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Related Questions
When constructing a confidence interval for a difference between two population proportions, why is it important to check that the number of successes and the number of failures in each sample is at least 10? Select the correct answer
A. So we can assume that the two samples are independent.
B. So we can assume the sampling distribution of Di-D is approximately Normal,
C. So we can assume that the observations within each sample are independent
D. So we can assume that population 1 and population 2 are approximately Normal.
E. So we can generalize the results to the populations from which the samples were selected.
Answers
The correct option is B. When constructing a confidence interval for a difference between two population proportions, it is important to check that the number of successes and the number of failures in each sample is at least 10 because it allows us to assume that the sampling distribution of Di-D is approximately normal.
So we can assume the sampling distribution of Di-D is approximately Normal.
In statistics, the confidence interval is a statistical measure used to calculate the degree of certainty in a statistical inference. It is a range of values around a point estimate of a population parameter within which the true population parameter is expected to fall with a given level of probability.
The confidence interval for a difference between two population proportions is calculated using the standard error of the difference between the sample proportions (SE p1 - p2).
The sampling distribution of the difference between the two sample proportions is approximately normal when the number of successes and failures in each sample is at least 10.
If the number of successes and failures is less than 10, the sampling distribution of Di-D may not be normal, and using a normal distribution to construct a confidence interval would not be appropriate.
Hence, it is important to check that the number of successes and the number of failures in each sample is at least 10 to assume the sampling distribution of Di-D is approximately normal.
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What does it mean when it askes that?
Answers
Answer:
4
1
6
Step-by-step explanation:
so you have to multiple the x's by 1/3
so 4
1
6
you want to buy a car which will cost you $10,000. You do not have sufficient funds to purchase the car. You do not expect the price of the car to change in the foreseeable future. You can either save money or borrow money to buy the car.
Plan 1: You decide to open a bank account and start saving money. You will purchase the car when you have sufficient savings. The nominal interest rate for the bank account is 6% per annum compounded monthly.
a) You will make regular deposits in your bank account at the start of each month for the next 2.5 years. Calculate the minimum required monthly savings to be deposited into the bank such that you would have sufficient funds to purchase the car in 2.5 years.
b) You will make regular deposits in your bank account at the start of each week for the next 2.5 years. Calculate the minimum required weekly savings to be deposited into the bank such that you would have sufficient funds to purchase the car in 2.5 years.
c) You will make regular deposits of $2,000 at the end of each year. Calculate how long will it take for you to have sufficient funds to purchase the car.
Plan 2: You decide to borrow $13,000 from the bank and purchase the car now, as well as cover some other expenses. The bank offers two options for the structure of the repayments.
- Option 1: The first repayment will not start until you graduate from university. Therefore, no month-end-instalments will be made for the first 36 months. Then, commencing at the end of the 37th month, a total of 30 month-end-instalments of $X will be made over the life of the loan. The nominal interest rate is 6% per annum compounded monthly.
d) Calculate X.
e) Your parents agree to help you repay the loan by contributing a lump sum of $1,800 when you successfully graduate from university. Calculate the new value of X.
- Option 2: For the first 36 months (while you are still studying), you will be making month-end-instalments of $Y. Then, commencing at the end of the 37th month (when you graduate from university), you will double the amount of monthly repayment for the remaining 30 month-end-instalments. The nominal interest rate is 6% per annum compounded monthly.
f) Calculate the value of Y.
Answers
a) To save enough funds to purchase the car in 2.5 years, monthly deposits of $373.69 are required, while weekly deposits of $86.21 are needed.
b) With annual deposits of $2,000, it will take approximately 5 years to accumulate sufficient funds to purchase the car. For borrowing options, under Option 1, the monthly installment amount is $349.56, which reduces to $291.55 with a $1,800 lump sum contribution from parents. Under Option 2, the monthly installment amount is $237.63 for the first 36 months, doubling thereafter.
a) To calculate the minimum required monthly savings, we use the future value formula with monthly compounding: \($10,000 = PMT * ((1 + 0.06/12)^(2.5*12) - 1) / (0.06/12)\). Solving for PMT, the monthly deposit required is approximately $373.69.
b) Similarly, for weekly deposits, we use the future value formula with weekly compounding: \($10,000 = PMT * ((1 + 0.06/52)^(2.5*52) - 1) / (0.06/52)\). Solving for PMT, the weekly deposit required is approximately $86.21.
c) Using the future value formula for annual deposits: \($10,000 = $2,000 * ((1 + 0.06)^t - 1) / 0.06\). Solving for t, the time required to accumulate $10,000, we find it will take approximately 5 years.
