Answer:
0.7558 = 75.58% probability this sale has occurred in Dallas
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Belt sold
Event B: Sold in Dallas.
Probability of belt being sold:
50% of 65%(made in Dallas)
30% of 100 - 65 = 35%(made in Phoenix). So
[tex]P(A) = 0.5*0.65 + 0.3*0.35 = 0.43[/tex]
Sold in Dallas:
50% of 65%. So
[tex]P(A \cap B) = 0.5*0.65 = 0.325[/tex]
What is the probability this sale has occurred in Dallas?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.325}{0.43} = 0.7558[/tex]
0.7558 = 75.58% probability this sale has occurred in Dallas
If the polygon is translated 3 units down and 4 units left, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates.
Answer:
A' (-2,-4) B' (-3,-7) C' (-1,-8) D' (1,-6)
Step-by-step explanation:
Just take it one point at a time and move each point down 3 and 4 left. Prime notation just means to put this little sign ' so it indicates that this is the new coordinate. So A was (2,-1) and A' (the new one) is (-2,-4)
You have $400,000 saved for retirement. Your account earns 5% interest. How much will you be able to pull
out each month, if you want to be able to take withdrawals for 25 years?
Answer:
$4,515.14
Step-by-step explanation:
First we need to get the amount after 25 years on $400,000 at 5% interest
Using the compound interest formula
A = P(1+r)^n
A = 400,000(1+0.05)^25
A = 400,000(1.05)^25
A = 400,000(3.3864)
A = $1,354,541.98
Since 25years = (25*12)months
25 years = 300months
Amount to be able to pull out each month = $1,354,541.98/300
Amount to be able to pull out each month = $4,515.14
Hence you will be able to pull out $4,515.14 each month
Find AB If AC = 12 and BC = 35
Answer:
37
Step-by-step explanation:
a² =b²+ç²a²=12²+35²a=√1369a=37Help Me Please.............................(7)
Answer:
Step-by-step explanation:
The first step contains the error.
2x - 10 = 22 Add 10 to both sides
+ 10 +10
2x = 32 Divide by 10
2x/2 = 32/2
x = 16
Which mode of transportation did you choose? Why?
Answer:
land
Step-by-step explanation:
because,bus are more comfortable and easier other transportation are dangerous than land transportation ❤️
hope i helped u
PLZ HELP
What is the x-intercept of the graph y = 2x - 14?
-14
-7
0
7
The following data are the daily number of minutes of smartphone use for a random sample of 8 students at your institution:
117, 156, 89, 72, 116, 125, 101, 100.
Required:
a. Test the null hypothesis according to which the true mean is greater or equal to 100 min against the alternative that it is less than 100. Use a significance level of 5% (state the null and the alternative hypothesis, the test statistic and the conclusion).
b. Compute a 90% confidence interval for the true mean number of minutes per day a student uses his or her smartphone. Is your finding consistent with your answer in (a) (Explain why or why not)
Answer:
We fail to reject the Null ;
(88.323, 130.677)
Step-by-step explanation:
Given the data :
117, 156, 89, 72, 116, 125, 101, 100
H0 : μ ≥ 100
H1: μ < 100
From the data: using calculator :
Mean, x = 109.5
Standard deviation, s = 25.33
The test statistic:
(x - μ) ÷ s/Sqrt(n)
(109.5 - 100) ÷ 25.33/sqrt(8)
Test statistic = 1.06
Since, same size is small, we use t test ;
Using the Pvalue calculator :
T at df = 8 - 1 = 7, α = 0.05
Pvalue = 0.161
Pvalue > α
0.161 > 0.05 ; Hence, we fail to reject H0.
B.)
C. I = mean ± Tcritical *s/√n
Tcritical = 2.365 at 95% and df = 7
109.5 ± 2.365(25.3264/√8)
109.5 ± 2.365(8.9542)
(109.5-21.1768 ; 109.5+21.1768)
(88.323, 130.677)
In conclusion true mean is in the confidence interval, so it is consistent.
Triangle RST reflectid over the x-and then translated 4 unita to the right What are the coordinates of the final image in its new position?
Answer:
R" (0,3)
S" (1,1)
T" (4,2)
Step-by-step explanation:
The reflection of the point (x, y) across the x-axis is the point (x, -y).
Translate right 4- add 4 to the x coordinate
R ( -4, -3 ) R' ( -4 , 3) R" ( 0 , 3)
S ( -3, -1) S' (-3 , 1) S" ( 1 , 1)
T ( 0 , -2) T' (0, 2) T" ( 4 , 2)
Tyler has to savings accounts that his grandparents opened for him . One of the accounts Pay 8% annual interest Where as the other pay 10% annual interest. If you have $700 more invested at 10% then you invested at 8%, how much do you have invested in each account If the total amount of interest You earn in a year is $106?
