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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Henry is filling up his fish tank with water at a constant rate.
At 2 minutes the water level is 16 cm. At 8 minutes the water level is at 34 cm.
Explain how you figured out the water level at 0 minutes.
Answer:
It would have started to be filled at 10 cm
Step-by-step explanation:
FInd teh difference between 8 and 2 which is 6
Find the difference between 34 and 16 which is 18
Divide 18 by 6 which is 3
Subtract 2(3) = 6 by 16 which is 10
Using the linear system to solve the problem. Then the water level at 0 minutes is 10 cm.
What is the linear system?It is a system of an equation in which the highest power of the variable is always 1. It is a combination of infinite points side by side.
Given
Henry is filling up his fish tank with water at a constant rate.
At 2 minutes the water level is 16 cm.
At 8 minutes the water level is at 34 cm.
We know that the linear equation
[tex]\rm y = mx +c[/tex]
Where
m be the rate of filling water in the tank.
c be the initial water in the tank.
y be the water level of the tank in cm.
x be the time in minutes.
At 2 minutes the water level is 16 cm. Then
[tex]\rm 16 = 2m + c[/tex] ...1
At 8 minutes the water level is at 34 cm. then
[tex]\rm 34 = 8m +c[/tex] ...2
From equations 1 and 2, we have
m = 3, and c = 10
Then the equation will be
[tex]\rm y = 3x + 10[/tex]
For x = 0, then y = 10
Thus, the water level at 0 minutes is 10 cm.
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Find the value of x so that f(x)=7.
Answer:
slope: 0
y intercept: (0, 7)
Step-by-step explanation:
To which set or sets of numbers does the number 5 belong?
Answer:
what are the options
Step-by-step explanation:
i would help but I don't know what to answer
Write the following equation in slope intercept form:
y + 9 = 3(x - 1)
The slope intercept form of the given equation y + 9 = 3(x - 1) is
y =3x-12 .
What is slope intercept form ?
The slope intercept is a form of two variable linear equation in x, y is given by
y = m x + c
y is y coordinate, x is x coordinate , m is called slope , c is y intercept
For the given equation
y + 9 = 3(x - 1)
⇒ y + 9 = 3x -3
Subtracting 9 from both sides of this equation, we get
⇒ y+9-9 = 3x-3-9
⇒ y = 3x - 12
This is the slope intercept form with m = 3 and c = -12
Therefore , the slope intercept form of the equation y + 9 = 3(x - 1) is
y =3x-12
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What value of x is in the solution set of 2(3x-1) 24x 6? a-10 b-5 c-3 d 1
Answer:
-1
Step-by-step explanation:
Step 1: Write inequality
2(3x - 1) ≥ 4x - 6
Step 2: Solve for x
Distribute 2: 6x - 2 ≥ 4x - 6Subtract 4x on both sides: 2x - 2 ≥ -6Add 2 to both sides: 2x ≥ -4Divide both sides by 2: x ≥ -2Step 3: Find
-10 ≥ -2? No
-5 ≥ -2? No
-3 ≥ -2? No
-1 ≥ -2? Yes
Test 4,580 for divisibility by 2, 3, 5, 9, and 10.
By 2 = 2290
By 3 = about 1526.6667 or you can just write 4580/3
By 5 = 916
By 9 = about 508.8889
By 10 = 458
1.
Solve -x + 9x = -4
Solution x= and x =
Answer:
x = - 1/2Step-by-step explanation:
-x + 9x = -4
8x = -4
x = -4/8
x = -1/2
SOMEBODY HELP PLS, WILL GIVE BRAINLIEST TO RIGHT ANSWER
Answer:
a. I, III, II
Step-by-step explanation:
To answer this question, lets take a look at I, II, and III.
First, lets take a look at I. It states that the m∠SQT = 180 by the definition of a straight angle. We can get that the m∠SQT = 180 just by looking at the image and by knowing our second given. So I just has to be below the second given.
Now, lets take a look at II. It states that m∠SQV + m∠VQT = 180 by the Substitution Property of Equality. We can find that m∠SQV + m∠VQT = 180 just by looking at the image along. But knowing that it is found by the Substitution Property of Equality, we can find that m∠SQV + m∠VQT = 180 was derived from the fact that m∠SQT = 180 and that m∠SQV + m∠VQT = m∠SQT, or I and III. So II was derived from I and III, and II should come after I and III.
Now lets look at III. It states that m∠SQV + m∠VQT = m∠SQT by the Angle Addition Postulate. Since III is found by the Angle Addition Postulate, we can find that III was derived from I, and III should come after I.
So knowing that II should come after III and I, and that III should come after I, we can find that the order should be I, III, II.
