Answer:[tex]z=a+bi=|z|(cos(θ)+isin(θ))tofindthtrigonometricform.√sin2(ga8A)+cos16(A)(cos(arctan(−1sin(ga8A)cos8(A)))+isin(arctan(−1sin(ga8A)cos8(A))))[/tex]
Step-by-step explanation:
In a mixture 60 liters, the ratio of milk and water 2:1.If this ratio is to be 1:2, then what is the quantity of water to be further added?
Answer:
Hello,
60L
Step-by-step explanation:
Quantity of water /Quantity of milk =2/1
Quantity of mixture= Quantity of water +Quantity of milk =60L
Quantity of milk =40 L
Quantity of water =20 L
Let say x the quantity of water to be added
New ratio =1/2=40/(20+x)
20+x=80 (cross products)
x=60 (L)
Solve each equation for the indicated variable. Solve for pi.
9514 1404 393
Answer:
π = 2A/r²
Step-by-step explanation:
Multiply by the inverse of the coefficient of π.
A = π(r²/2)
π = 2A/r²
What is the measure of the unknown angle?
Image of a straight angle divided into two angles. One angle is thirty five degrees and the other is unknown.
Answer:
145
Step-by-step explanation:
Angles in a straight line = 180
So,
Let unkown angle be x,
x+35=180
x=180-35
x=145
A random variable is not normally distributed, but it is mound shaped. It has a mean of 14 and a standard deviation of 3. If you take a sample of size 10, can you say what the shape of the sampling distribution for the sample mean is
Answer:
Step-by-step explanation:
from the question,
the mean 14
the standard deviation is 3
and sample size is 10.
since the n which is the sample size is 10, then the distribution is mound shaped.
why?
this is due to the fact that the random variable from which we took the sample is mound shaped.
The sampling distribution of the mean is normally distributed although the question says the random variable is not normally distributed. so the shape is bell shaped and normally distributed.
the standard deviation of the mean is
3/√10
= 0.948
Álgebra 2 need help
Answer:
first term = -1/5
I cant see part b (sorry its too blurry)
thirteenth term = -0.2
part d: -19a/95a -0.2a
Step-by-step explanation:
socratic
Write the function in terms of unit step functions. Find the Laplace transform of the given function. f(t) = 5, 0 ≤ t < 7 −3, t ≥ 7
Rewrite f in terms of the unit step function:
[tex]f(t)=\begin{cases}5&\text{for }0\le t<7\\-3&\text{for }t\ge7\end{cases}[/tex]
[tex]\implies f(t)=5(u(t)-u(t-7))-3u(t-7)=5u(t)-8u(t-7)[/tex]
where
[tex]u(t)=\begin{cases}1&\text{for }t\ge0\\0&\text{for }t<0\end{cases}[/tex]
Recall the time-shifting property of the Laplace transform:
[tex]L[u(t-c)f(t-c)]=e^{-cs}L[f(t)][/tex]
and the Laplace transform of a constant function,
[tex]L[k]=\dfrac ks[/tex]
So we have
[tex]L[f(t)]=L[5u(t)-8u(t-7)]=5L[1]-8e^{-7s}L[1]=\boxed{\dfrac{5-8e^{-7s}}s}[/tex]
In this exercise you have to find the laplace transform:
[tex]L[f(t)]=\frac{5-8e^{-7s}}{s}[/tex]
Rewrite f in terms of the unit step function:
[tex]f(t)=\left \{ {{5, for 0\leq t\leq 7} \atop {-3, for t\geq 7}} \right. \\f(t)= 5(u(t)-u(t-7)-3u(t-7)=5u(t)-8u(t-7)[/tex]
Where:
[tex]u(t)= \left \{ {{1, t\geq 0} \atop {0, t<0}} \right.[/tex]
Recall the time-shifting property of the Laplace transform:
[tex]L[u(t-c)f(t-c)]= e^{-cs}L[f(t)][/tex]
and the Laplace transform of a constant function,
[tex]L[k]=\frac{k}{s}[/tex]
So we have:
[tex]L[f(t)]= L[5u(t)-8u(t-7)]= 5L[1]-8e^{-7s}L[1]= \frac{5-8e^{-7s}}{s}[/tex]
See more about Laplace transform at : brainly.com/question/2088771
Write and solve a word problem involving a $145.00 price and a 5.5% sales tax.
