Answer:
A. We are 90% confident that the interval from nothing to nothing actually contains true mean attractiveness rating of all adult females.
Step-by-step explanation:
The population is set of items which are similar in nature and that are to be observed for an outcome. The Confidence Interval is a defined probability that the parameters lies in this range. Population parameter is quantity which enters in probability distribution of random variable. In the given question the confidence interval is 90% which means the parameters lies within this range.
A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 14 tablets. The entire shipment is accepted if at most 2 tablets do not meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 4.0% rate of defects, what is the probability that this whole shipment will be accepted?
Answer: the probability that this whole shipment will be accepted is 0.673
Step-by-step explanation:
This is a binomial distribution because the probabilities are either that of success or failure
The probability that a particular shipment of thousands of aspirin tablets actually has defects is 4% = 0.04. Then the probability that there would be no defect is 1 - 0.04 = 0.96
Since the shipment is accepted with at most even when there is defect, then the probability of success is 0.04 and that of failure is 0.96
The formula is expressed as
P(x = r) = nCr × p^r × q^(n - r)
Where
x represent the number of successes.
p represents the probability of success.
q = (1 - p) represents the probability of failure.
n represents the number of trials or sample.
From the information given,
p = 0.04
q = 0.96
n = 14
Since entire shipment is accepted if at most 2 tablets do not meet the required specifications, then the probability is
P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)
P(x = 0) = 14C0 × 0.04^0 × 0.96^(14 - 0) = 0.56
P(x = 1) = 14C1 × 0.04^1 × 0.96^(14 - 1) = 0.024
P(x = 2) = 14C2 × 0.04^2 × 0.96^(14 - 2) = 0.089
P(x ≤ 2) = 0.56 + 0.024 + 0.089 = 0.673
IMagicCards.com is a website that allows its members to trade their Magic: The Gathering cards with other members. Since the website's founders do not trust the value of money in relation to the cards, they require members to use only Magic cards as currency rather than money. Which characteristic of money does this scenario best relate to?
A. acceptability
B. portability
C. divisibility
D. durability
E. stability
Answer:
Answer: A
Step-by-step explanation:
The scenario best correlates with the principle of 'Acceptability' in money characteristics, where the Magic cards are accepted in place of traditional currency for trades on IMagicCards.com.
Explanation:Magic Cards as Currency
The scenario you've described involves the trading of Magic: The Gathering cards on IMagicCards.com. This website uses the cards themselves as a form of currency instead of traditional money. Assessing the relation to characteristics of money, this system best correlates with Acceptability. Acceptability is a key attribute of money, signifying that it must be widely accepted for the purchase of goods and services. In this context, the acceptance of Magic cards for trades is equivalent to the principle of acceptability in currency.
The other options do not seem to fit as appropriately in this case. Portability involves the ease with which units of currency can be transported for use in purchasing or trade. Divisibility refers to the ability of money to be divided into smaller units without loss of value. Durability means the currency must withstand the physical wear and tear. Stability pertains to the value of the money remaining relatively stable over time.
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Evaluate the following expression
[10×2+(30-15)÷7+3×8
Answer:
46.142857143
Step-by-step explanation:
10×2+(30-15)÷7+3×8
=10×2+15÷7+3×8
=20+15÷7+3×8
=20+2.142857143+3×8
=20+2.142857143+24
=46.142857143
a psychologist contends that the number of facts of a certain type that are remembered after t hours is given by the following function. f(t)equals startfraction 85 t over 99 t minus 85 endfraction find the rate of change at which the number of facts remembered is changing after 1 hour and after 10 hours.
Answer:
At t=1, Rate of Change=-36.86
At t=10 hours, Rate of Change =-0.0088
Step-by-step explanation:
The function which describes the number of facts of a certain type which are remembered after t hours is given as:
[TeX]f(t)=\frac{85t}{99t-85}[/TeX]
To determine the Rate of Change at the given time, we first look for the derivative of f(t).
