Answer: A
Step-by-step explanation: M= -28
6.1 Colby bought a laptop worth Rx for his university studies. The value of the laptop decreased at r% per annum using the reducing balance method. After 4 years, the value of the laptop was worth 31 of its original price. Calculate r, the rate of depreciation.
6.2 On 1 February 2014 , Ncominkosi took a loan from a bank to buy a car. His first payment for the loan was due on 31 July 2014 . Once he started paying the loan, it took him 6 years to fully pay the loan at an interest rate of 9,5% p.a. compounded monthly. In total, he paid the bank R596 458,10.
6.2.1 How much was his monthly instalment?
6.2.2 How much money did he borrow from the bank? Write down your answer to the nearest rand.
6.1). the rate of depreciation, r, is approximately 10.77%.
6.2.1). Ncominkosi's monthly installment amount was approximately R 10,505.29.
6.2.2). Ncominkosi borrowed approximately R 377,510.83 from the bank.
6.1) Let's assume the original price of the laptop is P. According to the reducing balance method, the value of the laptop after 4 years can be calculated as P * (1 - r/100)^4. We are given that this value is 31% of the original price, so we can write the equation as P * (1 - r/100)^4 = 0.31P.
Simplifying the equation, we get (1 - r/100)^4 = 0.31. Taking the fourth root on both sides, we have 1 - r/100 = ∛0.31.
Solving for r, we find r/100 = 1 - ∛0.31. Multiplying both sides by 100, we get r = 100 - 100∛0.31.
Therefore, the rate of depreciation, r, is approximately 10.77%.
6.2.1) To determine the monthly installment amount, we can use the formula for calculating the monthly payment on a loan with compound interest. The formula is as follows:
\(P = \frac{r(PV)}{1-(1+r)^{-n}}\)
Where:
P = Monthly payment
PV = Loan principal amount
r = Monthly interest rate
n = Total number of monthly payments
Let's calculate the monthly installment amount for Ncominkosi's loan:
Loan amount = Total amount paid to the bank - Interest
Loan amount = R 596,458.10 - R 0 (No interest is deducted from the total paid amount since it is the total amount paid)
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 9.5% / 12 = 0.0079167 (rounded to 7 decimal places)
Number of monthly payments = 6 years * 12 months/year = 72 months
Using the formula mentioned above:
\(P = \frac{0.0079167(Loan Amount}{1-(1+0.0079167)^{-72}}\)
Substituting the values:
\(P = \frac{0.0079167(596458.10}{1-(1+0.0079167)^{-72}}\)
Calculating the value:
P≈R10,505.29
Therefore, Ncominkosi's monthly installment amount was approximately R 10,505.29.
6.2.2) To determine the amount of money Ncominkosi borrowed from the bank, we can subtract the interest from the total amount he paid to the bank.
Total amount paid to the bank: R 596,458.10
Since the total amount paid includes both the loan principal and the interest, and we need to find the loan principal amount, we can subtract the interest from the total amount.
Since the interest rate is compounded monthly, we can use the compound interest formula to calculate the interest:
\(A=P(1+r/n)(n*t)\)
Where:
A = Total amount paid
P = Loan principal amount
r = Annual interest rate
n = Number of compounding periods per year
t = Number of years
We can rearrange the formula to solve for the loan principal:
\(P=\frac{A}{(1+r/n)(n*t)}\)
Substituting the values:
Loan principal (P) = \(\frac{596458.10}{(1+0.095/12)(12*6)}\)
Calculating the value:
Loan principal (P) ≈ R 377,510.83
Therefore, Ncominkosi borrowed approximately R 377,510.83 from the bank.
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I need a written response to solve all 4 steps
a. Find the slope of the line that passes through the points (2,-5) and (-2,3).
b. What are the slope and y-intercept of the equation 2x - 5y = -10?
c. Find the x value so that the line through the points (x,-9) and (0,1) has a slope of -4.
d. Write the equation of a line that passes through the point (-1,5) and has a slope of -7. Your answer should be given in the form y = mx + b.
