Answer:
a. E(X) = 0.333 minutes
b. [tex]\mathbf{\sigma_x =0.333 \ minutes}[/tex]
c. 0.9986
Step-by-step explanation:
a.
To find the mean time between counts
Let X be the random variable that illustrates the time between the successive log-ons, then X is exponential with the rate [tex]\lambda = 3[/tex] log-ons per minute.
i.e.
[tex]E(X) = \dfrac{1}{\lambda}[/tex]
[tex]E(X) = \dfrac{1}{3}[/tex]
E(X) = 0.333 minutes
b. Since X is attributed to an exponential distribution, The standard deviation between counts is:
[tex]\sigma_x = \dfrac{1}{3}[/tex]
[tex]\mathbf{\sigma_x =0.333 \ minutes}[/tex]
c.
Given that;
The average number of count per minute = 3
The value of X such that P(X < x) = 0.95 can be calculated as;
[tex]\int \limits ^x_0 \lambda e^{-\lambda t}= 0.95[/tex]
[tex]3\int \limits ^x_0 \lambda e^{3 t}= 0.95[/tex]
[tex]\bigg [ -e^{3t}\bigg ]^x_0 = 0.95[/tex]
[tex]e^{3t} = 1-0.95[/tex]
-3x = ㏑ (0.05)
-3x = - 2.9957
x = -2.9957/ -3
x = 0.9986
The value of x = 0.9986
Answer:
a) 3
b)3
c) 8.9872
Step-by-step explanation:
a) According to the question, mean is 3.
b) Since it is an exponential distribution, standard deviation equals to mean. Therefore, the answer is 3.
c) P[x<X]=0.95
f(x)= λ*e^(-λ*x)
∫f(x)dx, 0 to x
mean = 1/λ =3. So, λ= 1/3.
∫(1/3)*e^(-x/3)dx= 1/3*e^(-x/3)/(-1/3)=-e^(-x/3) 0 to x
-e^(-x/3)+1 = 0.95
-e^(-x/3)=-0.05
x/3=ln(0.05)
x=ln(0.05)*3= 8.9872
Bobby rode 18 miles in 24 minutes. At this rate, how
many miles did he ride in 4 minutes?
Write the function as a sum of partial fractions. Do not determine the numerical values of the coefficients.(a) x/x^2+xâ2(b) 6âx/x^2â3xâ54
The correct equations in the question are:
(a) [tex]\dfrac{x}{x^2+x-2}[/tex] (b) [tex]\dfrac{6-x}{x^2-3x-54}[/tex]
Answer:
Step-by-step explanation:
From above:
a) [tex]\dfrac{x}{x^2+x-2}[/tex]
We are to find the roots of the quadratic equation at the denominator.
i.e.
x²+x-2 = x² + 2x - x - 2
= x(x+2) - 1(x+2)
= (x -1 ) (x + 2)
Thus;
[tex]\mathbf{\dfrac{x}{x^2+x-2} = \dfrac{A}{x-1} + \dfrac{B}{x+2}}[/tex]
b) [tex]\dfrac{6-x}{x^2-3x-54}[/tex]
The quadratic equation roots can be calculated by finding two numbers that if we multiply then, we will get -54 and if we add or subtract them, we will get -3
x²-3x -54 = x² - 9x +6x - 54
= x(x-9) + 6(x-9)
= (x + 6) (x - 9)
[tex]\mathbf{\dfrac{6-x}{x^2-3x-54} = \dfrac{A}{x+6} + \dfrac{B}{x-9}}[/tex]
need help somebody pleaseee
Answer:
The second one I believe
PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE ANSWERRRRRRRRRRRRRRRRRRRR FASTTTTTTTTTTTTTTTTTT WILL GIVE BRAINLIST. PLEASEEEEEEEEEEEE
2. Melissa estimated that she would read 250 pages
last week. She read 290 pages. What is the
percent error of Melissa's estimate? Round to
the nearest whole percent.
I will give brainliest!!!
Answer:
Is it 11.6%?
Step-by-step explanation:
I divided 290/250
In the figure, is a median. If = 6 + 10 and = 2 + 12, find the length of . Show your work.
Answer:
26.
