Given:
The system of equations is [tex]y=-\frac{3}{2}x+12[/tex] and [tex]y=5x+28[/tex]
We need to determine the solution to the system of equations.
Solution:
The solution to the system of equations is the point of intersection of these two lines.
Let us solve the system of equations using substitution method.
Thus, we have;
[tex]5x+28=-\frac{3}{2}x+12[/tex]
Simplifying, we get;
[tex]\frac{13}{2}x+28=12[/tex]
[tex]\frac{13}{2}x=-16[/tex]
[tex]13x=-32[/tex]
[tex]x=-2.462[/tex]
Thus, the value of x is -2.462
Substituting x = -2.462 in the equation [tex]y=5x+28[/tex], we get;
[tex]y=5(-2.462)+28[/tex]
[tex]y=-12.31+28[/tex]
[tex]y=15.69[/tex]
Thus, the value of y is 15.69.
Therefore, the solution to the system of the equations is (-2.462, 15.69)
What is a difference of squares that has a factor of x+8?
Answer:
x^2 - 64
Step-by-step explanation:
A difference of squares is a special product in the form (a^2 - b^2)..their factored form is (a - b)(a + b)..
Thus here a = x and b = 8, thus if x + 8 is a factor, then x - 8 is also a factor..
(x + 8)(x - 8) <-- expand this out using difference of squares rules..
= (x)^2 - (8)^2
= x^2 - 64 <-- answer...
You could also expand that using FOIL (FOIL - first, outer, inner, last)..
(x + 8)(x - 8)
= (x)(x) + (x)(-8) + (8)(x) + (8)(-8)
= x^2 - 8x + 8x - 64 <-- the -8x and 8x cancels out..leaving you with..
= x^2 - 64
The difference of squares that has a factor of x+8 is x² - 64.
What is Algebraic Identity?An algebraic identity is an equality that holds for any values of its variables.
For example, the identity ( x + y )² = x² + 2xy + y²
(x+y)² = x² + 2xy + y²
(x+y)²=x²+2xy+y² holds for all values of x and y.
As, Difference of two squares
x² - y² = (x - y)(x + 8)
So, for difference of squares that has (x -8) as one of the factor.
The other factor is (x + 8)
So, we can write
(x - 8)(x + 8) = x² - 8²
= x² - 64.
Learn more about Algebraic Identity here:
https://brainly.com/question/28853516
#SPJ6
A 95% confidence interval for the proportion of students achieving a reading achievement score that is above the standard set by the teachers for a population of third grade students is (0.43, 0.49).
The margin of error of this interval is:
Group of answer choices
0.05
0.03
0.06
None of the above
Which statement correctly compares the ratios?
The ratio 9 to 12 is greater than 4 to 6.
The ratio 9 to 12 is less than 4 to 6.
O The ratio 9 to 12 is equal to 4 to 6.
The ratios cannot be compared.
HIERE
Answer:
its 9 to 12 is greater than 4 to 6.
Step-by-step explanation:
As per the given question, the correct option is the ratio 9 to 12 is greater than 4 to 6.
Explanation:In comparing the ratios 9 to 12 and 4 to 6, we first need to simplify both ratios. The ratio 9 to 12 can be simplified by dividing both numbers by their greatest common divisor, which is 3. This gives us a simplified ratio of 3 to 4.
Similarly, the ratio 4 to 6 can be simplified by dividing both numbers by their greatest common divisor, which is 2, giving us a simplified ratio of 2 to 3.
If we convert both ratios to decimals by dividing the first number by the second in each pair, we'll find that 9/12 = 0.75 and 4/6 = 0.67, which shows that the first ratio is greater. Therefore, we find that the correct statement is the ratio 9 to 12 is greater than 4 to 6.
Learn more about Ratios Comparison here:https://brainly.com/question/33628538
#SPJ3
Please help with this question!!?
Answer:
6 seconds
Step-by-step explanation:
The ball will hit the ground when its height is 0, so you can plug this into the equation to find your answer.
