Answer:
a) The sample mean is 1260 and the standard deviation is 48.
b) The 90% confidence interval for the mean of all tree-ring dates from this archaeological site is (1230, 1290).
Step-by-step explanation:
Question a:
Mean is the sum of all values divided by the number of values. So
[tex]\overline{x} = \frac{1285 + 1187 + 1222 + 1194 + 1268 + 1316 + 1275 + 1317 + 1275}{9} = 1260[/tex]
Standard deviation is the square root of the sum of the differences squared between each value and the mean, divided by the one less than the sample size. So
[tex]s = \sqrt{\frac{(1285-1260)^2 + (1187-1260)^2 + (1222-1260)^2 + (1194-1260)^2 + (1268-1260)^2 + ...}{8}} = 48[/tex]
The sample mean is 1260 and the standard deviation is 48.
Question b:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 9 - 1 = 8
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 8 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.8595
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.8595\frac{48}{\sqrt{9}} = 30[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 1260 - 30 = 1230
The upper end of the interval is the sample mean added to M. So it is 1260 + 30 = 1290
The 90% confidence interval for the mean of all tree-ring dates from this archaeological site is (1230, 1290).
What is the percent increase from 250 to 900?
1. Write the percent change formula for an increase.
Percent Increase =
Amount of Increase
Original Amount
2. Substitute the known quantities for the amount of the increase and the original amount.
Percent Increase =
900 − 250
250
3. Subtract.
Percent Increase =
650
250
Answer:
260% is the correct answer
Step-by-step explanation:
i hope i helped
Which of the following statements are correct? Select ALL that apply!
Select one or more:
O a. -1.430 = -1.43
O b. 2.36 < 2.362
O c.-1.142 < -1.241
O d.-2.33 > -2.29
O e. 2.575 < 2.59
O f. -2.25 -2.46
The weight of cell phones has been decreasing 20% each year since 1983.
Based on this information, if a cell phone in 1983 weighed 2.5 pounds, how much would a phone weigh in 1984?
Answer:
2 pounds
Step-by-step explanation:
so if we say we decrease 20% each year and we're only going one year. All you have to do is 2.5 - 20%
Would you favor spending more federal tax money on the arts? Of a random sample of n1 = 222 women, r1 = 51 responded yes. Another random sample of n2 = 174 men showed that r2 = 49 responded yes. Does this information indicate a difference (either way) between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts? Use ???? = 0.05.
Answer:
The p-value of the test is 0.242 > 0.05, which means that this information does not indicate a difference between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts.
Step-by-step explanation:
Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Women:
51 out of 222, so:
[tex]p_1 = \frac{51}{222} = 0.2297[/tex]
[tex]s_1 = \sqrt{\frac{0.2297*0.7703}{222}} = 0.0282[/tex]
Men:
49 out of 174, so:
[tex]p_2 = \frac{49}{174} = 0.2816[/tex]
[tex]s_2 = \sqrt{\frac{0.2816*0.7184}{174}} = 0.0341[/tex]
Does this information indicate a difference (either way) between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts?
Either way, so a two tailed test to see if the difference of proportions is different of 0.
At the null hypothesis, we test if it is not different of 0, so:
[tex]H_0: p_1 - p_2 = 0[/tex]
At the alternative hypothesis, we test if it is different of 0, so:
[tex]H_1: p_1 - p_2 \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the samples:
[tex]X = p_1 - p_2 = 0.2297 - 0.2816 = -0.0519[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0282^2+0.0341^2} = 0.0442[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-0.0519 - 0}{0.0442}[/tex]
[tex]z = -1.17[/tex]
P-value of the test and decision:
The p-value of the test is the probability of the differences being of at least 0.0519, either way, which is P(|z| > 1.17), that is, 2 multiplied by the p-value of z = -1.17.
Looking at the z-table, z = -1.17 has a p-value of 0.121.
0.121*2 = 0.242
The p-value of the test is 0.242 > 0.05, which means that this information does not indicate a difference between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts.
