Answer:
a
[tex]G = 0.007523 [/tex]
b
The number of cars the highway patrol officer would watch before a car that is seen is [tex]E(X) = 1.6027 [/tex]
The standard deviation is [tex]s = 0.9829 [/tex]
gg
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 71.5 \ miles/hour[/tex]
The standard deviation is [tex]\sigma = 4.75 \ miles/hour[/tex]
The speed limit is [tex] x = 70 \ miles /hour[/tex]
Generally the probability of getting a car that is moving with speed greater than the speed limit is mathematically represented as
[tex]p =P(X > x ) = P(X > 70) = P(\frac{X - \mu }{\sigma } > \frac{70 - 71.5 }{4.75})[/tex]
=> [tex] p= P(X > 70) = P(\frac{X - \mu }{\sigma } > \frac{70 - 71.5 }{4.75})[/tex]
=> [tex] p= P(X > 70) = P(\frac{X - \mu }{\sigma } > -0.31579 )[/tex]
Here
[tex]\frac{X - \mu }{\sigma } = Z(The \ standardized \ value \ of X )[/tex]
So
=> [tex] p= P(X > 70) = P(Z > -0.31579 )[/tex]
From the z-table
[tex]p = P(Z > -0.31579 ) = 0.62392[/tex]
So
[tex] p = P(X > 70) = 0.62392 [/tex]
Generally the probability of getting a car that is not moving with speed greater than the speed limit is mathematically represented as
[tex]q = 1 - p[/tex]
=> [tex]q = 1 - 0.62392 [/tex]
=> [tex]q = 0.37608 [/tex]
Generally the probability of getting 5 cars that are not speeding is mathematically represented as
[tex]G = q^5[/tex]
=> [tex]G = (0.37608)^5[/tex]
=> [tex]G = 0.007523 [/tex]
Generally the number of cars that the highway patrol officer is expected to watch until the first car that is speeding is gotten is mathematically represented as
[tex]E(X) = \frac{1}{p}[/tex]
=> [tex]E(X) = \frac{1}{0.62392}[/tex]
=> [tex]E(X) = 1.6027 [/tex]
Generally the standard deviation is mathematically represented as
[tex]s = \sqrt{\frac{1 - p }{ p^2} }[/tex]
=> [tex]s = \sqrt{\frac{1 -0.62392 }{ (0.62392)^2} }[/tex]
=> [tex]s = 0.9829 [/tex]
The probability that 5 cars pass and none are speeding is 0.007523 and the number of cars the highway patrol officer would watch before a car that is seen is E(X) = 1.6027
What is normal a distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
The distribution of passenger vehicle speeds traveling on a certain freeway in California is nearly normal with a mean of 71.5 miles/hour and a standard deviation of 4.75 miles/hour.
The speed limit on this stretch of the freeway is 70 miles/hour.
Generally, the probability of getting a car that is moving with speed greater than the speed limit is mathematically represented as;
[tex]p = P(X > x) = P(X > 70) = P(z = \dfrac{X - \mu}{\sigma } > \dfrac{70 - 71.5}{4.75})\\\\p = P(X > 70 ) = P(\dfrac{X -\mu}{\sigma} > -0.31579)[/tex]
From the z-table
[tex]p = P(X > 70)= P(z > -0.31579) \\\\p = 0.62392[/tex]
Generally, the probability of getting a car that is not moving with speed greater than the speed limit will be
q = 1 - p
q = 1 - 0.62392
q = 0.37608
Generally, the probability of getting cars that are not speeding will be
G = q⁵
G = 0.37608⁵
G = 0.007523
The number of cars that the highway patrol officer is expected to watch until the first car that is speeding is gotten will be
[tex]\rm E(X) = \dfrac{1}{p}\\\\E(X) = \dfrac{1}{0.62392}\\\\E(X) = 1.6027[/tex]
The standard deviation will be
[tex]\sigma = \sqrt{\dfrac{1-p}{p}}\\\\\\\sigma = \sqrt{\dfrac{1-0.63292}{0.62392}}\\\\\\\sigma = 0.9829[/tex]
More about the normal distribution link is given below.
