Answer:
(a) x follows a poisson distribution with parameter λ = 8 / hour
(b) P( X = 5 ) = 0.09160
P( X ≥ 5 ) = 0.9004
(c) the expected value of the number of nonconforming parts produced during a 120-min period = 16 nonconforming parts per 120 minutes
The standard deviation = 4
(d) P(X ≥ 20) = 0.5297
P( X ≤ 10) = 0.0108
Step-by-step explanation:
Suppose nonconforming parts are produced with a rate = 8 / hour (i.e. on average, 8 nonconforming parts will be made during a production period of one hour).
(a) If x denotes the number of nonconforming parts made during one hour, then : x follows a poisson distribution with parameter λ = 8 / hour
(b)
What is the probability that exactly 5 nonconforming parts are produced during a 1-hour period? What is the probability that at least 5 nonconforming parts are produced during a 1-hour period?
the probability that exactly 5 nonconforming parts are produced during a 1-hour period can be computed as:
P( X = 5 ) = [tex]e^{- \lambda } \lambda^x /x![/tex]
P( X = 5 ) = [tex]e^{- 8 }(8)^5 /5![/tex]
P( X = 5 ) = 0.09160
the probability that at least 5 nonconforming parts are produced during a 1-hour period
P( X ≥ 5 ) = 1 - P( X ≤ 4)
[tex]P( X \geq 5 ) = 1 - \sum \limits ^4_{x=0} e^{-\lambda} \lambda ^x/x![/tex]
[tex]P( X \geq 5 ) = 1 - (e^{-8} 8 ^4/4! + e^{-8} 8 ^3/3! + e^{-8} 8 ^2/2! +e^{-8} 8 ^1/1! + e^{-8} 8 ^0/0! )[/tex]
[tex]P( X \geq 5 ) = 1 - 0.0996[/tex]
P( X ≥ 5 ) = 0.9004
c) What are the expected value and standard deviation of the number of nonconforming parts produced during a 120-min period?
the expected value of the number of nonconforming parts produced during a 120-min period [tex]\lambda = 8 \times \dfrac {120}{60}[/tex]
= 16 nonconforming parts per 120 minutes
The standard deviation = [tex]\lambda^{1/2}[/tex]
The standard deviation = [tex](16)^{1/2}[/tex]
The standard deviation = 4
(d) What is the probability that at least 20 nonconforming parts produced during a 2.5-hour period? That at most 10 nonconforming parts produced during this period?
During a 2.5 - hour period , the expected value = 8 × 2.5 = 20
As such, the probability that at least 20 nonconforming parts produced during a 2.5-hour period is:
P(X ≥ 20) = 1 - P(X ≤ 19)
[tex]P( X \geq 20 ) = 1 - \sum \limits ^{19}_{x=0} e^{-\lambda} \lambda ^x/x![/tex]
[tex]P( X \geq 20 ) = 1 - (e^{-8} 8 ^{19}/19! + e^{-8} 8 ^{18}/{18}! + e^{-8} 8 ^{17}/17!+...+e^{-8} 8 ^2/2! +e^{-8} 8 ^1/1! + e^{-8} 8 ^0/0! )[/tex]
P(X ≥ 20) = 1 - 0.4703
P(X ≥ 20) = 0.5297
Probability that at most 10 nonconforming parts produced during this period is:
P( X ≤ 10) = [tex]\sum \limits ^{10}_{x=0} e^{-\lambda} \lambda ^x/x![/tex]
[tex]P( X \leq 10) = e^{8} 8 ^{10}/{10}! + e^{8} 8 ^{9}/{9}! + e^{8} 8 ^{8}/{8}! + ...+ e^{8} 8 ^{2}/{2}!+ e^{8} 8 ^{1}/{1}! + e^{8} 8 ^{0}/{0}![/tex]
P( X ≤ 10) = 0.0108
Following are the calculation to the given points:
For point a)
With parameter, x follows the poisson distribution is [tex]\lambda=\frac{8}{hour}[/tex]
For point b)
The probability that exactly 5 nonconforming parts are generated in a one-hour period.
[tex]\to P(X=5)=e^{-\lambda }\frac{\lambda ^{x}}{x!} =0.0916[/tex]
There is a good chance that at least 5 nonconforming parts exist.
[tex]\to P(X\geq 5) =1-P(X\leq 4)[/tex]
[tex]=1 -\sum_{x=0}^{4} \ e^{-\lambda } \frac{\lambda ^{x}}{x!} \\\\=1-0.0996\\\\=0.9004[/tex]
For point c)
Expected value for 120-minute period [tex]\lambda=8\times \frac{120}{60} =16[/tex] 120 minutes of nonconforming sections
[tex]\to \sigma ==(\lambda)^{\frac{1}{2} =(16)^{\frac{1}{2}} =4[/tex]
For point d)
Expected value for 2.5 hours
[tex]\to \lambda =8\times 2.5=20[/tex]
As a result, there is a good chance that at least 20 nonconforming items were manufactured.
[tex]\to P(X\geq 20)=1-P(X\leq 19)[/tex]
[tex]=1-\sum_{x=0}^{19}\ e^{-\lambda }\frac{\lambda^{x}}{x!}\\\\=1-0.4703\\\\=0.5297[/tex]
There is a chance that no more than 10 nonconforming parts were created.
[tex]\to P(X\leq 10)=\sum_{x=0}^{10}e^{-\lambda }\frac{\lambda ^{x}}{x!} =0.0108[/tex]
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At the market, Joey buys 3 avocados for $0.40 each and 5 lemons for $0.40 each. The cashier in training rings up 3 × 0.40 and then 5 × 0.40 to get the total. The experienced cashier says to add the 3 plus 5 in his head and then ring up 8 × 0.40.
What property says that these two totals would be the same?
multiplicative identity
associative property of multiplication
distributive property
commutative property of multiplication
Answer:
Distributive property
Step-by-step explanation:
3*$0.40 + 5*$0.40 = (3+5)*$0.40
Distributive law, in mathematics, the law relating the operations of multiplication and addition, stated symbolically, a(b + c) = ab + acAccording to distributive property multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.answer is distributive property
Step-by-step explanation:
hope this answer helps :)
How does -2x + x equal -x ?
Answer:
See below.
Step-by-step explanation:
[tex]-2x+x=-x[/tex]
because we combine like terms. You will essentially ignore the x and just do -2 + 1, which is -1. So, the answer would be -1x which is simply just -x.
To see why we can combine like terms, use the distributive property. So we have:
[tex]-2x+x[/tex]
This is the same thing as saying:
[tex]=(-2)x+(1)x[/tex]
Factor out the x:
[tex]=x(-2+1)[/tex]
Add:
[tex]=x(-1)[/tex]
And simplify:
[tex]=-1x\\=-x[/tex]
Answer:
Step-by-step explanation:
-2x + x could also be written as x - 2x, which is x(1 - 2), or -x. Here we can rearrange the terms as we wish (commutative property).
Find AB if AC = 6x-2 AB= 2x+12 BC =3x
Answer:
AB = 40 units
Step-by-step explanation:
Given:
AC = 6 x - 2
AB = 2 x + 12
BC = 3 x
Find:
AB
Computation:
Assume, AC is a straight line
So,
AC = AB + BC
6 x - 2 = 2 x + 12 + 3 x
6 x - 5 x = 14
x = 14
AB = 2 x + 12
AB = 2 (14) + 12
AB = 40 units
Thomas’s gross salary in 2017 was $68,000. If he qualifies for an $8,350 exemption when filing his taxes, how much does he owe for the year in federal income taxes? (Section 4.6 and 4.7) (1 point)
Answer: $14,912.5
Step-by-step explanation:
given data:
thomas salary in 2017 = $68,000
exemption = $8,350
solution:
thomas taxable income
= salary in 2017 - tax exemptions
= $68,000 - $8350
= $59,560
federal income tax = 25%
= 0.25 * $59,560
= $14,912.5
thomas Owe’s $14,912.5 in federal Income tax at the end of the year.
A Women making $29 an hour gets a 15% raise. How much money will she make after 4 hours of working with the increased hourly pay?
Answer:
$133.40
Step-by-step explanation:
First you have to find 15% of 29 which is 4.35. The way I figured this out was 10% of 29 is 2.9 and 5% of 29 is 1.45 and 2.9 + 1.45 = 4.35.
Then you want to add 4.35 to 29 which equals 33.35, her new hourly pay. Multiply 33.35 by the 4 hours she is working and you end up with $133.40.
Water flows through a pipe at a rate of 7 liters every 9.5 hours. Express this rate of flow in pints per week. Round your answer to the nearest whole number
Answer:
Water flow per week = 124 liters
Step-by-step explanation:
Given:
Water flow in 9.5 hours = 7 liters
Find:
Water flow per week
Computation:
Water flow per hour = 7 / 9.5
Hours in a week = 7 × 24 = 168 hours
Water flow per week = Hours in a week × Water flow per hour
Water flow per week = 168 × [7 / 9.5]
Water flow per week = 123.7894
Water flow per week = 124 liters
A construction uses a protactor and a ruler true or false
Answer:
True
Step-by-step explanation:
I just did a whole essay about thin in Geometry and I got an A.
Hope this helps! （づ￣3￣）づ╭❤～
Find the indicated angle measures. ok last one i promise y’all pls help-
Answer:
bfc = 64, afb = 126
Step-by-step explanation:
I solved in the picture
Hope this helps ^-^
Find the value of ab when a=5/12 and b=1/3
Step-by-step explanation:
When two letters are right next to each other, you multiply them. Since a and b are next to each other, we multiply them together.
[tex]A=\frac{5}{12}[/tex]
[tex]B=\frac{1}{3}[/tex]
To multiply fractions, you place them next to each other and multiply across.
[tex]\frac{5}{12}*\frac{1}{3} \\5*1=5\\12*3=36[/tex]
Our final answer: [tex]\frac{5}{36}[/tex] (we cannot simplify it any further)
8-|21 - 13 - 9| -| -4|
Answer:
8-1-4=8-1-4=3
Step-by-step explanation:
Order of operations: solve inside the absolute value first. 21-13-9=8-9=-1. The absolute value of -1 is 1.
subtract 6 from me then multiply by 2 if you subtract 40 and then divide by 4 you get 8 what number am I
Answer:
42
Step-by-step
do it backward starting from 8
Answer:
42
Step-by-step explanation:
For 5 days Lydia studied math for a certain amount of time and read for 15 minutes each day Represent the total amount of time Lydia studied and read over the 5-day period.
Since Lydia studied for 5 days
Then it will be 5*15=75 minutes in 5 days
There are three consecutive integers such that twice the sum of the smallest and the largest is eight more than twice the largest. Find the smallest integer in the sequence.
Answer: 4
Step-by-step explanation:
Let the consecutive integers be x, x+1 and x+2.
There are three consecutive integers such that twice the sum of the smallest and the largest is eight more than twice the largest. This means that:
2(x + x+2) = 2(x+2) + 8
2(2x + 2) = 2x + 4 + 8
4x + 4 = 2x + 12
Collect like terms
4x - 2x = 12 - 4
2x = 8
x = 8/2
x = 4
The smallest integer in the sequence is 4
Its chapter LCM .
After traveling every 84 km, a motorbike needs to fill petrol and after 120 km it needs to change Mobil. If these works are done together, after traveling what distance will both the works repeat again?
Answer:
Both works will be repeated at 840km
Step-by-step explanation:
Given
Fills Petrol = Every 84km
Change Mobil = Every 120km
Required
Determine the distance where both works are done at the same time
This solution to this question is to solve for the LCM of 84 and 120
Start by factoring 84
[tex]84 = 2 * 2 * 3 * 7[/tex]
Then, 120
[tex]120 = 2 * 2 * 2 * 3 * 5[/tex]
Then the LCM is as follows;
[tex]LCM = 2 * 2 * 2 * 3 * 5 * 7[/tex]
[tex]LCM = 840[/tex]
Hence, both works will be repeated at 840km
A school newspaper decides to survey all the students enrolled in a gym class to determine the percentage of these students who are
also on the football team. What is the population of this study?
A. students who take gym class
B. students who take gym class and are on the football team
C. all students in the school
D. students who are on the football team
Answer:
A sudents who take gym class
Step-by-step explanation:
the survey only asks for all the students enrolled in a gym class so they can compare with the data for all the students enrolled in the football team
Answer:
a
Step-by-step explanation:
0.000000000009256 scientific method
Answer:
9.256×10^−12
Step-by-step explanation:
to get standard notation we have a number less ten.
since it is a very small number it has a negative exponent
As a quality control manager for her distributing company, Zoe has 875.23 pounds of apples where she found 143.875 pounds of apples were rotten. How many pounds of fresh apples does she have? show your work.
Answer:
731.355
Step-by-step explanation:
875.230 - 143.875 = 731.355
apples rotten fresh
The pizza has an area of 78.5 in². What is the minimum width of a placemat that can be placed underneath it so that the pizza does not touch the table? Use 3.14 for pi. someone pls help me
Answer:
The minimum width of the placemat is 10 inches.
Step-by-step explanation:
Let suppose that placemat has a square form, whose width must be at least equal to the diameter of the pizza, so that pizza does not touch the table. Hence, the following relationship is obtained:
[tex]w = D[/tex]
Where:
[tex]w[/tex] - Width of the placemat, measured in inches.
[tex]D[/tex] - Diameter of pizza, measured in inches.
The area of the pizza, measured in square inches, is determined by this formula:
[tex]A = \frac{\pi}{4} \cdot D^{2}[/tex]
The diameter is cleared afterwards:
[tex]D = \sqrt{\frac{4\cdot A}{\pi} }[/tex]
If [tex]A = 78.5\,in^{2}[/tex] and [tex]\pi = 3.14[/tex], then:
[tex]D = \sqrt{\frac{4\cdot (78.5\,in^{2})}{3.14} }[/tex]
[tex]D = 10\,in[/tex]
The minimum width of the placemat is 10 inches.
The minimum width of a placemat that can be placed underneath the pizza so that the pizza wouldn't touch the table is; 10 inches
We are told that the pizza has an area of 78.5 in². Thus;
A = 78.5 in²
Now, the pizza is circular in shape and the minimum width of a placemat that can be placed underneath the pizza so that the pizza wouldn't touch the table will be the diameter of the pizza
Thus, area of a circle with diameter d is;
A = πd²/4
Plugging in the relevant values, we have;
78.5 = 3.14d²/4
d² = 78.5 × 4/3.14
d² = 100
d = √100
d = 10 inches.
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A survey reported that 40% of people save loose change to pay bills. The margin of error was given as 3.1 percentage points. Which confidence interval corresponds to the given information
Answer:
0.369≤[tex]\mu[/tex]≤0.431Step-by-step explanation:
The confidence interval boundaries is represented mathematically as shown below;
CI = p±E where;
p is the percentage of people surveyed
E is the margin of error
Given parameters
p = 40% = 0.4
E = 3.1% = 0.031
Required
Confidence interval corresponds to the given information.
Substituting the given parameters into the given formula:
CI = p±E
CI = 0.4±0.031
CI = (0.4-0.031, 0.4+0.031)
CI = (0.369, 0.431)
Hence the confidence interval that corresponds with the information is 0.369≤[tex]\mu[/tex]≤0.431.
Qual o resultado da subtração dos dois polinômios abaixo? (2x2 + 4x) (–2x2 + x – 6)
Answer:
-4x^4-6x^3-8x^2-24x
Step-by-step explanation:
[tex]\left(2x^2+4x\right)\left(-2x^2+x-6\right)\\[/tex]
distribuir parênteses
[tex]=2x^2\left(-2x^2\right)+2x^2x+2x^2\left(-6\right)+4x\left(-2x^2\right)+4xx+4x\left(-6\right)[/tex]
Aplicar regras de menos mais ;[tex]+\left(-a\right)=-a[/tex]
[tex]=-2\times\:2x^2x^2+2x^2x-2\times\:6x^2-4\times\:2x^2x+4xx-4\times\:6x[/tex]
simplificar
[tex]-2\times\:2x^2x^2+2x^2x-2\times\:6x^2-4\times\:2x^2x+4xx-4\times\:6x:\\\quad -4x^4-6x^3-8x^2-24x[/tex]
A coach for a little league baseball team is ordering trophies for the team. Players on the team are allowed to choose between 2 types of trophies. The gold baseball trophies cost $5.99 each and the uniform baseball trophies cost $6.49 each. The team orders g gold baseball trophies and u uniform baseball trophies. Write an expression that could represent the total cost of all of the trophies.
Answer:
y= 5.99(g) + 6.49(u)
Step-by-step explanation:
1) First you determine the variable in the equation $5.99, $6.49, g, and u.
2) Then analyze the equation and identify that each gold baseball trophy (g) is worth $5.99, and each uniform baseball trophy (u) is worth $6.49 each.
3) Since you are finding the total you insert a plus sign.
The expression that could represent the total cost of all of the trophies will be C = 5.99g + 6.49u
Cost of gold baseball trophies = $5.99
Cost of uniform baseball trophies = $6.49
Number of gold baseball trophies ordered = g
Number of uniform baseball trophies ordered = u
Therefore, the total cost will be:
= (5.99 × g) + (6.49 × u)
C = 5.99g + 6.49u
Therefore, the expression that could represent the total cost of all of the trophies is C = 5.99g + 6.49u
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How many solutions are there to the equation below?
12x + 32 = 12x - 7
O A. O
B. 1
O C. Infinitely many
Answer:
A
Step-by-step explanation:
12x + 32 = 12x - 7
12x - 12x + 32 = 12x - 12x - 7
32 = -7
This is a false statement so the answer is A) 0.
Additionally, you can see that we have the quantity 12x on both sides but on one side, it's being added by 32 and on the other, it's being subtracted by 7. How can a quantity added by 32 be equal to the same quantity subtracted by 7? It is impossible for a real number to do so, therefore, the answer is 0.
Answer:
Hey there!
Original Equation: 12x+32=12x-7
Subtract 12x: 32=-7
32 does not equal -7, so there is no solution.
Hope this helps :)
Write an expression to determine (represent) the ratio of the circle's circumference to its radius.
Answer:
C/r
Step-by-step explanation:
The ratio of the circle's circumference to its radius is 2π
Please find attached a diagram of a circle and its radius
A circle is a two dimensional figure bounded by one curved line. All the straight lines that are drawn from a certain point within it to the bounding line, are equal.
The radius of a circle is the distance from the center of a circle to its circumference.
The radius of a circle is represented by r
The circumference of a circle is the perimeter of a circle. It is the distance round a circle.
The formula for the circumference of a circle is 2πr
π = pi = 22/7
r = radius
A ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
The ratio of a circle's circumference to its radius is
2πr : r
Divide both sides of the equation by r
= 2π : 1
= 2π
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If A and B are independent events with P( A) = 0.60 and P( A| B) = 0.60, then P( B) is: a. 0.60 b. cannot be determined with the information given c. 0.36 d. 1.2
Answer:
B. cannot be determinedStep-by-step explanation:
For two events A and B to be independent, it means they can occur at the same time i.e the occurrence of one does not affect the other occurring. It is represented as P(A∩B) = P(A)P(B)
Given P( A) = 0.60 and P( A| B) = 0.60, to find P(B), we will use the formula for the conditional probability P( A| B) = P(A∩B) /P(B)
P( A| B) = P(A)P(B) /P(B)
P( A| B) = P(A)
Since P( A| B) = 0.60, therefore P(A) is also equal to 0.60 and P(B) cannot be determined since they cancelled out already
Clarissa has taken 4 tests (100 points each) and has an average of 82.5 What score does she have to get on the next test in order to bring her average up to 85?
Answer:
Clarissa needs a 95
Step-by-step explanation:
4 x 82.5 = 330
Keep trying numbers to see if they work
330 + 95 = 425
425 / 5 = 85
witch of the following is equivalent to -8-9(55+2x)
Answer:
-8-495-18x
Step-by-step explanation:
-8-9(55)-9(2x)
-8-495-18x
Starting with x = 0.773, express x as a fraction in simplest form.
Answer:
773/1000
Step-by-step explanation:
[tex]x = 0.773 \\ \\ x = \frac{773}{1000} \\ [/tex]
Use the commutative law of multiplication to write an expression equivalent to: (5x)y.
Answer:
(5y)x
Step-by-step explanation:
the commutative law of multiplication=ab=ba, a(bc)=c(ab)
(5x)y=(5y)x=5(xy)
write each ratio statement as a fraction and reduce to lowest terms if possible.(i)18 to 24 (ii)5 to 15 (iii)14:42 (iv) 15 cents to 18 cents.
Answer:
i) 3/4
ii) 1/3
iii) 1/3
iv) 5/6 cents
Step-by-step explanation:
Any ratio can be written as a fraction.
For example 3:4 can be writen as 3/4 or 14:42 as 14/42.
After you convert them to fractions you then simplify them by finding their highest common factor (HCF) and then divide both numerator and denominator by the HCF. When you cant simplify the fraction anymore, that is the fraction in its lowest terms.
Select the correct answer.
What are the domain and range of this function?
(x + 3)² - 5
A Domain: (0o,00)
Range (-00,00)
Domain: (-5,00)
Range: (-5,00)
C. Domain: (-0,00)
Range: (-5,00)
D. Domain: (-5,00)
Range: (-00,00)
Reset
Next
Answer:
Domain: [tex](-\infty,\infty)[/tex]
Range: [tex][-5,\infty)[/tex]
C
Step-by-step explanation:
Please refer to the graph.
Recall that the domain is the span of x-values covered by the graph, while the range is the span of y-values covered by the graph.
So we have the equation.
[tex]y=(x+3)^2-5[/tex]
This is a quadratic.
The domain of a quadratic is all real numbers. If you look at the graph, we can also see that the x-values will go on infinitely in both direction.
In interval notation, this is:
[tex](-\infty,\infty)[/tex]
For the range, note that the lowest the parabola goes is y=-5.
Therefore, our range is all values greater than or equal to -5.
In interval notation, this is:
[tex][-5,\infty)[/tex]
Note that we use brackets for the -5 because it is included in our range.
So, our answer is C
Answer:
Step-by-step explanation:
the domain and range of y = (x+3)^2 - 5
Doman: (-∞,∞). {x|x∈R}
Range:{-5,∞),{y|y≥-5}
the solution is C