Answer:
Following are the solution to the given points:
Step-by-step explanation:
For point a:
[tex]fx|H(x) = 1;0< x<1\\\\fX|T(x) = 2x; 0\leq x \leq 1\\\\fx(x) = P(H \bigcap X = x) +P(T \bigcap X=x)\\\\[/tex]
[tex]=P(H)fX|H(x)+P(T)fX|T(x)\\\\= p(1) + (1-p)2x\\\\= p(1 -2x)+2x\\\\[/tex]
Using the PDF of the X value
[tex]fX(x) =2x +p(1 - 2x); \ 0\leq x\leq 1[/tex]
0 ; otherwise
For point b:
[tex]E(X)=\int^{1}_{0} \ x fX (x)\ dx=\int^{1}_{0} \ x(2x+p(1-2x))\ dx\\\\=\int^{1}_{0} \ (2x^2+(x-2x^2)p) dx\\\\[/tex]
[tex]= 2(\frac{x^3}{3}) + (\frac{x^2}{2}-2(\frac{x^3}{3}) \begin{vmatrix} x=1\\ x=0\end{vmatrix} \\\\[/tex]
[tex]= \frac{2}{3} + (\frac{1}{2} - \frac{2}{3})p\\\\= \frac{2}{3} -\frac{p}{6}\\\\= \frac{(4 - p)}{6}[/tex]
In a game where only one player can win, the probability that Jack will win is 1/7 and the probability that Bill will win is 1/2. Find the probability that one of them will win. (Enter your probability as a fraction.)
The probability that one of them will win will be 9/14.
Since the probability that Jack will win is 1/7 and the probability that Bill will win is 1/2, then the probability that one of them will win will be:
= 1/7 + 1/2
= 7/14 + 2/14
= 9/14
Therefore, the probability that one of them will win will be 9/14.
Read related link on:
https://brainly.com/question/21689780
The graph shows the functior f(x) = 2X
What is the value of x when f(x) = 8?
Answer: b
Step-by-step explanation:
If a hypothesis is not rejected at a 5% level of significance, it _____.
a. will also not be rejected at the 1% level
b. may be rejected or not rejected at the 1% level
c. will always be rejected at the 1% level
d. will sometimes be rejected at the 1% level
Answer:
a. will also not be rejected at the 1% level.
Step-by-step explanation:
A hypothesis is rejected if:
The p-value is larger than the significance level.
Hypothesis is not rejected at a 5% level of significance
This means that the p-value is > 0.05.
At the 1% level:
p-value > 0.01, so it will never be rejected, and thus, the correct answer is given by option a.
Building A is 170 feet shorter than building B. The total height of the two building is 1490 feet. Find the height of each building.
Answer:
Building A is 660 feet and Building B is 830 feet
Step-by-step explanation:
Let x represent the height of building B.
Since building A is 170 feet shorter than building B, it can be represented by x - 170.
Create an equation and solve for x:
(x) + (x - 170) = 1490
2x - 170 = 1490
2x = 1660
x = 830
So, the height of building B is 830 feet.
Subtract 170 from this to find the height of building A:
830 - 170
= 660
Building A is 660 feet and Building B is 830 feet
Expand 3(5y-3) can someone answer this please
Answer:
15y -9
Step-by-step explanation:
3(5y-3)
Distribute
3*5y -3*3
15y -9
what’s the missing side of the polygons
Answer:
the missing side is 21!!!!!!!!
Evaluate z^2−3 z+4 , when z=−4
Answer:
8
Step-by-step explanation:
=z²-3z+4 when z is 4
=4²-3(4)+4
=16-12+4
=8
find x in this similar triangles
Answer:
6. x = 4
8. x = 13
Step-by-step explanation:
Using similar triangles theorem,
6. (5+4)/5 = (4x + 2)/(4x + 2 - 8)
9/5 = (4x + 2)/(4x - 6)
Cross multiply
9(4x - 6) = 5(4x + 2)
36x - 54 = 20x + 10
Collect like terms
36x - 20x = 54 + 10
16x = 64
16x/16 = 64/16
x = 4
8. (4x + 13)/20 = 52/16
(4x + 13)/20 = 13/4
Cross multiply
4(4x + 13) = 13(20)
16x + 52 = 260
16x = 260 - 52
16x = 208
x = 208/16
x = 13
Help please guys thanks
Answer:
5
Step-by-step explanation:
(625 ^2)^(1/8)
Rewriting 625 as 5^4
(5^4 ^2)^(1/8)
We know that a^b^c = a^(b*c)
5^(4*2)^1/8
5^8 ^1/8
5^(8*1/8)
5^1
5
Answer:
[tex]5[/tex]
Step-by-step explanation:
[tex] { {(625}^{2} )}^{ \frac{1}{8} } \\ { ({25}^{2 \times 2} )}^{ \frac{1}{8} } \\ {25}^{4 \times \frac{1}{8} } \\ {5}^{2 \times 4 \times \frac{1}{8} } \\ {5}^{ \frac{8}{8} } \\ {5}^{1} \\ = 5[/tex]
is 2012 a term of arithmetic sequence of 5,13,18
for the given A.P
5,9,13,...
First term (a)=5
common difference (d) = 9-5=4
Let Tn=2012
a +(n-1) d=2012
5 +(n-1) 4=2012
(n-1) 4=2012-5
(n-1)4=2007
n-1=501.75
n=1+501.75
n=502.75 -- - - - - -> which is not possible.
No.of terms can never in fraction.
Hence, 2012 is not a term of given A.P
Approximately 5% of calculators coming out of the production lines have a defect. Fifty calculators are randomly selected from the production line and tested for defects. What is the probability that exactly 2 calculators are defective?
Answer:
0.2611 = 26.11% probability that exactly 2 calculators are defective.
Step-by-step explanation:
For each calculator, there are only two possible outcomes. Either it is defective, or it is not. The probability of a calculator being defective is independent of any other calculator, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
5% of calculators coming out of the production lines have a defect.
This means that [tex]p = 0.05[/tex]
Fifty calculators are randomly selected from the production line and tested for defects.
This means that [tex]n = 50[/tex]
What is the probability that exactly 2 calculators are defective?
This is P(X = 2). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{50,2}.(0.05)^{2}.(0.95)^{48} = 0.2611[/tex]
0.2611 = 26.11% probability that exactly 2 calculators are defective.
what is the value of tan 0 in the unit circle below
Tangent = opposite / adjacent, or in this case Tangent = y / x.
Tan = (1/2) / ([tex]\sqrt{3}[/tex] / 2)
1 / [tex]\sqrt{3}[/tex]
[tex]\sqrt{3}[/tex] / 3
Hope this helps!
1. Consider a lottery with three possible outcomes:-$125 will be received with probability 0.2-$100 will be received with probability 0.3-$50 will be received with probability 0.5a. What is the expected value of the lottery
Answer:
The expected value of the lottery is $80
Step-by-step explanation:
To get the expected value, we have to multiply each outcome by its probability
Then we proceed to add up all of these to get the expected value of the lottery
we have this as ;;
125(0.2) + 100(0.3) + 50(0.5)
= 25 + 30 + 25 = $80
If all possible random samples of size N are drawn from a population with a mean of mu and a standard deviation of sigma, then as N becomes larger, the sampling distribution of sample means becomes approximately normal with a mean of muy(bar) and a standard deviation of sigmay(bar). This statement is known as the:
Answer:
"Central limit theorem" is the right answer.
Step-by-step explanation:
A hypothesis essentially claims that whenever there seems to be a small variance throughout the big confidence intervals, the sampling is based on averages as well as the sampling distribution (mean) usually nearly the same as the public's median.
When,
Mean = [tex]\mu_y[/tex]Standard deviation = [tex]\sigma_y[/tex]Sample size = Nis sufficiently larger than [tex]\bar Y \sim N(\mu_y, \sigma_y)[/tex]
Thus, the above is the right answer.
Answer theas question
(1) Both equations in (a) and (b) are separable.
(a)
[tex]\dfrac xy y' = \dfrac{2y^2+1}{x+1} \implies \dfrac{\mathrm dy}{y(2y^2+1)} = \dfrac{\mathrm dx}{x(x+1)}[/tex]
Expand both sides into partial fractions.