-16t^2+96t=0
Factoring out -16t, you get:
-16t(t-6), meaning that the solutions are 0 and 6 seconds. Since 0 is the starting point, the answer is 6 seconds. Hope this helps!
Given a polynomial f(x), if (x + 2) is a factor, what else must be true? f(0) = 2 f(0) = −2 f(2) = 0 f(−2) = 0
Answer:
f(-2) = 0
Step-by-step explanation:
If x + 2 is a factor, then f(x) = 0 when x + 2 = 0.
x + 2 = 0
x = -2
f(-2) = 0
For the polynomial, f(0) = 2 and f(-2) = 0.
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given x+2 is a factor,
And values of x from the options are x = 0, -2 and 2.
We will put the values of x to the factor,
f(0) = 0 +2 = 2
f(-2) = -2 +2 = 0
f(2) = 4
Therefore from the result only two options satisfy the factor and those are f(0) = 2 and f(-2) = 0.
To learn more about the Polynomials;
brainly.com/question/11536910
#SPJ2
A probability experiment is conducted in which the sample space of the experiment is
Upper S equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 comma 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSetS={7,8,9,10,11,12,13,14,15,16,17,18}.
Let event
Upper E equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 EndSetE={7,8,9,10,11,12}.
Assume each outcome is equally likely. List the outcomes in
Upper E Superscript cEc.
Find
?P(Upper E Superscript cEc?).
The outcomes in
Upper E Superscript cEc
are
StartSet nothing EndSet{}.
?(Use a comma to separate answers as? needed.)
?P(Upper E Superscript cEc?)equals=nothing
?(Type an integer or a simplified? fraction.)
Answer:
a) Eᶜ = {13,14,15,16,17,18}
The outcomes in Upper E Superscript c equals StartSet 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet
b) P(Eᶜ) = (1/2) = 0.5
P(Upper E Superscript c) = (1/2) equals 0.5
Step-by-step explanation:
The set that represents the universal set with all the sample spaces is set S and is given by
Upper S equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 comma 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet
S = {7,8,9,10,11,12,13,14,15,16,17,18}
Upper E equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 EndSet
Event E = {7,8,9,10,11,12}
a) Find Eᶜ
Eᶜ is the complement of event E; it includes all the outcomes in the universal set, S, that are not in the event E
Eᶜ = {13,14,15,16,17,18}
The outcomes in Upper E Superscript c equals StartSet 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet
b) P(Upper E Superscript c) = P(Eᶜ)
= n(Eᶜ) ÷ n(S)
Each outcome is equally likely, hence,
n(Eᶜ) = number of outcomes in the event Eᶜ = 6
n(S) = number of outcomes in the set S = 12
P(Eᶜ) = (6/12) = (1/2) = 0.5
Hope this Helps!!!
A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7 vinegar, and the second brand contains 12 vinegar. The chef wants to make 390 milliliters of a dressing that is 11 vinegar. How much of each brand should she use
Answer:
78 ml of 7% vinegar and 312 ml of 12% vinegar.
Step-by-step explanation:
Let x represent ml of 7% vinegar brand and y represent ml of 12% vinegar brand.
We have been given that chef wants to make 390 milliliters of the dressing. We can represent this information in an equation as:
[tex]x+y=390...(1)[/tex]
[tex]y=390-x...(1)[/tex]
We are also told that 1st brand 7% vinegar, so amount of vinegar in x ml would be [tex]0.07x[/tex].
The second brand contains 12 vinegar, so amount of vinegar in y ml would be [tex]0.12y[/tex].
We are also told that the chef wants to make 390 milliliters of a dressing that is 11% vinegar. We can represent this information in an equation as:
[tex]0.07x+0.12y=390(0.11)...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]0.07x+0.12(390-x)=390(0.11)[/tex]
[tex]0.07x+46.8-0.12x=42.9[/tex]
[tex]-0.05x+46.8=42.9[/tex]
[tex]-0.05x+46.8-46.8=42.9-46.8[/tex]
[tex]-0.05x=-3.9[/tex]
[tex]\frac{-0.05x}{-0.05}=\frac{-3.9}{-0.05}[/tex]
[tex]x=78[/tex]
Therefore, the chef should use 78 ml of the brand that contains 7% vinegar.
