please help me with this :)))
Answer:
C, 33 1/3%
Step-by-step explanation:
Because there are only two even number that follow this rule: 2<x≥6, and since there are only 6 possible outcomes, the probabilty is 2/6, which is 1/3. In a percent form, this is 100%*2/3, or 33 1/3%.
Suppose that an appliance is constructed in such a way that it requires that n independent electronic components are all functioning. Assume that the lifespan of each of these, Tj, is an exponential random variable with parameter λj.
a. Let X be the random variable giving the lifespan of the appliance. Find the CDF and PDF for X.
b. Find the expected value of X.
c. Now find the median lifespan of the appliance (that is, the time t at which half of the appliances are likely to have broken and half to be working ).
Answer:
Step-by-step explanation:
[tex]T_j \sim exp ( \lambda j) \ \ \ j = 1 (1) n \\ \\ f_{Tj}(tj) = \lambda j e^{-\lambda j tj } , tj>0 \\ \\ P\Big[ Tj> x\Big] = \int \limits ^{\infty}_{x} \lambda j e^{-\lambda j tj}\ dtj \\ \\ = e^{-\lambda j x}, x > 0 \\ \\ \\ \\ a) F_x (x) \\ \\ = P[X \le x ] \\ \\ = 1 - P[X> x] \\ \\ = 1 - \pi \limits ^{n}_{j =1} \Big\{ P[T_j > x ] \Big \}[/tex]
[tex]\text{This is because the appliance has the capacity to work for more than (x) }[/tex][tex]\text{hours if and only if all the "n" components work more than (x) hours.}[/tex]
[tex]\text{Then:}[/tex]
[tex]= 1 - e \ \pi^{n}_{j=1} \ e^{-\lambda j x} \\ \\ = 1 - e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}[/tex]
∴
[tex]CDF = 1 - e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}\ , \ x>0[/tex]
[tex]PDF =\Big( \sum \limits ^{n}_{j =1} \lambda j\Big) e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}\ , \ x>0[/tex]
[tex]f_x(x) = \Big( \sum \limits ^{n}_{j =1} \lambda j\Big) e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}\ , \ x>0[/tex]
(b)
[tex]E(x) = \int \limits ^{\infty}_{o }x f_x (x) \ dx \\ \\ = \int \limits ^{\infty}_{o }x \ \Big( \sum \limits ^{n}_{j =1} \lambda j\Big) e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}\ , \ dx[/tex]
[tex]= \dfrac{1}{\sum \limits ^n_{j=1} \lambda j} \ \ \int \limits ^{\infty}_{o} \Big [(\sum \limits ^n_{j=1} \lambda j )x \Big] e ^{-\Big ( \sum \limits ^{n}_{j=1} \lambda j \Big)x} \ \ d \Big( x \sum \limits ^n_{j=1} \lambda j \Big)[/tex]
[tex]= \dfrac{1}{\sum \limits ^n_{j= 1} \lambda j} \int \llimits ^{\infty}_{o} t e^{-t} \ dt[/tex]
[tex]= \dfrac{1}{\sum \limits ^n_{j= 1} \lambda j} \int \llimits ^{\infty}_{o} t e^{-t} \ dt \ \ \ \ \text{\Big[By transformation }t =( \sum \limits ^n_{j=1} \lambda j )x \Big][/tex]
[tex]= \dfrac{1}{\sum \limits ^n_{j= 1} \lambda j}[/tex]
(c)
[tex]Let \ \ l_y_{\dfrac{1}{2}} \text{ be the median}[/tex]
∴
[tex]F(l_y_{\dfrac{1}{2}}) = \dfrac{1}{2} \\ \\ 1 - e ^{-\Big (\sum \limits ^{n}_{j=1} \lambda j \Big)} {l_y}_{\frac{1}{2}} = \dfrac{1}{2} \\ \\ \dfrac{1}{2} = e^{-\Big (\sum \limits ^{n}_{j=1} \lambda j \Big) } {l_y}_{\frac{1}{2}} \\ \\ - In 2 = {-\Big (\sum \limits ^{n}_{j=1} \lambda j \Big)} {l_y}_{\frac{1}{2}} \\ \\ \\ \\ \mathbf{ {l_y}_{\frac{1}{2}} = \dfrac{ In \ 2}{\sum \limits ^{n}_{j=1} \lambda j }}[/tex]
Plz help quick I will give brainly points
identify each coefficient for 3m. this question is on my homework what Is the answer?
