The Ambell Company uses batteries from two different manufacturers. Historically, 60% of the batteries are from manufacturer 1, and 90% of these batteries last for over 40 hours. Only 75% of the batteries from manufacturer 2 last for over 40 hours. A battery in a critical tool fails at 32 hours. What is the probability it was from manufacturer 2?
Answers
Answer:
The probability that the battery in a critical tool fails at 32 hours was from manufacturer 2 is 0.625
Step-by-step explanation:
Given that:
60% of the batteries are from manufacturer 1
90% of these batteries last for over 40 hours
Let the number of the battery duration be n = 0.90
Therefore n' = 1 - 0.90 = 0.10
Let p = manufacturer 1 and q = manufacturer 2
q = 1 - p
q = 1 = 0.6
q = 0.4
Thus ; 40% of the batteries are from manufacturer 2
However;
Only 75% of the batteries from manufacturer 2 last for over 40 hours.
Let number of battery duration be m = 0.75
Therefore ; m' = 1 - 0.75 = 0.25
A battery in a critical tool fails at 32 hours.
Thus; the that the battery in a critical tool fails at 32 hours was from manufacturer 2 is:
[tex]= \dfrac{q \times m' }{ p \times n' + q \times m' }[/tex]
[tex]= \dfrac{0.4 \times0.25 }{ (0.6 \times 0.1) + (0.4 \times 0.25 ) }[/tex]
[tex]=\dfrac{0.1}{0.06+ 0.1}[/tex]
[tex]=\dfrac{0.1}{0.16}[/tex]
= 0.625
The probability that the battery in a critical tool fails at 32 hours was from manufacturer 2 is 0.625
The probability that the battery was from manufacturer 2 is 62.5%.
Since the Ambell Company uses batteries from two different manufacturers, and historically, 60% of the batteries are from manufacturer 1, and 90% of these batteries last for over 40 hours, while only 75% of the batteries from manufacturer 2 last for over 40 hours, if a battery in a critical tool fails at 32 hours, to determine what is the probability it was from manufacturer 2 the following calculation must be performed:
You must establish the percentage of failure of the total batteries, and determine what percentage of failures corresponds to each manufacturer. Manufacturer 1 = 60 x 0.1 = 6 Manufacturer 2 = 40 x 0.25 = 10 Total = 16 16 = 100 10 = X 100 x 10/16 = X 62.5 = X
Therefore, the probability that the battery was from manufacturer 2 is 62.5%.
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Related Questions
Values for relation g are given in the table. Which ordered pair would be found in the inverse of g? X Y 2 2 3 5 4 9 5 13 A: (4,9) B:(-3.-5) C:(13,5) D:(-2,-2)
Answers
Answer:
D (13,5)
Step-by-step explanation:
X 2 3 4 5
Y 2 5 9 13
So the ordered pairs are (2,2),(3,5), (4,9), (5,13)
and the ordered pairs for the inverse are
(2,2),(5,3), (9,4), (13,5)
from which D (13,5) is found among the options.
Answer:
b
Step-by-step explanation:
if ade has 23hand bag and he sells one for 409$ and he sells 22 for toby what will be the amount
Answers
Step-by-step explanation:
Hello there!
Its simple,
Given that, Ade had 23 hand bags.
selling price of each bag=$409
total sold bags= 22.
now, total amount he got was = no.of sold bag×sp of each bag.
so, total amount = 22×$409
=$8998.
Therefore, he has $ 8998 now.
Hope it helps...
helppppppppppppp pleaseeeeeeeeeeeeee
Answers
Answer:
work is shown and pictured
The soldering iron’s highest temperature setting is 400 °F. What is the soldering iron’s temperature in Centigrade?
Answers
Answer:
204.4(repeating) degrees
Step-by-step explanation:
The equation to go from F to C, is (F-32)×5/9. So 400-32 is 368.
368×5=1840
Than 1840/9=204.44 degrees. The 4 is repeating at the end.
Could someone answer the question with the photo linked below? Then explain how to solve it?
Answers
Answer:
Hey there!