Your question is not complete but I guess you want to know the total price to be paid. This will be:
= $145 + (5.5% × $145)
= $145 + (0.055 × $145)
= $145 + $7.975
= $152.975
For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.
(i) 242
(ii) 1280
(iii) 245
(iv)968
(v) 1728
(vi) 4851
Answer:
BELOW
Step-by-step explanation:
242: multiply it by 2 to get 484 and its square root is 22
1280: multiply it by 5 to get 6400 and its square root is 80.
245: multiply it by 5 to get 1225 and its square root is 35.
968: multiply it by 2 to get 1936 and its square root is 44.
1728: multiply it by 3 to get 5184 and its square root is 72
4851: multiply it by 11 to get 53361 and its square root is 231.
HOPE THIS HELPED
A research center poll showed that % of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief? 78 The probability that someone does not believe that it is morally wrong to not report all income on tax returns is . (Type an integer or a decimal.)
Question:
A research center poll showed that 78% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?
The probability that someone does not believe that it is morally wrong to not report all income on tax returns is . (Type an integer or a decimal.)
Answer:
[tex]q = 0.22[/tex]
Step-by-step explanation:
Given
Let p represent the given proportion
p = 78%
Required
Determine the probability that someone holds a contrary belief
Start by converting the given proportion to decimal
[tex]p = 78\%[/tex]
[tex]p = \frac{78}{100}[/tex]
[tex]p = 0.78[/tex]
In probability, the sum of opposite probability is equal to 1
Represent the probability that someone holds a contrary belief with q
So;
[tex]p + q = 1[/tex]
Make q the subject of formula
[tex]q = 1 - p[/tex]
Substitute 0.78 for p
[tex]q = 1 - 0.78[/tex]
[tex]q = 0.22[/tex]
Hence, the probability that someone does not believe is 0.22
What is the issue with the work? It is wrong. Please answer this for points!
Answer:
3 ( a ) : x = 3.6,
3 ( b ) : x = 5
Step-by-step explanation:
For 3a, we can calculate the value of x through Pythagorean Theorem, which seemingly was your approach. However, the right triangle with x present as the leg, did not have respective lengths 9.6 and 12. The right angle divides 9.6 into two congruent parts, making one of the legs of this right triangle 9.6 / 2 = 4.8. The hypotenuse will be 12 / 2 as well - as this hypotenuse is the radius, half of the diameter. Note that 12 / 2 = 6.
( 4.8 )² + x² = ( 6 )²,
23.04 + x² = 36,
x² = 36 - 23.04 = 12.96,
x = √12.96, x = 3.6
Now as you can see for part b, x is present as the radius. Length 3 forms a right angle with length 8, dividing 8 into two congruent parts, each of length 4. We can form a right triangle with the legs being 4 and 3, the hypotenuse the radius. Remember that all radii are congruent, and therefore x will be the value of this hypotenuse / radius.
( 4 )² + ( 3 )² = ( x )²,
16 + 9 = x² = 25,
x = √25, x = 5
1 A. All master photographers are artists.
2. Ansel Adams is a master photographer.
Therefore, Ansel Adams is an artist.
B. 1. All master photographers are artists.
2. Ansel Adams is an artist.
Therefore, Ansel Adams is a master photographer.
Answer:
A is the appropriate option.
Step-by-step explanation:
The question given is a conditional statement.
With the condition that all master photographers are artist. This implies that any person who is a master photographer is automatically an artist.
A. Comparing the statement here, since Ansel Adam's is a master photographer, he is an artist.
B. Ansel Adams is an artist, but it is possible that not all artists are master photographer.
A is the correct option.
1. All master photographers are artists.
2. Ansel Adams is a master photographer.
Therefore, Ansel Adams is an artist.
Answer:
The correct answer is A.
Step-by-step explanation:
help pls!!! Classify the following question: “President, vice president, and secretary are being chosen for the Environmental Club. In how many different ways can these three offices be filled from a list of ten members?”
the answer is: combation
if logx27 + logy4 =5
and logx27 - logy4 =1
find x and y
Answer:
Hello,
I have reply too quick in comments (sorry)
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}log_x (27)+log_y (4)=5\\log_x (27)-log_y (4)=1\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}2*log_x (27)=6\\2*log_y (4)=4\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}log_x (27)=3\\log_y (4)=2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x^{log_x (27)}=x^3\\y^{log_y (4)}=y^2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}27=x^3\\4=y^2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x=3\\y=2\\\end{array}\right.\\\\[/tex]
a college entrance exam company determined that a score of 25 on the mathematics portion of the exam suggests that a student is ready for
Answer:
Student is ready for college level mathematics.
The null hypothesis will be H0 = 25
The alternative hypothesis is Ha > 25
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the z - score for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence to test a hypothesis.
The perimeter of a rectangle is 80 inches, if the width is 18 inches what is the area of the rectangle? A.22 sq.in B.324 sq.in C.396 sq.in D.6,400 sq.in
Answer:
396 in^2
Step-by-step explanation:
The perimeter of a triangle is given by the formula:
● P = 2w+2L
L is the length and w is the width
■■■■■■■■■■■■■■■■■■■■■■■■■■
The width hereis 18 inches and the perimeter is 80 inches.
Replace w by 18 and P by 80 to find L.
● P= 2L+2w
● 80 = 2L + 2×18
● 80 = 2L + 36
Substrat 36 from both sides
● 80-36 = 2L+36-36
●44 = 2L
Divide both sides by 2
● 44/2 = 2L/2
● 22 = L
So the length is 22 inches
■■■■■■■■■■■■■■■■■■■■■■■■■■
The area of a rectangle is given by the formula:
● A= L×w
● A = 22×18
● A = 396 in^2
The Colonel spots a campfire at a bearing N 59∘59∘ E from his current position. Sarge, who is positioned 242 feet due east of the Colonel reckons the bearing to the fire to be N 34∘34∘ W from his current position.
Determine the distance from the campfire to each man, rounded to the nearest foot.
Colonel is about............................ feet away from the fire
Sarge is about............................... feet away from the fire
Answer:
i. Colonel is about 201 feet away from the fire.
ii. Sarge is about 125 feet away from the fire.
Step-by-step explanation:
Let the Colonel's location be represented by A, the Sarge's by B and that of campfire by C.
The total angle at the campfire from both the Colonel and Sarge = [tex]59^{0}[/tex] + [tex]34^{0}[/tex]
= [tex]93^{0}[/tex]
Thus,
<CAB = [tex]90^{0}[/tex] - [tex]59^{0}[/tex] = [tex]31^{0}[/tex]
<CBA = [tex]90^{0}[/tex] - [tex]34^{0}[/tex] = [tex]56^{0}[/tex]
Sine rule states;
[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{b}{Sin B}[/tex] = [tex]\frac{c}{Sin C}[/tex]
i. Colonel's distance from the campfire (b), can be determined by applying the sine rule;
[tex]\frac{b}{Sin B}[/tex] = [tex]\frac{c}{Sin C}[/tex]
[tex]\frac{b}{Sin 56^{0} }[/tex] = [tex]\frac{242}{Sin 93^{0} }[/tex]
[tex]\frac{b}{0.8290}[/tex] = [tex]\frac{242}{0.9986}[/tex]
cross multiply,
b = [tex]\frac{0.8290*242}{0.9986}[/tex]
= 200.8993
Colonel is about 201 feet away from the fire.
ii. Sarge's distance from the campfire (a), can be determined by applying the sine rule;
[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{c}{Sin C}[/tex]
[tex]\frac{a}{Sin 31^{0} }[/tex] = [tex]\frac{242}{Sin 93^{0} }[/tex]
[tex]\frac{a}{0.5150}[/tex] = [tex]\frac{242}{0.9986}[/tex]
cross multiply,
a = [tex]\frac{0.5150*242}{0.9986}[/tex]
= 124.8073
Sarge is about 125 feet away from the fire.
1. Approximate the given quantity using a Taylor polynomial with n3.
2. Compute the absolute error in the approximation assuming the exact value is given by a calculator.
Fourth underroot(94)
a. p3(94)
b. absolute error
Answer:
See the explanation for the answer.
Step-by-step explanation:
Given function:
[tex]f(x) = x^{1/4}[/tex]
The n-th order Taylor polynomial for function f with its center at a is:
[tex]p_{n}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(n)}a}{n!} (x-a)^{n}[/tex]
As n = 3 So,
[tex]p_{3}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(3)}a}{3!} (x-a)^{3}[/tex]
[tex]p_{3}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(3)}a}{6} (x-a)^{3}[/tex]
[tex]p_{3}(x) = a^{1/4} + \frac{1}{4a^{ 3/4} } (x-a)+ (\frac{1}{2})(-\frac{3}{16a^{7/4} } ) (x-a)^{2} + (\frac{1}{6})(\frac{21}{64a^{11/4} } ) (x-a)^{3}[/tex]
[tex]p_{3}(x) = 81^{1/4} + \frac{1}{4(81)^{ 3/4} } (x-81)+ (\frac{1}{2})(-\frac{3}{16(81)^{7/4} } ) (x-81)^{2} + (\frac{1}{6})(\frac{21}{64(81)^{11/4} } ) (x-81)^{3}[/tex]
[tex]p_{3} (x)[/tex] = 3 + 0.0092592593 (x - 81) + 1/2 ( - 0.000085733882) (x - 81)² + 1/6
(0.0000018522752) (x-81)³
[tex]p_{3} (x)[/tex] = 0.0092592593 x - 0.000042866941 (x - 81)² + 0.00000030871254
(x-81)³ + 2.25
Hence approximation at given quantity i.e.
x = 94
Putting x = 94
[tex]p_{3} (94)[/tex] = 0.0092592593 (94) - 0.000042866941 (94 - 81)² +
0.00000030871254 (94-81)³ + 2.25
= 0.87037 03742 - 0.000042866941 (13)² + 0.00000030871254(13)³ +
2.25
= 0.87037 03742 - 0.000042866941 (169) +
0.00000030871254(2197) + 2.25
= 0.87037 03742 - 0.007244513029 + 0.0006782414503 + 2.25
[tex]p_{3} (94)[/tex] = 3.113804102621
Compute the absolute error in the approximation assuming the exact value is given by a calculator.
Compute [tex]\sqrt[4]{94}[/tex] as [tex]94^{1/4}[/tex] using calculator
Exact value:
[tex]E_{a}[/tex](94) = 3.113737258478
Compute absolute error:
Err = | 3.113804102621 - 3.113737258478 |
Err (94) = 0.000066844143
If you round off the values then you get error as:
|3.11380 - 3.113737| = 0.000063
Err (94) = 0.000063
If you round off the values up to 4 decimal places then you get error as:
|3.1138 - 3.1137| = 0.0001
Err (94) = 0.0001
Does artistic ability determine which type of operating system a person prefers? Suppose that a market research company randomly selected n=259 adults who used a desktop or laptop outside of the workplace (tablets and smartphones were excluded).
Answer:
Your question lacks some parts attached below is the complete question
Answer : 2.66
Step-by-step explanation:
The expected number ( E ) can be calculated using the formula below
[tex]E = \frac{row total * column total }{gross total}[/tex]
since we are computing the number of subjects that would prefer Linux operating system and are also rated as exceptional
The row total to be used = 53 ( row total of exceptional )
The column total to be used = 13 ( column total of Linux )
The gross total to be used = summation of row total of both exceptional and no-exceptional = 259
BACK TO THE EQUATION
E = [tex]\frac{53*13}{259}[/tex] = 689 / 259
E = 2.6602 ≈ 2.66
What is the equation of the sinusoid?
Answer:
Hello,
Answer A
Step-by-step explanation:
if x=0 then sin(2*0)=sin(0)=0
if x= π/4 then sin(π/2)=1
if x= π/2 then sin(π)=0
The equation of the sinusoid will be y=Sin(2x)
What is an equation?It is defined as the relation between two variables, for a sinusoidal wave the equation will be in the form of Sin or Cos.
if x=0 then sin(2*0)=sin(0)=0
if x= π/4 then sin(π/2)=1
if x= π/2 then sin(π)=0
Hence the equation of the sinusoid will be y=Sin(2x)
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If why varies with the square of x and Y equals 24 when x equals 10 then the constant of proportionality is ____, and the value of y when x equals 20 is ____. Assume x is greater than or equal to 0. Select two answers
Answer:
Step-by-step explanation:
y varies with the square of x:
y = kx²
y equals 24 when x equals 10
24 = k·10²
constant of proportionality k = 0.24
when x = 20, y = 0.24·20² = 96
"select two answers" —where are the choices?
What is the volume of this rectangular pyramid?
_____ cubic millimeters
Answer:
Step-by-step explanation:
L = 9 mm
W = 9 mm
H = 10 mm
volume = LWH/3 = 9·9·10/3 = 270 mm³
Need help finding the value for A
Answer:
[tex]\text{n}(A \bigcup B)[/tex] = 6.
Step-by-step explanation:
We are given that n(A) = 4, n(B) = 5, and [tex]\text{n}(A \bigcap B)[/tex] = 3.
And we have to find the value of [tex]\text{n}(A \bigcup B)[/tex].
As we know that the union formula is given by;
[tex]\text{n}(A \bigcup B) = \text{n}(A) + \text{n}(B) - \text{n}(A \bigcap B)[/tex]
Now, substituting the values given in the question in the above formula, we get;
[tex]\text{n}(A \bigcup B) = 4+5-3[/tex]
[tex]\text{n}(A \bigcup B) = 9-3[/tex]
[tex]\text{n}(A \bigcup B) = 6[/tex]
Hence, the value of [tex]\text{n}(A \bigcup B)[/tex] = 6.
A triangle has vertices at (-4,-6),(3,3),(7,2). Rounded to two decimal places, which of the following is closest aporoximation of the perimeter of the triangle
Answer:
Perimeter= 29.12 unit
Step-by-step explanation:
Perimeter of the triangle is the length of the three sides if the triangle summef up together
Let's calculate the length of each side.
For (-4,-6),(3,3)
Length= √((3+4)²+(3+6)²)
Length= √((7)²+(9)²)
Length= √(49+81)
Length= √130
Length= 11.40
For (-4,-6),(7,2)
Length= √((7+4)²+(2+6)²)
Length= √((11)²+(8)²)
Length= √(121+64)
Length= √185
Length= 13.60
For (3,3),(7,2)
Length=√( (7-3)²+(2-3)²)
Length= √((4)²+(-1)²)
Length= √(16+1)
Length= √17
Length= 4.12
Perimeter= 4.12+13.60+11.40
Perimeter= 29.12 unit
What is (-i)^6 ? Please don’t guess. Thanks
Answer:
-1
Step-by-step explanation:
Hello, please consider the following.
[tex](-i)^6=(-1)^6\cdot(i^2)^3=1\cdot (-1)^3=\boxed{-1}\\[/tex]
Thank you
2/3a - 1/6 =1/3 please help me
Answer:
[tex]a = \frac{3}{4}[/tex]
Step-by-step explanation:
Let's convert everything to sixths to make it easier to work with.
[tex]\frac{4}{6}a - \frac{1}{6} = \frac{2}{6}[/tex]
Add 1/6 to both sides:
[tex]\frac{4}{6}a = \frac{3}{6}[/tex].
