x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary, if k = 1
x = -1, y = 6, z = 1 is the solution.
Ax = [tex]\left[\begin{array}{ccc}1&1&1\\1&2&3\\1&4&7\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]
and b = [tex]\left[\begin{array}{ccc}6\\14\\30\end{array}\right][/tex]
the augmented matrix is [A:B] = [tex]\left[\begin{array}{ccc}1&1&1:6\\1&2&3:14\\1&4&7:30\end{array}\right][/tex]
we need to reduce the augmented matrix [A:B] to row echelon form by applying elementary row transformations only.
operating R₂→R₂-R₁ , R₃→R₃-R₁
[A:B] = [tex]\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&3&6:24\end{array}\right][/tex]
operating, R₃→R₃-3R₃
~ [tex]\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&0&0:0\end{array}\right][/tex]
which is the row echelon, form of the matrix [A:B]
we have rank of [A:B] = the number of the non zero rows in echelon form = 2
also by the same elementary transformation we get,
A ~ [tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex]
∴ rank of A = 2
since rank A = rank [A:B] = 2 < number of unknowns
therefore, the given equation are consistent and will have an infinite number of solutions.
We see that the given system of equations is equivalent to the matrix equation
[tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}6\\8\\0\end{array}\right][/tex]
which gives the equations x + y + z = 6 ........(1)
and y + 2z = 8 .......(2)
from (2), y = 8 - 2z, putting the value of y in (1) we get,
x = 6 - y - z = 6 (8 - 2z) z = z - 2
taking z = k, we get x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary,
if k = 1
x = -1, y = 6, z = 1 is the solution.
To learn more about matrix, click here:
brainly.com/question/29132693
#SPJ4
16.0 meters Question 9(Multiple Choice Worth 2 points) (09.06 MC) 01.6 meters Sara's Kite flew 48 meters in the air. Tayjen's kite flew 5,860 centimeters in the air. How much higher was Tayjen's kite
Tayjen's kite flew 5,860 centimeters in the air then Tayjen's kite flew 10.6 meters higher than Sara's kite.
What is BODMAS?
BODMAS is an acronym used to remember the order of operations in arithmetic. The acronym stands for:
B - Brackets (or Parentheses)
O - Orders (exponents and roots)
DM - Division and Multiplication (performed left to right)
AS - Addition and Subtraction (performed left to right)
BODMAS provides a set of rules that dictate the order in which mathematical operations should be performed in an expression that contains multiple operations. It is important to follow the order of operations to ensure that the expression is evaluated correctly and consistently. For example, in the expression 5 + 3 x 2, if we follow the BODMAS rule, we first perform the multiplication (3 x 2) and then the addition (5 + 6), giving us the answer of 11. If we were to perform the addition first, we would get a different answer (5 + 3 = 8, and 8 x 2 = 16), which would be incorrect.
To compare the height of Sara's kite, which is measured in meters, with the height of Tayjen's kite, which is measured in centimeters, we need to convert Tayjen's kite's height to meters.
To do that, we divide the height of Tayjen's kite by 100, since there are 100 centimeters in a meter:
5,860 centimeters ÷ 100 = 58.6 meters
Now we can compare the heights of the two kites:
58.6 meters - 48 meters = 10.6 meters
Therefore, Tayjen's kite flew 10.6 meters higher than Sara's kite.
Learn more about Comparision of expression click here:
https://brainly.com/question/29051300
#SPJ1
The number in a bacteria lab can be modeled by the function L(t)= 880(3)^t+2. Write an equivalent function in the form L(t)= ab^t
The equivalent function to the given one is:
L(t) = 7,920*(3)^t
How to rewrite the function?Here we want to rewrite the function:
L(t) = 880*(3)^(t + 2)
Into the form:
L(t) = a*(b)^t
Remember the rule for exponents:
(x^a)*(x^b) = x^(a + b)
Then we can take our function:
L(t) = 880*(3)^(t + 2)
And rewrite this as:
L(t) = 880*(3^t)*(3^2)
L(t) = 9*880*3^t
L(t) = 7,920*(3)^t
That is the equivalent function.
Learn more about exponential functions at:
https://brainly.com/question/2456547
#SPJ1
Rashida measured the length of a beam to be 16 3/4
feet. The actual length of the beam is 17 1/2
feet.