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A rod with the density sigma(x) = 3 + sin(x) lies on the x-axis between x=0 and x = 3pi/4 find the center of mass of the rod
Answer:
10.7 grams
Step-by-step explanation:
hey there, again!
this is a similar process the mass is denisty*area HOWEVER keep in mind it's flat so the area is just x deltax while denisity is 3 + sin(x)
mass of rod = integral 0 to 3pi/4 of (3 + sin(x))*x deltax
= integral 0 to 3pi/4 of 3x + xsin(x) deltax
= 0 to 3pi/4 [3/2*x^2 + x(-cos(x)) + sin(x)]
= 10.7 grams
A line has a slope of -2/3 and passes through the point -3 and eight what is the equation of the line
Answer:
Y=-2/3x+10
Step-by-step explanation:
We have the slope -2/3, so we can find the y intercept by plugging in the given coordinate (-3,8). if y=mx+b, 8=-2/3(-3)+b. If you simplify the equation, you would get 8=-2+b, and then you would get 10=b. 10 would then be the y intercept.
How many atoms is 4.00 grams of iron
(Fe)?
Answer:
226
Step-by-step explanation:
what is the area of the figure?
Answer:
24
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
you can split it into two parts. One with 4 x 3 = 12 and the other with 2 x 6 = 12. then add them together and you get 24.
In a game you have 1/20 probability of winning $76 and a 19/20 probability of losing $9. What is your expected value?
Answer:
1
Step-by-step explanation:
The expected value for the given case is $-4.75.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lies in the close interval of 0 and 1 [0,1].
Given that,
The probability of winning $76 is 1/20.
And, the probability of losing $9 is 19/20.
The expected value for the given probability can be given by taking the product of the probability and the wining or losing amount and then substracting them as,
Expected value = 1/20 × 76 - 19/20 × 9
= 3.8 - 8.55
= -4.75
Hence, the expected value of amount for losing and winning the game is $-4.75.
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what is -7 + 4 = im gonna give you guys 5 days to firgure this out then i will tell the answer
Answer:
negitive 3
Step-by-step explanation:
i think of it like digging. Negitive going down and positive going up aka put dirt down in the whole. so i am down 7 so i add dirt because the 4 is positive. so then i am at 3. wait make that negitive 3. so the answer is negtive 3.
Answer:
-3
Step-by-step explanation:
A team won 8 of 24 games it played in one season what percentage of games did it win
Answer:
it would have won 1/3 or .333333
Step-by-step explanation:
8/24 simplifies to 1/3, which equals .33333
Answer:
I'm pretty sure it's 33%
Step-by-step explanation:
8 is 1/3 of 24 and 1/3 as a fraction is 33%
6/10 as hundredths in fraction form and decimal form
Answer:
60/100 and .6
Step-by-step explanation:
You want to estimate the number of students in your middle school who play video
games. Which of the following would represent a random, valid sample?
O 10 students from your homeroom class
O Your 5 best friends at the lunch table
100 randomly selected people from your apartment complex
O 100 students selected randomly as their enter your middle school in the morning
Answer:
100 students selected randomly as their enter your middle school in the morning
Step-by-step explanation:
Answer:
C (100 students selected randomly from your middle school)
Step-by-step explanation:
The first one is wrong because its only 10 people from your homeroom.
The next one is also wrong sense its only 5 people who could also share the same interests as you.
The next one is wrong because its not from their middle school
That leaves us with the last one, its selected randomly with a lot of people involved from their middle school.
Barbara signed up for dance lessons at Dance Unlimited. She was charged $55 per month for lessons and a one-time recital fee of $165. The equation represents the $495 total cost that Barbara paid to Dance Unlimited. 495 = 165 + 55 m How many months, m, did Barbara receive dance lessons from Dance Unlimited? F. 2.25 months G. 6 months H. 12 months J. 9 months
Answer:
G. 6 months
Step-by-step explanation:
1. 495-165 to remove the one-time payment = 330
2. 330/55 to find the number of months = 6
Barbara receive 6 months of dance lessons from Dance Unlimited
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, Barbara signed up for dance lessons at Dance Unlimited. She was charged $55 per month for lessons and a one-time recital fee of $165.
Let m be the no of months and f(m) is the total cost.