Blair & Rosen (B&R) plc is a U.K. based brokerage firm that specializes In building investment portfolios designed to meet the specific needs of its clients who are mostly private investors willing to invest their r savings in stocks and shares. One client who contacted B&R recently has a maximum of $500,000 to invest. The company`s investment advisor has decided to recommend the portfolio consisting of two investment funds: An internet fund where the companies are all active in internet businesses of one kind or another and the blue-chip fund which is more conservative and traditional. The internet fund has a projected annual return over the next few years of 12 %, while the blue-chip fund has a projected annual return of 9%. The investment advisor has decided that at most, $350,000 of the client`s funds should be invested in the internet fund. B&R services include risk rating for each investment alternative. The internet fund which is more risky of the two alternatives has a risk rating of 6 for every thousand dollar invested while the blue-chip fund has a risk rating of 4 per thousand dollar invested. So, for example, if $10000 is invested in each of the two investments funds, B&R risk rating for the portfolio would be 6(10) + 4(10)= 100. Finally B&R has developed a questionnaire to measure each client`s risk tolerance. Based on the responses, each client is classified as conservative, moderate or aggressive investor. The questionnaire results have classified the current client as a moderate investor. B&R recommends that a client who`s a moderate investor limit his or her portfolio to a maximum risk rating of 240. You have been asked to help the B&R investment advisor. What is the recommended investment portfolio for this client? What is the annual return for the portfolio? A second client , also with $500,000 has been classified as aggressive. B&R recommends that the maximum portfolio risk rating for an aggressive investor is 320. What is the recommended investment portfolio for this aggressive investor
Answer:
Blair & Rosen (B&R) Plc.
Recommendation for moderate investor:
Internet fund = 96/240 * $500,000 = $200,000
Blue-chip fund = 144/240 * $500,000 = $300,000
Annual return for the portfolio:
Internet fund = $200,000 * 12% = $24,000
Blue-chip fund = $300,000 * 9% = $27,000
Total portfolio returns = $51,000
Annual returns of portfolio = $51,000/$500,000 * 100 = 10.2%
Recommendation for aggressive investor:
Internet fund = 192/320 * $500,000 = $300,000
Blue-chip fund = 128/320 * $500,000 = $200,000
Step-by-step explanation:
a) Data and Calculations:
Maximum investible savings = $500,000
Projected annual return of the internet fund = 12%
Projected annual return of the blue-chip fund = 9%
Maximum determined amount to invest in the internet fund = $350,000
Risk rating for the internet fund = 6/1,000
Risk rating for the blue-chip fund = 4/1,000
Maximum risk rating for a moderate investor = 240
Maximum risk rating for an aggressive investor = 320
Recommendation for moderate investor:
Internet fund = 96/240 * $500,000 = $200,000
Blue-chip fund = 144/240 * $500,000 = $300,000
Annual return for the portfolio:
Internet fund = $200,000 * 12% = $24,000
Blue-chip fund = $300,000 * 9% = $27,000
Total returns = $51,000
Annual returns of portfolio = $51,000/$500,000 * 100 = 10.2%
Recommendation for aggressive investor:
Internet fund = 192/320 * $500,000 = $300,000
Blue-chip fund = 128/320 * $500,000 = $200,000
NEED HEELLLLPPPPPP!!
How many tens are in 6 hundreds
Answer:
60
Step-by-step explanation:
10 x 6 = 60
Hope this helped! :)
Two workers finished a job in 12 days. How long would it take each worker to do the job by himself if one of the workers needs 10 more days to finish the job than the other worker
Two workers finished a job in 7.5 days.
How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?
let t = time required by one worker to complete the job alone
then
(t+8) = time required by the other worker (shirker)
let the completed job = 1
A typical shared work equation
7.5%2Ft + 7.5%2F%28%28t%2B8%29%29 = 1
multiply by t(t+8), cancel the denominators, and you have
7.5(t+8) + 7.5t = t(t+8)
7.5t + 60 + 7.5t = t^2 + 8t
15t + 60 = t^2 + 8t
form a quadratic equation on the right
0 = t^2 + 8t - 15t - 60
t^2 - 7t - 60 = 0
Factor easily to
(t-12) (t+5) = 0
the positive solution is all we want here
t = 12 days, the first guy working alone
then
the shirker would struggle thru the job in 20 days.
Answer:7 + 17 = 24÷2 (since there are 2 workers) =12. Also, ½(7) + ½17 = 3.5 + 8.5 = 12. So, we know that the faster worker will take 7 days and the slower worker will take 17 days. Hope this helps! jul15
Step-by-step explanation:
a+b=60000
[tex]\frac{a}{b}=\frac{4}{1}[/tex]
a=?
b=?
Answer: a = 25.67
Step-by-step explanation:
You go to the doctor and he gives you 11 milligrams of radioactive dye. After 24 minutes, 6.75 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute. You will spend minutes at the doctor's office.
Step-by-step explanation:
11mg_6.5mg=4.5mg
in 24mins 4.5mgwas gone.
6.5mg_2mg=4.5mg
you have to lose 4.5mg more
answer 24+ 24
48 minutes
What is the endpoint of a line segment if the midpoint M( – 3, 4) and the other endpoint is E(7, – 2)?
Answers
(– 13, 10)
(10, – 13)
(– 1, 2)
(2, – 1)
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Answer:
(-13, 10)
Step-by-step explanation:
If M is the midpoint of segment DE, then ...
D = 2M -E
D = 2(-3, 4) -(7, -2) = (2(-3)-7, 2(4)+2) = (-13, 10)
The other end point is (-13, 10).
Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
d^2y/ dx^2 − 6 dy/dx + 9y = 0; y = c1e3x + c2xe3x When y = c1e3x + c2xe3x,
y'' - 6y' + 9y = 0
If y = C₁ exp(3x) + C₂ x exp(3x), then
y' = 3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x))
y'' = 9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x))
Substituting these into the DE gives
(9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x)))
… … … - 6 (3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x)))
… … … + 9 (C₁ exp(3x) + C₂ x exp(3x))
= 9C₁ exp(3x) + 6C₂ exp(3x) + 9C₂ x exp(3x))
… … … - 18C₁ exp(3x) - 6C₂ (exp(3x) - 18x exp(3x))
… … … + 9C₁ exp(3x) + 9C₂ x exp(3x)
= 0
so the provided solution does satisfy the DE.
Log6^(4x-5)=Log6^(2x+1)
Answer:
[tex]x = 3[/tex]
Step-by-step explanation:
Given
[tex]\log6^{(4x-5)} =\log6^{(2x+1)}[/tex]
Required
Solve for x
We have:
[tex]\log6^{(4x-5)} =\log6^{(2x+1)}[/tex]
Remove log6 from both sides
[tex](4x-5) = (2x+1)[/tex]
Collect like terms
[tex]4x - 2x = 5 + 1[/tex]
[tex]2x = 6[/tex]
Divide by 2
[tex]x = 3[/tex]
Simplify to the extent possible
(logx16)(log2x)
Answer:
[tex]{ \tt{ = ( log_{x}16)( log_{2}x) }}[/tex]
Change base x to base 2:
[tex]{ \tt{ = (\frac{ log_{2}16}{ log_{2}x } )( log_{2}x)}} \\ \\ { \tt{ = log_{2}(16) }} \\ = { \tt{ log_{2}(2) }} {}^{4} \\ = { \tt{4 log_{2}(2) }} \\ = { \tt{4}}[/tex]
Can you find a strategy for splitting any number so that you always get the largest product?
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Answer:
split the number into equal pieces
Step-by-step explanation:
Assuming "splitting any number" means identifying parts that have the number as their sum, the maximum product of the parts will be found where the parts all have equal values.
We have to assume that the number being split is positive and all of the parts are positive.
2 partsIf we divide number n into parts x and (n -x), their product is the quadratic function x(n -x). The graph of this function opens downward and has zeros at x=0 and x=n. The vertex (maximum product) is halfway between the zeros, at x = (0 + n)/2 = n/2.
3 partsSimilarly, we can look at how to divide a (positive) number into 3 parts that have the largest product. Let's assume that one part is x. Then the other two parts will have a maximum product when they are equal. Their values will be (n-x)/2, and their product will be ((n -x)/2)^2. Then the product of the three numbers is ...
p = x(x^2 -2nx +n^2)/4 = (x^3 -2nx^2 +xn^2)/4
This will be maximized where its derivative is zero:
p' = (1/4)(3x^2 -4nx +n^2) = 0
(3x -n)(x -n) = 0 . . . . . . . . . . . . . factor
x = n/3 or n
We know that x=n will give a minimum product (0), so the maximum product is obtained when x = n/3.
more partsA similar development can prove by induction that the parts must all be equal.
Answer:hi
Step-by-step explanation:
HELP ANYONE PLZZZ ?
1sr.
z(x)=x+1
If you input a 3 into z(x), what do you get for the output?
2nd.
n(x)=2/x
n(x) will give you an output for any number you use as an input except which of the following?
A. 0
B .3
C. 5
D. Trick question- you can get an output for every number you use as an input .
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Answer:
4A. 0Step-by-step explanation:
1. Input 3 for x and do the arithmetic.
z(x) = x+1
z(3) = 3+1 = 4 . . . . . the output is 4
__
2. The expression for n(x) has x in the denominator. The expression will be undefined when the denominator is zero, so x=0 cannot be used.
HELP PLS!!!!!!!!!!!!!!!!!!!!!!!!!!! n
We can split 200 into 100 x 2.
100 is a perfect square and its square root is 10. The 2 will remain under the radical.
ANSWER: 10 sqrt(2)
(Option 2)
Hope this helps!
please help, it’s urgent !!!
D
A
B
C
for more explanation please don't hesitate to just respond
A bank records deposits as positive numbers and withdrawals as negative numbers.
Mike withdrew $60 from his bank account 3 times.
what is the change in mikes account balance after all 3 withdrawals?
Find f(-2) for f(x) = 2•3^x
Ο Α. 1/18
O B. -18
O C. -36
OD. 2/9
Answer:
b
Step-by-step explanation:
2 * 3 to the -2 power. 3x-3=-9
2x-9=-18
The owner of a greenhouse wants to test the effectiveness of a new fertilizer on African violets. She has 60 violet seedlings that were grown for 8 weeks. She wants to test the new fertilizer on 10 of the plants, and decides to use a random number table to select a simple random sample. She labels the violets 01–60. Refer to the given line from a random number table. Which numbers represent the first 5 plants selected?
60633 78034 99602 83440 55120 61551
33, 03, 49, 02, 40
06, 33, 03, 49, 02
60, 63, 37, 80, 34
60, 37, 34, 28, 40
Answer:
60, 37, 34, 28, 40
(D)
ED2021
Determine if the triangle is Right, Acute or Obtuse.
Answer:
I think the right answer is: Acute
Hi, help with question 18 please. thanks
Answer:
See Below.
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle y^2 = 1 + \sin x[/tex]
And we want to prove that:
[tex]\displaystyle 2y\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right) ^2 + y^2 = 1[/tex]
Find the first derivative by taking the derivative of both sides with respect to x:
[tex]\displaystyle 2y \frac{dy}{dx} = \cos x[/tex]
Divide both sides by 2y:
[tex]\displaystyle \frac{dy}{dx} = \frac{\cos x}{2y}[/tex]Find the second derivative using the quotient rule:
[tex]\displaystyle \begin{aligned} \frac{d^2y}{dx^2} &= \frac{(\cos x)'(2y) - (\cos x)(2y)'}{(2y)^2}\\ \\ &= \frac{-2y\sin x-2\cos x \dfrac{dy}{dx}}{4y^2} \\ \\ &= -\frac{y\sin x + \cos x\left(\dfrac{\cos x}{2y}\right)}{2y^2} \\ \\ &= -\frac{2y^2\sin x+\cos ^2 x}{4y^3}\end{aligned}[/tex]
Substitute:
[tex]\displaystyle 2y\left(-\frac{2y^2\sin x+\cos ^2 x}{4y^3}\right) + 2\left(\frac{\cos x}{2y}\right)^2 +y^2 = 1[/tex]
Simplify:
[tex]\displaystyle \frac{-2y^2\sin x-\cos ^2x}{2y^2} + \frac{\cos ^2 x}{2y^2} + y^2 = 1[/tex]
Combine fractions:
[tex]\displaystyle \frac{\left(-2y^2\sin x -\cos^2 x\right)+\left(\cos ^2 x\right)}{2y^2} + y^2 = 1[/tex]
Simplify:
[tex]\displaystyle \frac{-2y^2\sin x }{2y^2} + y^2 = 1[/tex]
Cancel:
[tex]\displaystyle -\sin x + y^2 = 1[/tex]
Substitute:
[tex]-\sin x + \left( 1 + \sin x\right) =1[/tex]
Simplify. Hence:
[tex]1\stackrel{\checkmark}{=}1[/tex]
Q.E.D.
