Answer:
a) 0.0282 = 2.82% probability that all of the sprinklers will operate correctly in a fire
b) 0.6496 = 64.96% probability that at least 7 of the sprinklers will operate correctly in a fire.
Step-by-step explanation:
For each sprinkler, there are only two possible outcomes. Either they will operate correctly, or they will not. The sprinklers activate correctly or not independently, which means that the binomial probability distribution is used to solve this question.
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.
The researchers estimate the probability of a sprinkler to activate correctly to be 0.7.
This means that [tex]p = 0.7[/tex]
10 sprinklers.
This means that [tex]n = 10[/tex]
a. What is the probability that all of the sprinklers will operate correctly in a fire?
This is [tex]P(X = 10)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282[/tex]
0.0282 = 2.82% probability that all of the sprinklers will operate correctly in a fire.
b. What is the probability that at least 7 of the sprinklers will operate correctly in a fire?
This is:
[tex]P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{10,7}.(0.7)^{7}.(0.3)^{3} = 0.2668[/tex]
[tex]P(X = 8) = C_{10,8}.(0.7)^{8}.(0.3)^{2} = 0.2335[/tex]
[tex]P(X = 9) = C_{10,9}.(0.7)^{9}.(0.3)^{1}= 0.1211[/tex]
[tex]P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282[/tex]
Then
[tex]P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.2668 + 0.2335 + 0.1211 + 0.0282 = 0.6496[/tex]
0.6496 = 64.96% probability that at least 7 of the sprinklers will operate correctly in a fire.
Which of the following is the function for the graph below and shows the end behavior of the function as x>-00?
Answer:
A
Step-by-step explanation:
I just used a graphing calculator.
Just type in all the functions and pick the graph and function pair that match the picture.
I hope this helps!
pls ❤ and mark brainliest pls!
Assuming you want x to approach negative infinity, you have the correct answer. It is choice A.
=====================================================
Explanation:
The root x = -2 leads to the factor x+2. That means the answer is between A and B.
As x approaches negative infinity, i.e. as we move to the left, we're going down the red curve and y = f(x) is going to approach negative infinity as well.
In terms of symbols, we'd write [tex]x \to -\infty, \ f(x) \to -\infty[/tex]
Informally, we could say "it falls to the left" as a way to describe this left end behavior.
y = 95°, find the measure of x
9514 1404 393
Answer:
x = 100°
y = 95°
Step-by-step explanation:
It is probably easier to find y first. Opposite angles of an inscribed quadrilateral are supplementary, so ...
y = 180° -85° = 95°
The measure of an arc is double the measure of the inscribed angle subtending it. The arc subtended by angle y is ...
90° +x = 2y
x = 190° -90° = 100°
_____
Additional comment
The rule cited above regarding opposite angles of an inscribed quadrilateral comes from the theorem regarding inscribed angles. In the given diagram, the diagonal from the bottom vertex to the top one is a chord that divides the circle into two arcs. Their sum is 360°. The inscribed angle theorem tells you ...
2y +2(85°) = 360°
y + 85° = 180° . . . . . . . divide by 2; opposite angles are supplementary
Hello! Please help thanks
Answer:
A. [tex]\frac{5}{13}[/tex]
Step-by-step explanation:
Hi there!
We are given right triangle PQR, with PR=5, RQ=12, and PQ=13
We want to find the value of sin(Q)
Let's first recall that sine is [tex]\frac{opposite}{hypotenuse}[/tex]
In reference to angle Q, PR is the opposite side, RQ is the adjacent side, and PQ is the hypotenuse
So that means that sin(Q) would be [tex]\frac{PR}{PQ}[/tex]
Substituting the values of PR and PQ gives sin(Q) as [tex]\frac{5}{13}[/tex], which is A
Hope this helps!
How many ways are there to rearrange the letters of the word: COMBINATION?
Answer: 4,989,600 different ways
Step-by-step explanation:
How much more area does a large pizza with a 12 in. diameter have than a small pizza with an 8 in. diameter? Round your answer to the nearest square inch.
