Answer:
a) The probability that none of the lines experiences a surface finish problem in 41 hours of operation is 0.0498.
b)The probability that all three lines experience a surface finish problem between 24 and 41 hours of operation is 0.0346.
Step-by-step explanation:
[tex]Mean = \frac{1}{\lambda} = 41\\P(X\leq x)= 1-e^{-\lambda x}[/tex]
[tex]P(X>x)= e^{-\lambda x}[/tex]
a)
[tex]P(x> 41, y>41, Z>41) = (P(X>41))^{3}\\\\P(X>41)=e^{^{-\frac{41}{41}}}=e^{-1}[/tex]
[tex]P(x> 41, y>41, Z>41) = \left (e^{-1} \right )^{3}\\\\P(x> 41, y>41, Z>41) = e^{-3} = 0.0498.[/tex]
b)
[tex]\lambda =\frac{24}{41}\\P(X=1)=e^{-\lambda }\cdot \lambda =\left ( e^{-0.585} \right )\left ( 0.585 \right )\\P(X=1)=0.326[/tex]
For 3 where, P(X=1, Y==1, Z=1)
[tex]= (0.326)^{3} \\\\= 0.0346[/tex]
someone pls help me!!
Answer:
170
Step-by-step explanation:
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In July 2014 one Mexican peso was worth 0.075 U.S. dollars. How many Mexican pesos was $133.00 U.S. dollars worth?
Answer:
1,773.33 Mexican pesos
Step-by-step explanation:
Create a proportion where x was how many Mexican pesos it was worth:
[tex]\frac{1}{0.075}[/tex] = [tex]\frac{x}{133}[/tex]
Cross multiply and solve for x:
133 = 0.075x
1773.33 = x
So, it was worth approximately 1,773.33 Mexican pesos
How do I do this formula
Answer:
Step-by-step explanation:
your solution is almost true h=V/πr^2 but the final answer is 36/9π= (4π)cm
--->4×3.14=12.56cm
Use reduction of order to find a second linearly independent solution
(2x+5)y′′−4(x+3)y′+4y=0,x>−52,y1=e2x
Given that exp(2x) is a solution, we assume another solution of the form
y(x) = v(x) exp(2x) = v exp(2x)
with derivatives
y' = v' exp(2x) + 2v exp(2x)
y'' = v'' exp(2x) + 4v' exp(2x) + 4v exp(2x)
Substitute these into the equation:
(2x + 5) (v'' exp(2x) + 4v' exp(2x) + 4v exp(2x)) - 4 (x + 3) (v' exp(2x) + 2v exp(2x)) + 4v exp(2x) = 0
Each term contains a factor of exp(2x) that can be divided out:
(2x + 5) (v'' + 4v' + 4v) - 4 (x + 3) (v' + 2v) + 4v = 0
Expanding and simplifying eliminates the v term:
(2x + 5) v'' + (4x + 8) v' = 0
Substitute w(x) = v'(x) to reduce the order of the equation, and you're left with a linear ODE:
(2x + 5) w' + (4x + 8) w = 0
w' + (4x + 8)/(2x + 5) w = 0
I'll use the integrating factor method. The IF is
µ(x) = exp( ∫ (4x + 8)/(2x + 5) dx ) = exp(2x - log|2x + 5|) = exp(2x)/(2x + 5)
Multiply through the ODE in w by µ :
µw' + µ (4x + 8)/(2x + 5) w = 0
The left side is the derivative of a product:
[µw]' = 0
Integrate both sides:
∫ [µw]' dx = ∫ 0 dx
µw = C
Replace w with v', then integrate to solve for v :
exp(2x)/(2x + 5) v' = C
v' = C (2x + 5) exp(-2x)
∫ v' dx = ∫ C (2x + 5) exp(-2x) dx
v = C₁ (x + 3) exp(-2x) + C₂
Replace v with y exp(-2x) and solve for y :
y exp(-2x) = C₁ (x + 3) exp(-2x) + C₂
y = C₁ (x + 3) + C₂ exp(2x)
It follows that the second fundamental solution is y = x + 3. (The exp(2x) here is already accounted for as the first solution.)
Help pls with answer!!!Rewrite the function in the given form.
Answer:
[tex]g(x) = \frac{-2}{x-1}+5\\\\[/tex]
The graph is shown below.
=========================================================
Explanation:
Notice that if we multiplied the denominator (x-1) by 5, then we get 5(x-1) = 5x-5.
This is close to 5x-7, except we're off by 2 units.
