The simple interest rate that the money would be paid is 20%
Simple interestFrom the question, we are to determine the interest rate that the money would be paid
Using the formula for simple interest,
S.I = PRT/100
Where S.I is the simple interest
P is the principal
R is the rate
and T is the time
From the given information,
P = 2000
S.I = Amount - Principal = 3600 - 2000 = 1600
R = ?
T = 4
Putting the parameters into the equation, we get
1600 = (2000 ×R × 4) / 100
1600 = 20 × R × 4
1600 = 80R
R = 20%
Hence, the simple interest rate that the money would be paid is 20%
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Based on the length sir the segments in the hyperbola below, how long is the transverse axis?
Answer: The transverse axis of the hyperbola lies on the line y=–3 and has length 6; the conjugate axis lies on the line x=2 and has length 8.
Step-by-step explanation:
See attachment for the full question
The inverse of the demand function is; P = 9 - 0.25Q
The profit-maximizing price and quantity are; $8.5 and 2 units.
The maximum profit is; $1
How to find the inverse of a function?
A) The demand function we are given is;
Q = 36 - 4P
Making P the subject gives the inverse demand function;
P = (36 - Q)/4
P = 9 - Q/4
P = 9 - 0.25Q
B) The profit-maximization point is the point at which MR = MC.
MR refers to the marginal revenue and MC is the marginal cost.
MC can be calculated as the first derivative of the cost function:
C(Q) = 4 + 4Q + Q²
MC = C'(Q) = 2Q + 4
Total Revenue = Price * Quantity
Total Revenue = (9 - 0.25Q) * Q
Total Revenue = 9Q - 0.25Q²
MR is gotten by differentiating Total Revenue to get;
MR = 9 - 0.5Q
Applying the condition MR = MC, we have;
9 - 0.5Q = 4 - 2Q
Solving for Q gives Q = 2
Thus, profit maximizing quantity is 2.
Thus, profit maximizing price will be;
P(2) = 9 - 0.25(2)
P(2) = $8.5
C) Formula for Maximum Profit is;
Profit = Total Revenue - Total Cost
Total Revenue = 8.5 * 2
Total revenue = $17
Total Cost is;
C(2) = 4 + 4(2) + 2²
C(2) = $16
Thus;
Maximum Profit = 17 - 16 = $1
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Suppose f(x)=2^x. What is of g(x)=f(3x)?
Answer:
All you need to do is suppose x = 3x :
[tex] \tt \: g(x) = \boxed{ \tt{2^{3x} }} [/tex]
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On the number line above, points A, B, C, and D are integers, and AB: BC: CD = 3:2:1. What is the length of AC?
Using proportions, it is found that the length of AC is of 15 units.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The ratios in this problem are given as follows:
[tex]\frac{AB}{BC} = \frac{3}{2}[/tex].[tex]\frac{BC}{CD} = \frac{2}{1}[/tex].[tex]\frac{AB}{CD} = \frac{3}{1}[/tex].The entire length is of 18 units, AB is half of that, hence:
AB = 0.5 x 18 = 9 units.
BC is two thirds of the length from 6 to 15, hence:
BC = 2/3 x (15 - 6) = 6
Thus, the length of AC is:
AC = 9 + 6 = 15 units.
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Which of the following functions best describes this graph?
Answer:
C
Step-by-step explanation:
We can use process of elimination
D is incorrect because the roots are 3 and -4 and there are no negative roots visible
B is wrong because the roots -3 and -6 are both negative
You can factor A into (x-2)(x-3) and the roots are 2 and 3 but the roots on the graph look closer to 3 and 6
For C it can be factored as (x-6)(x-3) so the roots are 3 and 6 which look accurate
50 points!!! answer this quickly with an explanation
Answer:
x = 24°
Step-by-step explanation:
If two parallel lines are being intersected by the same line, the opposite inside angles are congruent. This means that ∠EFH should be equal to ∠JHF. However, we cannot set these angles equal because we do not know the value of ∠JHG.