What is the percent error in Rashida's measurement?
The percent error in Rashida's measurement while measuring the length of the beam is 4.29%.
What is meant by percent error?
The percent error is the distinction between the estimated value and the actual value in relation to the actual value. Percent errors show the magnitude of our measurement errors during an analysis procedure. We are getting close to the accepted or original value when the percent mistakes are smaller. The relative error is multiplied by 100 to get the percent error.
Given,
The actual length of beam = 17 and 1/2 feet = 17.5 feet
The measured length of beam = 16 and 3/4 feet = 16.75 feet
The formula to find the percent error is as follows:
Percent error = [tex]|\frac{Measured\ value - Actual\ value}{Actual\ value} | * 100[/tex]
= [tex]|\frac{16.75 - 17.5}{17.5} | * 100 =[/tex] 0.75/17.5 * 100 = 4.29%
Therefore the percent error in Rashida's measurement while measuring the length of the beam is 4.29%.
To learn more about percent error, follow the link.
https://brainly.com/question/1600371
#SPJ1
PLEASE HELP DUE TOMORROW:
Ok, so I know the answer is 9 but I'm not sure how to actually get that answer, and this assignment requires me to show work.
select the most correct statement below that describes the differences between type 1 and type 2 hypervisors?
A type 1 hypervisor functions as a compact operating system and runs directly on the host's hardware, but a type 2 hypervisor operates as a software layer on operating system, similar to other computer programs.
Which is the safer hypervisor, type 1 or type 2, and why that is more superior?
Native hypervisors are a safer solution. They are not dependent on the underlying OS, unlike hosted hypervisors. If you are attacked, the bare-metal hypervisor will improve your chances (Type 1). Because of this reliance, the type 2 server loses efficiency, performance, and speed. A Type 1 hypervisor operates directly on the hardware of the host computer. These hypervisors interface directly with the host computer's CPU, RAM, and physical storage, making them typically quicker and more effective than Type 2 hypervisors. eliminate the requirement to travel through the OS layer.
Learn more about hypervisors:
https://brainly.com/question/20892566
#SPJ4
what value represents the number of ways in which the expected classes are free to vary in the chi‑square goodness‑of‑fit test?
In the chi-square goodness-of-fit test, the number of ways in which the expected classes are free to vary is represented by the degrees of freedom (df) of the test.
The degrees of freedom for the chi-square goodness-of-fit test are calculated as df = k - 1, where k is the number of categories or classes being compared.
In this test, we compare the observed frequencies in each category with the expected frequencies, assuming that the null hypothesis is true. The null hypothesis is that there is no significant difference between the observed and expected frequencies, and any deviation between the two is due to chance.
The degrees of freedom are the reflection of the number of independent pieces of information that are available to estimate the expected frequencies.
The more degrees of freedom, the more likely it is that the observed frequencies could be due to chance, and the less significant the test result will be. Conversely, fewer degrees of freedom means that the observed frequencies are more likely to be significantly different from the expected frequencies, and the test result will be more significant.
Read more about the chi-square test:
brainly.com/question/29728594
#SPJ4
A figure is dilated by a scale factor of 3 and is rotated 90° clockwise.
Complete the description of the transformations that will transform the image back into the original figure. Drag and drop each choice into the correct boxes to complete the sentences below.
Answer:
Answers are below ----v
Step-by-step explanation:
1. Clockwise
2. 3
3. (y, -x)
4. (3x,3y)
Type the expression that results from the following series of steps: Start with t , add 6, divide by 2, then subtract 5.
Answer:
2(t+6)-5
Step-by-step explanation:
The unknown number is t
=> Adding 6 will make it t+6
=> Multiplying 2 will make it 2(t+6)
=> Subtracting 5 will make it 2(t+6)-5
Answer:
[tex]\frac{t+6}{2}[/tex] - 5
Step-by-step explanation:
[tex]\frac{t+6}{2}[/tex] - 5
to decide which thing of coffee is better value-for-money calculate the price per gram of a 250 g of coffee for 2949 stands and a 750 grams of coffee for $69.99
The second option has the better value-for-money.
Which coffe has the better value-for-money?To find the price per gram, you need to take the quotient between the cost and the mass for each case.
The first brand costs $29.49 for 250 grams, then the cost is:
c = $29.49/250g = $0.12 per gram.
The other brand costs $69.99 for 750 grams, then the cost per gram is:
C = $69.99/750g = $0.09 per gram
We can see that the second option has the better vale-for-money.
Learn more about costs at:
https://brainly.com/question/19104371
#SPJ1
solve the equations y=2x+56 and y=9x
The solution of the linear equations y = 2x + 56 and y = 9x will be (8, 72).
What is the solution to the equation?The possible value of the variables that satisfy the equation which is known as the solution of the equation.
The equations are given below.
y = 2x + 56 ....1
y = 9x ....2
From equations 1 and 2, then we have
9x = 2x + 56
7x = 56
x = 8
Then the value of the variable 'y' is given as,
y = 9(8)
y = 72
The solution of the linear equations y = 2x + 56 and y = 9x will be (8, 72).
More about the solution of the equation link is given below.
https://brainly.com/question/22613204
#SPJ1
2. 10,175 rounded to the nearest thousand 0 is the target, aka the number place I’m rounding to
PLSSS HELP ASAP PSLPLSPSL
find each value
The value of x is 7, therefore AC = 23 and BD = 23, which means diagonals AC = BD.
What is linear equations in two variables?
A linear equation in two variables is an equation that can be written in the form ax + by = c, where a, b, and c are constants, and x and y are variables. The graph of a linear equation in two variables is a straight line in the Cartesian coordinate system.
In a trapezium, the diagonals divide the trapezium into four triangles. The diagonals of a trapezium are also equal to the sum of the two parallel sides.
Let the two parallel sides of the trapezium be a and b. Then, we have:
8x - 33 = a + b ...(1)
37 - 2x = a + b ...(2)
We can solve for x by setting (1) and (2) equal to each other:
8x - 33 = 37 - 2x
10x = 70
x = 7
8(7) - 33 = 23
37 - 2(7) = 23
Therefore, the value of x is 7.
To learn more about the linear equations in two variables, visit:
https://brainly.com/question/24085666
#SPJ1
what is the value of y?
Answer:
y = 43
Step-by-step explanation:
47° , y and 90° lie on the straight line AB and sum to 180° , that is
47 + y + 90 = 180
y + 137 = 180 ( subtract 137 from both sides )
y = 43
Determine whether f has an inverse function. If it does, find the inverse function and state any restrictions on its domain:
f(x) =[tex]\frac{x - 7}{x + 4}[/tex]
The inverse function of f(x) = [tex]\frac{x-7}{x+4}[/tex] is f⁻¹(x) = [tex]\frac{4x+7}{1-x}[/tex].
What is the inverse function?A function that can reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "f-1" or "F-1." Here, (-1) should not be confused with an exponent or a reciprocal.
Given that the function is f(x) = [tex]\frac{x-7}{x+4}[/tex]
Change f(x) (or whatever the function name is) to "y". In this case you'd get:
y = [tex]\frac{x-7}{x+4}[/tex]
Now, switch x and y. Wherever you see y, put x. And wherever you see x, put y.
x = [tex]\frac{y-7}{y+4}[/tex]
Solve the new equation for y.
x (y + 4) = y - 7
xy + 4x = y - 7
4x + 7 = y - xy
4x + 7 = y (1 - x)
y = [tex]\frac{4x+7}{1-x}[/tex]
Change y back to function notation. The correct notation for the "inverse of f(x)" is "f⁻¹(x)". So that would give you:
f⁻¹(x) = [tex]\frac{4x+7}{1-x}[/tex]
To learn more about inverse function of f(x) visit:
brainly.com/question/17872426
#SPJ1
If the sum of 3 consecutive numbers is 114 find the numbers? WILL MARK BRAINLIEST!:)
If the sum of 3 consecutive even numbers is 114, we can represent the numbers as x, x+2, and x+4.
The sum of the three numbers is:
x + (x+2) + (x+4) = 3x + 6
We know that the sum is 114, so we can set up the equation:
3x + 6 = 114
Subtracting 6 from both sides gives:
3x = 108
Dividing both sides by 3 gives:
x = 36
Therefore, the three consecutive even numbers are 36, 38, and 40.
Answer:
37, 38, 39
Step-by-step explanation:
let the 3 consecutive numbers be
n , n + 1 , n + 2
then summing and equating to 114
n + n + 1 + n + 2 = 114
3n + 3 = 114 ( subtract 3 from both sides )
3n = 111 ( divide both sides by 3 )
n = 37
n + 1 = 37 + 1 = 38
n + 2 = 37 + 2 = 39
the 3 consecutive numbers are 37 , 38 , 39
how to turn 1/5 into and percentage and show how you did it
Answer:
Step-by-step explanation:
percentages are usually out of 100.
so you are turning 1/5 to x out of 100.
we can do thismany ways; i will be doing a ratio.
1:5
to
x:100
we can see that 5 times 20 equals 100, therefore, 1 times 20 would equal x.
so 20/100 is equal to 1/5.
Answer:
percentages are .so you are turning 1/5 to x out of 100. we can do this many way; I will be doing a ratio. of 1:5tox:100we can see that 5 times 20 equals 100, therefore, 1 time 20 would equal x.so 20/100 is equal to 1/5.
it takes half of a yard of ribbon to make a bow how many bows can be made with 7 yards of ribbon
Answer:
14 bows
Step-by-step explanation:
.5 yards is need for one bow if you have 7 yards you have 14(.5) yards
easier way a half goes into 7, 14 times since 14 divide by two is 7
Write a quadratic function in standard form whose graph satisfies the given condition(s). 13. vertex: (-9, -4)
Answer:
Tech 9 rock and no answer
Step-by-step explanation:
Match each pair of equivalent values.
1.
square root of 16
2. square of 8
3. 42
4. 12
5. √4
6. √144
k
16
1
4
2
64
12
Answer:
1 -
12 - ?
4 - square root of 16
64 -
16 -
2.828 - square root of 8
Step-by-step explanation:"
I need more terms to match them.
I need help. Please :(
Answer:
x-8
Step-by-step explanation:
the answer is x-8 correct answer x-8
Discussion topic
read this article discussing the value of specific polling results in us presidential elections.
your thoughts about the
article, in particular, comment about what surprised you or what you
thought might be interesting to understand more deeply. Also comment about any
statistical
discussion or information that you are now better able to understand because of your
background in statistics.
give
Overall, the article has given me a deeper appreciation for the role that statistics plays in the political landscape.
One statistical discussion that stood out to me was the concept of margin of error. This is a measure of the accuracy of a poll and is calculated by taking into account the sample size and the variability in responses. I now have a better understanding of how pollsters use this measure to determine the reliability of their results.
Additionally, the article highlighted the importance of understanding statistical significance, which refers to the likelihood that a particular result occurred by chance. This is an essential concept in statistics that helps to determine whether a particular result is reliable or not.
It has also emphasized the need to interpret polling data with caution and to be mindful of the potential for errors and biases.
To know more about statistics here.
https://brainly.com/question/14318705
#SPJ4
suppose lacrosse balls come in 3 colours: red, yellow, and blue. how many different combinations of colours are possible in a 6-pack of lacrosse balls?
There are 20 different combinations of colors possible in a 6-pack of lacrosse balls.
What is the combination?
A combination is a choice of items from a group of different items where the order of the choices is irrelevant. Either the process of combining or the condition of combining. a combination of several things a mixture of thoughts. something created through fusion: A chord is made up of several notes.
Here, we have
Given: lacrosse balls come in 3 colors: red, yellow, and blue.
We have to find the different combinations of colors that are possible in a 6-pack of lacrosse balls.
We apply here combination formula and we get
= ⁶C₃
= (6×5×4×3!)/(3!×3×2×1)
= 20
Hence, there are 20 different combinations of colors possible in a 6-pack of lacrosse balls.
To learn more about the combination from the given link
https://brainly.com/question/28570562
#SPJ1
In ΔLMN, m = 450 inches, � m∠M=74° and � m∠N=41°. Find the length of l, to the nearest 10th of an inch
In the triangle LMN the length of the side l as per given measures of side and angles is equal to 42.4 inches ( nearest tenth )
In triangle LMN,
Let us consider side length opposite to ∠L, ∠M, and ∠N be l , m , and n respectively.