Answer:
a. -2
b. s = 2 and y = -5
c. (2.5, -9)
d. -7x - 2
Step-by-step explanation:
a. In the image, I have used rise over run, which is -8/4 or -2.
b. slope formula is mx + b = y, where m is slope and b is the y-intercept. In the equation 2x - 5y = -10, 2 is the slope and -5 is the y-intercept.
c. Plug in all given numbers into an equation and the ones you do not have will be in the points you need it to be. Once you graph the equation you will receive (2.5, -9).
d. y = mx + b
5 = (-7)(-1) + b
5 = 7 + b
-2 = b
y = -7x - 2
If A - B = {2,4,6}, B - A = {0,1,3}, and A∪B = {0,1,2,3,4,5,6,7,8}. What is A∩B?
Answer:
{5,7,8}
Step-by-step explanation:
A-B = {2,4,6} => A={2,4,6}
B - A = {0,1,3} => B= {0,1,3}
A∪B = {0,1,2,3,4,5,6,7,8}
=> A = {2,4,5,6,7,8}
B= {0,1,3,5,7,8}
=> A∩B = {5,7,8}
What is the las digit of the product of all the numbers between 11 and 29?
The last digit of the product of all the numbers between 11 and 29 is 0.
A product is something that has undergone one or more multiplications.
Here, we're looking for the final digit of the product of all whole numbers greater than 11 and less than 29.
Next, we have the product as: 12*13*14*15*16*17*18*19*20*21*22*23*24*25*26*27*28
Now take note of the 20 that is present.
Any number multiplied by 20 will result in a zero, so:
Product = 20*(12*13*14*15*16*17*18*19*21*22*23*24*25*26*27*28)
Using only that, we can infer that 0 represents the final digit in the product of all the numbers between 11 and 29.
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Three friends all live
on the same street that runs west to east. Beth
lives 5 blocks from Ann. Carl lives 2 blocks from
Beth. If the street is represented by a number
line and Ann's house is located at 0, what are the
possible locations for Carl's house? Assume that
each unit on the number line represents 1 block.
Answer:
Carl lives seven blocks away from Ann
Step-by-step explanation:
You start at Ann's house ( 0 ) 0+5+2=7
Beth is five blocks from Ann ( 5 )
Carl lives two blocks from Beth ( 2 )
Answer:
carl can be at 4 or 2
Step-by-step explanation:
Given a rhombus with a side length of 8m. There is another rhombus inside.
Calculate the sim of the perimeters of both quadrilaterals!
What is the smallest positive integer n for which \(n^{2}\) is divisible by 18 and \(n^{3}\) is divisible by 640?
Answer:
120
Step-by-step explanation:
n^2 has a factor of 18, so factors of 3^2·2. Since n^2 is a perfect square, we know n must have a factor of 3·2 = 6.
n^3 has a factor of 640, so factors of 2^7·5. Since n^3 is a perfect cube, we know n must have a factor of 2^3·5 = 40.
The least common multiple of 6 and 40 is 120.
The smallest positive integer n is 120.
_____
Check
120^2/18 = 800
120^3/640 = 2700
Can someone help I don't get it!!!! Solve for T. Type your answer in the blank without "T="
Answer:
45
Step-by-step explanation:
arcAE = 180
arcABC : arcCDE = 3:1
ABC:CDE = 135:45
∠T = 1/2(135 - 45) = 45
Use the Far Arc -- Near Arc Formula: m∠T = 1/2(far-arc - near-arc) = 1/2(arcABC -arcCDE)
so let's recall that a full circle has a total of 360°, and we also know that these two arcs are on 3 : 1 ratio.
Now, let's notice the points A and E, the line AE passes through the center of the circle, that means the arc made by ABCE is half the circle or 180°.
So if we just divide 180 by (3 + 1) and then distribute accordingly to each arc, we'll see how many degrees each arc really has
\(\stackrel{\widehat{ABC}}{3}~~ : ~~\stackrel{\widehat{CDE}}{1}\qquad \implies \qquad \stackrel{\widehat{ABC}}{3\cdot \frac{180}{3+1}}~~ : ~~\stackrel{\widehat{CDE}}{1\cdot \frac{180}{3+1}} \\\\\\ \stackrel{\widehat{ABC}}{3\cdot 45}~~ : ~~\stackrel{\widehat{CDE}}{1\cdot 45}\qquad \implies \qquad\stackrel{\widehat{ABC}}{135}~~ : ~~\stackrel{\widehat{CDE}}{45}\)
Check the picture below.
