]
[tex] = 36\pi[/tex]
Answer:
Step-by-step explanation:
the surface area of a sphere ( orange)
SA=4*3.14*r^2
radius=3
SA=4*3.14*3*3=113.04
ANSWER ASAP PLS YEY BRAINLIEST AND STUFFsolve for x 2/3=x-1/5
Answer:
x = 13/15
Step-by-step explanation:
If x - 1/5 = 2/3,
you can find x by doing 2/3 + 1/5.
2/3 = 10/15
1/5 = 3/15
10/15 + 3/15 = 13/15!
Hope this helps! Happy Holidays! XD
Hamburger-R-Us offers 8 toppings on its made to order burgers. you can order plain or any combination of toppings. How many types of burgers are possible?
Step-by-step explanation:
For every topping, you can either "take-it or leave-it" for your burger. This means there are 2 options for every topping.
Hence number of possible burgers = 2⁸ = 256.
There are 50 balls in one box. The number of red balls is 30 and the number of blue and yellow balls are 20 . Find the number of blue balls in the box.
Answer:
ffgjjlii89888888888888999999uoggvjlpjk
Answer:10 blue balls
Step-by-step explanation:
What is the total cost or sale price to the nearest cent?
$65 Jacket; 35% Discount