Answer:
The value is [tex]P(Z' | N )= 0.92[/tex]
Step-by-step explanation:
From the question we are told that
The proportion of defective widgets produced by older widget is [tex]p = 23\% = 0.23[/tex]
The proportion of defective widgets produced by new widget is
[tex]q = 0.08[/tex]
Generally since we are considering the new machine in this question it then mean that the probability that widget was defective given that it was produce by the new machine is
[tex]P(Z | N ) = 0.08[/tex]
Here Z is the event that the widget was defective
N is the even that the widget was produced by the new machine
Also the probability that the widget was defective given that it was not produced by the new machine is
[tex]P(Z | N') = 0.23[/tex]
Generally from the question the probability that the widget was produced by the new machine is mathematically represented as
[tex]P( N) = \frac{3}{4}[/tex]
=> [tex]P( N) = 0.75[/tex]
Generally the probability that the widget is defective and that it was produced by the new is mathematically represented as
[tex]P( Z\ n \ N) = P(Z | N ) * P(N)[/tex]
=> [tex]P( Z\ n \ N) = 0.08 * 0.75[/tex]
=> [tex]P( Z\ n \ N) = 0.06[/tex]
Generally the probability that the widget is defective and that it was not produced by the new machine is
[tex]P(Z\ n \ N') = P( Z | N' ) * [1 -P(N)][/tex]
=> [tex]P(Z\ n \ N') = 0.23 * [1 -0.75][/tex]
=> [tex]P(Z\ n \ N') =0.0575[/tex]
Generally the probability that the widget is defective is
[tex]P(Z) = P(Z \ n \ N) + P(Z \ n \ N')[/tex]
=> [tex]P(Z) = 0.06 + 0.0575[/tex]
=> [tex]P(Z) = 0.1175[/tex]
Generally the probability that the widget is not defective and it produced by the new machine is mathematically represented as
[tex]P(Z' \ n \ N ) = P(N ) - P(Z \ n \ N)[/tex]
=> [tex]P(Z' \ n \ N ) =0.75 - 0.06[/tex]
=> [tex]P(Z' \ n \ N ) =0.69[/tex]
Generally the probability that the widget was produced by the new machine,given that a randomly chosen widget was tested and was found to be defective is mathematically represented as
[tex]P(Z' | N ) =\frac{P(Z' \ n \ N)}{P(N)}[/tex]
=> [tex]P(Z' | N )= \frac{0.69}{0.75}[/tex]
=> [tex]P(Z' | N )= 0.92[/tex]
tudents attending an international event were asked if they can speak Arabic or Chinese. 25% speak Arabic, 20% speak Chinese, 10% speak both languages. Assume random selection: a. What is the probability that the student can speak Chinese or Arabic
Answer:
P(A ∪ C) = 0.35
Step-by-step explanation:
Given:
25% speak Arabic
20% speak Chinese
10% speak both languages
Find:
Probability that the student can speak Chinese or Arabic P(A U C)
Computation:
P(A ∪ C) = P(A) + P(C) - P(A ∩ C)
P(A ∪ C) = 0.25 + 0.2 - 0.1
P(A ∪ C) = 0.35
In Fairbanks, Alaska, the average temperature in January is -9.7°F. The
average temperature in July is 62.4°F. On average, how many degrees
colder is Fairbanks in January than in July?
Answer:
72.1 degrees... 72 point 1 degress in case you cant see the ( . )
Step-by-step explanation:
62.4 minus -9.7= is 72.1
Evaluate -2x 2y, if x = -3 and y = -1.
* 12
* -12
* 18
* -18
Answer: -12
Step-by-step explanation:
If the equation is multiplying all the numbers, the equation would be -2x2y, which is making the new equation is -2(-3)2(-1). Multiply the numbers 6x-2, which is -12
Can you please help me?
Thank you so much☺
Answer:
Answer: 1. x = 10, y = 6 2. x = 12, y = 3 3. x = 5, y = 2.5 4. x = 1, y = 14 5. x = 0.6, y = 7 6. x = 11, y = 1
Step-by-step explanation:
Find the interest rate implied by the following combinations of present and future values:
Present Value Years Future Value Interest Rate
$310 12 496 %
138 5 194 %
210 8 210 %
Answer:
The interest rates implied by the combinations of present and future values are:
Present Value Years Future Value Interest Rate
$310 12 496 3.994%
138 5 194 7.049%
210 8 210 -0.000%
Step-by-step explanation:
a) Data and Calculations:
Present Value Years Future Value Interest Rate
$310 12 496 3.994 %
138 5 194 7.049%
210 8 210 -0.000%
b) You will need an annual return rate of 3.994% to reach the future value of $496.00.