Applying quotient rule:
[TeX]f^{'}(t)=\frac{-7225}{{\left( 85 - 99\,t\right) }^{2}}[/TeX]
At t=1
[TeX]f^{'}(1)=\frac{-7225}{(85-99)^{2}}[/TeX]
=-36.86
At t=10 hours
[TeX]f^{'}(10)=\frac{-7225}{(85-99(10))^{2}}[/TeX]
=-0.0088
The rate of change of the function is calculated by finding its derivative and evaluated by substituting the respective hours (1 hour and 10 hours). The rate of change after 1 hour is approximately -106.25, implying a decline per hour, and after 10 hours is approximately -0.918, indicating a slower rate of decline per hour.
Explanation:The rate of change of a function is calculated by finding the derivative of the function. The derivative of a function gives the rate of change of the function at any given point. Let's calculate the derivative of the function f(t) = 85 t / (99 t - 85).
The first step is to use the quotient rule for differentiation, which is given by [f'(x) = (g'(x)h(x) - g(x)h'(x))/h(x)²]. In this case, g(t) = 85 t and h(t) = 99 t - 85.The derivative of g(t) is g'(t) = 85 and the derivative of h(t) is h'(t) = 99.Substitute these values into the quotient rule to obtain f'(t).We get f'(t) = (85*(99 t - 85) - (85 t)*99) / (99 t -85)² = (-850)/ (99 t - 85)². This is the rate of change of the function f(t).
To find the rate of change after 1 hour and 10 hours, substitute t = 1 and t = 10 into f'(t).
For t = 1, f'(1) = -850 / (99*1 - 85)² ≈ -106.25, suggesting a rate of decrease.For t = 10, f'(10) = -850 / (99*10 -85)² ≈ -0.918, also a rate of decrease but slower than in the first hour.Learn more about Rate of Change here:https://brainly.com/question/20816247
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According to a poll, 55 % of Americans do not know that GOP stands for Grand Old Party (Time, October 17, 2011). Assume that this percentage is true for the current population of Americans. Let p ^ be the proportion in a random sample of 953 Americans who do not know that GOP stands for Grand Old Party. Find the mean and standard deviation of the sampling distribution of p ^ and describe its shape.
Answer:
[tex]\hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}}) [/tex]
The mean is given by:
[tex] \mu_{\hat p} = 0.55[/tex]
And the deviation:
[tex] \sigma_{\hat p} =\sqrt{\frac{0.55*(1-0.55)}{953}}= 0.0161[/tex]
Step-by-step explanation:
For this case we assume that the true population proportion of Americans do not know that GOP stands for Grand Old Party is 0.55 and we select a random sample of n = 953 americans
For this case we assume that we satisfy the conditions to use the normal approximation for [tex]\hat p[/tex]
1) np >10 , n(1-p)>10
2) Independence
3) Random sample
4) The sample size is less than 10% of the population size
We assume that all the conditions are satisfied and the distribution for [tex]\hat p[/tex] would be:
[tex]\hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}}) [/tex]
The mean is given by:
[tex] \mu_{\hat p} = 0.55[/tex]
And the deviation:
[tex] \sigma_{\hat p} =\sqrt{\frac{0.55*(1-0.55)}{953}}= 0.0161[/tex]
There are 5 marbles in a bag: 4 are blue and 1 is red. What is the probability that a blue marble gets picked?
Answer:
the answer is 80%
Step-by-step explanation:
4/5 = 80%
Answer:
in fraction form that is 4/5 or .8 chance of getting a blue marble
Step-by-step explanation:
because you divide the number of possible winning out comes 4 marbles by the total event 5 marbles
For 40 days in the summer, you are working in a small, student-run company that sends out merchandise with university branding to alumni around the world. Every day, you take a sample of 50 shipments that are ready to be shipped to the alumni and inspect them for correctness. Across all days, the average percentage of incorrect shipments is 5 percent. What would be the center line for a p-chart?