d) For Option 1, the monthly installment amount can be calculated using the present value formula: \($13,000 = X * (1 - (1 + 0.06/12)^-30) / (0.06/12).\) Solving for X, the monthly installment amount is approximately $349.56.
e) With a lump sum contribution of $1,800, the remaining loan amount becomes $13,000 - $1,800 = $11,200. Using the same formula as in (d), the new monthly installment amount is approximately $291.55.
f) For Option 2, the monthly installment amount during the first 36 months is $Y. After 36 months, the monthly installment amount doubles. Using the present value formula: \($13,000 = Y * (1 - (1 + 0.06/12)^-36) / (0.06/12) + 2Y * (1 - (1 + 0.06/12)^-30) / (0.06/12)\). Solving for Y, the monthly installment amount is approximately $237.63.
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help ASAP find the coordinates of the midpoint of the given segment given its endpoints are (-4,3) and (2,-1)
Answers
Answer:
Step-by-step explanation:
(-4 + 2)/2 = -2/2= -1
(3 - 1)/2 = 2/2= 1
(-1, 1)
Please someone help me with this number line
Answers
Factor 5x^2−14x+8.
PLS HELP IM STUCK
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\(5x^2-14x+8\\\\=5x^2-10x-4x +8\\\\=5x(x-2) -4(x-2)\\\\=(x-2)(5x-4)\)
5/7 x 14/20
Snannan
Answers
Answer:
\( \frac{1}{2} \: or \: 0.5 \)
Step-by-step explanation:
\( \frac{5}{7} \times \frac{14}{20} = \frac{5 \times 14}{7 \times 20} \)
It can be also written as -
\( = > \frac{5 \times 14}{20 \times 7} = \frac{5}{20} \times \frac{14}{7} = \frac{1}{4} \times 2 = \frac{1}{2} \)
In the diagram below, EF intersects AB and CD at G and H.respectively. Gl is kn drawn such that GH BIH.If mxE6B = 50 and m&DIG = 115, explain why AB CD. [4 pts)
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We are given the following information
Line EF intersects line AB and line CD
GH ≅ IH
m∠EGB = 50° and m∠DIG = 115°
We are asked to explain that why line AB is parallel is line CD.
As you can see, corresponding angles are equal so, m∠GHI = m∠EGB = 50°
We know that angles on a straight line equal 180°
\(m\angle GIH=180-115=65\degree\)Therefore, in triangle GHI, angle H equals 50, angle I equals 65 and angle G equals 65
Angles in a triangle equals 180
Therefore, lines AB and CD are parallel
Keith buy 3 yard of material to make a blanket. He trim off a total of 1/6 yard before he begin ewing. How much material remain for the blanket?
Answers
The material remained for the blanket after trimming off by Keith is 2.5 yards.
Simple subtraction and multiplication can provide the result. Beginning will be by the multiplication. Firstly finding the exact amount of material trimmed = 3×1/6
Performing multiplication and division on Right Hand Side of the equation
Trimmed material = 1/2 or 0.5
Now, we need to subtract the trimmed material from overall amount of material
Remaining material = 3 - 0.5
Performing subtraction on Right Hand Side of the equation
Remaining material = 2.5 yards
Hence, 2.5 yards of material remained.
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Which relations are functions? Select all that apply.
Answers
Answer:
A and C
Step-by-step explanation:
B has a domain connected to many other ranges which makes a relationship but confuses the whole function making it incorrect.
For answer D, the x coordinates 1 and 3 both have two y coordinates. That again makes a relationship but confuses the function making that answer incorrect.
In answer A, no domain is repeated in any of the points making it a function.
In answer C, again no domains are paired with more than one range making it a function. That why A and C are the answers
A child's parents deposit Rx into a savings account on the day of the child's birth to help towards her university education. The child will be able to withdraw regular half-yearly amounts from the savings account starting with a withdrawal of R12000 on her 19th birthday and ending with a final withdrawal on her 24th birthday. To keep up with inflation the withdrawals will need to increase at a rate of 6% p. each half-year from the second withdrawal onwards. If the savings account earns interest at a rate 8% p.a. compounded quarterly, then the value of Rx, to the nearest cent, that must be deposited initially into the savings account in order to fund the future growing withdrawals, is equal to: (Hint: Think carefully about where the Pv and Fv of the withdrawals is situated on the time line!) R120 468,80 R27 281,09 R26 746,17 R27 826,71 R25 427,36
Answers
The value of PV based on the question requirements is given as R27 281,09.
How to solveThere is a consistent increase in the withdrawals, with a growth rate of 6% per annum. The interest accrues at a yearly rate of 8%, and is compounded twice a year.