∴ f(m) = 55m + 165.
The equation represents the $495 total cost,
∴ 495 = 55m + 165.
55m = 330.
m = 330/55.
m = 6.
Barbara receives 6 months of dance lessons from Dance Unlimited.
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The length of a rectangular garden is 5 feet less than 4 times its width. Its area is 359 square feet. Find the length and width of the garden. Round answers to the nearest tenth of a foot. Show all work.
Given parameters:
Area of the rectangular garden = 359ft²
Unknown:
length and width of the garden = ?
To find the length and breadth of the garden, we need to define and know that the area of a rectangle is.
Area of a rectangle = Length x Breadth
From the problem statement;
Let w = width of the rectangular garden
L = length of the garden;
Now,
length of a rectangular garden is 5 feet less than 4 times its width
L = 4w - 5
Now let us substitute this into the equation;
Area = L x w
359 = (4w - 5)w
4w² - 5w - 359
Using:
w = -b ± √b² - 4ac / 2a
where b = -5 , a = 4 and c = -359
w = -(-5) ± √-5² - 4(4)(-359) / 2(4)
w = 5 ± √25 + 5744 / 8
w = 5 ± 75.9 / 8
w = [tex]\frac{5 + 75.9}{8} or \frac{5 - 75.9}{8}[/tex]
w = 10.1ft
The other solution is not possible it will be a negative value. Width value cannot be negative.
So L = 4w - 5 = 4(10.1) - 5 = 35.5ft
The length and breadth of the rectangular are 35.5ft and 10.1ft respectively.
How can you solve linear equations by combining like terms?
Answer: In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power. For example, 8xyz² and −5xyz² are like terms because they have the same variables and power while 3abc and 3ghi are unlike terms because they have different variables. Since the coefficient doesn't affect likeness, all constant terms are like terms.
I HOPE THIS HELPED ! :) mark me brainlist pls
Answer:
by combining them like the ordinary like ordinary integers.
Step-by-step explanation:
For example we have
8x + 4y = 3x - 6
you will bring 3x to the left so it will become -3x
8x - 3x + 4y = -6
then combine like terms
there you have
5x + 4y = -6
The given:
8x + 4y = 3x - 6
8x - 3x + 4y = -6
5x + 4y = -6
answer for the example: 5x + 4y = -6
1.
Subtract 24 from the product
of 12 and 8. 24
Answer:
12 multiplied by 8.24=98.88
Subtract 24 from 98.88=74.88
Proof practice for geometry!
Need Help!
idek dwjejdjjriiwknansns
Step-by-step explanation:
nmjwjw
What is the solution to the system of equations?
6x – 9y = 16
2x – 3y = 7
A) (5, 1)
B) (2, -1)
C) (3,
2
9
)
D) no solution
Answer:
no solution
Step-by-step explanation:
[1] 6x - 9y = 16
[2] 2x - 3y = 7
// Solve equation [2] for the variable x
[2] 2x = 3y + 7
[2] x = 3y/2 + 7/2
// Plug this in for variable x in equation [1]
[1] 6•(3y/2+7/2) - 9y = 16
[1] 0 = -5 => NO solution
No solution
Statements with nested quantifiers: English to logic, part 4. About A student club holds an election for officers. Before the voting, members can nominate each other. It is also possible for a member to nominate himself or herself. Some of the members are new members. Some of the members are currently officers. The domain is the set of members of the club. One of the members of the club is named Sam. Define the following predicates. N(x, y): person x nominated person y for a position. W(x): person x is a new member. O(x): person x is currently an officer. Give a quantified expression that is logically equivalent to each of the following statements.
(a) All the new members nominated all the officers.
(b) One of the current officers did not nominate anyone.
(c) Everyone nominated someone.
(d) Someone nominated everyone.
(e) Everyone nominated someone other than themselves.
(f) Exactly one person nominated Sam.
Answer:
someone please answer this equation
Step-by-step explanation:
i have this on my test and i really need help with it
which is the product of 7/9 and 6 in a fraction
Answer: 14/3
Step-by-step explanation: (7/9) (6) = 54/9 = 14/3
You need 660 mL of a 80% alcohol solution. On hand, you have a 40% alcohol mixture. How much of the 40%
alcohol mixture and pure alcohol will you need to obtain the desired solution?