Answer:
The central line of the p-chart is 0.05.
Step-by-step explanation:
In statistical quality control, the p-chart is a form of control chart used to observe the proportion of non-conforming or defective components in a random sample, where the sample proportion of defective items is defined as the fraction of the number of defective units to the size of the sample, n.
The central line of the p-chart is given by:
[tex]CL=\frac{\sum np}{\sum n}[/tex]
It is provided that:
The sample selected from a shipment for inspection every day is of size, n = 50.
The average percentage of incorrect shipments is 5%, i.e. p = 0.05.
Compute the number defective units in the sample as follows:
[tex]np=50\times \frac{5}{100}[/tex]
Compute the central line of the p-chart as follows:
[tex]CL=\frac{\sum np}{\sum n}[/tex]
[tex]=\frac{5\times 50}{100\times 50}\\[/tex]
[tex]=0.05[/tex]
Thus, the central line of the p-chart is 0.05.
The center line for a p-chart is calculated as the average percentage of defects across all samples, which in this case is 5%.
The center line for a p-chart is calculated as the average percentage of defects across all samples.
In this case, the average percentage of incorrect shipments is 5%.
Hence, the center line for the p-chart in this scenario would be 5%.
A study was conducted in which rats showed compassion by freeing a trapped rat. In the study, all six of the six female rats showed compassion by freeing the trapped rat while 17 of the 24 male rats did so. We found a 95% confidence interval for the difference in proportion of rats showing compassion, using the proportion of female rats minus the proportion of male rats, to be 0.104 to 0.480. In testing whether there is a difference in these two proportions:
What are the null and alternative hypotheses?
Answer:
If the proportion of female rats that show compassion = p₁
And
If the proportion of male rats that show compassion = p₂
And the difference between them is given as
μ₀ = p₁ - p₂
The null hypothesis and alternative hypothesis can be expressed as:
The null hypothesis that there is no significant evidence to conclude that there is a significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.
That is, there is no significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.
H₀: μ₀ = 0
or
H₀: p₁ = p₂
And the alternative hypothesis that there is evidence that the proportion of female rats that show compassion is significantly different from the proportion of male rats that show compassion.
That is, there is a significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.
Hₐ: μ₀ ≠ 0
or
Hₐ: p₁ ≠ p₂
Step-by-step explanation:
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and is usually about the absence of significant difference between two proportions being compared. It usually maintains that random chance is responsible for the outcome or results of any experimental study/hypothesis testing. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It proposes that there is indeed a significant difference between two proportions being compared. It usually confirms the theory being tested by the experimental setup.
It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, we want to check whether there is a significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.
If the proportion of female rats that show compassion = p₁
And
If the proportion of male rats that show compassion = p₂
And the difference between them is given as
μ₀ = p₁ - p₂
The null hypothesis and alternative hypothesis can be expressed as:
The null hypothesis that there is no significant evidence to conclude that there is a significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.
That is, there is no significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.
H₀: μ₀ = 0
or
H₀: p₁ = p₂
And the alternative hypothesis that there is evidence that the proportion of female rats that show compassion is significantly different from the proportion of male rats that show compassion.
That is, there is a significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.
Hₐ: μ₀ ≠ 0
or
Hₐ: p₁ ≠ p₂
Hope this Helps!!!
The null hypothesis, denoted as \( H_0 \), states that there is no difference in the proportion of female rats and male rats that show compassion by freeing a trapped rat. In mathematical terms, this can be expressed as:
[tex]\[ H_0: p_f - p_m = 0 \][/tex]
where [tex]\( p_f \)[/tex] is the proportion of female rats showing compassion and [tex]\( p_m \)[/tex] is the proportion of male rats showing compassion.
The alternative hypothesis, denoted as [tex]\( H_1 \) or \( H_a \)[/tex], states that there is a difference in the proportion of female rats and male rats that show compassion. This can be expressed as:
[tex]\[ H_1: p_f - p_m \neq 0 \][/tex]
This is a two-tailed test because the alternative hypothesis does not specify the direction of the difference, only that a difference exists.