Pythagorean Theorem:
[tex]a^2+b^2=c^2\\[/tex]
Let 6 be a, and 11 be b.
[tex]6^2+11^2=c^2\\[/tex]
[tex]36+121=c^2\\[/tex]
[tex]157=c^2[/tex]
[tex]\sqrt{157} =c[/tex]
Hope this helps :)
Answer:
[tex]12.529[/tex]
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {6}^{2} + {11}^{2} = {c}^{2} \\ 36 + 121 = {c}^{2} \\ 157 = {c}^{2} \\ \sqrt{157} = {c}^{2} \\ c = 12.529[/tex]
[tex]hope \: it \: helps \: < 3[/tex]
A study reports the mean change in HDL (high-density lipoprotein, or "good" cholesterol) of adults eating raw garlic six days a week for six months. The margin of error for a 95% confidence interval is given as plus or minus 7 milligrams per deciliter of blood (mg/dl). This means tha:_________a) There is a 95% probability that the true population mean is within 7 mg/dl. b) The study used a method that gives a results within 7 mg/dl of the truth about the population in 95% of all samples. c) 95% percent of the population has changed their HDL after eating raw garlic six days a week for six months. d) We can be certain that the study results is within 7 mg/dl of the truth about the population. e) We could be certain that the study result is within 7 mg/dl of the truth about the population if the conditions for inferences were satisfied.
Answers
Answer:
Option B
Step-by-step explanation:
The margin of error describes how many percentage points the results will differ from the real population value, thus 'the margin of error for a 95% confidence interval is given as plus or minus 7 milligrams per deciliter of blood (mg/dl)' can be interpreted as 'The study used a method that gives a results within 7 mg/dl of the truth about the population in 95% of all samples.'
Luke is organising a camping trip for the youth club. He is looking at the temperature and rainfall charts for Brighton and Newquay. What is the probability of it raining in July in Brighton? Give your answer as a fraction.
Answers
Answer:
The answer is 15.6/31 or 1/2
Step-by-step explanation:
The data in the question is sufficient to find an answer for it.
1. I look at the temperature and rainfall chart for Brighton, United Kingdom.
2. Check for rainy season and dry season.
3. The rainy season lasts approximately 5 months while the dry season (which still has some rainfall) lasts approximately 7 months. All together, 12 months of the calendar year.
4. July happens to fall within the dry season. The temperature and rainfall statistics are observed.
The number of rainfall days is 15.6 and we know there are 31 days in July.
If the approximate number of days it rains in Brighton, in July, is 15.6 then the probability of rainfall in the month is 15.6/31 which is = 0.503 or 0.5
Therefore, there's a 50% chance of having rainfall in Brighton, on any day in the month of July.
In fraction, 0.5 = 1/2
a.Find the L.C.M of 18, 40, and 75.
Answers
Answer:
1800
Step-by-step explanation:
Hello,
First of all we need to find the prime factorisation of the numbers.
18 = 2 * 3 * 3
40 = 2 * 2 * 2 * 5
75 = 3 * 5 * 5
It means that the LCM should have 5 * 5 , 2 * 2 * 2 and 3 * 3
Then LCM = 3 * 3 * 2 * 2 * 2 * 5 * 5 = 1800
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
1800
Step-by-step explanation:
→ First of all we need to find the prime factorisation of the numbers.
18 = 2 × 3 × 3 or 2 × 3²
40 = 2 × 2 × 2 × 5 or 2³ × 5
75 = 3 × 5 × 5 or 5² × 3
→ Now find the number that appear twice or more and write them down
3 and 3 from 18
2, 2 and 2 from 40
5 and 5 from 75
→ Now multiply all of these numbers together
3 × 3 × 2 × 2 × 2 × 5 × 5 = 3² × 2³ × 5² = 1800
what is the world smallest number that is divisible by all the numbers 1,2,3,4,5,6,7,8,9,10?
