Answer:
h = 76
Step-by-step explanation:
2 + h - 48 = 30
h + 2 - 48 = 30
h - 46 = 30
h - 46 + 46 = 30 + 46
h = 76
Answer:
2+h-48=30
2-48+h=30
-46+h=30
h=30+46
∴h=76
The population of a city in Texas is about 1,030,000. The population of the city in t years can be predicted using the equation P = 1,030,000(1.12)t. According to this equation, what will the approximate population of the city be in 9 years? 10,382,400
Answer:
2,856,271
Step-by-step explanation:
We presume your equation is intended to be ...
P = 1,030,000(1.12)^t
To find the prediction in 9 years, put 9 where t is and do the arithmetic.
P = 1030000(1.12^9) ≈ 2,856,271
In 9 years, the population is predicted to be about 2,856,271.
Answer:
To predict the population in nine years, substitute 9 for t in the equation and simplify:
P = 1,030,000(1.12)9
= 1,030,000 ∙ 2.77
= 2,853,100.
Step-by-step explanation:
The sum of two rational numbers is
Answer:
rational
Step-by-step explanation:
rational + rational=rational
Which of the following could represent the graph of f(x)=x^4+x^3-8x^2-12x
Answer:
Plot f(x)=x^4+x^3-8x^2-12x
Step-by-step explanation:
Please answer this question !! Thank you !! Will give brainliest !!
Answer:
m = 1/4
Step-by-step explanation:
We want to get the equation in slope intercept form
y = mx+b where m is the slope and b is the y intercept
x -4y +3 =0
Add 4y to each side
x -4y+3 +4y = 0+4y
x-3 = 4y
Divide each side by 4
1/4x -3/4 =y
the slope is 1/4 and the y intercept is -3/4
Data collected over an extended period of time show that women college soccer players have a relatively high rate of concussions, often with life-changing consequences. See Stanford Star Retires and Concussions Derail Promising Careers. For collegiate women soccer players the concussion rate is .63 per 1,000 participation hours (practice and game participation hours), for collegiate men soccer players the concussion rate is .41 per 1,000 participation hours (the concussion rate in college football is .61 per 1,000 participation hours). Use the Poisson distribution to answer the following questions.
a. What is the probability that the men's team experiences 2 or more concussions? (Use 3 decimal places).
b. What is the probability that the women's team experiences 2 or more concussions? (Use 3 decimal places).
The probability that the women's team experiences 2 or more concussions is 0.0013.
We are given that;
The concussion rate = 0.63 per 1,000 participation hours
Now,
The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space when these events occur with a known average rate and independently of the time since the last event.
The probability mass function of the Poisson distribution is given by:
[tex]$P(X=k)=\frac{\lambda^k e^{-\lambda}}{k!}$[/tex]
where X is the number of events occurring in the interval, k is a non-negative integer, and λ is the average rate of events per interval.
a. For collegiate men soccer players, the concussion rate is .41 per 1,000 participation hours.
Therefore, the average number of concussions per hour is λ = 0.41/1000 = 0.00041.
Let X be the number of concussions experienced by the men's team in an hour. Then X follows a Poisson distribution with parameter λ = 0.00041. We want to find P(X ≥ 2). Using the Poisson distribution formula,
[tex]$P(X \geq 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)$$= 1 - \frac{0.00041^0 e^{-0.00041}}{0!} - \frac{0.00041^1 e^{-0.00041}}{1!}$$= 1 - e^{-0.00041}(1 + 0.00041)$$\approx \boxed{0.0002}$[/tex]
b. For collegiate women soccer players, the concussion rate is .63 per 1,000 participation hours.
Therefore, the average number of concussions per hour is λ = 0.63/1000 = 0.00063.
Let Y be the number of concussions experienced by the women's team in an hour. Then Y follows a Poisson distribution with parameter λ = 0.00063. We want to find P(Y ≥ 2). Using the Poisson distribution formula,
[tex]$P(Y \geq 2) = 1 - P(Y < 2) = 1 - P(Y = 0) - P(Y = 1)$$= 1 - \frac{0.00063^0 e^{-0.00063}}{0!} - \frac{0.00063^1 e^{-0.00063}}{1!}$[/tex]
[tex]$= 1 - e^{-0.00063}(1 + 0.00063)$[/tex]
[tex]$\approx \boxed{0.0013}$[/tex]
Therefore, by poisson distribution formula answer will be 0.0013.
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Help please. help please. Below please
Answer:
x = 30pitch = 7Step-by-step explanation:
If you draw a horizontal line through the shaded triangle such that it intersects the left vertex, you see that it bisects the 60° angle at that vertex. The measure of x is the same as the measure of either half of that bisected angle, so is 30°.
The pitch associated in the table with an angle of 30° is 7.
x = 30pitch = 7A radio station dedicates 20% of their air time to commercials for each radio show. During a radio show, 30 minutes of commercials played. How long was the radio show?
Answer:
150 minutes (2.5 hours)
Step-by-step explanation:
We must consider that the total time that the radio program lasted represents the 100%.
Of that 100% we are told that 20% is dedicated to commercials. So the 30 minutes of commercials correspond to 20% of the air time, which can be represented in the following table:
Percentage of time time
20% ⇒ 30min
and we are looking for how long the show was on the air (the 100%).
So updating the table( I will call x the total time on the air):
Percentage of time time
20% ⇒ 30min
100% ⇒ x
This reationship between three values can be solve by the rule of three: multiply the cross quantities on the table (100 by 30) and divide by the remaining amount (20):
x = 100*30 / 20
x= 3000 / 20
x = 150 minutes
The radio show was 150 minutes (2.5 hours) long.
Using the critical value rule, if a two-sided null hypothesis cannot be rejected for a single mean at a given significance level, then the corresponding one-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will ______________ be rejected at the same significance level.
Answer:
If the null hypothesis is failed to be rejected in a two-sided test, we are not sure if a one-sided test will reject or not the null hypothesis, at the same significance level.
Step-by-step explanation:
When we performed a two-sided test and the null hypothesis failed to be rejected, when we perform a one-sided test we may reject or not the null hypothesis.
For instance, we have a 5% significance level test, where the test statistic is z=1.8.
For a two-sided test the critical values for α=5% are zc=±1.960. In this situation, the null hypothesis failed to be rejected.
But if we perform a one-sided test with the same significance level, we have a critical value z=1.645 and the conclusion is that the null hypothesis is rejected.
Then, if the null hypothesis is failed to be rejected in a two-sided test, we are not sure if a one-sided test will reject or not the null hypothesis, at the same significance level.
We are only sure that if a two-sided test rejects the null hypothesis, a one-side test with same significance level will always reject the null hypothesis.
In the months leading up to an election, news organizations conduct many surveys to help predict the results of the election. Often news organizations will increase the sample size in the last few weeks before the election. Which of the following is the primary reason they increase the sample size?
A. A larger sample size gives a narrower confidence interval.
B. A larger sample size allows more people to give their input.
C. A larger sample size gives a higher confidence level.
D. A larger sample size means the sampling method isn’t as important.
Answer:
A. A larger sample size gives a narrower confidence interval.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
As the sample size increases(n increases), the margin of error decreases, given a narrower, more precise confidence interval.
So the correct answer is:
A. A larger sample size gives a narrower confidence interval.
Find the nth term: 0, -6, -12, -18 …
Answer:
F(1) = 0
F(2) = -6 = 0 - 6 x 1 = F(1) - 6 x 1
F(3) = -12 = 0 - 6 x 2 = F(1) - 6 x 2
F(4) = -18 = 0 - 6 x 3 = F(1) - 6 x 3
...
F(n) = F(1) - 6 x (n - 1)
Hope this help!
:)
Help....!! I need to solve this simultaneous equation y=x-2 and y=3x+5 With working out if possible please....
Step-by-step explanation:
Y= x - 2. Y = 3x + 5
Putting value of y
x - 2 = 3x + 5
-2 - 5 = 3x - x
-7 = 2x
-7/2 = x
Putting value of x
Y = 3(-7/2) + 5
Y = - 10.5 + 5
Y = - 5.5
Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 32% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts (a) and (b) below.
a. Find the probability that both generators fail during a power outage (Round to four decimal places as needed.)
b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital? Assume the hospital needs both generators to fail less than 1% of the time when needed. (Round to four decimal places as needed.)
Answer:
a. 0.1024
b. 0.8976
Step-by-step explanation:
The probability that x generators don't fail when they are needed follows a binomial distribution, because we have n identical and independent events (2 backup generators) with a probability p of success (1-0.32=0.68) and a probability q of failure (0.32).
So, the probability that x generator success are calculated as:
[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*q^{n-x}\\P(x)=\frac{2!}{x!(2-x)!}*0.68^{x}*0.32^{2-x}[/tex]
Then, the probability that both generators fail during a power outage is equal to the probability that 0 generators success. It is calculated as:
[tex]P(0)=\frac{2!}{0!(2-0)!}*0.68^{0}*0.32^{2-0}=0.1024[/tex]
At the same way, the probability of having a working generator in the event of a power outage is equal to the probability that at least 1 generator success. It is calculated as:
[tex]P(x\geq1)=P(1)+P(2) \\P(1)=\frac{2!}{1!(2-1)!}*0.68^{1}*0.32^{2-1}=0.4352\\P(2)=\frac{2!}{2!(2-2)!}*0.68^{2}*0.32^{2-2}=0.4624\\P(x\geq1)=0.4352+0.4624=0.8976[/tex]
This probability is not high enough for the hospital, both generators fail approximately the 10% of the time when needed.
A student rolls a number cube 40 times. He rolls a 3 on the number cube 6 times. What is the experimental probability that he rolls a 3?
Answer:
[tex]\frac{6}{40}=\frac{3}{20}[/tex]
Step-by-step explanation:
The experimental probability is the number of times the desired result was obtained over the total number of times the experiment was carried out:
[tex]P=\frac{TimesTheEventOccurs}{TotalNumberOfTrials}[/tex]
In this case the Event we are looking for is rolling a 3 on the number cube.
The total number of trials is:
40
because the student rolls the cube 40 times.
and the times that he got the number 3 (the times the desired event occurs) is:
6
because he rolls a 3 on the number cube 6 times.
Thus our experimental probability to roll a 3 is:
[tex]P=\frac{6}{40}[/tex]
There are many cones with a volume of 72pi cubic inches. For example, one such cone could have a radius of 6 inches and a height of 6 inches.
Find another possible pair of measurements (radius and height) to make the same volume. (EXTRA CREDIT for each additional pair that you find.)
Answer:
Step-by-step explanation:
The volume of a cone of height h and circular base of radius r, is [tex] V = \frac{\pi r^2 h}{3}[/tex]. In this case we have that [tex]V=72\pi[/tex].Then, we have that
[tex]72\pi = \frac{\pi r^2 h}{3}[/tex]
multiplying by 3 on both sides and dividing by [tex]\pi[/tex] we have that
[tex]216 = r^2\cdot h[/tex]
Suppose that we know the value of r, then we can find the value of h by solving h, that is
[tex] h = \frac{216}{r^2}[/tex].
So, by choosing any positive value of r, we can find the value for h. Note that if r=6, then [tex]h= \frac{216}{6^2} = 6[/tex]. This means that the amount of credit is infinite :)
Rule double the last number number number than add 3
2. 7 17 _ _
Answer:
[tex]37[/tex]
[tex]77[/tex]
Step-by-step explanation:
[tex]17 \times 2 +3=37\\37 \times 2 +3=77[/tex]
Answer:
37 77
Step-by-step explanation:
2(17) + 3 = 37
2(37) + 3 = 77
WILL MARK BRAINLIEST
Teah was selling candy bars for a fundraiser. She spent $25 on a box of candy bars and sold each candy bar for $2.50. Her profit was $75. Teah wrote the equation 2.5c - 25 = 75 for this situation, and she found c = 40. Which statement is true about the solution c = 40?
A) The solution c = 40 is the number of candy bars Teah sold.
B) The solution c = 40 is the profit in dollars Teah made from each candy bar.
C) The solution c = 40 is the amount in dollars that Teah spent on a box.
D) The solution c = 40 is the selling cost of a box of candy bars, in dollars.
E) The solution c = 40 is the selling cost of each candy bar, in dollars.
Answer:
A
Step-by-step explanation:
You can substitute 40 into c, work out the equation and you'll get $75 as the profit. Each candy bar is $2.5 so c would be the number of candy bars she sold.
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. 1. Suppose a sample of 955 tenth graders is drawn. Of the students sampled, 812 read above the eighth grade level. Using the data, estimate the proportion of tenth graders reading at or below the eighth grade level. 2. Suppose a sample of 955 tenth graders is drawn. Of the students sampled, 812 read above the eighth grade level. Using the data, construct the 90% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level.
Answer:
The estimation for the proportion of tenth graders reading at or below the eighth grade level is given by:
[tex] \hat p =\frac{955-812}{955}= 0.150[/tex]
[tex]0.150 - 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.131[/tex]
[tex]0.150 + 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.169[/tex]
And the 90% confidence interval would be given (0.131;0.169).
Step-by-step explanation:
We have the following info given:
[tex]n= 955[/tex] represent the sampel size slected
[tex] x = 812[/tex] number of students who read above the eighth grade level
The estimation for the proportion of tenth graders reading at or below the eighth grade level is given by:
[tex] \hat p =\frac{955-812}{955}= 0.150[/tex]
The confidence interval for the proportion would be given by this formula
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
For the 90% confidence interval the significance is [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2=0.05[/tex], with that value we can find the quantile required for the interval in the normal standard distribution and we got.
[tex]z_{\alpha/2}=1.64[/tex]
And replacing into the confidence interval formula we got:
[tex]0.150 - 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.131[/tex]
[tex]0.150 + 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.169[/tex]
And the 90% confidence interval would be given (0.131;0.169).
Evaluate for x = 2. (12x + 8)/4
Answer:
8
Step-by-step explanation:
24+8=32 32 divided by 4 is 8
Answer: 8
Step-by-step explanation:
Plug in x as 2 and solve.
(12*2 + 8)/4
Start with parenthesis.
(32)/4
Now divide.
8
15. The solutions to (x+4)2 - 2 = 7 are
1) -4+ 5
3) -1 and -7
2) 4+ 5
4) 1 and 7
I
Answer:
Step-by-step explanation:
(x + 4)^2 - 2 = 7 simplifies to
(x + 4)^2 = 5
We must isolate x. To do this, take the square root of both sides, obtaining:
x + 4 = ±√5
There are two roots/solutions. They are:
x = -4 + √5 and x = -4 - √5
You must include the square root operator (√). Use " ^ " to denote exponentiation.
The solutions to the given equation (x + 4)² - 2 = 7 when calculated are; 1 and 7
How to Solve Algebra Problems?We are given the equation as;
(x + 4)² - 2 = 7
Add 2 to both sides to get;
(x + 4)² = 9
Find the square root of both sides to get;
x + 4 = ±3
Thus;
x = 3 + 4 and x = -3 + 4
x = 1 and 7
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What is the solution to this equation
Answer:
x=-10
Step-by-step explanation:
x+8=-2
x=-10 (Subtract 8)
Answer:
-10
Step-by-step explanation:
1. Write it out.
x+8=-2
2. Get x by itself.
To do this, we have to move the 8, but to do that that we have to move it to the other side of the equation. Because the opposite of addition is subtraction, we have to subtract 8 by both sides. x+8=-2
-8 -8
x=-10
And that's the answer! Hope this helped :)
Sample Response: Distance is a function of time. The constant rate of change is 64. Write
the equation Y=64x + 22. Substitute 4 in for x to get 278 miles,
Compare your response to the sample response above. Did your explanation
include that distance is a function of time?
include that the constant rate of change, or slope, is 64?
include the equation y = 64x + 22?
say to substitute 4 in for x to get 278 miles?
Answer:
Yes the explanation satisfy the questions stated.
See below for explanation
Step-by-step explanation:
From the question, distance is said to be a function of time and the constant rate of change is 64.
y = 64x + 22
The above is in the form of a Linear equation:
y = mx + c
Where y = dependent variable (distance)
x = independent variable (time)
m = slope = distance/time
c = constant = 22
m = constant rate of change = 64
If x (time) = 4
y (distance) = 278 miles
y = 64(4) + 22
y = 256 + 22
y = 256 + 22
y = 278 miles
Answer:
nclude that distance is a function of time?
include that the constant rate of change, or slope, is 64?
include the equation y = 64x + 22?
say to substitute 4 in for x to get 278 miles?
Step-by-step explanation:
The radius of a right circular cone is increasing at a rate of 1.6 in/s while its height is decreasing at a rate of 2.2 in/s. At what rate is the volume of the cone changing when the radius is 135 in. and the height is 135 in.
Answer:
Step-by-step explanation:
let radius=r
height=h
dr/dt=1.6 in/s
dh/dt=-2.2 in/s
volume v=1/3 πr²h
dv/dt=1/3 π[h*2r×dr/dt+r²×dh/dt]
when r=135 in
h=135 in
dv/dt=1/3 π[2×135×135×1.6+135²×(-2.2)]
=1/3 π[135²(3.2-2.2)]
=1/3π135²×1
=6075 π in³/s
Ninja blenders have a 2 year warranty, which means that Ninja guarantees replacement of the blender is it fails within the first 2 years. The blenders last an average of 36 months with a standard deviation of 6 months. What is the probability that Ninja will have to replace your blender if you were to buy one today
a 0.025
b 0.475
c 0.0001
d 0.0235
Answer:
d 0.0235
Step-by-step explanation:
We assume that the lifetime of the blenders follows a normal distribution, with mean of 36 months and standard deviation of 6 months.
We have to calculate the probability that the blenders have a lifetime lower than 24 months, and therefore apply the guarantee.
First, we calculate the z-score:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{24-36}{6}=\dfrac{-12}{6}=-2[/tex]
Then, the probability that the blenders lifetime is 24 or less is:
[tex]P(X<24)=P(z<-2)=0.023\\[/tex]
Given; y || 2
Prove: m<5+ m<2 + m<6 = 180°
Help
Answer:
<1=<5(alternative angle)
<3=<6(alternative angle)
<1+<2+<3=180(given)
<5+<2+<6=180(putting <1=<5 and <3=<5)
proved
A light bulb consumes 15300 watt-hours in 4 days and 6 hours . How many watt-hours does it consume per day?
Answer:
3600
Step-by-step explanation:
It consumes 3600 watt hours per day. Steps are included below.
We know that there is 24 hours in a day so we times 24 by the consumes watt hours that is 15300. So 24 times 15300. After that we need to time 4 times 24+6 = the answer that is 3600. That how you get the answer.
Steps:
1: 24*15300/(4*24+6)=3600
Answer: 3600 watt hours per day
Hope this helps.
Answer:
3,600
Step-by-step explanation:
In the question, there is energy consumption and a rate but not in an easy way.
In order to find out how much watt-hours the light bulb consumes per day, the easiest way is to multiply by the hour to find out how much it uses in a day.
In 4 days and 6 hours there are 102 hours.
[tex]4 \times 24 = 96[/tex]
[tex]96 + 6 = 102[/tex]The hours for 4 days...
[tex]96 + 6 = 102[/tex]
4 days plus 6 hours. The total time...
Now make the watt-hours usage an hourly rate...
[tex]15300 + 102 = 150[/tex]
150 watts/hour...
Take the hourly rate and multiply it by 24 (number of hours in a day) to find out how many watt-hours the lightbulb uses in a day...
[tex]150 \times 24 = 3600[/tex]
Can anyone help me with this question please
Answer:
1 = 130° , 2 =50° , 3 = 85°, 4=45°
Step-by-step explanation:
1 =45 + 85 = 130 { sum of opposite interior angle equals exterior angle}
2 = 180 - 1 { angles on a straight line equals 180}
= 180 -130 = 50°
4 = 180 - 135 = 45° { angles on a straight line equals 180}
3 = 135 -2 { sum of opposite interior angles equals exterior angle; 3 + 2 = 135}
3 = 135-50 = 85°
Note : sum of opposite interior angles equals external exterior angle, let's prove it:
If we look at the triangle at the bottom left, we have :
85, 45 and r { let's denote r as the missing angle}
So 85 + 45 + r = 180° { sum of angles of a triangle}
By simple arithmetic
r = 180 - ( 85+45) = 180 - 130 = 50°
but r + 4 = 180° { sum of angles in a straight line equals 180°}
4 = 180 - 50 = 130°
So you see 4 is the exterior angle of the triangle opposite to 85° and 45° interior angles}
Nuts and bolts are made separately and paired at random. The nut diameters (in mm) are normally distributed with mean 10 and variance .02. The bolt diameters (in mm) are also normally distributed with mean 9.5 and variance 0.02. Find the probability that a bolt is too large for its nut. In other words, find the probability that for a randomly selected nut and bolt, [size of nut − size of bolt] ≤ 0. (Alternatively, you could subtract in the ‘other’ direction and look for the probability that [size of bolt − size of nut] ≥ 0). Draw the distribution of the combination.
Answer:
- The probability that a bolt is too large for its nut = 0.00621
- The image of the drawing of this combined distribution is shown in the attached file to this solution.
Step-by-step explanation:
When independent, normal distributions are combined, the combined mean and combined variance are given through the relation
Combined mean = Σ λᵢμᵢ
(summing all of the distributions in the manner that they are combined)
Combined variance = Σ λᵢ²σᵢ²
(summing all of the distributions in the manner that they are combined)
For this question, the first distribution is the size of a nut, with mean 10 mm and a variance of 0.02
Second distribution is the size of a bolt, with mean 9.5 mm and a variance of 0.02.
The combined distribution is [size of nut − size of bolt]
Hence, λ₁ = 1, λ₂ = -1
μ₁ = 10 mm
μ₂ = 9.5 mm
σ₁² = 0.02
σ₂² = 0.02
Combined Mean = (1×10) + (-1×9.5) = 0.5 mm
Combined Variance = [(1)² × 0.02] + [(-1)² × 0.02] = 0.04
So, the combined distribution is also a normal distribution with a Mean of 0.5 mm and a variance of 0.04.
Standard deviation = √variance = √0.04 = 0.2 mm
The probability that a bolt is too large for its nut, [size of nut − size of bolt] ≤ 0, P(X ≤ 0)
To obtain this required probability, we first normalize/standardize 0 mm
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (0 - 0.5)/0.2 = - 2.50
To determine the required probability
P(x ≤ 0) = P(z ≤ -2.50)
We'll use data from the normal probability table for these probabilities
P(x ≤ 0) = P(z ≤ -2.50) = 0.00621
The image of the drawing of this combined distribution is shown in the attached file to this solution.
Hope this Helps!!!
On Monday, Richard worked for 4 hours and earned $36. On Tuesday, Richard worked for 6 hours and earned $54. On Wednesday, Richard worked for 5 hours and earned $45.
Answer:
Richard works for $9 per hour
Step-by-step explanation:
Answer:
The answer is proportional. He makes 9$ an hour
Step-by-step explanation:
Your welcome
An aquarium in the shape of a right rectangular prism is 12.5 inches long, 6 inches wide and 8 inches high. What is the total amount of water needed, to the nearest cubic inch, to fill 90% of the aquarium with water?
Answer:
The total amount of water needed is 540 cubic inches.
Step-by-step explanation:
A cubic prism has three dimension. Lenght l, width w and height h.
It's volume is:
[tex]V = l*w*h[/tex]
In this question:
[tex]l = 12.5, w = 6, h = 8[/tex]
Dimensions in inches, so the volume will be in cubic inches.
[tex]V = 12.5*6*8 = 600[/tex]
The volume is 600 cubic inches.
What is the total amount of water needed, to the nearest cubic inch, to fill 90% of the aquarium with water?
This is 90% of 600. So
0.9*600 = 540
The total amount of water needed is 540 cubic inches.
Customers arrive at a service facility according to a Poisson process of rate λ customers/hour. Let X(t) be the number of customers that have arrived up to time t. Let W1,W2,... be the successive arrival times of the customers.
(a) Determine the conditional mean E[W1|X(t)=2].
(b) Determine the conditional mean E[W3|X(t)=5].
(c) Determine the conditional probability density function for W2, given that X(t)=5.
Answer:
Step-by-step explanation:
Given that:
X(t) = be the number of customers that have arrived up to time t.
[tex]W_1,W_2[/tex]... = the successive arrival times of the customers.
(a)
Then; we can Determine the conditional mean E[W1|X(t)=2] as follows;
[tex]E(W_!|X(t)=2) = \int\limits^t_0 {X} ( \dfrac{d}{dx}P(X(s) \geq 1 |X(t) =2))[/tex]
[tex]= 1- P (X(s) \leq 0|X(t) = 2) \\ \\ = 1 - \dfrac{P(X(s) \leq 0 , X(t) =2) }{P(X(t) =2)}[/tex]
[tex]= 1 - \dfrac{P(X(s) \leq 0 , 1 \leq X(t)) - X(s) \leq 5 ) }{P(X(t) = 2)}[/tex]
[tex]= 1 - \dfrac{P(X(s) \leq 0 ,P((3 \eq X(t)) - X(s) \leq 5 ) }{P(X(t) = 2)}[/tex]
Now [tex]P(X(s) \leq 0) = P(X(s) = 0)[/tex]
(b) We can Determine the conditional mean E[W3|X(t)=5] as follows;
[tex]E(W_1|X(t) =2 ) = \int\limits^t_0 X (\dfrac{d}{dx}P(X(s) \geq 3 |X(t) =5 )) \\ \\ = 1- P (X(s) \leq 2 | X (t) = 5 ) \\ \\ = 1 - \dfrac{P (X(s) \leq 2, X(t) = 5 }{P(X(t) = 5)} \\ \\ = 1 - \dfrac{P (X(s) \LEQ 2, 3 (t) - X(s) \leq 5 )}{P(X(t) = 2)}[/tex]
Now; [tex]P (X(s) \leq 2 ) = P(X(s) = 0 ) + P(X(s) = 1) + P(X(s) = 2)[/tex]
(c) Determine the conditional probability density function for W2, given that X(t)=5.
So ; the conditional probability density function of [tex]W_2[/tex] given that X(t)=5 is:
[tex]f_{W_2|X(t)=5}}= (W_2|X(t) = 5) \\ \\ =\dfrac{d}{ds}P(W_2 \leq s | X(t) =5 ) \\ \\ = \dfrac{d}{ds}P(X(s) \geq 2 | X(t) = 5)[/tex]