Given the confidence interval for the difference in proportions is 0.104 to 0.480, we can see that the interval does not include zero. This suggests that at the 95% confidence level, there is evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating that there is a statistically significant difference between the proportions of female and male rats showing compassion
Rufus appears before Bill and Ted and offers them a bogus proposition: they must paint a house together with their magical guitars in a mere 5 hours. Ted, who is tired, knows that the fastest he can solo rock the paint job through the strings of his guitar is 19 hours. How hard does Bill have to jam to ensure the house is completed in time? Give your answer as the number of hours Bill must play; write your answer as a decimal rounded to two places, without any units.
Answer:
6.79
Step-by-step explanation:
-Let X denote the total amount of the job.
-The job has to be done in 5 hrs, therefore the portion done every hour is:
[tex]Rate=\frac{Total}{Time}\\\\=\frac{X}{5}\\\\=\frac{1}{5}X=0.2X[/tex]
Therefore, the rate of Bill and Ted working jointly must equal the rate calculated above:
[tex]R_{Bill}=\frac{X}{19}\\\\=\frac{1}{19}X\\\\R_{Bill}+R_{Ted}=R_{required}\\\\\frac{1}{19}X+R_{Ted}=\frac{1}{5}X\\\\R_{Ted}=\frac{1}{5}X-\frac{1}{19}X\\\\=\frac{14}{95}X\\\\\therefore \frac{14}{95}X=1\ hr\\\\X=1\div \frac{14}{95}\\\\=6.7857\approx 6.79[/tex][tex]hrs[/tex]
Hence, Bill working alone should complete the house in 6.79 hrs
A credit card company is about to send out a mailing to test the market for a new credit card. From that sample, they want to estimate the true proportion of people who will sign up for the card nation-wide. A pilot study suggests that about 0.5% of the people receiving the offer will accept it. To be within a tenth of a percentage point (0.001) of the true rate with 95% confidence, how big does the test mailing have to be?
Answer:
[tex]n=\frac{0.005(1-0.005)}{(\frac{0.001}{1.96})^2}=19111.96[/tex]
And rounded up we have that n=19112
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".
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.001[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.005(1-0.005)}{(\frac{0.001}{1.96})^2}=19111.96[/tex]
And rounded up we have that n=19112
Answer:
We need a mailing list of at least 191112 people.
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].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
For this problem, we have that:
[tex]\pi = 0.005[/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].
To be within a tenth of a percentage point (0.001) of the true rate with 95% confidence, how big does the test mailing have to be?
They need at least n people
n is found when [tex]M = 0.001[/tex]. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.001 = 1.96\sqrt{\frac{0.005*0.995}{n}}[/tex]
[tex]0.001\sqrt{n} = 1.96\sqrt{0.005*0.995}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.005*0.995}}{0.001}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.005*0.995}}{0.001})^{2}[/tex]
[tex]n = 19111.96[/tex]
We need a mailing list of at least 191112 people.
¿Cuál de las siguientes fracciones es
equivalente al decimal 0.18?
~= Ello
Answer:
? necesitamos más información.. ¿dónde están los fracciones?
Step-by-step explanation:
Which comparison is true?
38=36
38<36
38>36
Answer:
38 > 36
it is true it shows that 38 is greater than 36
A manufacturer has determined that a model of its washing machine has an expected life that is Exponential with a mean of four years to failure and irrelevant board burn-in period. He wants to testthe system and complete data collection. Find the probability that one of these washing machines will have a life that ends: (Note you can find the reliability of the washing machine life)
Complete question:
A manufacturer has determined that a model of its washing machine has an expected life that is Exponential with a mean of four years to failure and irrelevant board burn-in period. He wants to testthe system and complete data collection. Find the probability that one of these washing machines will have a life that ends: (Note you can find the reliability of the washing machine life)
a) After an initial four years of washing machine service
b) Before four years of washing machine service are completed
c) Not before six years of washing machine service.
Answer:
a) 0.3679
b) 0.6321
c) 0.2231
Step-by-step explanation:
Given:
Mean, u= 4
/\ = 1/u
= 1/4 = 0.25
The cummulative distribution function, will be:
For x≥0,
[tex] F(x) = 1 - e^-^0^.^2^5^X[/tex]
[tex]P(x<X) = F(X)[/tex]
a) After an intial four years:
[tex]P(x>4) = 1-(1-e^-^0^.^2^5^*^4^.^0)[/tex]
P(x>4) = 0.3679
b) Before four years:
[tex]P(x<4) = 1-(e^-^0^.^2^5^*^4^.^0)[/tex]
P(x<4) = 0.6321
c) Not before 6 years:
[tex]P(x>6) = 1-(1-e^-^0^.^2^5^*^4^.^0)[/tex]
P(x>6) = 0.2231
someone please help i’m very confused
(1) 132.67 square meters
(2) 379.94 square meters
Step-by-step explanation:
A barn is in the shape of a rectangle with each corner angle a right angle.
[tex] \therefore Central\: \angle \:(\theta) =90°[/tex]
Since, goat is tied at a corner of the barn, so she would be able to graze the grass of sector of circle with radius (r) = 13 m.
Area of field grazed by goat = area of sector of circle
[tex] = \frac{ \theta}{360 \degree} \times \pi {r}^{2} \\ \\ = \frac{90 \degree}{360 \degree} \times 3.14 \times {13}^{2} \\ \\ = \frac{1}{4} \times 3.14 \times 169\\ \\ = \frac{1}{4} \times530.66 \\ = 132.665 \\ = 132.67 \: {m}^{2} [/tex]
[tex] (2) \\ similarly \: for \: r \: = 22 \: m \\ area \: of \: sector = 379.94 \: {m}^{2} [/tex]
What is the median of this set of data 100,102,103,106,109
Step-by-step explanation:
In ascending order
100 , 102 , 103 , 106, 109
No of data (N) = 5
Now
Position of median
= ( N + 1) /2 th item
=( 5+1 )/2 th item
= 6 / 2 th item
= 3rd item
Therefore exact median = 103
Hope it will help you :)
Answer:
103
Step-by-step explanation:
100,102,103,106,109
Median position: (n+1)/2
(5+1)/2 = 3rd value
Median = 103
Find the sample size required to estimate the percentage of college students who use student loans to help fund their tuition. Assume that we want 95% confidence that the proportion from the sample is within two percentage points of the true population percentage. Record your answer as a whole number.
Answer:
We need a sample of size at least 2401.
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].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/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].
Assume that we want 95% confidence that the proportion from the sample is within two percentage points of the true population percentage.
We need a sample of size at least n.
n is found when [tex]M = 0.02[/tex]
We don't know the exact proportion, so we use [tex]\pi = 0.5[/tex], which is the case for which we are going to need the largest sample size.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.02\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.02}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96*0.5}{0.02})^{2}[/tex]
[tex]n = 2401[/tex]
We need a sample of size at least 2401.
Answer:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401[/tex]
And rounded up we have that n=2401
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".
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.02[/tex] or 2% points and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
We can use an prior estimation for p [tex]\hat p=0.5[/tex]. And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401[/tex]
And rounded up we have that n=2401
Find the area of the regular polygon.
Round to the nearest tenth.
16 ft
Given:
Given that the side of the regular polygon is 16 feet.
We need to determine the area of the polygon.
Area of the polygon:
The area of the polygon can be determined using the formula,
[tex]Area =\frac{s^2 n}{4 \ tan \frac{180}{n}}[/tex]
where n is the number of sides,
s is the side length.