Having an interest rate that is calculated and added every three months. The accelerated growth of withdrawals surpasses the pace at which interest is accumulating, causing the eventual depletion of the savings account's value.
To calculate the value of the savings account, we need to use the future value of an annuity formula. The formula is:
\(FV = PV * [((1 + r)^n - (1 + g)^n) / (r - g)]\)
where:
FV is the future value of the annuity
PV is the present value of the annuity
r is the interest rate
n is the number of payments
g is the growth rate
In this case, the present value is the amount that needs to be deposited into the savings account, the interest rate is 8% p.a. compounded quarterly, the number of payments is 6 (24 / 4), and the growth rate is 6% p.a. compounded semi-annually.
Plugging these values into the formula, we get:
\(FV = PV * [((1 + r)^n - (1 + g)^n) / (r - g)]\\FV = PV * [((1 + 0.02)^6 - (1 + 0.03)^6) / (0.02 - 0.03)]\\FV = PV * 10.766\)
Solving for PV, we get:
PV = FV / 10.766
PV = 27 281,09
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Click on the graph which represents a function.
3
1
1 2 3
- 3 -
-1
1 2 3
-1
-3
3
1
1
-2-1
3
-3 -2 -1
-1
-2
-3
Answers
Answer:
the numbers in your question are not clear
Answer:can you have it make since?
Step-by-step explanation:
if the probability is f(x) that a product fails the xth time it is being used, that is, on the xth trial, then its FAILURE RATE at the xth trial is the probability that it will fail on the xth trial given that it has not failed on the first x-1 trials; symbolically, it is given by
z(x) = f(x)/(1-F(x-1))
where F(x) is the value of the corresponding distribution function at x. Show that if X is a geometric random variable, its failure rate is constant and equal to p. p is the probability of success.
Answers
X is a geometric random, its variable is constant and equal to p.
How to find geometric random variable?To show that if X is a geometric random variable, its failure rate is constant and equal to p, we will use the definition of the geometric distribution and the failure rate formula.
Recall the probability mass function (PMF) of a geometric random variable X:f(x) = p(1-p)^(x-1), for x = 1, 2, 3, ...Compute the distribution function F(x) for a geometric random variable:
F(x) = P(X ≤ x) = 1 - (1-p)^xPlug f(x) and F(x-1) into the failure rate formula:
z(x) = f(x) / (1 - F(x-1))Substitute the expressions from Step 1 and Step 2:
z(x) = p(1-p)^(x-1) / (1 - (1 - (1-p)^(x-1)))Simplify the expression:
z(x) = p(1-p)^(x-1) / (1-p)^xObserve that (1-p)^x can be written as (1-p)^(x-1) * (1-p):
z(x) = p(1-p)^(x-1) / ((1-p)^(x-1) * (1-p))Cancel out the common terms in the numerator and denominator:
z(x) = p / (1-p)
As the expression for z(x) does not depend on x, the failure rate is constant and equal to p/(1-p). However, we need to show that it is equal to p.
Recall that p is the probability of success. Since failure and success are complementary events, the probability of failure is q = 1-p.
z(x) = p / (1-p) = p / q
Observe that the failure rate z(x) equals the probability of success p when divided by the probability of failure q. Since the failure rate for a geometric random variable only depends on the probability of success p and the probability of failure q, it is constant and equal to p.
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PLESSS help me with this :)
Marking as brainlist
Answers
Answer:
36
Step-by-step explanation:
3x3x2x2=36
Roberto' employer offer a liding paid vacation. When he tarted work, he wa given three paid day of vacation. For each ix-month period he tay at the job, hi vacation i increaed by two day. Let x repreent the number of 6-month period worked and y repreent the total number of paid vacation day. Write an equation that mode the relationhip between thee two variable
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An equation that mode the relationship between thee two variable is y=2x+3 .
Let x represent the number of 6-month period worked
Let y represent the total number of paid vacation day
According to the question,
When he started work, he was given three paid day of vacation. For each six-month period he pay at the job, his vacation is increased by two day.
Each year has 2 six-month periods. After 4.4 years Roberto will have worked 8.8 six-month periods. He will have been given vacation days for each of the 8 whole working periods he has completed. x=8 y=2*8+3 y=19
An equation that mode the relationship between thee two variable is y=2x+3 (Total vacation time equals 2 days times x plus the 3 days he was given at the start).
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write each of the following decimal in words 175.04
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Answer:
one-hundred and seventy-five and four hundreths
Step-by-step explanation:
Find the missing side lengths. Leave your answers as radicals in simplest form.