360 antza न Draw an angle with the given measure in standard position. SL 5x 180 472 5
We are asked to draw the following angle
\(-\frac{47\pi}{18}\)Let us first convert this angle to degrees
\(\begin{gathered} degrees=radians\times\frac{180\degree}{\pi} \\ degrees=-\frac{47\pi}{18}\times\frac{180\degree}{\pi} \\ degrees=-470\degree \end{gathered}\)So the angle is negative 470°
For positive angle, we need to draw in the counterclockwise direction
For negative angle, we need to draw in the clockwise direction
Recall that 360° is one complete rotation and 470° - 360° = 110°
Recall that 90° is equal to one quadrant so 110° - 90° = 20°
So, we need to draw one complete rotation plus one quadrant plus 20° in the clockwise direction.
Francisca is planning a two -week vacation to one of two cities and wants to base her decision on the weather history for the same dates as her vacation . She has collected the number of days that it has rained during this two - week period for each city over the past 10 years . The results are shown .
Francisca prefers less rainfall, she might choose City B, as it generally has fewer rainy days during the two-week period.
Here are the results for the number of rainy days during a two-week period over the past 10 years for the two cities:
City A:
Year 1: 8 rainy days
Year 2: 10 rainy days
Year 3: 7 rainy days
Year 4: 9 rainy days
Year 5: 6 rainy days
Year 6: 10 rainy days
Year 7: 8 rainy days
Year 8: 9 rainy days
Year 9: 7 rainy days
Year 10: 6 rainy days
City B:
Year 1: 4 rainy days
Year 2: 5 rainy days
Year 3: 6 rainy days
Year 4: 4 rainy days
Year 5: 5 rainy days
Year 6: 7 rainy days
Year 7: 3 rainy days
Year 8: 6 rainy days
Year 9: 5 rainy days
Year 10: 4 rainy days
Based on this information, Francisca can compare the number of rainy days between the two cities to make her decision. If she prefers less rainfall, she might choose City B, as it generally has fewer rainy days during the two-week period. However, other factors such as temperature, attractions, or personal preferences may also influence her decision.
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Find an LU factorization of the matrix A (with L unit lower triangular). A=
⎣
⎡
4
−8
10
−8
8
−4
3
5
−7
7
6
−7
0
3
−3
⎦
⎤
The LU factorization of matrix A is A = LU, where L = [[1, 0, 0], [-2, 1, 0], [1.5, -3, 1]] and U = [[4, -8, 10], [0, 24, -27], [0, 0, -12.5]].
Let's go step by step to find the LU factorization of matrix A.
Matrix A:
A =
[4, -8, 10]
[-8, 8, -7]
[6, -7, 3]
Step 1:
Initialize the L matrix as an identity matrix of the same size as A.
L =
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
Step 2:
Perform Gaussian elimination to obtain U.
- Multiply the first row of A by (1/4) and replace the first row of A with the result.
A =
[1, -2, 2.5]
[-8, 8, -7]
[6, -7, 3]
- Subtract 8 times the first row of A from the second row of A and replace the second row of A with the result.
A =
[1, -2, 2.5]
[0, 24, -27]
[6, -7, 3]
- Subtract 6 times the first row of A from the third row of A and replace the third row of A with the result.
A =
[1, -2, 2.5]
[0, 24, -27]
[0, 5, -12.5]
Step 3:
Update the L matrix based on the operations performed during Gaussian elimination.
L =
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
Step 4:
The resulting matrix A is the upper triangular matrix U.
U =
[1, -2, 2.5]
[0, 24, -27]
[0, 5, -12.5]
Therefore, the LU factorization of matrix A is:
L =
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
U =
[1, -2, 2.5]
[0, 24, -27]
[0, 5, -12.5]
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the graphs of the tangent, cotangent, secant, and cosecant functions all have ___ asymptotes.
The graphs of the tangent, cotangent, secant, and cosecant function all have vertical asymptotes.
Vertical asymptotes are vertical lines that the graphs approach but never touch or cross. These asymptotes occur at points where the functions become undefined or have a vertical discontinuity.
For the tangent function (tan(x)), the vertical asymptotes occur at x-values where the cosine function (cos(x)) equals zero. Since cos(x) is zero at every multiple of π/2, the tangent function has vertical asymptotes at x = π/2, 3π/2, 5π/2, and so on.
Similarly, for the cotangent function (cot(x)), the vertical asymptotes occur at x-values where the sine function (sin(x)) equals zero. Since sin(x) is zero at every multiple of π, the cotangent function has vertical asymptotes at x = π, 2π, 3π, and so on.
The secant function (sec(x)) and cosecant function (csc(x)) are reciprocal functions of the cosine and sine functions, respectively. Therefore, their graphs also have vertical asymptotes at the same x-values where the cosine and sine functions equal zero.
In conclusion, the graphs of the tangent, cotangent, secant, and cosecant function all have vertical asymptotes.
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Mr.Patterson, was the fastest teacher in the 5th grade, was able to complete 8 laps in 76 minutes . What is Mr. Patterson,s completion rate.(how many minutes does it take him to finish one lap)?
Mr Patterson could run 8 laps in 76 minutes, to determine how many minutes it takes him to finish one lap you can use cross multiplication:
8 laps ___ 76 minutes
1 lap ____ x minutes
Both relationships are at the same rate so that
\(\frac{76}{8}=\frac{x}{1}\)From this expression, we can determine the time it takes him to run one lap
\(\begin{gathered} x=\frac{76}{8} \\ x=9.5 \end{gathered}\)It takes Mr. Patterson 9.5minutes to run one lap.
How many x-intercepts does the graph of y = y2 have?
Consider the function f(x)=9x+4x^â1. For this function there are four important intervals: (â[infinity],A], [A,B) (B,C], and [C,[infinity]) where A, and C are the critical numbers and the function is not defined at B.
Find A
and B
and C
For this function, A is -2/3, B is 0 and C is 2/3.
To find the critical numbers of the function f(x) = 9x + 4\(x^{-1}\) , we need to find the values of x where the derivative of the function is equal to zero or undefined.
The derivative of f(x) is:
f'(x) = 9 - 4\(x^{-2}\) = 9 - 4/\(x^{2}\)
To find where the derivative is equal to zero, we set f'(x) = 0 and solve for x:
9 - 4/\(x^{2}\) = 0
4/\(x^{2}\) = 9
\(x^{2}\) = 4/9
x = ±2/3
Therefore, the critical numbers of f(x) are x = 2/3 and x = -2/3.
To find the intervals where the function is not defined, we need to look for values of x that make the denominator of the expression 4\(x^{-1}\) equal to zero. In this case, the function is not defined at x = 0.
Now we need to determine the sign of the derivative in each of the intervals (−∞,A], [A,B), (B,C], and [C,∞).
For x < -2/3, f'(x) is negative because 4/\(x^{2}\) is positive and 9 is greater than 4/\(x^{2}\) . Therefore, the function is decreasing on the interval (−∞,−2/3).
For −2/3 < x < 0, f'(x) is still negative because 4/\(x^{2}\) is positive and 9 is still greater than 4/\(x^{2}\) . Therefore, the function is decreasing on the interval (−2/3,0).
For 0 < x < 2/3, f'(x) is positive because 4/\(x^{2}\) is positive and 9 is less than 4/\(x^{2}\) . Therefore, the function is increasing on the interval (0,2/3).
For x > 2/3, f'(x) is still positive because 4/\(x^{2}\) is positive and 9 is still less than 4/\(x^{2}\) . Therefore, the function is increasing on the interval (2/3,∞).
Finally, the function is not defined at x = 0, so the interval [A,B) is (−∞,0) and the interval (B,C] is (0,∞).
Therefore, we have:
A = -2/3
B = 0
C = 2/3
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Unlike central banks in many countries, the Federal Reserve in the United States is not exclusively focused on achieving inflation targets. Instead, the law governing the Federal Reserve requires it to take ____________ into account.
Instead, the law governing the Federal Reserve
requires it to take a dual mandate into account.
The Federal Reserve's dual mandate, as stated in the Federal Reserve Act, is twofold:
1. Price Stability: The Federal Reserve aims to maintain stable prices and control inflation. While not exclusively focused on inflation targets, the Federal Reserve considers price stability as a crucial objective for promoting a healthy and sustainable economy.
2. Maximum Employment: The Federal Reserve also has a mandate to promote maximum employment. This means that it seeks to foster conditions that support robust job growth, reduce unemployment rates, and facilitate a strong labor market.