Line IG is intersected by line HJ. This means the value of ∠JHG is 24° (180° - 156° = 24°). Know that we know this value, we can set up an equation to find "x".
∠EFH = 2x
∠JHG = 24°
∠GHF = x
∠EFH = ∠JHF <----- Opposite interior angles are equal
∠EFH = ∠JHG + ∠GHF <----- Break ∠JHF into 2 angles
2x = 24 + x <----- Insert values
x = 24 <----- Subtract x from both sides
A farmer finds there is a linear relationship between the number of bean stalks, n , she plants and the yield, y , each plant produces. When she plants 30 stalks, each plant yields 30 oz of beans. When she plants 33 stalks, each plant produces 29 oz of beans. Find a linear relationship in the form y=mn+b that gives the yield when n stalks are planted.
The equation y = -0.5x +45 represent the linear relationship.
According to the statement
We have given that the When she plants 30 stalks, each plant yields 30 oz of beans and When she plants 33 stalks, each plant produces 29 oz of beans.
And we have to find the linear relationship between the plants which are stalks.
So, For this purpose,
When we consider this graph as a straight line, the two points lying on the line would be
(30, 30) and (34, 28) taking n as horizontal and y vertical
Using two point equation we find that
the equation of the line is
y-y1 / y2-y1 = x-x1 / x2-x1
Substitute the points as x =n and put the other values in it then
y-30 / 28-30 = x-30 / 34-30
Then
y = -0.5x +45
This represent the relationship.
So, The equation y = -0.5x +45 represent the linear relationship.
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in fact, the cleanup will consist of ripping out all the walls and ceilings of an
The percentage discount from the base price result is 2.16%.
How to compute the value?Discount percent will be:
= (Base price - New price)/Base price × 100
= (9.40 - 9.20)/9.40 × 100
= 0.20/9.40 × 100
= 2.16%
The new price will be:
= Base price - (2.16% of base price)
= 9.40 - (2.16% × 9.40)
= 9.20
Therefore, the percentage discount from the base price result is 2.16%.
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Complete question:
A rodent infestation has left a landlord with a major cleanup job; in fact, the cleanup will consist of ripping out all the walls and ceilings of an 1860-square-foot house to replace them. A trip to the local home improvement store reveals that 4'x8' sheets of drywall have three price points as indicated in the table. Another consideration for the landlord is that he is equipped with only a humble half-ton pickup truck, that can hold at most 20 sheets. His truck sips fuel, so he considers only wear and tear on his vehicle at $5 to haul all the sheets he will use for the job. The holding percentage is 20%. The landlord believes the entire job - all walls and ceiling - will require 10,080 square feet of drywall.
Consider the $9.40 per sheet figure as the base price and use the information in Scenario 11.4 to answer the following question. What percentage discount from the base price results in an optimal order quantity of 101 sheets?
1.42%
2.16%
2.03%
1.86%
If
xn = (n−1)cos(n2 +n+1) 2n−1
EXERCISES
then xn has a convergence subsequence.
The proof using Bolzano-Weierstrass Theorem is suggestive of the fact that the bounded sequence that is given has a subsequence that is convergent.
What is Bolzano-Weierstrass Theorem?The Bolzano-Weierstrass theorem, is a key conclusion regarding convergence in a finite-dimensional Euclidean space in mathematics, notably in real analysis.
According to the theorem above, each bounded sequence in Rⁿ has a convergent subsequence.
***See proof in the attached document.
Hence the given sequence is bounded. It is safe therefore to state that given Bolzano-Weierstrass theorem, the stated real bounded sequence has a convergent subsequence.
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∫[tex]\frac{xdx}{(x^{2}+4)^{3} }[/tex]
Substitute [tex]u=x^2+4[/tex] and [tex]du=2x\,dx[/tex]. Then the integral transforms to
[tex]\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \int \frac{du}{u^3}[/tex]
Apply the power rule.
[tex]\displaystyle \int \frac{du}{u^3} = -\dfrac1{2u^2} + C[/tex]
Now put the result back in terms of [tex]x[/tex].