FV (Future Value) $496.00
PV (Present Value) $310.00
N (Number of Periods) 12.000
I/Y (Interest Rate) 3.994%
PMT (Periodic Payment) $0.00
Starting Investment $310.00
Total Principal $310.00
Total Interest $186.00
c) You will need an annual return rate of 7.049% to reach the future value of $194.00.
FV (Future Value) $194.00
PV (Present Value) $138.00
N (Number of Periods) 5.000
I/Y (Interest Rate) 7.049%
PMT (Periodic Payment) $0.00
Starting Investment $138.00
Total Principal $138.00
Total Interest $56.00
d) You will need an annual return rate of -0.000% to reach the future value of $210.00.
FV (Future Value) $210.00
PV (Present Value) $210.00
N (Number of Periods) 8.000
I/Y (Interest Rate) -0.000%
PMT (Periodic Payment) $0.00
Starting Investment $210.00
Total Principal $210.00
Total Interest $-0.00
The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%?
Answer: 1 student scored above an 85%.
Step-by-step explanation:
Let X = percentage score in test (normally distributed).
Given: Sample size = 15 , mean score : [tex]\mu[/tex]= 74.8% = 0.748 ,standard deviation : [tex]\sigma=7.57[/tex]
Now, The probability that student scores above 85%:
[tex]P(X>85)=P(\dfrac{X-\mu}{\sigma}>\dfrac{85-74.8}{7.57})\\\\=P(Z>1.347)\\\\=1-P(Z<1.347)\\\\=1-0.9110= 0.089[/tex]
Probability that student scores above 85% = 0.089
Number of students scored above an 85% = 0.089 x 15 = 1.335 ≈ 1
hence, 1 student scored above an 85%.
What is the y coordinate of point T? Write a decimal coordinate. - 3 . 3 -777 1.7
Answer:
I never learned that sorry ♀️
1. Rosalie bought 0.2503 kg of garlic, 0.17 kg tomatoes, 2.05 kg of onions and 1.12 kg of
ginger. What was the total weight of this item?
answer is 3.5903 or 3 kg 5903 gram
Does the set of ordered pairs {(0,4),(2,6),(4,2), (6,2), (8,6)} represent a function?
Answer:
yes it does
Step-by-step explanation:
the x numbers do not repeat
Yes, the given relation is function.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given:
set of ordered pairs= {(0,4),(2,6),(4,2), (6,2), (8,6)}
As, we know that the function has one input with corresponding one output.
So, we can see from the ordered pair that no input value have repeated and have respective output.
Hence, the relation is function.
Learn more about function here:
https://brainly.com/question/23712366
#SPJ2
Ileana drew a marble at random from a bag containing 4 blue 3 red 2 yellow and 5 green marbles. What is the probability that she picked a marble that was not red?
Answer:
=11/14
Step-by-step explanation:
Step-by-step explanation:
Number of blue marbles n(blue)=4
Number of red marbles n(red)=3
number of yellow marbles n(yellow)= 2
number of green marbles n(green)=5
total number of marbles n(S)=4+3+2+5=14
P(red)=n(red)/n(S)
P(red)=3/14
We have to determine the probability that the card picked is not red which means the card can be blue or yellow or green.
P(not red)=1-P(red)
=1-3/14
=11/14
Answer:
11/14
Step-by-step explanation:
These are all the marbles that are there:
4 blue
3 red
2 yellow
5 green
If you want to figure out the probability of a marble not being red, you can either find the probability that the marble is blue, yellow, or green or you could subtract the probability that the marble is red from 1 (same thing either way)
There are 14 marbles and 11 of them are not red, so the the probability that a marble drawn will not be red is 11/14.