Dividing both sides by 4/6:
[tex]a = \frac{3}{6} \div \frac{4}{6}\\\\a = \frac{3}{6} \cdot \frac{6}{4}\\\\a = \frac{18}{24}\\\\a = \frac{3}{4}[/tex]
Hope this helped!
Last year, Rob set up the Road Runner Race for his school.
The race was 1,200 meters long and 188 people signed up to
run the race. 38 people did not show up to run. This year,
there will be 3 times as many runners as last year. How
many people will run the race this year?
Answer:
450 runners
Step-by-step explanation:
Write the equation of the line shown in the graph above in slope intercept form
A) y=2/3x+1
B) y=-x+2/3
C) y=-2/3x+1
D) 2x+3y=3
Answer:
C, y=-2/3x+1
Step-by-step explanation:
using points (0, 1) and (3, -1) obtained from the graph:
slope = -1-1/3-0 = -2/3
use one of the points above lets take (1, 0) and another point (x,y)
slope = y-0/x-1 = -2/3
y=-2/3x+1
simplify use the multiplication rule
Answer:
3
Step-by-step explanation:
[tex] \sqrt[4] {27} \cdot \sqrt[4] {3} = [/tex]
[tex] = \sqrt[4] {27 \cdot 3} [/tex]
[tex] = \sqrt[4] {3^3 \cdot 3^1} [/tex]
[tex] = \sqrt[4] {3^4} [/tex]
[tex] = 3 [/tex]
How do you solve an expansion?
[tex]\displaystyle\\(a+b)^n\\T_{r+1}=\binom{n}{r}a^{n-r}b^r\\\\\\(x+2)^7\\a=x\\b=2\\r+1=5\Rightarrow r=4\\n=7\\T_5=\binom{7}{4}x^{7-4}2^4\\T_5=\dfrac{7!}{4!3!}\cdot x^3\cdot16\\T_5=16\cdot \dfrac{5\cdot6\cdot7}{2\cdot3}\cdot x^3\\\\T_5=560x^3[/tex]
Answer:
[tex]\large \boxed{560x^3}[/tex]
Step-by-step explanation:
[tex](x+2)^7[/tex]
Expand brackets.
[tex](x+2) (x+2) (x+2) (x+2) (x+2) (x+2) (x+2)[/tex]
[tex](x^2 +4x+4) (x^2 +4x+4) (x^2 +4x+4)(x+2)[/tex]
[tex](x^4 +8x^3 +24x^2 +32x+16)(x^3 +6x^2 +12x+8)[/tex]
[tex]x^7 +14x^6 +84x^5 +280x^4 +560x^3 +672x^2 +448x+128[/tex]
The fifth term is 560x³.
A manufacturer knows that their items have a lengths that are skewed right, with a mean of 5.1 inches, and standard deviation of 1.1 inches. If 49 items are chosen at random, what is the probability that their mean length is greater than 4.8 inches? How do you answer this with the answer rounded 4 decimal places?
Answer:
0.9719
Step-by-step explanation:
Find the mean and standard deviation of the sampling distribution.
μ = 5.1
σ = 1.1 / √49 = 0.157
Find the z score.
z = (x − μ) / σ
z = (4.8 − 5.1) / 0.157
z = -1.909
Use a calculator to find the probability.
P(Z > -1.909)
= 1 − P(Z < -1.909)
= 1 − 0.0281
= 0.9719
The probability of the randomly used item mean length is greater than 4.8 inches is 0.9719
What is Probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
What is Standard deviation?In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values.
What is Mean?The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.
Given,
Mean = 5.1 inches
Standard deviation = 1.1 inches
Sample size = 49
New mean = 4.8
Z score = Difference in mean /(standard deviation / [tex]\sqrt{sample size}[/tex])
Z score = [tex]\frac{4.8-5.1}{1.1/\sqrt{49} }=-1.909[/tex]
Z score = -1.909
Then the probability
P(Z>-1.909)
=1-P(Z>-1.909)
=1-0.0281
=0.9719
Hence, The probability of the randomly used item mean length is greater than 4.8 inches is 0.9719
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