Answer:
[tex]P(X > 11) = 0.368[/tex]
[tex]P(X > 22) = 0.135[/tex]
[tex]P(X > 33) = 0.050[/tex]
[tex]x = 33[/tex]
Step-by-step explanation:
Given
[tex]E(x) = 11[/tex] --- Mean
Required (Missing from the question)
[tex](a)\ P(X>11)[/tex]
[tex](b)\ P(X>22)[/tex]
[tex](c)\ P(X>33)[/tex]
(d) x such that [tex]P(X <x)=0.95[/tex]
In an exponential distribution:
[tex]f(x) = \lambda e^{-\lambda x}, x \ge 0[/tex] --- the pdf
[tex]F(x) = 1 - e^{-\lambda x}, x \ge 0[/tex] --- the cdf
[tex]P(X > x) = 1 - F(x)[/tex]
In the above equations:
[tex]\lambda = \frac{1}{E(x)}[/tex]
Substitute 11 for E(x)
[tex]\lambda = \frac{1}{11}[/tex]
Now, we solve (a) to (d) as follows:
Solving (a): P(X>11)
[tex]P(X > 11) = 1 - F(11)[/tex]
Substitute 11 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-\frac{1}{11}* 11})[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-\frac{11}{11}})[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-1})[/tex]
Remove bracket
[tex]P(X > 11) = 1 - 1 + e^{-1}[/tex]
[tex]P(X > 11) = e^{-1}[/tex]
[tex]P(X > 11) = 0.368[/tex]
Solving (b): P(X>22)
[tex]P(X > 22) = 1 - F(22)[/tex]
Substitute 22 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-\frac{1}{11}* 22})[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-\frac{22}{11}})[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-2})[/tex]
Remove bracket
[tex]P(X > 22) = 1 - 1 + e^{-2}[/tex]
[tex]P(X > 22) = e^{-2}[/tex]
[tex]P(X > 22) = 0.135[/tex]
Solving (c): P(X>33)
[tex]P(X > 33) = 1 - F(33)[/tex]
Substitute 33 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-\frac{1}{11}* 33})[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-\frac{33}{11}})[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-3})[/tex]
Remove bracket
[tex]P(X > 33) = 1 - 1 + e^{-3}[/tex]
[tex]P(X > 33) = e^{-3}[/tex]
[tex]P(X > 33) = 0.050[/tex]
Solving (d): x when [tex]P(X <x)=0.95[/tex]
Here, we make use of:
[tex]P(X<x) = F(x)[/tex]
Substitute [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X<x) = 1 - e^{-\lambda x}[/tex]
So, we have:
[tex]0.95 = 1 - e^{-\lambda x}[/tex]
Subtract 1 from both sides
[tex]0.95 -1= 1-1 - e^{-\lambda x}[/tex]
[tex]-0.05=- e^{-\lambda x}[/tex]
Reorder the equation
[tex]e^{-\lambda x} = 0.05[/tex]
Substitute 1/11 for [tex]\lambda[/tex]
[tex]e^{-\frac{1}{11} x} = 0.05[/tex]
Solve for x:
[tex]x = -\frac{1}{1/11}\ ln(0.05)[/tex]
[tex]x = -11\ ln(0.05)[/tex]
[tex]x = 32.9530550091[/tex]
[tex]x = 33[/tex] --- approximated
What is 18 % of 120?
O 2. 160
O 666
0 21.6
0 15
Multiply 120 by 18%
Change 18% to a decimal: 0.18
120 x 0.18 = 21.6
Answer: 21.6
Move values to the lines to complete each equation.
|8| =
|-8| =
-|8| =
-|-8| =
Answer:
I think this is what you meant not sure tho
Step-by-step explanation:
|8| = correct as it is
|-8| = correct as it is
-|8| = |-8|
-|-8| = |8|
Please help and how do you know this answer
Answer:
21
Step-by-step explanation:
Answer:
1.67
Step-by-step explanation:
25/15 = 1.67
The mean is estimated by dividing the total of the values by the range of values.
A soft drink-dispensing machine uses paper cups that hold a maximum of 12 ounces. The machine is set to dispense a mean of 10 ounces of the drink. Because of an imprecise process, the amount dispensed actually varies; it is normally distributed with a standard deviation of 1 ounce. If we simulated the filling process, and had the random number .564, how many ounces would the cup contain? Give your answer to 3 decimal places.
Answer:
The cup would contain 10.16 ounces.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Mean of 10 ounces, standard deviation of 1 ounce:
This means that [tex]\mu = 10, \sigma = 1[/tex]
If we simulated the filling process, and had the random number .564, how many ounces would the cup contain?