[tex]\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \left(-\dfrac1{2u^2} + C\right) = -\dfrac1{4u^2} + C = \boxed{-\dfrac1{4(x^2+4)^2} + C}[/tex]
What type of polynomial is: 3x4−2x3−2
The given polynomial is a Quartic trinomial
Types of polynomialFrom the question, we are to determine the type of the given polynomial
The given polynomial is
3x⁴−2x³−2
The highest degree of the polynomial is 4. Thus, it is a Quartic Polynomial.
Also, the expression contains exactly 3 terms. Thus, it is a trinomial.
Hence, the given polynomial is a Quartic trinomial
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Solve the following system by graphing and identify the point of intersection -5x+2y=-4 2x-y=2
Answer: Point of intersection (0, -2)
Step-by-step explanation:
Answer:
S = (0, -2)
Step-by-step explanation:
Convert both standard form equations to slope-intercept form.
-5x+2y=-4 ⇒ y = 5/2(Decimal form: 2.5)x - 2
2x-y=2 ⇒ y = 2x - 2
Given:
⇒ L1 = y = 5/2x - 2
⇒ L2 = y = 2x - 2
The intersection is point:
⇒ S = (0, -2)
Steps:
To find intersection point we need to solve the following system of equations.
y = 5/2x - 2y = 2x-2STEP 1: Solve for x
5/2x - 2 = 2x - 2
5/2x - 2x = -2 + 2
1/2x = 0
x = 0
STEP 2: Solve for y by substituting x = 0 into first equation.
y = 5/2 * 0 - 2 = 0 - 2 = -2
what is the measure of XYZ?
46°
94°
a. 46°
b. 140°
c. 94°
d. 70°
Answer:
46+96=140°_÷__^_^^^^=^
Write down the 2×2 matrices representing the following transformations of the plane. (i) Reflection in the y-axis, (ii) Reflection in the line y = x (iii) Rotation through 180◦ about the origin (iv) Enlargement from the origin with scale factor λ.
The 2 x 2 matrices of the transformations are
[tex]\left[\begin{array}{cc}-1&0\\0&1\end{array}\right][/tex], [tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right][/tex], [tex]\left[\begin{array}{cc}-1&0\\0&-1\end{array}\right][/tex] and [tex]\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right][/tex]
(i) Reflection in the y-axisThe rule of reflection in the y-axis is
(x, y) ⇒ (-x, y)
This is represented as:
[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&y\end{array}\right][/tex]
When solved using a graphing calculator, we have:
[tex]\left[\begin{array}{cc}-1&0\\0&1\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&y\end{array}\right][/tex]
Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}-1&0\\0&1\end{array}\right][/tex]
(ii) Reflection in the line y = xThe rule of reflection in the line y = x is
(x, y) ⇒ (y, x)
This is represented as:
[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}y&x\end{array}\right][/tex]
When solved using a graphing calculator, we have:
[tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}y&x\end{array}\right][/tex]
Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right][/tex]
(iii) Rotation through 180◦ about the originThe rule of rotation through 180◦ about the origin is
(x, y) ⇒ (-x, -y)
This is represented as:
[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&-y\end{array}\right][/tex]
When solved using a graphing calculator, we have:
[tex]\left[\begin{array}{cc}-1&0\\0&-1\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&y\end{array}\right][/tex]
Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}-1&0\\0&-1\end{array}\right][/tex]
(iv) Enlargement from the origin with scale factor λ.The rule of the enlargement from the origin with scale factor λ.
(x, y) ⇒ (λx, λy)
This is represented as:
[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}\lambda x&\lambda y\end{array}\right][/tex]
When solved using a graphing calculator, we have:
[tex]\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}\lambda x&\lambda y\end{array}\right][/tex]
Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right][/tex]
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An advertiser claims that 80% of people stream their TV, 10% have cable, and the rest do not watch TV. To evaluate this claim, they take a sample and calculate a test statistic of
. If their rejection region is, what would their conclusion be?
The conclusion that they would arrive at based on the rejection region would be to reject the null hypothesis.
What is the rejection region?This is the region that tells us that we are not to accept the null. The conclusion would be to reject the null.
