The simplified numerator of the sum is 4x + 6
Given,
We have the following expression for this situation:
x / (x² + 3x + 2) + 3/(x + 1)
And here's where we can start:
x(x + 1) + 3(x² + 3x + 2) / (x² + 3x + 2) (x + 1)
We may now factor the terms x² + 3x + 2 = (x + 1) (x + 2) on the denominator and distribute the terms on the numerator to get:
x² + x + 3x² + 9x + 6 / (x + 2) (x + 1)²
4x² + 10x + 6 / (x + 2) (x + 1)²
Now, the numerator can be factored as follows:
4x² + 10x + 6 = (2x + 2) (2x + 3)
And if we substituted that, we got:
(2x + 2) (2x + 3) / (x + 2) (x + 1)²
We can now apply common factor 2 to the numerator as follows:
2(x + 1) (2x + 3) / (x + 2) (x + 1)²
Additionally, the x+1 can be cancelled on the numerator and denominator as follows:
2(2x + 3) / (x + 2) (x + 1) = 4x + 6/ (x + 2) (x + 1)
Therefore,
The simplified numerator of the sum is 4x + 6
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Members of a softball team raised $1186. 50 to go to a tournament. They rented a bus for $842. 50 and budgeted $21. 50 per player for meals. Write and solve an equation which can be used to determine xx, the number of players the team can bring to the tournament.
By solving the equation we know that 15 players can be brought to the tournament.
What do we mean by equations?Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.
For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
So, we know that:
Softball players raised $1186.50 to attend a tournament.
They allocated $21.50 for meals per player and paid $842.50 for the bus rental.
We must apply the following calculation to determine the total number of players they are permitted to bring:
Formula: Total amount of money= fixed cost + unitary variable cost × number of players
1186.50 = 842.50 + 21.50 × number of players
1186.50 - 842.50 = 21.50 × number of players
344/21.50 = number of players
15 = Number of players
Therefore, by solving the equation we know that 15 players can be brought to the tournament.
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A chorus has 50 girls and 35 boys. If two are chosen at random to sing a duet, what is the probability that both will be boys? hint: you can not have the same person twice in a duet.
Probabilities are used to determine the chances of an event.
The probability that both selections are boys is 0.1667
The given parameters are:
boys= 35
girls= 50
total= 85
Since two are chosen to sing a duet, then the selection is without replacement.
So, the probability that both selections are boys is
p=boys/ total * boys-1/ total -1
This gives
p= 0.4118*0.4048
Hence, the probability that both selections are boys is 0.1667
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a sample of 2,500 people was asked how many cups of coffee they drink in the morning. you are given the following sample information. cups of coffee frequency 0 600 1 800 2 900 3 200 2,500 the expected number of cups of coffee is . a. 1.28 b. 2.28 c. 1.5 d. 2
After using the mean, the expected number of cups of coffee is 1.28. So the option a is correct.
In the given question, a sample of 2,500 people was asked how many cups of coffee they drink in the morning.
We have to find the expected number of cups of coffee.
x Frequencyf(x) x^2 x∙f(x) x^2∙f(x)
0 600 0 0 0
1 800 1 800 800
2 900 4 1800 3600
3 200 9 600 1800
Total 2500 3200 6200
Mean = Sum of f.x/Sum of f
Mean = 3200/2500
Mean = 1.28
Mean = 1.28
The expected number of cups of coffee is 1.28.
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The table ummarize reult from 984 pedetrian death that were caued by automobile accident. Pedetrian intoxicated
Ye. No
Driver Intoxicated - Ye 51. 75
No 239. 619
If one of the pedetrian death i randomly elected, find the probability that the pedetrian wa intoxicated or the driver wa not intoxicated
If one of the pedestrian death is randomly elected, find the probability that the pedestrian was intoxicated or the driver was not intoxicated 0.6290.