Answers
Answer:
1
Step-by-step explanation:
1 ÷ 1 = 1
2 ÷ 1 = 2
3 ÷ 1 = 3
4 ÷ 1 = 4
5 ÷ 1 = 5
6 ÷ 1 = 6
7 ÷ 1 = 7
8 ÷ 1 = 8
9 ÷ 1 = 9
10 ÷ 1 = 10
Answer:
The world smallest number that is divisible by all the numbers 1,2,3,4,5,6,7,8,9,10 means that all the above numbers can divide that number without a remainder.
From the question the world smallest number that is divisible by the above numbers is
2520Hope this helps you
A city council consists of eight Democrats and eight Republicans. If a committee of six people is selected, find the probability of selecting two Democrats and four Republicans.
(Type answer a fraction Simplify your answer.)
Answers
Answer:
The probability is [tex]P[ D n R] = 0.196[/tex]
Step-by-step explanation:
From the question we are told that
The number of Democrats is [tex]D = 8[/tex]
The number of republicans is [tex]R = 8[/tex]
The number of ways of selecting selecting two Democrats and four Republicans.
[tex]N = \left {D} \atop {}} \right. C_2 * \left {R} \atop {}} \right. C_1[/tex]
Where C represents combination
substituting values
[tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1[/tex]
[tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(8-2)! 2!} * \frac{8! }{(8-4)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(6)! 2!} * \frac{8! }{(6)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 * 6!}{(6)! 2!} * \frac{8*7 *6! }{(6)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 }{ 2*1 } * \frac{8*7 }{ 1 *1 }[/tex]
=> [tex]N = 1568[/tex]
The total number of ways of selecting the committee of six people is
[tex]Z = \left {D+R} \atop {}} \right. C_6[/tex]
substituting values
[tex]Z = \left {8+8} \atop {}} \right. C_6[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6[/tex]
substituting values
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16! }{(16-6) ! 6!}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 * 10! }{10 ! 6!}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 }{6* 5 * 4 * 3 * 2 * 1}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = 8008[/tex]
The probability of selecting two Democrats and four Republicans is mathematically represented as
[tex]P[ D n R] = \frac{N}{Z}[/tex]
substituting values
[tex]P[ D n R] = \frac{1568}{8008}[/tex]
[tex]P[ D n R] = 0.196[/tex]
FIRST ANSWER GETS BRAINLIEST!!!
How do you write 0.00696 in scientific notation?
Answers
Answer:
6.96x10^-3
Step-by-step explanation:
0.00696
We move the decimal point to between 6 and 9
since the number with the decimal point should be between 0 and 9.
Then we count the numbers.
6.96x10^-3.
Hope this helps. ❤❤❤
Answer: 6.96 * 10^(-3)
Step-by-step explanation:
In scientific notation, you multiply a number that has a value in the ones place and no value in the tens place by 10 raised to an exponent.
Hope it helps <3
The assistant principal set up chairs in the auditorum for graduation. She placed
the chairs in 24 rows with 28 chairs in each row. How many chairs are set up in
the auditorium
Answers
Answer:
672 chairs
Step-by-step explanation:
24 × 28 = 672
hope this helps
Solve for y: 3(2y + 4) = 4(2y – 1/2).
The solution is y =
Answers
Answer:
Answer y=7
Step-by-step explanation:
Over the last three evenings, Melissa received a total of 126 phone calls at the call center. The first evening, she received 6 more calls than the third evening. The second evening, she received 4 times as many calls as the third evening. How many phone calls did she receive each evening? Number of phone calls the first evening: Number of phone calls the second evening: Number of phone calls the third evening:
Answers
Answer:
calls first evening = 26
calls second evening = 80
calls third evening = 20
Step-by-step explanation:
Let x = calls third evening
x+6 = calls first evening
4x = calls second evening
x+6 + 4x + x = total calls = 126
Combine like terms
6x+6 = 126
Subtract 6 from each side
6x =120
Divide by 6
6x/6 =120/6
x = 20
x+6 = calls first evening = 20+6 = 26
4x = calls second evening = 4*20 = 80
Let x = calls third evening = 20
Karen has 6 more than twice as many newspaper customers as when she started selling newspapers. She now has 98 customers. How many did she have when she started?