Step-by-step explanation:
Given, BD is a median. As it divides the AC equally, that's why it will AD=CD. Given, AD= 6x+10 and CD= 2x+12
Now, AD= CD
or, 6x+10=2x+12
or, 6x-2x= 12-10
or, 4x= 2
or, x= 1/2
So the value of x is 1/2. As BD divided AC equally, both AD and CD will be equal and AD+CD= AC.
So, 6x+10+2x+12= AC
or, 8x+22= AC
or, 8 X (1/2) + 22= AC
or, 4+22 = AC
or, AC= 26.=
a rectangle has a length of x3y4 inches and a width of xy7 inches . Which expression represents the ratio of the length of the rectangle to do width of the rectangle?
Given:
Length of the rectangle = [tex]x^3y^4[/tex] inches
Width of the rectangle = [tex]xy^7[/tex] inches
To find:
The ratio of the length of the rectangle to width of the rectangle.
Solution:
We have,
Length = [tex]x^3y^4[/tex] inches
Width = [tex]xy^7[/tex] inches
So, the ratio of the length of the rectangle to width of the rectangle is
[tex]Ratio=\dfrac{Length}{width}[/tex]
[tex]Ratio=\dfrac{x^3y^4}{xy^7}[/tex]
[tex]Ratio=\dfrac{x\times x^2\times y^4}{x\times y^4\times y^3}[/tex]
Cancel out the common factors.
[tex]Ratio=\dfrac{x^2}{y^3}[/tex]
[tex]Ratio=x^2:y^3[/tex]
Therefore, the required ratio is [tex]x^2:y^3[/tex].
Four hot air balloons each descend 295 feet per minute for 7 minutes. Find the total change in altitude for all 4 balloons.
The total change in altitude for all 4 balloons is
(blank) feet.
Answer:
There is descending of 8260 feet in altitude for all 4 balloons.
Write the Point Slope Form of the line of slope 5 and passing through the point (1, -1)
Answer: y+1 = 5(x-1)
Step-by-step explanation:
Match each equation with its graph
Answer:
The first graph would be y=5x+2
The second graph would be y=3x+3
The third graph would be y=2x+3
Step-by-step explanation:
First Graph: The x-intercept would be (-0.4, 0). The y-intercept would be (0, 2). The line in the graph goes through both of the points.
Second Graph: x = -1.
y=3
The line in the graph goes through both.
Third Graph: x = -1.5
y = 3
The line also goes through both.
40% as fraction and decimal
Answer:
40% as a decimal is 0.4
40% as a fraction is 2/5
Step-by-step explanation:
Let's go over each of these step by step.
First, let's see 40% as a fraction.
Since 40% is out of 100%, we can rewrite that as 40/100.
If you want to simplify it, let's do the following.
40/100
Divide both sides by 20, and you'll end up with:
2/5.
Now, let's do 40% as a decimal.
This is pretty simple.
40% is 40/100 as said before, and to find it as a decimal,
let's divide 40 and 100.
40 divided by 20 = 0.4
Therefore, we can conclude the following:
40% as a fraction is 40/100, or 2/5.
40% as a decimal is 0.4
Hope this helped! :)
(Sinθ-cosθ)(sinθ+cosθ)=1-2cos^2θ
Answer:
See below
Step-by-step explanation:
[tex]( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) = 1 - 2 { \cos}^{2} \theta \\ \\ LHS = ( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) \\ \\ = \sin^{2} \theta - \cos^{2} \theta \\ \\ =1 - \cos^{2} \theta - \cos^{2} \theta \\( \because \sin^{2} \theta =1 - \cos^{2} \theta) \\ \\ = 1 - 2 { \cos}^{2} \theta \\ = RHS[/tex]
Thus proved
Please Help me. And show your work
Answer:
30 girls, 20 boys
Step-by-step explanation:
in the tape diagram, we see a ration of 3:2 girls:boys
To solve, make it an equation`
3x+2x=50
5x=50
x=10
Then you multiply by 3 and 2 to get 30 and 20
Answer:
20:30
Step-by-step explanation:
50 divided into five is ten. There are exactly five boxes that make up ten kids for each box. There boxes are 30 kids in three boxes while two boxes are 20 kids and if you put all of that together it makes a total of 50 kids.
answer 6, as quick as you can please
9514 1404 393
Answer:
0 ft
Step-by-step explanation:
The line hangs down 15 feet from the top of each pole, so the distance between them must be zero if the total line length is 30 feet.
help me please.........
Answer:
1. true 2. true 3.true 4. false 5. false
Step-by-step explanation: 4/4-3/4 is 1/5. You multiply the top first (4-3=1) and the bottom isn't supposed to change. so the answer is 1/4
What is 1/3 of 4/5?
Answer:
0.26
is the answer
how many 1/4 cup servings are there in 3/8 cup peanut butter?
Answer:
1.5
Step-by-step explanation:
Answer:
1.5 i think
Step-by-step explanation:
1/4:2/8 so it would be 1/4 and 1/8 or 1.5
Pls solve 30 points math
Answer:
(6,0)
Step-by-step explanation:
What is the value of 3-(-2)?
Answer:
6
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
-(-2) is equal to +2, so the equation is 3+2 which is 5
Use the SLOPE FORMULA to find the slope of the line that passes through the given points.
(1.3) and (4-7)
Answer:
[tex]m=\frac{4}{5}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (1, -3)
Point (-4, -7)
Step 2: Find slope m
Substitute: [tex]m=\frac{-7+3}{-4-1}[/tex]Add/Subtract: [tex]m=\frac{-4}{-5}[/tex]Simplify: [tex]m=\frac{4}{5}[/tex]Write the equation of the line that is parallel to the line y = -3x + 12 and passes through the point (-1, 6). (2 points)
Answer:
x=−9. Explanation: x=12 is a line parallel to the y-axis passing through all points in the plane with an x-coordinate of 12. therefore a line ...
x=−9 Explanation: x=12 is a line parallel to the y-axis passing through all points in the plane with an x-coordinate of 12 therefore a line parallel ... More
17.9%of what number is 14.857
Answer:
83.100559
Step-by-step explanation:
0.179x=14.857
x=14.857/0.179
x=83.100559
someone helppp please!!
Answer:
because ΔMLN ≅ ΔYZX
=> MN = YX = 4
Step-by-step explanation:
Answer:
I think its four
Step-by-step explanation:
Miranda found 4 pieces of an ancient ceramic bowl. What fraction of the bowl is missing
how I'm supposed to answer this
Answer:
we need the total pieces
Step-by-step explanation:
how many pieces of the ancient ceramic bowl are there
4 pieces out of what?
we need the total pieces
plzzzzzzzz hurry thnx
Answer:
0.5, 50%
Step-by-step explanation:
Answer:
1/2 a pound = 0.5 of a pound1/2 a pound = 50% of a poundI hope this helps!
Find the equation of the line. Use exact numbers.
Find the equation of the line that is perpendicular to the given line and passes through the given point.
y = − 1/6x − 5; (14, 0)
The equation is y =______.
Answer:
The equation is y =6x-84.
Step-by-step explanation:
We need to find the equation of the line that is perpendicular to the given line and passes through the given point.
y = − 1/6x − 5; (14, 0)
Slope of required line
The equation of given line [tex]y = - \frac{1}{6} x - 5[/tex] is in slope-intercept form.
Comparing it with general formula of slope-intercept form [tex]y=mx+b[/tex] where m is slope and b is y-intercept. The slope of line m is: -1/6
So, the slope of required line that is perpendicular to given line is 6 because the equation of line that we need to find is perpendicular to the given line, so their slopes will be: [tex]m_1=-\frac{1}{m_2}[/tex]
So, slope = 6
Finding y-intercept of required line
Using slope =6 and point (14,0) we can find y-intercept of required line by slope-intercept formula
[tex]y=mx+b\\0=6(14)+b\\0=84+b\\b=-84[/tex]
Equation of required line:
The equation of required line having slope (m)= 6 and y-intercept (b)= -84 is:
[tex]y=mx+b\\y=6x-84[/tex]
The equation is y =6x-84.
What is the slope of the line?
Answer:
slope = 7/4
Step-by-step explanation:
slope is found by figuring the change in y-values over the change in x-values. Look for points on the line that go through an intersection of the graph lines exactly. I found the points (3, 4) and (-1, -3)
difference of y/difference of x = 4-(-3) / 3-(-1) = 7/4
HOPEFULLY MY LAST ONE!!!!
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
1/3
Step-by-step explanation:
Rise/run
10/30
I hope this is right and that it helps.
What is the answer to 5256÷52