Divide the applicable variety with the aid of using the whole variety. In this case, the applicable variety they may be requesting is "neither pedestrian nor driver."Neither/Total = 619/984 = 0.6290.Rounded to 4 figures that is 0.6290.This, of course, assumes that the published desk is formatted successfully and is correctly legible.Read more about pedestrian :
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Quincy has $10 in a savings account. The interest rate is 6%, compounded annually. Write an exponential equation for the growth of the balance in her account. (1 point)
f(t) = 10(1.06)t
f(t) = 10(0.06)t
f(t) = 1.06(10)t
f(t) = 0.06(10)t
An exponential equation for the growth of the balance in her account is [tex]10(1.06)^t[/tex].
What is Compound interest?Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.
Compound Interest =[tex]P(1+r/n)^rt[/tex]
We have been given that Quincy has $10 in a savings account. The interest rate is 6%, compounded annually.
The compound interest will be;
Compound Interest =[tex]P(1+r/n)^rt[/tex]
[tex]10(1+6/100)^t\\\\10(1+ 0.06)^t\\\\10(1.06)^t[/tex]
Hence, an exponential equation for the growth of the balance in her account is [tex]10(1.06)^t[/tex].
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Find the dimensions of a rectangle whose width is 8 meters less than its length, and whose area is 153 square meters.
Answer:
Dimensions: 15 cm × 7 cm
Step-by-step explanation:
Solve for K.
F = kq
K = ____.
Answer:
K=F/q
Step-by-step explanation:
construct the 80% confidence interval for the average amount spent by 8 to 11 year olds on a trip to the mall. assume the population is approximately normal. step 3 of 4: find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.
To find the critical value that should be used in constructing the 80% confidence interval for the average amount spent by 8 to 11 year olds on a trip to the mall.
What is critical value?the proper z-score for an 80% confidence interval must first be established. Both a z-table and a z-score calculator may be used for this.Using a z-table, i may search up the value of z such that 80% of the area under the standard normal curve is to the left of z to get the z-score. This number is around 0.84.We can then use this z-score to calculate the 80% confidence interval by taking the sample mean and adding or removing the product of the z-score and the standard error of the mean. The standard error of the mean is computed by dividing the standard deviation by the square root of the sample size.
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if you are looking to expand your company's presence online internationally, which of the following should you consider with regards to your online content?
You should consider option B - Translated but also locally adapted for the audience, with regard to your online content.
Any content that exists as digital data is considered online content. Otherwise called advanced media, computerized content is put away in computerized or simple capacity in unambiguous configurations.
A company's website should become more international in terms of content and supported languages if it wants to expand globally.
The content of a website must not only be translated into the language of the audience or user in that country but also adapted to fit the cultural and linguistic characteristics of that language, both of which are essential for expanding a website's or company's presence online internationally.
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(complete question)
If you are looking to expand your company's presence online internationally, which of the following should you consider with regards to your online content?
A . Translated by an automated tool only
B Translated but also locally adapted for the audience
C Translated into the native language
D Left the same, and not translated
A bag contains 5 red, 4 green, and 3 blue marbles. what is the probability of randomly selecting a blue marble, replacing it in the bag, and then randomly selecting a red marble?
Answer:
Probability of selecting a blue marble, then a red marble is 5/48---------------------
GivenMarbles: 5 red, 4 green, and 3 blueTotal number of marbles: 5 + 4 + 3 = 12Probabilities areP(blue) = blue / total = 3/12 = 1/4P(red) = red / total = 5/12The probability of the two events with replacement of marble isP(blue, red) = P(blue) × P(red) = 1/4 × 5/12 = 5 / 48What is the equation of the line that passes through the points (-2,-5) and (-4,-4)
The equation of the line that passes through the points (-2,-5) and (-4,-4): y = -1/2x - 6.
What is the Equation of a Line?Given the following points that a line passes through below:
(-2, -5) and (-4, -4).
First, find the slope (m):
Slope (m) = change in y / change in x = (-4 -(-5)) / (-4 -(-2))
Slope (m) = 1/-2
Slope (m) = -1/2.
Find the y-intercept (b) by substituting m = -1/2 and (x, y) = (-4, -4) into y = mx + b:
-4 = -1/2(-4) + b
-4 = 2 + b
-4 - 2 = b
-6 = b
b = -6
To write the equation of the line, substitute m = -1/2 and b = -6 into y = mx + b:
y = -1/2x - 6
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Which of the following values are solutions to the inequality 5x+5≥−9?
