Answer: a) 1.029, b) (-5.318, -1.282).
Step-by-step explanation:
Since we have given that
[tex]n_1=13\\\\n_2=17\\\\\bar{x_1}=1.9\\\\\bar{x_2}=5.2[/tex]
and
[tex]s_1=2.1\\\\s_2=3.5[/tex]
So, the standard error for comparing the means :
[tex]SE=\sqrt{\dfrac{s^2_1}{n_1}+\dfrac{s^2_2}{n_2}}\\\\SE=\sqrt{\dfrac{2.1^2}{13}+\dfrac{3.5^2}{17}}\\\\SE=\sqrt{1.0598}\\\\SE=1.029[/tex]
At 95% confidence interval, z = 1.96
So, Confidence interval would be
[tex]\bar{x_1}-\bar{x_2}\pm z\times SE\\\\=(1.9-5.2)\pm 1.96\times 1.0294\\\\=-3.3\pm 2.017624\\\\=(-3.3-2.018,-3.3+2.018)\\\\=(-5.318,-1.282)[/tex]
Hence, a) 1.029, b) (-5.318, -1.282).
2 dot plots. Both number lines go from 0 to 10. Plot 1 is titled Middleton. There is 1 dot above 1, 4 dots above 2, 5 dots above 3, 4 dots above 4, 4 dots above 5, 1 dot above 6, 0 dots above 7, 0 dots above 8, 1 dot above 9, 0 dots above 10. Plot 2 is titled Westwood. There are 0 dots above 0, 0 dots above 1, 4 dots above 2, 5 dots above 3, 4 dots above 4, 4 dots above 5, 3 dots above 6, and 0 dots above 7, 8, 9, and 10.
The two dot plots represent a sample of the number of people in households in two towns. Which statements are true about the data sets?
Check all that apply.
Both have the same number of data points.
Both means are between 3 and 4.
Both have the same median.
Both have the same range.
Westwood has less variability than Middleton.
Answer:
It is A,B,and E.
I just did the question and it was right
The true statements about the dot plots are (A) Both have the same number of data points, (B) Both means are between 3 and 4. and (C) Westwood has less variability than Middleton.
What is Mean?Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.
Given are two plots, Middleton and Westwood.
Data points in plot 1 are 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 9
Total number of data points in plot 1 or Middleton = 20
Data points in plot 2 are 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6
Total number of data points in plot 2 or Westwood = 20
So, both have the same number of data points.
Mean of Middleton = Sum of the data points / Total number of data points
= [1 + (4×2) + (5×3) + (4×4) + (4×5) + 6 + 9] / 20
= 75/20
= 3.75
Similarly,
Mean of Westwood = 77/20 = 3.85
So both means are between 3 and 4.
Median is the exact middle element when arranged in increasing or decreasing order.
Exact middle point is the average of 10th and 11th element.
Median of Middleton = (3 + 4)/2 = 3.5
Median of Westwood = (4 + 4)/2 = 4
Both have different medians.
Range of the data set is the difference of maximum point and minimum point.
Range of Middleton = 9 - 1 = 8
Range of Westwood = 6 - 2 = 4
Both have different ranges.
Range is a measure of variation.
Range of Westwood is less than range of Middleton.
So, Westwood has less variability than Middleton.
Hence the true statements are A, B and C.
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The square below represents one whole.
What percent is represented by the shaded area?
Answer:
13%
Step-by-step explanation:
There are 100 squares and 13 are shaded so
13/100=
13%
Answer:
13%
Step-by-step explanation:
The culinary herb cilantro, Coriandrum sativum, is very polarizing; some people love it and others hate it. A genetic component is suspected to be at play. A survey of 12087 American adults of European ancestry asked whether they like or dislike the taste of cilantro. A total of 3181 said that they dislike the taste of cilantro.
(a) Estimate with 95% confidence (and interpret) the proportion of all American adults of European an- cestry who dislike the taste of cilantro
(b) Estimate with 95% confidence (and interpret) a lower confidence bound for the proportion of all Amer- ican adults of European ancestry who dislike the taste of cilantro
Answer:
The 95% confidence (and interpret) the proportion of all American adults of European an- cestry who dislike the taste of cilantro
( 0.2552 , 0.2709)
b) The lower bound for the proportion of all American adults of European ancestry who dislike the taste of cilantro is 0.2552
Step-by-step explanation:
Explanation:-
Given data a survey of 12087 American adults of European ancestry asked whether they like or dislike the taste of cilantro.
large sample size 'n' = 12087 American adults
in survey A total of 3181 said that they dislike the taste of cilantro.
so The sample proportion 'p' = [tex]\frac{3181}{12087} = 0.2631[/tex]
a) Estimate with 95% confidence (and interpret) the proportion of all American adults of European ancestry who dislike the taste of cilantro.
[tex](p - 1.96 \sqrt{\frac{pq}{n} } ,p + 1.96\sqrt{\frac{pq}{n} } )[/tex]
[tex](0.2631 - 1.96 \sqrt{\frac{0.2631 X 0.7369}{12087} } ,0.2631 + 1.96\sqrt{\frac{0.2631 X 0.7369 }{12087} } )[/tex]
(0.2631 - 0.00784 , 0.2631 + 0.00784 )
( 0.2552 , 0.2709)
b) The lower bound for the proportion of all American adults of European ancestry who dislike the taste of cilantro is 0.2552
We are 95% confident that the proportion of all American adults of European ancestry who dislike the taste of cilantro is between 25.5% and 27.1%, and at least 25.5% dislike the taste.
Explanation:This question is related to confidence intervals in statistics. To compute a confidence interval for a population proportion, we mainly need the sample proportion and the size of the sample. Here, the proportion is the number of respondents that dislike cilantro (3181) divided by the total number of respondents (12087).
Thus, the sample proportion (value of p) is 3181/12087 = 0.263 or 26.3%.
The formula for a confidence interval is:
CI = p +/- Z * sqrt[ (p(1-p)) / n ],
where Z is the Z-score (for 95% confidence, Z = 1.96), p is the sample proportion, and n is the sample size.
Applying the values, we get:
CI = 0.263 +/- 1.96 * sqrt[ (0.263)(1 - 0.263) / 12087 ]
After calculation, the 95% confidence interval is about (0.255, 0.271). This means we are 95% confident that the proportion of all American adults of European ancestry who dislike the taste of cilantro is between 25.5% and 27.1%.
For the lower bound, we can take the lower limit of our confidence interval, which is 0.255 or 25.5%. This means we are 95% confident that at least 25.5% of all American adults of European ancestry dislike the taste of cilantro.
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The plot shows the temperatures (in ºF) for a group of children who visited a doctor’s office.
A plot shows the temperature of children at a doctor's office. 1 child had a temperature of 96 degrees; 2, 97 degrees; 5, 98 degrees; 2, 99 degrees; 1, 100 degrees.
What conclusions can be drawn from the data set? Check all that apply.
Answer:
the answer is 1,3,4,5
Step-by-step explanation:
Suppose that $7,000 is invested at an interest rate of 6%, compounded continuously. Find the amount in the account after five years if no withdrawals are made
Answer:
9100
Step-by-step explanation:
I=Prt
I=7,000(.06)5
I=420(5)
I=2,100
2,100+7,000=9,100
Rachel poured 4/5 of a gallon of water into a bucket. Later, she added 3/10 of a gallon more. How much water is in the bucket now?
Answer:
1 1/10 gallons
Step-by-step explanation:
Add 4/5 gallon + 3/10 gallon
Get a common denominator of 10
4/5*2/2 + 3/10
8/10 +3/10
11/10
Change from an improper fraction to a mixed number
10/10 + 1/10
1 1/10 gallons
Answer:
1.1
Step-by-step explanation:
If she added the first 4/5 then she added the 3/10 then you have to add them to figure out how much water is in the bucket.
Coin Toss Results H = Heads T = Tails T H T H T H T T T T H T H T T Find the experimental probability of tossing heads.
Answer:
1/3
Step-by-step explanation:
Answer:
1/3
Step-by-step explanation:
took a test and its correct.
Erin spent $15.30 on ingredients for cookies she's making for the school bake sale. How many cookies must she sell at $0.35 apiece to make a profit
Answer:
She would have to sell 44 cookies or more.
Step-by-step explanation:
Answer:
She would have to sell 44 cookies or more
Step
Two-digit natural numbers are formed, with replacement, from the digits 0 through 9.
How many numbers are greater than 45?
There are 54 two-digit numbers greater than 45. This is calculated by finding the range of valid two-digit numbers (46 to 99) or carefully counting possible combinations without including 45.
Explanation:The two-digit numbers greater than 45 are any numbers from 46 to 99. We can find the amount of these numbers by subtracting 45 from 99. So, there are 54 two-digit numbers greater than 45.
Another way to visualize this is by considering the two-digit possibilities. The first digit can range from 4 to 9 (six possibilities), and the second digit can range from 0 to 9 (ten possibilities). However, since 40-45 are not included, we subtract 5 from the total possibilities, resulting in 60 (=6*10) -5 = 55. Therefore, it seems that we have one number too many, but we must not forget that 45 itself is not included, hence the total numbers exceeding 45 are 54 (55-1).
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These are the means and standard deviations for samples of prices from two
different brands of shoes
Brand A
Mean: $50
Standard deviation: $5
Brand B
Mean: $40
Standard deviation: $8
Select the two true statements,
A. Brand A has a higher average price than brand B.
B. Brand A's prices are more spread out than brand B's prices.
C. Brand A has a lower average price than brand B.
D. Brand A's prices are less spread out than brand B's prices,
Answer:
A. Brand A has a higher average price than brand B.
D. Brand A's prices are less spread out than brand B's prices.
Step-by-step explanation:
We are given the means and standard deviations for samples of prices from two different brands of shoes below;
Brand A Brand B
Mean : $50 Mean : $40
Standard deviation : $5 Standard deviation : $8
Now, from the given statements;
Statement A is correct that Brand A has a higher average price than brand B because as given above Mean of Brand A ($50) > Mean of Brand B ($40).
Also, Statement D is correct that Brand A's prices are less spread out than brand B's prices because the Variance of Brand A is less than the variance of Brand B, i.e.;
Variance of Brand A = [tex]5^{2}[/tex] = $25
Variance of Brand B = [tex]8^{2}[/tex] = $64
Clearly, $25 < $64, so statement D is also correct.
Therefore, the two true statements are Statement A and Statement D.
Final answer:
A. Brand A has a higher average price than brand B.
D. Brand A's prices are less spread out than brand B's prices.
Explanation:
The true statements are that Brand A has a higher average price and less variability in prices than Brand B, which is represented by a lower standard deviation for Brand A.
To expand on these points:
Brand A has a mean price of $50 which is higher than Brand B's mean price of $40, confirming that Brand A has a higher average price (Statement A).
Brand A's standard deviation is $5, while Brand B's standard deviation is $8. A standard deviation is a measure of spread or variability in a set of data. The fact that Brand A's standard deviation is lower indicates that its prices are less variable and more closely clustered around the mean, hence less spread out compared to Brand B (Statement D).
Please help
Prove that the median to the hypotenuse of a right triangle is half the hypotenuse.
To compare lengths, use the _____ Formula.
Answer:
it is the midpoint formula because that is the only equation of that is being divided by 2. The formula is X1 +X2 divied by 2 then it is Y1 + Y2 dived by two which gives you half of something like a line
Step-by-step explanation:
Answer:
mid point
Step-by-step explanation:
Help me answer please.
Answer:
see explanation
Step-by-step explanation:
(a)
For the graph to display direct proportion it must pass through the origin.
The graph shown does not pass through the origin thus does not represent direct proportion.
(b)
Given that q is directly proportional to r then the equation relating them is
q = kr ← k is the constant of proportion
To find k use the condition q = 76 when r = 20, thus
76 = 20k ( divide both sides by 20 )
3.8 = k
q = 3.8r ← equation of proportion
When r = 45, then
q = 3.8 × 45 = 171
S is directly proportional to the fifth power of t
[tex]\[ s = kt^5 \][/tex]
This equation represents the model for the statement "s is directly proportional to the fifth power of t".
When two variables [tex]\( s \)[/tex] and [tex]\( t \)[/tex] are directly proportional to each other, it means that as one variable increases, the other variable also increases by a constant factor. Mathematically, we can express this relationship as:
[tex]\[ s = kt^n \][/tex]
Where:
- [tex]\( s \)[/tex] is the dependent variable.
-[tex]\( t \)[/tex] is the independent variable.
- [tex]\( k \)[/tex] is the constant of proportionality.
- [tex]\( n \)[/tex] is the exponent representing the power to which the independent variable is raised.
In this case, the statement says that s is directly proportional to the fifth power of t . So, we have:
[tex]\[ s = kt^5 \][/tex]
This equation represents the model for the statement "s is directly proportional to the fifth power of t".
Complete correct question:
Write a model for the statement
s is directly proportional to the fifth power of t.
please answer tyty :)
Answer:
3
Step-by-step explanation:
0 indicates no relationship. must be full number.
Compare to the graph f(x)=x^2 the graph of g(x)=(x-2)+3 is the result of translating f(x)
1.2 units up 3 units to the right
2. 2 units down and 3 units up
3. 2 units right and 3 units up
4 2 units left and 3 units right
Answer:
i believe it is 4 but i'm not so sure
Step-by-step explanation:
:)
The graph of g(x)=(x-2)^2+3 compared to the graph of f(x)=x^2 is translated 2 units to the right and 3 units upwards.
Explanation:To understand the transformation of graphs in mathematical terms, consider the initial function f(x) = x^2. The transition to the new function g(x)=(x-2)^2+3 is a result of a shift or translation of the graph. This transformation behaves as per the following rule: g(x) = f(x-h)+k where 'h' units is the horizontal displacement and 'k' units is the vertical displacement.
In the function g(x), x shifts two units to the right (as indicated by (x-2)) and three units upward (as indicated by +3).
So, the correct answer is 2 units right and 3 units up.
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Which point do The graphs F and G have in common
Answer:
1,0
Step-by-step explanation:
Answer:
1,0
Step-by-step explanation:
The diagram shows the number of dollars each child has in a family. How can you redistribute the money so that each child has the same amount? Check all that apply.
A balance diagram going from 1 to 9. 2 circles are above 4 and 2 circles are above 8.
Each child who has $8 must give away $4.
Each child who has $8 must give away $2.
Each child who has $4 must be given $4.
Each child who has $4 must be given $2.
When fairly balanced, each child has $6.
When fairly balanced, each child has $7.
Answer:
2,4,5
Step-by-step explanation:
Answer:2,4,and5
Step-by-step explanation:Common sense
Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 22 and a mean diameter of 200200 inches. If 8383 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.20.2 inches? Round your answer to four decimal places. Answer
Answer:
The probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches is 0.5319.
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean μ and standard-deviation σ and appropriately huge random-samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
Then, the mean of the distribution of sample mean is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the distribution of sample mean is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]\mu=200\\\sigma=22\\n=83[/tex]
Since n = 83 > 30, the Central Limit Theorem can be used to approximate the sampling distribution of sample mean diameter of the shafts.
Then:
Mean: [tex]\mu_{\bar x}=\mu=200[/tex]
Standard deviation: [tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{22}{\sqrt{83}}=2.415[/tex]
Compute the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches as follows:
[tex]P(\bar X-\mu_{\bar x}<0.20)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{0.20}{2.415})[/tex]
[tex]=P(Z<0.08)\\=0.53188\\\approx0.5319[/tex]
*Use a z-table.
Thus, the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches is 0.5319.
A school bought pens, each costing $1, and pencils, each costing $0.5. The cost of the whole purchase was $220. How many pens and pencils were purchased if there were 80 more pencils than pens?
Answer:
200 pencils and 120 pens
Step-by-step explanation:
Let the number of pencils be x while pens be y.
Considering the cost of whole purchase then, we get the equation
0.5x+y=220
Considering the number of items bought, then the equation is
x-y=80
Adding the two equations then we have
1.5x=300
x=300/1.5=200
Consideeing that x-y=80 and x is 200 then
200-y=80
y=200-80=120
Therefore, the pencils were 200 and pens 120 pieces
If a six-sided die is rolled 30 times, how many times can you expect to get a 6?
5 times,I hoped this helped you out,if not sorry
What are the zeroes of the function y=3(x-a)(x+b) in terms of a and b?
Answer:
a, -b
Step-by-step explanation:
When x is a, the function becomes
[tex]f(a)=3(a-a)(a+b)[/tex]
as you see, a-a is 0, and as your whole function is multiplied by this, it makes it 0.
[tex]f(-b)=3(-b-a)(-b+b)[/tex]
As you see -b+b is 0, and once again, this would make the whole function 0.
An experiment that claimed to show that meditation reduces anxiety proceeded as follows. The experimenter interviewed the subjects and rated their level of anxiety. Then the subjects were randomly assigned to two groups. The experimenter taught one group how to meditate and they meditated daily for a month. The other group was simply told to relax more. At the end of the month, the experimenter interviewed all the subjects again and rated their anxiety level. The meditation group now had less anxiety. What property of good experiments is missing from the study? control group randomization using enough subjects blinding
Answer:
Experiement lacked blindness concept
Step-by-step explanation:
In good experiments, the results are totally unbiased and unknown to anyone, even to those conducting the experiment.
In the given case, the interviewer had an idea about which group had gone for meditation so it was obvious that they would yield less anxiety.
Here the concept of blinding was missing, which is essential for a good and fair experiment. A good experiemnt is a double blinded experiement or atleast it should be single blinded
How many 5 digit codes are possible if the first digit cannot be 0 and digits can be repeated?
Answer:
Step-by-step explanation:
Zip codes with 5 digits (all five digits can be repeated): 10^5=100,000 if first digit is 0, its no longer 5-digit right? Zip codes with no digit being repeated: 10*9*8*7*6=30,240 if first digit is 0, its no longer 5-digit right? Zip codes with at least one digit being repeated: 90000-27216 = 62784 ?N
A survey is to be conducted to determine the average driving in miles by Minnesota State University, Mankato students. The investigator wants to know how large the sample should be so that he/she can be 92% confident on the estimate and the estimate is within 1.5 miles of the true average. A similar study conducted in past and it was found that the standard deviation of the students’ driving distances was 8.2 miles.
Answer:
[tex]n=(\frac{1.75(8.2)}{1.5})^2 =91.52 \approx 92[/tex]
So the answer for this case would be n=92 rounded up to the nearest integer
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =1.5 and we are interested in order to find the value of n, if we solve n from equation (b) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 92% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.04;0;1)", and we got [tex]z_{\alpha/2}=1.75[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.75(8.2)}{1.5})^2 =91.52 \approx 92[/tex]
So the answer for this case would be n=92 rounded up to the nearest integer
An ant arrives at the snail’s starting position at time minutes and follows the snail’s path. During the interval minutes, the ant travels in the same direction as the snail with a constant acceleration of 2 inches per minute per minute. The ant catches up to the snail at time minutes. The ant’s velocity at time is B inches per minute. Find the value of B.
QUESTION BEGINNING
Given a snail is traveling along a straight path. The snail’s velocity can be modeled by [tex]v(t)=1.4ln(1+t^2)[/tex] inches per minute for 0 ≤ t ≤ 15 minutes.
Answer:
B=22.35 Inches per minutes
Step-by-step explanation:
If the snail's velocity is [tex]v(t)=1.4ln(1+t^2)[/tex] per minute, its displacement for 0 ≤ t ≤ 15 minutes is given by the integral:
[tex]\int v(t) dt=\int (1.4ln(1+t^2))dt=76.04307[/tex]
The constant acceleration of the ant is 2 Inches per minute.
The velocity of the ant therefore, twill be:
[tex]\int 2 dt=2t+K, $where K is a constant of integration$[/tex]
For the interval, 12≤t≤15, the displacement of the ant is:
[tex]\int_{12}^{15}(2t+K) dt=81+3K[/tex]
Since the snails displacement and that of the ant are equal in 12≤t≤15.
81+3K=76.04307
3K=76.04307-81
3K=-4.95693
K=-1.65231
At t=12, the velocity of the ant is therefore:
2t+K=2(12)-1.65231=22.348 Inches per minutes
B=22.348 Inches per minutes
Final answer:
The question examines a scenario involving an ant accelerating to catch up with a snail, focusing on determining the ant's velocity at the catch-up point. Utilizing the principle of kinematics and acceleration, the answer lies in relating the acceleration to the final velocity, dependent on the time variable, which underscores the direct relationship between acceleration and velocity increase.
Explanation:
The question essentially deals with kinematics, specifically with the scenario of an ant accelerating from rest to catch up with a snail. Given the ant accelerates at 2 inches per minute per minute, and eventually matches velocities with the snail, the goal is to find the ant's velocity (B inches per minute) at the moment it catches up.
Firstly, we know the acceleration (a) is 2 inches/minute2. From kinematic equations, specifically v = u + at, where 'u' is the initial velocity (0 in this case since the ant starts from rest), 'a' is acceleration, and 't' is time, we can plug in our values. The time variable 't' here represents the duration from when the ant starts until it catches up with the snail, which is not explicitly given but is critical in understanding the rate of acceleration's contribution to velocity.
For the purpose of solving this problem, without explicit time or distances, we focus on the principle that the ant's final velocity (B) is a product of its acceleration over a given period: B = 0 + (2)t. Thus, the value of 'B' entirely depends on the time 't', demonstrating a direct correlation between acceleration duration and velocity increase.
An SRS of 2,500 individuals was taken from a city with population 1 million, to estimate the percentage of city residents with a graduate degree. 555 people in the sample had a graduate degree. The proportion of individuals in the city with a graduate degree is estimated as 23%. Say the true percentage of individuals in the city who have a graduate degree is 22%. In this case, the standard error of the sample proportion is closest to:
Answer:
The standard error of the sample proportion is closest to 1%
Step-by-step explanation:
Standard error of the sample proportion is given as
σₓ = √[p(1-p)/n]
where
p = sample proportion = estimated to be 23% = 0.23
n = Sample size = 2500
σₓ = √[p(1-p)/n]
σₓ = √[0.23×0.77/2500]
σₓ = 0.0084166502 = 0.00842
σₓ = 0.00842 = 0.842%
Hence, it is easy to see that the standard error of the sample proportion is closest to 1%.
Hope this Helps!!!
C is the center of a circle. Find the length of arc AB to two decimal points
Answer:
d
Step-by-step explanation:
C is the center of a circle. Find the length of arc AB to two decimal points
Answer:
d
Step-by-step explanation:
s=13.68
A study conducted by the Toledo police at the intersection of Byrne and Heatherdowns for the 7 to 9 AM drive time revealed the follwoing number of vehicles that proceeded through the intersection after the light changed. The information reported is for a SAMPLE of 6 days during a 1 month period.6 12 7 12 8 9Find the mean, median, mode and standard deviation for the SAMPLE.
Answer:
(a)Mean=9
(b)Median=9.5
(c)Mode=12
(d)Standard Deviation=2.53
Step-by-step explanation:
The sample of the number of vehicles that proceeded through the intersection after the light changed for 6 days during a 1 month period is given below:
6 12 7 12 8 9
(a)Mean
[tex]Mean=\frac{6+12+ 7+ 12+ 8+ 9}{6} \\=\frac{54}{6} \\Mean=9[/tex]
(b)Median
First, arrange in ascending order
6,7,8,9,12,12
Since we have two terms in the middle, we take the average.
[tex]Median=\frac{8+9}{2}\\Median=8.5[/tex]
(c)Mode
The mode is the number with the highest frequency. The mode number of cars is 12.
(d)Standard Deviation
[tex]S.D.=\sqrt{\dfrac{\sum_{i=1}^{n}(x-\bar{x})^2}{n-1}}[/tex]
[tex]S.D.=\sqrt\frac{(6-9)^2+(7-9)^2+(8-9)^2+(9-9)^2+(12-9)^2+(12-9)^2}{6-1}[/tex]
[tex]=\sqrt{6.4} \\S.D.=2.53[/tex]
A political candidate has asked his/her assistant to conduct a poll to determine the percentage of people in the community that supports him/her. If the candidate wants a 6% margin of error at a 90% confidence level, what size of sample is needed? Be sure to round accordingly.
A sample size of 188 would be needed to achieve a 6% margin of error at a 90% confidence level.
Used the formula for sample size calculation:
[tex]n = \dfrac{z^2 \times p (1 - p)}{E^2}[/tex]
Where: n = sample size.
Z = Z-score corresponding to the desired confidence level.
p = estimated proportion of the population that supports the candidate.
E = desired margin of error.
Here we have to give that,
90% confidence level corresponds to a Z-score of approximately 1.645.
That is, z = 1.645
p = 0.5
E = 0.06
Substituting the given values into the formula, we get:
[tex]n = \dfrac{z^2 \times p (1 - p)}{E^2}[/tex]
[tex]n = \dfrac{(1.645)^2 \times 0.5(1 - 0.5)}{0.06^2}[/tex]
[tex]n = \dfrac{0.6765}{0.0036}[/tex]
[tex]n =187.9[/tex]
Rounded to whole numbers,
[tex]n = 188[/tex]
Therefore, the size of the sample would be 188.
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In order to achieve a 6% margin of error and a 90% confidence level in a poll, the correct sample size must be determined using the error bound formula. A larger and representative sample will minimize the margin of error and improve the poll's precision and accuracy. A number of key factors, like identification of the target population and select a random sample, should be considered while conducting a poll.
Explanation:The subject matter dealt with here involves conducting a poll to gauge public opinion, with a desired accuracy defined by a 6% margin of error and a 90% confidence level. This is primarily related to Statistics, a branch of Mathematics.
To determine an appropriate sample size for a given margin of error and confidence level, the error bound formula is utilized. Although the actual formula could appear complex for some, many online calculators can complete the task. The 90% confidence level means that if we were to take multiple sets of samples, roughly 90% of the calculated confidence intervals would contain the true population mean or proportion.
Furthermore, sample size influences the margin of error; a larger sample reduces the margin of error and makes the poll result more precise and accurate. As a rule of thumb, the sample should be random and representative of the population in question to ensure the accuracy and reliability of poll results.
Take note that many criteria must be met to conduct a valid and scientifically accurate poll, some of which include: identifying the desired population of respondents, ensuring the sample is both random and representative of the wider population, and interviewing a sufficient number of citizens to achieve a reasonable sample size.
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Which choices are equivalent to the quotient below? Check All That Apply.
Answer:
A, E
Step-by-step explanation:
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