Answer: About 63 in²
Step-by-step explanation:
Area of circle = π · r²
r = radius lengthπ ≈ 3.14Area of large pizza:
[tex]\pi *r^{2} =3.14*6^{2} =3.14*36=113.04[/tex]
Area of small pizza:
[tex]\pi *r^{2} =3.14*4^{2} =3.14*16=50.24[/tex]
Difference in area:
[tex]113.04-50.24=62.8[/tex]
Issac put $5 in a shoe box every day for the months of april, may, and june. He then spent 75% of the money on baseball cards. How much money is left in his shoe box.
A sample of 4 children was drawn from a population of rural Indian children aged 12 to 60 months. The sample mean of mid-upper arm circumference was 150 mm with a standard deviation of 6.73. What is a 95% confidence interval for the mean of mid-upper arm circumference based on your sample
Answer:
The 95% confidence interval for the mean of mid-upper arm circumference based on your sample is between 139.29 mm and 160.71 mm.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 4 - 1 = 3
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 3 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 3.1824
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 3.1824\frac{6.73}{\sqrt{4}} = 10.71[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 150 - 10.71 = 139.29 mm
The upper end of the interval is the sample mean added to M. So it is 150 + 10.71 = 160.71 mm
The 95% confidence interval for the mean of mid-upper arm circumference based on your sample is between 139.29 mm and 160.71 mm.
y you work from 7 a.m. to 4 p.m. The state you live in requires that you take a 30-minute break during any shift longer than 6 hours. This break does not count towards your hours. How many hours did you work today? Remember 30 minutes is equal .5 hours
Answer:
You’ve worked 7 hours and 30 minutes
Step-by-step explanation:
For the function G defined by G(x) = 5x + 3, find G(2)
G(x)=5x+3
[tex]\\ \sf\longmapsto G(2)[/tex]
[tex]\\ \sf\longmapsto 5(2)+3[/tex]
[tex]\\ \sf\longmapsto 10+3[/tex]
[tex]\\ \sf\longmapsto 13[/tex]
Option c is correct
20 POINTS! The answer is x=4 and x= -5, how should I word it, saying how he is wrong?
Answer:
The student took the numbers for the factors 5, -4 for the zeros instead of solving the equation
The zeros are -5, 4
Step-by-step explanation:
x^2 +x - 20=0
What 2 number multiply to -20 and add to 1
5*-4 = -20
5+-4 = 1
(x+5)(x-4) =0
Using the zero product property
x+5 = 0 x-4 =0
x=-5 x=4
Answer:
Solution given:
equation is:
x²+x-20=0
doing middle term factorisation
note:we need to get 1 while subtracting factor of the product of constant and coefficient of x².
20*1=20=2*5*2*1
we get 1 while subtracting 5-2*2=5-4
now substitute value 5-4 at coefficient of x
we get
x²+(5-4)x-20=0
now
distribute
x²+5x-4x-20=0
taking common from each two term
x(x+5)-4(x+5)=0
again taking common (x+5) and keeping remaining at another bracket
(x+5)(x-4)=0
either
x+5=0
x=-5
or
x-4=0
x=4
Error is:
x= 4 not -4
x=-5 not 5.
A.Yes, since the slopes are the same and the y-intercepts are the same.
B.No, since the y-intercepts are different.
C.Yes, since the slopes are the same and the y-intercepts are different.
D.No, since the slopes are different.
Answer:
C
Step-by-step explanation:
one line is
y = 3x/7 + 11
its slope is 3/7
the y-intercept is, of course, when x=0. there y=11
the other is
-3x + 7y = 13
7y = 3x + 13
y = 3x/7 + 13/7
its slope is 3/7 (the same as the other line)
the y-intercept (x=0) is y = 13/7 (different to the other line)
Answer:
C. Yes, since the slopes are the same and the y-intercepts are different.
Step-by-step explanation:
[tex]y=\frac{3}{7} x+11[/tex] and [tex]-3x+7y=13[/tex]
→ Rearrange the second equation to make y the subject
7y = 3x + 13
→ Divide everything by 7
[tex]y=\frac{3}{7} x+\frac{13}{7}[/tex]
A polynomial function has real coefficients, a leading coefficient of 1, and the zeros -6, 1, and 1. Write a polynomial function of least degree in standard form.
