Using the binomial distribution, we find that:
a) There is a 0.648 = 64.8% probability that there will be at least two hurricanes from which the home will experience no damage before the second hurricane from which the home will experience damage.
b) There is a 0.1728 = 17.28% probability that the home will experience its second damage from the fourth hurricane, given that the home has not experienced two damages from the first two hurricanes.
c) The mode is of 7.5 hurricanes.
For each hurricane, there are only two possible outcomes. Either it causes damage, or it does not. The probability of the home experiencing damage from a hurricane is independent of any other hurricane, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
It gives the probability of exactly x successes on n trials, with p probability.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The mode of the number of trials needed for q successes is given by:
[tex]M = \frac{q}{p}}[/tex]
In this problem, there is a 0.4 probability of experiencing damage from a hurricane, thus [tex]p = 0.4[/tex].
Item a:
This is the probability of at most 1 damage in 3 hurricanes, which is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
With [tex]n = 3[/tex].
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.4)^{0}.(0.6)^{3} = 0.216[/tex]
[tex]P(X = 1) = C_{3,1}.(0.4)^{1}.(0.6)^{2} = 0.432[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.216 + 0.432 = 0.648[/tex]
0.648 = 64.8% probability that there will be at least two hurricanes from which the home will experience no damage before the second hurricane from which the home will experience damage.
Item b:
1 in the first three, with 0.432 probability.Damage in the fourth, with 0.4 probability.Then
[tex]0.432(0.4) = 0.1728[/tex]
0.1728 = 17.28% probability that the home will experience its second damage from the fourth hurricane, given that the home has not experienced two damages from the first two hurricanes.
Item c:
Damage from 3 hurricanes, thus q = 3.Then:
[tex]M = \frac{3}{0.4}} = 7.5[/tex]
The mode is of 7.5 hurricanes.
A similar problem is given at https://brainly.com/question/24923631
The lunch check is $16.98. Estimate the tip
using a rate of 15%
Find the value of y' when x
O if
xy^8 + e^y/5 =
= e.
It looks like the given equation says
[tex]xy^8 + e^{y/5} = e[/tex]
When x = 0, you have
[tex]0\cdot y^8 + e^{y/5} = e \\\\ e^{y/5} = e^1 \\\\ \dfrac y5 = 1 \\\\ y=5[/tex]
Differentiating both sides with respect to x gives
[tex]\left(xy^8 + e^{y/5}\right)' = e' \\\\ \left(xy^8\right)' + \left(e^{y/5}\right)' = 0 \\\\ x\left(y^8\right)' + x'y^8 + e^{y/5}\left(\dfrac y5\right)' = 0 \\\\ 8xy^7y' + y^8 + \dfrac15e^{y/5}y' = 0[/tex]
That is, the derivative operator distributes over sums, and the derivative of a constant is 0; apply the product rule on the first term and chain rule on the second; then use chain rule one more time.
Now plug in x = 0 and y = 5, and solve for y' :
[tex]8\cdot0\cdot5^7y' + 5^8 + \dfrac15e^{5/5}y' = 0 \\\\ 5^8 + \dfrac15e y' = 0 \\\\ \dfrac15e y' = -5^8 \\\\ y' = \boxed{-\dfrac{5^9}e}[/tex]
(7x³-11x-1)-(12x³+x²-8)
Answer:
[tex]- 5 {x}^{3} - {x}^{2} - 11x + 7 \\ [/tex]
Step-by-step explanation:
Before solving that we have to know that,
[tex]( + ) \times ( + ) = ( + ) \\ ( - ) \times (- ) = ( + ) \\ ( + ) \times ( - ) = (- )[/tex]
Let's solve now.
[tex]7 {x}^{3} - 11x - 1 - (12 {x}^{3} + {x}^{2} - 8) \\ 7 {x}^{3} - 11x - 1 - 12 {x}^{3} - {x}^{2} + 8 \\ 7 {x}^{3} - 12 {x}^{3} - {x}^{2} - 11x - 1 + 8 \\ = - 5 {x}^{3} - {x}^{2} - 11x + 7[/tex]
Hope this helps you.
