a) The probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $210 of the population mean is 0.9482.
b) When trying to estimate the population mean, a greater sample size offers the benefit of improving the estimation's accuracy.
a. The z-score is calculated as follows:
z = (x - μ) ÷ (σ ÷ √n)
Where the sample size is n, the sample mean is x, the population mean is y, and the population standard deviation is z.
By entering the specified values, we obtain:
n = 30: z = (x - 17,545) ÷ (2,160 ÷ √30) = (x - 17,545) ÷ 216
n = 50: z = (x - 17,545) ÷ (2,160 ÷ √50) = (x - 17,545) ÷ 174
n = 100: z = (x - 17,545) ÷ (2,160 ÷ √100) = (x - 17,545) ÷ 132
n = 400: z = (x - 17,545) ÷ (2,160 ÷ √400) = (x - 17,545) ÷ 53
To find the odds that a sampling distribution could be within $210 of both population mean and the z-score, we must first figure out the likelihood that now the z-score would be within 1.96 standard deviations of the mean. This is because the 95th percentile, or the number under which 95% of the data lies, is represented by the z-score of 1.96, which is the value in this case.
To ascertain the likelihood, we must attempt searching up the z-scores in a z-table and get the pertinent probabilities. A z-table is a table that lists the probability associated with various z-scores.
Using the z-scores we used to develop the concept, we could look up the alternatives in a z-table and find the following probability:
n = 30: 0.4056
n = 50: 0.5082
n = 100: 0.6690
n = 400: 0.9482
For each of the aforementioned sample sizes, the likelihood that a sampling of taxpayers from this income category who itemized deductions will exhibit a sample mean that is within $210 of the population mean is:
n = 30: 0.4056
n = 50: 0.5082
n = 100: 0.6690
n = 400: 0.9482
b. The likelihood that the sample means will closely match the true population mean is thereby increased.
The standard deviation averages commonly fall as the sample size rises. In other words, as the sample mean becomes less likely to depart from the actual population mean, the likelihood that the random variable will be close to the population mean increases.
For instance, in the aforementioned case, the likelihood that they would give it a shot would be within 210 of a population mean would rise from 0.4056 for a random sample of just 30 to 0.9482 for a random sample of 400.
This means that the likelihood that they give it a chance will fall within the allowed range of the sample % likewise increases as the sample size increases.
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how is factoring symbolically and factoring with algebra tiles similar
The two methods are identical because by both using algebra tiles and factoring symbolically, one need to think of the factors.
What is factoring?Factoring simply has to do with the process of writing a number or another mathematical object as a product of different factors, and this is usually smaller or simpler objects that are of the same kind.
Factoring is a common mathematical process that's used for separating the factors, or numbers, which multiply to form another number. Some numbers are affected by multiple factors.
For example, in a situation when you multiply the factors 6 and 4, 8 and 3, 12 and 2, and 24 and 1, you get the number 24.
Algebra tiles are rectangular and square tiles that represent numbers and variables. Using algebra tiles allows us to solve our problems in a more visual manner. It allows us to see exactly what quantities we're dealing with. It's as if we're using building blocks to assist us.
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A coach has $1280 in the budget to spend on team jackets. The team held a fundraiser and earned $1176. Each jacket costs $75. How many jackets can the coach Buy?
Pls Help
Answer: 32 jackets
Step-by-step explanation:
add 1280 to 1176 then divide the sum by 75
Which equations are true equations? Select all correct answers. 48 ÷ 8 + 2³ = 5 + 3²/ 48 ÷ 8 + 2³ = 5 + 3² / 15052=30−42−12 150 /12 8⋅72−12=22−2⋅3
The equations out of the following that are true would be:
A) and B): [tex]48[/tex] ÷ [tex]8+2^3=5+3^2[/tex] ←(Options A and B were the same.)
The remaining two I am not certain if they are true or not. The way they were laid out made little to no sense. If you could maybe evaluate further on the other options, perhaps I can double check them for you and see if there are any other remainder options that are true. However, I know for certain that A and B are true.
3.