I hope you find my answer and explanation to be helpful. Happy studying.
11. Solve the following equation. –4 = seven over thirty-three times x (1 point) x = one hundred thirty two over seven x = Negative one hundred thirty two over seven x = Negative seven over one hundred thirty two x = Negative thirty three over twenty eight
Answer:
C. x = Negative seven over one hundred thirty two
Step-by-step explanation:
Solve the following equation.
–4 = seven over thirty-three times x
A. x = one hundred thirty two over seven
B. x = Negative one hundred thirty two over seven
C. x = Negative seven over one hundred thirty two
D. x = Negative thirty three over twenty eight
Evaluate the function for the indicated input
[tex]f(0)=0^2+0-6=\boxed{-6}[/tex].
Hope this helps.
A box of LED light bulbs was tested to see how long the light bulbs last. The standard deviation of the light bulb lifetime data was five years. Which of the following is the best interpretation of this value?
Fifty percent of the light bulb lifetime data is below five years.
The difference between the longest and shortest light bulb lifetime was five years.
The lifetime of the light bulbs typically varies by about five years from the mean.
The middle half of the light bulb lifetime data has a range that is five years wide.
The difference between the longest and shortest light bulb lifetime was five years is correct interpretation so option (B) will be correct.
What is the standard deviation?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.
In other meaning, standard deviation shows the deviation of the value of data from the mean.
Standard deviation is how much-given data is deviate from the mean of it.
So the difference between the longest to shortest gives an idea about this deviation.
Hence "The difference between the longest and shortest light bulb lifetime was five years is a correct interpretation".
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find the area of each shaded region
Which product is negative?
0 -3.4.(-2) · (–7)
0 -3.5.(-6). 4
0 -4.(-6) · (-3) - (-5)
0 -7.(-3) · (–9). O
Answer:
The answer would be -3.5.(-6). 4
Step-by-step explanation:
Solve for x: [x] - 8 = -5
O x = -13 and x = -3
O x = 3 and x = -3.
O x = 3 and x = 13
O No solution
A person invested $6,000 in an account growing at a rate allowing the money to
double every 11 years. How much money would be in the account after 19 years, to the
nearest dollar?
Answer:
P(19)=$19,852
To the nearest dollar.
Step-by-step explanation:
Exponential Growth
The natural growth of some magnitudes can be modeled by the equation:
[tex]P(t)=P_o(1+r)^t[/tex]
Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.
We are given the condition that an investment of Po=$6,000 in an account doubles every 11 years. The final value of the investment in t=11 is P(11)=$12,000.
Substituting into the general equation:
[tex]12,000=6,000(1+r)^{11}[/tex]
Dividing by 6,000 and swapping sides:
[tex](1+r)^{11}=2[/tex]
Taking the 11th root:
[tex]1+r=\sqrt[11]{2}[/tex]
[tex]1+r=1.065[/tex]
Substituting into the formula:
[tex]P(t)=6,000(1.065)^t[/tex]
Now we need to find the money in the account after t=19 years:
[tex]P(19)=$6,000(1.065)^{19}[/tex]
P(19)=$19,852
To the nearest dollar.
The remainder after diving x^4+3x^3-8x^2+5x-9 by x+5 is ____.
Use the polynomial remainder theorem. It says that a polynomial [tex]f(x)[/tex] has remainder [tex]f(c)[/tex] upon division by [tex]x-c[/tex].
Here we have
[tex]f(x)=x^4+3x^3-8x^2+5x-9[/tex]
and [tex]c=-5[/tex], so the remainder is
[tex]f(-5)=(-5)^4+3(-5)^3-8(-5)^2+5(-5)-9=\boxed{16}[/tex]
H-E-B sells steak for $6.10 per pound. What would be the cost of 2.6 pounds of steak
Answer:
the answer is $15.86
Simplify by dividing 3/5 divide by (-4/9).
Answer:
a)-27/20
Step-by-step explanation:
3/5 ÷ (-4/9)
3/5 × (-9/4)
-27/20
Hope it will help
Baron, Gab, and Oliver can paint a room together in 2 hours, 1f Gab does the job alone. he can paint the same room in 5 hours. If Baron works alone, he can paint the room in hours. If Oliver works alone, how long would it take him to paint the room?
Answer:
11 hours
Step-by-step explanation:
I hope this help!
What type of number is 8/2?
Choose all answers that apply:
А
Whole number
B
Integer
C
Rational
D
Irrational
Answer:
A,B,C
Step-by-step explanation:
It is A because 8/2 simplifies to 4 which is a whole number.
4 is an integer, idk if its asking for 8/2 as itself but a fraction isnt an integer.