The dual mandate recognizes the importance of both price stability and employment in achieving overall economic stability and well-being. It reflects the broader responsibilities assigned to the Federal Reserve in managing monetary policy and guiding the nation's economic performance.
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absolute value of -4 + 1
Answer:
-3
Step-by-step explanation:
Which problem can be solved by determining 5 ÷ 1/4?
Answer:
\(20\)
Explanation:
\(5\) ÷ \(\frac{1}{4}\)
To change the division sign into a multiplication sign, you need to change (1/4) into its reciprocal.
\(5\) × \(\frac{4}{1}\)
\(5\) × \(4\)
\(20\)
In order for you to use the goodnees-of-fit test, the test of independence, or the test of homogeneity, the expected frequencies for each cell needs to be at least:____.
The condition for the expected value in the goodness of fit test is that the expected frequency is at least 5.
According to the statement
we have to find the condition of the expected values in the case of testing of goodness-of-fit test.
So, For this purpose we know that the
The goodness of fit test is of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected.
So, The main condition of the expected value for the goodness of fit test is
For each category, the expected frequency is at least 5.
Without this condition the test is not possible, so overall this the main condition related the goodness of fit test.
So, The condition for the expected value in the goodness of fit test is that the expected frequency is at least 5.
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Solve -2y + 1 = y-5.
оа
Ob
y = 2
y=-2
y = -6
ос
od
Y = 6
Answer:2y+1=y-5.
We move all terms to the left:
2y+1-(y-5.)=0
We add all the numbers together, and all the variables
2y-(y-5)+1=0
We get rid of parentheses
2y-y+5+1=0
We add all the numbers together, and all the variables
y+6=0
We move all terms containing y to the left, all other terms to the right
y=-6
Step-by-step explanation:
Ramil and Carly decided to make more baked goods for the bake sale. They used 1/8 less flour to make bread
Using fraction formula ,
The flour used by ramil and Carly for making bread is 33/40lb
Fraction: fraction is a number represented as a quotient, in which a numerator is divided by a denominator.
We have given that,
Ramil and Carly used 1/2 lb flour to make the bread.
They used 1/8lb less flour to make bread than to make cookies.
So, they used flour to make the cookies = 1/2+1/8
= 5/8lb
Therefore they used 5/8lb flour to make the cookies.
they used 1/5 lb more breads to make cookies than to make brownies. Mathematically, they used cookies for making the brownies is
= 1/5 + 5/8
=(8 + 25)/40 = 33/40lb
Therefore , they used 33/40lb flour to make the brownies.
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Complete question:
Ramil amd carly decided to make more baked goods for the bake sale. They used 1/8 lb less flour to make bread than to make cookies. She used 1/5 lb more to make cookies than to make brownies. If she used 1/2 lb of flour to make the bread, how much flour did she use to make the brownies
Marbles in an urn. Imagine you have an urn containing 5 red, 3 blue, and 2 orange marbles in it.
(a) What is the probability that the first marble you draw is blue?
(b) Suppose you drew a blue marble in the first draw. If drawing with replacement, what is the probability of drawing a blue marble in the second draw?
(c) Suppose you instead drew an orange marble in the first draw. If drawing with replacement, what is the probability of drawing a blue marble in the second draw?
(d) If drawing with replacement, what is the probability of drawing two blue marbles in a row?
(e) When drawing with replacement, are the draws independent? Explain.
Given: An urn containing 5 red, 3 blue, and 2 orange marbles in it.
To find:
What is the probability that the first marble you draw is blue?
Total number of marbles in the urn= 5+3+2 = 10 Probability of the first marble being blue = Number of blue marbles/Total number of marbles= 3/10Therefore, the probability that the first marble you draw is blue is 3/10.Suppose you drew a blue marble in the first draw. If drawing with replacement.
What is the probability of drawing a blue marble in the second draw?
When we are drawing with replacement, the urn is filled back with marbles after every draw. Hence, the number of marbles remains the same in every draw. The probability of drawing a blue marble in the first draw = 3/10Therefore, in the second draw also, the probability of drawing a blue marble is 3/10.So, the probability of drawing a blue marble in the second draw when drawing with replacement, given that a blue marble was drawn in the first draw is 3/10.Suppose you instead drew an orange marble in the first draw. If drawing with replacement.
what is the probability of drawing a blue marble in the second draw?