This means that we have to find X when Z has a pvalue of 0.564. So X when Z = 0.16. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.16 = \frac{X - 10}{1}[/tex]
[tex]X - 10 = 0.16*1[/tex]
[tex]X = 10.16[/tex]
The cup would contain 10.16 ounces.
Question 7 (1 point)
The angle of elevation from point P to the top of the pole is 65°. Point Pis 21 feet from the base of the flagpole. To
the nearest tenth, what is the height of the pole?
65°
21 ft.
Plz help
Answer:
h = 452.5 ft
Step-by-step explanation:
Angle of elevation from P to top of the pole = 65°
Horizontal distance between the pole and point P = 21 ft
By Applying tan rule in the given triangle ABP,
tan(∠APB) = [tex]\frac{AB}{PB}[/tex]
tan(65°) = [tex]\frac{h}{21}[/tex]
h = 21[tan(65°)]
h = 452.491
h ≈ 452.5 ft
Therefore, height of the pole is 452.5 ft.
A line with a slope of 8 and includes the points (8,-10) and (10,w).What is the value of k?
Answer:
w = 6
Step-by-step explanation:
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]
[tex]\frac{w-[-10]}{10-8}=8\\\\\frac{w+10}{2}=8\\\\w+10= 8*2\\[/tex]
w +10 = 16
w = 16 - 10
w = 6
15=1.5t
Solve the equation for the variable. Remember to write t= when you write your answer!
Answer:
t = 10
Step-by-step explanation:
15 = 1.5 × t
15/1.5 = t
10 = t
mark me as brainlistCalculate and give your answer
its simplest form.
8 /7
X
7/8
Your answer
Answer:
1 I believe if your asking in in simplified form and if 8/7 and 7/8 are multiplied
Step-by-step explanation:
A rhombus and a triangle are equal in areas. if the base and height of the triangle are 24.8 cm and 5.5 cm respectively and the length of one diagonal of the rhombus is 22 cm, find the length of other diagonal of the rhombus.
As we know that
Area of triangle = ½ × Base × Height
Area = ½ × 24.8 × 5.5Area = 1 × 12.4 × 5.5Area = 12.4 × 5.5Area = 68.2 cm²Now,Area of rhombus = ½ × D1 × D2
68.2 = ½ × 22 × D268.2 × 2 = 22 × D2136.4 = 22 × D2136.4/22 = D26.2 = D2D2=6.2Hence :-Other Diagonal is 6.2 cm.[tex]\begin{gathered} \\ \end{gathered}[/tex]
what is 1/2 divided by 6?
Answer:
1/12 or 0.0833
Step-by-step explanation:
1/2 divided by 6
1/2x6
1/12!
Answer: Fraction Form: 1/12
Decimal Form: 0.0833
Expanded Decimal Form: 0.08333333333
If I Helped, Please Mark Me As Brainliest, Have A Great Day :D
Which student solved the equation 107 d = 1,733.4 correctly?
Gianna's work: 107 d = 1,733.4. 1,733.4 times 107 = 185,473.8.
Teddy's work: 107 d = 1,733.4. 1,733.4 minus 107 = 1,626.4.
Sid's work: 107 d = 1,733.4. 1,733.4 + 107 = 1,880.4.
Sammi's work: 107 d = 1,733.4. 1,733.4 divided by 107 = 16.2.
Answer:
It's D, Sammi's work. Hope it helps! Remember your perfect, your awesome, your worth it, just the way you are, you deserve this world! Have an amazing day!
Step-by-step explanation:
Answer:
The person above me is correct.
An amount of $42,000 is borrowed for 6 years at 9% interest, compounded annually. If the loan is paid in full at the the end of hat period how much must be paid back?
Answer:
70,438.20
Step-by-step explanation:
To calculate the future value you use the following formula
FV=PV(1+i)^n
Plug in our numbers and get
FV=42000(1+.09)^6
42000*1.09^6=70,438.20
A number is greater than 8. The same number is less than 10. The inequalities x > 8 and x < 10 represent the situation.
Which best explains the number of possible solutions to the inequality?
O There is one solution because 9 is the only number between 8 and 10.
There are a three solutions because 8, 9, and 10 are possible solutions.
There are a few solutions because there are some fractions and decimals between 8 and 10.
There are infinite solutions because there is always another number between any two numbers.
Mark this and retum
Save and Exit
Next
Submit
Answer:
There are infinite solutions because there is always another number between any two numbers.
Step-by-step explanation:
Pick any number (including decimal) add an extra decimal after the smallest one and then you have a number between them. E.g.
1.234 and 2.987
1.2341, 1.2342, 1.2343, ... are all between them
Answer:
D
Step-by-step explanation:
Look at the following number sequence.