Answer:
[tex]{ \sf{ \underline{ {x}^{2} + 5x - 6 }}}[/tex]
Step-by-step explanation:
[tex](x + 6)(x - 1) \\ = {x}^{2} - x + 6x - 6 \\ = {x}^{2} + 5x - 6[/tex]
A four digit password is a number that begins with a 3. If digits can be repeated how many possible passwords are there? show and explain your work
Answer:
The answer is 1,000
SInce the beginning number is 3 and there are ten possible numbers to put in the remaining three slots, there are exactly 1,000 possible combinations for a 3-digit code. The answer is 1,000. There are 3 rows of 10 digits. The number of combinations 10 to the thid power which is 1000 (10 * 10 * 10)
What is the derivative of (x + 1) sin x?
Answer:
By the Sum Rule, the derivative of 1−sin(x) 1 - sin ( x ) with respect to x x is ddx[1]+ddx[−sin(x)] d d x [ 1 ] + d d x [ - sin ( x ) ] .
find x on this special right triangle, 45 is not an option!!!!
let the line between 2 tria be y
sin 60/8√2 = sin 90/y
y=13.06
sin 45/13.06 = sin 90/x
x=18.46
Answer:
First, find the hypotenuse of the right triangle with the 60° & 30°.
Hypotenuse = hsin(x) = opposite side/hypotenuse[tex]sin(60) = \frac{8\sqrt{2}}{h} \\\\sin(60)h=8\sqrt{2}\\\\\frac{\sqrt{3}}{2} h=8\sqrt{2}\\\\h=\frac{8\sqrt{2}}{\frac{\sqrt{3}}{2}}=8\sqrt{2}*\frac{2}{\sqrt{3}} =\frac{16\sqrt{2} }{\sqrt{3}} =\frac{16\sqrt{2}(\sqrt{3}) }{\sqrt{3}(\sqrt{3})} =\frac{16\sqrt{6} }{3}[/tex]
Use that side length to find x.
sin(x) = opposite side/hypotenuse[tex]sin(45)=\frac{\frac{16\sqrt{6}}{3}}{x}\\\\sin(45)x=\frac{16\sqrt{6}}{3} \\\\\frac{\sqrt{2}}{2}x=\frac{16\sqrt{6}}{3} \\\\x=\frac{\frac{16\sqrt{6}}{3}}{\frac{\sqrt{2}}{2}}=\frac{16\sqrt{6}}{3}*\frac{2}{\sqrt{2}}=\frac{16\sqrt{2}\sqrt{3}(2)}{3\sqrt{2} }=\frac{32\sqrt{3} }{3}[/tex]
Operations and scientific notation math project need to know how to find the scientific notation
Answer:
how did not orderstan that
what are the answers to the questions below?
Answer:
You have to follow PEMDAS or parenthesis, exponents, multiplication, division, addition, and subtraction. It's an order to solve equations. I listed the steps and the answers for you below :) I have throughly checked them so they should be correct! yw :D
Step-by-step explanation:
1. 5x + 4x - 6x = 24
9x - 6x = 24
3x = 24
24/3 = 8
x = 8
2. 8y + 5 - 4y + 1 = 46
8y - 4y = 4y
5 + 1 = 6
4y + 6 = 46
4y = 46 - 6
4y = 40
40/4 = 10
y = 10
3. 33 = 5 ( x + 8 ) + 3
33 = 5x + 40 + 3 (because we distributed)
33 = 5x + 43
5x + 43 = 33 (just rewriting it to make it easier)
5x = 33 - 43
5x = -10
-10/5 = -2
so x = - 2
4. 2m + 3 ( m - 8 ) = 1
2m + 3m - 24 = 1
we got 3m - 24 because we distributed the 3
5m - 24 = 1
5m = 25
25/5 = 5
m = 5
5. p + p - 2p + 4p = - 48
2p - 2p + 4p = - 48
4p = - 48
- 48 / 4 = - 12
p = - 12
6. 2 ( y + 5 ) + 3y = 25
2y + 10 + 3y = 25
5y + 10 = 25
5y = 25 - 10
5y = 15
15/5 = 3
y = 3
7. 1/4 h + 3/4 h + 1/2 h + 2 = 5
1/4 h + 3/4 h + 1/2 = 3/2 h
3/2 h + 2 = 5
3/2 h = 5 - 2
3/2 h = 3
h = 2
8. 60 = 4 ( k + 3 ) + 2 ( k - 3 )
60 = 4k + 12 + 2k - 6
4k + 12 + 2k - 6 = 60
6k + 6 = 60
6k = 60 - 6
6k = 54
k = 9
9. - 2 ( d + 1.4 ) - 1.8 = 20.6
-2d + - 2.8 - 1.8 = 20.6
-2d - 2.8 = 22.4
-2d = 25.2
d = - 12.6
10. 8 - 2 ( w + 4 ) = 10
8 + - 2 w + - 8 = 10
-2w + 9 + - 8 = 10
-2w = 10
10 / -2 = -5
w = -5
6) Frazer cycles the first 20 miles at an average speed of 21mph. The second
part is more uphill, and he only manages 13mph. By what percentage did his
speed decrease?