Answers
The lengths of the missing sides are:
x = 6
y = 3√2
How to find the missing side lengths of the triangle?Here we can see a right triangle, we want to find the two missing lengths in it.
We know the measure of one angle, and the length of the adjacent cathetus of it, then we can use trigonometric relations:
cos(a) = (adjacent cathetus)/hypotenuse
tan(a) = (opposite cathetus)/(adjacent cathetus)
Replacing the values that we know, we will get:
cos(45°) = 3√2/x
Solving for x:
x = ( 3√2)/cos(45°) = 3√2*(2/√2) = 6
And to get the value of y we use the other:
tan(45°) = y/ ( 3√2)
1 = y/ ( 3√2)
( 3√2) = y
These are the lengths.
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Find the slope of the line tangent to the graph of y = 10x/x-3 at x = -2.
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The slope of the line tangent to the graph of y = (10x) / (x - 3) at x = -2 is -30/25, which can also be simplified to -6/5 or -1.2.
To find the slope of the line tangent to the graph of y = (10x) / (x - 3) at x = -2, we'll follow these steps:
1. Find the derivative of the function y = (10x) / (x - 3).
2. Substitute x = -2 into the derivative to find the slope at that point.
Let's calculate the slope:
1. Finding the derivative of the function:
To find the derivative, we can use the quotient rule. Let u(x) = 10x and v(x) = x - 3.
The derivative of the function y = (10x) / (x - 3) is given by:
y' = [v(x) * u'(x) - u(x) * v'(x)] / (v(x))^2
Applying the quotient rule:
y' = [(x - 3) * (10) - (10x) * (1)] / (x - 3)^2
Expanding and simplifying:
y' = (10x - 30 - 10x) / (x^2 - 6x + 9)
y' = -30 / (x^2 - 6x + 9)
2. Substituting x = -2 into the derivative:
slope = y'(-2)
slope = -30 / [(-2)^2 - 6(-2) + 9]
slope = -30 / (4 + 12 + 9)
slope = -30 / 25
Therefore, the slope of the line tangent to the graph of y = (10x) / (x - 3) at x = -2 is -30/25, which can also be simplified to -6/5 or -1.2.
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Need help on number 4, will give as many points for correct answer!!
Answers
Answer:
n = 8
Step-by-step explanation:
Since this is a right angle, the sum of the angle is 90 degrees.
33 + 8n - 7 = 90
Add like terms
26 + 8n = 90
Subtract on both sides
8n = 64
Divide on both sides
n = 8
Helplp meeeeeeeee plz.Answer only if you know the answer.
Answers
Answer:
I think the answers would be 12 and 9.
sorry if it's wrong...
Step-by-step explanation:
What is the probability that the block he pulls out will be yellow?
A. 1/4
B. 1/3
C. 3/1
D. 4/1
Answers
Answer:
The probability that he will pull out a yellow block it 1/4.
Step-by-step explanation:
There are 4 blocks in the bag, each a different color. Since there is only one yellow out of 4 different blocks, the fraction would be 1/4.
Hope this helps!
Suppose that you just turned 25 years old and that you wish to receive a monthly. ordinary ắnnuity, of $7,593 for 30 years (ages 65−95, end of month payments). How much would your monthly contributions also be at the end of each month until age 60 , if you let the funds vest until age 65 with no further contributions? Your EAR is 6.9%?
Answers
The monthly contributions required at the end of each month until age 60, with no further contributions and a vesting period until age 65, would be approximately $783.19.
We can use the present value of an annuity formula. Given that the Effective Annual Rate (EAR) is 6.9%, we need to adjust the interest rate to a monthly rate.
First, let's calculate the monthly interest rate (r) from the EAR:
r = (1 + EAR)^(1/12) - 1
= (1 + 0.069)^(1/12) - 1
= 0.0056728
Next, let's calculate the number of periods (n) from age 25 to age 60 (35 years):
n = 35 * 12
= 420 months
Using the present value of an annuity formula, we can solve for the monthly contributions (PMT):
PMT = PV / [(1 - (1 + r)^(-n)) / r]
where:
PV = Present Value (annuity amount)
r = Monthly interest rate
n = Number of periods
PV = $7,593 * 12 * 30
= $2,736,840
PMT = 2,736,840 / [(1 - (1 + 0.0056728)^(-420)) / 0.0056728]
= $783.19
Therefore, the monthly contributions required at the end of each month until age 60, with no further contributions and a vesting period until age 65, would be approximately $783.19.
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What is the equation of the line that passes through the points (-2, 1) and (1, 10)?
Answers
Answer:
y = 3 x + 7
Step-by-step explanation:
Line through (-2, 1) and (1, 10):
y = 3 x + 7
Answer:
Y = 3x + 7
Step-by-step explanation:
M = y2-y1 / x2-x1
Hope this helps. Pls give brainliest.