Substituting n = 3 and s = 16, we get;
[tex]Area =\frac{16^2 (3)}{4 \ tan \frac{180}{3}}[/tex]
Simplifying, we get;
[tex]Area =\frac{(256) (3)}{4 \ tan \ 60}[/tex]
[tex]Area = \frac{768}{6.928}[/tex]
Dividing, we get;
[tex]Area = 110.85[/tex]
Rounding off to the nearest tenth, we have;
[tex]Area = 110.9[/tex]
Thus, the area of the regular polygon is 110.9 square units.
Subtract 11 from n then divide by 5
Answer:
I think it's 55.
Step-by-step explanation:
11-n/5
n=11*5
n=55
Answer:
[tex]\frac{n-11}{5}[/tex]
Step-by-step explanation:
1) Subtract 11 from n to get [tex]n-11[/tex] You cannot find a solution for it because there is no value for n.
2) You divide that by 5 so you would just put n-11 over 5 to create a fraction that would look like [tex]\frac{n-11}{5}[/tex]
I am not sure if this is what you were asking but this is the most I can do for you with the information that you gave.
A silo is in the shape of a cone. The silo is meters tall, and its base has a radius of meters. Rice costs per cubic meter. How much will it cost to fill the silo with rice?
Answer:
pic not their put plz so i can answer
Step-by-step explanation:
The Polar Express movie is $12 and it will be on sale for $8.What is the percent of change
if the cost decreased $4?
please help
Answer:
33.333%.
Step-by-step explanation:
Take the cost changed ($4) and divide it by it's normal price ($12).
$4/$12 = .33333
Multiply that by 100 to get its percent. 33.333%
Answer:
- 33.3%
Step-by-step explanation:
You calculate percent change by dividing the change by the absolute value of the original. In this instance, it would be -4/12 which equals -0.3333. Multiply that by 100 and you get the percent.
Given EP = FP and GQ = FQ, what is the perimeter of ΔEFG?
Given:
In the given ΔEFG,
EP = FP and GQ = FQ
Again,
EP = [tex]4y+2[/tex]
FP = [tex]2x[/tex]
FQ = [tex]3x-1[/tex]
GQ = [tex]4y+4[/tex]
PQ = [tex]x+2y[/tex]
To find the perimeter of ΔEFG.
Formula
The perimeter of a triangle is the sum of all the sides.By Midpoint Theorem we get, a line segment joining the mid points of two sides of a triangle is parallel and half to the third side.In this given triangle, EG║PQ and EG = [tex]\frac{1}{2}[/tex]PQ
Now,
By given condition,
[tex]2x = 4y+2[/tex] ----- (1)
[tex]3x-1 =4y+4[/tex]---------(2)
From (1) we get, [tex]4y = 2x-2[/tex]
Putting this value into (2) we get,
[tex]3x-1 = 2x-2+4[/tex]
or, [tex]x = 3[/tex]
From (1) we get,
[tex]4y = 2(3)-2[/tex]
or, [tex]4y = 4[/tex]
or, [tex]y = 1[/tex]
So,
EF = [tex]2x+4y+2[/tex] = [tex]2(3)+4(1)+2 = 12[/tex] unit
FG = [tex]3x-1+4y+4 = 3(3)-1+4(1)+4 = 16[/tex] unit
PQ =[tex]3+2(1) = 5[/tex] unit
EG = [tex]2(5) = 10[/tex] unit
The perimeter of ΔEFG = EF+FG+EG = 16+10+12 unit = 38 unit
Hence,
The perimeter of the given triangle is 38 unit.
The perimeter of the ΔEFG when EP = FP and GQ = FQ should be 38 units.
Calculation of the perimeter:Since
EP = 4y + 2
FP = 2x
FQ = 3x - 1
GQ = 4y + 4
PQ = x + 2y
So,
2x = 4y +2 ..(1)
4x - 1 = 4y + 4........(2)
So,
3x - 1 = 2x - 2 + 4
y = 1
Now
= EF + FG + FG
= 16 + 10 + 12
= 38 units
hence, The perimeter of the ΔEFG when EP = FP and GQ = FQ should be 38 units.
