Answers
Answer:
DF = 11
Step-by-step explanation:
From the question given above, the following data were obtained:
EH = 8
HG = 3
EF = DG
DF =?
Since, EF = DG, it also means that EG = DF.
Next we shall determine EG. This can be obtained as follow:
EG = EH + HG
EH = 8
HG = 3
EG = 8 + 3
EG = 11
Finally, we shall determine EF. This is illustrated below:
EG = DF
EG = 11
DF =?
11 = DF
Therefore,
DF = 11
Related Questions
Which side lengths form a right triangle?
Answers
Answer: A and C
Step-by-step explanation: To see if it can be the side lengths of a right triangle we have to use the Pythagoras Theorem which is [tex]a^2 +b^2 = c^2\\[/tex]
C is always the largest length. Now we can sub the numbers in
[tex]5^2+\sqrt{6} ^2=\sqrt{31} ^2[/tex]
The squares and the square roots cancel each other out so we end up with
25+6=31
this is true so those are possible sides for a right triangle
Now for b:
[tex]\sqrt{5}^2 + \sqrt{5}^2 =50^2[/tex]
Again the squares and square roots cancel each other out
5+5=2500
This isn't true so it isn't the possible sides for a right triangle
Finally option C:
[tex]9^2+12^2=15^2[/tex]
81+144=225
225=225
This is true so it can be the side lengths that form a right triangle
2x + 3y = 34
slove for y
Answers
Answer:
34/3, -2/3
Step-by-step explanation:
See image below:)
Step-by-step explanation:
2x + 3y = 34
3y = 34 - 2x
y = 3x - 2x/3
An unknown radioactive material is measured to have a half life of 3 months. When the material was first found, there was 2000mg. a) Write an equation that models the mass of the material, t months. b) Use your equation to determine the mass of material in 4 year c) Calculate around how many months it will take to have 750 mg left
Answers
Answer:
OK!!.
N=N(½)ⁿ
n= Time/half life
N=Remaining Mass
N°=Initial Mass or Mass before decay.
t= time taken to decay(Its in Months in this case)
t½= Half Life of the Material. This is the time taken to decay to half its initial value.
N°= 2000mg
a).Equation that Models this is
since n=t/t½
N=N°(½)ⁿ =
N=N°(½)^t/t¹'². This should be your answer.
b). We're asked to find the remaining mass of substance in 4years.
t= 4years
Our Half life is in Months... So we gotta convert or time t from year to Months too.
4yrs === 4x12 = 48Months.
N° was given as 2000mg
N=N°(½)^t/t½
N= 2000(½)^48/3
N=2000(½)^16
Using your calc to evaluate (½)^16... Then multiply by 2000
N=0.0305mg will remain after 4years.
Or After 16Half Lives since 1 half life is 3months
c). We're looking for t this time
N=N°(½)^t/t½
Since it asked for 750mg to remain ... 750 is now our N --- Remaining Mass
750 = 2000(½)t/3
To Isolate "t" and make it the subject
750/2000 = (½)^t/3
0.375 = (½)^t/3
Taking ln(natural log) of both sides
Ln(0.375) = Ln(0.5)^t/3
From the rule of logarithm...
You can bring the power (I.e t/3) to the front
You'll have
Ln(0.375) = t/3Ln(0.5)
Dividing both sides by Ln(0.5) to isolate t
Ln(0.375)/Ln(0.5) = t/3
t/3 = 1.415
t= 3x1.415
t=4.25months.
Have a great day.
Hope this helps... I'm open to questions if you have any too.
The ration of men to women in a community is 25:12.If there are 240 women..(i) how many men are in the community?..(ii) What is the total number of people in the community?
Answers
Answer:
500 men
740 total people in community
Step-by-step explanation:
25:12 ratio
When using a ratio both sides should go up the same amount of times to get the number you are trying to reach. Since the women's amount was 240 we need to find the times it took to get from 12 to 240. You take the 240 and divide by 12. We find that the 12 was multiplied 20 times to get to 240. So you turn to the men's side and find the amount using the 25. We use X to signify the amount we are trying to find and the amount of times that 25 goes into X will be 20 to keep the ratio of men to women as specified. When solving for X you multiply both sides of the equation by 25 to find the amount. X will equal 500 (=20*25).