A tank contains 1000 L of brine (salt water) with 15 kg of dissolved salt. Pure water enters the tank at a rate of 10 L/min. The solution is kept throughly mixed and drains from the tank at the same rate. How much salt is in the tank after t minutes
Answer:
[tex]y=15e^{e^{- \frac{t}{100}}}kg[/tex]
Step-by-step explanation:
Let y(t) represent the amount of salt in the tank after t minutes. Therefore:
[tex]\frac{dy}{dt}=rate\ in-rate\ out[/tex]
Pure water is entering at a rate of 10 L/min, therefore rate in = 0
The tank contains 1000 L of brine (salt water) with 15 kg of dissolved salt, and a mixed solution leaving at 10 L/min hence;
[tex]rate\ out = \frac{y(t)\ kg}{1000\ L}*10\ L/min= \frac{y(t)\ kg}{100\ min}\\\\Therefore:\\\\\frac{dy}{dt}=0- \frac{y(t)}{100} \\\\\frac{dy}{dt}=- \frac{y(t)}{100}\\\\\frac{dy}{y}=- \frac{1}{100}dt\\\\\int\limits{\frac{dy}{y}} =\int\limits- \frac{1}{100}dt\\\\lny=- \frac{t}{100}+C\\\\Taking\ exponetial\ of\ both\ sides:\\\\y=e^{- \frac{t}{100}+C}\\\\y=e^C.e^{- \frac{t}{100}}\\\\y=Ae^{- \frac{t}{100}}(A=e^C)\\\\at\ y=15kg, t=0\\\\15=Ae^{e^{- \frac{0}{100}}}\\\\A=15\\\\[/tex]
[tex]y=15e^{e^{- \frac{t}{100}}}kg[/tex]
explain why the answers are different.
The first question shows how the value of x is bigger than the value of -3 while the second question shows how the value of x is smaller than the value of -3.
Hope this helps!
2) Which of the following equations has a slope (m) of -3 and a y-intercept 1 point
(b) of 8? *
O y = -3x - 8
O y=-3x + 8
Oy= 8x - 3
The science club is going on a field trip to the science museum. The club has at most $800 to spend on the trip. The bus for the trip costs $100, and meals at the museum cost $4.50 per student. If admission to the museum is $12 per student and $16 per adult, and there are six chaperones attending, how many students can go on the trip? Write inequality to represent the situation. do not solve the inequality. Defined the variable.
Answer:
38 students
Step-by-step explanation:
100+(16x6)=196
800-196=631
4.50+12=16.5
63/116.5=38.24
Answer:
100+4.50(s)+12(s)+96 less than or equal to 800
[tex] \leqslant [/tex]
s=students
Step-by-step explanation:
they can spend up to 800 dollars OR LESS. They have a charge of 100 dollars for the bus, plus a charge of 4.50 per student for lunches, plus a charge of 12 dollars per student for admissions plus 16 dollars times 6 (96) for the chaperones. All of this gives us our inequality above.
I really hope this helps!
PS: the reason why the adults don't get their own variable is because it says to define the variable not variable(s). You also cannot group the adults with the students because the student costs and the adult costs are two totally seperate and different amounts. if you just used variable p for people it wouldn't work because you wouldn't know how many adults were required to pay adult admission.
Charlotte and Barry are each assigned a paper for a class they share. Charlotte decides to write 12 pages at a time while Barry decides to write 2 pages at a time. If they end up writing the same number of pages, what is the smallest number of pages that the papers could have had?
Answer:
12 ( or 24, depending on what the question is asking)
Step-by-step explanation:
The lowest common multiple of 12 and 2 is 12.
If Charlotte doesn't write anymore pages after writing the original twelve, and Barry writes 2 pages six times, they both write the same number of pages. So, the smallest number of pages is 12
However, if the question is asking for the smallest total number of pages, then the answer is 24 since they both write 12 pages each.
solve for x
x+12+22+x=14
Answer:
X = -10
Step-by-step explanation:
Combine like terms
2x + 34 = 14
minus 34.
2x = -20
divide by 2
x = -10
Answer:
x=-10???
Step-by-step explanation:
I just combined like terms and got it from there.
please help
simplify this
2³+4×8
Answer:
40
Step-by-step explanation:
2³ + 4×8
8 + 32 = 40
PEMDAS:
Handle the exponents, multiply, then add.
g About 52% of American adults live in middle-income households. Suppose a sample of 20 American adults is selected. Let X be the number of adults from the sample that live in middle-income households. What is the probability distribution of X
Answer:
P (x= 0) = 0.00384
P (x= 1) = 0.000009133
P (x= 2) = 0.00009399
P (x= 3) = 0.0061
P (x= 4) = 0.00281
P (x= 5) = 0.00975
P (x= 6) = 0.0264
P (x= 7) = 0.05772
P (x= 8) = 0.0202
P (x= 9) = 0.14550
P (x= 10) = 0.1733
P (x= 11) = 0.17077
P (x= 12) = 0.138751
P (x= 13) = 0.0925
P (x= 14) = 0.0501
P (x= 15) = 0.0217
P (x= 16) = 0.00735
P (x= 17) = 0.00187
P (x= 18) = 0.000259
P (x= 19) = 2 0.0000385
P (x= 20) =0.000000208
Step-by-step explanation:
This is a binomila probability distribution as the success and failure are same and number of trials is fixed.