Answer: 3
Step-by-step explanation: The number in front of your variable is called your coefficient so we say that 3 is the coeficient.
Make sure to understand that a variable
is just a letter that represents any number.
16 is the sum of a number and 2.
What is the equation?
Answer:
14
Step-by-step explanation:
[tex]x + 2 = 16 \\ x = 16 - 2 \\ x = 14[/tex]
Like this ？？？
Answer:
16 = 2 + 14
Step-by-step explanation:
Sum means to add to numbers, so we are finding x + 2 = 16.
x + 2 - 2 = 16 - 2
x = 14
Pls help! The question is in the picture down below!
Answer:
Let me know if there is anything you don't get
∠3 = 102 because ∠1 and ∠3 are supplementary and 102 + 78 = 180
∠4 = 102 because ∠1 and ∠4 are consecutive interior angles
∠5 = 78 because ∠1 and ∠5 are corresponding angles
∠6 = 133 because ∠2 and ∠6 are supplementary angles
∠7 = 47 because ∠2 and ∠7 are vertical angles
∠8 = 47 because ∠2 and ∠8 are opposite interior angles
∠9 = 133 because ∠8 and ∠9 are supplementary, and we just saw ∠2=∠8
∠10 = 102 because ∠1 and ∠10 are supplementary
You could have used a whole bunch of different relations, but I wanted to focus on ∠1 and ∠2 since those were told to us
Step-by-step explanation:
For this question you need to know several parts of geometry. Let me know if anything doesn't make sense.
First, parallel lines are two or more lines which are angles in such a way that no matter how long they are they will not cross. In other words they are slanted at the same angle. you can see this with lines a and b in this picture.
Second, a transversal is a line that crosses through two or more parallel lines. A transversal creates a number of angles that have special properties. I would like you to look specifically at line c as I describe these angles. line c is a transversal to Ines a and b. Also line d is also a transversal.
There are seven special angles to know.
The easiest is supplementary angles. This you don't need parallel lines, but if any two lines ever cross this creates 4 angles. you can actually look at where lines c and b intersect in your problem. Angles 2. 6 and 7 are labeled but there is one more unlabeled one. Now, 180 degrees is a straight line. With angles you can see angles 6 and 7 add together to be a straight line. Similarly 2 and 6 do as well. These are two sets of supplementary angles.
To list off the supplementary angles here 9 and 8 are supplementary, as are 2 and 6, 6 and 7, 1 and 3, 1 and 10, and finally 4 and 5.
From supplementary angles comes vertical angles. Again, if you look at angles 2, 6 and 7 we already know ∠2 + ∠6 = 180 and ∠6 + ∠7 = 180. Well lets say ∠6 = 133. Well then, we could use algebra to see that both ∠2 AND ∠7 are 47 degrees. This is the property of vertical angles. if you have two lines intersecting, any two angles that have a third in between the are called vertical angles, and are equal.
some examples of vertical angles are ∠2 and ∠7as well as ∠3 and ∠10,
Finally we go into parallel line specific angles. If you have two or more parallel lines with a transversal, so in particular look at a and b as the parallel lines and c as the transversal. The transversal creates some special angles. in particular, the transversal crosses a and b at the same angle, so angles 8 and 7 have the same value. These are known as corresponding angles, since they correspond tot he same position with a transversal crossing through parallel lines.
the corresponding angles in the picture are ∠8 and ∠7, ∠3 and ∠4 and finally ∠1 and ∠5. the last two using line d as a transversal.
