(a) The probability function for the random variable X is P(X = x) = [tex]^{3}C_{x}(0.15)^x(0.85)^{3-x}[/tex] at X=0,1,2 and 3 otherwise it is 0.
(b) The mean number of components out of 3 that fail, E[X] is 0.45.
(c) The var(X) is 0.3825.
(d) The probability that the entire system is successful, is 0.9966.
(e) The probability that the system fails is 0.0034.
(a) In the given question we have to write out a probability function for the random variable X.
Let X denote number of component out of 3 that fail. SO the random variable X can take 0, 1, 2 and 3.
Here the components act independently and that they equivalent in the sense that all 3 of them have an 85% success rate.
So the failure rate, 1-0.85 = 0.15
Thus X follows binomial distribution with parameters n=3 and p=0.15.
The probability function for the random variable X is
P(X = x) = [tex]^{3}C_{x}(0.15)^x(0.85)^{3-x}[/tex] at X=0,1,2 and 3 otherwise it is 0.
(b) Now we have to find E[X], the mean number of components out of 3 that fail.
E[X] = np
E[X] = 3*0.15
E[X] = 0.45
(c) Now we have to find the var(X).
var(X) = np(1-p)
var(X) = 3*0.15p(1-0.15)
var(X) = 0.3825
(d) Now we have to find the probability that the entire system is successful.
P(at least one component will work) = 1-P(All the component fail)
P(at least one component will work) = 1-P(X = 3)
P(at least one component will work) = 1-[tex]^3C_{3}(0.15)^3(0.85)^{3-3}[/tex]
P(at least one component will work) = 1-0.0034
P(at least one component will work) = 0.9966
(e) Now we have to find the probability that the system fails.
P(All the component fail) = P(X = 3)
P(All the component fail) = [tex]^3C_{3}(0.15)^3(0.85)^{3-3}[/tex]
P(All the component fail) = 0.0034
To learn more about probability link is here
brainly.com/question/14210034
#SPJ4
Let a, b, and c be real numbers where a ≠ b ≠ c ≠ 0. Which of the following functions could represent the graph below?
f(x) = x²(x-a)²(x-b)4(x-c)
f(x) = x³(x-a)³(x-b)(x-c)²
f(x) = x²(x-a)(x-b)³(x-c)³
f(x) = (x-a)^2(x-b)(x-c)^6
The characteristics of polynomial graphs' intercepts reveal the multiplicity's characteristics. The function is a potential representation of the graph; f(x) = x²·(x - a) (x - a) , ²·(x - b) (x - b),⁴·(x - c) (x - c).
How to find the calculation?The alternative provides a function that can represent a graph;
f(x) = x²·(x - a) (x - a)
²·(x - b) (x - b)
⁴·(x - c) (x - c)
Reason:
The graph's description is as follows:
Three points on the graph deviate from the x-axis.
Therefore;
The first equation is satisfied by the graph's even multiplicity at three places, such as x2, (x - a)2, and (x - b)4.
The graph once almost linearly crosses the x-axis.
Therefore;
The first equation's function contains a single zero or component, such as (x - c), so;
The function is a potential representation of the graph;
f(x) = x²·(x - a) (x - a)
²·(x - b) (x - b)
⁴·(x - c) (x - c).
To Learn more About polynomial graphs' intercepts refer to:
https://brainly.com/question/28576088
#SPJ1
Caleb's school is five blocks due north of his home, and is the closest to the straight-line distance from Caleb's s
A) 389 f t
B) 825 f t
C) 1,260 ft
(D) 1,481 ft
If Caleb's school is five blocks due north of his home, the figure that is closest to the straight-line distance from Caleb's s is (D) 1,481 ft.
What is distance?Distance can be defined as how far an object is from another object.
Using Pythagoreans theorem
Hypotenuse =√Perpendicular² + Base²
Where:
Perpendicular = 275 feet ×5 = 1375ft
Base = 275 feet × 2 = 550ft
Let plug in the formula
Hypotenuse =√ 1375 ft² + 550ft
Hypotenuse =√1,890,625 + 302,500
Hypotenuse =√2,193,128
Hypotenuse = 1,480.9ft
Hypotenuse = 1,481ft (Approximately)
Therefore the correct option is D.
Learn more about distance here:https://brainly.com/question/26550516
#SPJ1
A customer spends a total of $52.25 at an amusement park. The customer buys a $30.25 ticket to enter the park and 4 game tickets.
If each game ticket costs the same amount, x, which statement is true?
Responses
An equation that can be used to find x is 4(x+30.25)=52.25, and each game ticket costs $5.50.
An equation that can be used to find x is 4 ( x + 30.25 ) = 52.25 , and each game ticket costs $ $ 5.50 .
An equation that can be used to find x is 4(x+30.25)=52.25, and each game ticket costs $18.00.
An equation that can be used to find x is 4 ( x + 30.25 ) = 52.25 , and each game ticket costs $ $ 18.00 .
An equation that can be used to find x is 4x+30.25=52.25, and each game ticket costs $5.50.
An equation that can be used to find x is 4 x + 30.25 = 52.25 , and each game ticket costs $ $ 5.50 .
An equation that can be used to find x is 4x+30.25=52.25, and each game ticket costs $18.00.
Answer: I believe its: An equation that can be used to find x is 4x+30.25=52.25, and each game ticket costs $5.50.
Step-by-step explanation:
well, 52.25 - 30.25 is 22$
22 divided by 4 is 5.50
4 times x plus 30.25 is 52.25
so 4x+30.25= 52.25
5400 dollars is placed in an account with an annual interest rate of 9%. To the
nearest tenth of a year, how long will it take for the account value to reach 15500
dollars?
Answer:
12.2 years
Step-by-step explanation:
To solve, use the exponential growth formula:
[tex]A_t=A_0(1+r)^x[/tex]
where
[tex]A_t[/tex] = Amount as a function of time ($15500)
[tex]A_0[/tex] = Original amount ($5400)
[tex]r[/tex] = rate (.09)
[tex]x[/tex] = time in years
So,
[tex]15500=5400(1+.09)^x\\15500(\frac{1}{5400})=5400(1.09)^x(\frac{1}{5400})\\2.87=1.09^x\\\log_{1.09}2.87=\log_{1.09}1.09^x[/tex]
Use the logarithmic rules that state [tex]\log_{a}a=1[/tex] and [tex]\log_{a}a^b=b\log_{a}a[/tex]:
So,
[tex]\log_{1.09}2.87=x\\12.24\ years=x[/tex]
Frank bought two pork roasts. One roast weighed five and seven-eighths pounds and the other roast weighed nine and five-sixths pounds. What is the total weight of the pork roasts?
Answer:
15[tex]\frac{17}{24}[/tex]
Step-by-step explanation:
5 [tex]\frac{7}{8}[/tex] + 9 [tex]\frac{5}{6}[/tex] We can write the fractions as equivalent fractions with a common denominator of 24
[tex]\frac{7}{8}[/tex] x[tex]\frac{3}{3}[/tex] = [tex]\frac{21}{24}[/tex]
[tex]\frac{5}{6}[/tex] x [tex]\frac{4}{4}[/tex] = [tex]\frac{20}{24}[/tex]
5[tex]\frac{21}{24}[/tex] + 9[tex]\frac{20}{24}[/tex]
5 + 9 + [tex]\frac{21}{24}[/tex] + [tex]\frac{20}{24}[/tex]
14 + [tex]\frac{41}{24}[/tex]
14 + [tex]\frac{24}{24}[/tex] + [tex]\frac{17}{24}[/tex] I broke up [tex]\frac{41}{24}[/tex] because [tex]\frac{24}{24}[/tex] is another name for 1
14+1 + [tex]\frac{17}{24}[/tex]
15[tex]\frac{17}{24}[/tex]
find the unit tangent vector,the principal normal vector,andequation in x,y,z for the osculating plane at the point on thecurve corresponding to the indicated value of t.r(t)=i + 2tj +t^2k; t=1
The equation of oscilating plane at the point on the curve corresponding to the indicated value of t, r(t)=i + 2tj +t^2k; t=1 is
x - 1 = 0.
Unit tangent vector, T(t) at t = 1 is
T(t) = (√2/2 ) j +(√2/2 ) k
Principle Normal vector at t = 1 is N(1) = - (√2/2 ) j + (√2/2 ) k
We have , x,y,z for the osculating plane at the point on the curve corresponding to the indicated value of t.
r(t) = i + 2t j + t² k
So, r'(t) = 0 i + 2 j + 2t k
Unit tangent vector , say T(t) is
T(t) = (0 i + 2 j + 2t k )/√0+(2)²+ (2t)²
T(t) =( 2 j + 2t k)/√4+ 4t² = 2(j+k)/2√1+t²
T(t) = (j + t k) / √1+t²
At t = 1 , T(t) = (j + k )/√1+1 = (j+k)/√2
T(t) = (√2/2 ) j + (√2/2 ) k
Now, tangent vector and normal vector prependicular to each other.
So, principle vector is N(1) = - (√2/2 ) j + (√2/2 ) k
Now, binormal vector is B = T×N
= | i j k |
| 0 √2/2 √2/2 |
| 0 -√2/2 √2/2 |
= <1,0,0>
Equation of oscilating plane is
1( x- 1) + 0(y - 2) + 0( z - 1) = 0
=> x = 1
Hence, equation of oscilating plane is x-1 = 0
To learn more about Unit tangent vector , refer:
https://brainly.com/question/15303761
#SPJ4
Evaluate the function
f(n) = 4x + 5; Find f(2)
Answer: 13
Step-by-step explanation: To find f(2), you can put 2 into all of the x spots, thus making the equation 4(2)+5. From there you can do PEMDAS and multiply 4 and 2 to get 8, and then add 5 to get 13.
The implicational rule of inference that permits us to derive a specific instance from a universal statement isa. Existential Generalization.b. Existential Instantiation.c. Universal Generalization.d. Universal Instantiation.
Option D is the correct answer, Universal Instantiation is The implicational rule of inference that permits us to derive a specific instance from a universal statement.
It is the process of deriving an individual statement from a general one by replacing the variable with a name or another referring expression called Instantiation.
Universal Instantiation is also called universal specification or universal elimination, it is a valid rule of inference from the truth about each member of a class of individuals to the truth about a particular individual of that class.
Example: "No humans can fly. John Doe is human. Therefore John Doe can not fly."
∀xA⇒A(x↔a}
for every formula A and every term a, where A(x↔a} is the result of substituting a for each free occurrence of x in A. A(x↔a} is an instance of
∀xA.
To know more about Universal Instantiation:
https://brainly.com/question/14992064
#SPJ4
sort these items into the order that you would use them in order to calculate the confidence interval for the mean.
The order of calculate the confidence interval for the mean are as follows:
1. Select sample stat
2. select desired confidence
3. determine margin of error
4. specify upper and lower limits
Now, According to the question:
The order of calculate the confidence interval for the mean are as follows:
1. Select sample stat
2. select desired confidence
3. determine margin of error
4. specify upper and lower limits
Let's know:
What is Confidence Interval?
A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.
The common notation for the parameter in question is θ. Often, this parameter is the population mean μ , which is estimated through the sample mean bar x.
The level C of a confidence interval gives the probability that the interval produced by the method employed includes the true value of the parameter θ.
Learn more about Confidence Interval at:
https://brainly.com/question/16256721
#SPJ4
Which graph represents the solution set of the system of inequalities?
y < -3x-2
y ≤ x-2
The graph that represents the solution to the system of inequalities is graph (a).
What is system of inequality?
A group of two or more inequalities in one or more variables is referred to as a system of inequalities. When a problem requires a variety of solutions and those solutions must satisfy multiple constraints, systems of inequalities are used.
The given system of inequalities is,
y < -3x - 2
y ≤ x - 2
y < -3x - 2 means that the left-hand side of the inequality will be shaded, and the line of the inequality will be a dotted line.
y ≤ x - 2 means that the left-hand side of the inequality will be shaded, and the line of the inequality will be a closed line.
The above highlights means that the shaded region that represent the solution to the system of inequalities will be at the left-hand side
Hence, graph (a) represents the system of inequalities.
To know more about system of inequalities, click on the link
https://brainly.com/question/28230245
#SPJ1
Help please my final grade depends on it
Answer:
$5.98 credit
Step-by-step explanation:
the slope OR "m" in y=mx in this equation is given to be: -0.16
To find the answer you know that the calling time (x) is 37 minutes, therefore you multiply 3 by -0.16 to find the credit after 37 mins
y=mx
y=(0.16)(37)
y=5.92
u (x comma y )space equals space 5 (x plus y )u (x comma y )space equals space 5 y u (x comma y )space equals space 5 x u (x comma y )space equals space 5 x squared plus 5 y squared
To solve this system of differential equations using the series method, we can assume that the solution can be expressed as a power series in both x and y:
[tex]u(x,y) = a0 + a1x + a2y + a3xy + a4x^2 + a5y^2 + ...[/tex]
Substituting this expression into each of the differential equations and collecting the coefficients of each term gives us the following system of equations:
a0 + 5a0 = 0
a1 + 5a2 = 0
a2 + 5a1 = 0
a4 + 5a4 = 0
a5 + 5*a5 = 0
Solving this system of equations gives us the following values for the coefficients:
a0 = 0
a1 = 0
a2 = 0
a3 = 0
a4 = 0
a5 = 0
Therefore, the power series expansion of the solution is:
u(x,y) = 0
This means that the only solution to the differential equations is the trivial solution u(x,y) = 0.
Note that this method of solving differential equations using power series is only applicable if the differential equations are linear and homogeneous, which means that the coefficients of the terms in the differential equations do not depend on x and y, and the right-hand sides of the equations are all equal to 0. If the differential equations are nonlinear or inhomogeneous, other methods may be required to find their solutions.
To learn more about differential equations, visit:
brainly.com/question/14620493
#SPJ4
Given f(x) = 4x2 – 4x + 1 and g(x) = 2x – 1, which of the following are expression(s) for f · g? Select all that apply.
A. 6x3 + 6x2 – 6x + 1
B. (2x – 1)3
C. 8x3 – 12x2 + 6x – 1
D. 4x2 – 2x
The value for the expression, (f * g)(x) is calculated as: C. 8x³ - 12x² - 6x - 1.
How to Evaluate the Expressions of Functions?We are given the following functions,
f(x) = 4x² – 4x + 1 and g(x) = 2x – 1.
To find the value of the expression, (f * g)(x), it means we have to multiply the functions together. See the steps explained below.
(f * g)(x) = f(x) * g(x)
Plug in the values:
(f * g)(x) = f(x) * g(x) = (4x² – 4x + 1)(2x – 1)
(f * g)(x) = 4x²(2x – 1) - 4x(2x – 1) + 1(2x – 1)
Apply the distribution property of equality:
(f * g)(x) = 8x³ – 4x² - 8x² + 4x + 2x – 1
Combine like terms:
(f * g)(x) = 8x³ - 12x² - 6x - 1
Therefore, the answer is: C. 8x³ - 12x² - 6x - 1.
Learn more about evaluating functions on:
https://brainly.com/question/2284360
#SPJ1
Properties of Definite Integrals A definite integral is a function that assigns a value to the area under a curve on a given interval.
Properties of Definite Integrals A definite integral is a function that assigns a value to the area under a curve on a given interval are additive , linearity , continuity , monotonicity and upper and lowersums.
1. Additivity: The definite integral of a sum is equal to the sum of the definite integrals.
2. Linearity: The definite integral of a linear function is equal to the product of the function's slope and the length of the interval.
3. Continuity: The definite integral of a continuous function is equal to the area under the curve between two points.
4. Monotonicity: If a function is increasing or decreasing on a given interval, then the definite integral of the function is also increasing or decreasing.
5. Upper and Lower Sums: The upper and lower sums of a function are the sums of the areas of rectangles constructed under or over the curve between two points. The definite integral of the function is equal to the difference between the upper and lower sums.
Learn more about integral here
https://brainly.com/question/18125359
#SPJ4
Biologist Theodore Garland, Jr. studied the relationship between running speeds and morphology of 49 species of cursorial mammals (mammals adapted to or specialized for running). One of the relationships he investigated was maximal sprint speed in kilometers per hour and the ratio of metatarsal-to-femur length.
A least-squares regression on the data he collected produces the equation
ŷ =37.67+33.18x
where x is metatarsal-to-femur ratio and ŷ is predicted maximal sprint speed in kilometers per hour. The standard error of the intercept is 5.69 and the standard error of the slope is 7.94.
Construct a 80% confidence interval for the slope of the population regression line. Give your answers precise to at least two decimal places.
Lower limit: ____ Upper limit: ____
A 80% confidence interval for the slope of the population regression line is answers precise to at least two decimal places is Lower limit : 16.4083 and Upper limit : 49.9587 .
Given :
A least-squares regression on the data he collected produces the equation
y =37.67 + 33.18x
where x is metatarsal - to - femur ratio and ŷ is predicted maximal sprint speed in kilometers per hour. The standard error of the intercept is 5.69 and the standard error of the slope is 7.94.
The sample number is 49 species (here we assume that all the individuals of a the same species are summarised with a central tendency measure.
33.18 - 2.1123 ( 7.94 ) ≤ β ≤ 33.18 + 2.1123 ( 7.94 )
16.4083 ≤ β ≤ 49.9587 .
Learn more about the confidence here:
https://brainly.com/question/29048041
#SPJ4
1. Which equation describes the line with
slope -4 and y-intercept 2?
A y=-4x+2
B y=-4x-2
C y=4x-2
D y = 4x + 2
Answer:
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Therefore, the equation of the line with slope -4 and y-intercept 2 is y = (-4)x + 2.
simplify the expression: 6(1+9t)
Answer:
Hi!
The answer would be: 6 + 54t
I hope this helped you! :)
Step-by-step explanation:
Answer:
54t + 6
Step-by-step explanation:
Simplify the expression. Use the distributive property. The distributive property states that an expression which is given in form of a(b + c) can be solved into (ab) + (ac). Distribute and multiply 6 to all terms within the parenthesis. Then, simplify:
[tex]6(1 + 9t)\\\\=(6 * 1) + (6 * 9t)\\= (6) + (54t)\\ = 54t + 6[/tex]
54t + 6 is your answer.
~
Learn more about distributive property, here:
https://brainly.com/question/6276874
On a 3 section math test a student correctly answered 17/20 11/15 20/25 what percentage of questions on the entire test did the student answer correctly
Step-by-step explanation:
17 of 20
11 of 15
20 of 25
that is in total
17+11+20 = 48
of
20+15+25 = 60
so, he answered 48 of 60 correctly
48/60 = 4/5 = 0.8 = 80%
Answer:
79.44%
Step-by-step explanation:
We are given that there are 3 sections to this test and how the student scored in each of those sections. Let us add all of these fractions together.
[tex]\frac{17}{20} +\frac{11}{15} +\frac{20}{25} =\frac{143}{60} \\[/tex]
We must now divide this amount by 3 to find the average of the three sections. This gives us [tex]\frac{143}{180}[/tex].
These means that the student answered [tex]\frac{143}{180}[/tex] of the questions correctly, or 79.44%.
Lisa read 2/5 of her book over the weekend and 1/3 of it on monday. What fraction of the book is left?
Answer:
4/15
Step-by-step explanation:
To answer this question, we're gonna want to convert the fractions so that they have the same denominator (the number on the bottom of the fraction) and it's easy for us to visualize what's going on. AKA, we need to find the least common denominator (LCD).
We're going to multiply 2/5 and 1/3 by a number so they have the same denominator. In this case, that would mean multiplying them by the other fractions denominator. So multiplying 2/5 by 3 and 1/3 by 5.
2/5x3= 6/15. 1/3x5=5/15.
Now we're viewing the book in 15ths instead of both 5ths and 3rds.
6+5=11, so we know that 11/15 of the book has been read.
15/15-11/15=4/15
4/15 of the book is left to read.
Hope this explanation helped!
A distribution of values is normal with a mean of 200 and a standard deviation of 19. From this distribution, you are drawing samples of size 33. Find the interval containing the middle-most 86% of sample means: Enter your answer using interval notation. In this context, either inclusive [] or exclusive () intervals are acceptable. Your numbers should be accurate to 1 decimal places.
The interval containing the middle-most 86% of sample mean in the interval notation is is (196.4, 203.5)
The 50 +/- 86/2 percentile will make up the center 86% of the sample means' distribution.
The 86th percentile's z-score is 1.08
sample mean population mean = 200
standard deviation from mean = 19
sample size = 33.
Standard error (SE) is equal to 19 / sqrt(33) = 3.3077.
86th percentile x can be located using the formula z = (x - population mean)/sample error.
1.08 = (x - 200)/3.3077
x = 3.3077* 1.08 + 200 = 203.57
that is the interval's upper bound.
it is 3.5721 over the population mean (203.57 - 200).
Due to the symmetry of the normal distribution, the interval's bottom bound will be 1.66 standard deviations below the population mean (200 - 3.572 = 196.428).
then the interval is (196.4, 203.5).
To learn more about mean
brainly.com/question/17514579
#SPJ4
$80 at q $100 at qlet q represent the quantity of output and suppose the price of the good is $125 then the marginal revenue is
For the given diagram 1. d) all of them are correct, 2. d)none of them are correct and Total Revenue is 3. b. $90,125
1.
Marginal Revenue is
the change in Total Revenue/Change in units of output produced
In the given question the price of the output is fixed at $125.
Hence no matter what the quantity of output sold, every additional output produced will generate an additional revenue of $125.
hence option d) all of them are correct has to be chosen.
2.
Now we already know that if the price has been fixed at $125, the marginal revenue generated cannot be anything but $125.
Hence, option d) None of them are correct.
3.
Total Revenue = Price X Quantity
Here it is given that the Price is $175
Output is 515 units
Hence, the Total Revenue will be $(175 X 515)
= $90125
Hence, option b. $90125 is correct.
To know more about Cost and Revenue visit
https://brainly.com/question/21859959
#SPJ4
Complete Question
(Image Attached)
03 Multiple Choice
0/20
Select all of the expressions that are equivalent to (9x+6)-(8x-4).
M. 2(x + 1)
P. 2x + 6
R. 2x + 2
S. 2(x + 3)
T. 8x
the manager of a store increases the price of a popular product the new price x+0.07x
Answer:
The new price of the product will be 1.07x, where x is the original price.
The manager has increased the price by 0.07x, which is 7% of the original price. This is equivalent to multiplying the original price by 1 + 0.07, or 1.07.
So, the new price of the product is 1.07 times the original price, or 1.07x.
What is -5 5/8+3 1/2?
Answer: -2 1/8
Step-by-step explanation:
3 1/2 = 3 4/8
5 5/8 - 3 4/8 = 2 1/8
Add the negative sign back to get -2 1/8
A transportation company has 8 shuttle buses. The company changed the oil and filter of each shuttle three times during the year 2021. If changing oil and filter each time for each shuttle cost $63, how much did the company spend on changing oil and filter during 2021, in total?
The cost of changing the oil and filter during 2021, in total is $1512.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a transportation company has 8 shuttle buses. The company changed the oil and filter of each shuttle three times during the year 2021. If changing the oil and filter each time for each shuttle cost $63.
The cost will be calculated by multiplying the number of buses by the number of times it is changed with the cost of each time change.
Cost = 63 x 3 x 8
Cost = $1512
To know more about an expression follow
https://brainly.com/question/13450789
#SPJ1
HEPPPP ASPP!!! PLEASE I BEG YOU !!
John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck. Which table shows the relationship between h, the number of hours john’s brother works, and c, the total cost of the project ?
According to the given questions the answer is for 3 hour $560, for 8 hour cost $685 and for 12 hour cost $785.
What are time and work?A crucial concept that time and labour have in common with some other mathematical topics is the concept of proportionality. Because efficiency grows inversely linked to the amount of time needed when the quantity of work is constant.
What is work time problem in math?The fundamental equation for solving is 1/r+1/s=1/h. Let's choose Hrithik as our example. Let's assume that Hrithik completes 1/20 of something like the work in a day and Dhoni completes 1/30 of the work in a day. They will accomplish 1/20 + 1/30 = 5/60 = 1/12th of something like the work in a day if they collaborate.
Briefing:Given that John paid $485 to build a deck.
And he will pay $25 per hour to his brother for building the deck.
one hour of work costs John $25 + $485 .
Total cost of building deck = $25 × h number of hours + $485
3 hour of work costs $25 × 3 = $75 + $485 = $560
8 hour of work costs = $25 × 8 = $200 + $485 = $685
12 hour of work costs = $25 × 12 = $300 + $485 = $785
To know more about work and time visit:
https://brainly.com/question/16734978
#SPJ1
The complete question is-
John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck. Which table shows the relationship between h, the number of hours John’s brother works, and c, the total cost of the project?
h c
0 485
3 510
8 535
12 560
h c
0 510
3 535
8 560
12 585
h c
0 485
3 560
8 685
12 785
h c
0 510
3 585
8 710
12 810
The Bay Area Online Institute (BAOI) has set a guideline of 60 days for the time it should take to complete an independent study course. In analyzing the times taken to complete the course for 16 random students, BAOI found the average time it took to complete the course was 72 hours with a standard deviation of 20 hours. Consider the possible inferences BAOI can make about the time it takes to complete this course if they assume that the time it takes is normally distributed: i. At the 5% level, BAOI can infer that the average time to complete exceeds 60 hours. ii. At the 1% level, BAOI can infer that the average time to complete exceeds 60 hours. What is true about i. and it: O Only (l) is true O There is insufficient information to determine which of the other answers shown here is correct. O Neither (1) nor (ii) is true O Both (1) and (ii) are true O Only ) is true
As per the given standard deviation, only (i) is true.
The term standard deviation refers the measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.
Here have given that the Bay Area Online Institute (BAOI) has set a guideline of 60 days for the time it should take to complete an independent study course.
Here by analyzing the times taken to complete the course for 16 random students, BAOI found the average time it took to complete the course was 72 hours with a standard deviation of 20 hours.
So, let us consider the possible inferences BAOI can make about the time it takes to complete this course if they assume that the time it takes is normally distributed:
i. For the 5% level, BAOI can infer that the average time to complete exceeds 60 hours.
ii. For the 1% level, BAOI can infer that the average time to complete exceeds 60 hours.
Here we are trying to determine if they should spend at least 480 minutes a day studying.
Now, our knoll is that the mean is 480 and then we are looking for evidence that they are studying less than 480.
Here we don't know the population standard deviation so we're going to use a distribution.
In the given, critical values are going to be a distribution with degrees of freedom.
So, if we look at a chart 11 of freedom, we can see our critical value. I'm going to center to zero if I draw our T.
Therefore, the tail probability of.05 and the rest of it is.95%.
Based on these value we have conform that option (1) is correct.
To know more about Standard deviation here.
https://brainly.com/question/16555520
#SPJ4
consider the following payoff matrix. two airlines, delta and united, compete against each other in a certain city. they must choose whether to lower or raise airline fares. the given entries show the expected revenue from this decision.
Both Alpha and Beta Have a dominant strategy to price low
delta and united both Have a successful pricing plan
What do the terms "alpha" and "Beta" mean pricing?
Using an approach known as alpha-beta pruning, the mini max algorithm can examine fewer nodes in its search tree.
Reason: Regardless of what the other party decides, both firms opt for low prices. Therefore, it is both companies' dominating strategy.
Both Alpha and Beta advise against raising prices.
Reason: Regardless of what the other enterprises do, both businesses have decided against raising prices. So the prevalent method is to keep costs the same.
The major strategy of both businesses is to remain the same. Therefore, both statements A and B are true.
Due to the fact that both companies always opt to remain the same, regardless of what the other player does.
Both Alpha and Beta Have a dominant strategy to price low
To learn more about strategy visit:
brainly.com/question/15860574
#SPJ4
The table represents a linear function. Find the missing values to complete the table.
A) x = 1, y=17/3
B) x= 1, y = 21/3
C) x = 5, y = 17/3
D) x = 5, y = 21/3
The value of missing x = 5
The value of missing y = 17 / 3
How to find the Slope ?The standard line equation, y = mx + b, or the slope formula, m = (y2 - y1)/(x2 - x1), can both be used to find the slope, m.
According to the given information
Let two points be [tex](x_{1} , y_{1} )[/tex] and [tex](x_{2} , y_{2} )[/tex] are ( 3 , 8 ) and ( 6 , 15 )
Slope of the two points = [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]
= [tex]\frac{15-8}{6-3}[/tex]
= 7 / 3
Let the equation passing through points ( 3 , 8 ) be
[tex]( y - y_{1}) = m(x - x_{1})[/tex]
y - 8 = 7/3( x - 3 )
3y - 24 = 7x - 21
3y = 7x - 21 + 24
3y = 7x + 3
When x = 2
3y = 14 + 3
y = 17 / 3
When y = 38/5
114/3 = 7x + 3
7x = 114/3 - 3
21x = 114 - 9
x = 5
So
The value of missing x = 5
The value of missing y = 17 / 3
To know more about Slope
https://brainly.com/question/6328621
#SPJ1
the student government claims that 70% of all students favor an increase in student fees to buy indoor potted plants for the classrooms. a random sample of 12 students produced 2 in favor of the project.
(a) What is the probability that 2 or fewer in the sample will favor the project, assuming the student government's claim is correct? (Use 3 decimal places.) (b) Do the the data support the student government's claim, or does it seem that the percentage favoring the increase in fees is less than 70%? The data do not give us any indication that the percent favoring the increase in fees differs from 70%. The data seem to indicate that the percent favoring the increase in fees is greater than 70%. The data seem to indicate that the percent favoring the increase in fees is less than 70%. The data seem to indicate that the percent favoring the increase in fees is equal to 70%.
The probability that 2 or fewer in the sample will favor the project is 4.368 × 10⁻⁶ and Also The data seem to indicate that the percent favoring the increase in fees is less than 70%
According to the question,
It is given that according to the student's government
The probability that number of students in favor of increment in fees : p = 0.70
The probability that number of students against the increment : q = 0.30
Sample Size : n = 12
Number of students follows Binomial distribution
(a) We have to find the probability that 2 or fewer in the sample will favor the project
P( x ≤ 2) = P(0) + P(1) + P(2)
As we know ,
P(x) = ⁿCₓpˣq⁽ⁿ⁻ˣ⁾
=> P( x ≤ 2) = ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹ + ¹²C₂p²q¹⁰
=> P( x ≤ 2) = 1×(0.30)¹² + 12×(0.70)(0.30)¹¹ + 12×11/2 × (0.70)²(0.30)¹⁰
=> P( x ≤ 2) = (0.30)¹⁰ [ 0.09 + 0.21 + 0.48]
=> P( x ≤ 2) = 5.9×10⁻⁶[0.78]
=> P( x ≤ 2) = 4.368 × 10⁻⁶
Which is very close to zero
(b) The data doesn't support the student government claim.
The data seem to indicate that the percent favoring the increase in fees is less than 70%.
To know more about Binomial distribution here
https://brainly.com/question/29137961
#SPJ4