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A marketing firm would like to test-market the name of a new energy drink targeted at 18- to 29-year-olds via social media. A study by the Pew Research Center found that 35% of U.S. adults (18 and older) do not use social media (Pew Research Center website, October 2015). The percentage of U.S. young adults age 30 and older is 78%. Suppose that the percentage of the U.S. adult population that is either age 18–29 or uses social media is 67.2%. a. What is the probability that a randomly selected U.S. adult uses social media? b. What is the probability that a randomly selected U.S. adult is aged 18–29? c. What is the probability that a randomly selected U.S. adult is 18–29 and a user of social media? Anderson, David R.. Essentials of Statistics for Business and Economics (p. 198). Cengage Learning. Kindle Edition.
To find the probabilities of a randomly selected U.S. adult using social media and being aged 18-29, we can use probability concepts and the given information.
Explanation:To solve this problem, we can use the concept of probability. Let's define the following events:
A: randomly selected U.S. adult uses social mediaB: randomly selected U.S. adult is aged 18-29From the information given, we have P(A' ∩ B') = 35%, P(A' ∩ B) = 0, P(A ∩ B') = 67.2%. We need to find the probabilities P(A) and P(B).
Using the formula for the probability of the complement of an event, we have P(A') = 35%.Using the given value of the percentage of U.S. young adults age 30 and older (78%), we have P(B') = 100% - 78% = 22%.Using the formula P(A ∩ B') = P(A) - P(A ∩ B), we have P(A) = P(A ∩ B') + P(A' ∩ B') = 67.2% + 35% = 102.2%.Using the formula P(B) = P(B') - P(A' ∩ B'), we have P(B) = 22% - 0% = 22%.Therefore, the probability that a randomly selected U.S. adult uses social media is 102.2%, the probability that a randomly selected U.S. adult is aged 18-29 is 22%, and the probability that a randomly selected U.S. adult is 18-29 and a user of social media is 67.2%.
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a. Probability of a randomly selected U.S. adult using social media is 45.2%.
b. Probability of a randomly selected U.S. adult being aged 18-29 is 65%.
c. Probability of a randomly selected U.S. adult being 18-29 and a user of social media is approximately 29.38%.
a. Probability a randomly selected U.S. adult uses social media:
Probability of being 18-29 or use social media = 67.2%
Percentage of US adults aged 30 and older = 78%
Thus, percentage of US adults aged 18-29 = 100% - 78% = 22%
Probability of using social media = 67.2% - 22% = 45.2%
b. Probability of a randomly selected U.S. adult being aged 18-29:
Percentage of adults not using social media = 35%
Thus, percentage of adults aged 18-29 = 100% - 35% = 65%
c. Probability of a randomly selected U.S. adult being 18-29 and a user of social media:
Probability of using social media = 45.2%
Probability of being 18-29 = 65%
Probability of being 18-29 and using social media = 0.452 * 0.65 = 29.38%
what is the area of a rectangle that is 6 5/7 by 7 3/5
Answer:
51.0264 units squared
Step-by-step explanation:
1) convert the fractions into decimals.
5/7+6=6.714 and 3/5+7=7.6
2) Use the formula A=lw to find the area of the rectangle
[tex]6.714*7.6=51.0264[/tex]
Q 4.12: Suppose that a hypothesis test is conducted. 12 out of 100 subjects have the necessary qualities. The null hypothesis is that the proportion of the subjects who have the necessary qualities is equal to 0.2, while the alternative hypothesis is that this proportion is less than 0.2. The p-value is 0.023. Using a 5% significance level, state the conclusion to the hypothesis test in context.
Answer:
Because our p-value of .023 is lower than the alpha-level of .05, we reject the null hypothesis. There is sufficient evidence to conclude that the proportion of subjects who have the necessary qualities is less than .2. Our test provided a statistically significant result.
Note: An alpha-level of .05 is synonymous with a 5% significance level.What is the result of subtracting the second equation from the first?