[tex]\left(\dfrac1y - \dfrac{2y}{2y^2+1}\right)\,\mathrm dy = \left(\dfrac1x - \dfrac1{x+1}\right)\,\mathrm dx[/tex]
Integrate both sides:
[tex]\ln|y| - \dfrac12 \ln\left(2y^2+1\right) = \ln|x| - \ln|x+1| + C[/tex]
[tex]\ln\left|\dfrac y{\sqrt{2y^2+1}}\right| = \ln\left|\dfrac x{x+1}\right| + C[/tex]
[tex]\dfrac y{\sqrt{2y^2+1}} = \dfrac{Cx}{x+1}[/tex]
[tex]\boxed{\dfrac{y^2}{2y^2+1} = \dfrac{Cx^2}{(x+1)^2}}[/tex]
(You could solve for y explicitly, but that's just more work.)
(b)
[tex]e^{x+y}y' = 3x \implies e^y\,\mathrm dy = 3xe^{-x}\,\mathrm dx[/tex]
Integrate both sides:
[tex]e^y = -3e^{-x}(x+1) + C[/tex]
[tex]\ln(e^y) = \ln\left(C - 3e^{-x}(x+1)\right)[/tex]
[tex]\boxed{y = \ln\left(C - 3e^{-x}(x+1)\right)}[/tex]
(2)
(a)
[tex]y' + \sec(x)y = \cos(x)[/tex]
Multiply both sides by an integrating factor, sec(x) + tan(x) :
[tex](\sec(x)+\tan(x))y' + \sec(x) (\sec(x) + \tan(x)) y = \cos(x) (\sec(x) + \tan(x))[/tex]
[tex](\sec(x)+\tan(x))y' + (\sec^2(x) + \sec(x)\tan(x)) y = 1 + \sin(x)[/tex]
[tex]\bigg((\sec(x)+\tan(x))y\bigg)' = 1 + \sin(x)[/tex]
Integrate both sides and solve for y :
[tex](\sec(x)+\tan(x))y = x - \cos(x) + C[/tex]
[tex]y=\dfrac{x-\cos(x) + C}{\sec(x) + \tan(x)}[/tex]
[tex]\boxed{y=\dfrac{(x+C)\cos(x) - \cos^2(x)}{1+\sin(x)}}[/tex]
(b)
[tex]y' + y = \dfrac{e^x-e^{-x}}2[/tex]
(Note that the right side is also written as sinh(x).)
Multiply both sides by e ˣ :
[tex]e^x y' + e^x y = \dfrac{e^{2x}-1}2[/tex]
[tex]\left(e^xy\right)' = \dfrac{e^{2x}-1}2[/tex]
Integrate both sides and solve for y :
[tex]e^xy = \dfrac{e^{2x}-2x}4 + C[/tex]
[tex]\boxed{y=\dfrac{e^x-2xe^{-x}}4 + Ce^{-x}}[/tex]
(c) I've covered this in an earlier question of yours.
(d)
[tex]y'=\dfrac y{x+y}[/tex]
Multiply through the right side by x/x :
[tex]y' = \dfrac{\dfrac yx}{1+\dfrac yx}[/tex]
Substitute y(x) = x v(x), so that y' = xv' + v, and the DE becomes separable:
[tex]xv' + v = \dfrac{v}{1+v}[/tex]
[tex]xv' = -\dfrac{v^2}{1+v}[/tex]
[tex]\dfrac{1+v}{v^2}\,\mathrm dv = -\dfrac{\mathrm dx}x[/tex]
[tex]-\dfrac1v + \ln|v| = -\ln|x| + C[/tex]
[tex]\ln\left|\dfrac yx\right| -\dfrac xy = C - \ln|x|[/tex]
[tex]\ln|y| - \ln|x| -\dfrac xy = C - \ln|x|[/tex]
[tex]\boxed{\ln|y| -\dfrac xy = C}[/tex]
Fraces bonitas para decirle a tu nv?
minimo 6
Answer:
it's. is now the MA plz I miss you
si pudiera escoger entre vivir eternamente y vivir dos veces
yo escogeria vivir dos veces porque vivir una vida eterna sin ti a mi lado seria el mayor sufrimiento, ahora vivir dos veces me dejaria tranquilo porque despues del final de mi vida podria volver a encontrarme contigo y vivir todos los momentos bellos una vez mas y eso seria un sueño volviendose realidad
If f(x) = negative 3X -2, what if f(-5)?
Answer:
f(- 5) = 13
Step-by-step explanation:
Substitute x = - 5 into f(x)
f(x) = - 3x - 2 , then
f(- 5) = - 3(- 5) - 2 = 15 - 2 = 13
What number can go in the box to make the number sentence true?
6 + 0 = 10
0.
4.
6.
10.
Which of the following scatterplots would have a trend line with a negative slope?
Answer:
A scatter plot shows a negative trend if y tends to decrease as x increases. A scatter plot shows no trend if there is no obvious pattern.
PLEASE HELPPPPPPPPPPP
Answer:
P(S or T) = 3/4
Step-by-step explanation:
A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken. a. What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean
Answer:
expected value is the mean : 10.5
Standard error for the sampling distribution : 0.375
it has a bell-shaped curve with 99.7% of the values between 9.375 and 11.625
Step-by-step explanation:
Which of the following is a solution to 2sin2x+sinx-1=0?
Answer:
270 degrees
Step-by-step explanation:
If you plug in 270 in place of the x's, the function is true!
This is correct for Plate/Edmentum users!! Hope I could help :)
Find the size of unknown angles
Step-by-step explanation:
2x+3x+x+20=180
6x+20=180
6x=160
x=160/6
x=26.667
Answer:
2X=53.2 , 3X=79.8 , X+20=46.6
Step-by-step explanation:
3X+2X+X+20=180
therefore,
6X+20=180
6X =180-20
6X =160
X = 160 over 6
X =26.6
now,
3X = 26.6 x3
=79.8
2X =26.6 x2
=53.20
X+20 =26.6+20
=46.6
Im not sure if it's right. Because the total does not make 180 degrees.
What’s the equation?
Answer:
The answer is D.
Step-by-step explanation:
15. Find the x- and y-intercepts for the lineal equation - 3x + 4y = 24
Please explain steps! ❤️
Answer:
x (-8,0)
y (0,6)
Step-by-step explanation:
at the x-intercept, y = 0
at the y-intercept x=0
sub those values into your equation!
for the x-intercept,
-3x = 24
x = -8
for the y-intercept,
4y = 24
y = 6
what are the zeros of this function?
Answer:
the Ans is c
Step-by-step explanation:
actually I don't know how to explain
Which expression is equivalent to 3(x - y) + y? 3x - 4y 3x - 3y 3x - 2y 3(x - 2y)
9514 1404 393
Answer:
(c) 3x - 2y
Step-by-step explanation:
Use the distributive property to eliminate parentheses, then collect terms.
3(x -y) +y = 3x -3y +y = 3x +(-3+1)y = 3x -2y
Now we have to find,
The expression which is equivalent to,
→ 3(x - y) + y
Let's get the solution,
→ 3(x - y) + y
→ 3x - 3y + y
→ 3x - 2y
Hence, required expression is 3x - 2y.
Divide 5x^2+3x-2 by x + 1
5x + 8
I used long division
Ophelia is making homemade spaghetti sauce by combining 48 oz of tomato paste with 6 cups of water.ophelia needs to make a small batch of sauce using only 20 ounces of tomato paste how many cups of water will she need.show your work
Answer:
1 cup per 8 oz
48/6 = 8
every 1 cup of water 8 oz of tomato paste.
Step-by-step explanation:
can i brainlist
PLEASE HELP I REALLY NEED THIS
How is an inequality different from an equation?
What are four ways inequality can be written?
What would the graph of each inequality look like on a number line? (use an example)
What would the graph of an equation look like on a number line(use an example)
Pam has 15 candies in a jar, her sister threw in some more ( the ones she doesn’t like) and now Pam has 27. Write an equation to determine how many candies ( x) her sister put in the jar. Solve using both inverse operations and a balance scale.
Explain the Golden Rule for solving equations
using an example.
What does it mean if a situation has a condition or constraint? Give an example.
Give an example of a situation that contains an independent and dependent variable. Explain if your data is continuous or discrete.
Answer:
inequality is mostly represented on a number line but equation is not.
