By definition of conditional probability,
P(X ≤ 0.5 | X ≤ 1) = P((X ≤ 0.5) and (X ≤ 1)) / P(X ≤ 1)
but if X ≤ 0.5, then it's automatic that X ≤ 1, so
P(X ≤ 0.5 | X ≤ 1) = P(X ≤ 0.5) / P(X ≤ 1)
Given the PDF of X,
[tex]f_X(x) = \begin{cases}2e^{-2x}&\text{if }x\ge0\\0&\text{otherwise}\end{cases}[/tex]
the CDF would be
[tex]P(X\le x) = F_X(x) = \displaystyle\int_{-\infty}^x f_X(t)\,\mathrm dt[/tex]
[tex]F_X(x) = \begin{cases}0&\text{if }x<0\\1-e^{-2x}&\text{if }x\ge0\end{cases}[/tex]
So we have
P(X ≤ 0.5 | X ≤ 1) = (1 - exp(-2 × 0.5)) / (1 - exp(-2 × 1))
… = (1 - exp(-1)) / (1 - exp(-2))
… = (1 - 1/e) / (1 - 1/e ²)
… = (e ² - e) / (e ² - 1)
… = e / (e + 1) ≈ 0.7312
Solve the following formula for a.
Answer:
B is correct .trust me
Step-by-step explanation:
Steve thinks he can drive legally 30 minutes after he drinks 5 beers. The legal limit is BAC = 0.08. Give a 90% prediction interval for Steve’s BAC. Can he be confident he won’t be arrested if he drives and is stopped?
Answer: Hello your question has some missing data attached below is the missing data
How well does the number of beers a student drinks predict his or her blood alcohol content (BAC)? Sixteen student volunteers at Ohio State University drank a randomly assigned number of 12-ounce cans of beer. Thirty minutes later, a police officer measured their BAC. Here are the data. The students were equally divided between men and women and differed in weight and usual drinking habits. Because of this variation, many students don’t believe that number of drinks predicts BAC well.
answer:
prediction interval : (0.040 , 0.114)
Step-by-step explanation:
Given data:
Confidence level = 90%
Legal limit ( BAC ) = 0.08
solution
sample size = 16
Degree of freedom ( df ) = 14
critical t value = 1.761
X = 4.81
Σ(x-x)² (Sx) = 72.44
also standard error of estimates = 0.0204
Y= -0.01270 + 0.01796 * 5 = 0.077
given that ; the predicted value of Y at x = 5
Considering individual response Y
standard error = 0.0211
margin of error = 1.761 * 0.021 = 0.0371
Hence the limits of the prediction interval is :
Lower limit = 0.077 - 0.037 = 0.040.
Upper limit = 0.077 + 0.037 = 0.114
Finally
90% prediction interval = (0.040 , 0.114)
What is the area of the right triangle with sides 10,26 and 24
Answer:
[tex]\boxed {\boxed {\sf 120 \ units^2}}[/tex]
Step-by-step explanation:
We are asked to find the area of a triangle. The formula for calculating this is:
[tex]a= \frac{1}{2} bh[/tex]
This is a right triangle, so the base and height are the legs of the triangle. The 2 smallest sides are the legs because the longest side is the hypotenuse. Since the side lengths are 10, 26, and 24, the base and height must be 10 units and 24 units.
b= 10 unitsh= 24 unitsSubstitute these values into the formula.
[tex]a= \frac{ 1}{2} ( 10 \ units)(24 \ units)[/tex]
Multiply the numbers in parentheses.
[tex]a= \frac{1}{2}(240 \ units^2)[/tex]
Multiply by 1/2 or divide by 2.
[tex]a= 120 \ units^2[/tex]
The area of the triangle is 120 units squared.
Triangle DEF has sides of length x, x+3, and x−1. What are all the possible types of DEF?
Triangle DEF is scalene
Must click thanks and mark brainliest
The triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.
What is a scalene triangle?A scalene triangle is a type of triangle which have all the sides to be unequal and similarly, all the angles will also be unequal to each other.