This happens when the rejection region is found to be around the area that is in the critical value.
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How many ways can three different numbers be selected from 10 numbers to open a keypad lock?
A. 324 B. 260 C. 648 D. 720
There are 720 ways through which 3 numbers can be selected from 10 numbers to open a keypad lock.
Given that there are 10 numbers are 3 numbers are required to open a keypad lock.
Permutations are the number of ways in which objects can be selected without replacements to form subsets.
It is expressed as n[tex]P_{r}[/tex]=n!/(n-r)!.
Factorial of a number is the product of consecutive numbers less than the number.
Total numbers available=10
Numbers to be selected=3
Number of ways can be found by using permutations.
Number of ways =10[tex]P_{3}[/tex]
=10!/(10-3)!
=10!/7!
=10*9*8*7!/7!
=10*9*8
=720 ways.
Hence there are 720 ways through which 3 numbers can be selected from 10 numbers.
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On Monday the change in the value of one share of a companies stock can’t be represented as -$2.85 Tuesday the value of one share of the companies that changes again which of these describes a situation that would bring the total change for the two days to zero dollars
Step-by-step explanation:
If a stock's price falls all the way to zero, shareholders end up with worthless holdings. Once a stock falls below a certain threshold, stock exchanges will delist those shares.strong earning result in the stock price moving up and vice versa.
in the question you asked,the situation that will make stock price move from -$2.85 to zero means the stock, bond, or commodity market, or an index representing them, currently trades higher than it did at some specific point in the past.
Company XYZ closed at $46.07 per share with a P/E ratio of 16.66. Answer the following questions.
a.How much were earnings per share?
b.Does the stock seem overpriced, underpriced, or about right given that the historical P/E ratio is 12-14?
The amount of earnings per share is $2.77.
Earnings per sharea. Earnings per share = price per share / (P/E) ratio
Earnings per share = $46.07 / 16.66
Earnings per share= $2.77
B. Overpriced or underpriced stock
At P/E ratio = 12
Earnings per share = $46.07 / 12
Earnings per share = $3.84
Earning yield = ( Earning per share / market value )× 100
Earning yield = (3.84 / $46.07 ) × 100
Earning yield = 8.34%
At P/E ratio = 13
Earnings per share = $46.07 / 13
Earnings per share = $3.54
Earning Yield= (3.54 / 46.07 ) × 100
Earning Yield= 7.68%
At P/E ratio = 14
Earnings per share = $46.07 / 14
Earnings per share = $ 3.3
Earnings yield= ( 3.3 / 46.07 )×100
Earnings yield= 7.16%
Average of earning yield given P/E ratio is 12-14
Average of earning yield= ( 8.34 + 7.68 + 7.16 ) / 3
Average of earning yield= 7.73%
Earning yield = ( Earning per share / market value ) × 100
Earning yield= ( 2.77 / 46.07 ) ×100
Earning yield = 6.01%
Hence, Based on the above the stock is underpriced.
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what percentage was the price of the shirt reduced
10-A biased die is thrown thirty times and the number of sixes seen is eight. ( The probability of face six is 8 = 4 ) If the die is thrown a further twelve times find:
30 15
(a) the probability that a six will occur exactly twice; (b) the expected number of sixes: () = ;
(c) the variance of the number of sixes.
Using the binomial distribution, we have that:
a) There is a 0.2111 = 21.11% probability that a six will occur exactly twice.
b) The expected number of sixes is of 3.2.
c) The variance of the number of sixes is of 2.35.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the parameters are given by:
p = 8/30 = 0.2667, n = 12.
Item a:
The probability is P(X = 2), hence;
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{12,2}.(0.2667)^{2}.(1-0.2667)^{10} = 0.2111[/tex]
Item b:
The expected number of the binomial distribution is:
E(X) = np.
Hence:
E(X) = 12 x 8/30 = 3.2.
Item c:
The variance of the binomial distribution is:
V(X) = np(1-p).
Hence:
E(X) = 12 x 8/30 x 22/30 = 2.35.