You will need
mL of the 40% solution
and
mL of pure alcohol.
Submit Question
Let a be the amount of 40% solution and b be the amount of pure alcohol that you will use.
You want to end up with a volume of 660 mL, so
a + b = 660
For each mL of solution used, the 40% solution would contribute 0.4 mL of alcohol, and the pure alcohol will contribute 1 mL of alcohol. In the desired solution, you want a concentration of 80% alcohol, so that it contains 0.8 • 660 mL = 528 mL of alcohol, and
0.4a + b = 528
Solve the system of equations above. Subtracting the second from the first eliminates b and lets us solve for a :
(a + b) - (0.4a + b) = 660 - 528
0.6a = 132
a = 220
Then
220 + b = 660
b = 440
So you will need 220 mL of the 40% solution and 440 mL of pure alcohol.
Please help!!!!!!!!!!!!!
Answer:
37, 3, 37
Step-by-step explanation:
If you flip a coin 11 times, what is the probability of ending up with more heads than tails?
Answer:
55%
Step-by-step explanation:
3x square - 6x + 3=0
Answer: 1
Step-by-step explanation:
First you need to multiply 3 x 3 (9), because that's all 3 squared means.
Now the equation should be 9x-6x+3=0
Next we need to combine like terms. Do 9x - 6x which should give you 3x
Now your equations should be 3x+3=0
Now for the somewhat harder part...
Under the three (the one without the x) write -3 and under the zero write the same thing. the +3-3 cancels out so just put a line or something across it.
0-3= -3
so now you should have...
3x=-3 ignore the 3x, at this point it's useless in getting the answer because it would cancel out.
-3 divided by -3 is 1 because a negative (-) divided by a negative (-) equals a positive (+).
The answer should be x = 1
A girl is swimming 1 meter below sea level and dives down another .5 meters. How far below sea level is she now?
Answer:
1.5 meters
Step-by-step explanation:
If she is already below sea level by 1 meter and she goes down .5 meters more, she would be 1.5 meters below the sea level.
What is 6P3? A) 20 B) 18 C) 630 D) 120
Answer:
120
Step-by-step explanation:
Use the permutation and combination formulas to evaluate.
Answer:
20
Step-by-step explanation:
just took the test
Work out the percentage change when 1.20 is increased to 1.80
Answer:
Step-by-step explanation:
PERCENT CHANGE
The percentage change from 1.20 to 1.80 is 50 %
Our percent calculator uses this formula:
((y2 - y1) / y1)*100 = your percentage change
(where y1=start value and y2=end value)
((1.80 - 1.20) / 1.20) * 100 = 50 %
You are buying tickets to a school event. You may purchase at most 8 tickets to receive a discount. Write an inequality to express the number of tickets you can buy with a discount.
Determine if the conclusion that follows from the given statements below is valid. If valid which law was used?
1. if a number is a natural number then it is a whole number
2. if a number is a whole number then it is an integer
Conclusion : if a number is a natural number then it is an integer
Answer:
the conclusion is not valid
Answer: The conclusion is valid by the law of syllogism
The law of syllogism follows the basic form:
If P, then Q
If Q, then R
Therefore, if P then R
We can write it like this
[tex]P \to Q \\\\Q \to R\\\\\therefore P \to R[/tex]
We can think of it like starting at town P, moving to Q, then to R. Or we could go from P directly to R if we aren't worried about the town in the middle (town Q).
What is the solution to this equation?
3(4x + 3) = 2x - 5(3 - x) + 2
A.
o o
O
-
O
D.
-
Answer:
-0.86
Step-by-step explanation:
12x + 9 = 2x - 15 + 5x + 2
Combine
19x = -22
6th grade math i mark as brainly
Answer:
Points G and J are correct.
Step-by-step explanation:
of the 50 students in the cafitera, 7 have red hair. If there are 750 students in the school, predict the number of students who have red hair.
14=−2c−6−3c what is the value of c?
Answer:
c=-4
Step-by-step explanation:
14=-2c-6-3c
14=-5c-6
20=-5c
-4=c