Then 240 women plus 500 men equals to 740 people in the community.
Women
240/12 = 20
Men
X/25=20
X=20*25
X=500
240 women+500 men=740 people
Only answer if you're very good at math.Please I keep on posting this but nobody is helping me.
What is the 4th term of the expansion of (1 - 2x)^n if the binomial coefficients are taken from the row of Pascal's triangle shown below?
1 6 15 20 15 6 1
A: 240x^4
B: 160x^3
C: -160x^3
D: -20x^3
Answers
The fourth term of the given expansion is [tex]-280x^{3}[/tex].
What is binomial expansion?
The binomial expansion is used to expand and write the terms which are equals to the natural number exponent of the sum or differences of two terms.
The general term of the binomial expansion is given by[tex]T_{r+1} =nC_{r} x^{n-r} y^{r}[/tex]
According to the given question
We have,
A binomial expression, [tex](1-2x)^{n}[/tex]
and, the binomial coefficients are taken from the row of Pascal's triangle 1 6 15 20 15 6 1
⇒ n = 7
Therefore,
The fourth term of the expansion of [tex](1-2x)^{n}[/tex] is given by
[tex]T_{3+1} = 7C_{3} 1^{7-3} (-2x)^{3}[/tex]
[tex]T_{4} =\frac{(7)(6)(5)(4)(3!)}{3!(4)(3)(2)} (1)(-2x)^{3}[/tex]
[tex]T{4} = -280x^{3}[/tex]
Hence, the fourth term of the given expansion [tex](1-2x)^{3}[/tex] is [tex]-280x^{3}[/tex].
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Determine the value of y, if x is 1.
y = |x| +7
Help plsss
Answers
Answer:
8
Step-by-step explanation:
The absolute value (the lines both sides of x) simply mean the number in between is positive. Since 1 is already positive, just add it to 7!
Choose the expression that represents “three less than seven times a number
Answers
Answer: 3-7x
Step-by-step explanation: x represents the "a number" portion since it is a variable
To perform a certain type of blood analysis, lab technicians must perform two procedures. The first procedure requires either one, two, or three steps. The second procedure requires either one or two steps. Answer the first and second questions using this information.List the experimental outcomes associated with performing the blood analysis. (Hint: The first procedure has three possible outcomes (steps needed), the second procedure has two possible outcomes (steps needed)).
Answers
Answer:
____ 1 _____ 2 ____ 3
1 __ 1, 1 ____ 1, 2 __ 1, 3
2 __2, 1 ____2, 2 __ 2, 3
Step-by-step explanation:
Given that :
Steps required for procedure One : Either 1, 2, or 3
Steps required for procedure two : Either 1 or 2
The first procedure has 3 possible steps
The second procedure has 2 possible steps
. The experimental outcome associated with performing the blood analysis is displayed in the table below :
____ 1 _____ 2 ____ 3
1 __ 1, 1 ____ 1, 2 __ 1, 3
2 __2, 1 ____2, 2 __ 2, 3
expand 3e(e+4)
Hhhhhhh
Answers
Answer:
[tex]3e^{2} + 12e[/tex]
Step-by-step explanation:
[tex]3ee+3e4[/tex]
[tex]3ee+3 * 4e[/tex]
[tex]3e^{2} + 12e\\[/tex]
[tex]3 \: {e}^{2} + 12 \: e[/tex] ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]3 \: e \: ( \: e + 4 \: ) \\ \\ = 3 \: e \times \: e + 3 \: e \times 4 \\ \\ = 3 \: {e}^{2} + 12 \: e[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique }}{\orange{♡}}}}}[/tex]
Adam bought three kinds of
bagels at the bagel store. He
bought twice as many onion bagels as plain
bagels. He bought four more sesame
bagels than he did plain bagels. Adam ate
one of the sixteen onion bagels he bought
as soon as he got home. How many bagels
does Adam have left?
Answers
9514 1404 393
Answer:
35
Step-by-step explanation:
The 16 onion bagels are twice as many as plain bagels, so there were 8 plain bagels.
There were 4 more sesame bagels than plain bagels, so there were 12 sesame bagels.
Adam has 8 plain, 12 sesame, and 15 onion bagels left, for a total of 35 bagels left.
Write the simplified expression that represents the perimeter of the triangle below.
X - 3
4x + 4
2x + 1
Show Work
Answers
Answer:
Just plus everything together
X-3+4X+4+2X+1
Step-by-step explanation:
PLZ HELP ME!!!!
how much water must be evaporated from 32 ounces of a 4% salt solution to make an 8% salt solultion?
Answers
Answer:
16 ounces.
Step-by-step explanation:
An 8% solution is 2 times stronger than a 4% solution.
So in the 8% solution we will have 1/2 of the volume as a 4% , so 1/2 * 32
= 16 ounces of water must be evaporated.
The number 16 ounces of water must be evaporated from 32 ounces of a 4% salt solution to make an 8% salt solution.
What is a linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
To find the amount of water that must be evaporated from 32 ounces of a 4% salt solution to make an 8% salt solution:
0.96(32) - x = 0.92(32 - x)
30.72 - x = 29.44 - 0.92x
x - 0.92x = 30.72 - 29.44
0.08x = 1.28
x = 16
Therefore, 16 ounces must be evaporated.
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Ack, sorry im gonna need a way to delete this lol.
Thanks to the people who tried.
ima need someone to delete this.
Answers
To compute a student's Grade Point Average (GPA) for a term, the student's grades for each course are weighted by the number of credits for the course. Suppose a student had these grades: 3.7 in a 5 credit Math course 1.8 in a 3 credit Music course 2.8 in a 5 credit Chemistry course 2.8 in a 4 credit Journalism course What is the student's GPA for that term
Answers
Answer:
2.89, rounded to the nearest hundredth
Step-by-step explanation:
Given that GPA is weighted by credits, we must first multiply each grade by its credit amount and sum those up to weigh the credits. Then, we divide by the total amount of credits to get the GPA per credit.
So, we start with math,
3.7 *5 + 1.8 *3 + 2.8 * 5 + 2.8 * 4 = 49.1 as the total GPA weighted per credit.
Then, to find the average per credit, we divide by the total amount of credits, which is 5 + 3 + 5 + 4 = 17.
Our answer is 49.1/17 = 2.89, rounded to the nearest hundredth
below is a table showing the investment and the investment period of
Answers
Answer:
hey. pls complete your question.
Dhani has 4 cards numbered 1 through 4. He removes 2 cards at random and adds their values.
What is the probability that the sum is less than or equal to 5?
7/12
2/3
3/5
3/4
Answers
Answer:
[tex]2/3[/tex]
Step-by-step explanation:
The total number of sums (not distinct) is [tex]4\cdot 3=12[/tex], because we're removing without replacement.
Count the sums that fit the stipulation (sum [tex]\leq[/tex] 5):
[tex]1,2,\\2,1\\1,3\\3,1\\1, 4\\4, 1\\2, 3, \\3,2[/tex]
There are 8 sums that work. Therefore, the desired answer is [tex]\frac{8}{12}=\boxed{\frac{2}{3}}[/tex]
Which of the following can be used to describe the following:
-20, – 17, – 14, – 11, ...
Geometric Series
Arithmetic Series
Geometric Sequence
Arithmetic Sequence
Answers
Answer: Arithmetic Sequence
Step-by-step explanation: It has a common difference of +3 at a constant rate
fourier { 2 if -2 < x < 0 ; 0 if 0 < x < 2}
Answers
The Fourier series expansion of f(x) is
[tex]\displaystyle\frac{a_0}2+\displaystyle\sum_{n=1}^\infty \left(a_n\cos\left(\frac{2\pi nx}P\right)+b_n\sin\left(\frac{2\pi nx}P\right)\right)[/tex]
where P = 4 is the period of f(x), and the coefficients are
[tex]a_0=\displaystyle\frac2P\int_{-2}^2f(x)\,\mathrm dx=2[/tex]
[tex]a_n=\displaystyle\frac2P\int_{-2}^2f(x)\cos\left(\frac{2\pi nx}P\right)\,\mathrm dx=\frac{2\sin(n\pi)}{n\pi}=0[/tex]
[tex]b_n=\displaystyle\frac2P\int_{-2}^2f(x)\sin\left(\frac{2\pi nx}P\right)\,\mathrm dx=\frac{2(\cos(n\pi)-1)}{n\pi}=\begin{cases}0&\text{for }n=2k\\-\frac4{(2k-1)\pi}&\text{for }n=2k-1\end{cases}[/tex]
(where k is a positive integer)
The series for f(x) reduces to
[tex]\displaystyle f(x)=1-\displaystyle\sum_{k=1}^\infty \frac4{(2k-1)\pi}\sin\left(\frac{\pi(2k-1)x}2\right)[/tex]
(I've attached a plot showing the original function in blue and the Fourier expansion with k = 10 terms)
The slope-intercept form of the equation of a line that passes through point (–3, 8) is y = –y minus 3 equals negative StartFraction 2 Over 3 EndFraction left-parenthesis x plus 8 right-parenthesis.x + 6. What is the point-slope form of the equation for this line?