The fraction above is obviously rational number.
All the types for the number 8/2 is,
A. Whole number
B. Integer
C. Rational
Given that,
The number is,
⇒ 8/2
Now, simplify the number as,
⇒ 8/2
⇒ 4
Clearly, 4 is a whole number and it is an integer.
Here, 4 is written as, 4/1
So, it is also an rational number.
So, the correct options are,
A. Whole number
B. Integer
C. Rational
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An app developer projects that he will earn $20.00 for every 8 apps downloaded. Write
an equation to represent the proportional relationship between the number of apps and the total earnings
y = 2.5x
I hope this helps
The required equation is y=2.5x.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Given that,
Earning of app developer for 8 apps = $20.00
Earning of app developer for 1 app = $2.5
Earning of app developer for x app = $2.5x
Assume, earning of app developer for x app is y
So the equation,
Earning of app developer y=2.5x
The required equation is y=2.5x.
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Planet Earth has a mass of 5.9726 × 10 24 kilograms. And although 70% of the Earth's surface is made of water, the water's mass is only 5 × 10 -4 percent of the Earth's total mass. Use scientific notation to estimate the mass of the planet's water. In your final answer, include all of your estimates and calculations.
Given parameters:
Mass of the earth = 5.9726 x 10²⁴kg
Mass of percent water on earth = 5 x 10⁻⁴% of the total mass of the earth
Unknown:
Mass of water on earth = ?
Solution
This is pretty straight forward;
Mass of water on earth = mass percent of water x mass of earth
Input the parameters and solve;
Mass of water on earth = [tex]\frac{5 x 10^{-4} }{100}[/tex] x 5.9726 x 10²⁴
= 5 x 10⁻⁴ x 10⁻² x 5.9726 x 10²⁴
= 5 x 5.9726 x 10⁻⁴⁺⁽⁻²⁾ ⁺²⁴
= 29.863 x 10¹⁸kg
or 2.9863 x 10¹⁹kg
Mass of water on earth is 2.9863 x 10¹⁹kg
Find the intercepts of the given line:
y=−6x+21
Answer:
x-intercept = 3.5y-intercept = 21Step-by-step explanation:
x-intercept is for y = 0
y-intercept is for x = 0
Substitute
For y = 0
-6x + 21 = 0 |subtract 21 from both sides
-6x = -21 |divdie both sides by (-6)
x = -21/(-6)
x = 21/6
x = 3.5
For x = 0
y = -6(0) + 21
y = 0 + 21
y = 21
The Corner Cafe offers a 10% off senior citizen discount. If Mr. and Mrs. Schmidt order $36.00 worth of food and are senior citizens, how much can they expect to save?
Answer:
$3.60
Step-by-step explanation:
$36.00 × 10%= $3.60
PLS HELP QUICK WILL GIVE BRAINLIEST!!!!
Answer:
what is the question you need done..?i cant see the question
of equ
final equation is a true sta
A 4x - 3= 2x + 13
Answer:
8
Step-by-step explanation:
Step 1:
4x - 3 = 2x + 13 Equation
Step 2:
4x = 2x + 16 Add 3 on both sides
Step 3:
2x = 16 Subtract 2x on both sides
Step 4:
x = 16 ÷ 2 Divide
Answer:
x = 8
Hope This Helps :)
Answer:
x=8
Step-by-step explanation:
4X-3=2x+13
+3. +3
4X=2x+16
-2x. -2x
2x=16
/2. /2
x=8
PLEASE HELP ME MY TEACHER IS MAKING ME REDO THIS AND I'M GONNA FAIL HER CLASS IF I DON'T FINISH THIS
Answer:
8 3/4 ?
Step-by-step explanation:
divide
srry if its not what your looking for
Which expression is the result of factoring the expression below by taking out its greatest common factor?
4x^2+ 16x– 4 = ?
Answer:
Step-by-step explanation:
If you factor out the greatest common factor (4), your expression should be
4 (x^2 + 4x - 1)
Answer:
[tex]4(x^2+4x-1)[/tex]
Step-by-step explanation:
Find the equation, in standard form, of the line passing through the points
(2,-3) and (4,2).
A. 5x+2y=16
B. 5x – 2y=16
C. y=5/2x+8
D. 2x – 3y=9
Answer:
B
Step-by-step explanation:
To solve for the slope:
(2-(-3))/(4-2)=5/2
y=5/2x+b
plugin points:
2=5/2(4)+b
2=10+b
b=-8
so equation of the line is y=5/2x-8
and in standrd form its 5x-2y=16
is negative 2 rashihol
Answer:
Yes, -2 is a "rashihol" number