Let me know if you have any other questions :-):-)
What were some of their hardships in r obstacles that Martin Luther king jr had in their life?
In your own words
Answer: I would say that some of the Three challenges Martin Luther King Jr. faced in the battle for equal rights included the opposition of "good" white people to his tactics, his realization that the only way to win civil rights was to proceed nonviolently, and pushback against his plan in the late 1960s to unite Black people and white people in a war on poverty.
Step-by-step explanation:
Answer:
Martin Luther king faced many hardships and challenges in the duration of his life. His right to freedom of speech was violated constantly, resulting in him to get arrested, threatened, bombed, and even stabbed. He was targeted by people who didn’t want change. They wanted things to stay the way they were, where segregation was enforced, and the inequality of races continued. Although he was a subject to violence all his life, he never gave up and his dream impacted the world and became a reality.
Step-by-step explanation:
What is the inverse of the function g(x) = x^3/8 + 16 ?
Answer:
[tex] \hookrightarrow \: { \rm{f(x) = \frac{ {x}^{3} }{8} + 16}} \\ [/tex]
• let f(x) be m:
[tex]{ \rm{m = \frac{ {x}^{3} }{8} + 16}} \\ [/tex]
• make x the subject of the function:
[tex]{ \rm{8m = {x}^{3} + 128}} \\ \\ { \rm{ {x}^{3} = 8m - 128 }} \\ \\ { \rm{ {x}^{3} = 8(m - 16) }} \\ \\ { \rm{x = \sqrt[3]{8} \times \sqrt[3]{(m - 16)} }} \\ \\ { \rm{x = 2 \sqrt[3]{(m - 16)} }}[/tex]
• therefore:
[tex]{ \boxed{ \rm{ {f}^{ - 1} (x) = 2 {(m - 16)}^{ \frac{1}{3} } }} }\\ [/tex]
Right triangle CDE has its right angle at vertex
D. The length of DE is 8 feet and the length of
CE is 17 feet. What is the length, in feet, of CD?
A) 11
B) 12
C) 14
D) 15
The length of the side CD which is the base of the right triangle CDE is 15 feet which is option D.
We have,
We can use the Pythagorean theorem to solve for the length of the height CD in the right triangle CDE.
Where CE is the hypotenuse and De is the base.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we have:
CD² + DE² = CE²
Plugging in the given lengths:
CD² + 8² = 17²
CD² + 64 = 289
CD² = 289 - 64
CD² = 225
CD = √225
CD = √15²
CD = 15
Thus,
The length of the side CD which is the base of the right triangle CDE is D. 15 feet.
Learn more about the Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ3
What is the 7th term of the sequence 64, -16, 4, -1?
Answer:
0.25
Step-by-step explanation:
the pattern is dividing by -4. so divide -1 by -4 and you get 0.25.
Rajan had Rs. 6000 in his bank account on a particular day. A week later he deposited Rs.
1500 and next day, he had to withdraw ଵ
ଷ
rd of his total balance. Find his balance amount in
the bank after withdrawal.
step by step plzzz
Answer:
Step-by-step explanation:
Deposited 60000(debit)
cash 60000(credit)
Deposited 1500(debit)
cash 1500(credit)
debit 61500 credit 61500
The following figures are similar. Solve for x.
Answer:
i need a picture
Step-by-step explanation:
pls help find the area of this triangle
Answer:
c
Step-by-step explanation:
h × b then Divide by 2......
3. A cookie recipe called for 3 1/2 cups of sugar for every 2 1/6 cups of flour.
a. What is the unit rate of cups of
sugar to cups of flour?
b. How many cups of sugar would
you need if you used 6 cups of
flour?