Tyler invested $___at 8%, and $___at 10%
Suppose that an appliance is constructed in such a way that it requires that n independent electronic components are all functioning. Assume that the lifespan of each of these, Tj, is an exponential random variable with parameter λj.
a. Let X be the random variable giving the lifespan of the appliance. Find the CDF and PDF for X.
b. Find the expected value of X.
c. Now find the median lifespan of the appliance (that is, the time t at which half of the appliances are likely to have broken and half to be working ).
Answer:
Step-by-step explanation:
[tex]T_j \sim exp ( \lambda j) \ \ \ j = 1 (1) n \\ \\ f_{Tj}(tj) = \lambda j e^{-\lambda j tj } , tj>0 \\ \\ P\Big[ Tj> x\Big] = \int \limits ^{\infty}_{x} \lambda j e^{-\lambda j tj}\ dtj \\ \\ = e^{-\lambda j x}, x > 0 \\ \\ \\ \\ a) F_x (x) \\ \\ = P[X \le x ] \\ \\ = 1 - P[X> x] \\ \\ = 1 - \pi \limits ^{n}_{j =1} \Big\{ P[T_j > x ] \Big \}[/tex]
[tex]\text{This is because the appliance has the capacity to work for more than (x) }[/tex][tex]\text{hours if and only if all the "n" components work more than (x) hours.}[/tex]
[tex]\text{Then:}[/tex]
[tex]= 1 - e \ \pi^{n}_{j=1} \ e^{-\lambda j x} \\ \\ = 1 - e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}[/tex]
∴
[tex]CDF = 1 - e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}\ , \ x>0[/tex]
[tex]PDF =\Big( \sum \limits ^{n}_{j =1} \lambda j\Big) e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}\ , \ x>0[/tex]
[tex]f_x(x) = \Big( \sum \limits ^{n}_{j =1} \lambda j\Big) e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}\ , \ x>0[/tex]
(b)
[tex]E(x) = \int \limits ^{\infty}_{o }x f_x (x) \ dx \\ \\ = \int \limits ^{\infty}_{o }x \ \Big( \sum \limits ^{n}_{j =1} \lambda j\Big) e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}\ , \ dx[/tex]
[tex]= \dfrac{1}{\sum \limits ^n_{j=1} \lambda j} \ \ \int \limits ^{\infty}_{o} \Big [(\sum \limits ^n_{j=1} \lambda j )x \Big] e ^{-\Big ( \sum \limits ^{n}_{j=1} \lambda j \Big)x} \ \ d \Big( x \sum \limits ^n_{j=1} \lambda j \Big)[/tex]
[tex]= \dfrac{1}{\sum \limits ^n_{j= 1} \lambda j} \int \llimits ^{\infty}_{o} t e^{-t} \ dt[/tex]
[tex]= \dfrac{1}{\sum \limits ^n_{j= 1} \lambda j} \int \llimits ^{\infty}_{o} t e^{-t} \ dt \ \ \ \ \text{\Big[By transformation }t =( \sum \limits ^n_{j=1} \lambda j )x \Big][/tex]
[tex]= \dfrac{1}{\sum \limits ^n_{j= 1} \lambda j}[/tex]
(c)
[tex]Let \ \ l_y_{\dfrac{1}{2}} \text{ be the median}[/tex]
∴
[tex]F(l_y_{\dfrac{1}{2}}) = \dfrac{1}{2} \\ \\ 1 - e ^{-\Big (\sum \limits ^{n}_{j=1} \lambda j \Big)} {l_y}_{\frac{1}{2}} = \dfrac{1}{2} \\ \\ \dfrac{1}{2} = e^{-\Big (\sum \limits ^{n}_{j=1} \lambda j \Big) } {l_y}_{\frac{1}{2}} \\ \\ - In 2 = {-\Big (\sum \limits ^{n}_{j=1} \lambda j \Big)} {l_y}_{\frac{1}{2}} \\ \\ \\ \\ \mathbf{ {l_y}_{\frac{1}{2}} = \dfrac{ In \ 2}{\sum \limits ^{n}_{j=1} \lambda j }}[/tex]
2.
Select the correct answer.
The national apple growers organization recently released its first crop of a new apple variety. It gathered data on the weight of the new apples.
It found a population mean of 4.85 ounces and a standard deviation of 0.92. Each sample size was 500 apples. By the central limit theorem,
which interval do 99.7% of the sample means fall within?