The probability of drawing an orange marble in the first draw = Number of orange marbles/Total number of marbles= 2/10= 1/5In the second draw, the urn is filled back with marbles and the total number of marbles remains the same. The probability of drawing a blue marble in the second draw= Number of blue marbles/Total number of marbles= 3/10Therefore, the probability of drawing a blue marble in the second draw, given that an orange marble was drawn in the first draw, when drawing with replacement, is 3/10. If drawing with replacement.
What is the probability of drawing two blue marbles in a row?When we draw with replacement, the probability of drawing a blue marble is 3/10 for every draw. As we are drawing with replacement, each draw is an independent event. The probability of drawing two blue marbles in a row = (Probability of the first marble being blue) × (Probability of the second marble being blue) = (3/10) × (3/10)= 9/100Therefore, the probability of drawing two blue marbles in a row when drawing with replacement is 9/100.
When drawing with replacement, are the draws independent?Yes, when we draw with replacement, the draws are independent. This is because the urn is filled back with marbles of the same kind after each draw. Hence, the probability of drawing a certain color remains the same in every draw. Therefore, every draw is an independent event.
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Some ____ are faster than others, and so scientists and corporations spend a lot of money and time trying to find the best one for a particular problem. Group of answer choices significant digits equations algorithms matrices
Some Algorithms are faster than others, and so scientists and corporations spend a lot of money and time trying to find the best one for a particular problem.
Algorithms are step-by-step procedures or sets of rules for solving a specific problem or accomplishing a particular task. In the context of the given statement, algorithms are compared based on their speed or efficiency in solving problems. Scientists and corporations invest resources to research and develop algorithms that can provide optimal solutions for various problems. The search for the best algorithm involves analyzing their performance, considering factors such as execution time, accuracy, scalability, and resource utilization
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3 Z The quadratic equation whose roots twice the roots of :2X2-8X+5=0
As a general rule in computing the standard error of the sample mean, the finite population correction factor is used only if the:
Group of answer choices
1. sample size is more than half of the population size.
2. sample size is smaller than 5% of the population size.
3. sample size is greater than 5% of the sample size.
4. None of these choices.
The finite population correction factor is used in computing the standard error of the sample mean when the sample size is smaller than 5% of the population size.
The finite population correction factor is a adjustment made to the standard error of the sample mean when the sample is taken from a finite population, rather than an infinite population.
It accounts for the fact that sampling without replacement affects the variability of the sample mean.
When the sample size is relatively large compared to the population size (more than half), the effect of sampling without replacement becomes negligible, and the finite population correction factor is not necessary.
In this case, the standard error of the sample mean can be estimated using the formula for sampling with replacement.
On the other hand, when the sample size is small relative to the population size (less than 5%), the effect of sampling without replacement becomes more pronounced, and the finite population correction factor should be applied.
This correction adjusts the standard error to account for the finite population size and provides a more accurate estimate of the variability of the sample mean.
Therefore, the correct answer is option 2: the finite population correction factor is used when the sample size is smaller than 5% of the population size.
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Kate bought a bag of grapes that was 3.2 pounds. The bag of grapes cost $6.24. What was the price per pound for the bag of grapes.
Answer:
$1.95
Step-by-step explanation:
3.2 pounds -> $6.24
1 pound -> $6.24÷3.2=$1.95
The price per pound for the bag of grapes will be $1.95.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Kate bought a bag of grapes that was 3.2 pounds.
And, The bag of grapes cost $6.24.
Now,
Since, The bag of grapes cost $6.24.
Hence, The price per pound for the bag of grapes = $6.24 ÷ 3.2
= $1.95
Thus, The price per pound for the bag of grapes will be $1.95.
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A survey is handed out by loud volunteers on a street corner. Some people are suspicious of the volunteers and choose to not participate in the survey. This is an example of:
This introduces nonresponse bias, as the survey results may not accurately represent the opinions and characteristics of the entire population being surveyed.
Nonresponse bias occurs when individuals who choose not to participate in a survey differ in important ways from those who do participate, leading to potential distortions in the survey results. In this case, the suspicion of the volunteers expressed by some people influences their decision not to participate, resulting in a nonresponse bias.
To determine the extent of nonresponse bias, researchers typically compare the characteristics of the respondents and non-respondents. If the non-respondents significantly differ from the respondents in terms of demographic factors, attitudes, or other relevant variables, it suggests the presence of nonresponse bias.
In this particular scenario, the suspicion expressed by certain individuals towards the volunteers leads them to opt out of participating in the survey. This introduces nonresponse bias, as the survey results may not accurately represent the opinions and characteristics of the entire population being surveyed. To mitigate nonresponse bias, researchers can employ techniques such as follow-up surveys or weighting adjustments to ensure a more representative sample and minimize the potential impact of nonresponse on the survey findings.
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9.
Deerhaven had a population of 42,000 in 1960 and a population of 58,000 in
1990. Based on this data, the city planner developed an exponential model to
predict the city's population in 2013. As it turns out, the city had a population of
75,000 in 2013. Which of these is the best description of how close the prediction
was to the actual population in 2013?
A Within 100 people
B Within 1,000 people
C Within 10,000 people
D Within 100,000 people
Hi
The best description of how close the prediction was to the actual population in 2013 is option (A) with in 100 people
To solve this problem, we can use the exponential growth formula:
P(t) = P0 × e^(rt)
where P(t) is the population at time t, P0 is the initial population, r is the growth rate, and e is the mathematical constant approximately equal to 2.718.
We can use the given data to find the growth rate r:
58,000 = 42,000 × e^(r×30)
Dividing both sides by 42,000:
e^(r×30) = 58,000/42,000 = 1.38
Taking the natural logarithm of both sides:
r×30 = ln(1.38)
r = ln(1.38)/30
r ≈ 0.0106
Now we can use this growth rate to predict the population in 2013:
P(53) = 42,000 × e^(0.0106×53) ≈ 74,480
So the predicted population of 74,480 is within 520 people of the actual population of 75,000
Therefore, the correct option is (A) Within 100 people.
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Find all the sides and angles of the triangle!
The values of b, angle C and angle A are 6.3, 49° and 80° respectively
What is cosine rule?The Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
b² = c²+a²-2abcos C
b² = 5²+8²-2(5)(8)cos 51
b² = 25+64-80cos51
b² = 89-50.35
b² = 39.35
b = 6.3
Using sine rule
8/sinA = 6.3/sin51
8× sin51 = 6.3sinA
6.2 = 6.3sin A
sinA = 6.2/6.3
sinA = 0.984
A = sin^-1( 0.984)
A = 80°( nearest degree)
angle C = 180-(51+80)
= 180-131
= 49°
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Complete the proof that the diagonals of a parallelogram bisect each other as a two-column proof. Given:
ABCD is a parallelogram.
B
E
D
Reasons
Statements
1. ABCD is a E
V
1. Given
2. Definition of
v
2. AB 112
3. ZABE_22
BAE LE
3. Alternate Interior Angles Theorem
4. AB ?
v
are congruent.
5. ΔΑΒΕ Δ:
4. Opposite sides of a
5. ASA Triangle Congruence Theorem
6. CPCTC
6. AENE
and BE
V
The proof shows that the diagonals of a parallelogram bisect each other. The given information states that ABCD is a parallelogram. Using the properties of a parallelogram and congruent triangles, the proof demonstrates that the diagonals of the parallelogram, represented by segments AE and BD, bisect each other.
1. ABCD is a parallelogram. (Given)
2. AB and CD are parallel and congruent. (Definition of a parallelogram)
3. ∠ABE and ∠EDA are alternate interior angles and are congruent. (Alternate Interior Angles Theorem)
4. AB and DE are congruent. (Opposite sides of a parallelogram are congruent)
5. ΔABE and ΔDEA are congruent by ASA (Angle-Side-Angle) congruence. (Corresponding parts of congruent triangles are congruent)
6. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
7. AE and BD bisect each other. (Congruent corresponding parts of congruent triangles)
The proof begins by stating that ABCD is a parallelogram. This implies that opposite sides are parallel and congruent. Using the alternate interior angles theorem, it is shown that the angles ∠ABE and ∠EDA are congruent. Then, the congruence of sides AB and DE is established based on the property that opposite sides of a parallelogram are congruent. By proving that ΔABE and ΔDEA are congruent using the ASA congruence criterion, it follows that corresponding parts of congruent triangles are congruent (CPCTC). Finally, it is concluded that the diagonals AE and BD bisect each other.
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