Answers
Answer:
46 customers
Step-by-step explanation:
If the number of original customers is n, we can write the following equation:
98 = 2n + 6
92 = 2n
46 = n
Simplify 3 (2x + 1) - 2 (x + 1)
Answers
Let's simplify step-by-step.
3(2x+1)−2(x+1)
Distribute:
=(3)(2x)+(3)(1)+(−2)(x)+(−2)(1)
=6x+3+−2x+−2
Combine Like Terms:
=6x+3+−2x+−2
=(6x+−2x)+(3+−2)
=4x+1
4x+1 is the answer to the question
what is the measure of SR?
Answers
Answer:
RS = 8
Step-by-step explanation:
Given:
Secant QU = internal secant segment PU + external secant segment PQ = 7 + 9 = 16
Secant QS = internal secant segment RS + external secant segment RQ = (3x - 5) + 8
To find the measure of RS, we need to find the value of x.
Thus, recall the "Two Secant Theorem"
According to the theorem,
(RS + RQ)*RQ = (PU + PQ)*PQ
Thus,
[tex] (3x - 5 + 8)*8 = (7 + 9)*9 [/tex]
[tex] (3x + 3)*8 = (16)*9 [/tex]
[tex] 24x + 24 = 144 [/tex]
Subtract 24 from both sides
[tex] 24x + 24 - 24 = 144 - 24 [/tex]
[tex] 24x = 120 [/tex]
Divide both sides by 24
[tex] \frac{24x}{24} = \frac{120}{24} [/tex]
[tex] x = 5 [/tex]
Plug in the value of x into (3x - 5) to find the measure of RS
RS = 3(5) - 5 = 15 - 7
RS = 8
Compute the values of dy and Δy for the function y=e^(2x)+6x given x=0 and Δx=dx=0.03.
Answers
Answer:
dy = 8·dxΔy = 0.24Step-by-step explanation:
The derivative of your function is ...
y' = dy/dx = 2e^(2x) +6
At x=0, the value is ...
y'(0) = 2e^0 +6 = 8
dy = 8·dx
__
Δy = y'(0)·Δx
Δy = 8(.03)
Δy = 0.24
If the 2nd and 5th terms of a
G.P are 6 and 48 respectively,
find the sum of the first four
terms
Answers
Answer:
45
Step-by-step explanation:
The n th term of a GP is
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
where a is the first term and r the common ratio
Given a₂ = 6 and a₅ = 48, then
ar = 6 → (1)
a[tex]r^{4}[/tex] = 48 → (2)
Divide (2) by (1)
[tex]\frac{ar^4}{ar}[/tex] = [tex]\frac{48}{6}[/tex] , that is
r³ = 8 ( take the cube root of both sides )
r = [tex]\sqrt[3]{8}[/tex] = 2
Substitute r = 2 into (1)
2a = 6 ( divide both sides by 2 )
a = 3
Thus
3, 6, 12, 24 ← are the first 4 terms
3 + 6 + 12 + 24 = 45 ← sum of first 4 terms
what is the average when you add 122.99%, 108.46% and 102.65%? I don't know how to add percentages.
Answers
Answer:
111.33667
Step-by-step explanation:
You add percentages just like you would any other number.
122.9% + 108.46% + 102.65% = 334.01%
334.01%/3 = 111.33667
Which equations represent the asymptotes of the hyperbola?
Answers
Answer:
see below
Step-by-step explanation:
The equation of the hyperbola can be written as ...
((x -h)/a)² -((y -k)/b)² = 1
This has asymptotes ...
(x -h)/a ± (y -k)/b = 0
Solving for y, we have ...
y = ±(b/a)(x -h) +k
Filling in the given values a=6, b=8, h=1, k=2, we have ...
y = ±8/6(x -1) +2
[tex]y=\dfrac{\pm4x\mp4+6}{3}\\\\\boxed{y=\dfrac{4x+2}{3}\ \text{and }y=\dfrac{10-4x}{3}}[/tex]
Answer:
A. y = 4x+2/3 and y = 10-4x/3
Step-by-step explanation:
this is the correct answer for the question on edmentum and Plato
The distance S that a certain object falls from a height of 350 ft in T seconds is given by the following formula.