How to solve
9514 1404 393
Answer:
38.1% decrease
Step-by-step explanation:
A percentage change is found from ...
% change = (change)/(original amount) × 100%
= (new value - original amount)/(original amount) × 100%
= (13 -21)/21 × 100% = -8/21 × 100% ≈ -38.1%
Frazer's speed decreased by 38.1% during the second part.
_____
Additional comment
A negative % change represents a decrease; a positive % change represents an increase.
Which side of the pentagon on the right corresponds to
side KJ on the pentagon on the left.
Answer:
side st.Step-by-step explanation:
st corresponds to kj since a it has five sides.Write each percent as a fraction in simple form 15 3/5%
Answer:
39/250
Step-by-step explanation:
15 3/5 = 78/5 and percent means per 100, so
(78/5)/100 = (78/5)(1/100)
=78/500 = 39/250
Please
Help me asap!!
Answer:
z -2 = 10
Step-by-step explanation:
11z-9-10z+7 = 10
Combine like terms on the left side
11z -10z -9+7 =10
z -2 = 10
Answer: z=12
Step-by-step explanation:
[tex]11z-9-10z+7=10\\z-9+7=10\\z-2=10\\z=12[/tex]
12 workers take 4 hours to complete a job. How long would it take 15 workers to complete the job?
Answer:
3.2 hours
Step-by-step explanation:
12 workers * 4 hours = 48 worker hours
15 workers * x hours = 48 worker hours
48 /15 =3.2 hours
Answer:
3 hours and 12 minutes.
Step-by-step explanation:
12 Workers complete a job in 4 hours
1 worker complete a job 12 × 4 = 48
15 workers complete a job = 48/15 = 3³/¹⁵ = 3¹/⁵
= 3 hours + 1/5 × 60 minutes = 3 hours 12 minutes.
Simplify the following expression:
Step-by-step explanation:
[tex]{ \bf{( \frac{ - 10 {a}^{3} {b}^{5} \times 6 {a}^{6} {b}^{2} }{ {12a}^{9} {b}^{5} } ) {}^{3} }} \\ \\ = { \sf{( \frac{ - 60 {a}^{9} {b}^{7} }{12 {a}^{9} {b}^{5} } ) {}^{3} }} \\ \\ = { \sf{(5 {b}^{2}) {}^{3} }} \\ = { \sf{125 {b}^{5} }}[/tex]
Execute the following 18/3+2*8-5.
Aakash, Bao Ying, Chris and Donna all live on the same street as their school, which
runs from east to west.
• Aakash lives 5 blocks to the west.
• Bao Ying lives 4 blocks to the east.
• Chris lives 2: blocks to the west. .
