Answer:
a) 0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.
b) 0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.
c) 0.064 = 6.4% probability that 7 of them are discovered.
Step-by-step explanation:
For itens a and b, we use conditional probability.
For item c, we use the binomial distribution along with the conditional probability.
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.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
a) If it has an emergency locator, what is the probability that it will not be discovered?
Event A: Has an emergency locator
Event B: Not located.
Probability of having an emergency locator:
66% of 72%(Are discovered).
20% of 100 - 72 = 28%(not discovered). So
[tex]P(A) = 0.66*0.72 + 0.2*0.28 = 0.5312[/tex]
Probability of having an emergency locator and not being discovered:
20% of 28%. So
[tex]P(A cap B) = 0.2*0.28 = 0.056[/tex]
Probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.056}{0.5312} = 0.105[/tex]
0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.
b) If it does not have an emergency locator, what is the probability that it will be discovered?
Probability of not having an emergency locator:
0.5312 of having. So
[tex]P(A) = 1 - 0.5312 = 0.4688[/tex]
Probability of not having an emergency locator and being discovered:
34% of 72%. So
[tex]P(A \cap B) = 0.34*0.72 = 0.2448[/tex]
Probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2448}{0.4688} = 0.522[/tex]
0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.
c) If we consider 10 light aircraft that disappeared in flight with an emergency recorder, what is the probability that 7 of them are discovered?
p is the probability of being discovered with the emergency recorder:
0.5312 probability of having the emergency recorder.
Probability of having the emergency recorder and being located:
66% of 72%. So
[tex]P(A \cap B) = 0.66*0.72 = 0.4752[/tex]
Probability of being discovered, given that it has the emergency recorder:
[tex]p = P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4752}{0.5312} = 0.8946[/tex]
This question asks for P(X = 7) when [tex]n = 10[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{10,7}.(0.8946)^{7}.(0.1054)^{3} = 0.064[/tex]
0.064 = 6.4% probability that 7 of them are discovered.
Work out the area of the triangle 5 cm and 12 cm
Answer:
30cm²
Step-by-step explanation:
base (5cm) × height (12cm) = 60cm ÷ 2
Please help me for brainliest.
Answer:
Step-by-step explanation:
D
Answer:
D
Step-by-step explanation:
Let's look at the statement.
7y = 14x and y = 2x does have infinitely many solutions. Why? Because the first equation can be rearranged to look like the second one. If you divide 7y and 14x by 7, you end up with y = 2x. Look familiar? This means the set of equations has infinitely many solutions.
6 X (22 + 9) = 6 x 22 + 6 x 9
This is an example of ______
property.
Answer:Distributive property
Step-by-step explanation:
6 X (22 + 9) = 6 x 22 + 6 x 9 is an example of the distributive property where you can distribute the multiplication to each term inside the parentheses.
The distributive property states that when you multiply a number by the sum of two or more numbers, you can distribute the multiplication to each term inside the parentheses. Mathematically, it can be expressed as:
a x (b + c) = (a x b) + (a x c)
In the given equation, we have:
6 x (22 + 9) = 6 x 22 + 6 x 9
By applying the distributive property, we distribute the multiplication of 6 to each term inside the parentheses:
6 x 22 + 6 x 9
This simplifies to:
132 + 54
Therefore, the distributive property allows us to break down the multiplication of a number by the sum of two or more numbers into separate multiplications, resulting in the same outcome.
To know more about distributive click here :
https://brainly.com/question/13818728
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The sum of eight and twice a number is 42
Answer:
8 + 2n = 42
Step-by-step explanation:
the sum of eight: ___+ 8
and twice(2) a number(could be any variable but for now i choose n): 2n + 8
is 42 (literally mean it equals 42): 2n + 8 = 42
find the value of x. (geometry)
Answer:
18.02 units
Step-by-step explanation:
WILL GIVE BRAINIEST TO THE FIRST PERSON WHO ANSWERS THEM ALL CORRECTLY, BUT U HAVE TO BE QUICK!!!
Answer:
A) a^8
B) 16a^14
C)a^mn
D)24a^yz
E)a^3
F)5a^2
G) a^5
H)a^m-n
Intrigued by a 2013 study at the University of Nebraska that suggested marijuana smokers may be thinner than other adults, a group of students did a project to explore the relationship between body mass index (BMI) and amount of time spent under the influence of marijuana (measured in hours per week). Based on a random sample of 33 students at their university, they used BMI as the response variable. The equation of the least-squares regression line is: hours per month under influence = 49.2−1.15 BMI. Also, r2=0.134 .
this question is incomplete, the complete question is:
1. is this model effective
2. what is the correlation coefficient for this data.
3. for a student with a bmi of 25, what is the predicted number of hours under the influence.
Step-by-step explanation:
1. first of all this model is not effective because we have r² as 0.134. this tells us that only 13.4 percent of the of the variations that exist in this data has been explained by the model
1. we get the correlation coefficient by
[tex]+-\sqrt{r^{2} }[/tex]
the regression slope coefficient has a negative sign. this is what we would use in calculating the correlation coefficient.
[tex]-\sqrt{r^{2} }[/tex]
= -√0.134
= -0.366
therefore the correlation coefficient is -0.366
2. to get the number of hours under the influence with a bmi of 25
the equation is
49.2-1.15bmi
= 49.2-1.15(25)
= 49.2-28.75
= 20.45
Find the measure of angle 1
A. 90
B. 110
C. 180
Answer:
90°
Step-by-step explanation:
whoever answers, i will give brainliest :)
This is due soon, pls help!
Answer:
69
98
Step-by-step explanation:
area= lenght*width
area= 5451
length= 79
which means that
5451=79*width
width=69
Preimieter= 2L+2W
302=2L+2(53)
302=2L+106
196=2L
L=98
A twin-engined aircraft can fly 816 miles from city A to city B in 4 hours with the wind
and make the return trip in 6 hours against the wind. What is the speed of the wind?
Answer:
,mnl.khvmfjdrykytdd7ir rvrtuy
Step-by-step explanation:
Pls help me answer the question attached
Answer:
A.
Step-by-step explanation:
(2/3)*6.75=4.5
pls help soonnnnn i need number 2
Answer:
3 3/16 lbs is the total amount the puppies weigh
3). What is the area of a square with 16cm sides? *
Helpppppppppppppppppp
Answer:
Step-by-step explanation:
256
Answer:
256
Step-by-step explanation:
16 x 16=256
Consider the following hypothesis test. H0: μ ≥ 55 Ha: μ < 55 A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use α = 0.01.
(a) x = 54 and s = 5.3 Find the value of the test statistic. (Round your answer to three decimal places.)
Find the p-value. (Round your answer to four decimal places.)
State your conclusion.
(b) x = 53 and s = 4.6
Find the value of the test statistic. (Round your answer to three decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
(c) x = 56 and s = 5.0
Find the value of the test statistic.
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
Answer:
Step-by-step explanation:
Given that:
[tex]H_o: \mu \ge 55 \ \\ \\ H_1 : \mu < 55[/tex]
(a) For x = 54 and s = 5.3
The test statistics can be computed as:
[tex]Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }[/tex]
[tex]Z = \dfrac{54-55}{\dfrac{5.3}{\sqrt{36}} }[/tex]
[tex]Z = \dfrac{-1}{\dfrac{5.3}{6} }[/tex]
Z = -1.132
degree of freedom = n - 1
= 36 - 1
= 35
Using the Excel Formula:
P-Value = T.DIST(-1.132,35,1) = 0.1326
Decision: p-value is greater than significance level; do not reject [tex]\mathbf{H_o}[/tex]
[tex]Conclusion: \ There \ is \ insufficient \ evidence \ to \ conclude \ that \[/tex] [tex]\mu < 55[/tex]
b
For x = 53 and s = 4.6
The test statistics can be computed as:
[tex]Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }[/tex]
[tex]Z = \dfrac{53-55}{\dfrac{4.6}{\sqrt{36}} }[/tex]
[tex]Z = \dfrac{-2}{\dfrac{4.6}{6} }[/tex]
Z = -2.6087
degree of freedom = n - 1
= 36 - 1
= 35
Using the Excel Formula:
P-Value = T.DIST(-2.6087,35,1) =0.0066
Decision: p-value is < significance level; we reject the null hypothesis.
[tex]Conclusion: \ There \ is \ sufficient \ evidence \ to \ conclude \ that[/tex] [tex]\mu < 55[/tex]
c)
For x = 56 and s = 5.0
The test statistics can be computed as:
[tex]Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }[/tex]
[tex]Z = \dfrac{56-55}{\dfrac{5.0}{\sqrt{36}} }[/tex]
[tex]Z = \dfrac{56-55}{\dfrac{5.0}{\sqrt{36}} }[/tex]
Z = 1.2
degree of freedom = n - 1
= 36 - 1
= 35
Using the Excel Formula:
P-Value = T.DIST(1.2,35,1) = 0.88009
Decision: p-value is greater than significance level; do not reject [tex]\mathbf{H_o}[/tex]
[tex]Conclusion: \ There \ is \ insufficient \ evidence \ to \ conclude \ that \[/tex] [tex]\mu < 55[/tex]
estimate each product 1/3 x 28
Answer:
28/3 approximated to 9 1/3
Step-by-step explanation:
multiply the fractions and estimate it to it's alternativve form
You are given the following equation: (x+3)^2 + (y+9)^2 = 144 What is the
radius? *
Answer:
12
Step-by-step explanation:
(x-h)^2 + (y-k)^2 = r^2 so taking the square root of 144 gives you 12
Math 7th grade... help pls thanks
Answer:
35
Step-by-step explanation:
1 bracelet costs $7
5 bracelets is 7*5=35
As we can see with the numbers they gave us every bracelet costs 7 dollars, 1 =7, 2=14 and so on. With this information we can just take the number 5 and multiply it by 7 which would equal 35. Or you could add 7 to 21 and then 7 to 28. Whichever one works for you.
Hope this helped
A book has 200 pages. If I have read 1/10 of the part of the book then how much part of the book is left to read.
A) 10
B) 20
C) 180
D) 190
Please give correct answer with explanation.
Answer:
180 pages
Step-by-step explanation:
200*1/10
= 200/10
= 20 pages
total pages =200
read = 20 pages
left to read =200-20
=180 pages
Solve x2 – 3x - 108 = 0.
A. X = -9 and x = 12
B. x = 9 and x = 12
C. X = 9 and x=-12
D. X=-9 and x = -12
Answer:
-9 and 12
Step-by-step explanation:
DJ Ali is making a playlist for a friend; she is trying to decide what 99 songs to play and in what order they should be played. If she has her choices narrowed down to 1616 blues, 2323 country, and 1515 jazz songs, and she wants to play an equal number of blues, country, and jazz songs, how many different playlists are possible
Answer: 1.637 x 10¹⁴ different playlists
Step-by-step explanation: Since DJ Ali needs to choose 9 songs and wishes that the number of blues, country and jazz songs are the same, she needs to pick 3 songs of each type. The total number of ways she can choose the songs, without considering their order is:
The number of possible ways of ordering those nine song is:
There are 1.637 x 10¹⁴ different possible playlist.
Answer:
If she wanted to play 99 songs and play an equal amount of blues, country, and jazz she would play 33 songs from each category.
33 blues
33 country
33 jazz
= 99 songs
Step-by-step explanation:
Please help i need to help
Answer:
4.25
Step-by-step explanation:
Step 1: 23-(17-12)²+6.25
Step 2: 23-5²+6.25
Step 3: 23-25+6.25
what is 66.6% recurring as a fraction?
Answer:
Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is
1
number to the right of the decimal point, place the decimal number over
10
1
(
10
)
. Next, add the whole number to the left of the decimal.
66
6
10
Reduce the fractional part of the mixed number.
66
3
5
Convert
66
3
5
to an improper fraction.
333
5
Step-by-step explanation:
$75 is divided into 5 piles how much in each pile
Answer:
15
Step-by-step explanation:
75/5=15
Answer: 15 dollars in each pile.
Step-by-step explanation:
Since there is 75 in total, and we have to divide the 75 equally between the 5 piles, we can use the division equation: 75 / 5.
75 / 5 = 15.
Therefore, there will be 15 dollars in each pile. Hope this helps and good luck!
Jake has 4 hours before bedtime. He must spend 1 1/2 hours doing homework. The rest of the time will be spent doing puzzles. It takes Jake 3/4 hour to
complete each puzzle. Write an equation that models the number of puzzles (p) that Jake can complete before bedtime.
Answer:
3 1/2 = 1/2*p-2
Explanation: p is number of puzzles
Answer:
He completes 3 1/3 puzzles
Step-by-step explanation:
1 hour 30 mins+ 45 minutes+45 minutes+45 minutes+15 minutes = 4hrs
Solve for z.
2 + 8 - z = -24
Answer:
Z=34
Step-by-step explanation:
Answer:
z = 34
Step-by-step explanation:
Given
2 + 8 - z = -24
Combine Like Terms-
10 - z = -24
Rearrange Terms-
-z + 10 = -24
Subtract 10 from both sides
-z + 10 - 10 = -24 -10
Simplify
-z = -34
Divide -1 from both sides
-z/-1 = -34/-1
Answer-
z = 34
Create and manipulate a data frame.
i) Create a `data.frame` named `my.trees` that has the following columns: - `
Girth = c(10.3, 10.6, 10.8, 13.5, 13.7, 13.8, 14.0)` - `
Height = c(70, 65, 63, 72, 81, 83, 66)` - `
Volume = c(10.3, 10.3, 10.2, 16.4, 18.8, 19.7, 15.6)`
ii) Extract the second observational unit.
iii) Extract the `Height` column referring to it by name.
iv) Print out a data frame of all the observations except for the firt observation.
There are two mystery numbers. The sum of 7 times the first number and 5 times the second number is -11. The sum of 10 times the first number and 8 times the second number is -20. What are the two numbers?
Which inequality is the solution to 20+2 <
Ž -8?
Answer:
the 20 +2
Step-by-step explanation:
Why does paying off the highest interest rate credit card first make the most mathematical sense?
Answer:
Paying off the highest interest rate credit card first makes the most mathematical sense because it will save you more money and allow you to redirect funds to other financial goals faster. Paying off the highest interest rate first is better because this way you get to avoid financial problems and avoid having to pay too much money of interest since the card with the highest interest rate is usually the one that will cause you the most financial pain.
Can someone explain this to me? Pls
Step-by-step explanation:
In Triangle (the symbolΔ)QRS,
Angle R is congruent to Angle Q,
And side QR=11
And side SQ=8
Find.The length of RS.