S = 350 - 16t^2 + vt
Find S when T = 2 and V = -4
S = ??ft
Answers
Answer:
278 feet.
Step-by-step explanation:
S = 350 - 16t^2 + vt
t =2; v = -4.
S = 350 - 16 * (2)^2 + 2 * (-4)
S = 350 - 16 * 4 - 8
S = 350 - 64 - 8
S = 350 - 72
S = 278 feet.
Hope this helps!
Adam is going to cook a turkey for 14 people
Answers
Answer:
they divied the turkey into 14 pices
Step-by-step explanation:
If ABC~DEF and the scale factor from ABC to DEF is 3/4, what is the length of DF?
Answers
Answer:
the length of DF = 3/4 AC
see below for explanation
Step-by-step explanation:
ABC is said to be approximately equal to DEF
The scale factor from ABC to DEF = 3/4
From the question, we can tell the original and new shape is a triangle because the lettering to indicate the vertices for both are 3.
We can deduce from the question, ΔABC was dilated to form ΔDEF
In dilation, the length of each of the corresponding side of the new figure is equal to the multiplication of each of the corresponding sides of the old figure and thee scale factor.
In the absence of cordinates for each vertices and length of each sides, ΔABC has 3 sides :
AB, BC and AC
ΔDEF has 3 sides : DE, EF and DF
If AB corresponds to DE
BC corresponds to EF
AC corresponds to DF
Then:
length DE = scale factor × AB = 3/4 AB
length EF = scale factor × BC = 3/4 BC
length DF = scale factor × AC = 3/4 AC
Therefore, the length of DF = 3/4 AC
Please help
ASAP
ANSWERS
A-48.21
B-66.35
C-53.68
D-28.34
Answers
Answer:
B
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos54° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{39}{AB}[/tex] ( multiply both sides by AB )
AB × cos54° = 39 ( divide both sides by cos54° )
AB = [tex]\frac{39}{cos54}[/tex] ≈ 66.35 → B
What is the measure of o?
Answers
Answer:
2π radians
Step-by-step explanation:
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Third-degree, with zeros of −3, −1, and 2, and passes through the point (1,10).
Answers
Answer:
[tex]\Large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]
Step-by-step explanation:
Hello,
Based on the indication, we can write this polynomial as below, k being a real number that we will have to identify (degree = 3 and we have three zeroes -3, -1, and 2).
[tex]\Large \boxed{k(x+3)(x+1)(x-2)}[/tex]
We know that the point (1,10) is on the graph of this function, so we can say.
[tex]k(1+3)(1+1)(1-2)=10}\\\\4*2*(-1)*k=10\\\\-8k=10\\\\k=\dfrac{10}{-8}=-\dfrac{5}{4}[/tex]
Then the solution is:
[tex]\large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Let x and y be real numbers satisfying 2/x=y/3=x/y Determine the value of x^3
Answers
Answer:
64/27Step-by-step explanation:
If x and y be real numbers satisfying 2/x=y/3=x/y, then any two of the equation are equated as shown;
2/x = y/3 ... 1 and;
y/3 = x/y... 2
From equation 1, 2y = 3x ... 3
and from equation 2; y² = 3x ... 4
Equating the left hand side of equation 3 and 4 since their right hand sides are equal, we will have;
2y = y²
2 = y
y = 2
Substituting y = 2 into equation 3 to get the value of x;
2y = 3x
2(2) = 3x
4 = 3x
x = 4/3
The value of x³ will be expressed as (4/3)³ = 4*4*4/3*3*3 = 64/27
Please help! Find the perimeter and total area of the composite shape below!
Answers
Answer:
Perimeter = 19.42 in and area = 26.13 in^2.
Step-by-step explanation:
The perimeter = 2 * 5 + length of the semicircle
= 10 * 3.14 * 3
= 19.42 in.
Total area = area of the semicircle + area of the triangle
= 1/2 * 3.14 * 3^2 + 3 * 4
= 26.13 in^2.
Factor d^2-10d+10 by grouping
Answers
Answer:
(d-5-√15)(d-5+√15)
Step-by-step explanation: