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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What is the percentage of data between 90 and 140?
Answer:
50%
Step-by-step explanation:
Maurice Luken deposited $3,021 in a savings account that paid 5.5 percent interest
compounded daily. How much interest did he earn in 31 days?
9514 1404 393
Answer:
$14.14
Step-by-step explanation:
The amount of interest earned is ...
I = P((1 +r/365)^n -1) . . . . interest on principal P at annual rate r compounded daily for n days
I = 3021(1 +0.055/365)^31 -1) ≈ 14.14
$14.14 in interest is earned in 31 days.
If two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might intersect, but we need to know whether the objects are in the same position at the same time. Suppose the trajectories of two particles are given by the vector functions for t 0. Do the particles collide? If they collide find t. If not enter NONE.
r1(t) = t^2, 8t − 15, t^2
r2(t) = 11t − 30, t^2, 13t − 40
t=
Answer:
Step-by-step explanation:
[tex]r_1(t) = < t^2 , 8t-15,t^2> \\ \\ r_2(t) = < 11t-30, \ t^2 , \ 13t-40> \\ \\ at \ r_1 = r_2 \\ \\ t^2 = 11t - 30 , \ \ \ \ \ \ \ \ \ \ \ \ 8t - 15 = t^2 , \ \ \ \ \ \ \ \ \ t^2 = 13t -40 \\ \\ t^2 - 11t + 30\ \ \ \ \ \ \ \ \ \ \ \ t^2 -8t + 15 , \ \ \ \ \ \ \ \ \ \ \ \ t^2 -13t + 40 \\ \\ t^2 -8t-3t + 30=0 \ \ \ \ \ \ t^2 - 2t -4t + 15=0 \ \ \ \ \ \ t^2 - 1t - 13t + 40 =0[/tex]
[tex](t-6)(t-5) \ \ \ \ \ \ \ \ \ \ \ (t-5)(t-3) \ \ \ \ \ \ \ \ \ \ \ (t-5)(t-8)[/tex]
[tex]\mathbf{The \ common \ value \ of \ t \ = \ 5}[/tex]
Combine like terms
x + 10x-30= -8
Answer: x=2
Isolate the variable by dividing each side by the factors that don't contain variables.
What is the value of 8+(7+1)^2÷4(1/2)^4
Will Mark Brainliest
^=exponents
Answer:
264
Step-by-step explanation:
8+(7+1)^2 / 4(1/2)^4
8+ 8^2 / 4(1/2)^4
8+64/4(1/16)
8+64 / 1/4
8 + (64*4)
8+256
264
A container has 3 blue marbles, 2 red marbles, and 4 yellow marbles. You are going to pull out one marble, record its color, put it back in the container and draw another marble. What is the probability of pulling out a yellow marble, followed by a blue marble?
The number line is 0 to 1 true or false 2/8 is close to 0
Answer:
True
Step-by-step explanation:
from the scale 0-1, 2/8 is closer to 0 because you round 2 down to 0, which gives you 0.
What is the total surface of the pyramid in square centimeters? A: 17.5 B:70 C:140 D:35
Answer:
C:140
Step-by-step explanation:
because 7 x 5 in the tiangle.
Solve for n. 24 = 3(n-5)
Answer:
Step-by-step explanation:
Given
24 = 3(n - 5)
24/3 = n - 5
n- 5 = 8
n = 8+5
n = 13
hope it helps :)
Answer:
n = 13
Step-by-step explanation:
8=n-5
-n=-5-8
-n=-13
n=13
tell what place the digit is in for the following number 14,632.708
4
0
7
Answer:
4 is in the one thousands place. The 0 is in the hundredths place. The 7 is in the tenths place.
The square pyramid has a base area of 144 square centimeters and a height of 12 centimeters. Find the volume.
Step-by-step explanation:
the answer is 576 cubic centimetre.
Answer:
Its 576 cubic centimeters
Step-by-step explanation:
Figure A is a scale image of Figure B. Figure A: 7.2 , 4. Figure B: 3 , x. What is the value of x
Answer: 5.4
Step-by-step explanation:
Answer:
5.2
Step-by-step explanation:
True or False: x is the same/equal to 1x
Answer:
Yes
Step-by-step explanation:
Because you're multiplying by 1 so it stays the same value
Can someone please help meeee I’m desperateeee
Answer:
Step-by-step explanation:
1)(-3x+10)(50-x)=180
-4x+60=180
-4x=120
x=-30
2)6x+2+2x=90
8x=88
x=11
larger angle: 68°
3) a=3x°
4)(7x-5)=-2x+22
9x=27
x=3
DBE=16°
5)(x-39)=2x-59)
x=20
Question 6
If a truck can drive 24,4 miles in 1 gallon, how many miles would I be able to drive with a filled 30 gallon tank?
Answer: 732 mi
Step-by-step explanation:
Assuming you meant 24.4
What is the perimeter of the shape?
40 feet
43 feet
51 feet
67 feet
Answer:
40 feet?
Step-by-step explanation:
11 ft + 3 ft + 4 ft + 6 ft + 3 ft + 3 ft + 4 ft + 6 ft = 40
In ΔGHI, i = 64 inches, g = 91 inches and ∠H=134°. Find the length of h, to the nearest inch.
Answer:
143
Step-by-step explanation:
delta math
The length of h, to the nearest inch. is 57.4 inch.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
Here, given that,
In ΔGHI, i = 64 inches, g = 91 inches and ∠H=134°
Now. we know that,
a sinA =b sinB =c sinC
We get,
length of h = 57.4 inch.
hence, The length of h, to the nearest inch. is 57.4 inch.
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A rock is thrown upward from the top of a high cliff overlooking the ocean at a speed of 96 feet per second . The rock's height above ocean can be modeled by the equation H(t) = - 16t ^ 2 + 96t + 112 . How long will it take seconds for the rock to hit the ocean? Do not include units in your answer.
Answer:
7
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
In this question:
The height of the rock after t seconds is given by the following equation:
[tex]H(t) = -16t^2 + 96t + 112[/tex]
How long will it take in seconds for the rock to hit the ocean?
This is t for which:
[tex]H(t) = 0[/tex]
So
[tex]-16t^2 + 96t + 112 = 0[/tex]
Simplifying by -16
[tex]t^2 - 6t - 7 = 0[/tex]
So a quadratic equation with [tex]a = 1, b = -6, c = -7[/tex]
[tex]\Delta = b^{2} - 4ac = (-6)^2 - 4*1*(-7) = 36 + 28 = 64[/tex]
[tex]t_{1} = \frac{-(-6) + \sqrt{64}}{2*1} = 7[/tex]
[tex]t_{2} = \frac{-(-6) - \sqrt{64}}{2*1} = -1[/tex]
Since time is a positive measure, it will take 6 seconds for the rock to hit the ocean, and the answer is 7.
Which of the following shapes have an area of 48 square feet? Select all that apply.
A scalene triangle with a base of 8 feet and a height of 6 feet.
A right triangle with a base of 9 feet and a height of 10 2/3 feet.
A rectangle with a base of 19.2 feet and a height of 2.5 feet.
A parallelogram with a base of 16 feet and a height of 3 feet.
Alice has $90 to spend on
new clothes. She wants to buy
some shirts for $20 each. If
she has a coupon for $10 off
her total purchase, how many
shirts can she buy?
Answer:
5
step by step explanation:
if she gets $10 off of her purchase that means she would have a little extra money to another shirt
To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35models of Make A and 35 models of Make B. The mean braking distance for Make A is 41feet. Assume the population standard deviation is 4.6 feet.The mean braking distance for Make B is 45feet. Assume the population standard deviation is 4.3 feet.At alphaequals0.10,can the engineer support the claim that the mean braking distances are different for the two makes of automobiles
Answer:
There is sufficient evidence to support the claim.
Step-by-step explanation:
Given
[tex]\alpha = 0.10[/tex]
Make A
[tex]\bar x_1 = 41[/tex]
[tex]\sigma_1= 4.6[/tex]
[tex]n = 35[/tex]
Make B
[tex]\bar x_2 = 45[/tex]
[tex]\sigma_2 = 4.3[/tex]
[tex]n = 35[/tex]
First, we state the null and alternate hypothesis
[tex]H_0 : \mu_1 = \mu_2[/tex]
[tex]H_1 : \mu_1 \ne \mu_2[/tex]
Next, calculate test statistic:
[tex]z = \frac{(\bar x_1 - \bar x_2)-(\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}}[/tex]
[tex]z = \frac{(41- 45)-0}{\sqrt{\frac{4.6^2}{35}+\frac{4.3^2}{35}}}[/tex]
[tex]z = \frac{-4}{\sqrt{0.6046+0.5283}}[/tex]
[tex]z = \frac{-4}{\sqrt{1.1329}}[/tex]
[tex]z = \frac{-4}{1.0643}[/tex]
[tex]z = -3.7583[/tex]
The critical value at [tex]\alpha = 0.10[/tex] is: [tex]\±1.282[/tex]
[tex]-3.7583 < -1.282[/tex]
So, we reject [tex]H_0[/tex]
This implies that; there is sufficient evidence to support the claim.
Stuck on this problem, can't find 3x
Answer:
x equals 10, angle measure is 30°
Step-by-step explanation:
By using the Vertical Angles Theorem which states that opposite angles formed by 2 intersecting lines are congruent we can find that the measure of the angle with 3x is equal to the measure of it's opposite angle or 30°. Using this we can make an equation that can find us our answer.
3x = 30
Divide both sides by 3
3x/3 = 30/3
x = 10
HELP PLSSSSS I BEG YOUUUUUUUUUUUUUUUUU
Answer:
just shade in the same thing
just shade in the same thing
A researcher found that 55% of families in the United States have one child under the age of 21, 22% have two children under the age of 21, 15% have three children under the age of 21, 5% have 4 children under the age of 21and 3% have 5 or more children under the age of 21. If a family is selected at random, what is the probability the family has at least 3 children under the age of 21? (Express your answer as a percent, Please include the % symbol.)
Answer:
23% probability the family has at least 3 children under the age of 21.
Step-by-step explanation:
If a family is selected at random, what is the probability the family has at least 3 children under the age of 21?
15% have three children under the age of 21
5% have 4 children under the age of 21
3% have 5 or more children under the age of 21.
So:
15% + 5% + 3% = 23%
23% probability the family has at least 3 children under the age of 21.
Kylee bought a backpack at Tilly's for $32. The same backpack is on sale today for $24. What is the percent
of change? Round your answer to the nearest tenth.
Answer:
25
Step-by-step explanation:
what is the simplified expression of 6h +(-7.1d)-15+4d-3.4h
Answer:
6h+ (-7.1d) -15+4d-3.4h
Step-by-step explanation:
Definition the value of a number regardless of its sign Definition
9
On a field trip, there are 3 adults for every 45 students. Which graph models a relationship with
the same unit rate?
А
с
101
9
10
9
8
7
7
6
5
4
b
6.
5
4
3
2
3
2
1
0
30
60
90 120 150
30
60 90 120 156
B
D
10T
9
8
10
9
6
5
Answer:
I believe the answer is C
PLEASE HELP! I NEED HELP Use synthetic division!
For each ordered pair determine if it is a solution to 7x+5y=9
(-4,-3)
(-3,6)
(5,0)
(2,-1)