Given that:-
Triangle DEF has sides of length x, x+3, and x−1it is given that all the sides of the triangle are x, x+3, and x−1 we can clearly see that for any value of x all the three sides will have different values. we can conclude from this that the triangle DEF is a scalene triangle.
Therefore triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.
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find the maximum number of children to whom 30 sweaters and 45 trousers can be equally divided. also how many sweaters and trousers will each get?
Answer:
five kids .each 6 sweaters and 9 trousers
Step-by-step explanation:
fHãy tìm hàm gốc f(t) có hàm ảnh Laplace như dưới đây:
F(p)=6/p(2p^2+4p +10)
It looks like we're given the Laplace transform of f(t),
[tex]F(p) = L_p\left\{f(t)\right\} = \dfrac6{p(2p^2+4p+10)} = \dfrac3{p(p^2+2p+5)}[/tex]
Start by splitting up F(p) into partial fractions:
[tex]\dfrac3{p(p^2+2p+5)} = \dfrac ap + \dfrac{bp+c}{p^2+2p+5} \\\\ 3 = a(p^2+2p+5) + (bp+c)p \\\\ 3 = (a+b)p^2 + (2a+c)p + 5a \\\\ \implies \begin{cases}a+b=0 \\ 2a+c=0 \\ 5a=3\end{cases} \implies a=\dfrac35,b=-\dfrac35, c=-\dfrac65[/tex]
[tex]F(p) = \dfrac3{5p} - \dfrac{3p+6}{5(p^2+2p+5)}[/tex]
Complete the square in the denominator,
[tex]p^2+2p+5 = p^2+2p+1+4 = (p+1)^2+4[/tex]
and rewrite the numerator in terms of p + 1,
[tex]3p+6 = 3(p+1) + 3[/tex]
Then splitting up the second term gives
[tex]F(p) = \dfrac3{5p} - \dfrac{3(p+1)}{5((p+1)^2+4)} - \dfrac3{5((p+1)^2+4)}[/tex]
Now take the inverse transform:
[tex]L^{-1}_t\left\{F(p)\right\} = \dfrac35 L^{-1}_t\left\{\dfrac1p\right\} - \dfrac35 L^{-1}_t\left\{\dfrac{p+1}{(p+1)^2+2^2}\right\} - \dfrac3{5\times2} L^{-1}_t\left\{\dfrac2{(p+1)^2+2^2}\right\} \\\\ L^{-1}_t\left\{F(p)\right\} = \dfrac35 - \dfrac35 e^{-t} L^{-1}_t\left\{\dfrac p{p^2+2^2}\right\} - \dfrac3{10} e^{-t} L^{-1}_t\left\{\dfrac2{p^2+2^2}\right\} \\\\ \implies \boxed{f(t) = \dfrac35 - \dfrac35 e^{-t} \cos(2t) - \dfrac3{10} e^{-t} \sin(2t)}[/tex]
What is the measure of m?
Answer:
√245
Step-by-step explanation:
altitude on hypotenuse theorem:
m^2=7*35
m^2=245
m=√245
What is the volume of a cone below?
Given FE=23.5, find BD.
Answer:
11.75
Step-by-step explanation:
The required triangle is attached below :
The triangle AFE has it's by the mid segment as BD ;as B is the mid-point of line EA ; and D is the mid-point of line FA ;
HENCE, The Length of the midsegment BD = 1/2FE
Hence, BD =. 1/2 * 23.5
BD = 23.5 / 2 = 11.75
4. Lynn can walk two miles intenta
24 minutes. At this rate, how long will
it take her to walk 6 miles?
Please answer this and show the work/explain
2/7m - 1/7 = 3/14
(2/7)m - (1/7) = 3/14
2m/7 =(3/14) + (1/7)
2m/7 = (3/14) + 2(1/7)
here we are multiplying 2 with 1/7 to make the denominator same for addition.
2m/7 = (3/14) +(2/14)
2m/7 = (3 + 2)/14
2m/7 = 5/14
2m = (5 *7)/14
2m = 35/14
2m = 5/2
m = 5/4
m = 1.25
So the value of "m" is 1.25
What is the image of -8 ,8 after a dilation by a scale factor of one fourth centered at the origin?
Answer:
(-2, 2)
Step-by-step explanation:
If you have a point (x, y) and you do a dilation by a scale factor K centered at the origin, the new point will just be (k*x, k*y)
So, if the original point is (-8, 8)
And we do a dilation by a scale factor k = 1/4
Then the image of the point will be:
(-8*(1/4), 8*(1/4))
(-8/4, 8/4)
(-2, 2)
find the value of the trigonometric ratio. make sure to simplify the fraction if needed
Answer:
Sin A = o/h
= 9/41
Step-by-step explanation:
since Sin is equal to opposite over hypotenuse, from the question, the opposite angle of A is 9 and hypotenuse angle of A is 41. Thus the answer for Sin A= 9/41
HELP WITH 16 What is the value of X
Answer:
C - 136
(115+157)/2
Step-by-step explanation:
Find the measure of the incanted angle to the nearest degree
Answer:
Sinx = 21/40
x = inverse of sin (21/40)
x= 31.6682
hope u got it
Answer:
31.6 degrees
Step-by-step explanation:
sin-¹(p/h) = 31.6
Help please!??!!?!?
9514 1404 393
Answer:
a) CP = SP/1.1
b) CP = $59.50
c) GST = $5.95
Step-by-step explanation:
a) Divide by the coefficient of CP.
SP = 1.1×CP
CP = SP/1.1
__
b) Use the formula with the given value.
CP = $65.45/1.1 = $59.50
__
c) You can do this two ways: subtract CP from SP, or multiply CP by 0.1.
GST = SP -CP = $65.45 -59.50 = $5.95
GST = CP×0.10 = $59.50 × 0.10 = $5.95
What are the x-intercepts for the function ƒ(x) = -x(x − 4)?
A 0
B -1, 4
C 4
D 0, 4
What are the solutions to the quadratic equation 4x2 − x − 3 = 0?
Answer:
D
Step-by-step explanation:
f(x)=-x(x-4)
f(x)=-x²+4x
-x²+4x=0
x(-x+4)=0
x=0, x=4
(2)
4x²-x-3=0
(4x²+3x)-(4x-3)=0
x(4x+3)-1(4x+3)=0
x=1, x=-3/4
A 10-ft ladder, whose base is sitting on level ground, is leaning at an angle against a vertical wall when its base starts to slide away from the vertical wall. When the base of the ladder is 6 ft away from the bottom of the vertical wall, the base is sliding away at a rate of 4 ft/sec. At what rate is the vertical distance from the top of the ladder to the ground changing at this moment?
Answer:
2.5/ft per sec
Step-by-step explanation:
its vertica.
The height of the ladder is decreasing at a rate of 24 ft/sec.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
Let's denote the distance between the base of the ladder and the wall by x.
The length of the ladder = L.
Now,
L = 10 ft
dx/dt = 4 ft/sec
x = 6 ft.
The rate of change of the height of the ladder with respect to time.
Using the Pythagorean theorem, we have:
L² = x² + y²
Differentiating both sides with respect to time t, we get:
2L (dL/dt) = 2x(dx/dt) + 2y(dy/dt)
Substituting L = 10 ft, x = 6 ft, and dx/dt = 4 ft/sec.
20(dL/dt) = 12(4) + 2y(dy/dt)
Simplifying and solving for dy/dt.
dy/dt = (20/2y)(dL/dt) - 24
Now,
The height of the ladder.
Using the Pythagorean theorem again, we have:
y² = L² - x²
= 100 - 36
= 64
y = 8
Now,
Substituting y = 8 ft, dL/dt = 0
(since the length of the ladder is constant), and dx/dt = 4 ft/sec.
dy/dt
= (20/2(8))(0) - 24
= -24 ft/sec
Therefore,
The height of the ladder is decreasing at a rate of 24 ft/sec.
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Which of the following graphs represents a one-to-one function? On a coordinate plane, a function has two curves connected to a straight line. The first curve has a maximum of (negative 6, 4) and a minimum of (negative 4.5, negative 1). The second curve has a maximum of (negative 3.5, 2) and a minimum of (negative 2.5, 0.5). The straight line has a positive slope and starts at (negative 2, 1) and goes through (1, 2). On a coordinate plane, a circle intersects the x=axis at (negative 2, 0) and (2, 0) and intercepts the y-axis at (0, 4) and (0, negative 4). On a coordinate plane, a v-shaped graph is facing up. The vertex is at (0,0) and the function goes through (negative 4, 4) and (4, 4). A coordinate plane has 7 points. The points are (negative 4, 1), (negative 3, 4), (negative 1, 3), (1, negative 3), (3, negative 4), (4, negative 2), (5, 3). Mark this and return
Answer:
d. this graph
Step-by-step explanation:
Value of [(3/2)^(-2)] is *
Answer:
[tex] { (\frac{3}{2} )}^{ - 2} \\ = { (\frac{2}{3}) }^{2} \\ = \frac{4}{9} \\ thank \: you[/tex]
Which of the following rational functions is graphed below?
o
A. F(x) = 1/2x
B. AX) = 1/x-2
C. F(x) = 1/x+2
Answer:
Option B.
Step-by-step explanation:
We can see that we have an asymptote at x = 2
Remember that in a rational function, the asymptote is at the x-value such that the denominator is equal to zero.
So, the denominator is something like:
(x + a)
we have that the denominator is zero when x = 2
Then:
(2 + a) = 0
solving that for a, we get:
a = -2
Then the denominator of the rational function is:
(x - 2)
For the given options, the only one with this denominator is option B, then the correct option is B.
Answer:
B. f(x) = 1/x-2
Step-by-step explanation:
Math is ez bro.
substitute for A,P and T in the fomula A=P (1+r)^t,give that A=1 000 000,P=10 000 and T=2,and express as a quadratic equation
A = 10,00,000
P = 10,000
T = 2
1000000 = 10000(1+r/100)^2
1000000 = 10000((100 + r)/100)^2
1000000 = 10000× 100 + r/100 × 100 + r/100
1000000 = 10000 + r^2
1000000 - 10000 = r^2
990000 = r^2
√99000 = r
Quadratic Equation
10000(1+r/100)^2
the mode of 3,5,1,2,4,6,0,2,2,3 is
giving out brainliest
The figure to the right shows the graphs of the cost and revenue functions for a
company that manufactures and sells small radios. The solid red line represents the
revenue function, R(x) = 55x; the dashed blue line represents the cost function,
C(x) = 15,000 + 30x. Use the formulas to find R(300) - C(300). Describe what this means for the company
(Type integers or decimals.)
R(300) - C(300) = ???
which represents a $ ???
loss for the company
B. R(300) - C(300) = ??
which represents a ??
gain for the company
From the formula R(300) - C(300) we understand that is loss of 7500 for the company.
The given functions are R(x) = 55x and C(x) = 15,000 + 30x.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is R(300) - C(300).
Now, R(300) = 55 × 300 = 16500
C(300) = 15,000 + 30 × 300
=15,000 + 9000
= 24,000
Now, R(300) - C(300) = 16500-24000
= -7,500
Therefore, from the formula R(300) - C(300) we understand that is loss of 7500 for the company.
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Given two dependent random samples with the following results: Population 1 30 35 23 22 28 39 21 Population 2 45 49 15 34 20 49 36 Use this data to find the 90% confidence interval for the true difference between the population means. Assume that both populations are normally distributed. Step 1 of 4: Find the point estimate for the population mean of the paired differences. Let x1 be the value from Population 1 and x2 be the value from Population 2 and use the formula d=x2−x1 to calculate the paired differences. Round your answer to one decimal place.