A pitcher has 17. 6 fluid ounces of iced tea in it. Erin pours
12. 06 fluid ounces of tea into a glass to drink. How many fluid ounces
of tea remain in the pitcher? Show how to solve the problem
by adding on
5.56 fluid ounce of tea remain in the pitcher
In mathematics, a variable is an alphabet that represent an unknown number. We let required amount as variable and then try to calculate its value
According to the question,
Total ounces of iced tea a pitcher contains = 17.6 fluid ounces
Amount of tea Erin pours to drink = 12.06 fluid ounces
Let "x" fluid ounce of tea remain in the pitcher
So , total was 17.6
=> x + 12.06 = 17.6
Solving for x
Subtracting by 12.06 both the sides
=> x + 12.06 - 12.06 = 17.6 -12.06
=> x = 5.56 fluid ounce
Hence , 5.56 fluid ounce of tea remain in the pitcher
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Given the functions below, find f(2)-g(-7).
f(x)=-|3-8x| g(x)=x^2+4x
The value of f(2)-g(-7) is -34
What is function?A function is defined as a relation between a set of inputs having one output each.
Given are two functions, f(x) = -|3-8x| and g(x) = x²+4x
f(2) = -|3-8x2|
= -|3-16|
= -13
g(x) = (-7)²+4(-7)
= 49-28
= 21
f(2)-g(-7) = -13-21 = -34
Hence, The value of f(2)-g(-7) is -34
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in a sample of 62 swim instructors, 37 said that the butterfly stroke is the most difficult to teach. find the critical value used to test a claim that a majority of swim instructors think that the butterfly is the most difficult stroke to teach at the 1% significance level.
The critical value used to test the hypothesis that the butterfly is the most challenging stroke to teach at the 1% significance level is 0.84
Given that,
Of the 62 swim teachers who participated in the survey, 37 claimed that teaching the butterfly stroke is the most challenging. Find the criticial value used to test the hypothesis that the butterfly is the most challenging stroke to teach at the 1% level of significance.
This is right tailed test
Z [tex]\alpha[/tex] = Z 0.01 = 0.84 ( Using z table )
Therefore, the critical value used to test the hypothesis that the butterfly is the most challenging stroke to teach at the 1% significance level is 0.84
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Denise works for a company where the IT department charges her department for actual usage of a SharePoint server, determining how often users log in and how much storage space her department consumes. What type of IT funding model is the company deploying?
chargeback
The company is deploying chargeback type of IT funding model where the IT department charges her department for actual usage of a SharePoint server, determining how often users log in and how much storage space her department consumes.
What is IT model funding?Traditional IT and project finance methods offer a key business risk and, if not modified, jeopardize the future of technology-based enterprises.
This excerpt from the whitepaper Changing the Finance Method by Keanen Wold, Levi Geinert, Shaun Norris, Charles Betz, Beth Dumke, Sam Guckenheimer, and Troy Magennis discusses that contradiction over how traditional financing methods handle ethical concerns and also what Agile and DevOps teams require to execute successfully.
Balancing the high-risk investment in innovation (research and development department) with regular business-as-usual responsibilities has always been difficult for organizations. Too much risk might, in the case of an unexpected failure, result in a business's dissolution; too little innovation could ultimately cause the company to be overtaken and lose market share to rivals and new upstarts.
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Carlton is a project manager for a landscape design company. He is analyzing the duration of four current projects. Which graph best shows how many days each project has lasted? A. B. C. D.
Answer:i am pretty sure it is c
Step-by-step explanation:
this is because it says Which graph best shows how many days each project has lasted? and c is the only one that is talking about days
Which best describes the solution for the
system of linear equations graphed below?
A. (3, 0) only
B. (6,0) only
C. no solution
D. infinitely many solutions
Answer:
C no solution.
Step-by-step explanation:
The lines are parallel, they will never intersect.
Josue earns $.50 for each delivery he makes plus an additional $10.00 per day. Write and solve an inequality to represent the number of packages Joshua has to deliver so that he can make more than $20.00 each day?
Answer:
.5x + 10 > 20
Step-by-step explanation:
x represents each delivery he makes:
.5x + 10 > 20
This shows that for the inequality to be true, it must total over $20
Hope this helped!
Jean is x years old and her younger brother Johnathan is y years old. What is the sum of their ages 5 years ago
The sum of their ages 5 years ago is x + y -10.
What is subtraction?The process of subtracting one number from another is known as subtraction.
Given that, Jean is x years old and her younger brother is y years old.
Age of Jean 5 years ago is:
x - 5
The age of Johnathan 5 years ago is:
y - 5
The sum of their ages 5 years ago is:
x - 5 + y - 5
= x + y -10
Hence, the sum of their ages 5 years ago is x + y -10.
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what is the ratio of the area of a square inscribed in a semicircle with radius $r$ to the area of a square inscribed in a circle with radius $r$? express your answer as a common fraction.
The ratio of the area of a square inscribed in a semicircle to the area of a square inscribed in a circle is 2/5.
What is a semicircle?
A semicircle in mathematics is a one-dimensional locus of points that makes up one-half of a circle. A semicircle's entire arc always measures 180 degrees. There is only one symmetry line in it.
For instance, if the radius is known, we can use the formula, which states that the area of a semicircle is equal to half that of a circle. As a circle's area is r2, Therefore, a semicircle's area is equal to 1/2(r2), where r is its radius. 3.14, or 22/7, is the value of.
Solution Explained:
Let's assume and take
The dimensions of the little square ABCD = 2 x 2 =4
of the little triangle's hypotenuse Radius of the semi-circle for BCG
H=sqrt(5) = The semicircle's radius
IHJK = 2sqrt is the diagonal of the huge square (5)
One side of the large square is IHJK when sin(45) x 2sqrt(5) = sqrt(10).
Therefore, the area of ABCD/area of IHJK is equal to 4/sqrt(10)2 = 2/5.
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i neeeeeeeed this answer to be right please
The measure of the angle RQP = 60 degrees and the value of x is 16 and the measure of the arc RMP is 240 degrees.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).
It is given that:
A circle:
The measure of the arc RMP = 360 - Arc RP
The measure of the arc RMP = 360 - 120 = 240 degrees
The measure of the angle RQP = 1/2[240 - 120]
The measure of the angle RQP = 60 degrees
In the second circle:
9(9 + x) = 15(15)
9 + x = 25
After solving we get:
x = 16
Thus, the measure of the angle RQP = 60 degrees and the value of x is 16 and the measure of the arc RMP is 240 degrees.
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Which ratio is equivalent to 3/15
1/3
3/5
1/5
15/3
Answer:
It should be 1/5
Since the fractional versions of the ratios are equal, the ratios are equivalent.
Renata Corporation purchased equipment in 2018 for $328,400 and has taken $147,780 of regular MACRS depreciation. Renata Corporation sells the equipment in 2020 for $197,040.What is the amount and character of Renata's gain or loss?
The gain Renata Corporation got from the sale of equipment is $16420
The tax depreciation method used in the United States is called MACRS, or Modified Accelerated Cost Recovery System. In other words, the method used to determine your business's tax deductions based on the depreciation of your tangible (depreciable) assets is known as MACRS depreciation.
Equipment Book value =
Purchase price - MACRS depreciation
= $328, 400 - $147,780
=$1,80,620
Gain = sale price - Book value
= $197, 040 - $180620
=$ 16420
Gain up to total depreciation is to be treated as ordinary income, that is up to $147, 780. since the gain is $16,420 within depreciation, it is treated as ordinary income.
Renata Corporation has a gain of $16,420 of which $16, 420 is treated as ordinary income due to the section 1245 recapture
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The volume of the circumscribed cylinder is 2154.04π cm^3. Find the radius of the sphere…show all work and steps.
The measure of the radius of the sphere is given as follows:
r = 359 cm.
How to obtain the volume of the cylinder?
The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h
Which is the base area given by πr² multiplied by the height h.
In the context of this problem, the parameters are given as follows:
The radius of the cylinder is the same as the radius of the sphere, which is of r.The height of the cylinder is twice the radius of the sphere, hence it is or 2r.The volume of the circumscribed cylinder is 2154.04π cm^3, hence the equation to solve for r is given as follows:
πr²h = 2154.04π
2πr³ = 2154.04π
2r³ = 2154.04
r = cube root of (2154.04/2)
r = 359.
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19. For an overdue book, the school library
charges a 25¢ penalty, plus 5¢ for every
day the book is overdue. The town library
charges a 5¢ penalty, plus 10¢ for every
day the book is overdue. For what number
of days is the total fee at both libraries
the same?
Answer:
On the 4th day, the sum of penalties and charges will be the same in both the school library and the town library.
Step-by-step explanation:
School library
Penalty-25
Every day charge-5
City library
Penalty-5
Every day charge-10
Let the day when total fee at both libraries will be same be x
Total charge in school library-25+5x
Total charge in city library-5+10x
They both amount to be equal
Use the Laplace transform to solve the following initial value problem: y + 10y + 25y = 0 y(0) = - 3, y'(0) = 3 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)} find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y (s) = and write the above answer in its partial fraction decomposition, Y(s) = A/s + a + B/(s+a)2 Y (s) = + Now by inverting the transform, find y(t) =
On solving the given question, by the Help of LaPlace Inverse form we got - [tex]y(t) = \frac{-7}{2} + \frac{1}{2}e^{-8t}[/tex]
What is The Laplace transform?In terms of its usefulness in resolving physical issues, the Laplace transform is an important transform that is probably second only to the Fourier transform. The Laplace transform is especially helpful in solving linear ordinary differential equations, such as those that arise in the analysis of electronic circuits.
Take Laplace for DE we get -
[tex]L(y)" + 8L(y)' =0\\s^2Y (s) - sy(0) - y'(0) 8(sY(s) - y(0))=0\\Y(s)(s^2 + 8s) + 3s 4 + 24 =0\\Y(s)(s^2 + 8s) = -3s - 28\\Y(s) = \frac{-3s - 28}{(s^2 + 8s) } \\Right Side = \\\frac{-7}{2s} + \frac{1}{2(s+8)} \\ Now taking inverse LaPlace - \\y(t) = \frac{-7}{2} + \frac{1}{2}e^{-8t}[/tex]
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Which number set includes only RATIONAL numbers? O a O b O c Od {-4/5, 0, 0.121314..., 97/3) (-0.123123...., 0, n/2, V100, 77/4} (-66/7, 0, 0.13, V45, 98/5} (-2/3, 0, 0.321, 149, 101/3}
PLEASE HELP
The number form that includes only rational numbers are
(-2/3, 0, 0.321, √49, 101/3}
What is rational number?A rational number is one that has the form p/q, where p and q are both integers and q is not zero
Rational function means that the equation will be a fraction
examining the numbers
(-2/3, 0, 0.321, √49, 101/3}
-2/3 is already a fraction
0 = 0/1 hence can be written as a fraction
√49 = 7 = 7/1
101/3 already a fraction
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A truck that can carry no more than 7200 lb is being used to transport refrigerators and upright pianos. Each refrigerator weighs 200 lb and each piano weighs 425 lb. Write and graph an inequality to show how many refrigerators and how many pianos the truck could carry.Will 18 refrigerators and 11 pianos overload the truck? Explain.
Answer: Yes, it will overload the truck.
Step-by-step explanation:
To begin, form an algebraic equation.
200(r) + 425(f)
Second, substitute your numbers for the variables.
200(18) + 425(11) = ?
Third, multiply your numbers of fridges by the weight of each.
3600 + 4675 = 8275 is the total
Finally, determine whether or not if it is greater than the weight limit the truck has.
7200 < 8275
Therefore, the total weight is greater than the weight limit.
Identify the value of y.
The figure shows a right triangle. One leg has a length of 9 units. The other leg has a length of y units. The hypotenuse has a length of y plus 3 units.
y = 6
y = 12
y = 3
y = 15
Answer:
Y=12
Step-by-step explanation:
ya bae
does the series converge? if the series does converge, find the sum. (if the quantity diverges, enter diverges.)
The given series [tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] is convergence and the sum of the series is 33/28.
In the given question we have to check whether the series converge or not. If the series does converge, then we have to find the sum.
The given series is [tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex].
Firstly we check the convergence of the given series.
When a series approaches a limit, it is considered to be convergent if both convergent and divergent behaviour occur. The deletion of a finite number of terms from the beginning of a series has no impact on convergence or divergence.
We can write the series as:
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right[/tex]
As |0.3|<1 and |0.2|<1
Then [tex]\sum_{n=1}^{\infty}(0.3)^{n-1}\text{ and }\sum_{n=1}^{\infty}(0.2)^n[/tex] is convergent.
So [tex]\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right[/tex] is also convergent.
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-(0.2)\sum_{n=1}^{\infty}(0.2)^{n-1} \right[/tex]
Series [tex]\sum_{n=1}^{\infty}(x)^{n-1}[/tex] converges to 1/x-1 for |x|<1.
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{1-0.3}-(0.2)\frac{1}{1-0.2}[/tex]
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{0.7}-\frac{0.2}{0.8}[/tex]
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] = 10/7 - 1/4
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] = 33/28
Hence, the sum of the given series is 33/28.
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The right question is:
Determine whether the series is convergent or divergent.
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex]
If is is convergent, find the sum. (If the quantity diverges, enter diverges.)
Using the t Distribution Table, find the critical value(s) for the t test for a right-tailed test with n=8 and a =0.01. Enter the answers separated by a comma if needed. Critical value(s) - Using The Distribution Table, find the critical value(s) for the test for a left-tailed test with n=23 and a =0.05. Enter the answers separated by a comma if needed. Critical value(s)
The critical value for right tailed test is 2.998, the critical value for left tailed test is - 1.717.
How to using t distribution table?First, we must know the following data,
df = degree of freedom = n - 1
α = significance level
Next, t test have three type of test which is
Two or Both tailed test, for this test we use negative and positive value.One right tailed test, for this test we use positive value.One left tailed test, for this test we use negative value.Then, to find critical value using the t distribution table search df value in left column of table and search the α in the top row of the table (depending on the type of test, use one tail row for this case). For example, see attached image.
Thus, the right tailed test critical value is 2.998, and the left tailed test critical value is - 1.717.
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Football player one pushes against football player two, causing player two to slow down from moving any farther down the field. Which term best describes the work in this situation?
Negative work was done on player two.
Positive work was done on player two.
No work was done on either player.
Negative work was done on player one.
The work that has been done on player 2 by player 1 is a negative work. Option A.
What is work done?We define the work done as a situation in which the force that is applied moves a distance in the direction of the force. In this case we ought to know that a negative work is said to be done when the object is found to slow down at te application of the force. The meaning of this is that the force acts in such a way as to slow down motion which makes it a negative force.
For the fact that football player one pushes against football player two, causing player two to slow down from moving any farther down the field, a negative work is done.
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Line a passes through the points (−5, −2) and (−5, −5), while line b passes through (0, 4) and (5, 4).
Which statement best describes the relationship between lines a and b?
A. a and b are intersecting.
B. a and b are parallel.
C. a and b are collinear.
D. a and b are perpendicular.
Based on the slopes of both lines, the relationship between both lines is: D. a and b are perpendicular.
What is the Relationship between Parallel lines or Perpendicular Lines?The relationship between two lines that are parallel is that they have the same slope, while the relationship between perpendicular lines is that their slopes are negative reciprocals of each other.
Find the slope of the line that passes through (-5, -2) and (-5, -5):
Slope (m) = change in y / change in x = (-5 -(-2)) / (-5 -(-5))
m = (-5 + 2) / (-5 + 5)
m = -3/0 [cannot divide, therefore, the slope is undefined).
The line is therefore a vertical line.
Find the slope of the line that passes through (0, 4) and (5, 4):
Slope (m) = change in y / change in x = (4 - 4) / (5 - 0)
m = 0/5
m = 0
This line is an horizontal line.
In conclusion, the relationship between a vertical and a horizontal line is that they are perpendicular to each other, therefore, the answer is: D. a and b are perpendicular.
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Suppose you are doing a two sample test of means, and assume that the population variances are equal. We have the following data:
Sample 1: n1= 16, XX1 = 44, s1= 5
Sample 2: n2= 9, XX2 = 41, s2= 6
Find the test statistic.
t = 1.341
Correct option is " B " the is the test statistics is 1.341 when sample 1: n₁=16, x₁=44, and s₁=5 and sample 2:x₂ = 41, s₂ = 6, n₂ = 9.
Given that,
Assume you are conducting a two-sample test of averages and that the variances in the population are identical. The information below is ours:
Sample 1: n₁=16, x₁=44, and s₁=5.
Sample 2:x₂ = 41, s₂ = 6, n₂ = 9.
We have to find the test statistic.
We know that,
n₁ = 16
x₁ = 44
s₁ = 5
n₂ = 9
x₂ = 41
s₂ = 6
We have
t= (x₂ - x₁)/√(n₁-1)s₁²+(n₂-1)s₂²/n₁+n₂-2(1/n₁+1.n₂)
t = 1.341.
Therefore, Correct option is " B " the is the test statistics is 1.341 when sample 1: n₁=16, x₁=44, and s₁=5 and sample 2:x₂ = 41, s₂ = 6, n₂ = 9.
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when she chooses a password, eloise always uses exactly ten different characters: five letters (a, b, c, d, and e) and five numbers (2, 3, 4, 5, and 6). additionally, she always ensures that no pair of letters is consecutive and that no pair of numbers is consecutive. how many different passwords conform to these rules?
These rules of five letters (a, b, c, d, and e) and five numbers allow for 28,800 different passwords. Additionally, she makes sure that no two letters or two numbers are ever placed back-to-back.
What is counting principle?The basic counting concept is a method for keeping track of all the potential outcomes in a scenario. According to this statement, there are n*m methods to carry out both of these acts if there are n ways to execute one activity and m ways to conduct another action after that.
Here,
Eloise has 10 alternatives since the password's initial character can be any letter or number. She has five alternatives, and her second selection must be from the set (letter or number) that has not previously been utilized. She has four choices remaining, and Choice 3 is from the same group as Choice 1. She gets four possibilities since Choice 4 is the second item in the same set as Choice 2. The choices 5 and 6 come from separate sets, each of which has three possibilities; the choices 7 and 8 come from separate sets, each of which has two options; and the choices 9 and 10 come from separate sets, each of which has only one option left.
10 5 4 4 3 3 2 2 1 1
10 ×5 ×4 ×4 ×3 ×3 ×2 ×2 ×1 ×1 = 28,800
28,800 different passwords conform to these rules of five letters (a, b, c, d, and e) and five numbers (2, 3, 4, 5, and 6). additionally, she always ensures that no pair of letters is consecutive and that no pair of numbers is consecutive.
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1. use the equation to answer these questions. (a) what is the solution to the equation? (b) what is the extraneous solution? why? (c) in general, what is an extraneous solution?
a. The solution of the equation x + 2 = √3x + 10 is x = -3 or x =2.
b. Extraneous solution is x= -3.
c. Extraneous solution does not satisfy original equation.
As given in the question,
Given equation :
x + 2 = √3x + 10
a. Squaring both the sides
( x + 2 )² = ( √3x + 10 )²
⇒ x² + 4x + 4 = 3x + 10
⇒ x² + x - 6 =0
⇒ x² + 3x -2x -6 =0
⇒ ( x+ 3) ( x -2) =0
⇒ x= -3 or x = 2
b. Extraneous solution:
x = -3
-3 + 2 = √3(-3)+ 10
⇒ -1 ≠ 1 extraneous solution.
x= 2
2+ 2 =√3(2) +10
⇒4 = 4 not extraneous.
c. Extraneous solution does not satisfy original equation
Therefore, the solution of the equation is x = -3 or x=2and its extraneous solution is x =-3. Extraneous solution does not satisfy original equation.
The complete question is :
Use the equation below to answer these questions.
x + 2 = √3x + 10
a) What is the solution to the equation?
b) What is the extraneous solution? Why?
c) In general, what is an extraneous solution?
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cos x = - 0.809, find the values of x. ( - 180≤ x ≥ 180 )
Answer:
cos x = - 0.809, find the values of x. ( - 180≤ x ≥ 180 )
x = - 135° and x = 45°
a group of clerks must sort 1775 files. each clerk sorts at the constant rate of 30 files per hour. some of the clerks stop working at the end of the first hour; the same number of clerks stop working at the end of the second hour; and the same number of clerks stop working at the end of the third hour. the group finishes the sorting in 3 hours and 10 minutes. find the number of files sorted during the first one and a half hours of sorting.
The number of files sorted in the first one and a half hours of sorting is 945.
Here, we are given that a group of clerks must sort 1775 files.
Each clerk sorts at a constant rate of 30 files per hour.
Let the number of clerks who start working initially be x.
Thus, they will sort 30x files in the first hour.
After the first hour, let the number of clerks who stop working be a
Thus, the number of files sorted in the second hour will be 30(x - a)
Similarly, the number of files sorted in the third hour will be 30(x - 2a)x
In the last 10 minutes, the number of files sorted will be 5(x - 3a)
Thus, we can form the following equation-
30x + 30(x - a) + 30(x - 2a) + 5(x - 3a) = 1775
30x + 30x - 30a + 30x - 60a + 5x - 15a = 1775
95x - 105a = 1775
19x - 21a = 355
x = (355 + 21a)/ 19
since x and a both have to be integers, (355 + 21a) must be divisible by 19.
This is the case when a = 3
⇒ x = (355 + 21*3)/ 19
x = 418/ 9
x = 22
Now, the number of files sorted in first one and a half hours will be-
30x + 15(x - a)
= 30*22 + 15(22 - 3)
= 660 + 15*19
= 660 + 285
= 945
Thus, the number of files sorted in the first one and a half hours of sorting is 945.
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