Measure of side m = 450 inches
Measure of ∠M = 74°
Measure of ∠N = 41°
Sum of all the angles in a triangle is equal to 180°
m ∠M + m ∠N + m ∠L = 180°
⇒ 74° + 41° + m ∠L = 180°
⇒ m ∠L = 180° - 115°
⇒ m ∠L = 65°
Using sine law of triangle we have,
sin L / l = sin M / m = sin N / n
⇒sin L / l = sin M / m
Substitute the value we get,
⇒ sin 65° / l = sin 74° / 450
⇒ l = sin 65° × ( 450 / sin 74°)
⇒ l = 0.9063 × ( 450 / 0.9613 )
⇒ l = 42.43 inches
⇒ l = 42.4 inches ( nearest tenth )
Therefore, the measure of the side length l in a triangle LMN is equal to 42.4 inches ( nearest tenth ).
The above question is incomplete, the complete question is:
In ΔLMN, m = 450 inches, m ∠M=74° and m ∠N=41°. Find the length of l, to the nearest 10th of an inch.
Learn more about length here
brainly.com/question/30100801
#SPJ4
Answer: 424.3
Step-by-step explanation: n ΔLMN, m = 450 inches, m∠M=74° and
m∠N=41°. Find the length of l, to the nearest 10th of an inch.
A.A.S.→Law of Sines
Plug in. Opposite sides go together. 450 sin, 65 sin 74 ≈ 424.2742 ≈ 424.3
l=
sin74
450sin65
≈424.2742≈424.3
Use the drop-down menus to complete the statements
to match the information shown
by the graph.
The correct drop down menus from the graph are:
First box: faster than, slower than, at the same rate as.Second box: greatest x-value, line, y-intercept, slope.Third box: greater than, less than, equal to.Fourth box: greatest x-value, x-intercept, y-intercept, slope, origin.Fifth box: minutes per gallon, gallons per minute.What is our observation on the graph?Pool A is filling up slower than Pool B because the slope of the graph of Pool A is less than that of the graph for Pool B.
The slope of the graph tells you the unit rate in gallons per minute. Its means the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.
Read more about graph
brainly.com/question/19040584
#SPJ1
Jordan's t-shirt business sells long sleeve shirts for $18 and short sleeve shirts
for $13. He needs to make at least $350 to buy a new heat press machine. So
far, fewer than 30 people have purchased shirts. Which system of inequalities
fits this scenario?
OS+L=30
13S+18 L = 350
OS+L<30
13S+18L 350
OS+L< 30
13S+18L 350
OS+L≥ 30
13S+18L 350
The system of inequalities that will model the given scenerio are -
S + L < 30
13S + 18L ≥ 350
What is equation modelling?Equation modelling is the process of writing a given mathematical statement (or word problem) in the form of a mathematical equation for the correct analysis of the given problem (or situation).
Given is that Jordan's t-shirt business sells long sleeve shirts for $18 and short sleeve shirts for $13. He needs to make at least $350 to buy a new heat press machine.
Let {S} represent the short sleeves and {L} represents the long sleeves. So, we can model the equations as -
S + L < 30
13S + 18L ≥ 350
Therefore, the system of inequalities that will model the given scenerio are -
S + L < 30
13S + 18L ≥ 350
To solve more questions on system of inequalities, visit the link below
https://brainly.com/question/19526736
#SPJ9
using diagonals from a common vertex, how many triangles could be formed from a 15-gon
13 triangles could be formed from a 15-gon.
What is Vertex?The vertex of an angle is the intersection of two lines, rays, or segments. A diagonal is a line segment with vertices as its endpoints. The intersection of two edges or sides forms a polygon's vertex. A vertex is created when three edges of a polyhedron collide.
Given:
The number of triangles formed by connecting one of the vertices to the rest of the vertices is equal to n - 2.
We have 15- gon.
So, the number of Triangles can be formed is n-2.
= 15 -2
= 12 Triangles.
Learn more about Vertex here:
https://brainly.com/question/1554019
#SPJ9
The Question attached here seems to be incomplete / inappropriate.
The complete question is
Using diagonals from a common vertex, how many triangles could be formed from a 15-gon (diagonal)?
In ΔNOP, \overline{NP} NP is extended through point P to point Q, \text{m}\angle OPQ = (9x-19)^{\circ}m∠OPQ=(9x−19) ∘ , \text{m}\angle PNO = (2x+5)^{\circ}m∠PNO=(2x+5) ∘ , and \text{m}\angle NOP = (3x+16)^{\circ}m∠NOP=(3x+16) ∘. Find \text{m}\angle NOP. M∠NOP
The measure of angle NOP is found by solving an equation that is obtained by using the fact that the sum of the angles in a triangle is 180 degrees. The solution is m∠NOP to obtain the answer of 53.13 degrees.
In the problem, we are given a triangle NOP, where \overline{NP} is extended through point P to point Q. We are given the measures of three angles: m∠OPQ, m∠PNO, and m∠NOP.
We are asked to find the measure of angle NOP.To find the measure of angle NOP, we can use the fact that the sum of the angles in a triangle is always 180 degrees. So, we add up the measures of the three angles we know:
m∠OPQ + m∠PNO + m∠NOP = 180
We are given the measures of m∠OPQ, m∠PNO, and m∠NOP in terms of x. We substitute these values and get an equation in terms of x:
(9x-19) + (2x+5) + (3x+16) = 180
Simplifying the left side of the equation, we combine like terms:
14x + 2 = 180
We can then isolate x by subtracting 2 from both sides of the equation:
14x = 178
And then we can solve for x by dividing both sides of the equation by 14:
x = 12.71
Now that we know x, we can use it to find the measure of angle NOP, which is what we were asked to do. We substitute x = 12.71 into the equation for m∠NOP:
m∠NOP = 3x + 16 = 3(12.71) + 16 = 53.13
Therefore, the measure of angle NOP is 53.13 degrees.
To learn more about triangle Click here:
brainly.com/question/2773823
#SPJ4
The Jacob family plans to attend a concert. An
adult ticket (a) is $7.50 each and a child's ticket (c)
is $5.00 each. Mr. Jacob purchased a total of 11
tickets for a total of $65. How many of each kind of
ticket was purchased?
Answer:Mr. Jacob purchased 7 adult tickets at $7.50 each, and 4 child tickets at $5.00 each, for a total of 11 tickets at a cost of $65.
Step-by-step explanation:
PLEASE SOLVE
the graphs of y=px+w and y=rx+s are perpendicular and p=100|r|. Find the values of p and r
P=_
R=_
Answer:
Step-by-step explanation:
. if these particular light bulbs have a mean lifetime of 2 months with a standard deviation of 0.25 months (per the manufacturer), determine the probability that this box of 40 lightbulbs will last for 5 years.
The probability that a box of 40 light bulbs will last for 5 years is very low, due to the short mean lifetime of 2 months and the relatively high standard deviation of 0.25 months.
The mean lifetime of a particular type of light bulb is given as 2 months, and the standard deviation is given as 0.25 months. The mean lifetime represents the average time that the light bulbs will last, while the standard deviation represents how much the lifetimes of the bulbs vary from the mean.
To determine the probability that a box of 40 light bulbs will last for 5 years, we need to convert the given information into a format that we can work with. 5 years is equal to 60 months, and since we have 40 light bulbs, we can assume that the lifetimes of the bulbs are independent and identically distributed. This means that the probability of one bulb lasting for 60 months is the same as the probability of any other bulb lasting for 60 months.
Next, we need to calculate the standard deviation of the sample mean. The standard deviation of the sample mean represents how much the means of different samples of size 40 would vary from the population mean. The formula for the standard deviation of the sample mean is given by the following equation:
standard deviation of the sample mean = standard deviation of the population / square root of the sample size
In this case, the standard deviation of the population is given as 0.25 months, and the sample size is 40. Therefore, the standard deviation of the sample mean is:
0.25 / sqrt(40) = 0.0395
Now that we have the mean lifetime and the standard deviation of the sample mean, we can use the normal distribution to determine the probability that a box of 40 light bulbs will last for 5 years. We can assume that the lifetimes of the bulbs follow a normal distribution with a mean of 2 months and a standard deviation of 0.0395 months (which is the standard deviation of the sample mean).
To find the probability that a bulb will last for 60 months, we can use the following equation:
z = (x - μ) / σ
where z is the standard score, x is the value we want to find the probability for (60 months in this case), μ is the mean, and σ is the standard deviation.
Plugging in the values, we get:
z = (60 - 2) / 0.0395 = 1509.49
To find the probability corresponding to this standard score, we can use a standard normal distribution table or a calculator. The probability is extremely small (close to zero), which means that it is highly unlikely that all 40 light bulbs will last for 5 years.
To know more about probability here.
https://brainly.com/question/11234923
#SPJ4