After corresponding angles opposite interior angles I think are the next logically to look at. Opposite means they are on two different parallel lines and on different sides of the transversal, while interior means they are between the parallel lines. so if you look at the parallel lines a and b there are angles 8 and 2 that are interior angles. Since 8 is against line a and 2 is against line b, and ∠8 is above transversal c while ∠2 is below it, they are opposite angles. so 8 and 2 are opposite interior angles. Now, if you look at ∠8 and ∠7 you know these are corresponding angles, then ∠7 and ∠2 are vertical angles. This means opposite interior angles are equal.
A list of opposite interior angles are ∠8 and ∠2, and ∠10 and ∠4.
Alongside opposite interior, there are opposite exterior angles. opposite means on different parallel Ines and on opposite sides of the transversal, while this time exterior means not between the parallel lines. Now just like we figured with opposite interior angles
The only labeled pair of opposite exterior angles are ∠9 and ∠6. Now just like we figured with opposite interior angles, let's start with ∠8 and ∠9, which are supplementary. then ∠8 and ∠7 are corresponding angles so ∠9 and ∠7 are supplementary. We can also see ∠7 and ∠6 are supplementary. well, since ∠9 + ∠7 = 180 = ∠6 + ∠7 then ∠9 = 180 - ∠7 = ∠6 so ∠9 = ∠6. This shows opposite exterior angles are equal.
So we did two kinds of opposite angles, it might make sense there are non opposite angles. And there are. these are called consecutive angles. There are consecutive exterior and consecutive interior angles. An example of each are ∠1 and ∠4 for consecutive interior, consecutive because they are on the same side of the transversal, and interior because they are between the two parallel lines. ∠3 and ∠5 are consecutive exterior angles.
You can use similar reasoning we have been so far to conclude all consecutive angles are supplementary
Trisha and Beth are going to play a couple video games. Trisha has her favorite and beth has adifferent favorite. if 2 games are chosen at random out of the total games, what is the chance that both of their favorites are chosen?
Answer:
2/12 or 1/6
Step-by-step explanation:
12 games total
they have 2 games that are there favorite
In a lumberjack competition, a contestant is blindfolded and then spun around 9 times. The contestant then immediately tries to hit a single point (the target) in the middle of a horizontal log with an axe (while still blindfolded). The contestant receives
15 points if their swing is within 3cm of the target.
10 points if their swing is between 3cm and 10cm of the target.
5 points if their swing is between 10cm and 20cm of the target
zero points if their swing is further away from the target (and someone may lose a finger!).
Let Y record the position of the hit, so that Y = y > 0 corresponds to missing the target point to the right by y cm and Y = - y < 0 corresponds to missing the target to the left by y cm. Assume that Y is normally distributed with mean mu = 0 and variance 100 cm^2. Find the expected number of points that the contestant wins.
Answer:
9.364 is the expected number of points.
we can approximate this to 10 points if we want a whole number
Step-by-step explanation:
We have these variables:
[0,5,10,15]
P(x= 0) = p(y>20)+p(y<-20) = 2p(y>20)
P(x=5) = p(-20<=y<=10)+p(10<=y<=20) = 2p(10<=y<=20)
P(x=10) = p(-10<=y<=-3)+p(3<=y<=10) = 2p(3<=y<=10)
P(x=15) = p(-3<=y<=3) = 2p(0<=y<=3)
Z = y/10
Therefore
P(x= 0) = 2(y>20)
= 2p(z>2) = 2(1-p<=2)
= 2(1-0.9772)
= 0.0456
P(x= 5)
= 2p(10<=y<=20)
= 2p(1<=z<=2)
= 2(0.9772-0.8413)
= 0.2718
P(x= 10)
= 2p(3<=y<=10)
= 2p(0.3<=z<=1)
= 2(0.8413-0.6179)
= 0.4468
P(x = 15)
= P(0.6179-0.3821)
= 0.2358
To get expected value of Y
0(0.0456)+5(0.2718)+10(0.4468)+15(0.2358)
= 1.359 + 4.468 + 3.537
= 9.364
E[Y] = 9.364
A line that includes the point (7,0) has a slope of 1. What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
Step-by-step explanation:
i think that the equations might be y = x - 7
The Total cost to rent 5 chairs and 3 tables is $31 dollars. What is the cost to rent each chair and each table? No links please
Answer:
b
Step-by-step explanation:
The height of a thrown ball is a quadratic function of the time it has been in the air. The graph of the quadratic function is the parabolic path of the ball.The vertex of the graph is (1, 20) and the path of the ball includes the point (0,4). What is an expression that defines this function? Write the quadratic function in vertex form.
Answer:
f(x) = a(x - 1) + 20
Step-by-step explanation:
Vertex form is written in this format: f(x) = a(x - h) + k. The vertex point is written in the form (h,k). To write the vertex in the equation, fill in the digits where they belong.
Hope it helps!
The ball's parabolic route is represented by the quadratic function's graph. The quadratic function is x²-2x+4=0.
Given that,
A thrown ball's height is a quadratic function of the amount of time it has been in the air. The ball's parabolic route is represented by the quadratic function's graph. The ball's route includes the location (1, 20), which is the graph's vertex (0,4).
We have to find what does the expression for this function look like? In vertex form, write the quadratic function.
What is the vertex form of a parabola?Use y= a(x-h)² + k as the vertex form of a parabola.
(The parabola opens upward if "a" is positive and downward if "a" is negative.) Additionally, the vertex of the (h,k) is a parabola.
The vertex of the parabola (h,k) is (1,20)
The a value is 4 and y as 0.
y=a(x-h)²+k
0=4(x-1)²+20
0=4(x²-2x+1)+20
0=4x²-8x-4+20
0=4x²-8x+16
4x²-8x+16=0
x²-2x+4=0
Therefore, the quadratic function is x²-2x+4=0.
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helppppppppppppppppppppp
Answer:
26 square feet
Step-by-step explanation:
I dont know if this is right
Carl has visited 49 of the 50 states.
What percent of the states has he visited?
Need help quick
Answer:
98%
Step-by-step explanation:
Solve for x In the equation.
Answer:
x = 16
Step-by-step explanation:
[tex] \frac{2x - 5}{x + 8} = \frac{22.5}{20} [/tex]
Cross multiply
[tex] (2x - 5)*20 = (x + 8)*22.5 [/tex]
[tex] 40x - 100 = 22.5x + 180 [/tex]
Collect like terms
40x - 22.5x = 100 + 180
17.5x = 280
Divide both sides by 17.5
x = 280/17.5
x = 16
What is the horizontal distance from the origin to the point (8, 1)?
Answer:
Me encanta el pollo, de todos modos, un día que es hoy, por cierto, fui a la tierra de los pollos y caminé en México, ¿sabías que es mi sueño? ¿Olvidé que mi nombre es jemma y me gusta caminar? párrafo así que nos vemos
slove for q: q/10 = 4
Answer:
4
Step-by-step explanation:
Answer:
1/10 = 4
Step-by-step explanation:
Find the largest number which divides 248 and 1032 leaving the remainder 8 in each case.
Answer:
...... .................
Find the missing dimension of the cylinder. Round your answer to the nearest whole number.
Answer:
d≈21.99
Step-by-step explanation:
In a pre-election poll, 58% of a large random sample of voters responded as planning to vote for the school enhancement millage. A 95% confidence interval was computed for the proportion of all such voters who plan to vote for the school enhancement millage. Review each of the following statements regarding the meaning of the 95% confidence level. Determine if it is a correct (true) meaning or incorrect (false).
Answer: Hello the statement related to your question is missing attached below is the statement
answer : The statement is false
Step-by-step explanation:
The statement is false
This is because a confidence interval gives a range of values for an unknown parameter.
A 95% confidence interval is calculated and it gives a lower and upper limit in which the 58% of the voters can fall into i.e. The 58% of voters can fall within the upper and lower limit of the 95% confidence interval and not exactly 95% . Hence the statement is false.
what is 4x-2=3(x-3)
Answer:
x = -7
Step-by-step explanation:
4x - 2 = 3(x - 3)
use the distributive property
4x - 2 = 3x - 9
+9 +9
4x + 7 = 3x
-4x -4x
7 = -1x
x = -7
Hope I helped! Have a nice day! Plz mark as brainliest!!! :D
-XxDeathshotxX
Convince yourself that there are 3 similar triangles in the diagram. Choose the
similarity statement that represents the relationship among the 3 triangles.