Solve the inequality −8≤8+y
Answers
Answer: -16 ≤ y
Step-by-step explanation: All we need to do is subtract 8 on both sides.
Hope this helped! :)
3/8 x 3/4=
9/32
1/2
9/24
1/8
Answers
Answer:
9/32
Step-by-step explanation:
3 x 3 = 9. 8 x 4 = 32. 9/32
Could I please get assistance with this question. Create a mini cricket/rugby clinic explanation where you teach learners about cricket/rugby while incorporating Mathematics or English literacy. Your explanation should be informative and insightful.
Answers
Introduce the sport of cricket/rugby and explain its history and rules.
Use cricket/rugby as a context for teaching Mathematics or English literacy. For example:
Mathematics: You can use cricket/rugby statistics to teach learners about probability, percentages, and data analysis. For instance, you can ask learners to calculate the batting average of a cricket player or the conversion rate of a rugby team. You can also ask learners to solve word problems related to cricket/rugby, such as "If a cricket team scores 240 runs in 50 overs, what is their run rate per over?"
English literacy: You can use cricket/rugby as a context for teaching learners about reading comprehension, writing, and vocabulary. For instance, you can ask learners to read a cricket/rugby article and summarize it in their own words. You can also ask learners to write a persuasive essay on why cricket/rugby is the best sport. Additionally, you can teach learners cricket/rugby-specific vocabulary, such as "wicket," "boundary," "try," and "conversion."
Use cricket/rugby drills and exercises to reinforce the Mathematics or English literacy concepts you have taught. For example:
Mathematics: You can ask learners to measure the distance between the wickets or the length of the cricket pitch using a tape measure. You can also ask learners to count the number of runs scored in a cricket match or the number of tries scored in a rugby match.
English literacy: You can ask learners to write a cricket/rugby-themed story or poem using the vocabulary they have learned. You can also ask learners to read a cricket/rugby rulebook and explain the rules in their own words.
Overall, incorporating Mathematics or English literacy into a cricket/rugby clinic can make the learning experience more engaging and meaningful for learners. By using cricket/rugby as a context for teaching these subjects, learners can see the real-world applications of what they are learning and develop a deeper understanding of the concepts.
Can anyone help me with my homework
Answers
Answer:
I use standard form
Step-by-step explanation:
I use the standard form.
Four identical rectangles form the square. What is the perimeter of the square, if the perimeter of each rectangle is 40 inches?
Answers
Answer:
64
Step-by-step explanation:
so basically first I wanted to find the width, if you draw a model, it would be easy, so
I make 4 rectangles, one on top of the other for all of them.
so if you turn it clockwise 90 degrees, the rectangles are the same so if you draw them together then they over lap you can see that you can make a x:y for the lengths. If the width of the rectangle is 1 then the length of the rectangle is 4, 1:4 , so now we use the perimeter of 40 so now if the width is w and the length is l then wl is 20 (40/2) si niw 20/(1+4) which is 20/5 which is 4, so now we know that the width of the rectangle is 4 and the length is 4x4 which is 16 so now we can calculate the perimeter of the square, we know that the side length of the square is 16, so all we have to do is 16x4 which is 64.
enter the factor under the radical
\((a - b) \sqrt{a - b} \)
Answers
\(\\ \rm\longmapsto (a-b)\sqrt{a-b}\)
\(\\ \rm\longmapsto (a-b)(a-b)^{\frac{1}{2}}\)
\(\\ \rm\longmapsto (a-b)^{1+\dfrac{1}{2}}\)
\(\\ \rm\longmapsto (a-b)^{\dfrac{3}{2}}\)
Answer:
\(\dashrightarrow \: { \tt{(a - b) \sqrt{a - b} }} \\ \\ \dashrightarrow \: { \tt{ {(a - b)}^{1} {(a - b)}^{ \frac{1}{2} } }}\)
• from law of indices:
\({ \boxed{ \rm{ ({x}^{n} )( {x}^{m} ) = {x}^{(n + m)} }}}\)
therefore:
\(\dashrightarrow \: { \tt{ {(a - b)}^{(1 + \frac{1}{2} )} }} \\ \\ \dashrightarrow \: { \tt{ {(a - b)}^{ \frac{3}{2} } }}\)
Two lines intersect as shown.
(2x+20) •
609
Which is the value of x ?
Answers
Answer:
\(2x + 20 = 60 \\ 2x = 60 - 20 \\ 2x = 40 \\ x = \frac{40}{2} \\ x = 20\)