3.5 to 2.167
2.80
Step-by-step explanation:
- What is 175% of 852
Answer:
1491
Step-by-step explanation:
1.75 times 852 equals 1491
Kala is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges $ 79 and allows unlimited mileage.
Company B has an initial fee of $65 and charges an additional $0.70 for every mile driven.
For what mileages will Company A charge less than Company B?
Use m for the number of miles driven, and solve your inequality for m.
Answer: 21 miles
Step-by-step explanation:
what number is the opposite of - 5/12
Answer:
5/12
Step-by-step explanation:
opposite is on the other side of the number line. 5/12 is the answer
I NEED HELP ON THIS SO I CAN PASS
Answer:
the answer is 1st.
because _ ✖️ _= +
Another way to write above expression is :
[tex]{ \bigg( - \dfrac{2}{3} \bigg) }^{2} [/tex]Am i right on this one?
Answer:
yes
Step-by-step explanation:
brainliest please
Yes this is correct, i cant really explain since i already did this question on paper but I CAN tell you it is right
What is the quotient in the simplest form ? 3/5 divided by 2/7
Does anyone know this?
Answer:
8/21
Step-by-step explanation:
-1/3 + 5/7=1×7 =-7/21 +15/21
- × -
3. 7
-7/21 + 15/21= -7+15 = 8/21
-----
21
What is the difference in length between the shortest worm (3/4) and the longest worm (1 1/2)
Answer: 3/4 difference
Step-by-step explanation:
Turn 1 1/2 improper = 3/2
Multiply it by 2 (to make the denominator the same)
Do 6/4 minus 3/4 to get 3/4 as your answer.
Hope that helps! :))
q(x)= 1/2x - 3; q(x) =-4. Find the value of x
Answer:
[tex]q(x) =-5[/tex]
Step-by-step explanation:
I am solving this using Function Notation.
We are given:
[tex]q(x)= \frac{1}{2}x - 3[/tex]
While we are to find:
[tex]q(x) =-4[/tex]
In Function Notation, replace all the "[tex]x[/tex]" you see with the value you are given.
So, in this case,
[tex]q(x)= \frac{1}{2}x - 3\\\\=\frac{1}{2}x - 3[/tex]
Would become
[tex]q(x)= \frac{1}{2}x - 3\\\\=\frac{1}{2}(-4) - 3[/tex]
Now we can solve.
[tex]\frac{1}{2}(-4) - 3[/tex]
Use PEMDAS; Parenthesis first;
[tex]\frac{1}{2}(-\frac{4}{1})[/tex]
Cross divide: 1 cancels 1, -4 ÷ 2 = -2
Hence, we are left with
[tex](-2) - 3[/tex]
[tex]-5[/tex]
Therefore, the value of x is -5
or
Joey bought 3 packs of white T-shirts and 5 packs of blue T-shirts for his basketball team. The white T-shirts come in packs of 9, and the blue T-shirts come in packs of 7. How many T-shirts did Joey buy in all?
is the product of 2 numbers always the LCM
Answer
I guess so.
To find the LCM you need to know the lowest digit as possible.
For example,
Question: What is the LCM of 8 and 6?
Answer: Table of 8: 8, 16, 24, 32, 40,48
Table of 6: 6, 12, 18, 24, 30, 36, 42, 48
Now look at the tables again and, did you see the LCM???......
If so your answer would be 24.
Step-by-step explanation:
Whoever answers I’ll mark brainliest
Answer:
Right Triangle.
Step-by-step explanation:
A right triangle always has a 90 degree angle.
Answer:Right angle
Step-by-step explanation:the box down there signals its a 90 degree angle
3/5x+1/4=-1/2 standard form
Answer:
Hello there your answer is 12 x + 5 y = − 10!
36 workers can complete a piece of work in 12 days how many workers should be removed to complete the same work in 24 days
please explain step by step
Two friends go out to eat and order the same meal. They pay a 6% sales tax and a 20% tip on their meals. The total bill, including tax and tip, is $27.72. How much did each meal cost before tax and tip? (Assume that the friends pay a tip on the cost of the meals only.) IF CORRECT I WILL GIVE BRAINLIEST!!