Only answer if sure
Answer:
second option.
Step-by-step explanation:
On a map, the distance of two inches is equal to ten miles. How many
miles does 4 inches represent on the map?
10
20
30
40
A manufacturer of cream filled donuts collected data from its automatic filling process. The amount of cream inserted into the donuts is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 donuts. The correct value of t to construct a 90% confidence interval for the true mean amount of cream filling is _______.
Answer:
The appropriate solution is "1.7109". A further explanation is provided below.
Step-by-step explanation:
The given values are:
Sample size,
n = 25
Degree of freedom,
[tex]df=n-1[/tex]
[tex]=25-1[/tex]
[tex]=24[/tex]
At 90% confidence level,
[tex]\alpha=1-90 \ percent[/tex]
[tex]=1-0.9[/tex]
[tex]=0.1[/tex]
and,
[tex]\frac{\alpha}{2}=\frac{0.1}{2}[/tex]
[tex]=0.05[/tex]
Now,
The correct values of t will be:
= [tex]t_{\frac{\alpha}{2}, df }[/tex]
= [tex]t_{0.05,24}[/tex]
= [tex]1.7109[/tex]
Mike needs to buy a water tank. The tank must fit inside a storage box that is shaped like a cube with the side lengths of 30 feet. Water tanks are available in cylinders, cones, square pyramids, and spheres. Mike wants to buy the tank that has the largest capacity. What shape tank should Mike buy?
Answer:
sphere
Step-by-step explanation:
sphere has a larger volume
Ali's dog weighs 8 times as much as her cat together the two pets weigh 54 lb how much does Ali's dog weigh
Answer:
48
Step-by-step explanation:
Cat = x
Dog = 8x
x + 8x = 54
9x = 54
x = 6, Dog = 8 * 6 = 48
please help A hologram projection of Leia is 5.5 feet tall. The angle from the ground to the top of the hologram is 25°. How far away from the hologram is the Jedi Trainee?
Answer:
11.7947881
depends now how you wanna round it
Step-by-step explanation:
tan(25)=5.5/x
x=5.5/tan(25)
x=11.7947881
this is how we round it in my school
x≈11.8
Can somebody help me plsssss
5,0 is not a solution to the system of linear inequalities.
180 students in a 10th grade class high school take a survey about which video game consoles they own. 80 students answer that one of the consuls is a PlayStation 90 answer that one of the consules is an Xbox out of these there are 30 who are both systems > continue reading on picture pls help very important
Answer:
Ur answer is in attachment
Step-by-step explanation:
please mark me as brainliest
The probability that a student has both box and a console is 1/6 and the P(B/A) = 0.378
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening being equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here, the number of students with both video games is 30 thus
The probability that a student has both box and a console is 30/180=1/6
And the conditional probability P(B/A) is = 1/6/0.44
= 0.378
Hence, The probability that a student has both box and a console is 1/6, and the P(B/A) = 0.378
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Simplify.
Remove all perfect squares from inside the square root.
√56z^7
Answer:
[tex]2[/tex][tex]z^{3}[/tex][tex]\sqrt{14z}[/tex]
Step-by-step explanation:
The simplified form of √56z⁷ is 2z³√(14z⁴ ) in the given question.
To simplify √56z⁷, we can break down the number 56 into its prime factors and remove any perfect square factors from inside the square root.
When simplifying a square root expression, removing perfect square factors from inside the square root helps simplify the expression further. This is because the square root of a perfect square is a whole number.
First, let's factorize 56:
56 = 2 * 2 * 2 * 7
Since 2 is a perfect square, we can remove it from inside the square root:
√56z⁷ = √(2 * 2 * 2 * 7 * z⁷ )
Simplifying further:
√56z⁷ = 2z³√(2 * 7 * z)
Therefore, the simplified form of √56z⁷ is 2z³ √(14z⁴ ).
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Wayne charges the following for repairing washing machines:
£28 call-out charge + £16 for each half-hour he spends on the repair
If a repair costs £76, how long did it take?