X = The set of months in a year?
there are 12 set of months in a year
What numbers are to the right of 0 on the number line?
Answer:
Positive numbers.
Step-by-step explanation:
Numbers after zero are positive numbers, which can be any number (whole or decimal/fraction). But numbers before zero are negative numbers which can be also whole or decimal fraction.
Example for numbers to the right of 0: 7, 6.5, 8/10
Please help me out really need it
Answer:
[tex]{ \tt{hypotenuse = { \boxed{5}}}} \\ { \tt{opposite = { \boxed{3}}}} \\ { \tt{adjacent = { \boxed{4}}}} \\ \\ { \tt{ \sin \angle R = \frac{{ \boxed{3}}}{{ \boxed{5}}} }} \\ \\ { \tt{ \cos \angle R = \frac{{ \boxed{4}}}{{ \boxed{5}}} }} \\ \\ { \tt{ \tan \angle R = \frac{ \boxed{3}}{{ \boxed{4}}} }}[/tex]
Let X be an exponential r.v. with mean 6 and Y be an uniform r.v. over [4, 10] independent of X. Find the variance of 2X+3Y.
Var[2X + 3Y] = 2² Var[X] + 2 Cov[X, Y] + 3² Var[Y]
but since X and Y are given to be independent, the covariance term vanishes and you're left with
Var[2X + 3Y] = 4 Var[X] + 9 Var[Y]
X follows an exponential distribution with parameter λ = 1/6, so its mean is 1/λ = 6 and its variance is 1/λ² = 36.
Y is uniformly distributed over [a, b] = [4, 10], so its mean is (a + b)/2 = 7 and its variance is (b - a)²/12 = 3.
So you have
Var[2X + 3Y] = 4 × 36 + 9 × 3 = 171
14x-(-5x+6-3x-4)=4(5x)+10
ayudaaa pora doy corona
Answer:
x = 10
General Formulas and Concepts:
Pre-Algebra
Distributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
14x - (-5x + 6 - 3x - 4) = 4(5x) + 10
Step 2: Solve for x
[Distributive Property] Distribute negative: 14x + 5x - 6 + 3x - 4 = 4(5x) + 10Combine like terms: 22x - 10 = 4(5x) + 10Multiply: 22x - 10 = 20x + 10[Subtraction Property of Equality] Subtract 20x on both sides: 2x - 10 = 10[Addition Property of Equality] Add 10 on both sides: 2x = 20[Division Property of Equality] Divide 2 on both sides: x = 10Robin will choose a movie from the Red Box when all movies are in stock. If she
randomly chooses a Romance, Comedy, or Action, what is the probability she will
choose a Romance?
Romance - 24
Action - 32
Comedy - 25
Science Fiction - 5
Horror - 6
Answer:
32
Step-by-step explanation:
Please help!!! Find the domain of the function y = 2 cot(5∕8x).
A) All real numbers except odd integer multiples of 8π∕5
B) All real numbers except 0 and integer multiples of 8π∕5
C) All real numbers except 0 and integer multiples of 4π∕5
D) All real numbers except odd integer multiples of 4π∕5
Answer:
B) All real numbers except 0 and integer multiples of 8π∕5
Step-by-step explanation:
Cotangent function:
The cotangent function is given by:
[tex]y = \cot{ax} = \frac{\cos{ax}}{\sin{ax}}[/tex]
Domain:
All real values except those at which:
[tex]\sin{ax} = 0[/tex]
The sine is 0 for 0 and all integer multiples of [tex]\frac{1}{a}[/tex]
In this question:
[tex]a = \frac{5}{8}[/tex], so the values outside the domain are 0 and the integer multiples of [tex]\frac{8}{5}[/tex]. Then the correct answer is given by option b.