- 2x + 7y = 10
3x+ 7y = 2
Expected value is
a. (Probability of state A+Value in state A) (Probability of state B+Value in state B)
b. (Probability of state A*Value in state A)-(Probability of state B*Value in state B)
c. (Probability of state A*Value in state A)+(Probability of state B*Value in state B)
d. (Probability of state A-Value in state A) (Probability of state B-Value in state B)
Answer:
(C). (Probability of state A*Value in state A)+(Probability of state B*Value in state B)
Step-by-step explanation:
The expected value of a probability distribution, E(X) is defined as:
[tex]E(x)=\sum_{i=1} ^{k} x_{i} \cdot P(x_{i})\\$Where x=An Outcome\\P(x)=Probability of that Outcome[/tex]
Given Outcome A and B, the Expected Value therefore is:
Expected Value = (Probability of state A*Value in state A)+(Probability of state B*Value in state B)
Final answer:
The expected value for two mutually exclusive events A and B is calculated as the sum of the products of the probabilities of each event and their corresponding values, thus option c is the correct answer.
Explanation:
The concept of expected value in probability is a fundamental idea in mathematics, particularly in probability theory and statistics. The expected value is calculated as the sum of all possible values, each multiplied by the probability of its occurrence. In the context of two mutually exclusive events A and B, the expected value is computed using the formula:
Expected value = (Probability of state A * Value in state A) + (Probability of state B * Value in state B).
Thus, the correct answer to the student’s question is option c.
U1.51.4
This excerpt mostly introduces
the character of King Henry, or Harry.
the setting of the port of Mars.
the conflict of a war between England and France.
the setting of the fields of war.
Answer: the character of king Henry, or Harry
Step-by-step explanation:
Zoe keeps track of the miles per gallon her car gets per week. She has accumulated the following data:
(1, 24), (2, 24.38), (3, 24.76), (4, 25.14)
What is the common difference or ratio?
Answer:
The common difference is 0.38
Step-by-step explanation:
If you look at the data, you can find that the y-value is getting 0.38 added to it. 24 + 0.38 is 24.38. 24.38 + 0.38 is 24.76. 24.76 + 0.38 = 25.14. Therefore, the common difference is 0.38.
Answer:
0.38
Step-by-step explanation:
It was right when I did it on flvs.
Prism A has a length of 2 units, height of 7 units, and width of 1 unit. Prism B has a length of 3 units, height of 2 units, and width of 3 units.
Which prism has a greater volume?
Prism
.
Prism B has larger volume than Volume of prims A.
What is volume?Volume is the scalar quantity of any object that specified occupied space in 3D.
For example, the space in our room is referred to as volume.
Volume has units of cube example meter³,cm³, etc.
Given that;
Prism A has a length of 2 units, height of 7 units, and width of 1 unit. Prism B has a length of 3 units, height of 2 units, and width of 3 units.
Since, The volume of the rectangular prism is given as,
V = length × height × width
Put length as 2 unit cubes, height as 7 unit cubes, and width as 1 unit cubes.
For prism A;
V = 2 x 7 x 1 = 14 units³.
Put length as 3 unit cubes, height as 2 unit cubes, and width as 3 unit cubes.
For prism B;
V = 3 x 2 x 3 = 18 units³.
Hence, Prism B has larger volume than Volume of prims A.
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There are two water tanks, Tank #1 fills into Tank #2.
Tank #1 has 200 gallons in it and losing 2 gallons each minute. Tank #2 has 60 gallons in it.
How long will it take for both Tanks to have the same amount of water in them?
Answer:
35 minutes
Step-by-step explanation:
The total amount of water is 200 +60 = 260 gallons. The two tanks will have equal amounts when each has half that, or 130 gallons.
If the volume in tank 2 is increasing at 2 gallons per minute, it will increase by 70 gallons from 60 gallons to 130 gallons in 70/2 = 35 minutes.