In other words,
5x-7 = (5x-5)-2
since -7 = -5-2
Based on that, we can then say,
[tex]g(x) = \frac{5x-7}{x-1}\\\\g(x) = \frac{5x-5-2}{x-1}\\\\g(x) = \frac{(5x-5)-2}{x-1}\\\\g(x) = \frac{5(x-1)-2}{x-1}\\\\g(x) = \frac{5(x-1)}{x-1}+\frac{-2}{x-1}\\\\g(x) = 5+\frac{-2}{x-1}\\\\g(x) = \frac{-2}{x-1}+5[/tex]
This answer can be reached through alternative methods of polynomial long division or synthetic division (two related yet slightly different methods).
-------------------------
Compare the equation [tex]g(x) = \frac{-2}{x-1}+5\\\\[/tex] to the form [tex]g(x) = \frac{a}{x-h}+k\\\\[/tex]
We can see that
a = -2h = 1k = 5The vertical asymptote is x = 1, which is directly from the h = 1 value. If we tried plugging x = 1 into g(x), then we'll get a division by zero error. So this is why the vertical asymptote is located here.
The horizontal asymptote is y = 5, which is directly tied to the k = 5 value. As x gets infinitely large, then y = g(x) slowly approaches y = 5. We never actually arrive to this exact y value. Try plugging in g(x) = 5 and solving for x. You'll find that no solution for x exists.
The point (h,k) is the intersection of the horizontal and vertical asymptote. It's effectively the "center" of the hyperbola, so to speak.
The graph is shown below. Some points of interest on the hyperbola are
(-1,6)(0,7) .... y intercept(1.4, 0) .... x intercept(2, 3)(3, 4)Another thing to notice is that this function is always increasing. This means as we move from left to right, the function curve goes uphill.
If f(x) =4x2 - 8x - 20 and g(x) = 2x + a, find the value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).
Answer:
The possible values are a = -2.5 or a = 4.5.
Step-by-step explanation:
Composite function:
The composite function of f(x) and g(x) is given by:
[tex](f \circ g)(x) = f(g(x))[/tex]
In this case:
[tex]f(x) = 4x^2 - 8x - 20[/tex]
[tex]g(x) = 2x + a[/tex]
So
[tex](f \circ g)(x) = f(g(x)) = f(2x + a) = 4(2x + a)^2 - 8(2x + a) - 20 = 4(4x^2 + 4ax + a^2) - 16x - 8a - 20 = 16x^2 + 16ax + 4a^2 - 16x - 8a - 20 = 16x^2 +(16a-16)x + 4a^2 - 8a - 20[/tex]
Value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).
This means that when [tex]x = 0, f(g(x)) = 25[/tex]. So
[tex]4a^2 - 8a - 20 = 25[/tex]
[tex]4a^2 - 8a - 45 = 0[/tex]
Solving a quadratic equation, by Bhaskara:
[tex]\Delta = (-8)^2 - 4(4)(-45) = 784[/tex]
[tex]x_{1} = \frac{-(-8) + \sqrt{784}}{2*(4)} = \frac{36}{8} = 4.5[/tex]
[tex]x_{2} = \frac{-(-8) - \sqrt{784}}{2*(4)} = -\frac{20}{8} = -2.5[/tex]
The possible values are a = -2.5 or a = 4.5.
Determine which diagram could be used to prove triangle ABC is congruent to triangle EDC using similarity transformations
Answer:
A
Step-by-step explanation:
edge 2021
Determine the angles of b and c . Let a =40’ if b is a compliment of a and c is a supplement of b find these measures
Answer:
b = 50°
c = 130°
Step-by-step explanation:
Two angles A and B are complementary if:
A + B = 90°
And two angles are supplementary if:
A + B = 180°
Then, we know that:
a = 40°
b is a complement of a (this means that a and b are complementary angles)
c is a supplement of b (this means that b and c are supplementary angles).
From the first statement, we have that:
b + a = 90°
Replacing the value of a we get
b + 40° = 90°
b = 90° - 40° = 50°
b = 50°
And now we can use that b and c are supplementary, then:
b + c = 180°
replacing the value of b we get:
50° + c = 180°
c = 180° - 50° = 130°
c = 130°
Then the values we wanted are:
b = 50°
c = 130°
Claire went to the animal shelter and noticed that 6/8 of the animals were rabbits. Out of all the rabbits 4/6 were female. What fraction of the animals were female rabbits?