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Please draw the number line and show me if possible:)
The solution to the given inequality expression is expressed as x ≥ 6
Solving inequalitiesGiven the inequality expression shown below;
5x-9/7≥3
Cross multiply
(5x -9)≥7(3)
Expand
5x-9≥21
Add 9 to both sides
5x ≥ 21 + 9
5x ≥ 30
x ≥6
The solution to the given inequality expression is expressed as x ≥ 6
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Ross Martin arrived at the following tax information gross salary 56,145 interest earnings 205 dividend income 65 standard deduction 12,000 itemized deductions 11,250 adjustments to income 1200 what amount with Ross report as taxable income income
The amount that Ross report as taxable income will be $31965.
What is a taxable income?Taxable income refers to the base upon which an income tax system imposes the tax.
In other words, the taxable income is the income over which the government imposed tax. It includes some or all items of income and is reduced by expenses and other deductions.
From the information:
Gross salary = $56,145
Interest earnings = $205
Dividend income = $65
Standard deduction = $12,000
Itemized deductions = $11,250
Adjustments to income = $1,200
The taxable income is given by:
= Gross salary + Interest earnings + Dividend income - Standard deduction - Itemized deductions - Adjustment to income
= 56145 + 205 + 65 - 12000 - 11250 - 1200
= $31965
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The weight of toys a toddler owns has a population mean of 15.8kg and a population standard deviation of 4.2kg. What is the probability a toy store owner could select a sample of 49 toddlers and find the sample mean to be
(a) 15.1kg or less? (answer?)
(b) 15.1kg or more? (answer?)
Leave all answers to 4 decimal places.
The weight of toys a toddler owns has a population mean of 15.8kg and a population standard deviation of 4.2kg. then the probability a toy store owner could select a sample of 49 toddlers and find the sample mean to be 15.1kg or less is 0.121 and 15.1kg or more is 0.879.
Given Information:
Population mean, μ = 15.8 kg
Population standard deviation, σ = 4.2 kg
For finding the probability for the sample mean, we first need to find the standard score.
(a) For sample mean to be 15.1kg or less,
z = (x - μ) / (σ/√n)
Here, x = 15.1
⇒ z = (15.1 - 15.8) / (4.2/√49
z =-0.7 / (4.2/7)
z = -1.17
Now, we can use the z-table to find the probability of the sample mean to be 15.1kg or less.
∴ P(x ≤ 15.1) = 0.121
(b) Now, to find the probability of sample mean to be 15.1kg or more, we can simply subtract P(x ≤ 15.1) from 1.
⇒ P(x ≥ 15.1) = 1 - P(x ≤ 15.1)
P(x ≥ 15.1) = 1 - 0.121
P(x ≥ 15.1) = 0.879
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what is the value of x 44 inches and 55 inches triangle
Answer: I don't know what you are talking about, but if x is the area, then the answer is 1,210.
Step-by-step explanation: 44 x 55 x 1/2 = 1,210. The formula for the area of a triangle is 1/2 times length times height. Therefore, x = 1,210
Hope this helps.
Which of the following rational functions is graphed below?
Answer: D
Step-by-step explanation:
There are vertical asymptotes at x=7 and x=-3, so the denominator should have factors of (x-7) and (x+3).
This eliminates everything except for D.
When given -5(x + 4) = 90 and trying to prove that x = -18, what should be placed in line A of the two-column proof? Statement Reason 1. -5(x + 4) = 90 1. Given 2. -5x − 20 = 90 2. _____A______ 3. _______B________ 3. Addition Property of Equality 4. x = -22 4. ____C_______ Subtraction Property of Equality Distributive Property
The 4 reasons for the Algebra proof are respectively;
Given; Distributive property; Addition Property; Division Property
How to use algebra properties?We want to use algebra properties to find the value of x in the expression; -5(x + 4) = 90
Statement 1; -5(x + 4) = 90
Reason 1; Given
Statement 2; -5x - 20 = 90
Reason 2; Distributive property of Algebra because we distributed -5 into the bracket terms.