Sales tax and tip will increase the price of an item.
The cost of each meal is: $10.89
Let the cost of both meals be x.
A 20% tip means that, the current price is:
[tex]Price = x \times (1 + 20\%)[/tex]
A 6% sales tax on the meal means that, the current price is:
[tex]Price = x \times (1 + 20\%) \times (1 + 6\%)[/tex]
So, we have:
[tex]Price = x \times (1 + 0.20) \times (1 + 0.06)[/tex]
[tex]Price = x \times (1.20) \times (1.06)[/tex]
[tex]Price = x \times 1.272[/tex]
The amount paid is $27.72
So, the equation becomes
[tex]27.72= x \times 1.272[/tex]
Make x the subject
[tex]x = \frac{27.72}{1.272}[/tex]
[tex]x = 21.78[/tex]
So, the cost of each meal is:
[tex]Each= \frac{21.78}{2}[/tex]
[tex]Each= 10.89[/tex]
Hence, the cost of each meal is: $10.89
Read more about sales tax at:
https://brainly.com/question/19715580
Algebra 2 Need help with b
Answer:
a. was incorrect a = -0.109569028 so...
y = -0.109569028(x + 7)² + 54
b. It's been the above vertex equation for a parabola then
set y = 40 equal to the parabolic equation, we get
40 = -0.109569028x² - 1.533966392x + 48.631117628
solve for x we get
x = -18.3036867393939 or ~ 18.3 feet
Step-by-step explanation:
y = a(x - h)² + k
(h, k) = vertex = (-7, 54)
x = h is the axis of symmetry -7
y = a(x -(-7))² + 54
y = a(x + 7)² + 54
solve for a by inputting the point (15.2, 0)
0 = a(15.2 + 7)² + 54
-54 = a(22.2)²
-54 = 492.84a
a = -54/492.84
a = -0.109569028
Equivalent fractions
Answer: Like 1/3=2/6 and 2/3=4/6, 1/4=2/8 then 3/4=6/8.
Step-by-step explanation: Hope this help. hit me up if u need some more help
Answer:
1) 1/2 = 18/36 = 9/18 = 8/16 = 21/42 = 24/48
2) 5/6 = 40/48 = 10/12 = 25/30 = 15/18 = 20/24
3) 1/3 = 3/9 = 9/27 = 30/90 = 2/6 = 4/12
4) 3/4 = 18/24 = 12/16 = 6/8 = 15/20 = 27/36
5) 4/9 = 8/18 = 20/45 = 16/36 = 24/54 = 12/27
Step-by-step explanation:
The main explaination for this is to take your denominator -- your bottom number of the fraction -- and divide it by the denominator to which you're trying to compare it to. Multiply your numerator to the compared to find your full fraction.
For example, say the fraction is 1/2. You're trying to figure out it's equivalent through the pair _/100. Take your 100 and divide it by 2, your other denominator, which leaves you with 50. Take the 50 and multiply it by the compared numirator to find your full fraction, which in this case is 50/100.
Hopes this helps you!
A shop sells packs of black pens, packs of red pens and packs of green pens.
There are
2pens in each pack of black pens
5 pens in each pack of red pens
6 pens in each pack of green pens
On Monday,
number of packs
of black pens sold:
number of packs of red pens sold: number of packs of green pens sold =7:3:4
A total of 212 pens were sold.
Work out the number of green pens sold.
Answer:96 green pens
7x ,3x,4x
assume that the black pens amd red pens and green pens are sold respictely
7x.2+3x.5+4x.6=212
53x=212
x=4
number of green pens sold
4x.6=4x4x6=96
What is -5 - 9 - 13 equal to?
Answer: -27
Step-by-step explanation: subtract -5 and - 9 to get -14, then subtract -13 and -14 to get -27
