A population has standard deviation o=17.5.
Part 1 of 2
(a) How large a sample must be drawn so that a 99.9% confidence interval for u will have a margin of error equal to 4.1? Round the answer up to the nearest integer. (Round the critical value to no less than three decimal places.) A sample size of is needed to be drawn in order to obtain a 99.9% confidence interval with a margin of error equal to 4.1.
Part 2 of 2
(b) If the required confidence level were 95%, would the necessary sample size be larger or smaller? (Choose one) V , because the confidence level is (Choose one) V .
Answer:
a) A sample of 198 must be drawn.
b) Smaller, because the confidence level is smaller.
Step-by-step explanation:
Question a:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.999}{2} = 0.0005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.0005 = 0.9995[/tex], so Z = 3.291.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
How large a sample must be drawn so that a 99.9% confidence interval for u will have a margin of error equal to 4.1?
This is n for which M = 4.1. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]4.1 = 3.291\frac{17.5}{\sqrt{n}}[/tex]
[tex]4.1\sqrt{n} = 3.291*17.5[/tex]
[tex]\sqrt{n} = \frac{3.291*17.5}{4.1}[/tex]
[tex](\sqrt{n})^2 = (\frac{3.291*17.5}{4.1})^2[/tex]
[tex]n = 197.3[/tex]
Rounding up:
A sample of 198 must be drawn.
(b) If the required confidence level were 95%, would the necessary sample size be larger or smaller?
We have that:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
Solving for n
[tex]\sqrt{n} = \frac{z\sigma}{M}[/tex]
That is, n and z are directly proportion, meaning that a higher value of z(higher confidence level) leads to a higher sample size needed.
95% < 99.9%, so a smaller confidence interval.
Smaller, because the confidence level is smaller.
Please Help!!
No links or I’ll report you!
A. 11
B. 13
C. 8
D. 7
Answer:
The answer is 13.
Step-by-step explanation:
Angle ABC and PQR are equivalent, although angle PQR is just scaled down by a factor of 9. Line CA is 54, line PR is 6, 54/6=9. So, line PQ has to be equal to 9 because 81/9=9. So you input all values into the expression until you get the product of 9.
Work: 2(13)-17=9, so 13 is your answer.
A standard number cube, labeled numbers 1-6 on each side, is rolled three times. Mary says the chance of rolling a 2 all three times is 1/8. But John disagrees and says the probability for rolling a 2 all three times is 1/216. Who calculated the correct probability or rolling a 2 the three times the n number cube is rolled? Show work to justify your reasoning.
Answer: john answer it correctly
Step-by-step explanation:
6.6.6_=216
Solve for x: 3-a/x-a=1/a
PLEASE HELP NEED ASAPPP WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWERRRR
Answer:
x= -a2(the 2 means squared)/1-3a+a2
Step-by-step explanation:
I rll hope this helps
Answer:
x= a^2
----------------
1 - 3a + a^2
Step-by-step explanation:
what is the answer
-3x+6(2x+4)=15
Answer:
x=-1
Step-by-step explanation:
use math a way
Please help on both questions. I would appreciate it.
Answer:
first one is 4.5 second one is 45
Step-by-step explanation:
13 Hannah deposits $3,000 into each of two
savings accounts.
• Account I earns 4% annual simple
interest.
• Account II earns 4% interest
compounded annually.
Hannah does not make any additional
deposits or withdrawals. What is the sum
of the balances of Account I and Account
II at the end of 2 years?
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Answer:
$6484.80
Step-by-step explanation:
Account I:
The balance in the account after 2 years will be ...
A = P(1 +rt)
A = $3000(1 +0.04(2)) = $3240
__
Account II:
The balance in the account after 2 years will be ...
A = P(1 +r)^t
A = $3000(1 +0.04)^2 = $3244.80
__
The sum of the two balances after 2 years is ...
$3240 +3244.80 = $6484.80
- Yesterday Billy earned $30 trimming
hedges for Mrs. Gant. Today he will earn
$10 an hour for weeding her garden. If
he weeds her garden for 8 hours, how
much in all will he earn working for
Mrs. Gant?
If the surface area of a cube is 150 cm2, what is the volume of the cube
Answer:
V = 125 in^3
Step-by-step explanation:
A cube has 6 sides, and the area of each is equal to the side length squared:
A = 6x^2
A is given as 150 cm^2, and so is equal to 6x^2. Thus, x = the side length = 5 cm.
The volume of the same cube is given by V = x^3, which here is 5^3 in^3, or V = 125 in^3
In the data set below, what are the lower quartile, the median, and the upper quartile. 13, 16, 16, 17, 51, 57, 62, 72, 92, 97
Answer:
I'm rusty on this but I believe:
the median is 54
the lower quartile = 16
the upper quartile is 72
. The admission fee for a basketball game is $5 for students and $7 for adults. At one of the girl’s home games, 150 people attended the game and $866 was collected. How many students and how many adults attended the game?
Answer:
Adults =58, Students=92
Step-by-step explanation:
A prisoner is trapped in a cell containing three doors. The first door leads to a tunnel that returns him to his cell after two days of travel. The second leads to a tunnel that returns him to his cell after three days of travel. The third door leads immediately to freedom. (a) Assuming that the prisoner will always select doors 1, 2 and 3 with probabilities 0.5, 0.3, 0.2 (respectively), what is the expected number of days until he reaches freedom
Answer:
10.5 days
Step-by-step explanation:
Given :
P(d1) = 0.5 ; P(d2) = 0.3 ; P(d3) = 0.2
For d1: 2days of freedom ; then back to cell
For d2 : 3 days of freedom ; then back to cell
For d3 :, complete freedom.
Let number of days till freedom is attained = x
x = E(x | d1)p(d1) + E(x | d2)p(d2) + E(x | d3)p(d3)
x = (2 + x)(0.5) + (3 + x)(0.3) + (1 * 0.2)
x = 1 + 0.5x + 0.9 + 0.3x + 0.2
x = 2.1 + 0.8x
x - 0.8x = 2.1
0.2x = 2.1
x = 2.1 / 0.2
x = 10.5 days
Hence, expected number of days to attain freedom = 10.5 days
special triangles 45-45-90
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Answer:
x = y = (√10)/2
Step-by-step explanation:
In an isosceles right triangle, the side lengths are equal, and they are equal to (√2)/2 times the hypotenuse length.
x = y = (√5)(√2)/2
x = y = (√10)/2
Answer:
x = y = [tex]\frac{1}{2}[/tex] [tex]\sqrt{10}[/tex]
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{\sqrt{2} }{2}[/tex]
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{\sqrt{5} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )
2x = [tex]\sqrt{10}[/tex] ( divide both sides by 2 )
x = [tex]\frac{1}{2}[/tex] [tex]\sqrt{10}[/tex]
Since the base angles are 45° then the triangle is isosceles with both legs congruent , thus
x = y = [tex]\frac{1}{2}[/tex] [tex]\sqrt{10}[/tex]
Find the surface area of the pyramid.
The surface area is_square meters.
Answer:
173.26
Step-by-step explanation:
Use technology or a z-score table to answer the question.
The weights of members of a baseball league are normally distributed with a mean of 176 pounds and a standard deviation of 11.4 pounds. Consider a league membership of 120 members.
How many of the members will weigh 165 pounds or more?
A.)67
B.)76
C.)80
D.)100
Answer:
D. 100
Step-by-step explanation:
1. Find the z-score: 165-176/11.4 = -1.2
2. Find the percentage of the z-score. Here it's 16.85%
3. Because we are searching for the amount of members that weigh MORE than 165 pounds and not LESS, we need to find the greater percentage by subtracting 16.85% from 100% which is 83.15%. This is the percentage of people that weigh more than 165 pounds.
4. Multiply the percentage by the number of members: 83.15%*120 = 99.78
5. Round it to a whole number because someone can't be 0.78 of a person. You get 100 members.
Also, I took the test :)
NEED HELP ASAP FREE BRAINLIST
Answer:
D). 10699
Step-by-step explanation:
D is right the math is hard to explain.
5/16 divided by 3 1/5
Answer:
25/256
Step-by-step explanation:
(5/16) / (3 1/5)
(5/16) / (16/5)
(5/16) * (5/16)
5*5 / 16*16
25/256
Sabrina read a total of 185 pages in three days.
On the first day, she read 85 pages
· On the second and third days, she read the same
How many pages did she read on the third day?
Answer:
Sabrina read 50 pages on the third day.
Step-by-step explanation:
Since Sabrina read a total of 185 pages in three days, and on the first day, she read 85 pages, while on the second and third days, she read the same amount, to determine how many pages did she read on the third day the following calculation must be performed:
(185 - 85) / 2 = X
100/2 = X
50 = X
Therefore, Sabrina read 50 pages on the third day.
Use the elimination method to solve the system of equations. Choose the
correct ordered pair.
10x+2y=64
3x - 4y = -36
O A. (4, 12)
B. (2,10)
o
C. (-5,8)
O D. (-3, 11)
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Answer:
A. (4, 12)
Step-by-step explanation:
Adding the second equation to twice the first will eliminate y.
2(10x +2y) +(3x -4y) = 2(64) +(-36)
23x = 92 . . . . . . . . simplify
x = 4 . . . . . . . . . divide by 23
This value matches choice A: (4, 12).
What is the first error Zoe made in her proof?
a. Zoe used an invalid reason to justify the congruence of a pair of sides or angles
b. Zoe only established some of the necessary conditions for a congruence criterion.
c. Zoe established all necessary conditions, but then used an inappropriate congruence criterion.
d. Zoe used a criterion that does not guarantee congruence
iui
Answer:
a
Step-by-step explanation:
To prove congruence
1 ∠ A ≅ ∠ C → given
2 ∠ DEA ≅ ∠ BEC → vertically opposite angles
3. AE ≅ EC → given
We then have 2 angles and the included side ( side between the 2 angles )
congruent in both triangles, thus Δ AED ≅ Δ CEB ( ASA postulate )
Zoes' error was in assuming ∠ DEA ≅ ∠ BEC was given
Zoe used an invalid reason to justify the congruence of a pair of sides or angles.
Option a is correct.
From given diagram it is observed that,
Line segment AD and CB are parallel and AC is transversal line. So that alternate angles A and C are equal.
[tex]\angle A=\angle C[/tex]
When two lines intersect at any point then vertically opposite angles are equal.
So that, [tex]\angle DEA=\angle BEC[/tex]
Given that , [tex]AE=EC[/tex]
The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Hence, both triangles are congruent to each other.
Learn more:
https://brainly.com/question/25920974
PLEASE HELP 9) (6 pts.) The perimeter of a rectangle is 100 feet. The length is 10 more than 3 times the width. Define variables and write a system of equations that could be used to find the length and width of the rectangle. For this problem you are NOT being asked to solve the system, just to set it up.
Step-by-step explanation:
sorry i am unable to understand what it is asking but if you inform me more i would love to help
An empty swimming pool is to be filled to the top. The pool is shaped like a rectangular prism with length 12 m, width 8 m, and depth 4 m.
Suppose water is pumped into the pool at a rate of 24 m per hour. How many hours does it take to fill the empty pool? (NO LINKS , links will get you reported / booted
Answer:
16 hours
Step-by-step explanation:
first find the volume if the pool 12x8x4=384 then divide by how many meters per hour 384÷24=16
This is a scale drawing of a field. The scale is 1 in.: 10 ft. What is the actual length of the
longer side of the field?
7 in.
5 in.
50 ft
10 ft
70 ft
Answer:7ft
Step-by-step explanation:
i got it right
The radius of a. circular garden is 15 feet. About how much fencing will be needed to enclose the garden?
Answer:
94.2 ft of fencing
Step-by-step explanation:
To answer this, find the circumference, C, of the garden, using the circumference formula C = 2(pi)r.
Here, with r = 15 ft, we get C = 2(3.14)(15 ft) = 94.2 ft of fencing will enclose this garden.
1 hundredth+3 tenths equal what
.Answer:
The answer is .31
Step-by-step explanation:
When there is a “th” at the end of the number it signals that the number is to the right of the decimal.
Tenths are immediately to the right of the decimal, next is hundredths, then thousandths, and so on.
A recent survey reported that small businesses spend 24 hours a week marketing their business. A local chamber of commerce claims that small businesses in their area are not growing because these businesses are spending less than 24 hours a week on marketing. The chamber conducts a survey of 88 small businesses within their state and finds that the average amount of time spent on marketing is 23.2 hours a week. Assuming that the population standard deviation is 4.2 hours, is there sufficient evidence to support the chamber of commerce’s claim at the 0.05 level of significance?
Step 1 of 3:
State the null and alternative hypotheses for the test. Fill in the blank below. H0Ha: μ=24: μ⎯⎯⎯⎯⎯⎯⎯⎯24
Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places.
Step 3 of 3: Draw a conclusion and interpret the decision.
Answer:
Following are the responses to the given choices:
Step-by-step explanation:
In step 1:
State the zero and alternate test hypotheses. Insert underneath.
[tex]H_0 : \mu = 24: H_a : \mu < 24[/tex]
[tex]H_0[/tex] Smaller companies in their region are and they spend at least 24 hours per week on the marketing of the these companies
[tex]H_1[/tex] There really is no growth for smaller firms in their area because the companies spend or less 24 hours per week on marketing.
In step 2:
Each test statistics meaning is calculated. Around two decimal places for your reply.
[tex]z=\frac{\bar{X}-\mu_{0}}{\frac{\sigma}{\sqrt{n}}}=\frac{23.2-24}{\frac{4.2}{\sqrt{88}}}=-1.787[/tex]
In step 3:
Draw a start and write the decision.
Since it is observed that [tex]z=-1.787 < z_c=-1.64[/tex] it is then concluded that the null hypothesis is rejected.
Consequently we consider that small companies in their field may not expand, as they spend or less 24 hours per week on marketing.
Please solve for all three parts of the question.
Answer:
f(-5) = 25
f(0) = -2
f(5) = 16
Step-by-step explanation:
Given the functions;
To get f(-5), we will use the function of x where x is less than 0 since -5 is less than zero
at where x < 0, f(x) = x^2
f(-5) = (-5)^2
f(-5) = 25
b) For f(0), where the point where x = 0, f(x)= -2
Hence the value of f(o) = -2
c) For f(5), the function where x > 5 is f(x) = 2x+6
f(x) = 2x+6
f(5) = 2(5)+6
f(5) = 16
Someone plsssssssssssssssssssssssssssssssssssssssssss help (Becca’s dog walking business started with 1 dog. She walks 2 additional dogs each month. How many dogs does she walk in the third month?)
1. Use the given Taylor polynomial p 2 to approximate the given quantity.
2. Compute the absolute error in the approximation assuming the exact value is given by a calculator.
Approximate e-0.07 using f(x) = e-x and p2(x) = 1 - x + x2/2
Answer:
Part 1:
P₂(0.07)=0.93245≈[tex]e^{-0.07}[/tex]
Part 2:
Error=[tex]0.5618*10^{-4}[/tex]
Step-by-step explanation:
Given:
[tex]f(x)=e^{x}\\f(-0.07)=e^{-0.07}[/tex]
P₂(x)=[tex]1-x+\frac{x^2}{2}[/tex]
Solution:
Part 1:
P₂(x)=[tex]1-x+\frac{x^2}{2}[/tex]
We have x=0.07
Put Value of x in above Equation:
P₂(0.07)=[tex]1-0.07+\frac{0.07^2}{2}[/tex]
P₂(0.07)=0.93245≈[tex]e^{-0.07}[/tex]
Part 2:
[tex]e^{-0.07}[/tex]=0.93239382 (Calculated using Calculator)
Error=|[tex]e^{-0.07}[/tex]-P₂(0.07)|=|0.93239382-0.93245|=0.00005618
Error=|0.93239382-0.93245|
Error=0.00005618
Error=[tex]0.5618*10^{-4}[/tex]
How much will you pay for an item that is $13.35 on sale for 30% off?
$4.005
$9.33
$9.35
$10.35
Answer:
$9.35
Step-by-step explanation:
Find the sale price by multiplying 13.35 by 0.7, since this will be 70% of the original price
13.35(0.7)
= 9.345
This rounds to approximately 9.35
So, you will pay $9.35
Answer:
9.35 would be the answer!
Step-by-step explanation:
i would really appreciate a brainliest if this helped! <3