Upon substituting [tex]x=78[/tex] in equation (1), we will get:
[tex]y=390-78[/tex]
[tex]y=312[/tex]
Therefore, the chef should use 312 ml of the brand that contains 12% vinegar.
Josh has a drawer full of unmatched socks. There are 3 purple socks, 2 blue socks, 6 black socks, 4 brown socks, 5 yellow socks. If he reaches in his drawer, what is the probability of him drawing out a purple sock?Immersive Reader (9 Points) 1/5 2/5 3/5 3/20
Answer:
3/20
Step-by-step explanation:
because there is only 3 purple socks out of 20 socks total
The volume of a cube is given by the expression s to the power of 3, and its surface area is given by the expression 6s to the power of 2, where s is the length of the cube’s side. What is the volume of a cube with a side length of 5 inches?
Answer:
The volume of the cube would be 125in³
Step-by-step explanation:
The volume of a cube is s³ (side). 5 x 5 x 5 = 125.
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. Step 2 of 2 : Suppose a sample of 1291 tenth graders is drawn. Of the students sampled, 1098 read above the eighth grade level. Using the data, construct the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.
Answer:
The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.13, 0.168).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
1291 tenth graders, 1098 read above the eighth grade level.
1291 - 1098 = 193 read at or below this level.
We want the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level.
So [tex]n = 1291, \pi = \frac{193}{1291} = 0.149[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.149 - 1.96\sqrt{\frac{0.149*0.851}{1291}} = 0.13[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.149 - 1.96\sqrt{\frac{0.149*0.851}{1291}} = 0.168[/tex]
The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.13, 0.168).
Finish the following proof for Theorem 1.4.12. Assume B is a countable set. Thus, there exists f : N -+ B, which is 1-1 and onto. Let A ~ B be an infinite subset of B. We must show that A is countable. Let nI = min{n EN: f(n) E A}. As a start to a definition of g: N -+ A, set g(l) = f(nI). Show how to inductively continue this process to produce a 1-1 function 9 from N onto A.
Answer:
A is a countable set
Step-by-step explanation:
Assume B is a countable set, Go through the attached file for a detailed step by step explanation of the proof that A is a countable set.
The ratios in an equivalent ratio table are 3:12, 4:16, and 5:20. If the first number in the ratio is 10, what is the second number?
Answer:
The second number is 40
Step-by-Step:
There is a pattern in the ratio table: you need to multiply the first number by 4, and the answer is the second number. So if the first number is 10, you will need to multiply that by 4 to get the second number. So the second number is 40
Suppose that $4000 is deposited at 2% compounded quarterly. How much money will be in the account at the end of 6 years?
Answer:
$4,508.64
Step-by-step explanation:
The compound interest formula can answer this for you.
A = P(1 +r/n)^(nt)
where A is the account balance, P is the principal invested (4000), r is the annual interest rate (.02), n is the number of times per year interest is compounded (4), and t is the number of years (6).
Putting the given values into the formula, doing the arithmetic tells us ...
A = $4000(1 +.02/4)^(4·6) = $4000·1.005^24 ≈ $4,508.64
There will be $4,508.64 in the account at the end of 6 years.
Find the area of a sector of a circle whose radius is 7 cm and whose central angle is 45
degrees. Use pi = 3.14.
Answer:
The area of a sector of a circle = 19.2325
Step-by-step explanation:
Explanation:-
Given θ be the measure of angle and radius of circle
The area of a sector of a circle (see diagram)
[tex]A = \frac{theta}{360} \pi r^{2}[/tex]
Given the radius of circle 'r' = 7cm and given angle θ = 45°
The area of a sector of a circle
[tex]A = \frac{45}{360} \pi( 7)^{2}[/tex]
Use pi =3.14
[tex]A = \frac{45X 3.14( 7)^{2}}{360}[/tex]
A = 19.2325
Final answer:-
The area of a sector of a circle = 19.2325
45 POINTS! NEED HELP QUESTION IS A IMAGE.
A portion of the Quadratic Formula proof is shown. Fill in the missing statement.