Here p =0.52 and q= 1-0.52= 0.48
n= 20 Now the probability distribution of X = 0,1,2,--------20
Applying the binomial distribution we can find the probability distribution of X taking the different values as
P (x= 0) = 20c0 (0.52)^0 (0.48)^20= 0.00384
P (x= 1) = 20c1 (0.52)^1 (0.48)^19= 0.000009133
P (x= 2) = 20c2 (0.52)^2 (0.48)^18= 0.00009399
P (x= 3) = 20c3 (0.52)^3 (0.48)^17= 0.0061
P (x= 4) = 20c4 (0.52)^4 (0.48)^16= 0.00281
P (x= 5) = 20c5 (0.52)^5 (0.48)^15= 0.00975
P (x= 6) = 20c6 (0.52)^6 (0.48)^14= 0.0264
P (x= 7) = 20c7 (0.52)^7 (0.48)^13= 0.05772
P (x= 8) = 20c8 (0.52)^8 (0.48)^12= 0.0202
P (x= 9) = 20c9 (0.52)^9 (0.48)^11= 0.14550
P (x= 10) = 20c10 (0.52)^10 (0.48)^10= 0.1733
P (x= 11) = 20c11 (0.52)^11 (0.48)^9= 0.17077
P (x= 12) = 20c12 (0.52)^12 (0.48)^8= 0.138751
P (x= 13) = 20c13 (0.52)^13 (0.48)^7= 0.0925
P (x= 14) = 20c14 (0.52)^14 (0.48)^6= 0.0501
P (x= 15) = 20c15 (0.52)^15 (0.48)^5= 0.0217
P (x= 16) = 20c16 (0.52)^16 (0.48)^4= 0.00735
P (x= 17) = 20c17 (0.52)^17 (0.48)^3= 0.00187
P (x= 18) = 20c18 (0.52)^18 (0.48)^2= 0.000259
P (x= 19) = 20c19 (0.52)^19 (0.48)^1= 0.0000385
P (x= 20) = 20c20 (0.52)^20 (0.48)^0= 0.000000208
7. Aluminum has 3 valence electrons. What property of an element can be determined by
the number of valence electrons?
a Group/family
b. Metal, Nonmetal, or Metalloid
C. Reactivity
d. Atomic Number
Solve for x. What is the root? If there is no root, choose none.
Answer:
4
Step-by-step explanation:
1/9 , Find the quotient in its simplest form .
Answer:
the simplest form of 1/9 is: 1/9
Step-by-step explanation:
1. A number that will divide evenly into both the numerator and denominator so it can be reduced. No such number exists for 1 and 9.
2. The numerator must be greater than the denominator, an improper fraction, so it can be converted to a mixed number. 1 is not greater than 9.
A company produces very unusual CD's for which the variable cost is $ 20 per CD and the fixed
costs are $ 30000. They will sell the CD's for $ 49 each. Let x be the number of CD's
produced.
Write the total cost C as a function of the number of CD's produced.
C= $
Write the total revenue R as a function of the number of CD's produced.
R= $
Write the total profit P as a function of the number of CD's produced.
P= $
Find the number of CD's which must be produced to break even.