OA.
4.81 and 4.89
OB.
4.73 and 4.97
Ос. .
4.84 and 4.86
OD
4.77 and 4.93
Answer:
B. 4.73 and 4.97
Step-by-step explanation:
To solve this question, we need to understand the Empirical Rule and the Central Limit Theorem.
Empirical Rule:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Standard deviation of 0.92, sample of 500:
This means that [tex]\sigma = 0.92, n = 500, s = \frac{0.92}{\sqrt{500}} = 0.04[/tex]
By the central limit theorem, which interval do 99.7% of the sample means fall within?
Within 3 standard deviations of the mean. So
4.85 - 3*0.04 = 4.85 - 0.12 = 4.73
4.85 + 3*0.04 = 4.85 + 0.12 = 4.97
So, option B.
Answer:
4.73 and 4.97
Please give me brainliest, I really need it.
List two solutions for the equation: y = 4.5x + 9
Answer:
say 5 and 6
Step-by-step explanation
you just multiply it
Dan is randomly selecting an outfit to wear to school. He can choose from 3 shirts: blue striped, red striped, or white. He
can choose from 3 pairs of shorts: tan, blue, or plaid.
Determine whether each statement is true or false.
Select True or False for each statement.
The probability that Dan chooses a striped shirt and a pair of tan shorts is
O True
o
False
There are 6 possible outcomes in the sample space.
O
True
O
False
The probability that Dan chooses a striped shirt and a pair of blue shorts is
o
True
O False
There are 2 ways to choose a red striped shirt and a pair of tan shorts.
O True
O False
Answer:i dont know :(
Step-by-step explanation:
im sorry :(
Answer:
1. true
2. false
3. false
4. false
Step-by-step explanation:
hope this helps
please mark brainiest
please give 5 stars
thank you
Need help please thanks
Answer:
6.
Just count the x's on the graph...
Write the left side of the identity in terms of sine and cosine. Rewrite the numerator and denominator separately. (Do not simplify.) Simplify the fraction from the previous step such that both the fractions have the common denominator The expression from the previous step then simplifies to using what? A. Addition and a Reciprocal Identity B. Addition and a Pythagorean Identity
Answer:
[tex](a)[/tex] [tex]\frac{2}{cos\theta}/\frac{1}{sin\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
[tex](b)[/tex] [tex]\frac{2sin\theta}{cos\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
(c) Addition and Quotient identity
Step-by-step explanation:
Given
[tex]\frac{2sec\theta}{csc\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex] --- The expression missing from the question
Solving (a): Write the left hand side in terms of sin and cosine
In trigonometry:
[tex]sec\theta = \frac{1}{cos\theta}[/tex]
and
[tex]csc\theta = \frac{1}{sin\theta}[/tex]
So, the expression becomes:
[tex]\frac{2 * \frac{1}{cos\theta}}{\frac{1}{sin\theta}} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
[tex]\frac{\frac{2}{cos\theta}}{\frac{1}{sin\theta}} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
Rewrite as:
[tex]\frac{2}{cos\theta}/\frac{1}{sin\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
Solving (b): Simplify
[tex]\frac{2}{cos\theta}/\frac{1}{sin\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
Change / to *
[tex]\frac{2}{cos\theta}*\frac{sin\theta}{1} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
[tex]\frac{2sin\theta}{cos\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
Solving (c): The property used
To do this, we need to further simplify
[tex]\frac{2sin\theta}{cos\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
Take LCM
[tex]\frac{2sin\theta+ 4sin\theta}{cos\theta} =6tan\theta[/tex]
Add the numerator
[tex]\frac{6sin\theta}{cos\theta} =6tan\theta[/tex]
Apply quotient identity
[tex]\frac{sin\theta}{cos\theta} = tan\theta[/tex]
This gives
[tex]\frac{6sin\theta}{cos\theta} = 6tan\theta[/tex]
Hence, the properties applied are:
Addition and Quotient identity
How many time does 217.39 go into 5000
Answer is in the photo. I can't attach it here, but I uploaded it to a file hosting. link below! Good Luck!
tinyurl.com/wpazsebu
find the standard form of the equation of a parabola with a vertex at the origin and with a focus at (-4,0) and a directrix at x=4
Adalia has a cooler where the inside is in a shape of a rectangular prism. The inside of the cooler is 20 inches wide, 14 inches high, and 12 inches long. What is the volume in cubic inches of the inside of the cooler?
( will give brainliest if u help)
Answer:
A.