Statement 3; -5x = 110
Reason 3; Addition property of equality because we added 20 to both sides to achieve that.
Statement 4; x = -22
Reason 4; Division property of equality because we divided both sides by -5 to obtain x = -22.
Thus, the 4 reasons are respectively;
Given; Distributive property; Addition Property; Division Property
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in how many ways can the letters in the word payment be arranged if the letters are taken 6 at a time
Considering the definition of permutation, in 5040 ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 6 at a time.
What is PermutationPermutation is placing elements in different positions. So, permutations of m elements in n positions are called the different ways in which the m elements can be arranged occupying only the n positions.
That is, permutations refer to the action of arranging all the members of a set in some sort of order or sequence.
In other words, permutations (or Permutations without repetition) are ways of grouping elements of a set in which:
take all the elements of a set.the elements of the set are not repeated.order matters.To obtain the total of ways in which m elements can be placed in n positions, the following expression is used:
[tex]mPn=\frac{m!}{(m-n)!}[/tex]
where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.
This caseIn this case, you have:
the letter word "PAYMENT", where the number of letters is 7.the letters are taken 6 at a time.Then, you know that:
m= 7n=6Replacing in the definition of permutation:
[tex]7P6=\frac{7!}{(7-6)!}[/tex]
Solving:
[tex]7P6=\frac{7!}{1!}[/tex]
7P6= 5040
Finally, in 5040 ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 6 at a time.
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Number graph ranging from negative one to seven on the x axis and negative four to four on the y axis. Two lines that are perpendicular to each other intersect at (two, one). The line with a positive slope is labeled a and the line with a negative slope is labeled b. Use the graph to state the solution for the system. x + 2y = 4 (line a) 3x – 2y = 4 (line b) (2, –1) (2, –1) (2, 1) (2, 1) (–2, 1)
The solution for the system of lines is defined as follows,
x-Intercept for line a: (4,0)
y-Intercept for line a: (0,2)
x-Intercept for line b: (1.5, -0)
y-Intercept for line b: (0,-2)
Line a and b intersect at (2,1)
Solving the System of Lines:
Line a: x + 2y = 4
Line b: 3x – 2y = 4
From the graph,
Line a intersect x-axis at (4,0) and y-axis at (0,2)
Line b intersect x-axis at (-1.5,0) and y-axis at (0,-2)
x + 2y = 4
x = 4-2y
Since point P lies on bot the lines A and B, it will satisfy the equations of both a and b.
Thus, substituting x = 4-2y in the equation of line b, we get,
3(4-2y) - 2y = 4
12 - 6y - 2y = 4
8y = 8
y = 1
Putting y=1 in the equation of line a, x = 4-2y, we get,
x = 4-2(1)
x = 4-2
x = 2
Hence, point P≡(2,1).
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A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them that the last 18 houses that sold in their neighborhood took an average time of 100 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 20 days. (You may find it useful to reference the z table.)
a. What assumption regarding the population is necessary for making an interval estimate for the population mean?
multiple choice
Assume that the central limit theorem applies.
Assume that the population has a normal distribution.
b. Construct the 99% confidence interval for the mean sale time for all homes in the neighborhood. (Round final answer to 2 decimal places.)
The 99% Confidence interval for the mean sale time for all homes in the neighborhood is:87.857, 112.143.
Confidence intervala. The assumption is: Assume that the population has a normal distribution.
The CI is exact for the normal populations and for small samples the z-interval method should be used in a situation where the variable is normally distributed.
b. Confidence interval:
CI=Sample mean±z-score×Standard deviation/√Size of the sample
CI=100-2.576×20/√18, 100+2.576×20/√18
CI=100-12.143, 100+12.143
CI=87.857, 112.143
Therefore the 99% Confidence interval is 87.857, 112.143.
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choose the correct option that explains what steps were followed to obtain the system of equations below x+6y = 5
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution of system B will be the same as the solution of system A.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
System A:
x + 6y = 5 and; 3x - 7y = -35
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3.
System B:
x + 6y = 5 and; - 25y = -50
The solution of system B will be the same as the solution of system A.
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