Statements Reasons
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative 4 times a times c all over 4 times a squared plus b squared over 4 a squared Find a common denominator on the right side of the equation
x squared plus b over a times x plus the quantity b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Add the fractions together on the right side of the equation
the quantity x plus b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Rewrite the perfect square trinomial on the left side of the equation as a binomial squared
? Take the square root of both sides of the equation
x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c end quantity, all over 4 times a squared
x plus b over 2 times a all squared equals plus or minus b squared minus 4 times a times c, all over 4 times a squared all squared
the square root of x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 4 times a squared
x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 4 times a squared
Answer:
Take the square root of each side
D (x+b/2a) =±sqrt( (b^2-4ac)/ 4a^2)
Step-by-step explanation:
We have
(x+b/2a) ^2 = (b^2-4ac)/ 4a^2
We need to take the square root of each side to continue to isolate x
(x+b/2a) =±sqrt( (b^2-4ac)/ 4a^2)
Answer:
Option 3
Step-by-step explanation:
[x + b/2a]² = (b² - 4ac)/4a²
Taking square root both sides, you get this:
x + b/2a = +/- sqrt(b² - 4ac)/2a
Remember we're trying to make x the subject,
So does get rid of the square by applying square root both sides
Item 6
Simplify the expression.
p^5⋅p^2
Answer:
p^7
Step-by-step explanation:
p^5⋅p^2 = p ^(5+2) = p^7
Scientists measure how much water and debris flows past a river station at different time of the year. The water and debris are called discharge. the table show the average discharge at a research station on a certain river in 2 months. How many more quarts of discharge per second are there in march than February? How many quarts of discharge per second were recorded in march and February. There are blank more quarts per second in march and February
Answer:
2664
Step-by-step explanation:
(2285gallons - 1619gallons) =
666 gallons * 4quarts(in a gallon) =
2664 Quarts
HELP ASAP PLEASE
What type of graph would have the title, "Daily Low Temperatures Last Week"?
a. stem-and-leaf plot
b. line graph
c. bar graph
d. line plot
Answer:
line graph
Step-by-step explanation:
I've been trying this for days I can't get my head round it any help would be appreciated.
The one line of symmetry is vertical, so we could fold the hexagon in half in such a way that the vertices A and B would meet at the same point, and the same goes for the pairs C,F and D,E. Because of this symmetry, we know angle AFE is congruent to BCD, and angle FED is congruent ot CDE.
Let x be the measure of angle CDE.
In any convex polygon with n sides, the interior angles sum to (n - 2)*180º in measure. ABCDEF is a hexagon, so n = 6.
We have 2 angles of measure 123º, 2 of measure x, and 2 of measure 2x. So
2(123º + x + 2x ) = (6 - 2)*180º
246º + 2x + 4x = 720º
6x = 474º
x = 79º
Angle AFE is congruent to angle BCD, which is twice the measure of CDE, so angle AFE has measure 2*79º = 158º.
Two candidates ran for class president. The candidate that won received 80% of the 290 total votes. How many votes did the winning candidate receive?
Answer:
232 total votes
Step-by-step explanation:
change 80% to a decimal.... .8 and then multiply that by 290
Answer:
232
Step-by-step explanation:
80% of 290 is 232
290-232 is 58
20% of 290 is 58
A new postsurgical treatment was compared with a standard treatment. Eight subjects received the new treatment, while eight others (the controls) received the standard treatment. The recovery times, in days, are given below.
New Treatment Standard
12 18
13 23
15 24
19 30
20 32
21 35
24 39
Can you conclude that the mean recovery time for those receiving the new treatment differs from the mean for those receiving the standard treatment.
Answer:
1323
Step-by-step explanation:
Alton High School sold adult and student tickets for a school play. Of the 128 tickets sold, 84 were student tickets. What percent of the total tickets sold, rounded to the nearest percent, were adult tickets?
Answer:
66%Step-by-step explanation:
84/128=.65625
.65625x100=65.625=66%
Final answer:
To calculate the percentage of adult tickets sold for the school play, subtract the student tickets from the total tickets sold to find the number of adult tickets (44), and then divide by the total number of tickets and multiply by 100 to get the percentage, which is approximately 34%.
Explanation:
The question asks us to find what percent of the total tickets sold at a school play were adult tickets. Alton High School sold a total of 128 tickets, of which 84 were student tickets. To calculate the number of adult tickets, we subtract the number of student tickets from the total number of tickets: 128 - 84 = 44 adult tickets.
Next, we calculate the percent of adult tickets out of the total tickets sold by using the formula:
Percent = (Number of adult tickets / Total number of tickets) imes 100
Plugging in our numbers, we get:
Percent = (44 / 128) imes 100
Percent = 0.34375 imes 100
Percent ≈ 34%
Rounded to the nearest percent, we find that approximately 34% of the tickets sold were for adults.
On Saturday, Cannor drives 62 1/4 miles each hour. If he travels 4 hours, how many miles does he travel altogether?
Final answer:
To find the total distance Cannor travels, multiply his hourly distance of 62 1/4 miles by the total travel time of 4 hours, resulting in 249 miles.
Explanation:
The question asks about calculating the total distance traveled by Cannor on Saturday. Since Cannor drives 62 1/4 miles each hour and travels for 4 hours, we can find the total distance by multiplying the number of miles driven in an hour by the number of hours traveled.
To calculate this, convert 62 1/4 to an improper fraction which is 249/4 and multiply it by 4 (the number of hours):
Total Distance = (249/4 miles/hour) × 4 hours
When we do the multiplication, the hours unit cancels out and we get:
Total Distance = 249 miles
This calculation shows how far Cannor will travel altogether if he maintains his speed for the entire duration of his trip.
Marcela took out a $600 discount loan with a 4% annual interest rate over a period of 8 months. How much money does marcela get from the bank when she receives the loan? Round to the nearest dollar.
Answer:
Step-by-step explanation:
4 % of 600 over 8 months is 16
600-16=584
Students arrive randomly at the help desk of the computer lab. There is only one service agent, and the time required for inquiry varies from student to student. Arrival rates have been found to follow the Poisson distribution, and the service times follow the negative exponential distribution. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. On average, how long does it take to service each student?
Considering Poissoniated student arrivals and exponential service times in a queueing situation, with an average service rate of 20 students per hour, it takes on average 3 minutes to service each student.
Explanation:
The student's question pertains to the field of queueing theory, more specifically dealing with Poisson arrivals and exponential service time. In this context, the given arrival rate (λ) is 12 students per hour and the service rate (μ) is 20 students per hour.
Since the service rate is provided in terms of how many students can be serviced per hour (20 students per hour), to find the average service time for each student, we take the reciprocal of the service rate.
Therefore, average service time = 1/μ = 1/20 = 0.05 hours per student.
Note that 0.05 hours is equivalent to 3 minutes, hence on average, it takes 3 minutes to service each student.
Learn more about Poisson Arrivals and Service Times here:https://brainly.com/question/37190818
#SPJ11
a whole number is squared. the result is between 200 and 260. the number is between?
Final answer:
The whole number squared resulting in a number between 200 and 260 must have the original whole number between 15 and 16.
Explanation:
If a whole number is squared and the result is between 200 and 260, we must determine which whole numbers will yield a square within that range. We find the square roots of both 200 and 260 to identify the range of whole number bases. The square root of 200 is approximately 14.14, and the square root of 260 is approximately 16.12. Therefore, the number must be greater than 14 but less than or equal to 16 because squaring whole numbers greater than 16 gives results exceeding 260. Hence, the number is between 15 and 16.
5x+9=24 solve the equation
Answer:
x=3
Step-by-step explanation:
24-9
15/5
3
x=3
Answer:
x = 3
Step-by-step explanation:
3 * 5 + 9 =24
The population of a certain species of fish has a growth rate of 2.2% per year. It is estimated that the the current population is 350,000. Estimate the number of years it will take the fish population to reach 1,000,000. Round your answer to the nearest tenth.
We have been given that the population of a certain species of fish has a growth rate of 2.2% per year. It is estimated that the the current population is 350,000.
We are asked to find the time it will take the fish population to reach 1,000,000.
We will use exponential growth formula to solve our given problem.
An exponential growth function is in form [tex]y=a\cdot (1+r)^x[/tex], where,
y = Final amount,
a = Initial amount,
r = Growth rate in decimal form,
x = Time
[tex]2.2\%=\frac{2.2}{100}=0.022[/tex]
[tex]y=350,000\cdot (1+0.022)^x[/tex]
To find the time for the fish population to reach 1,000,000, we will substitute [tex]x=1,000,000[/tex] in our equation as:
[tex]1,000,000=350,000\cdot (1+0.022)^x[/tex]
[tex]1,000,000=350,000\cdot (1.022)^x[/tex]
[tex]\frac{1,000,000}{350,000}=\frac{350,000\cdot (1.022)^x}{350,000}[/tex]
[tex]2.8571428571428571=(1.022)^x[/tex]
Now we will take natural log on both sides:
[tex]\text{ln}(2.8571428571428571)=\text{ln}((1.022)^x)[/tex]
[tex]\text{ln}(2.8571428571428571)=x\cdot \text{ln}(1.022)[/tex]
[tex]x=\frac{\text{ln}(2.8571428571428571)}{\text{ln}(1.022)}[/tex]
[tex]x=\frac{1.0498221244986776733}{0.0217614917815127}[/tex]
[tex]x=48.2421947[/tex]
Upon rounding to nearest tenth, we will get:
[tex]x\approx 48.2[/tex]
Therefore, it will take approximately 48.2 years for the fish population to reach 1,000,000.
Answer:
47.7
Step-by-step explanation:
right answer
A manager wants to determine the number of containers to use for incoming parts for a kanban system to be installed next month. The process will have a usage rate of 83 pieces per hour. Because the process is new, the manager has assigned an inefficiency factor of .18. Each container holds 53 pieces and it takes an average of 80 minutes to complete a cycle. How many containers should be used? (Round up your answer to the next whole number.) Number of containers As the system improves, will more or fewer containers be required? More Fewer
Answer:
2 containers should be used
As the system improves, neither more or fewer containers be required
Step-by-step explanation:
According to the given data we have the following:
D=83 pieces per hour.
T=80 minutes=1.33 hour
X=0.18
C=53
In order to calculate how many containers should be used we would have to use the following formula:
Number of containers=DT(1+X)
C
Number of containers=(83)(1.33)(1+0.18)
53
Number of containers=2.45=2
2 containers should be used.
As the system improves, neither more or fewer containers be required
The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 32 mm and standard deviation 7.3 mm. (a) What is the probability that defect length is at most 20 mm? Less than 20 mm?
Answer:
The probability that defect length is at most 20 mm (or less than 20 mm) is 0.0505
Step-by-step explanation:
Mean defect length = u = 32
Standard deviation = [tex]\sigma[/tex] = 7.3
The distribution is normal and we have the value of population standard deviation so we will use the concept of z-score and probability from z-table to find the said probability.
We have to find the probability that the defect length is at most 20 mm. At most 20 mm means equal to or lesser than 20 mm. Since the normal distribution is a continuous distribution, the probability of at most is approximately equal to probability of lesser than.
If X represents the distribution of defect lengths, then we can write:
P(X ≤ 20) ≅ P(X < 20)
We can find the probability of defect length being lesser than 20 mm by converting it to z-score and find the corresponding probability from the z-table.
The formula to calculate the z-score is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Substituting the values, we get:
[tex]z=\frac{20-32}{7.3}=-1.64[/tex]
Therefore, P(X < 20) is equivalent to P(z < -1.64)
From z-table we can find the probability of z being lesser than - 1.64, which comes out to be:
P(z < -1.64) = 0.0505
Therefore, we can conclude that:
The probability that defect length is at most 20 mm (or less than 20 mm) is 0.0505