• Donna lives 61 blocks to the east.
a. Draw a picture that represents the positions of their houses along the street.
b. Find how far is each house from every other house?
c. Represent the relative position of the houses on a number line, with the school at
zero, points to the west represented by negative numbers, and points to the east
represented by positive numbers.
d. How can you see the answers to part (b) on the number line? Using the numbers
(some of which are positive and some negative) that label the positions of houses on
the number line, represent these distances using sums or differences.
ko
The distance between each of the students' houses are:
Aakash & Bao Ying live 9 blocks away from each other
Aakash & Chris live 3 blocks away from each other
Aakash & Donna live 66 blocks away from each other
Bao Ying & Chris live 6 blocks away from each other
Bao Ying & Donna live 57 blocks away from each other
Chris & Donna live 63 blocks away from each other
To solve this question, we represent each with the first letter of their names.
So, we have:
[tex]A= 5\ west[/tex] --- Aakash
[tex]B= 4\ east[/tex] ---- Bao Ying
[tex]C = 2\ west[/tex] --- Chris
[tex]D = 61\ east[/tex] ---- Donna
I've added the picture and the number line that represent the scenario as an attachment.
To calculate how far each lives from each other's, we start by representing west as negative and east as positive.
So, the representations become:
[tex]A = -5[/tex]
[tex]B = 4[/tex]
[tex]C = -2[/tex]
[tex]D = 61[/tex]
The absolute difference of each represents how far they live from one another.
Aakash & Bao Ying Aakash & Chris Aakash & Donna
[tex]AB = |-5 -4| =9[/tex] [tex]AC = |-5 --2| =3[/tex] [tex]AD = |-5 -61| =66[/tex]
Bao Ying & Chris Bao Ying & Donna
[tex]BC = |4 --2| =6[/tex] [tex]BD = |4 -61| =57[/tex]
Chris & Donna
[tex]CD = |-2 -61| =63[/tex]
This means that
Aakash & Bao Ying live 9 blocks away from each other
Aakash & Chris live 3 blocks away from each other
Aakash & Donna live 66 blocks away from each other
Bao Ying & Chris live 6 blocks away from each other
Bao Ying & Donna live 57 blocks away from each other
Chris & Donna live 63 blocks away from each other
To carry out the above computations from the number line, we simply count the numbers from one to the other.
For instance:
There are 3 numbers from Akash to Chris.
This means that: Aakash & Chris live 3 blocks away from each other
Learn more about number line at:
https://brainly.com/question/13189025
k = 2; f(x) = 2x3 + 3x2 - 4x + 4; Lower bound? (1 point)
A cement mixture costs $33 a ton. It is composed of Grade A cement at $36 a ton and Grade B cement at
$24 a ton. How were these two cements mixed?
Slide 1.
1) The polygons below ore similor. Find the value of y.
8.
10
Answer:
y =6
Step-by-step explanation:
We can write a ratio to solve
3 y
----- = ----------
4 8
Using cross products
3*8 = 4y
24 = 4y
Divide by 4
24/4 = 4y/4
6 = y
On the first day of travel, a driver was going at a speed of 40 mph. The next day, he increased the speed to 60 mph. If he drove 2 more hours on the first day and traveled 20 more miles, find the total distance traveled in the two days.
The Total mileage is "400" and the further solution can be defined as follows:
Let t become the time he spent commuting on the first day of his vacation.
It is then calculated as [tex]t + 2[/tex].
[tex]\to 40\times(t+2) = 60(t) + 20 \\\\\to 40t+80 = 60t + 20 \\\\\to 80-20 = 60t + 40t \\\\\to 60 = 20t \\\\\to t=\frac{60}{20} \\\\\to t=\frac{6}{2} \\\\\to t= 3\\\\[/tex]
It traveled [tex]40\times (3 + 2) + 20 = 40\times 5 + 20 = 200+20=220[/tex] miles on its first day of operation.
The car traveled [tex]180\ miles[/tex] on the second day, which was [tex]60 \ miles \times 3[/tex].
So,
Total mileage= first day traveled + second day traveled [tex]= 220+ 180= 400 \miles[/tex]
Learn more:
Total distance traveled: brainly.com/question/20670144
i don’t quite get the concept yet and i really don’t wanna bother the teacher again :/ please help
Answer:
they are asking which claims are true vs false
Step-by-step explanation:
I totally get not wanting to bother our teachers again,... (that is why we're here)
m (AB = 20
m<ABD = 140
m (AD = 60
I think they want to know which ones (based on the "graph") are true,...