SHOW ALL WORK
Answer:
1/2 or 0.5
Step-by-step explanation:
6/8 x 4/6 = 24/48
Answer:
1/2
Step-by-step explanation:
A cyclist completes a journey of 500 m in 22 seconds, part of the way at 10 m/s and the remainder at 50 m/s. How far does she travel at each speed. solve by forming simultaneous equation
Answer:
150 m at 10 m/s
350 m at 50 m/s
Step-by-step explanation:
x + y = 500
x/10 + y/50 = 22
~~~~~~~~~~~~~~~~~
x + y = 500
5x + y = 1100
~~~~~~~~~~~~~~~~
x + y = 500
-5x - y = -1100
-4x = -600
x = 150
y = 350
Solve for the following equation for x. l x/4 + 3 l < 6
Answer:
this is the answer I got! i don't know if it helps, but I hope it does
Simplify the given expression below:
(4 + 21) – (1 – 71)
Hey there!
(4 + 21) - (1 - 71)
4 + 21 = 25
= 25 - (1 - 71)
1 - 71 = -70
= 25 - (-70)
= 25 + 70
= 95
Answer: 95
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Find the indicated confidence interval. Assume the standard error comes from a bootstrap distribution that is approximately normally distributed. A 90% confidence interval for a mean μ if the sample has n-80 with X-22.1 and s = 5.6, and the standard error is SE = 0.63.
The 90% confidence interval is to :_________
Answer:
(21.064 ; 23.136)
Step-by-step explanation:
Given :
Sample, n = 80
Mean, xbar = 22.1
Standard deviation, s = 5.6
Standard Error, S. E = 0.63
Confidence interval :
Xbar ± Zcritical * S.E
22.1 ± (1.645 * 0.63)
22.1 ± 1.036
Lower boundary = 22.1 - 1.036 = 21.064
Upper boundary = 22.1 + 1.048 = 23.136
(21.064 ; 23.136)
aulo uses an instrument called a densitometer to check that he has the correct ink colour.
For this print job the acceptable range for the reading on the densitometer is 1.8 ± 10%.
What is the acceptable range for the densitometer reading?
Answer:
The range is from 1.62 to 1.98.
Step-by-step explanation:
We have to solve for the percentage of the particular value if the range of the answer should be +/- 10% of the particular value.
The value given is 1.8, we thus want to find 10% of that: 1.8 * 10/100 = 0.18
Then, add this value to the original value of 1.8: 1.8+0.18 = 1.98
Furthermore, subtract .18 from from the original value of 1.8: 1.8-0.18 = 1.62
The range will be between these two numbers, so the range is from 1.62 to 1.98.
A circle has center O(2, 3) and radius 10. Which of the following points is on the circle?
Answer:
(2,3) (4,2) (5,2) (1,4) (0,2)
Step-by-step explanation:
because all these points have something common to each other. Now pay attention in your class and stop cheating!!
Answer:
Step-by-step explanation:
eq. of circle is (x-2)²+(y-3)²=10²
now substitute the values of x and y
which satisfies the above eq.that point lies on the circle.
The volume of a pyramid is 240 cubic centimeters. The pyramid has a rectangular base with sides 6cm by 4cm. Find the altitude and lateral surface area of the pyramid if the pyramid has equal lateral edges
Answer:
altitude = 30 cm
lateral surface area = 301 cm² (approximately)
Step-by-step explanation:
let the altitude be x,
240=6*4*x/3
or, x=30 cm
Lateral surface area,
=l×√(w/2)²+h²]+w×√[(l/2)²+h²]
=6×√[(4/2)²+30²]+4×√[(6/2)²+30²]
≈300.99806
≈ 301 cm²
Answered by GAUTHMATH
The total number of labor hours for a construction project by week x is given by: Week 1 4 7 10 13 16 19 Total hours 25 158 1254 5633 9280 10,010 10,100 Look at its scatter plot, an appropriate model for this data is:
Answer:
Logistic model
Step-by-step explanation:
A scatter plot is a mathematical representation or diagram which is used to shoe the relation between two given variables. It uses the Cartesian coordinates which is used to display the values for a typically two variables for the given set of data.
In the context, a scatter plot is made between two variables. The two variables are the total number of hours and the number of weeks.
From the graph shown, we can say that model is a logistic model as the shape of the graph is S shaped.
Therefore, the appropriate model for the data given is logistic model.
The angle of elevation of the top of the tower from a point on the ground is 30 degree, If the height of the tower is 40 space m e t e r s, then the distance between the tower and the point is
Answer:
[tex]40\sqrt3\ m[/tex]
Step-by-step explanation:
Given that,
The height of the tower, h = 40 m
The angle of elevation is 30°
We need to find the distance between the tower and the point. Let the distance is x. Using trigonometry,
[tex]\tan(30)=\dfrac{h}{x}\\\\\dfrac{1}{\sqrt3}=\dfrac{40}{x}\\\\x=40\sqrt3\ m[/tex]
So, the distance between the tower and the point is equal to [tex]40\sqrt3\ m[/tex].
87,521 rounded to the nearest hundred
Answer:
87,500
Step-by-step explanation:
Since the last 2 digits arent 5 or greater than 5 it can not be rounded to the next hundred.
Answer:
875
Step-by-step explanation:
th t h t u
8 7 5 2 1
the hundred is 5 so the next digit after that is 2 remember 0 to 4 round down 5 to 9 round up
so 875
Type the equation used and answer for credit:
2). The population, P(x), of white rhinos in 2001 was 11,670. The population is declining by 9% each year.
A) The general Population equation is modeled by: P(x) = (blank)
What is the population expected to be in the year 2021?
B) the Evaluated equation I used to get the following answer is(blank)
, and there are (blank)
rhinos expected.
Answer:
a) 11670-0.09%
b)11670-1.8%=11459
Step-by-step explanation:
Determine whether the point is on the graph of the equation 2x+7y=13
(-4,3)
Is (-4,3) on the graph of 2x+7y=13?
Yes or no?
Answer:
(I) yessssssssssssssssssssssss
Answer:
yes it is.
Step-by-step explanation:
i did this and it was correct
Sketch the graph of y = 2(x – 2)2 and identify the axis of symmetry
Answer:
x = 2
Step-by-step explanation:
The minimum point of the curve is (2, 0). Hence, axis of symmetry is x = 2
There are two points of the form (x,-4) that have a distance of 10 units from the point (3,2). Give the x value for one of those points.
Answer:
x = - 5
Step-by-step explanation:
[tex]Let \ (x _ 1 , y _ 1 ) \ and \ (x _ 2 , y _ 2 ) \ be \ the \ points. \\\\The \ distance \ between \ the \ points \ be ,\ d = \sqrt{(x_2 - x_1)^2 + ( y _ 2 - y_1)^2}[/tex]
Given : d = 10 units
And the points are ( x , - 4) and ( 3 , 2 ).
Find x
[tex]d = \sqrt{( 3 - x)^2 + ( -4 - 2)^2} \\\\10 = \sqrt{( 3 - x)^2 + ( -6)^2} \\\\10^2 = [ \ \sqrt{( 3 - x)^2 + 36} \ ]^2 \ \ \ \ \ \ \ \ \ [ \ squaring \ both \ sides \ ] \\\\100 = ( 3 - x )^2 + 36\\\\100 - 36 = ( 3 - x )^ 2\\\\( 3 - x ) = \sqrt{64}\\\\3 - x = \pm 8\\\\3 - x = 8 \ and \ 3 - x = - 8\\\\-x = 8 - 3 \ and \ -x = - 8 - 3\\\\-x = 5 \ and \ -x = - 11\\\\x = - 5 \ and \ x = 11\\\\[/tex]
Check which value of x satisfies the distance between the points.
x = 11
[tex]d = \sqrt{(3-11)^2 + (-2--4)^2} = \sqrt{(-8)^2 + (-2+4)^2}= \sqrt{64+4} = \sqrt {68} \ units[/tex]
does not satisfy.
x = - 5:
[tex]d = \sqrt{ (3 -- 5)^2 + ( - 4 - 2)^2} = \sqrt{8^2 + 6^2} = \sqrt{100} =10 \ units[/tex]
Therefore , x = - 5
How many vertices (corners) does a cube have?
How many faces does a rectangular prism have?
How many edges does a rectangular prism have?
How many edges does a square-based pyramid have?
How many vertices (corners) does a square-based pyramid have?
How many faces does a triangular prism have?
How many vertices (corners) does a triangular prism have?
kb 2021
Answer:
The answer is below
Step-by-step explanation:
a) A cube is a three dimensional solid with 6 square faces.
A cube has 8 vertices
b) A rectangular prism is a three dimensional solid with two parallel rectangular bases.
A rectangular prism has 6 faces.
c) A rectangular prism is a three dimensional solid with two parallel rectangular bases.