6, 9, 12, 15, . . .
Based on the pattern, what are the next two terms?
Answer:
18, 21
Step-by-step explanation:
By finding the difference between each term, you can find the pattern. 9-6=3, 12-9=3, 15-12=3, so we know that each term is 3 more than the last.
Therefore, by following the pattern of +3, the next term is 15+3=18 and the one after that is 18+3 = 21
Answer:
the next two terms would be 18 and 21
Help me write an explanation
Answer:
9.375 grams
Step-by-step explanation:
30 days = 3(10 days)
m = 75·0.5³ = 9.375 grams
Tell whether the ordered pair is a solution to the system of linear equations. 1 point
63 + 3y = 12
(5.-6):
4x + y = 14
Yes
No
Maybe
Next
Page 1 of 3
Forms
Tell whether the ordered pair is a solution to the system of linear equations
Yes
No
Maybe
Answer:
(5,-6) is a solution
Step-by-step explanation:
Given
[tex]6x + 3y = 12[/tex]
[tex]4x + y = 14[/tex]
Required
Tell whether (5,-6) is a solution
In (5,-6): x = 5 and y = -6.
Substitute these values in the given equations
[tex]6x + 3y = 12[/tex] becomes
[tex]6 * 5 + 3 * -6 = 12[/tex]
[tex]30-18 = 12[/tex]
[tex]12 = 12[/tex]
[tex]4x + y = 14[/tex] becomes
[tex]4 * 5 - 6 = 14[/tex]
[tex]20 - 6 = 14[/tex]
[tex]14 = 14[/tex]
Because both solutions are true, then (5,-6) is a solution
what is the simplifed form of the fraction below?
24/30
Answer:
4/5
Step-by-step explanation:
this can be divided by 6 to get you this answer
The measure of an angle is 166º. What is the measure of its supplementary angle?
HELP PLZZ
Answer:
14
Step-by-step explanation:
To make 166 a supplementary angle you should add 14 because supplementary angles equal 180.
Answer:
14
Step-by-step explanation:
Supplementary angles add to 180 degrees.
Let x be the unknown supplement
x+166 = 180
x+166-166 = 180-166
x =14
The unknown supplement is 14
Are the hypontuse and the height of this triangle the same?
Answer:th hypotenuse and the height can’t possibly be the same size because the Pythagorean theorem is a^2 +b^2=c^2
Step-by-step explanation:
Answer:
hypotenuse is equal to side of this square.
but hypotenuse is never be equal to hieght of the triangle.
Determine the equation of straight line which passes through the point (a, b)and perpendicular to ax+by=5
Answer:
[tex]y=\frac{b}{a} x.[/tex]
Step-by-step explanation:
1) if the required straight line is 'l', the given point is A(a;b), then the required equation of line can be written in form:
[tex]\frac{x-a}{x_1-a} =\frac{y-b}{y_1-b},[/tex]
where (x₁;y₁) is other point B, which belongs to the 'l';
2) from the equation it is possible to detect the coordinates of the perpendicular, they are (x₁-a;y₁-b);
3) if the given perpendicular is ax+by=5, then the coordinates of the vector (a;b) are coordinates of the vector, which belongs to the required line 'l', and then: x₁-a=a and y₁-b=b;
4) if to substitute the a=x₁-a and b=y₁-b into the required equation of line 'l', then:
[tex]\frac{x-a}{a} =\frac{y-b}{b};[/tex]
5) finally, the equation is: ay=bx, or y=b/a *x (slope-interception form).
note: the suggested solution is not the only way.
What is the number of the parking space covered by the car?
The length of the base of an isosceles triangle is x. The length of a leg is 4x - 2. The perimeter of the triangle is 95. Find x.
Answer:
x = 11
Step-by-step explanation:
sides of triangle measure: 'x', '4x-2' and '4x-2' since isosceles means both legs are equal
perimeter is the sum of all sides, so set up equation:
95 = 4x - 2 + 4x - 2 + x
95 = 8x - 4 + x
95 = 9x - 4
99 = 9x
x = 11
How are these three numbers related. 50 1/2, 1/4, 202
Answer: If you divide 202/4=50.5 or 50 1/2
Step-by-step explanation:
The map of a town is placed on a coordinate grid. Use the map to find
the distance between the post office and the lake.
When it is 7 AM in New York, it is noon in London. A plane leaves London
at noon London time and arrives in New York at 11 AM New York time
the same day. A second plane leaves New York at 12 noon New York time
for London. What time in London is it when the second plane arrives?
Assume both planes fly for the same number of hours.
