Answer:
Step-by-step explanation:
(-3).(+9)-(-24)-(+6).(+2)
The thickness X of aluminum sheets is distributed according to the probability density function f(x) = 450 (x2 - x) if 6 < x < 12 0 otherwise 5-1 Derive the cumulative distribution function F(x) for 6 < x < 12. The answer is a function of x and is NOT 1! Show the antiderivative in your solution. 5-2 What is E(X) = {the mean of all sheet thicknesses)? Show the antiderivative in your solution.
Solution :
Given :
[tex]f(x) = \left\{\begin{matrix}\frac{1}{450}(x^2-x) & \text{if } 6 < x < 12 \\ 0 & \text{otherwise}\end{matrix}\right.[/tex]
1. Cumulative distribution function
[tex]$P(X \leq x) = \int_{- \infty}^x f(x) \ dx$[/tex]
[tex]$=\int_{- \infty}^6 f(x) dx + \int_{6}^x f(x) dx $[/tex]
[tex]$=0+\int_6^x \frac{1}{450}(x^2-x) \ dx$[/tex]
[tex]$=\frac{1}{450} \int_6^x (x^2-x) \ dx$[/tex]
[tex]$=\frac{1}{450}\left[\frac{x^3}{3}-\frac{x^2}{2}\right]_6^x$[/tex]
[tex]$=\frac{1}{450}\left[ \left( \frac{x^3}{3} - \frac{x^2}{2}\left) - \left( \frac{6^3}{3} - \frac{6^2}{2} \right) \right] $[/tex]
[tex]$=\frac{1}{450}\left[\frac{x^3}{3} - \frac{x^2}{2} - 54 \right]$[/tex]
2. Mean [tex]$E(x) = \int_{- \infty}^{\infty} \ x \ f(x) \ dx$[/tex]
[tex]$=\int_{6}^{12}x . \left( \frac{1}{450} \ (x^2-x)\right)\ dx$[/tex]
[tex]$=\frac{1}{450} \int_6^{12} \ (x^3 - x^2) \ dx$[/tex]
[tex]$=\frac{1}{450} \left[\frac{x^4}{4} - \frac{x^3}{3} \right]_6^{12} \ dx$[/tex]
[tex]$=\frac{1}{450} \left[ \left(\frac{(12)^4}{4} - \frac{(12)^3}{3} \right) - \left(\frac{(6)^4}{4} - \frac{(6)^3}{3} \right) $[/tex]
[tex]$=\frac{1}{450} [4608 - 252]$[/tex]
= 17.2857
A bricklayer needs to order 6 300 kg of building sand.
a) Write 6 300 kg in grams, giving your answer in standard form.
One grain of this sand approximately weighs 7 x 10°g.
b) How many grains of sand are there in 6 300 kg of sand? Give your answer in standard from.
Answer:
It would be 6300000. I can't write this in standard form.
Step-by-step explanation:
Answer:
6.3 x 10^6
Step-by-step explanation:
Levi makes the minimum salary for actuary. Andres maybe the median salary for cpa. Who makes more money
Answer:
Andres
why?
Because he is median salary for cpa
In one state lottery game, you must select four digits (digits may be repeated). If your number matches exactly the four digits selected by the lottery commission, you win.
1) How many different numbers may be chosen?
2) If you purchase one lottery ticket, what is your chance of winning?
3) There are ___ different numbers that can be chosen. (Type a whole number.)
4) There is a ___ chance of winning.*
*The answer choices for number 4 are:
1 in 10,000
1 in 6,561
1 in 100
1 in 1,000
1 in 9,999
Answer:
Part 1)
10,000 different numbers.
Part 2)
A) 1 in 10,000.
Step-by-step explanation:
Part 1)
Since there are four digits and there are ten choices for each digit (0 - 9) and digits can be repeated, then we will have:
[tex]T=\underbrace{10}_{\text{Choices For First Digit}}\times\underbrace{10}_{\text{Second Digit}}\times\underbrace{10}_{\text{Third Digit}}\times \underbrace{10}_{\text{Fourth Digit}} = 10^4=10000[/tex]
Thus, 10,000 different numbers are possible.
Part 2)
Since there 10,000 different tickets possible, the chance of one being the correct combination will be 1 in 10,000.
This is equivalent to 0.0001 or a 0.01% chance of winning.
In a pool of water filled to a depth of 10 ft, calculate the fluid force on one side of a 3 ft by 4 ft rectangular plate if it rests vertically on its 4 ft edge at the bottom of the pool. Remember that water weighs 62.4 lb/ft3
9514 1404 393
Answer:
6,364.8 lb
Step-by-step explanation:
The centroid of the plate is its center, so is 1.5 ft above the bottom of the pool, or 8.5 ft below the surface. The area of the plate is (3 ft)(4 ft) = 12 ft². Then the fluid force is ...
(62.4 lb/ft³)(8.5 ft)(12 ft²) = 6,364.8 lb
..................................................................
Answer:
Hello?
Step-by-step explanation:
Cole biked at 5 mph for 1 hours. Which of the following choices show how far he biked?
A=5.5 miles
B=6.5 miles
C=7.5 miles
D=10 miles
Answer:
Most Likely A, 5.5 Miles
Step-by-step explanation:
However the question doesn't make sense as the logical answer is simply 5 miles, but the safest choice is 5.5
Which of the following situations WOULD NOT represent a binomial application? A. Choosing a card randomly from a standard deck and noting its color (remember color has only two outcomes black or red) B. Choosing a card randomly from a standard deck and noting whether its a face card C. Choosing a card randomly from a standard deck and noting its suit D. Choosing a card randomly from a standard deck and noting whether or not it's an ace
Answer:
Choosing a card randomly and noting its suit
Step-by-step explanation:
Choosing a card randomly and noting its suit
This is because binomial distributions only work for bernoulli trials (a trail in which there are only two outcomes)
Simplify the expression
Answer: …
Step-by-step explanation: you need an image
Answer:
what expression?
Step-by-step explanation:
Can you please help me with this question
-moves "The string of a kite is perfectly taut" and always makes an angle of 35 degrees above horizontal. (a) If the kite flyer has let out 500 feet of string, how high is the kite? (b) If the string is let out at a rate of 10 feet per second, how fast is the kite's height increasing?
Answer:
a) [tex]h=286.8ft[/tex]
b) [tex]\frac{dh}{dt}=5.7ft/s[/tex]
Step-by-step explanation:
From the question we are told that:
Angle [tex]\theta=35[/tex]
a)
Slant height [tex]h_s=500ft[/tex]
Generally the trigonometric equation for Height is mathematically given by
[tex]h=h_ssin\theta[/tex]
[tex]h=500sin35[/tex]
[tex]h=286.8ft[/tex]
b)
Rate of release
[tex]\frac{dl}{dt}=10ft/sec[/tex]
Generally the trigonometric equation for Height is mathematically given by
[tex]h=lsin35[/tex]
Differentiate
[tex]\frac{dh}{dt}=\frac{dl}{dt}sin35[/tex]
[tex]\frac{dh}{dt}=10sin35[/tex]
[tex]\frac{dh}{dt}=5.7ft/s[/tex]
Yess again pls help!
Tyyy
the volume of a rectangular pyramid with a length of 7 feet, a width of 6 feet, and a height of 4.5 feet.
Answer:
Volume = 63 feet
Step-by-step explanation:
To find the volume of a cube or a rectangular prism, the formula is
(L x W x H)/3. In other words, it is the length of the prism, times the width of the prism, times the height of the prism, whole divided by three, since it has a "triangular shape."
Let's substitute in values for these letters, L, W, and H. You said the length was 7, the width was 6, and the height was 4.5. Therefore, it will result in
(7 x 6 x 4.5)/3. That results in 189/3, which is 63.
Hope this helped!!!
A senior class of 420 students will rent buses and vans for a class trip. Each bus can transport 50 students and 3 chaperones and costs $1200 to rent. Each van can transport 10 students and 1 chaperone and costs $100 to rent. There are 36 chaperones available (so they can't all go in vans). How many vehicles of each type should be rented in order to minimize the cost
Answer:
37 buses and 1 van.
Step-by-step explanation:
The cost to rent a van is $1200 for 50 students and 3 chaperones, while a bus for 10 students and a chaperone is $100 .
The cost of renting buses for 50 students is $500
What we do is rent 37 buses and 1 van
37 buses will take in 370 students with empty 2 spaces in 2 buses for chaperones since the chaperones are 36.
Then rent 1 van to take in 50 students and 1 chaperone.
The total cost here will be
$3700 + $1200 = $ 4900
This will help to safe cost.
would someone mind looking over my answers to geometry!!
Answer:
Question 1: x = 6
Question 2: Correct!
Question 3: x = 11
Question 4: Correct!
Step-by-step explanation:
Question 1:
Angle 22x - 2 DOESN'T equal 50 degrees. Only Alternate Interior Angles will equal each other. These two angles are Same Side Interior Angles, meaning if you added them together, they would equal 180 degrees.
Knowing that adding 22x - 2 and 50 will equals 180 degrees, here's how we solve for x:
First, subtract 50 from 180 to find what angle 22x - 2 will equal:
180 - 50 = 130
130 = 22x - 2
Now use basic algebra to solve for x:
130 = 22x - 2
(add 2 to both sides)
132 = 22x
(divide both sides by 22)
x = 6
Question 3:
Angle 5x + 15 DOESN'T equal 9x + 11. They make up a line, which is 180 degrees, so they are supplementary angles.
With that in mind, to solve for x, add the two equations and set it equal to 180:
5x + 15 + (9x + 11) = 180
Now use basic algebra to solve for x:
5x + 15 + 9x + 11 = 180
(add like terms)
14x + 26 = 180
(subtract 26 from both sides)
14x = 154
(divide 14 from both sides)
x = 11
Hope it helps (●'◡'●)
Which choice is equivalent to(√6)( √8). How do you solve
A. 4√6
B. 4√3
C. 16√3
D. 3√16
Answer:
B
Step-by-step explanation:
(6)^1/2 × (8)^1/2
6^1/2 × 2 (2)^1/2
4 (3)^1/2
The ocean surface is at 0 ft elevation. A diver is underwater at a depth of 138 ft. In this area, the ocean floor has a depth of 247 ft. A rock formation rises to a peak 171 ft above the ocean floor. How many feet below the top of the rock formation is the diver?
Answer:
The ocean surface is at 0 ft elevation. A diver is underwater at a depth of 138 ft. In this area, the ocean floor has a depth of 247 ft.
Step-by-step explanation:
A radioactive substance decays exponentially: The mass at time t is m(t) = m(0)e^kt, where m(0) is the initial mass and k is a negative constant. The mean life M of an atom in the substance is
[infinity]
M = âk â« te^kt dt.
0
For the radioactive carbon isotope, 14C, used in radiocarbon dating, the value of k is -0.000121. Find the mean life of a 14C atom.
Answer:
mean life = 8264.5 s
Step-by-step explanation:
k = - 0.000121
The relation is given by
[tex]m = mo e^{kt}[/tex]
Now, the mean life is the life time for which the sample retains.
The mean life is the reciprocal of the decay constant.
The relation between the mean life and the decay constant is
[tex]\tau =\frac{1}{k}\\\\\tau = \frac{1}{0.000121} = 8264.5 seconds[/tex]
The time for a professor to grade a student’s homework in statistics is normally distributed with a mean of 13.3 minutes and a standard deviation of 2.0 minutes. What is the probability that randomly selected homework will require less than 17 minutes to grade?
Answer:
0.96784
Step-by-step explanation:
17-13.3/2
=1.85
p(x<1.85)
=0.96784
The probability that randomly selected homework will require less than 17 minutes to grade is 0.9678.
Mean [tex]\mu[/tex]=13.3 minutes
Standard deviation[tex]\sigma[/tex]=2 minutes
What is a z-score?The value of the z-score tells you how many standard deviations you are away from the mean.
So, the z-score of the above data
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{17-13.3}{2}[/tex]
[tex]z=1.85[/tex]
From the standard normal table, the p-value corresponding to z=1.85
Or, p(x<1.85)=0.9678 or 96.78%
Hence, the probability that randomly selected homework will require less than 17 minutes to grade is 0.9678.
To get more about the z-score visit:
https://brainly.com/question/25638875
if f(x)=-5^x-4 and g(x)=-3x-2,find (f+g) (x)
Answer: (f-g)(x) = - 5^x + 3x - 2
Step-by-step explanation:
if f(x) = -5^x - 4 and g(x)= - 3x - 2,find (f-g)(x)
(f-g)(x) = -5^x - 4 - (-3x - 2)
(f-g)(x) = -5^x - 4 + 3x + 2
(f-g)(x) = - 5^x + 3x - 2
Square Footage Frequency
0-499 5
500-999 17
1000-1499 36
1500-1999 115
2000-2499 125
2500-2999 81
3000-3499 47
3500-3999 45
4000-4499 22
4500-4999 7
The accompanying frequency distribution represents the square footage of a random sample of 500 houses that are owner occupied year round. Approximate the mean and standard deviation square footage.
Answer:
2424.5
904.16
Step-by-step explanation:
the mean = ∑frequency /n
∑f = 5+17+36+115+125+81+47+45+22+7 = 500
∑xf = 1212250
∑x²f = 3347037625
sample mean = 1212250/500
= 2424.5
variance = 1/500-1[3347037625 - 1212250²]
= 815710.02
standard deviation is = √variance
standard deviation = √815710.02
= 904.16
A cell site is a site where electronic communications equipment is placed in a cellular network for the use of mobile phones. The numbers y of cell sites from 1985 through 2011 can be modeled byy = 269573/1+985e^-0.308t where t represents the year, with t = 5 corresponding to 1985. Use the model to find the numbers of cell sites in the years 1998, 2003, and 2006.
Answer:
(a) 3178
(b) 14231
(c) 33152
Step-by-step explanation:
Given
[tex]y = \frac{269573}{1+985e^{-0.308t}}[/tex]
Solving (a): Year = 1998
1998 means t = 8 i.e. 1998 - 1990
So:
[tex]y = \frac{269573}{1+985e^{-0.308*8}}[/tex]
[tex]y = \frac{269573}{1+985e^{-2.464}}[/tex]
[tex]y = \frac{269573}{1+985*0.08509}[/tex]
[tex]y = \frac{269573}{84.81365}[/tex]
[tex]y = 3178[/tex] --- approximated
Solving (b): Year = 2003
2003 means t = 13 i.e. 2003 - 1990
So:
[tex]y = \frac{269573}{1+985e^{-0.308*13}}[/tex]
[tex]y = \frac{269573}{1+985e^{-4.004}}[/tex]
[tex]y = \frac{269573}{1+985*0.01824}[/tex]
[tex]y = \frac{269573}{18.9664}[/tex]
[tex]y = 14213[/tex] --- approximated
Solving (c): Year = 2006
2006 means t = 16 i.e. 2006 - 1990
So:
[tex]y = \frac{269573}{1+985e^{-0.308*16}}[/tex]
[tex]y = \frac{269573}{1+985e^{-4.928}}[/tex]
[tex]y = \frac{269573}{1+985*0.00724}[/tex]
[tex]y = \frac{269573}{8.1314}[/tex]
[tex]y = 33152[/tex] --- approximated
help me plz----------------------------
9514 1404 393
Answer:
A. 5 should have been subtracted in step 4
Step-by-step explanation:
No question is stated, so there is no "answer."
__
If we assume the question is, "What error did Keith make?" then choice A properly describes it.
Step 4 should look like ...
x -5 = 7y . . . . . . . 5 should be subtracted from both sides
and the final result should be ...
g(x) = (x -5)/7
I need help solving this problem .
Step-by-step explanation:
here is the answer to your question
A large container holds 4 gallons of chocolate milk that has to be poured into bottles. Each bottle holds 2 pints.
If the ratio of gallons to pints is 1: 8,
bottles are required to hold the 4 gallons of milk.
Answer:
64 Bottles
Step-by-step explanation:
that is the procedure above
A town recently dismissed 5 employees in order to meet their new budget reductions. The town had 4 employees over 50 years of age and 16 under 50. If the dismissed employees were selected at random, what is the probability that no more than 1 employee was over 50
Answer:
0.7513 = 75.13% probability that no more than 1 employee was over 50
Step-by-step explanation:
The employees are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[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]
In this question:
4 + 16 = 20 employees, which means that [tex]N = 20[/tex]
4 over 50, which means that [tex]k = 4[/tex]
5 were dismissed, which means that [tex]n = 5[/tex]
What is the probability that no more than 1 employee was over 50?
Probability of at most one over 50, which is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
In which
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,20,5,4) = \frac{C_{4,0}*C_{16,5}}{C_{20,5}} = 0.2817[/tex]
[tex]P(X = 1) = h(1,20,5,4) = \frac{C_{4,1}*C_{16,4}}{C_{20,5}} = 0.4696[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.2817 + 0.4696 = 0.7513[/tex]
0.7513 = 75.13% probability that no more than 1 employee was over 50
1. You measure 24 textbooks' weights, and find they have a mean weight of 75 ounces. Assume the population standard deviation is 3.3 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.
2. You measure 37 backpacks' weights, and find they have a mean weight of 45 ounces. Assume the population standard deviation is 10.1 ounces. Based on this, construct a 95% confidence interval for the true population mean backpack weight.
3. You measure 30 watermelons' weights, and find they have a mean weight of 37 ounces. Assume the population standard deviation is 4.1 ounces. Based on this, what is the maximal margin of error associated with a 90% confidence interval for the true population mean watermelon weight.
4. A student was asked to find a 99% confidence interval for widget width using data from a random sample of size n = 16. Which of the following is a correct interpretation of the interval 11.8 < μ < 20.4?
A. There is a 99% chance that the mean of a sample of 16 widgets will be between 11.8 and 20.4.
B. The mean width of all widgets is between 11.8 and 20.4, 99% of the time. We know this is true because the mean of our sample is between 11.8 and 20.4.
C. With 99% confidence, the mean width of all widgets is between 11.8 and 20.4.
D. With 99% confidence, the mean width of a randomly selected widget will be between 11.8 and 20.4.
E. There is a 99% chance that the mean of the population is between 11.8 and 20.4.
5. For a confidence level of 90% with a sample size of 23, find the critical t value.
Answer:
(73.845 ; 76.155) ;
(41.633 ; 48.367) ;
1.273 ;
C. With 99% confidence, the mean width of all widgets is between 11.8 and 20.4. ;
1.717
Step-by-step explanation:
1.)
Given :
Mean, xbar = 75
Sample size, n = 24
Sample standard deviation, s = 3.3
α = 90%
Confidence interval = mean ± margin of error
Margin of Error = Tcritical * s/√n
Tcritical at 90% ; df = 24 - 1 = 23
Tcritical = 1.714
Margin of Error = 1.714 * 3.3/√24 = 1.155
Confidence interval = 75 ± 1.155
Confidence interval = (73.845 ; 76.155)
2.)
Given :
Mean, xbar = 45
Sample size, n = 37
Sample standard deviation, s = 10.1
α = 95%
Confidence interval = mean ± margin of error
Margin of Error = Tcritical * s/√n
Tcritical at 95% ; df = 37 - 1 = 36
Tcritical = 2.028
Margin of Error = 2.028 * 10.1/√37 = 3.367
Confidence interval = 45 ± 3.367
Confidence interval = (41.633 ; 48.367)
3.)
Given :
Mean, xbar = 37
Sample size, n = 30
Sample standard deviation, s = 4.1
α = 90%
Margin of Error = Tcritical * s/√n
Tcritical at 90% ; df = 30 - 1 = 29
Tcritical = 1.700
Margin of Error = 1.700 * 4.1/√30 = 1.273
5.)
Sample size, n = 23
Confidence level, = 90%
df = n - 1 ; 23 - 1 = 22
Tcritical(0.05, 22) = 1.717
Which division problem does the diagram below best illustrate?
A diagram with 8 ovals containing 4 squares each.
O 16 divided by 4 = 4
O 32 divided by 4 = 8
O 36 divided by 4 = 9
O 8 divided by 2 = 4
Answer:
The answer is 32 divided by 4
Step-by-step explanation:
Because in each box there is 4. There are 8 ovals all together. So 8×4, you get 32 and divide it by the number of squares in an oval which is 4
Answer:
the answer is 32 divided by 4=8
Step-by-step explanation:
because when you look at the ovals there's eight ovals and in side there's four squares..
HOPE THIS HELPS!!!!!
A loan of £1000 has a compound interest rate of 2.7% charged monthly. Express the original loan as a percentage of the total amount awed after 2 months if no payment are made
Answer:
£1054.729
Step-by-step explanation:
To find compound interest you need to use the equation 1000(1.027)^x.
To find the interest rate (1.027):
100 + 2.7 = 102.7
102.7 / 100 = 1.027
The value of x is the amount of months if no payment is made in this situation, so 2 would be the x value for this problem.
Hope this helps!