A rectangular prism has 12 edges.
d) A square-based pyramid is a pyramid with a square base.
A square-based pyramid has 8 edges
e) A triangular prism is a three dimensional solid with two parallel triangular bases.
A triangular prism has 5 faces.
f) A triangular prism is a three dimensional solid with two parallel triangular bases.
A triangular prism has 6 vertices.
Luke makes fruit cakes for a stall at a village fete. It costs Luke £1.80 for
the ingredients for each cake. If he wants to make exactly 35% profit on
each cake, how much money should Luke charge for each cake?
Answer:
2.43
Step-by-step explanation:
1.80 x 0.35 + 1.80
100 POINTS!!!!!
Directions: Respond to this question to demonstrate your understanding of the topic/content. Be sure to provide adequate and relevant details learned in the module to support your response. Pay close attention to organizing your response so it makes sense and uses correct grammar. Your response should be at least 5-7 sentences at a minimum.
Question: Given answer the questions that follow.
a. Your friend claims the graph of f(x)=2x increases at a faster rate than the graph of g(x)=x2 when x ≥ 0. Is your friend correct? Explain your reasoning.
b. How are the 2 functions different?
Answer:
a. The friend is incorrect.
2(x) is the same as x(2). PEMDAS does not apply to the same order of operation under normal conditions and both are directly proportional functions.
b. The parentheses are the only thing making the functions different. After you simplify from the parentheses, both values have the same priority.
Step-by-step explanation:
Choose ASA SAA or neither to describe this figure
Answer:
SAA
Step-by-step explanation:
HOPE IT HELPS YOU IN YOUR LEARNING PROCESS.
If the domain of the coordinate transformation (, ) = ( + 2,− − 4) is (1, -4), (3, -2), (0, −1), what is the range?
A. (-2, -5), (0, -7), (1, -4)
B. (0, 3), (-2, 5), (-3, 2)
C. (3, 0), (5, -2), (2, -3)
D. (-5, -2), (-7, 0), (-4, 1)
Answer:
A. (-2, -5), (0, -7), (1, -4)
Step-by-step explanation:
The following transformation is applied:
[tex](x,y) \rightarrow (y + 2, -x - 4)[/tex]
To find the range:
We apply the transformation to the points in the domain. Thus:
[tex](1,-4) \rightarrow (-4 + 2, -1 - 4) = (-2, -5)[/tex]
[tex](3,-2) \rightarrow (-2 + 2, -3 - 4) = (0, -7)[/tex]
[tex](0,-1) \rightarrow (-1 + 2, 0 - 4) = (1, -4)[/tex]
Thus the correct answer is given by option a.
Find the slope of the line graphed below.
Answer:
Step-by-step explanation:
two points are (-5,-2) and (-1,3)
slope=(3-(-2))/(-1-(-5))=(3+2)/(-1+5)=5/4
Forces of 9 lbs and 13 lbs act at a 38º angle to each other. Find the magnitude of the resultant force and the angle that the resultant makes with each force.
Answer: [tex]R=20.84\ lb\quad 22.57^{\circ},15.43^{\circ}[/tex]
Step-by-step explanation:
Given
Two forces of 9 and 13 lbs acts [tex]38^{\circ}[/tex] angle to each other
The resultant of the two forces is given by
[tex]\Rightarrow R=\sqrt{a^2+b^2+2ab\cos \theta}[/tex]
Insert the values
[tex]\Rightarrow R=\sqrt{9^2+13^2+2(9)(13)\cos 38^{\circ}}\\\Rightarrow R=\sqrt{81+169+184.394}\\\Rightarrow R=\sqrt{434.394}\\\Rightarrow R=20.84\ lb[/tex]
Resultant makes an angle of
[tex]\Rightarrow \alpha=\tan^{-1}\left( \dfrac{b\sin \theta}{a+b\cos \theta}\right)\\\\\text{Considering 9 lb force along the x-axis}\\\\\Rightarrow \alpha =\tan^{-1}\left( \dfrac{13\sin 38^{\circ}}{9+13\cos 38^{\circ}}\right)\\\\\Rightarrow \alpha =\tan^{-1}(\dfrac{8}{19.244})\\\\\Rightarrow \alpha=22.57^{\circ}[/tex]
So, the resultant makes an angle of [tex]22.57^{\circ}[/tex] with 9 lb force
Angle made with 13 lb force is [tex]38^{\circ}-22.57^{\circ}=15.43^{\circ}[/tex]
Answer:
Step-by-step explanation: