a) The cumulative distribution function F of X is: F(x) = P(X ≤ x) = 1
b) The mean E(X) is: E(X) = 0.5 hours.
c) The variance Var(X) is: the variance of X is approximately 0.0833 hours².
To find the cumulative distribution function (CDF) of X, we need to consider two cases: when the boy comes back inside before 45 minutes and when the boy is brought inside by his mother after 45 minutes.
(a) Cumulative Distribution Function (CDF) F of X:
For 0 ≤ x < 0.75 (when the boy comes back inside before 45 minutes):
Since the boy comes back inside uniformly distributed on the interval [0, 1], the CDF is simply the probability that the boy comes back inside before time x.
The probability of the boy coming back inside before x is equal to x, as it is a uniform distribution.
F(x) = P(X ≤ x) = x
For 0.75 ≤ x ≤ 1 (when the mother brings the boy inside after 45 minutes):
If the boy is not back inside at 45 minutes (0.75 hours), his mother brings him inside.
Therefore, the probability of the boy coming back inside before x in this case is 1.
F(x) = P(X ≤ x) = 1
(b) Mean (Expected Value) E(X):
The expected value of X, denoted by E(X), is the average time the boy spends outside before coming back inside.
For a uniform distribution on the interval [0, 1], the expected value is the midpoint of the interval.
Therefore, E(X) = (1 + 0) / 2 = 0.5 hours.
(c) Variance Var(X):
The variance of X, denoted by Var(X), measures the spread or variability of the random variable X around its mean.
For a uniform distribution on the interval [0, 1], the variance is given by:
Var(X) = (1² - 0²) / 12 = 1 / 12 ≈ 0.0833 hours²
So, the variance of X is approximately 0.0833 hours².
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Help! I’ll reward brainest its pretty easy
I really need help with this trigonometric function, i am struggling and it would mean a lot.
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant and cotangent. These six trigonometric ratios are abbreviated as sin, cos, tan, csc, sec, cot.
I would suggest calculator soup they have a trigonometric function calculator
And here is how to solve trigonometric function,
Put the equation in terms of one function of one angle.
Write the equation as one trig function of an angle equals a constant.
Write down the possible value(s) for the angle.
If necessary, solve for the variable.
Miss Johnson bought a pair of jeans on sale for $30. The original price was $50. By what percent did the price of the jeans change?
Answer:
the price changed by 40%
Answer:
40%
Step-by-step explanation:
30 x 2 = 60
50 x 2 = 100
100-60=40
State a cubic or quartic function with the least degree possible in intercept form for the given graph. Assume that all x-intercepts are integers, and that the constant factor a is either 1 or −1.
Enter the correct value in the box to answer the question.
y= ?
Answer:
y = [tex]-x^{3} - 2x^{2} + 5x + 6[/tex]
Step-by-step explanation:
The function will be cubic. The x-intercepts are -4, -1, and 2
The constant factor is -1 because the graph falls on the right. So,
y = -(x + 4)(x + 1)(x - 2)
y = -[tex]x^{3} -2x^{2} + 5x +6[/tex]
4 to the power of3 -(2+2to the power of 3) x 5
Answer:
14
Step-by-step explanation:
Given the following equation;
4³ - (2 + 2³) * 5
4*4*4 - (2 + 2*2*2) * 5
64 - (2 + 8) * 5
64 - (10) * 5
64 - 50 = 14
Note: the rule of BODMAS was applied.
At a state university on the west coast, 13% of undergraduate students are of Asian origin. Among students of Asian origin, 11% major in Humanities, 7% in Social Sciences, 31% in Biological and Physical Sciences, 36% in engineering, and the remaining 15% in Business. Among students of other ethnicities, 19% major in Humanities, 16% in Social Sciences, 12% in Biological and Physical Sciences, 18% in engineering, and the remaining 35% in Business. One undergraduate student majoring in Business is randomly selected from this university. Find the probability that the student is not of Asian origin.
Answer:
0.9398 = 93.98% probability that the student is not of Asian origin.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Business student
Event B: Not of Asian origin.
Probability that the student is an undergraduate majoring in business.
15% of 13%(Of Asian origin).
35% of 100 - 13 = 87%(Not of Asian origin). So
[tex]P(A) = 0.15*0.13 + 0.35*0.87 = 0.324[/tex]
Business student and not of Asian origin:
35% of 87%. So
[tex]P(A \cap B) = 0.35*0.87 = 0.3045[/tex]
One undergraduate student majoring in Business is randomly selected from this university. Find the probability that the student is not of Asian origin.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.3045}{0.324} = 0.9398[/tex]
0.9398 = 93.98% probability that the student is not of Asian origin.
Can you help with this I don’t know how to solve this.
Answer:
[tex]arclength = 13.44 ft[/tex]
Step-by-step explanation:
We are given PS = 28 feet, which is the length of the diameter.
The formula for arc length is [tex]2\pi r\frac{x}{360}[/tex], where x is the degrees.
So, we need to find the radius. We know that the radius is half of the diameter, so:
[tex]\frac{28}{2}=14 ft[/tex]
We also need to find ∠TXS. Since we know the diameter is a line that crosses the center point of the circle, we also know that ∠PXT and ∠TXS add up to 180°. So:
∠PXT + ∠TXS = 180
125 + ∠TXS = 180
∠TXS = 180 - 125
∠TXS = 55°
Now, we can use the arc length formula:
[tex]arclength=2\pi r\frac{x}{360}[/tex]
[tex]arclength=2\pi (14)\frac{55}{360}[/tex]
[tex]arclength=13.43903524...[/tex]
[tex]arclength = 13.44 ft[/tex]
Check my work to make sure! Hope this helps!
A rectangular boad is 1100 millmeters long and 900 millmeters wide. what is the area of the board in square meters?
Answer:
1100 mm = 1.1 m, and 900 mm = 0.9 m.
So the area is 1.1 x 0.9 = 0.99 m^2
The area of the rectangular board is 0.99 square meters.
Given that a rectangular board is 1100 millimeters long and 900 millimeters wide.
We need to find the area of the board,
To find the area of the rectangular board in square meters, we need to convert the given dimensions from millimeters to meters and then calculate the area.
Given:
Length of the board = 1100 millimeters
Width of the board = 900 millimeters
To convert millimeters to meters, we divide the given values by 1000:
Length in meters = 1100 mm / 1000 = 1.1 meters
Width in meters = 900 mm / 1000 = 0.9 meters
The formula to calculate the area of a rectangle is:
Area = Length × Width
Substituting the values, we get:
Area = 1.1 meters × 0.9 meters
Area = 0.99 square meters
Therefore, the area of the rectangular board is 0.99 square meters.
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5
Find two numbers with a sum of 15 and a difference of 3.
Step-by-step explanation:
let the no be x and y
x+y=15
y=15-x.......eqn i)
x-y=3..........eqn ii)
putting value of y from eqn i ) to eqn ii)
x-y=3
x-(15-x)=3
x-15+x=3
2x-15=3
2x=18
x=9
no,putting value of x in eqn i)
y=15-x
y=15-9
y= 6
So,the value of x is 9 and y is 6
Geometry HELP PIC ADDED
1. v=
2.u=
3.u=
4.v=
Answer:
(No rounding done.)
1. 10
2. 14.1421
3. 8
4. 6.9282
Step-by-step explanation:
To find 1, you need to use tangent. Let's say the missing side is x. You need to use tan(45) = x/10 to be able to solve. If you don't know how to do that, you just need to multiply by 10 on both sides, that way the 10 cancels out and all you get is x. Tan(45) multiplied by 10 is 10.
Now, find 2 with sine. The equation is sin(45) = 10/x. First, you need to multiply both sides by x so you get 10 alone. Now, divide both sides by sin(45) to cancel out the left side and get the answer to 2. 10/sin(45) = 14.1421 (I don't know if you need to round).
To find 3, you need to use cosine. The equation would be cos(60) = 4/x. Again, multiply both sides by x to get 4 alone. Next, divide both sides by cos(60). 4/cos(60) is 8.
To find 4, you need to use sine again. The equation is sin(60) = x/8. Multiply both sides by 8, and there's your answer. 6.9282.
What line is parallel to y=5x+2 ?
Answer:
i think this is a awer
Step-by-step explanation:
n example of a line parallel to y = 5x - 2 would be y = 5x + 6. The difference between the two lines is where they cross the y-axis. Another example would the line in standard form, 10x - 2y = 8.Nov 9, 2015
Answer:
y=5x +6
Another example would the line in standard form, 10x - 2y = 8.
Can someone help quick please
Answer:
PC = 4 cm
Step-by-step explanation:
AP = 4 cm
Because AB = BC, PB = PB, and we know that angle PBA = 90 degrees: triangle PBA is congruent to triangle PBC by the Side-Angle-Side theorem.
PC = AP because corresponding parts of congruent triangles are congruent.
Find the area of this figure
Using lengths a, b, and c in the right triangle shown, how are the trigonometric functions of defined?
Answer:
take a pic.of question
Step-by-step explanation:
gotta see the triangle
y=4x+5 cuando x=9
Porfavor es para hoy
Answer:
y = 41
Step-by-step explanation:
y=4x+5 cuando x=9
y=4*9+5
y=36+5
y=41
PLS help i've been trying this for an hour i still don't get it
Can 4 in, 2 in., 8 in make a triangle.
write 18 1/4 as a decimal
Answer: 18.25
Step-by-step explanation: Lets start off with this: 1/4 is the same as 25 (like if you use quarters, you know 4 quarters makes a dollar, and one quarter is 25)
So, since we have 18 and 25, converting it to a decimal is easy. Put the numbers together (18 and 25) Then just add decimal in the middle.
OR
18 x 4 (which is 72) then add 72 to the numerator (1) which will give you 73 (72 + 1) Finally, divide 73 by 4, (4 is denominator) which will then give you 18.25 :D
The mixed number [tex]18\frac{1}{4}[/tex] written as a decimal is 18.25.
To write [tex]18\frac{1}{4}[/tex] as a decimal, we can convert the mixed number into an improper fraction and then divide the numerator by the denominator.
The mixed number to an improper fraction.
[tex]18\frac{1}{4}[/tex] = (18 × 4 + 1)/4
= 73/4
Divide the numerator by the denominator.
73 ÷ 4
= 18.25
Therefore, [tex]18\frac{1}{4}[/tex] written as a decimal is 18.25.
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If f(x) = 3x – 4 and g(x) = x, find the value of f(3) – g(2).
Answer:
3
Step-by-step explanation:
f(3) = 3(3)-4
f(3)= 9-4
f(3) = 5
g(2) = (2)
g(2) = 2
f(3)-g(2) = ?
(5) - (2) = ?
(5) - (2) = 3
Can Someone Please Help Me. ?
1.7. Examine parallelogram ABCD below.
B
5x+12
с
9y - 2
7y+4
A
8x - 6
D
Determine which of the following values are correct. Select all that apply.
A. y=1
B. x = 2
C. y=3
D. X = 6
E. AD = 42
F. AB = 25
Answer:
So.
The correct is (C, D, E and F)
And (A and B) isn't correct
Step-by-step explanation:
I hope that is useful for you :)
Evan uses 1/3 of his tickets to ride the loop-d-loop. how many tickets does he use?
Answer: 1/3 of 24 tickets is 8
Step-by-step explanation:
1/3 of 24 is 8.
The way I usually find this is by multiplying different numbers by three and seeing if it equals (in this case) 24.
8 x 3 = 24
Because eight goes into twenty-four three times, eight is one-third of twenty-four.
Hope this helps✨
HELP PLEASE IT'S DUE
Answer:
1) no solution
2) no solution
Step-by-step explanation:
7(2 + 5v) = 3v +14
14 + 35v = 3v + 14
The 14s cancel each other out.
35v ≠ 3v
no solution
36 - 7p = -7(p - 5)
36 - 7p = -7p + 35
The -7s cancel each other out.
36 ≠ 35
no solution
Need help fast please
Answer:
The answer for the first one is 1/f3
the second one is b-5 i think
third one is 8k^5/m4
last one is -9
hope this helped
Step-by-step explanation:
Type the answer in the box.
d = 6 y = 10 g = 8
Step-by-step explanation:
[tex](6) + \frac{1}{2} (10 + 8)[/tex]
[tex]6 + \frac{1}{2} (18)[/tex]
[tex]6 + \frac{18}{2} [/tex]
[tex]6 + 9[/tex]
[tex]15[/tex]
Answer:
15
Step-by-step explanation:
Paul has some money in his wallet, all in $1 bills. He buys a hat and has $6 left, as shown in
the model below.
How much did Paul pay for the hat?
Enter your answer in the box.
Answer:
we need to see the model
Step-by-step explanation:
model please
u={1,2,3,4,5,6,7,8,9}
a={2,4,6,8}
b={3,6,9}
What is the set AUB?
Answer:
AUB = {2,3,4,6,8,9}
Step-by-step explanation:
The set u should not be included in set AUB
You are the manager of a firm that sells its product in a competitive market at a price of $48. Your firm's cost function is C = 60 + 2Q 2. Your firm's maximum profits are
Answer:
the correct answer is truly
Step-by-step explanation:
STOP CHEATING ON THID APP
The following radical equation has a solution set {x = ?} and an extraneous root x = ?.
Answer:
x=2; the extraneous root x=42.
All the details are in the attached picture, the answer is marked with red colour.
The solution set is {2, 42} & the extraneous root is 42
What is extraneous root ?
If there are two roots in an equation, and one of them does not properly satisfy the equation, then the root is called extraneous root of that equation.
What are the roots ?Given equation is,
[tex]2+\sqrt{2x-3}=\sqrt{x+7}[/tex]
Squaring both sides we get,
[tex]2^{2} +2(2)(\sqrt{2x-3} )+(\sqrt{2x-3}) ^{2} = (\sqrt{x+7}) ^{2}[/tex]
⇒ [tex]4+4\sqrt{2x-3} +2x-3=x+7\\[/tex]
⇒ [tex]4\sqrt{2x-3} =6-x[/tex]
Again, squaring both sides we get,
⇒ [tex](4\sqrt{2x-3}) ^{2} =(6-x)^{2}[/tex]
⇒ [tex]16(2x-3)=6^{2} -12x+x^{2}[/tex]
⇒ [tex]32x-48=36-12x+x^{2}[/tex]
⇒ [tex]x^{2} -44x+84=0[/tex]
⇒ [tex]x^{2} -42x-2x+84=0[/tex]
⇒ [tex](x-42)(x-2)=0[/tex]
So, x = 2 & 42
Here extraneous root is 42.
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PLEASE HELP!
Which figure has the smaller volume, the cone with a diameter of 7 in. and a height of 5 in. or the sphere with a diameter
of 5 in.?
A. Sphere
B. Cone
Answer:
(A) Sphere
Step-by-step explanation:
The sphere has a smaller volume.