The number of CD's which must be produced to break even is no
Answer:
Kindly check explanation
Step-by-step explanation:
Given that:
Variable cost = $20
Fixed cost = $30000
selling price = $49
Number of CD's produced = x
Cost (C) as a function of number of CD's produced :
Fixed cost + (variable cost * Number produced)
C = $30000 + ($20 * x)
C = $30000 + 20x
Revenue :
Selling price per CD * number of CDs produced
$49 * x
R = 49x
PROFIT:
REVENUE - COST
$30000 + 20x - 49x
30000 - 29x
Number of CD's which must be produced to break even:
Break even quantity = Fixed costs / (Sales price per unit – Variable cost per unit)
Break even quantity = 30000 / (49 - 20)
= 30000 / 29
= 1034.48
= 1034
Find the quotient. Round to the nearest hundredth. 8,240 ÷ 30
order the number from least to greatest: 10^5 10^-99 10^-17 10^14 10^-5 10^30
Answer:
I think it goes like this: 10^-99, 10^-17, 10^-5, 10^5, 10^14, 10^30
Step-by-step explanation:
Find the value of h(45) for the function below.h(x)=1/9(90-x)
Answer:
5
Step-by-step explanation:
90-45 = 45
45 x 1/9 = 5
45 x 1/9 is the same thing as saying 45/9, FYI
Answer:
5
Step-by-step explanation:
sub 45 into x
h(x) = h(45)
h(45) = 1/9(90-45)
= 1/9(45)
= 5
^^
If twice the number, added to 3 is divided by the number plus 9, the result is three halves. Find the number
Answer:
x=21
Step-by-step explanation:
(3+2x)/(x+9)=3/2
(x+9)(3+2x)=(3/2)(x+9)
3+2x=(3x+27)/2
2(3+2x)=3x+27
6+4x=3x+27
x=21
After the first essay examination in a class, a random sample of five papers was selected. The grades were 60, 75, 80, 70, and 90. What would be the 90% confidence interval for the mean grade of all the students?
Answer:
68.6433≤x≤82.3568
Explanation
confidence interval formula is expressed as
CI = xbar ± z × S/√n
xbar is the mean
z is the z score at 90% = 1.645
s is the Standard deviation
N is the sample size = 5
xbar = 60+75+80+70+ 90/5
xbar = 375/5
xbar = 75
Get standard deviation
SD =√\sum(x-xbar)²/N
SD = √(60-75)²+(75-75)²+(80-75)²+(70-75)²+(90-75)²/5
SD = √15²+0²+5²+5²+15²/5
SD = √225+50+225/5
SD = √500/5
SD =√100
SD = 10
Substitute the derived values into the formula
CI = 75±1.645 × 10/√5
CI = 75 ± (1.645×4.4721)
CI = 75±7.3568
CI = (75-7.3568, 75+7.3568)
CI = (67.6433, 82.3568)
Hence the 90% confidence interval of the student is:
68.6433≤x≤82.3568
the graph shows favorite sports among third graders in a school how many third graders pick basketball or baseball than football as their favorite sport
Answer:
do you have the graph?
Step-by-step explanation:
Suppose the scores on a chemistry test were normally distributed with a mean of 78 and a standard deviation of 10. If a student who completed the test is chosen at random,a.Find the probability that the student earned between 80 and 90 points.b.Find the probability that the student earned either less than 80 points or more than 90 points.
Answer:
a) 0.30567
b) 0.69433
Step-by-step explanation:
We solve using z score formula
z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
,a.Find the probability that the student earned between 80 and 90 points.
For 80 students
z = 80 - 78/10
= 0.2
P-value from Z-Table:
P(x = 80) = 0.57926
For 90 students
z = 90 - 78/10
= 1.2
P-value from Z-Table:
P(x = 90) = 0.88493
The probability that the student earned between 80 and 90 points.
P(x = 90) - P(x = 80)
= 0.88493 - 0.57926
= 0.30567
b.Find the probability that the student earned either less than 80 points or more than 90 points.
For less than80 students
z = 80 - 78/10
= 0.2
P-value from Z-Table:
P(x < 80) = 0.57926
For 90 students
z = 90 - 78/10
= 1.2
P-value from Z-Table:
P(x<90) = 0.88493
P(x>90) = 1 - P(x<90) = 0.11507
The probability that the student earned either less than 80 points or more than 90 points.
= 0.57926 + 0.11507
= 0.69433
The weights of cockroaches follow a Normal distribution with mean 80 grams and standard deviation 2 grams. Use normal table to answer the question below:
What percent of cockroaches weigh greater than 85 grams?
Answer:
0.621%
Step-by-step explanation:
First of all let's find the z-score which is given by the formula;
z = (x' - μ)/σ
We are given;
Mean; μ = 80 g
Standard deviation; σ = 2 g
Test score; x' = 85 g
Thus;
z = (85 - 80)/2
z = 5/2
z = 2.5
From the z-distribution table attached, at z = 2.5, the probability is:
P(z > 2.5) = 1 - 0.99379 = 0.00621 or 0.621%