Answer:
by the time second plane arrives in London it is 08:00 am
What is the difference between 100 and 33?
Answer:
67
Step-by-step explanation:
100 - 33 = 67
The difference between 100 and 33 is 67.
The answer is 67 if you go to your calculator app and do 67+33 it equals 100
Ten 4th grade girls and ten 7th grade girls were randomly selected. Their heights, in inches, are recorded below:
4th Grade
44, 48, 48, 51, 52, 52, 54, 54, 57, 60
7th Grade
52, 55, 57, 57, 58, 60, 60, 62, 64, 65
On average, 7th grade girls tend to be about (these are your answer options for your answer put one of these numbers and tell me which grade) 6,7,5,8 inches taller than 4th grade girls, and ( Answer choices ) there is more variability in the height of 4th grade girls or there is more variability in the height of 7th grade girls.
Answer:
7
Step-by-step explanation:
average of 7th grade - average of 8th grade = 7
average of 7th = (52+55+57+57+58+60+60+62+64+65)/10
= 590/10
= 59
average of 4th = 44+48+48+51+52+52+54+54+57+60
= 520/10
= 52
59 - 52 = 7
please give me brainliest if it is helpful for you
Answer: Hoped I help
7 and there is more variability in the height of 7th grade girls
Step-by-step explanation:
4th grade
44+48+48+51+52+52+54+54+57+60
found the median which is 52 and 52 but you add them and divide them by 2 to get the median which is 104/2= 52
7th grade
52+55+57+57+58+60+60+62+64+65
median is 60 + 58=118/2= 59
59-52= 7
and
there is more variabilty in the hieght f 7th grade girls. because 4th grade has a lot of modes already while 7th grade has only like two so 7th grade will have more variability.
The height h(n) of a bouncing ball is an exponential function of the number n of bounces.
One ball is dropped and on the first bounce reaches a height of 6 feet. On the second
bounce it reaches a height of 4 feet.
PLEASE HURRY
Answer:
The height of a bouncing ball is defined by [tex]h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}[/tex].
Step-by-step explanation:
According to this statement, we need to derive the expression of the height of a bouncing ball, that is, a function of the number of bounces. The exponential expression of the bouncing ball is of the form:
[tex]h = h_{o}\cdot r^{n-1}[/tex], [tex]n \in \mathbb{N}[/tex], [tex]0 < r < 1[/tex] (1)
Where:
[tex]h_{o}[/tex] - Height reached by the ball on the first bounce, measured in feet.
[tex]r[/tex] - Decrease rate, no unit.
[tex]n[/tex] - Number of bounces, no unit.
[tex]h[/tex] - Height reached by the ball on the n-th bounce, measured in feet.
The decrease rate is the ratio between heights of two consecutive bounces, that is:
[tex]r = \frac{h_{1}}{h_{o}}[/tex] (2)
Where [tex]h_{1}[/tex] is the height reached by the ball on the second bounce, measured in feet.
If we know that [tex]h_{o} = 6\,ft[/tex] and [tex]h_{1} = 4\,ft[/tex], then the expression for the height of the bouncing ball is:
[tex]h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}[/tex]
The height of a bouncing ball is defined by [tex]h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}[/tex].
Answer:
9 (2/3) ² but insted of 2 its n
Step-by-step explanation:
How many solutions does the system of equations have?
Answer:
The system has just one solution, it is (1,4).
Step-by-step explanation:
When we have a system of linear equations, the solution is given by the intersection point of the two lines.
So if we see the graph, the intersect point is at (1,4). Therefore, the system has a unique solution.
I hope it helps you!
A school administrator claims that the average GPA of Which explanations are justified based on the evidence
the senior class is 3.53. You think that the average GPA you obtained? Check all that apply
is greater than that, so you select a random sample of
100 seniors and calculate their average GPA. The
It is possible that the population mean is 3.53, but
sample mean GPA is 3.70
the sample result is greater than that due to
You have some evidence that the mean GPA may be
sampling variability
greater than 3.53 because the sample mean of your It is possible that the school administrator made a
random sample is 3.70.
mistake, and the population mean is greater than
3.53
The fact that the sample mean is greater than the
claimed population mean proves that the average
GPA of the senior class is greater than 3.53
The sample mean of 3.70 cannot be correct
because the claimed population mean is 3.53.
The population mean of 3.53 cannot be correct
because the calculated sample mean is 3.70
Done
Answer:
its the first two
It is possible that the population mean is 3.53, but the sample result is greater than that due to sampling variability.
It is possible that the school administrator made a mistake, and the population mean is greater than 3.53.
Step-by-step explanation:
edg 2021
Answer:
A
B
Step-by-step explanation:
EDG 2020-2021