Answer:
(-14.8504 ; 0.5644)
Step-by-step explanation:
Given the data:
Population 1 : 30 35 23 22 28 39 21
Population 2: 45 49 15 34 20 49 36
The difference, d = population 1 - population 2
d = -15, -14, 8, -12, 8, -10, -15
The confidence interval, C. I ;
C.I = dbar ± tα/2 * Sd/√n
n = 7
dbar = Σd/ n = - 7.143
Sd = standard deviation of d = 10.495 (using calculator)
tα/2 ; df = 7 - 1 = 6
t(0.10/2,6) = 1.943
Hence,
C.I = - 7.143 ± 1.943 * (10.495/√7)
C.I = - 7.143 ± 7.7074
(-14.8504 ; 0.5644)
A kite is a ........... quadrilateral
Answer:
yes
Step-by-step explanation:
The complete sentence is,
A kite is a convex quadrilateral.
We have to given that,
To find a kite is which type of a quadrilateral.
We know that,
A quadrilateral known as a kite has four sides that may be divided into two pairs of neighboring, equal-length sides.
The two sets of equal-length sides of a parallelogram, however, are opposite one another as opposed to being contiguous.
Hence, The complete sentence is,
A kite is a convex quadrilateral.
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HELPPP!!!
find the area of a triangle with a height of 9cm and a base of 5 cm
Answer:
A = 22.5 cm^2
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh where b is the base and h is the height
A = 1/2(5)(9)
A = 45/2
A = 22.5 cm^2
[tex]\begin{gathered} {\underline{\boxed{ \rm {\red{Area \: \: of \: \: triangle \: = \: \frac{1}{2} \: \times \: base \: \times \: height}}}}}\end{gathered}[/tex]
Base of triangle = 5 cm.Height of triangle is 9 cm.Solution[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \frac{1}{2} \: \times \: 5 \: cm \: \times \: 9 \: cm[/tex]
[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \frac{1}{2} \: \times \: 45 \: cm[/tex]
[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \frac{45 \: {cm}^{2} }{2} \: \\ [/tex]
[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \cancel\frac{45}{2} \: \: ^{22.5 \: {cm}^{2} } \: \\ [/tex]
[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: 22.5 \: {cm}^{2} [/tex]
Hence , the area of triangle is 22.5 cm²
How do we solve this?
Answer:
[tex] = - \frac{1}{36(6x + 1) ^{6} } + c[/tex]
I hope I helped you^_^Answer:
[tex]-\frac{1}{36\left(6x+1\right)^6} +C[/tex]
Step-by-step explanation:
we're going to us u substitution
[tex]\int (6x+1)^-7 dx[/tex]
[tex]u=6x+1[/tex]
[tex]\int\frac{1}{6u^7} du[/tex]
take out the constant, [tex]\frac{1}{6}[/tex]
[tex]\frac{1}{6}[/tex] · [tex]\int u^-7du[/tex]
next use the power rule, [tex]\int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1[/tex]
[tex]\frac{1}{6}\cdot \frac{u^{-7+1}}{-7+1}[/tex]
simplify by substituting [tex]6x+1[/tex] for [tex]u[/tex]
[tex]\frac{1}{6}\cdot \frac{(6x+1)^{-7+1}}{-7+1} = -\frac{1}{36\left(6x+1\right)^6}[/tex]
add a constant, [tex]C[/tex]
[tex]-\frac{1}{36\left(6x+1\right)^6} +C[/tex]
2
7) through: (-3,0), slope
3
Answer:
Step-by-step explanation:
Point-slope equation for line of slope m that passes through (x₀, y₀):
y-y₀ = m(x-x₀)
Slope =3 and (x₀, y₀)=(-3,0)
y = 3(x+3)
y = 3x+ 9
:::::
Slope-intercept equation for line of slope m and y-intercept b:
y = mx+b
m=1 and b= -4:
y = x-4
Please Help!!! Thank you!
find x
Answer:
If the hypotenuse of the 30 60 90 triangle is 7 sqrt 3, then the length of the longer side is equal to 7 x 3, or 21.
Now going to the 45 45 90 triangle, we can see that x is equal to 21[tex]\sqrt{2}[/tex]. This is because the hypotenuse of a 45 45 90 triangle is equal to the side length times sqrt 2.
So our answer is, 21[tex]\sqrt{2}[/tex].
Let me know if this helps!