y – 3 = –StartFraction 8 Over 5 EndFraction x plus StartFraction 2 Over 3 EndFraction equals StartFraction one-half EndFraction minus StartFraction 1 Over 5 EndFraction x.(x + 8)
y + 3 = –y plus 3 equals negative StartFraction 2 Over 3 EndFraction left-parenthesis x minus 8 right-parenthesis.(x – 8)
y + 8 = –y plus 8 equals negative StartFraction 2 Over 3 EndFraction left-parenthesis x minus 3 right-parenthesis.(x – 3)
y – 8 = –y minus 8 equals negative StartFraction 2 Over 3 EndFraction left-parenthesis x plus 3 right-parenthesis.(x + 3)
Answers
y – 8 = –y minus 8 equals negative StartFraction 2 Over 3 EndFraction left-parenthesis x plus 3 right-parenthesis.(x + 3)
Step-by-step explanation:
Help please asp. !!!
Answers
Answer:
12.86 cm³ of water is saved
Step-by-step explanation:
✔️Since width of new ice ball must be the same as the length of original cube, therefore, diameter of the ice ball = 3 cm
Radius of ice ball = ½(3) = 1.5 cm
Volume of the new sphere ice ball = ⁴/3πr³
Substitute
Volume of new sphere ice ball = ⁴/3 × π × 1.5³ = 14.14 cm³
✔️To find out how much water would be saved using the new sphere ice ball, let's find the volume of the cube then find the difference of both.
Volume of original ice cube with length 3 cm:
Volume of cube = s³
s = 3 cm
Volume of cube = 3³ = 27 cm³
Volume of water saved = 27 cm³ - 14.14 cm³
= 12.86 cm³
Find x round to the nearest degree?
Answers
i don't think this is complete question there isn't value for x
Help please, it’s for average rate of change.
Answers
Answer in fraction form = -3/2
Answer in decimal form = -1.5
=========================================
Work Shown:
[tex]m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(1)-g(-3)}{1-(-3)}\\\\m = \frac{0-6}{1-(-3)}\\\\m = \frac{0-6}{1+3}\\\\m = \frac{-6}{4}\\\\m = -\frac{3}{2}\\\\m = -1.5\\\\[/tex]
Effectively, we're finding the slope through the points (-3, 6) and (1, 0)
The g(b)-g(a) represents how y changes when going from x = a to x = b.
A cable network offers members a Basic plan for $7.26 per month. For $3.00 more per month, the cable network offers a Standard plan, which includes HD movies. During one week, 310 new subscribers paid a total of $2580.60 for their plans. How many Basic plans and how many Standard plans were purchased?
___Basic plans and ___ Standard plans were purchased
Answers
Answer:
110 basic plans and 200 standard plans were purchased.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
x is the number of basic plans.
y is the number of standard plans.
310 new subscribers
This means that [tex]x + y = 310[/tex], and so, [tex]y = 310 - x[/tex]
A cable network offers members a Basic plan for $7.26 per month. For $3.00 more per month. Total paid of $2580.60.
This means that:
[tex]7.26x + 10.26y = 2580.6[/tex]
Since [tex]y = 310 - x[/tex]
[tex]7.26x + 10.26(310 - x) = 2580.6[/tex]
[tex]7.26x + 3180.6 - 10.26x = 2850.6[/tex]
[tex]3x = 330[/tex]
[tex]x = \frac{330}{3}[/tex]
[tex]x = 110[/tex]
Then
[tex]y = 310 - x = 310 - 110 = 200[/tex]
110 basic plans and 200 standard plans were purchased.
Based on the family the graph below belongs to, which equation could represent the graph?
Answers
where is the graph????
Step-by-step explanation:
Find the value of unknown figure plz tell i will mark as brainliest
Answers
Answer:
1. [tex]2^{3}[/tex] x [tex]3^{6}[/tex]
ii. 18
b. -12
2. nth = a + (n - 1)d
ii. k = 103
3. [tex]x^{o}[/tex] = [tex]27^{o}[/tex]
4. Volume = 25.025 [tex]m^{3}[/tex]
Step-by-step explanation:
1. Prime factors of 5832 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3
= [tex]2^{3}[/tex] x [tex]3^{6}[/tex]
ii. [tex]\sqrt[3]{5832}[/tex] = 18
b. 2[tex]a^{2}[/tex] - 3[tex]b^{2}[/tex] + 3abc
a = 3, b = 2, c = -1
Thus,
2[tex](3)^{2}[/tex] - 3[tex](2)^{2}[/tex] + 3(3 x 2 x -1)
= 18 - 12 - 18
= -12
2. The required formula is;
nth = a + (n - 1)d
where: a is the first term, n is the number of terms in the sequence and d is the common difference.
b. kth term = 304, then
304 = -2 + (k - 1) 3
= -2 + 3k -3
= 3k - 5
3k = 304 + 5
3k = 309
k = [tex]\frac{309}{3}[/tex]
= 103
k = 103
3. Comparing <DAB and < EBC;
<DAB ≅ <EBC = [tex]x^{o}[/tex]
<BEC = [tex]90^{o}[/tex] (right angle property)
<C = [tex]63^{o}[/tex]
Thus,
<B + <C + <E = [tex]180^{o}[/tex] (sum of angles in a triangle)
[tex]x^{o}[/tex] + [tex]63^{o}[/tex] + [tex]90^{o}[/tex] = [tex]180^{o}[/tex]
[tex]x^{o}[/tex] + 153 = [tex]180^{o}[/tex]
[tex]x^{o}[/tex] = 180 - 153
= 27
[tex]x^{o}[/tex] = [tex]27^{o}[/tex]
4. Volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
where r is the radius and h is the height of the cylinder.
Diameter = 3.5 m, h = 2.6 m
r = [tex]\frac{3.5}{2}[/tex]
r = [tex]\frac{7}{4}[/tex] m
So that,
Volume = [tex]\frac{22}{7}[/tex] x [tex](\frac{7}{4}) ^{2}[/tex] x 2.6
= [tex]\frac{22}{7}[/tex] x [tex]\frac{49}{16}[/tex] x [tex]\frac{13}{5}[/tex]
= 25[tex]\frac{1}{40}[/tex]
Volume = 25.025 [tex]m^{3}[/tex]
Segment EG is an angle bisector of angle FGH. Noah wrote a proof to show that triangle HEG is congruent to triangle FEG. Noah's proof is not correct. Which line of Noah's proof is incorrect, and why1. Side EG is congruent to side EG because they're the same segment.
2. Angle EGH is congruent to angle EGF because segment EG is an angle bisector of angle FGH.
3. Angle HEG is congruent to angle FEG because segment EG is an angle bisector of angle FGH.
4. By the Angle-Side-Angle Triangle Congruence Theorem, triangle HEG is congruent to triangle FEG.
Line 2 is incorrect; there is not enough information given to state this.
Line 2 is incorrect; there is not enough information given to state this.
Line 2 is incorrect; even though segment EG is a bisector, angles EGH and FGH are not necessarily congruent.
Line 2 is incorrect; even though segment , EG, is a bisector, angles , EGH, and , FGH , are not necessarily congruent.
Line 3 is incorrect; we don't know anything about the lengths of HG, FG, HE, and EF, so this line is not valid based on the given information.
Line 3 is incorrect; we don't know anything about the lengths of , HG, , , FG, , , HE, , and , EF, , so this line is not valid based on the given information.
Line 4 is incorrect; Angle-Side-Angle is not a valid congruence theorem.
Line 4 is incorrect; Angle-Side-Angle is not a valid congruence theorem.
Answers
Answer:
Line 3 is incorrect; we don't know anything about the lengths of HG, FG, HE, and EF, so this line is not valid based on the given information.
Step-by-step explanation:
In the Noah's poof of the construction, segment EG would divide angle FGH into two equal parts, which makes line 2 to be valid. i.e <EGH ≅ <EGF. And it can also be observed that line 4 is a valid theorem in proving the congruent nature of triangles.
But line 3 is not valid because of the condition of the statement. Furthermore, segments FG, EG, HG, HE and FE may not be congruent. Thus, the condition of the statement in line 3 is incorrect.
Which system of equations can be used to find the roots of the equation 4x2 = x3.
ly=-4x²
ly=x²+2x
(y = x² - 4x² + 2x
»
O
ly=0
0
o y
Jy = 4x²
Lva-x-2x
ly=44²
ly=x²+2x
o
Answers
Answer:
The second answer
Y=X³-4X²+2X
Y=0
The system of equations can be used to find the roots of the given equation is y = 4x², y = x³+2x
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
For example, 3x – 5 = 16 is an equation.
Given is an equation, 4x² = x³+2x, we need to identify the system of equations can be used to find the roots of this,
An equality can be transformed in a system of equations by making each side equal to a new variable. In this case the variable y was made equal to each side.
See that may find the solution of such system by graphing both functions in a same coordinate system, where the intersection of the functions would show the solution of the system.
The attached image. In such graph, the red curve is the function y = x² and the blue function is y = x³ + 2x.
The intersection point is (0,0) meaning that the solution is x = 0, y = 0.
Hence, the system of equations can be used to find the roots of the given equation is y = 4x², y = x³+2x
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CAN SOMEONE HELP ME WITH THIS?!
Answers
Answer:
a = 14
b = 24
c = 24.9
A = 33.2 degrees
B = 70 degrees
C = 76.8 degrees
Step-by-step explanation:
a/sin(A) = b/sin(B) = c/sin(C)
14/sin(A) = 24/sin(70)
sin(A)×24 = sin(70)×14
sin(A) = sin(70)× 14/24 = sin(70) × 7/12 = 0.548154029...
A = asin(0.548154029...) = 33.240464... degrees
the sum of all angles in a triangle is airways 180 degrees.
C = 180 - 70 - 33.240464... = 76.75954... degrees
24/sin(70) = c/sin(76.75954...)
c = 24×sin(76.75954...)/sin(70) = 24.86133969...
can someone help me please?! I'll give brainlest for correct answer
Answers
1.) The answers:
A) BME
B) MER
C) Mm
D) xBy
E) Straight
F) REB
G) MEB and BER
H) xBy
A manufacturer claims that the mean lifetime,u , of its light bulbs is 51 months. The standard deviation of these lifetimes is 7 months. Sixty bulbs are selected at random, and their mean lifetime is found to be 53 months. Can we conclude, at the 0.1 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 51 months?
Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult a list of formulas.)
the null hypothesis:
The alternative hypotehsis:
The type of test statistic (choose Z, t, Chi-square, or F)
The value of the test statistic (round to at least three decimal places:
Can we conclude that the mean lifetime of the bulbs made by this manufacture differ from 51 months?
Answers
Answer:
We reject H₀, and conclude thet the mean lifetime of the bulbs differ from 51 month
Step-by-step explanation:
Manufacturing process under control must produce items that follow a normal distribution.
Manufacturer information:
μ = 51 months mean lifetime
σ = 7 months standard deviation
Sample Information:
x = 51 months
n = 60
Confidence Interval = 90 %
Then significance level α = 10 % α = 0.1 α/2 = 0,05
Since it is a manufacturing process the distribution is a normal distribution, and with n = 60 we should use a Z test on two tails.
Then from z- table z(c) for α = 0,05 is z(c) = 1.64
Hypothesis Test:
Null Hypothesis H₀ x = μ
Alternative Hypothesis Hₐ x ≠ μ
To calculate z statistics z(s)
z(s) = ( x - μ ) / σ /√n
z(s) = ( 53 - 51 ) / 7 /√60
z(s) = 2 * 7.746 / 7
z(s) = 2.213
Comparing z(s) and z(c)
z(s) > z(c) then z(s) is in the rejection region
We reject H₀, and conclude thet the mean lifetime of the bulbs differ from 51 month