The possible values of the solutions to the inequality 5x + 5 ≥ −9 are: I, II, and III.
How to Find the Values of the Solutions to an Inequality?To find the possible values of the solution to a given inequality, solve the inequality given using the properties of equality to isolate the variable.
Given the inequality:
5x + 5 ≥ −9
Subtract 5 from both sides:
5x + 5 - 5 ≥ −9 - 5 [subtraction property of inequality]
5x ≥ -14
Divide both sides by 5
5x/5 ≥ -14/5
x ≥ -2.8
This means that all the possible values of x are greater than or equal to -2.8.
1, 4, and 6 are greater than -2.8, therefore, the values of the solutions are: I, II, and III.
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A company offers a nut mixture with 7 peanuts for every 3 almonds. The company changes the mixture to have 9 peanuts for every 5 almonds, but the number of nuts per container does not change.
Plsssss help i'm so stuck :(
a. How many nuts are in the smallest possible container?
Answer:
70
Step-by-step explanation:
Nut mixture 1: 7 peanuts for every 3 almonds.
Therefore, the container has to hold nuts in multiples of 10, since 7+3=10 and 7 is not divisible by 3.
Nut mixture 2: 9 peanuts for every 5 almonds.
Therefore, the container has to hold nuts in multiples of 14, since 9+5=14 and 9 is not divisible by 5.
To find the number of nuts in the smallest possible container, find the least common multiple (LCM) of 10 and 14.
To find the LCM, list the multiples of each number and locate the smallest multiple that is exactly divisible by both the numbers:
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, ...Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, ...Therefore, the LCM of 10 and 14 is 70.
So there are 70 nuts in the smallest possible container.
please answer this question
The answers to the problems are calculated. The first answer is
2.7 ÷ 3= 0.9
What is division?Division is the process of dividing a number by a given number.
(a)
The given expression is 2.7 ÷ 3=_______.
Perform division to find the answer,
2.7/3
= 0.9
(b)
The given expression is 1.6÷ 4=_______.
Perform division to find the answer,
1.6/4
= 0.4
(c)
The given expression is 3.5÷ 5=_______.
Perform division to find the answer,
3.5/5
= 0.7
(d)
The given expression is 0.48 ÷ 6=_______.
Perform division to find the answer,
0.48/6
= 0.08
(e)
The given expression is 8.19 ÷ 2.1=_______.
Perform division to find the answer,
8.19/2.1
= 3.9
(f)
The given expression is 12.32 ÷ 7.7=_______.
Perform division to find the answer,
12.32/7.7
= 1.6
(g)
The given expression is 25.3 ÷ 4.6=_______.
Perform division to find the answer,
25.3/4.6
= 5.5
(h)
The given expression is 146.32 ÷11.8=_______.
Perform division to find the answer,
146.32/11.8
= 12.4
Hence, the answers to the problems are calculated. The first answer is
2.7 ÷ 3= 0.9
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Which polynomial function's graph is shown here?
OA)/(x) = (x + 1)(x+3)(x+4)
OB)/(x) = (x + 1)(x-3) (x+4)
OC)/(x) = (x-1) (x+3)(x-4)
OD)/(x) = (x-1) (x-3) (x-4)
find the missing side. round to the nearest 10th.
i need the answer to all 3, will mark brainliest
Answer:
6) x=20.64
7) x=12.423
8) x=26.5
Step-by-step explanation:
for how many pairs of consecutive integers in is no carrying required when the two integers are added?
The number of pairs of consecutive integers in is no carrying required when the two integers are added are 156.
How we make the pairs of consecutive integers?At the point when the last 3 digits of the continuous numbers are _999 and _000. Just conceivable case-1999, 2000
At the point when the last 2 digits of the continuous numbers are _ _ 9 9 and _ _ 0 0. Potential cases-5 (Comparing to (0,1) (1,2) (2,3) (3,4) (4,5) in the 100th spot)
At the point when the last digit of the successive numbers is of the structure _ _ _ 9 and _ _ _ 0. Potential Cases-5*5 = 25
At the point when none is of that structure. Potential cases-5*5*5 = 125
Reply = 125+25+5+1 = 156
Thus,there are 156 ways to make the pairs of the consecutive integers.
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Identify the variation as direct, inverse, joint or combined. Y = 7x inverse combined joint direct.
The given variation y = 7x is a direct variation where any increase in the variable x also increases the value of the variable y.
The given variation is represented as -
y = 7x
We have to identify if the given variation is direct or inverse or joint or combined.
Let us first the different mathematical relationships mentioned here.
Direct variation is a mathematical relationship established between two different variables that can be represented in the form of an equation where one variable is a multiple of the other by a constant.Inverse variation is a mathematical relationship established between two different variables where any increase in one variable leads to the decrease in the other variable.Joint variation is a mathematical relationship where one variable is dependent on two or more variables.Combined variation is a mathematical relationship which is basically a combination of direct, inverse, as well as joint variation.Now that we know the definitions of different types of variations, let us look into the given variation, which is -
y = 7x
We can see that the variable y is 7 times the multiple of another variable x. Thus, this is a case of direct variation such that any increase in the variable x also increases the value of the variable y.
Therefore, the given variation y = 7x is a direct variation type.
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Exercie 11-50,evaluate the limit if it exit. If not,determine whether the one ided limit exit(finite or infinite)lim(xto2^{-})(x-3/x-2)
The function's one sided limit is [tex]+\infty[/tex].
Given function,
[tex]\lim_{x \to 2^-} \frac{x-3}{x-2}\\\\= \frac{2-3}{2-2}\\\\=\frac{-1}{0}\\\\=\infty[/tex]
Thus, it reaches infinity then the limit does not exist.
From the given function, it is observed x belongs to [tex]2^-[/tex] it means it's graph will start from left.
To determine it's one sided limit, substitute a smaller number which is very close to 2 i.e.1.9999
It's one sided limit will be
[tex]\lim_{x \to 2^-} \frac{x-3}{x-2}\\\\=lim_{x \to 2^-}(x-3)*lim_{x \to 2^-}(\frac{1}{x-2})\\\\=(1.9999-3)*(\frac{1}{1.99999-2})\\\\=-1.0001*(\frac{1}{-0.0001})\\\\[/tex]
When denominator is a very small number in a fraction then the fraction equals to infinity.
[tex]=-1.0001*-\infty\\=+\infty[/tex]
Hence, the function's one sided limit reaches to positive infinity.
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What does f/g )( x mean?.
The expression (f/g) (x) means that the function f(x) is divided by g(x).
According to the question,
We have the following information:
f/g(x)
Now, this expression can be simply expressed as f(x) divided by g(x) where the two functions are also expressed in terms of x.
For example, it can be better understood as with the following two functions:
f(x) = 2x+1
g(x) = 5x
Now, the expression f/g(x) can be simply expressed as follows:
f/g(x) = (2x+1)/5x
In other words, it can be expressed as f(x) is divided by g(x).
Hence, the expression (f/g) (x) means that the function f(x) is divided by g(x).
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what are the odds of randomly generating an even number with the first two odd numbers and unique numbers
The odds of randomly generating an even number with the first two odd numbers and unique numbers = [tex]\frac{10}{16}= \frac{5}{8}[/tex].
Sum will be even if either both numbers are odd or both numbers are even .
So, Total no. of way to select numbers for making sum even
= 5C2 + 4C2 = 10 + 6 = 16
And, Total numbers of ways to select two odd numbers such that sum is even = 5C2 = 10
Probability that both numbers are odd = [tex]\frac{10}{16}= \frac{5}{8}[/tex]
Hence the answer is the odds of randomly generating an even number with the first two odd numbers and unique numbers = [tex]\frac{10}{16}= \frac{5}{8}[/tex].
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For each sequence find the first 4 terms and the 10th term n 5 , , , , ...,
The first 4 terms are 6,7,8,9 and the 10th term is 15 for given sequence.
Given:
n + 5
substitute n = 1,2,3,4....
= n+5
= 1+5
= 6
= 2+5
= 7
= 3+5
= 8
= 4+5
= 9
First four terms are 6,7,8,9
[tex]T_10 =[/tex] a + (n-1)d
= 6 + (10-1)1
= 6+9*1
= 15
10th term = 15
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Full question:
For each sequence find the first 4 terms and the 10th term:
n + 5.
(A.2) Please determine whether the following is a equivalence relation.
a) [1010001000101000001000001]
b) [0001001000001001001000000]
c) Domain is {0,1}6. Define relation R: xRy if y can be obtained from x by swapping any two bits.
Using Equivalence relation conditions ,
option (b) and option (c) are shows equivalence Relation.
Equivalence Relation : A relation is called (∼ ) an equivalence relation on a set A if it satisfies the following three properties:
a) reflexivity: for all a∈A,
a∼a
b) symmetry: for all a,b∈A,
if a∼b then b∼a.
c) transitivity: for all a,b,c∈A,
if a∼b and b∼c then a∼c.
first consider the matrix ,
A = [10100 ; 01000; 10100; 00010; 00001]
A = matrix form start [10100 end brackets
01000
10100
00010
00001]
it is a 5×5 matrix and row 1ˢᵗ and 3ʳᵈ are equivalent which implies determinnant is zero .
So, Matrix A is not equivalent relation.
b) let B = [00010;01000;00100;10010;00000]
we can see that last row (5ᵗʰ ) and last Colomn (5ᵗʰ )have zero enteries.
by simple row and column operation and proper arrangements we get an identity matrix of 4× 4 with 5ᵗʰcolumn and row zero enerties.
So, Identity matrix is always satisfied all three conditions of equivalence Relation.
c) Now, We have the first relation R defined as:
xRy : a relation between x and y exist if y can be obtained from x by swapping any two bits
i. Reflexivity: Any string is clearly related to itself as we can get the same string by swapping a bit with itself.
ii. Symmetry: Let xRy, then y is obtained from x by swapping two bits. Thus, x can be obtained from y by swapping the same bits. Hence the relation is symmetric.
iii. Transitive: Consider the three strings a = 1 0 1 0 1 0, b = 1 0 0 1 1 0, c = 1 0 0 1 0 1. Then b can be obtained from a by swapping the middle two bits, and c can be obtained from b by swapping the last two bits, but, c cannot be obtained from a by swapping two bits only. Hence aRb, bRc but a is not related to c. Therefore the relation is not transitive.
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What is the greatest common multiple of 10 and 40?.
The greatest common multiple of 10 and 40 is 10.
What is meant by greatest common multiple?The greatest common divisor (GCD) of two or more integers, where at least one of them is not zero, is the largest positive integer that is a divisor of both numbers. For example, the GCD of 8 and 12 equals 4.
In the divisibility preorder relation, the GCD of a and b is their greatest positive common divisor. This signifies that a and b's common divisors are the same as their GCD divisors. The Euclidean algorithm or Euclid's lemma are widely used to establish this. This is the definition of "greatest" in the context of GCD generalizations.
Foe calculating the GCD of 10 and 40, we have to find the factors of 10 and 40.
Factors of 10:
1, 2, 5, 10
Factors of 40:
1, 2, 4, 5, 10, 20, 40
From all these factors we have to choose the greatest factor that is exactly divisible by both 10 and 40 are 1, 2, 10, and 5.
So, the greatest common multiple of 10 and 40 is 10.
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X corporation has 2100 shares outstanding. John owns 900 shares, Mary owns 400 shares Z corporation owns 400 shares and Y partnership owns 400 shares. John and Mary are equal partners of Y partnership. John owns 30 percent of Z corporation. A Applying stock attribution rules, how many shares are owned by John B Assume John owns 60 percent of Z corporation, how many shares are owned by John?
Answer:
Step-by-step explanation:
it 10
How many roots are there if the discriminant of quadratic equation is greater than zero?.
Two distinct real roots are there if the discriminant of quadratic equation is greater than zero.
What is quadratic equation ?
ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
There are two different real roots when the discriminant is higher than 0. There is just one real root when the discriminant is equal to 0. There are exactly two unique imaginary roots when the discriminant is smaller than zero, but no real roots. In this instance, there are two actual roots.