Step-by-step explanation:
took test
Is this A,B,C or D helppppp
Answer:
D
Step-by-step explanation:
D goes thru positive 4 and negative 3
Solve this before 6:00 and i will give brainliest
Answer:
4
Step-by-step explanation:
Use PEMDAS. Use a calulator to solve 3 and 1/3 times 1.9+19.5 divided by 4 and 1/2 and after you solve that solve 62/75- 0.16. Divided the first answer by the second. Now move to 3.5+4 and 2/3+ 2 and 2/15 then solve. Next solve 0.5 times ( 1 and 1/20+ 4.1) and with the answer you got from the equation above divided that by the answer just solved. Now divided the number on the left with the number on the right and you should get 4.
Solve.
a - 6 > 1
I need help quick!
Answer: 8
Step-by-step explanation:
8-6 = 2 which is greater
anything above 7 is correct
Answer:
a>7
Step-by-step explanation:
a-6>1
a>1 +6
a>7
thank u i hope it helps
what is -6.77626358E-21 written in scientific notion with three significant digits
Answer:
-6.78 x 10^-21
Step-by-step explanation:
-6.77626358E-21
= -6.78 x 10^-21
Beryllium is an extremely lightweight metal that is used in many industries, such as aerospace and electronics. Long-term exposure to beryllium can cause people to become sensitized. Once an individual is sensitized, continued exposure can result in chronic beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium, workers were categorized by their duration of exposure (in years) and by their disease status (diseased, sensitized, or normal.) The results were as follows:
Duration of Exposure
< 1 1 to < 5 >= 5
Diseased 12 10 18
Sensitized 14 18 13
Normal 66 142 210
Required:
a. Compute the expected frequencies of diseased workers.
b. Compute the expected frequencies of sensitized workers.
c. How many degrees of freedom are there?
Answer:
1. Has been answered below
2. Degree of freedom is 4
Step-by-step explanation:
Row 1: 12+10+18 = 40
Row 2: 14+18+13 = 45
Row 3: 66+142+210 = 418
Grand total = 40+45+418 = 503
Column 1 : 12+14+66 = 92
Column 2: 10+18+142 = 170
Column 3: 18+13+210 = 241
Total = 92+170+241 = 503
Expected frequencies of diseased workers
92x40/503 = 7.316
170x40/503 = 13.52
241 x 40/503 = 19.165
Expected frequencies of sensitized workers
92x45/503 = 8.23
170x45/503 = 15.20
241x 45/503 = 21.56
2.
Degree of freedom
= (Number of row -1)(number of column - 1)
= 3-1 * 3-1
= 2x2
= 4
1x1
wdwdwadwdwadwa dwa dwa daw dwa dw adw dw da dw dwa dw adw da daw dw dawd wd wdwdw
Answer:
1
Step-by-step explanation:
1x1 is 1 because 1x1 is 1
Answer:
1
Step-by-step explanation:
In the elimination method would you add or subtract the following system? (Elimi
2x+5y=-2
-2x-7y=-6
(1 Point)
Add
Subtract
(Worth 10 points)
Answer:
You will add!
Step-by-step explanation:
Words words words
Please help with this
Answer:
[tex]S_{25}=555[/tex]
Step-by-step explanation:
Given that,
In an AP, the 6th term is 39 i.e.
[tex]a_6=a+5d\\\\39=a+5d\ ....(1)[/tex]
In the same AP, the 19th term is 7.8 i.e.
[tex]a_{19}=a+18d\\\\7.8=a+18d\ ......(2)[/tex]
Subtract equation (1) from (2).
7.8 - 39 = a+18d - (a+5d)
-31.2 = a +18d-a-5d
-31.2 = 13d
d = -2.4
Put the value of d in equation (!).
39 = a+5(-2.4)
39 = a- 12
a = 39+12
a = 51
The sum of n terms of an AP is given by :
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
Put n = 25 and respected values,
[tex]S_{25}=\dfrac{25}{2}[2(51)+24(-2.4)]\\\\=555[/tex]
Hence, the sum of first 25 terms of the AP is equal to 555.
Complete please! All of them
Answer: #1: 15/12 aka 1 3/12 #2: < #3 11/9 aka 9 2/11
Step-by-step explanation: Hope it helps ya
which situation shows a constant rate of change?
Answer: option D
Step-by-step explanation: just did it
C was wrong and showed option D was the correct answer
Algebra 2
Can you help me pls
Answer:
In50=3.912023005
Step-by-step explanation:
press it on your calculator
i have been struggling with this question for 30mins. if you answer it can you please show work? thank you
Answer:
a)22
Step-by-step explanation: