Answer:
a) 0.3125 per hour
b) 2.225 hours
c) 8.9 hours
d) 12.1 hours
e) 80%
Step-by-step explanation:
Given that:
mean time = 3.2 hours, standard deviation (σ) = 2 hours
The mean service rate in jobs per hour (λ) = 2 jobs/ 8 hour = 0.25 job/hour
a) The average number of jobs waiting for service (μ)= 1/ mean time = 1/ 3.2 = 0.3125 per hour
b) The average time a job waits before the welder can begin working on it (L) is given by:
[tex]L=\frac{\lambda^2\sigma^2+(\lambda/\mu)^2}{2(1-\lambda/\mu))} =\frac{0.25^2*0.2^2+(0.25/0.3125)^2}{2(1-0.25/0.3125)}=2.225\ hours[/tex]
c) The average number of hours between when a job is received and when it is completed (Wq) is given as:
[tex]W_q=\frac{L}{\lambda}=2.225/0.25=8.9\ hours[/tex]
d) The average number of hours between when a job is received and when it is completed (W) is given as:
[tex]W=W_q+\frac{1}{\mu} =8.9+\frac{1}{0.3125}=12.1 \ hours[/tex]
e) Percentage of the time is Gubser's welder busy (P) is given as:
[tex]P=\frac{\lambda}{\mu}=0.25/0.3125=0.8=80\%[/tex]
Simplify and express in exponential form: 8^-1 * 3^3/ 2^-4 * 9^-2
Answer:
2^1* 3^7
Step-by-step explanation:
8^-1 * 3^3/ 2^-4 * 9^-2
Negative exponents move from the numerator to the denominator or from the denominator to the numerator
2^4*9^2* 3^3 /8^1
Rewriting 9^2 as 3^2^2 = 3^4 and 8 = 2^3
2^4 * 3^3 * 3^4 / 2^3
2^4/ 2^3 = 2 and 3^3 * 3^4 = 3^(3+4) = 3^7
2* 3^7
Answer:
Step-by-step explanation:
[tex]\frac{8^{-1}*3^{3}}{2^{-4}*9^{-2}}=\frac{(2^{3})^{-1} * 3^{3}}{2^{-4}*(3^{2})^{-2}}\\\\=\frac{2^{3*-1}*3^{3}}{2^{-4}*3^{2*-2}}\\\\=\frac{2^{-3}*3^{3}}{2^{-4}*3^{-4}}\\\\=2^{-3+4}*3^{3+4}\\\\=2^{1}*3^{7}\\\\=2*3^{7}[/tex]
what is the midpoint of the horizontal (-2,3) and (10,3)
The measurement of the circumference of a circle is found to be 64 centimeters, with a possible error of 0.9 centimeter. (a) Approximate the percent error in computing the area of the circle. (Round your answer to two decimal places.) 2.81 Correct: Your answer is correct. % (b) Estimate the maximum allowable percent error in measuring the circumference if the error in computing the area cannot exceed 1%. (Round your answer to one decimal place.)
Answer:
(a) 2.81%
(b) 0.5%
Step-by-step explanation:
We have the following information from the statement:
P = 64 + - 0.9
(a) We know that the perimeter is:
P = 2 * pi * r
if we solve for r, we have to:
r = P / 2 * pi
We have that the formula of the area is:
A = pi * r ^ 2
we replace r and we are left with:
A = pi * (P / 2 * pi) ^ 2
A = (P ^ 2) / (4 * pi)
We derive with respect to P, and we are left with:
dA = 2 * P / 4 * pi * dP
We know that P = 64 and dP = 0.9, we replace:
dA = 2 * 64/4 * 3.14 * 0.9
dA = 9.17
The error would come being:
dA / A = 9.17 / (64 ^ 2/4 * 3.14) = 0.02811
In other words, the error would be 2.81%
(b) tell us that dA / A <= 0.01
we replace:
[P * dP / 2 * pi] / [P ^ 2/4 * pi] <= 0.01
solving we have:
2 * dP / P <= 0.01
dP / P <= 0.01 / 2
dP / P <= 0.005
Which means that the answer is 0.5%
The Venn diagram below is used for showing odd numbers and prime numbers.
Place the numbers 1, 2, 3, 4 and 5 in the Venn diagram.
Answer:
See attached
Step-by-step explanation:
Given the numbers 1,2,3,4 and 5
Odd Numbers =1, 3 and 5Prime Numbers = 2, 3 and 5Let O be the event that the number is Odd
Let E be the event that the number is Prime
Then the intersection of Odd and Prime Numbers: [tex]O \cap P =\{3,5\}[/tex]
Since 4 is neither odd nor prime, we place it outside of the two circles.
See the attached diagram for the required Venn diagram.
The graph of y=-3x+2 is:
Answer:
C.
Step-by-step explanation:
Any equation is always infinite. You plug in values to receive values, and since there is an unlimited amount of numbers and values, the graph of the equation will show infinite solutions to the equation.
You can test this by trying to zoom out of your graphing calc. Notice that you'll never be able to get a definite max or min.
The height of seaweed of all plants in a body of water are normally distributed with a mean of 10 cm and a standard deviation of 2 cm. Which length separates the lowest 30% of the means of the plant heights in a sampling distribution of sample size 15 from the highest 70%? Round your answer to the nearest hundredth. Use the z-table below:
0.00 0.01 0.02 0.030.04 0.05 0.06 0.08 0.09 0.07 -0.8 0.212 0.209 0.206 0.203 0.201 0.198 0.195 0.192 0.189 0.187 -0.7 0.242 0.239 0.236 0.233 0.230 0.227 0.224 0.221 0.218 0.215 -0.6 0.274 0.271 0.268 0.264 0.261 0.258 0.255 0.251 0.248 0.245 -0.5 0.309 0.305 0.302 0.298 0.295 0.291 0.288 0.284 0.281 0.278 -0.4 0.345 0.341 0.337 0.334 0.330 0.326 0.323 0.319 0.316 0.312 -0.3 0.382 0.378 0.374 0.3710.367 0.363 0.359 0.356 0.352 0.348
Round the z-score and i to two decimal places. Provide your answer below: Z-Score =
Answer:
Step-by-step explanation:
Hello!
The variable of interest is:
X: height of seaweed.
X~N(μ;σ²)
μ= 10 cm
σ= 2 cm
You have to find the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70
P(X≤x)= 0.30
P(X≥x)= 0.70
Using the standard normal distribution you have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then using the formula Z= (X-μ)/σ translate the Z value to the corresponding X value.
P(Z≤z)= 0.30
In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.
z= -0.52
Now you have to clear the value of X:
Z= (X-μ)/σ
Z*σ= X-μ
X= (Z*σ)+μ
X= (-0.52*2)+10= 8.96
The value of seaweed height that divides the bottom 30% from the top 70% is 8.96 cm
I hope this helps!
Answer:-0.53 and 9.72
Step-by-step explanation:
A local road rises 14 feet for every 472 feet of highway. What is the slope of the highway?
Info:
Use rise over run when finding slope
U can solve by yourlsf by knowing:'
"A line with a positive slope (m > 0), as the line above, rises from left to right whereas a line with a negative slope (m < 0) falls from left to right. A line with the slope zero (m = 0) is horizontal whereas a line with an undefined slope is vertical. ... You can interpret a slope of a line as the rate of change."
Answer:
+14/472
Hpe this helps
The slope of the highway is +0.02967.
What is slope?At any surface, where the level of one end is higher or lower than the level of another end is called slope. Its notation is m.
The given condition is,
Road rises 14 feet for every 472 meter of highway ,
As we know height of the road increases for 14 feet for 472 meter of highway,
So the slope will be positive,
And slope of this can be defined as +14/472 or 0.02967.
To know more about Slope on:
https://brainly.com/question/6501549
#SPJ2
Pleassssseeeeeeee hhhheeeellllpppp
Answer:
it always add's one block
Step-by-step explanation:
3 blocks add 1 block every time there is a new pattern.
what is the factor to x^2-9x-22=
Answer:
(x - 11)(x + 2)
Step-by-step explanation:
You have to find factors that add up to -9 and multiply up to -22. First numbers to pop up should be 11 and 2. Now you simply figure out which signs go where, and to produce -9, 11 has to be subtracted and 2 has to be added to x.
helpppp :,[ also stay safe and have a great day!!!!!!!!!!!!!!!!!!!!!!1111
Answer:
35÷7=5
Step-by-step explanation:
we have 7 small boxes in an oval and there are 5 ovals
All the boxes add up to 35
Answer:
B) 35/7 = 5
Step-by-step explanation:
First, I counted the number of groupings, which is 5. That will be our answer, since they circled them.
Then, I counted how many boxes were in each group. 7. That will represent the divisor or the number that we will be dividing by.
If you multiply the numbers, they will equal 35. 5*7=35 Since they are asking which division problem the diagram represents, 35 is the dividend or the number that we start with.
If ABCD is a rectangle, and m∠ADB=55°, what is the value of x?
Answer:
x= 70
Step-by-step explanation:
Rectangles have four right angles (angles of 90 degrees).
The point of intersection of the diagonals divides each one of them into two equal parts.
Knowing this, we can conclude that:
m\angle c=m\angle b=55\°
Therefore, since the sum of the interior angles of a triangle is 180 degrees, we can find the value of "x":
x+m\angle c+m\angle b=180\°\\x=180\°-55\°-55\°\\x=70\°
One half of one third of one quarter of one fifth of a number is 2.
What is the number?
Answer: 240
Step-by-step explanation:
[tex]\dfrac{1}{2}\times \dfrac{1}{3}\times \dfrac{1}{4}\times \dfrac{1}{5}x=2\\\\\\\dfrac{1}{120}x=2\\\\\\(120)\dfrac{1}{120}x=2(120)\\\\\\\large\boxed{x=240}[/tex]
Solve the equation. And write all solutions in general form.
Answer:
x = pi/2 + 2 pi n x = pi + 2 pi n where n is an integer
x = 5pi /3 + 2 pi n
Step-by-step explanation:
8 cos^2 x + 4 cos x-4 = 0
Divide by 4
2 cos^2 x + cos x-1 = 0
Let u = cos x
2 u^2 +u -1 =0
Factor
(2u -1) ( u+1) = 0
Using the zero product property
2u-1 =0 u+1 =0
u = 1/2 u = -1
Substitute cosx for u
cos x = 1/2 cos x = -1
Take the inverse cos on each side
cos ^-1(cos x) = cos ^-1(1/2) cos ^-1( cos x) =cos ^-1( -1)
x = pi/2 + 2 pi n x = pi + 2 pi n where n is an integer
x = 5pi /3 + 2 pi n
Whats TWO equivalent expressions for 2(3j+ 5 + 6j). Rember TWO equivalent expressions not one.
Answer:
2(9j+5) and 18j+10
Step-by-step explanation:
1) group like terms
2) distribute
please mark brainliest
If Ricky borrowed $4600 at a rate of 16% interest per year compounded quarterly,
calculate the amount due at the end of 8 years if the interest is compounded
quarterly.
Answer: $16137.07
Step-by-step explanation:
A = p(1+r/n)^nt
A= 4600(1+0.16/4)^4x8
A= 16137.07
Which polynomial function could be represented by the graph below? On a coordinate plane, a cubic function crosses the x-axis at (negative 3, 0), (0, 0), (2, 0). f(x) = x3 + x2 – 6x f(x) = x3 – x2 – 6x f(x) = –2x3 – 2x2 + 12x f(x) = –2x3 + 2x2 + 12x
Answer:
third one
Step-by-step explanation:
when
x=0, y=0
x=1, y=8
x=2 y=0
and so on.
Answer:
C. f(x)= -2x^3 -2x^2 +12x
Step-by-step explanation:
edge 2020
During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes.a. What is the expected number of calls in one hour?b. What is the probability of three calls in five minutes?c. What is the probability of no calls in a five-minute period?
Answer:
Step-by-step explanation:
This is a poisson distribution. Let x be a random representing the number of calls in a given time interval.
a) the expected number of calls in one hour is the same as the mean score in 60 minutes. Thus,
Mean score = 60/2 = 30 calls
b) The interval of interest is 5 minutes.
µ = 5/2 = 2.5
We want to determine P(x = 3)
Using the Poisson probability calculator,
P(x = 3) = 0.21
c) µ = 5/2 = 2.5
We want to determine P(x = 0)
Using the Poisson probability calculator,
P(x = 0) = 0.08
The World Issues club has decided to donate 60% of all their fundraising activities this year to Stephen Lewis Foundation. This foundation was created to help ease the pain of HIV/AIDS in Africa. Lewis, a Canadian, works for the United Nations trying to determine ways to stop the spread of this deadly disease from crippling an entire continent. Choose a variable to represent the money earned during fundraising activities and the revenue generated for the foundation Use these variables to create an equation that will determine the amount of money the foundation will receive. In their latest bake sale, the club raised $72. Calculate the amount the foundation will receive. At the end of the year, the World Issues Club mailed a cheque to the foundation for $850. How much money did they fundraise in total?
Answer:
$43.20$1416.67Step-by-step explanation:
Let the money earned during fundraising activities =x
Since the World Issues club has decided to donate 60% of all their fundraising activities this year to Stephen Lewis Foundation.
The amount of money the foundation will receive
=60% of x
= 0.6x
In the bake sale, the club raised $72.
Therefore, the amount the foundation will receive =0.6*72=$43.20
At the end of the year, the World Issues Club mailed a cheque to the foundation for $850.
Therefore:
0.6x=850
x=850/0.6
x=$1416.67
The total amount of money the club raised is $1416.67.
what is the sum of 4m(m-6) and 8(m-4)?
Step-by-step explanation:
4m2 - 24m + 8m - 32
4m2 - 16m - 32
g Suppose I will flip a fair coin until it lands Heads for the first time, and you will receive $2 if the game lasts for 1 round, $4 if the game lasts for 2 rounds, $8 if the game lasts for 3 rounds, and in general, $2n if the game lasts for n rounds. How much would you be willing to pay to play this game once
Answer:
Step-by-step explanation:
The main idea is that I would like to pay less than what I'm expecting to win, so in that way, I get a profit out of playing this game. Let X be the number of tosses until I get a Heads. By definition, this is a geometric random variable with parameter p = 1/2.
Let Y the amount I received for playing. So, we want to calculate the expected value of Y.
We can calculate it as follows
[tex]E[Y] = 2 P(X=1)+ 4 P(X=2)+ 8 P(X =3) + \dots = \sum_{n=1}^infty 2^n P(X=n)[/tex]
Since X is a geometric random variable, we have that [tex] P(X=n) = (\frac{1}{2})^{n-1}\frac{1}{2}[/tex]
Then,
[tex] E[Y] = \sum_{n=1}^\infty 2^{n} (\frac{1}{2})^{n-1} \frac{1}{2} = \sum_{n=1}^\infty 2^{n-1} \cdot \frac{1}{2^{n-1}} = \sum_{n=1}^\infty 1 = \infty[/tex]
So, we expect to have an infinite amount. Given this, we can pay as much as we want to play the game.
NEED HELP ASAP 10 pOINTS!!!!
Answer:
Since it's a right angled triangle
15² = 13² + x²
x² = 15²-13²
x² = 56
x = √56
x= 2√14
Hope this helps.
if sec theta = 5/3 and the terminal point determined by theta is in quandrant 4, then:
(view photo for answer options)
please help!
Answer:
C.
Step-by-step explanation:
I believe the answer is C.
Secant is just 1/cos
In that case,
sec∅ = 5/3 = cos∅ = 3/5
Which part of Earth belongs to the geosphere?
air
plants
minerals
water
Help plz
Answer: Minerals
Step-by-step explanation:
The Mineral belongs to the geosphere option (3) Mineral is correct.
What is the geosphere?Different definitions of the geosphere have conflicting uses. It can be used to refer to the atmosphere, lithosphere, hydrosphere, and cryosphere as a whole. Different mass and/or energy flows can be exchanged between the various geosphere collectives.
We have a statement:
Which part of Earth belongs to the geosphere?
The options are:
airplantsmineralswaterAs we know, air belongs to the atmosphere.
Plants belong to the biosphere
Water belongs to the hydrosphere
Mineral belongs to the geosphere
The mineral is the part of the earth that belongs to the geosphere.
Thus, the Mineral belongs to the geosphere option (3) Mineral is correct.
Learn more about the geosphere here:
https://brainly.com/question/5137630
#SPJ5
if cos theta < 0 and cot theta > 0, then the terminal point determined by theta is in:
A. Quadrant 1
B. Quadrant 3
C. Quadrant 4
D. Quadrant 2
please help me !
Answer:
If cosine theta < 0 and cotangent theta > 0, then the terminal point determined by theta is in: quadrant 3.
Step-by-step explanation:
hope this helps you :) my answer is the Step-by-step explanation: and the answer :)
Considering the signals of the sine and the cosine of the trigonometric function, it is found that it's quadrant is given by:
B. Quadrant 3
What are the signals of the sine and the cosine in each quadrant?Q1: cos > 0, sin > 0.Q2: cos < 0, sin > 0.Q3: cos < 0, sin <0.Q4: cos > 0, sin < 0.In this problem, we have that the cosine is negative, and the cotangent is positive. Cotangent is cosine divided by sine, hence if it is positive, both cosine and sine have the same signal, since cos < 0, sine is negative, they are in third quadrant and option B is correct.
More can be learned about the quadrants of trigonometric functions at https://brainly.com/question/24551149
#SPJ2
a. Find the common factors of 12 and 20.
[2marks]
2. Hence find the highest common factor(HCF) of 12 and 20.
[1mark)
A school purchases workbooks in packs of 25 and text books in packs of 15.
The school needs exactly the same number of workbooks as textbooks so
they can be paired up for the students. What is the minimum number of each
pack that must be bought so that all the books are paired? You must show all
[3marks]
of your working
Answer:
a. Common factors of 12 and 20 = 2, 2
2. Highest common factor of 12 and 20 = 4
3 packs of workbooks and 5 packs of text books to be purchased.
Step-by-step explanation:
a.) To find the common factors of 12 and 20:
First of all, let us find the factors of 12 and 20
12 = 2 [tex]\times[/tex] 2 [tex]\times[/tex] 3
20 = 2 [tex]\times[/tex] 2 [tex]\times[/tex] 5
The common factors are underlined above i.e. 2, 2.
2. The highest common factor between 12 and 20 is 2 [tex]\times[/tex] 2 = 4
-------------------------------------------
Workbooks are in packs of 25
Textbooks are in pack of 15
The school needs exactly same number of workbooks and textbooks.
And we have to find such least number.
This least number can simply be calculated by finding the LCM (Least Common Multiple).
LCM of two numbers p and q is the minimum number which is completely divisible by both the numbers p and q.
Let us find LCM of 25 and 15 using factorization method:
15 = 3 [tex]\times[/tex] 5
25 = 5 [tex]\times[/tex] 5
The common part is considered only once:
So LCM = 3 [tex]\times[/tex] 5 [tex]\times[/tex] 5 = 75
Hence, number of packs of workbooks to be bought = [tex]\frac{75}{25} = 3[/tex]
number of packs of textbooks to be bought = [tex]\frac{75}{15} = 5[/tex]
So, the answer are:
a. Common factors of 12 and 20 = 2, 2
2. Highest common factor of 12 and 20 = 4
3 packs of workbooks and 5 packs of text books to be purchased.
Answer:
A school purchases workbooks in packs of 25 and text books in packs of 15. The school needs exactly the same number of workbooks as textbooks so they can be ...
1 answer
·
Top answer:
Answer:a. Common factors of 12 and 20 = 2, 22. Highest common fact
Step-by-step explanation:
In an inventory of standardized weights, 8% of the weights are found to exceed 10.282 grams and 6% weighs below 9.69 grams. If weight is a continuous random variable distributed normally, find the mean and standard deviation for this distribution.
Step-by-step explanation:
We are given here for the random variable X:
P( X > 10.282) = 0.08 and P(X < 9.69) = 0.06
From standard normal tables, we have:
P(Z < 1.405) = 0.92. Therefore P(Z > 1.405) = 0.08
Therefore, the z score of 10.282 is 1.405
Therefore, Mean + 1.405*Std Dev = 10.282
Also from standard normal tables, we have:
P(Z < -1.555) = 0.06
Therefore, Mean - 1.555×Std Dev = 9.69
Subtracting the second equation from first, we get here:
Std Dev(1.405 + 1.555) = 10.282 - 9.69
Std Dev = 0.2
Now the mean can be computed as:
Mean = 1.555*Std Dev + 9.69 = 1.555*0.2 + 9.69 = 10.001
Therefore 10.001 is the required mean and 0.2 is the required standard deviation for the distribution here.
what is the Y intercept of the quadratic function f(x)=(x-6)(x+3)
Answer:
(0,-24)Option C is the correct option.
Solution,
Given that,
[tex]f(x) = (x - 8)(x + 3)[/tex]
put f(x)=y
[tex]y(x - 8)(x + 3) - - > equation \: (i)[/tex]
For finding y- intercept
put x=0
We get,
[tex]y = (0 - 8)(0 + 3) - - > from \: {eq}^{n} \: (i)[/tex]
[tex]y = ( - 8) \times 3 \\ y = - 24 \\ y - intercept = (0 ,- 24)[/tex]
hope this helps...
Good luck on your assignment..
To study the effect of neighborhood on academic performance, 1000 families were given federal housing vouchers to move out of their low-income neighborhoods. No improvement in the academic performance of the children in the families was found one year after the move.Requried:a. What are the explanatory and response variables?b. What are the subjects, factor(s), and treatment?c. What does no significant difference mean in describing the outcome of this study?d. Explain clearly why the lack of improvement in academic performance after one year does not necessarily mean that neighborhood does not affect academic performance.e. In particular, identify some lurking variables whose effect on academic performance may be confounded with the effect of the neighborhood
Answer:
Check below for the answers and explanations to the questions.
Step-by-step explanation:
a) The explanatory variable is "the neighborhood" because it is the one that can be controlled/varied by the experimenter and also determines the outcome of the experiment.
The response variable is the "academic performance of the children" since it is the outcome of the experiment.
b) The subjects of the study are the children of the 1000 families that were given federal housing vouchers to relocate.
The factors of the study are:
1. the low income neighborhood
2. the federal housing estate
Treatment is the combination of various levels of the factor. In this case, it is the neighborhood of the families.
c) No significant difference means that the mean of the academic performance of the children while living the low-income neighborhood equals the mean of their academic performance while living in the federal housing estate. Which means that the null hypothesis is accepted.
d) The period of evaluation after relocation is very small compared to the time that has been spent in the low-income neighborhood. The observation has to take a longer time to discover the effect of the new neighbourhood on the academic performance of the children. Therefore the lack of improvement in academic performance after one year does not necessarily mean that neighborhood does not have effect on academic performance.
e) some other variables that are not considered in this study are:
The average Intelligence Quotient of the children
The parental training
The schools attended by the children
Average number of hours spent on study
Solve for b. -11b+7 = 40 Two step equations
Step-by-step explanation:
-11b + 7 = 40
-11b = 40 - 7
-11b = 33
b = 33/-11
b = - 3
triangles DEF and D'E'F' are shown on the coordinate plane below:
Answer:
Option B
Step-by-step explanation:
Triangle DEF was rotated 90 degrees counter clockwise to create Triangle D'E'F'.
Answer:
it was b
Step-by-step explanation:
