Answer:
42.86%
Step-by-step explanation:
3/7 as a decimal is 0.4286... and to convert that into a decimal, you move the decimal point right twice.
0.4286 = 42.86%
I hope this helped!
Final answer:
To convert the fraction 3/7 into a percent, divide 3 by 7 to get the decimal 0.4286, then multiply by 100 to get 42.86%.
Explanation:
Converting a Fraction to a Percent
To convert a fraction like 3/7 into a percent, follow these steps:
Convert the fraction to a decimal by dividing the numerator by the denominator. For 3/7, divide 3 by 7 to get approximately 0.4286.Convert the decimal to a percent by multiplying it by 100. So, 0.4286 times 100 equals 42.86.Therefore, 3/7 as a percent is 42.86%.
A percent (or per cent) is a way of expressing a number as a fraction of 100. The term "percent" comes from the Latin per centum, which means "by the hundred." It is often represented by the symbol "%."
In 2010 as part of the General Social Survey, 1295 randomly selected American adults responded to this question: "Some countries are doing more to protect the environment than other countries are. In general, do you think that America is doing more than enough, about the right amount, or too little?" Of the respondents, 473 replied that America is doing about the right amount. What is the 95% confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment. Group of answer choices (0.352, 0.378) (0.343, 0.387) (0.339, 0.391) (0.331, 0.400)
Answer:
(0.339, 0.391)
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 1295, \pi = \frac{473}{1295} = 0.365[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.365 - 1.96\sqrt{\frac{0.365*0.635}{1295}} = 0.339[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.365 + 1.96\sqrt{\frac{0.365*0.635}{1295}} = 0.391[/tex]
So the correct answer is:
(0.339, 0.391)
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.
A B C or D? I need help
Answer:
The answer is (A)
Answer:
The answer is A.
Step-by-step explanation:
This is because the plus sign after the first mixed number gets multiplied to the second mixed number. When a plus sign gets multiplied to something that is negative already, then the answer is negative, so the equation will still stay the same and be -3 1/8 - 2 1/2.
if this answer helped u, please mark as brainliest!
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:
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
100 POINTS.
PLEASE PROVIDE STEP BY STEP ANSWER
THANK YOU.
Step-by-step explanation:
W(x) = (10x⁴ − 8) (30x + 25)^0.5
A) Take log of both sides.
ln(W) = ln[(10x⁴ − 8) (30x + 25)^0.5]
ln(W) = ln(10x⁴ − 8) + ln[(30x + 25)^0.5]
ln(W) = ln(10x⁴ − 8) + 0.5 ln(30x + 25)
Take derivative.
W' / W = 40x³ / (10x⁴ − 8) + 0.5 (30) / (30x + 25)
W' / W = 20x³ / (5x⁴ − 4) + 3 / (6x + 5)
W' = W [20x³ / (5x⁴ − 4) + 3 / (6x + 5)]
W'(x) = (10x⁴ − 8) (30x + 25)^0.5 [20x³ / (5x⁴ − 4) + 3 / (6x + 5)]
B) Evaluate at x = 0.
W'(0) = (0 − 8) (0 + 25)^0.5 [0 / (0 − 4) + 3 / (0 + 5)]
W'(0) = (-8) (5) (0 + 3/5)
W'(0) = -24
Answer:
[tex]\textsf{A)}\quad W'(x) = (10x^4 - 8) \cdot (30x + 25)^{0.5} \left(\dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5} \right)[/tex]
[tex]\textsf{B)}\quad W'(0)=-24[/tex]
Step-by-step explanation:
Part AGiven function:
[tex]W(x) = (10x^4 - 8) \cdot (30x + 25)^{0.5}[/tex]
Take the natural logarithm of both sides:
[tex]\ln \left(W(x)\right) = \ln \left( (10x^4 - 8) \cdot (30x + 25)^{0.5} \right)[/tex]
Use properties of logarithms to simplify:
[tex]\ln \left(W(x)\right) = \ln (10x^4 - 8) +\ln(30x + 25)^{0.5} \\\\\\ \ln \left(W(x)\right) = \ln (10x^4 - 8) +0.5 \ln(30x + 25)[/tex]
Differentiate both sides with respect to x:
[tex]\dfrac{d}{dx} \ln \left(W(x)\right) = \dfrac{d}{dx} \left( \ln (10x^4 - 8) + 0.5 \ln (30x + 25) \right)[/tex]
Apply the chain rule on the right-hand side:
[tex]\dfrac{W'(x)}{W(x)} = \dfrac{1}{10x^4 - 8} \cdot \dfrac{d}{dx} (10x^4 - 8) + 0.5 \cdot \dfrac{1}{30x + 25} \cdot \dfrac{d}{dx} (30x + 25) \\\\\\ \dfrac{W'(x)}{W(x)} = \dfrac{1}{10x^4 - 8} \cdot (40x^3) + 0.5 \cdot \dfrac{1}{30x + 25} \cdot (30) \\\\\\ \dfrac{W'(x)}{W(x)} = \dfrac{40x^3}{10x^4 - 8} + \dfrac{15}{30x + 25} \\\\\\ \dfrac{W'(x)}{W(x)} = \dfrac{2(20x^3)}{2(5x^4 - 4)} + \dfrac{5(3)}{5(6x + 5)} \\\\\\ \dfrac{W'(x)}{W(x)} = \dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5}[/tex]
Multiply both sides by W(x) to solve for W'(x):
[tex]W'(x) = W(x) \left(\dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5} \right)[/tex]
Substitute W(x) back in:
[tex]W'(x) = (10x^4 - 8) \cdot (30x + 25)^{0.5} \left(\dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5} \right)[/tex]
Therefore, the derivative W'(x) is:
[tex]W'(x) = (10x^4 - 8) \cdot (30x + 25)^{0.5} \left(\dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5} \right)[/tex]
[tex]\dotfill[/tex]
Part BTo find W'(0), substitute x = 0 into W'(x):
[tex]W'(0) = (10(0)^4 - 8) \cdot (30(0) + 25)^{0.5} \left(\dfrac{20(0)^3}{5(0)^4 - 4} + \dfrac{3}{6(0) + 5} \right) \\\\\\ W'(0) = (0 - 8) \cdot (0 + 25)^{0.5} \left(\dfrac{0}{0 - 4} + \dfrac{3}{0 + 5} \right) \\\\\\ W'(0) = (- 8) \cdot (25)^{0.5} \cdot \left( \dfrac{3}{5} \right) \\\\\\ W'(0) = (- 8) \cdot 5 \cdot \dfrac{3}{5} \\\\\\ W'(0)=-24[/tex]
Therefore, the value of W'(0) is -24.
Four-legged animals run with two different types of motion: trotting and galloping. An animal that is trotting has at least one foot on the ground at all times, whereas an animal that is galloping has all four feet off the ground at some point in its stride. The number of strides per minute at which an animal breaks from a trot to a gallop depends on the weight of the animal.
1. Use the table and the method of this example to find an equation that relates an animal's weight x (in pounds) and its lowest galloping speed y (in strides per minute).
weight, X 25 35 50 75 500 1000
Galloping speed, Y 191.5 184.7 175.8 162.2 124.9 113.2
Answer:
Galloping speed Y=179.984-0.076 weight X
Step-by-step explanation:
The required equation is
y=a+bx
where y is galloping speed and x is weight of animal.
We have to estimate intercept a and slope b.
x y xy x²
25 191.5 4787.5 625
35 184.7 6464.5 1225
50 175.8 8790 2500
75 162.2 12165 5625
500 124.9 62450 250000
1000 113.2 113200 1000000
sumx=1685
sumy=952.3
sumxy=207857
sumx²=1259975
[tex]slope=b=\frac{n(sumxy)-(sumx)(sumy)}{nsumx^{2}-(sumx)^{2} }[/tex]
[tex]slope=b=\frac{6(207857)-(1685)(952.3)}{6*(1259975)-(1685)^{2} }[/tex]
[tex]slope=b=\frac{-357483.5}{4720625}[/tex]
slope=b=-0.07573.
intercept=a=ybar-b*xbar
[tex]ybar=\frac{sumy}{n}[/tex]
[tex]ybar=\frac{952.3}{6}[/tex]
ybar=158.7167
[tex]xbar=\frac{sumx}{n}[/tex]
[tex]xbar=\frac{1685}{6}[/tex]
xbar=280.8333
intercept=a=ybar-b*xbar
intercept=a=158.7167-(-0.07573)*280.8333
intercept=a=158.7167+21.2675
intercept=a=179.9842
rounding intercept and slope to 3 decimal places
intercept=179.984.
slope=-0.076
The required equation is
Galloping speed Y=179.984-0.076 weight X
The required equation is galloping speed Y = 179.984 - 0.076 weight X.
Given that,
Four-legged animals run with two different types of motion: trotting and galloping.
The number of strides per minute at which an animal breaks from a trot to a gallop depends on the weight of the animal.
We have to determine,
An equation that relates an animal's weight x (in pounds) and its lowest galloping speed y (in strides per minute).
According to the question,
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
The required linear equation is,
y = a + bx
Where y is galloping speed and x is weight of animal.
To estimate intercept a and slope b from the table showing below.
x y x.y x²
25 191.5 4787.5 625
35 184.7 6464.5 1225
50 175.8 8790 2500
75 162.2 12165 5625
500 124.9 62450 250000
1000 113.2 113200 1000000
Then,
sum of x = 1685 , sum of y = 952.3 , sum of xy = 207857 , sum of x² = 1259975.
Therefore, Slope of b is given by the formula;
[tex]b = \dfrac{(sum\ of \ xy )- (sumx).(sumy)}{n(sumx^{2})- (sumx)^{2} }\\\\b = \dfrac{6(207857)-1685(952.3)}{6(1259975)-(1685)^{2} }\\\\b = \dfrac{-357483.5}{4720625}\\\\b = -0.7573[/tex]
Then,
[tex]Y_b_a_r = \dfrac{sumx}{n} = \dfrac{952.3}{6} = 158.71\\\\X_b_a_r = \dfrac{sumy}{n} = \dfrac{1685}{6} = 280.83[/tex]
Therefore, The intercept is given by,
[tex]intercept = a = Y_b_a_r-b\times X_b_a_r\\\\intercept = a = 158.7167 - (-0.07573)\times 280.8333\\\\intercept = a = 158.7167 + 21.2675\\\\intercept = a = 179.984[/tex]
On rounding intercept and slope to 3 decimal places,
intercept = 179.984.
slope = -0.076
Hence, The required equation is galloping speed Y = 179.984 - 0.076 weight X.
To know more about Linear equation click the link given below.
https://brainly.com/question/14824234
7. The ruler below has eleven marks and can be used to measure lengths
from one unit to twelve units.
Design a ruler which can be used to measure all the lengths from one
unit to twelve units but this time put the minimum possible number
of marks on the ruler.
Answer:
use 6cm twice and that adds up to 12cm .six is the minimal possible number
A ruler designed to measure lengths from one unit to twelve units with the minimum number of marks would only have marks at every unit. This results in only eleven markings (from 1 to 11), as the 0 marks the start and the twelfth unit marks the end.
Explanation:The subject of the student's question pertains to the design of a ruler with the minimum possible number of marks that can measure lengths from one to twelve units. To achieve this, the ruler should only be marked at every unit. This way, there would be only eleven marks (1-11), as the 0 marks the start of the ruler and the twelfth unit is considered the end of the ruler but does not require a mark. Therefore, only the spaces between these numbers need to be marked to enable measurement all the way up to twelve units.
In practice, such a ruler is less precise than a ruler with more marks as the latter can measure smaller lengths more accurately. However, the task demands the bare minimum for a measure from 1 to 12, thus we have eleven marks.
Learn more about Ruler Design here:https://brainly.com/question/34207880
#SPJ11
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).
Learn more about Number Counting here:https://brainly.com/question/33310551
#SPJ11
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 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
please answer tyty :)
Answer:
3
Step-by-step explanation:
0 indicates no relationship. must be full number.
A department store wants to know what fraction of its customers in a certain market have store credit cards, and what their average balance might be. Of the 120 customers surveyed, 30 had store credit cards. Amongst those customers, the average balance was $600, with a sample standard deviation of $80. Find the 98% confidence interval for the average credit card balance. ( , ) Round your answers to two decimal places.
Answer:
The 98% confidence interval for the average credit card balance is
(564.04, 635.96).
Step-by-step explanation:
We have to calculate the 98% confidence interval on the average credit card balance.
The sample will consist of the n=30 customers that have credit card.
The sample has a mean of $600 and a standard deviation of $80.
As the population standard deviation is estimated from the sample standard deviation, we will use a t statistic.
The degrees of freedom are:
[tex]df=n-1=30-1=29[/tex]
The critical value for a 98% CI and 29 degrees of freedom is t=2.463 (this can be looked up in a t-table).
Then, the margin of error is:
[tex]E=t\cdot s/\sqrt{n}=2.463*80/\sqrt{30}=197.04/5.48=35.96[/tex]
Then, the upper and lower bounds of the confidence interval are:
[tex]LL=\bar X-E=600-35.96=564.04\\\\UL=\bar X+E=600+35.96=635.96[/tex]
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.
Learn more about graph transformation here:https://brainly.com/question/19040905
#SPJ3
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
Suppose task B follows task A. The likelihood that a problem will occur with task A is 0.5, and the time to correct the problem would be 2 months. The likelihood that a problem will occur with task B is 0.2, and the time to correct the problem would be 3 months. The risk consequence of both activities is 3.5 months 5.7 months 1.6 months cannot be determined. True or false?
Answer:
The risk consequence of both activities is 1.6 months.
Step-by-step explanation:
We can define a randome variable D: total delay time for the project, and calculate its expected value.
This would be the risk consequence of both activities.
The expected delay time for the project is the sum of the expected delay for task A plus the expected delay for task B. It is assumed the likelihood of a problem in any task is independent of the other.
Then, each expected delay for a task is equal to the probability of a problem multiplied by the consequence (delay time).
[tex]E(D)=E(D_a)+E(D_b)=p_aT_a+p_bT_b\\\\E(D)=0.5*2+0.2*3=1+0.6=1.6[/tex]
The risk consequence of both activities is 1.6 months.
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]
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.
Learn more about Confidence Interval here:https://brainly.com/question/34700241
#SPJ11
I need help please.
Answer:2
4 th root of 1024 is 5
Since 4 x4x4x4x4=1024
So 1+2x=5
-1 PN both sides
2x= 4
Divide by 2
X=2
Step-by-step explanation:
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!!!
Find the median, first quartile, third quartile, and interquartile range of the data.
132, 127, 106, 140, 158, 135, 129, 138
Please hurry
Median: 133.5
Lower/First quartile: 128
Upper/Third quartile: 139
Interquartile range: 139 - 128 = 11
so your interquartile range is 11
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
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).
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.
What is the height of a cylinder with a volume of 384 pi cubic inches and a radius of 8 inches? Round to the nearest tenth of an inch.
inches___
The height of the cylinder with a volume of 384π cubic inches and a radius of 8 inches is 6 inches.
To find the height of a cylinder with a known volume and radius, we use the formula for the volume of a cylinder, which is V = πr²h, where 'V' is the volume, 'r' is the radius, and 'h' is the height. We are given a volume of 384π cubic inches and a radius of 8 inches. Plugging these values into the formula gives us:
384 π = π (8²) h
384 π = 64π h
h = 384 π ÷ 64π
h = 6 inches
Therefore, the height of the cylinder is 6 inches.
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.
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
I swear they got me doing algebra in 8th grade i wanna refund please help me... again
Answer: C represents a function
Step-by-step explanation: It represents a function because there is exactly one range for each domain, and only one. In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation. Quite often algebraic functions are algebraic expressions using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power.
A swimming pool is circular with a 20-ft diameter. The depth is constant along east-west lines and increases linearly from 1 ft at the south end to 6 ft at the north end. Find the volume of water in the pool. (Round your answer to the nearest whole number.) ft3
Answer:
[tex]1100 \text{feet}^3[/tex]
Step-by-step explanation:
GIVEN: A swimming pool is circular with a [tex]20\text{ feet}[/tex] diameter. The depth is constant along east-west lines and increases linearly from [tex]1\text{ feet}[/tex] at the south end to [tex]6\text{ feet}[/tex] at the north end.
TO FIND: Find the volume of water in the pool.
SOLUTION:
Consider the image attached.
when two similar figures are attached a new cylinder is formed. volume of swimming pool is half of volume of new cylinder formed.
radius of new cylinder [tex]=\frac{\text{diameter}}{2}=\frac{20}{2}=10\text{ feet}[/tex]
height of new cylinder [tex]=6+1=7\text{ feet}[/tex]
volume of cylinder [tex]=\pi r^2h=\frac{22}{7}\times(10)^27[/tex]
[tex]=2200\text{ feet}^3[/tex]
Volume of swimming pool [tex]=\frac{\text{volume of cylinder}}{2}=\frac{2200}{2}[/tex]
[tex]=1100\text{ feet}^3[/tex]
Hence volume of water in the pool is [tex]1100 \text{feet}^3[/tex].
Final answer:
To find the volume of water in a swimming pool with varying depths, calculate the volume by considering different height sections of the pool.The volume of water in the pool is approximately 13,287 ft³.
Explanation:
A swimming pool is circular with a 20-ft diameter. The depth is constant along east-west lines and increases linearly from 1 ft at the south end to 6 ft at the north end.
Given the pool's dimensions, you can calculate the volume of water in the pool by breaking it into sections of different heights.
The volume of water in the pool is approximately 13,287 ft³.
According to a report on sleep deprivation by the Centers for Disease Control and Prevention, the proportion of California residents who reported insucient rest or sleep during each of the preceding 30 days is 8.0%, while this proportion is 8.8% for Oregon residents. These data are based on simple random samples of 11,545 California and 4,691 Oregon residents. Calculate a 95% con dence interval for the di erence between the proportions of Californians and Oregonians who are sleep deprived and interpret it in context of the data.
Answer:
[tex](0.08-0.0888) - 1.96 \sqrt{\frac{0.08(1-0.08)}{11545} +\frac{0.088(1-0.088)}{4691}}= -0.0175[/tex]
[tex](0.08-0.0888) + 1.96 \sqrt{\frac{0.08(1-0.08)}{11545} +\frac{0.088(1-0.088)}{4691}}= 0.0015[/tex]
And the 95% confidence interval would be given (-0.0175;0.0015).
We are confident at 95% that the difference between the two proportions is between [tex]-0.0175 \leq p_A -p_B \leq 0.0015[/tex]
And since the confidence interval contains the 0 we have enough evidence to conclude that the population proportions are not significantly different at 5% of significance.
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]p_A[/tex] represent the real population proportion for California
[tex]\hat p_A =0.08[/tex] represent the estimated proportion for California
[tex]n_A=11545[/tex] is the sample size required for California
[tex]p_B[/tex] represent the real population proportion for Oregon
[tex]\hat p_B =0.088[/tex] represent the estimated proportion for Brand B
[tex]n_B=4691[/tex] is the sample size required for Oregon
[tex]z[/tex] represent the critical value for the margin of error
Solution to the problem
The sample proportion have the following distribution
[tex]\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]
The confidence interval for the difference of two proportions would be given by this formula
[tex](\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}[/tex]
For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.
[tex]z_{\alpha/2}=1.96[/tex]
And replacing into the confidence interval formula we got:
[tex](0.08-0.0888) - 1.96 \sqrt{\frac{0.08(1-0.08)}{11545} +\frac{0.088(1-0.088)}{4691}}= -0.0175[/tex]
[tex](0.08-0.0888) + 1.96 \sqrt{\frac{0.08(1-0.08)}{11545} +\frac{0.088(1-0.088)}{4691}}= 0.0015[/tex]
And the 95% confidence interval would be given (-0.0175;0.0015).
We are confident at 95% that the difference between the two proportions is between [tex]-0.0175 \leq p_A -p_B \leq 0.0015[/tex]
And since the confidence interval contains the 0 we have enough evidence to conclude that the population proportions are not significantly different at 5% of significance.