We are aware that the discriminant of a quadratic equation can be used to determine the type of roots in the equation. There will be two real and separate roots to the equation if the discriminant is bigger than zero.
There will be a real root in the equation if the discriminant is zero. The equation will only have two complex roots rather than any real roots if the discriminant is smaller than zero.
The locations where an equation's curve intersects the x-axis can be used to define an equation's roots graphically.
Therefore, the curve crosses the x-axis twice if an equation has two roots. This graph is provided by;
quadratic equation of the kind discriminant;
ax^2 + bx + c = 0 is given by D = b^2 -4ac.
If D>0, the equation has 2 real and distinct roots. They are given by
[tex]x = \frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
If D=0, the equation has a real root, which is given by,
x = -b/2a
If D<0, the equation has complex roots.
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help!!!!!!!!!!!!!explain and answer!!!!!!!
Answer:
a) 125 ml milk
b) 7.5g
Step-by-step explanation:
since 8 pancakes you need 250 ml of milk then you divide 250 by 2 since 8/2 is 4
250/2
125 ml milk
b)
We do the same as the other problem we find how much you need for 4 pancakes
5/2
2.5
Now you multiply by 3 since 4x3=12
2.5x3
7.5 g
Hopes this helps please mark brainliest
in a study of the u.s. census, informants would be , whereas respondents would be .
In a study of the u.s. census, informants would be statisticians respondents would be any U.S.citizens
Detailed meaning of survey research: Survey research is a research method involving the use of standardized questionnaires or interviews to collect data about people and their preferences, thoughts, and behaviors in a systematic manner. Although census surveys were conducted as early as Ancient Egypt, survey as a formal research method was pioneered in the 1930-40s by sociologist Paul Lazarsfeld to examine the effects of the radio on political opinion formation in the United States. This method has since become a very popular method for quantitative research in the social sciences.
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a plane flying at an altitude of 7 miles above a radar antenna passes directly over the radar antenna (see figure). let d be the ground distance from the antenna to the point directly under the plane and let x be the angle of elevation to the plane from the antenna. (d is positive as the plane approaches the antenna.) write d as a function of x. d
A function of d which is the ground distance from the antenna to the point directly under the plane and x which is the angle of elevation to the plane from the antenna is written as
d = 7/tan x How to write the functionThe function is written using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The direction of movements describes a right triangle of
opposite = 7 miles
adjacent = d miles
The function is written using tan, TOA let the angle be x
tan x = Opposite / Adjacent
tan x = 7 / d
d = 7 / tan x
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In an application to etimate the mean number of mile that downtown employee commute to work round trip each day, the following information i given: n = 20 = 4. 33 = 3. 50 The point etimate for the true population mean i
Using T-test, the upper limit for a 95 percent confidence interval estimate for the true population mean is: 5.965.
T-Test:
When population data are limited, small samples should be used to estimate confidence intervals for the population mean. If your sample size is less than 30 and we don't know the population standard deviation, then you have the normal distribution instead, and use the t distribution instead of the normal distribution.
We have given that,
Estimate the mean number of mile that downtown employee commute to work round trip each day,
sample mean (X-bar) = 4.33
sample size (n) = 20
standard deviations of sample (s) = 3.50
we have to calculate the value of true population .
The degree of freedom is going to be equal to (20 - 1 )= 19 for the sample size, 20. The confidence interval is 95 percent. The level of significance of the alpha is 100% - 95% = 5% that's confidence interval is 5 percent, which is basically in decimal.05.
Upper limit of Population mean = x-bar + t∗s√n
t value at 0.05 and degree of freedom 19 is 2.09
Upper Limit : 4.33 + 2.09×3.50√20
=5.965~ 6
the upper limit for a 95 percent confidence interval estimate for the true population mean is: 5.965.
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Complete Question:
In an application to estimate the mean number of miles that downtown employees commute to work roundtrip each day, the following information is given: n=20, Xbar-4.33, s-3.5.
Based on this information, the upper limit for a 95 percent confidence interval estimate estimate for the true population mean is:
a)1,638
b) 3,5
c) 4,33
d) 4.33 +- 1.638