Answer:
P( B∩ A₁ ) = 0.25
P( B∩ A₂ ) = 0.08
P( B∩ A₃ ) = 0.06
Step-by-step explanation:
As we know that
P( B∩ A₁ ) = P( B| A₁) × P(A₁)
P( B∩ A₂ ) = P( B| A₂) × P(A₂)
P( B∩ A₃ ) = P( B| A₃) × P(A₃)
As we have
P(A₁) = 0.50, P(A₂) = 0.20, and P(A₃) = 0.30.
P(B | A₁) = 0.50, P(B | A₂) = 0.40, and P(B | A₃) = 0.20
⇒P( B∩ A₁ ) = P( B| A₁) × P(A₁)
= 0.50(0.50)
= 0.25
⇒P( B∩ A₁ ) = 0.25
Now,
⇒P( B∩ A₂ ) = P( B| A₂) × P(A₂)
= 0.40(0.20)
= 0.08
⇒P( B∩ A₂ ) = 0.08
Now,
⇒P( B∩ A₃ ) = P( B| A₃) × P(A₃)
= 0.20(0.30)
= 0.06
⇒P( B∩ A₃ ) = 0.06
∴ we get
P( B∩ A₁ ) = 0.25
P( B∩ A₂ ) = 0.08
P( B∩ A₃ ) = 0.06
Create a word problem that can be represented by the following system of equations.
X + y = 50
2x + 4y = 120
Answer:
Step-by-step explanation:
You run a train station that sells children tickets for 2 dollars and adult tickets for 4 dollars
The total tickets sold on Saturday was 50
The train station made 120
How many adult tickets and kid tickets did they sell?
(40 kids, 10 adults)
A pen cost $40 and the book cost $10
The word problem that can be represented by the equation is: John bought one pen and one book for $50. He went the next day and bought 2 pens and 4 books for $120.
x + y = 50 ....... i
2x + 4y = 120 .... ii
Let x = pen
Let y = book.
From equation i, x = 50 - y
Since 2x + 4y = 120
2(50 - y) + 4y = 120
100 - 2y + 4y = 120
Collect like terms
-2y + 4y = 120 - 100
2y = 20
y = 10
Therefore, a book cost $10
Since x + y = 50
x + 10 = 50
x = 50 - 10
x = 40
A pen cost $40
Read related link on:
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00:00
A fruit farm has a total of 386 apple trees, peach trees, and pear trees.
There are 156 apple trees and 126 peach trees. How many pear trees are there?
Enter your answer in the box.
pear trees
Answer:
A s h i t load
Step-by-step explanation:
Answer:
104
Step-by-step explanation:
156+126=282 & 386-282=104 so,the answer is 104
3x + y = 19
2x - y = 6
Answer:
Step-by-step explanation:
(x,y)=(5,4)
Consider the following hypothesis test: H 0: 50 H a: > 50 A sample of 50 is used and the population standard deviation is 6. Use the critical value approach to state your conclusion for each of the following sample results. Use = .05. a. With = 52.5, what is the value of the test statistic (to 2 decimals)? Can it be concluded that the population mean is greater than 50? Select b. With = 51, what is the value of the test statistic (to 2 decimals)? Can it be concluded that the population mean is greater than 50? Select c. With = 51.8, what is the value of the test statistic (to 2 decimals)? Can it be concluded that the population mean is greater than 50? Select
Answer:
Part a:
The calculate value of Z = 2.946 lies in the critical region so the null hypothesis is rejected and alternate hypothesis is accepted that population mean is greater than 50.
Part b:
The calculate value of Z = 1.17851 does not lie in the critical region so the null hypothesis is accepted that population mean is not greater than 50.
Part c:
The calculate value of Z = 2.1213 lies in the critical region so the null hypothesis is rejected and concluded that population mean is greater than 50.
Step-by-step explanation:
Data as given
H 0: μ ≤ 50 against the claim H a: μ> 50 one tailed test
Z (0.05)= ± 1.645
Sample size n= 50
Using the central limit theorem
Population Standard Deviation= σ=s=6
X= 52.5 , 51 and 51.8
Part a:
Z= x-μ/ s/ √n
Z= 52.5- 50 / 6/ √50
Z= 2.5/0.84853
z= 2.946
The calculate value of Z = 2.946 lies in the critical region so the null hypothesis is rejected and alternate hypothesis is accepted that population mean is greater than 50.
Part b:
Z= x-μ/ s/ √n
Z= 51- 50 / 6/ √50
Z= 1/0.84853
z= 1.17851
The calculate value of Z = 1.17851 does not lie in the critical region so the null hypothesis is accepted that population mean is not greater than 50.
Part c:
Z= x-μ/ s/ √n
Z= 51.8- 50 / 6/ √50
Z= 1.8/0.84853
z= 2.1213
The calculate value of Z = 2.1213 lies in the critical region so the null hypothesis is rejected and concluded that population mean is greater than 50.
Which is the greater rate, 15 miles in 12 minutes or 25 miles in 20 minutes?
An optical inspection system is used to distinguish among different part types. The probability of a correct classification of any part is 0.93. Suppose that three parts are inspected and that the classifications are independent. Let the random variable X denote the number of parts that are correctly classified. Determine the probability mass function of X.
Probability Mass Function of X
x f(x)
0
1
2
3
Answer:
Follows are the solution to this question:
Step-by-step explanation:
Let P(X = x) mark x model number classified correctly.
The mass function of the probability:
[tex]\to f(0) = P(X=0) = (0.03)^3 = 0.0000\\\\\to f(1) = P(X=1) = (3 C_1)\times (0.97)\times (0.03)^2 = 0.0026\\\\\to f(2) = P(X=2) = (3 C_2)\times (0.97)^2 \times (0.03) = 0.0847\\\\\to f(3) = P(X=3) = (0.97)^3 = 0.9127\\\\[/tex]
[tex]x \ \ \ \ f(x) \\\\0\ \ \ \ 0.0000\\\\1\ \ \ \ 0.0026\\\\2\ \ \ \ 0.0847\\\\3\ \ \ \ 0.9127[/tex]
Triangle JLM is shown below.
M
17 in.
25 in.
J
8 in. K
20 in.
What is the area of triangle JLM?
O A 350 in.2
O B. 240 in.
OC. 300 in.2
O D. 210 in.2
Answer:
D) 210 in²
Step-by-step explanation:
Solve for KM.
8²+b²=17²
64+b²=289
b²=289-64
b²=225
b=√225
b=15 (Which is the length of KM, the height of the triangle)
Area=1/2bh
A=1/2(28)(15)
A=210
Yesterday, there were 80 problems assigned for homework. Harry did 20% of them correctly. How many problems did Harry get right?
Answer:
16 i think
Step-by-step explanation:
Brainliest :)
(Score for Question 3: ___ of 5 points)
(a) Order the popularity of the choices from greatest to least.
(b) It was estimated that 280 people were going to vote. If this was true, how many people would have voted for Goron? Show your work.
(c) 40 people voted for “Other.” Was the estimate of total voters from Part (b) accurate? Explain.
this is for k12 so click off if u dont have an answer or ill report
Goron should get 98 votes
The question breaks down to taking 35% of 280.
Votes = 35/100 * 280 = people who will vote for Goron
Votes = 9800 / 100 = people who will vote for Goron.
Votes = 98
what is 6,383 in expended form?
Answer:
expanded notation form:
6,383 =
6,000
+ 300
+ 80
+ 3
expanded factors form:
6,383 =
6 × 1,000
+ 3 × 100
+ 8 × 10
+ 3 × 1
expanded exponential form:
6,383 =
6 × 103
+ 3 × 102
+ 8 × 101
+ 3 × 100
Step-by-step explanation:
i wasn't entirely sure what you needed but i hope this helps :) have a great day !!
EASY TRUE OR FALSE QUESTION
Answer:
Its false
Step-by-step explanation:
It cant increase
Answer:
it issss false
HELP PLEASE ITS URGENT
What is m
Look at the image above
Answer:
m∠F = 90°
Step-by-step explanation:
By the property of a kite,
"One pair of the opposite angles are congruent"
m∠E ≅ m∠G
m∠E = m∠G = 113°
Sum of the interior angles of a polygon = (n - 2) × 180°
Here, n = number of sides of the polygon
For a kite, n = 4
Therefore, sum of the interior angles of the given kite = (4 - 2) × 180°
= 360°
Therefore, m∠E + m∠F + m∠G + m∠H = 360°
113° + m∠F + 113° + 44° = 360°
m∠F = 360° - 270°
m∠F = 90°
Someone was interested in determining if there is a difference in the proportion of US adults that working hard was the most important thing for a child to learn in 2012 and 2018. They found data on this in the General Social Survey. In 2018, out of 1542 respondents, 415 said it was the most important. In 2012, out of 1323 respondents, 326 said it was the most important. Find the margin of error with 95% confidence.
Answer:
0.01521
Step-by-step explanation:
The Margin of Error for Difference in Proportions is given as:
z × √p1 × (1 - p1)/n1 - p2 × (1 - p2)/n2
z = z score for 95% confidence interval
= 1.96
In 2018, out of 1542 respondents, 415 said it was the most important.
p1 = x1/n1
x1= 326 n1 = 1323
p1 = 326/1323
0.246409675
Approximately = 0.246
In 2012, out of 1323 respondents, 326 said it was the most important.
p2 = x2/n2
x2 = 415, n2 = 1542
p2= 415/1942
p2 = 0.2136972194
Approximately = 0.214
Margin of Error =
1.96 × √0.246× (1 - 0.246)/1323- 0.214 × (1 - 0.214)/1542
1.96 × √0.0005699169 - 0.0005097276
1.96 × √(0.0000601893)
1.96 × 0.0077581763
= 0.0152060256
Approximately = 0.01521
Therefore, Margin of Error = 0.01521
You can use the formula for margin of error for difference in proportion to find the margin of error with 95% confidence.
The margin of error with 95% confidence for the given data is given by
MOE = 0.32
How to calculate margin of error for difference in proportion to find the margin of error ?Suppose we've two samples with sample sizes [tex]n_1[/tex] and [tex]n_2[/tex] respectively. Let the interested quantities found out in those samples out of their sample sizes are [tex]x_1[/tex] and [tex]x_2[/tex] respectively. Then we have the margin of error for difference in proportion to find the margin of error as:
[tex]MOE = Z_{\alpha/2} \times \sqrt{\dfrac{p_1(1-p_1)}{n_1} + \dfrac{p_2(1-p_2)}{n_2}}[/tex]
where we have:
[tex]p_1 = \dfrac{x_1}{n_1}\\\\p_2 = \dfrac{x_2}{n_2}[/tex]
and
[tex]\alpha = \text{Level of significance}[/tex]
Using the given data to get the margin of error[tex]Year = 2015\\n_1 = 1542\\x_1 = 415\\\\Year = 2012\\n_2 = 1323\\x_2 = 326\\\\\alpha = 100-95\% = 1-0.95 = 0.05[/tex]
For 95% confidence, we have Z score as 1.96
The proportions are calculated as:
[tex]p_1 = \dfrac{415}{1542} = 0.269\\\\p_2 = \dfrac{326}{1323} = 0.246[/tex]
Thus, margin of error is calculated as
[tex]MOE = 1.96 \times \sqrt{\dfrac{0.269 \times 0.731}{1542} + \dfrac{0.246 \times 0.754}{1323}} = 1.96 \times \sqrt{0.000127 + 0.00014}\\\\MOE = 1.96 \times 0.01634 = 0.032[/tex]
The margin of error with 95% confidence for the given data is given by
MOE = 0.32
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. The scatterplot shows the time spent playing a video game and the number of points scored by several students. Video Game 1,350 1,200 1,050 900 Number of Points Scored 750 600 450 300 150 0 5 10 15 20 25 30 35 40 45 Time (minutes) Based on the scatterplot, which is the best prediction of the number of points scored by a student who spends 45 minutes playing the video game?
Answer:
c is the answer
Step-by-step explanation:
is the not maybe
please help me please i really need help please
On a scale drawing, the scale is 12 inch = 1 foot. What are the dimensions on the scale drawing for a room that is 22 feet by 17 feet?
Answer:
......
Step-by-step explanation:
Answer
11 inches by 8.5 inches
Step-by-step explanation:
We can use proportions to solve this problem, drawing on top, real life on bottom
1/2 inch x inches
-------------- = ----------
1 ft 22ft
Using cross products
1/2 * 22 = x*1
11 =x
11 inches
1/2 inch x inches
-------------- = ----------
1 ft 17ft
Using cross products
1/2 * 17 = x*1
8.5 =x
The sum of eight times a number and negative exceeds twelve.
Answer:8x + -4 > 12
8x > 16
x > 2
Step-by-step explanation:
Please help ASAP I need to solve AD
Answer:
6
Step-by-step explanation:
All sides on a rhombus are equal
HELP PLEASE WILL GIVE BRAINLIST
Which triangle side lengths form a right triangle? Choose all that apply.
5,6,7
6, 8, 14
8,15, 17
10,12,15
15, 20, 25
16, 18, 20
Answer:
8.,15,17
Step-by-step explanation:
use pythagoras theorem formula
Simplify
-3(2.5-k)+0.5(7+8k)
Answer:
-7•5+3k+3•5+4k
-7•5+3•5+4k+3k
-4+7k
Find the reciprocal of the number 2/7
Answer:
7/2
Step-by-step explanation:
The reciprocal is basically just flipping the fraction upside down. Reciprocal is also called inverse.
What is 13/20 as a part to part ratio
65%
Convert fraction (ratio) 13 / 20 Answer: 65%
What are the truck ID’s of trucks that have carried small shipments. Small shipments are defined as those that weigh less than 800 pounds? (HInt: Avoid duplcates.)
Table for the question is attached in the picture below :
Answer:
SELECT distinct(TRUCK_ID), WEIGHT from SHIPMENT where WEIGHT < 800 ;
Step-by-step explanation:
The Structured query language (SQL) defined above, returns only the TRUCK_ID and Weight column from the shipment table as they are the only two columns listed after the select keyword. The condition is added using the WHERE keyword on the weight table, this filters the result returned to include only rows where the weight value is less than 800. The distinct keyword used alongside the TRUCK_ID column ensures that a certian TRUCK_ID value isn't returned more than once (Hence, it is used to avoid duplicates).
There are 4 games at the carnival Kevin played all the games in 24 minutes. How many minutes did he spend at each game if he spent an equal amount of time at each?
Answer:
6 minutes at each game
Step-by-step explanation:
24 minutes divided by 4 games, if he spends and equal amount of time at each game it would be 24/4=6
Answer:
6
Step-by-step explanation:
24/4=6
What expression is equivalent to 4/5 X +11/5
Answer:
8/10 X 22/10
Step-by-step explanation:
When you multiply every number by 2, then the expression will still be equivalent.
Answer:
(4x + 11)/5
Step-by-step explanation:
4/5x + 11/5 = 4x/5 + 11/5 = (4x + 11)/5
Ms. Gallegos burns 236 calories riding her bike each hour. She wants to burn more than 590 calories riding her bike at the same rate. Which inequality represents all possible values for t, the number of hours Ms. Gallegos must ride her bike to burn more than 590 calories?
Answer:
T = 2.5
Step-by-step explanation:
Hope this helps!
Answer:
T >2.5
Step-by-step explanation:
guys why does my bottle thats called shampoo taste like soap and its fluffy it says cucumber edition i wanted to taste it but it tastes nothing like cucumber and it makes me gassy please help and explain how to stop this
Answer:
I'm pretty sure you can stop it by not drinking shampoo.
Step-by-step explanation:
shampoo is bad for you.
Answer:
Stop eating the shampoo
Step-by-step explanation:
If, you don't eat the cucumber shampoo it will not make you gassy.
If Tom travels 680 miles in 8 hours, how far does he travel per hour?
Answer:
85 mph
Step-by-step explanation:
It is because 680 / 8 = 85
Answer: 85 miles an hour
Step-by-step explanation:
divide distance by time
680 / 8 = 85 miles per hour
:)
THIS ASSIGNMENT IS DUE IN 5 MINUTES...IF ITS CORRECT ILL MARK IT AS BRAINIEST, thanks in advance❤️! (this is my second time posting this, the answer isn’t 80...if you don’t know how to do this please don’t try answering the question) Find the area of the regular polygon given below
Answer:
400
Step-by-step explanation:
Answer:
11,011.055
Step-by-step explanation: