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
Suppose that time spent on hold per call with customer service at a large telecom company is normally distributed with a mean µ = 8 minutes and standard deviation σ = 2.5 minutes. If you select a random sample of 25 calls (n=25), What is the probability that the sample mean is between 7.8 and 8.2 minutes?
Answer:
0.3108 is the probability that the sample mean is between 7.8 and 8.2 minutes.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 8 minutes
Standard Deviation, σ = 2.5 minutes
Sample size, n = 25
We are given that the distribution of time spent is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
Standard error due to sampling =
[tex]=\dfrac{\sigma}{\sqrt{n}} = \dfrac{2.5}{\sqrt{25}} = 0.5[/tex]
P(sample mean is between 7.8 and 8.2 minutes)
[tex]P(7.8 \leq x \leq 8.2)\\\\ = P(\displaystyle\frac{7.8 - 8}{0.5} \leq z \leq \displaystyle\frac{8.2-8}{0.5})\\\\ = P(-0.4 \leq z \leq 0.4})\\\\= P(z < 0.4) - P(z < -0.4)\\\\= 0.6554 -0.3446= 0.3108[/tex]
0.3108 is the probability that the sample mean is between 7.8 and 8.2 minutes.
Suppose 100 stastisticians attended a conference of the American Statistical Society. At the dinner, among the menu options were a Caesar salad, roast beef, and apple pie. 35 had the Caesar salad, 28 had the roast beef, and 45 had the apple pie for dessert. Also, 15 had at least two of those three offerings, and 2 had all three. How many attendees had none of the three
Answer: 26 attendees had none of the three.
Step-by-step explanation:
The Venn diagram illustrating the situation is shown in the attached photo.
C represents the set of statisticians that had Caesar salad.
R represents the set of statisticians that had roast beef.
A represents the set of statisticians that had apple pie for dessert.
x represents the number that had Caesar salad and apple pie for dessert only.
y represents the number that had Caesar salad and roast beef.
z represents the number that had roast beef and apple pie for dessert only.
If 15 had at least two of those three offerings,it means that
x + y + z = 15
Therefore,
35 - (x + y + 2) + 28 - (y + z + 2) + 45 - (x + z + 2) + 2 + none = 100
35 - x - y - 2 + 28 - y - z - 2 + 45 - x - z - 2 + 2 + none = 100
35 + 28 + 45 - x - x - y - y - z - z - 2 - 2 - 2 + 2 + none = 100
108 - 2x - 2y - 2z - 4 + none = 100
108 - 4 - 2(x + y + z) + none = 100
Since x + y + z = 15, then
104 - 2(15) + none = 100
74 + none = 100
none = 100 - 74 = 26
Suppose ADB pays an interest of 2%, Barclays pays an interest of
4% and GCB pays an interest of 5% per annum and an amount of ¢350 more was invested in
Barclays than the amount invested in ADB and GCB combined. Also, the amount invested in
Barclays is 2 times the amount invested in GCB.
Correction
https://brainly.in/question/16846717
Answer:
Amounts invested in each bank:
GCB=$1,713,33
Barclays=$3,426.66
ADB=$1,363.33
Step-by-step explanation:
-Given that ADB pays 2% pa, GCB pays 4% and Barclays pays 5%
-From the information provided, the amount invested in each of the 3 banks can be expressed as:
-Let X be the Amount invested in GCB:
[tex]GCB=X\\\\Barclays=2X\\\\ADB=2X-X-350=X-350[/tex]
-Since the total interest earned on all 3 accounts after 1 year is $250, we can equate and solve for X as below:
[tex]I=Prt\\\\I_{GCB}=X\times 0.05\times1= 0.05X\\\\I_{Barclays}=2X\times 0.04\times 1=0.08X\\\\I_{ADB}=(X-350)\times 0.02\times 1=0.02X-7\\\\I=I_{GCB}+I_{ADB}+I_{Barclays}\\\\250=0.05X+0.08X+(0.02X-7)\\\\250=0.15X-7\\\\0.15X=257\\\\X=1713.33\\\\GCB=\$1713.33\\Barclays=2X=\$3426.66\\ADB=X-350=\$1363.33[/tex]
Hence, the amounts invested in each bank is GCB=$1,713,33 , Barclays=$3,426.66 and ADB=$1,363.33
Answer:
Amounts invested in each bank:
GCB=$1,713,33
Barclays=$3,426.66
ADB=$1,363.33
Step-by-step explanation:
The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 9.3 minutes and a standard deviation of 2.6 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)
Answer:
a) 0.6062
b) 0.9505
c) 0.679
Step-by-step explanation:
The customer service center in a large new york department store has determined tha the amount of time spent with a customer about a complaint is normally distributed, with a mean of 9.3 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be
(a) less than 10 minutes?
(b) longer than 5 minutes?
(c) between 8 and 15 minutes?
a) The Z score (z) is given by the equation:
[tex]z=\frac{x-\mu}{\sigma}[/tex],
Where:
μ is the mean = 9.3 minutes,
σ is the standard deviation = 2.6 minutes and x is the raw score
[tex]z=\frac{x-\mu}{\sigma}=\frac{10-9.3}{2.6}=0.27[/tex]
From the z tables, P(X < 10) = P(z < 0.27) = 0.6062 = 60.62%
b) The Z score (z) is given by the equation:
[tex]z=\frac{x-\mu}{\sigma}[/tex],
[tex]z=\frac{x-\mu}{\sigma}=\frac{5-9.3}{2.6}=-1.65[/tex]
From the z tables, P(X > 5) = P(z > -1.65) = 1 - P(z < -1.65) = 1 - 0.0495 = 0.9505 = 95.05%
c) For 8 minutes
[tex]z=\frac{x-\mu}{\sigma}=\frac{8-9.3}{2.6}=-0.5[/tex]
For 15 minutes
[tex]z=\frac{x-\mu}{\sigma}=\frac{15-9.3}{2.6}=2.19[/tex]
From the z tables, P(8< X < 15) = P(-0.5 < z < 2.19) = P(z < 2.19) - P(z< -0.5) = 0.9875 - 0.3085 = 0.679 = 67.9%
The question pertains to finding a probability concerning the time taken to resolve a customer's complaint. The time follows a normal distribution with a mean of 9.3 minutes and a standard deviation of 2.6 minutes. We need to calculate the Z-score with the required time, mean and standard deviation, which can then be referenced on a standard normal distribution table to find the probability.
Explanation:The question is about finding the probability of the time spent with a customer in a Customer Service Center of a department store in New York, given that the time that is spent follows a normal distribution with a mean of 9.3 minutes, and a standard deviation of 2.6 minutes.
To calculate this, we'll use the standard normal distribution, Z-score, which standardizes the distribution. The Z-score is a measure of how many standard deviations an element is from the mean. It can be calculated by using the formula: Z = (X - μ) / σ
where X is the time about which we want to find the probability, μ is the mean, and σ is the standard deviation.
Unfortunately, the exact time (X) you want to find the probability for was not provided in your question. However, assuming X to be a given time, t, you substitute t, 9.3 (the mean), and 2.6 (the standard deviation) into the formula to get a Z-score. Then, by referencing the Z-score on a standard normal distribution table, you can find the probability for a complaint taking at an amount of time, t, to be resolved.
Learn more about Normal Distribution here:https://brainly.com/question/34741155
#SPJ11
Model Price ($) Model Price ($) Retail Outlet Deluxe Standard Retail Outlet Deluxe Standard 1 39 27 5 40 30 2 39 29 6 39 35 3 46 35 7 35 29 4 38 31 The manufacturer's suggested retail prices for the two models show a $10 price differential. Use a .05 level of significance and test that the mean difference between the prices of the two models is $10.
To test the claim that the mean difference between the prices of the two models is $10, we can use a t-test for dependent samples.
Explanation:To test the claim that the mean difference between the prices of the two models is $10, we can use a t-test for dependent samples.
The null hypothesis (H0) is that the mean difference is equal to $10, while the alternative hypothesis (Ha) is that the mean difference is not equal to $10.We calculate the sample mean difference and the standard deviation of the differences.We calculate the t-statistic using the formula: t = (sample mean difference - hypothesized mean difference) / (standard deviation of the differences / sqrt(n)), where n is the number of pairs of observations.We compare the t-statistic to the critical value from the t-distribution with n-1 degrees of freedom at a significance level of 0.05.If the absolute value of the t-statistic is greater than the critical value, we reject the null hypothesis and conclude that the mean difference is not equal to $10. Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the mean difference is not equal to $10.©
Melissa rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total less than 12.
Answer:
35/36
Step-by-step explanation:
total outcome: 6 x 6 = 36
getting 12: 1/36
getting less than 12: 1 - 1/36 = 35/36
Answer:
35/36
Step-by-step explanation:
The sum can be between 2 and 12.
P(sum < 12) = 1 - P(sum = 12)
Sum = 12: (6,6)
P(sum < 12) = 1 - 1/36
35/36
smaller and larger solution
(x+6)(-x+1)=0
Answer:
x = -6,1
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Use the data table provided to calculated the values requested below. Provide all answers to three decimal places.
Has at least 1 child Has no children Total
Supports bans 1739 3089 4828
Does not support bans 746 1142 1888
Total 2485 4231 6716
1. Conditional proportion of support for the ban among those with at least one child: ________
2. Conditional proportion of support for the ban among those with no children: __________
3. Difference in proportion of supporters for the ban between those with at least one child and those with no children (at least 1 child - no children): ___________
4. Relative risk of supporting the ban for those with at least one child compared to those with no children: _________
Answer:
1) 0.700
2) 0.730
3) 0.030
4) 0.959
Step-by-step explanation:
1) proportion of support for the ban with at least one child =
[tex]\frac{no of support atleast 1 child}{Total no of atleast 1 child\\}[/tex]
= [tex]\frac{1739}{2485}[/tex]
= 0.700
2) proportion of support for the ban with no child =
= [tex]\frac{no of support with no child}{Total of no child}[/tex]
= [tex]\frac{3089}{4231}[/tex]
= 0.730
3) Difference in proportion of supporters for the ban between those with atleast one child and those with no child
= 0.700 - 0.730
= -0.03
4) Relative risk = [tex]\frac{proportion with atleast on child}{proportion with no child}[/tex]
= [tex]\frac{0.700}{0.730}[/tex] = 0.959
According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, 62% of graduates from public universities had student loans. We randomly select 50 sample college graduates from public universities and determine the proportion in the sample with student loans.
Answer:
[tex]\frac{31}{50}[/tex]
Step-by-step explanation:
percentage of graduates with loan = 62%
total sample = 50
Number of student in the sample with student loan
= (percentage of graduates with loan) x (total sample)
= 62% x 50
= 31
Proportion of student in the sample with student loan = [tex]\frac{31}{50}[/tex]
Describe how you would find 24+ 36 using mental math
To solve 24+36 using mental math, break it down into simpler steps. First, add 20 + 30 = 50. Then, add 4 + 6 = 10. Finally, combine 50 + 10 to get 60.
Explanation:To solve the equation 24+36 using mental math, you can break it down into simpler steps. First, add the tens together: 20 + 30 = 50. Then add the remaining units: 4 + 6 = 10. Finally, combine these results: 50 + 10 = 60. Therefore, 24 + 36 equals 60 when using mental math strategies.
Learn more about Mental Math here:https://brainly.com/question/29289479
#SPJ2
Drag each length to match it to an equivalent length.
(2 yards 5 inches) (2 feet 8 inches) (1 yard 1 foot) (9 feet)
l 3 yards l________________l
l 77 inches l________________l
l 48 inches l________________l
L 32 inches l________________l
HELP ME I WILL GIVE YOU 31 POINTS
Answer:
2 yards 5 inches=77 inches
9 feet= 3 yards
2 feet 8 inches= 32 inches
1 yard 1 foot= 48 inches
hope this helps!
The table representing the equivalent lengths in each case is-
3 yards : 2 yards 5 inches
77 inches : 9 feet
48 inches : 2 feet 8 inches
32 inches : 1 yard 1 foot
What is algebraic expression?An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
Given is to complete the table by matching the equivalent lengths for -
3 yards
77 inches
48 inches
32 inches
In one yard there are 36 inches. We can write the equivalent length in each case as -
3 yards : 2 yards 5 inches
77 inches : 9 feet
48 inches : 2 feet 8 inches
32 inches : 1 yard 1 foot
Therefore, the table representing the equivalent lengths in each case is-
3 yards : 2 yards 5 inches
77 inches : 9 feet
48 inches : 2 feet 8 inches
32 inches : 1 yard 1 foot
To solve more questions on equivalent expression, visit the link-
https://brainly.com/question/1041084
#SPJ3
Many variants of poker are played with both cards in players’ hands and shared community cards. Players’ hand are some combination of the two sets of cards. For parts (a) and (b), consider playing such that Anna, Brad, Charlie, and Dre each have 2 cards for themselves, and build a 5 card hand out of those 2 cards and 3 shared cards. Assume a standard 52-card deck is being used.
What is the probability that Anna has a flush, where her 2 cards and the 3 community cards share a suit?
Answer:
Step-by-step explanation:
Given that Anna has a flush, this means that the three shared cards and the 2 cards with Anna has the same suit, therefore given this condition the probability that Brad also has a flush is computed here as:
= Probability that Brad has the same suit cards as those shared cards and Anna
= Probability that Brad selected 2 cards from the 8 cards remaining of that suit
= Number of ways to select 2 cards from the 8 cards of that same suit / Total ways to select 2 cards from the remaining 47 cards
= 0.0259
Therefore 0.0259 is the required probability here.
the little calculation is shown in the picture attached
Credit card balances follow a nearly normal distribution with a mean of $2,900 and a standard deviation of $860. A local credit union believes their customers are carrying an above average credit card balance, so they carry out a study to determine their customers' debt. If the study results in a standard error of $43, what sample size was used in the study
Answer:
A sample size of 400 was used in the study.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation(standard error) [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this problem, we have that:
[tex]\sigma = 860, s = 43[/tex]
We have to find n.
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]43 = \frac{860}{\sqrt{n}}[/tex]
[tex]43\sqrt{n} = 860[/tex]
[tex]\sqrt{n} = \frac{860}{43}[/tex]
[tex]\sqrt{n} = 20[/tex]
[tex](\sqrt{n})^{2} = 20^{2}[/tex]
[tex]n = 400[/tex]
A sample size of 400 was used in the study.
A campus radio station surveyed 500 students to determine the types of music they like. The survey revealed that 198 like rock, 152 like country, and 113 like jazz. Moreover, 21 like rock and country, 22 like rock and jazz, 16 like country and jazz, and 5 like all three types of music. What is the probability that a radomly selected student likes jazz or country but not rock?
Answer:
The probability that a randomly selected student likes jazz or country but not rock is 0.422.
Step-by-step explanation:
The information provided is:
Total number of students selected, N = 500.
The number of students who like rock, n (R) = 198.
The number of students who like country, n (C) = 152.
The number of students who like jazz, n (J) = 113.
The number of students who like rock and country, n (R ∩ C) = 21.
The number of students who like rock and Jazz, n (R ∩ J) = 22.
The number of students who like country and jazz, n (C ∩ J) = 16.
The number of students who like all three, n (R ∩ C ∩ J) = 5.
Consider the Venn diagram below.
Compute the probability that a randomly selected student likes jazz or country but not rock as follows:
P (J ∪ C ∪ not R) = P (Only J) + P (Only C) + P (Only J ∩ C)
[tex]=\frac{80}{500}+\frac{120}{500}+\frac{11}{500}\\=\frac{211}{500}\\=0.422[/tex]
Thus, the probability that a randomly selected student likes jazz or country but not rock is 0.422.
So, the required probability is,
P(Jazz or country but not rock) =0.422
To understand the calculations, check below.
Probability:It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that the number of students is 500.
Then the students like rock and country is [tex]21-5=16[/tex]
The students like rock and Jazz is [tex]22-5=17[/tex]
The students like country and Jazz is [tex]16-5=1[/tex]
Students like only rock is [tex]198-16-5-17=160[/tex]
Students like the only country are [tex]152-16-5-11=120[/tex]
Students like only Jazz are [tex]113-17-5-11=80[/tex]
So, the P(Jazz or country but not rock) is,
[tex]P(Jazz\ or\ country\ but\ not\ rock)=\frac{120+11+80}{500} \\P(Jazz\ or\ country\ but\ not\ rock)=0.422[/tex]
Learn more about the topic of Probability:
https://brainly.com/question/6649771
What is the slope of the line shown on the graph?
a 5/4
b 4/5
c -5/4
d -4/5
Answer:
B
Step-by-step explanation:
Take 2 points and use the slope formula
The 2 points: (0,0) and (5,4)
The slope formula is:
[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{2} }[/tex]
We can say (0,0) is our first point, and (5,4) is our second, and substitute them in. y2 is 4, y1 is 0, x2 is 5, and x2 is 0.
[tex]m=\frac{4-0}{5-0}[/tex]
[tex]m=\frac{4}{5}[/tex]
So, the slope if 4/5, or choice B
I have a algebraic problem
7277+x=10245
Answer:
x = 2968
Step-by-step explanation:
7277 + x = 10245
-7277 -7277 (Subtract 7277 from both sides to leave x by itself)
_____________
x = 2968
Could you give brainliest
Answer:
x =2968
Step-by-step explanation:
7277+x=10245
Subtract 7277 from each side
7277-7277+x=10245-7277
x =2968
Gianna bought some new bracelets for $29.99 and a sales tax of $2.40 was added to the cost. What was the sales tax rate (percent)? Round to the nearest percent.
Answer:
8% is the final answer.
Step-by-step explanation:
(2.4/29.99)x100
=0.08x100
=8%
1x2x2x2..........50=50!
Students in a statistics class participated in a project in which they attempted to estimate the true mean height of all students in their large high school. The students were split into 4 groups. Each group had their own sampling method and they used it to select a sample each day for 50 days. Below are the estimated 50 samples. After the samples were collected and the means were plotted the teacher visited the school nurse who told her that the true mean height of all students in the school is 67.5 inches. Which group produced sample statistics that estimated the true value of the parameter with relatively low bias and low variability.
Answer: Group B
Step-by-step explanation:
The histogram constructed by group 2 is centered at 67.5, which is the true mean height of all students at the school, so this histogram displays low bias. The values of the statistics also do not vary greatly from the mean, as can be seen by the lower variability of the histogram. Group 2 produced sample statistics that estimated the true value of the parameter with relatively low bias and low variability.
Answer:
The correct answer is (B).
Step-by-step explanation:
The histogram constructed by group 2 is centered at 67.5, which is the true mean height of all students at the school, so this histogram displays low bias. The values of the statistics also do not vary greatly from the mean, as can be seen by the lower variability of the histogram. Group 2 produced sample statistics that estimated the true value of the parameter with relatively low bias and low variability.
Can someone please help me ill give them brainliest awnser if its correct
it's also worth 20 pts
Answer:
153.9380400259 in2
Step-by-step explanation:
Answer:
49 pi or 153.86
Step-by-step explanation:
The area of a circle can be found using
a=pi*r^2
We know the radius is 7 so we can substitute that in
a=pi*7^2
a=pi*49
The answer in terms of pi is 49pi units^2
For an exact answer, substitute 3.14 in for pi
a=pi*49
a=3.14*49
a=153.86
The area is also 153.86 units^2
equation of a line that has a slope of -2 and passes through the point (-1,8)
Answer:
y= -2x +6
Step-by-step explanation:
Since we have a point, and the slope, we can use the point slope formula
[tex]y-y_{1} =m(x-x_{1} )[/tex]
m is the slope, y1 is the y coordinate of the point, and x1 is the x coordinate of the point
In this case, m is -2, y1 is 8, and x1 is -1, so we can substitute them in
y-8= -2(x--1)
Now, we need to solve for y
y-8=-2(x+1)
Distribute the -1
y-8= -2x-2
Add 8 to both sides
y= -2x +6
North Country Rivers of York, Maine, offers one-day white-water rafting trips on the Kennebec River. The trip costs $69 per person and wetsuits are x dollars each. Simplify the expression using the distributive property to find the total cost of one trip for a family of four if each person uses a wetsuit. 4(69 + x)
Answer:
4x + 276
Step-by-step explanation:
Multiply 4 by 69 and x.
The Hilbert Drug Store owner plans to survey a random sample of his customers with the objective of estimating the mean dollars spent on pharmaceutical products during the past three months. He has assumed that the population standard deviation is known to be $15.50. Given this information, what would be the required sample size to estimate the population mean with 95 percent confidence and a margin of error of ±$2.00? Question 33 options: 231 15 16 163
Answer:
a) 231
The sample to estimate the population mean with 95 percent confidence and a margin of error of ±$2.00
n = 231
Step-by-step explanation:
Explanation:-
Given data the population standard deviation is known σ =$15.50
Given the margin of error ±$2.00
we know that 95 percent confidence interval of margin of error is determined by
[tex]M.E = \frac{Z_{\alpha }S.D }{\sqrt{n} }[/tex]
cross multiplication √n we get ,
[tex]\sqrt{n} = \frac{Z_{\alpha }S.D }{M.E }[/tex]
squaring on both sides, we get
[tex](\sqrt{n} )^2 = (\frac{Z_{\alpha }S.D }{M.E })^2[/tex]
[tex]n = (\frac{Z_{\alpha }S.D }{M.E })^2[/tex]
the tabulated z- value = 1.96 at 95% of level of significance.
[tex]n = (\frac{1.96(15.50) }{2 })^2[/tex]
n = 230.7≅231
Conclusion:-
The sample to estimate the population mean with 95 percent confidence and a margin of error of ±$2.00
n = 231
The required sample size to estimate the mean dollars spent on pharmaceutical products with 95% confidence and ±$2.00 margin of error is 231.
Explanation:To estimate the required sample size, we need to use the formula:
Sample size = (Z^2 * σ^2) / E^2
Where:
Z is the z-score for the desired confidence level (in this case, 95% confidence level corresponds to a z-score of 1.96)σ is the population standard deviation (given as $15.50)E is the desired margin of error (given as $2.00)
Plugging in the values into the formula gives us:
Sample size = (1.96^2 * 15.50^2) / 2^2 = 231.36
Rounding up to the nearest whole number, the required sample size is 231.
Learn more about Sample size calculation here:https://brainly.com/question/34288377
#SPJ3
Martha’s annual salary last year was $72,000. What was her gross pay each month?
Answer:
$6000
Step-by-step explanation:
so she made 72000 in a year, a year as 12 months so to find the monthly rate we just need to divide 72000 by 12 which gives 6000
Answer:
The Correct answer is 6000
Step-by-step explanation:
All you do is divide all the months in a year by how much she got paid to find salary.
It is estimated that the total time Americans will spend on taxes this year is 7.8 billion hours! According to the White House budget office, tax work accounts for approximately 80% of the paperwork burden of the federal government. If 7.8 billion hours is 80% of the total time spent on federal government paperwork, how many hours are equivalent to 50% of the total time spent on federal government paperwork?
Answer:
4.875 billion hours
Step-by-step explanation:
-Let X be the total time spent on taxes and 7.8 billion (80%) is time on paper work.
#We equate and cross multiply to get the total time on taxes:
[tex]0.8=7.8\\1=X\\\\\therefore X=\frac{1\times 7.8}{0.8}\\\\\\=9.75[/tex]
-let y be the 50% amount of time spent. we equate to find it in actual hours:
[tex]1=9.75\\0.5=y\\\\y=\frac{9.75\times 0.5}{1}\\\\=4.875[/tex]
Hence, 50% of the time is equivalent to 4.875 billion hours
What is the factored expression of 6k+21?
A. 3(2k+6)
B. 3(k+6)
C. 3(2k+7)
Answer:
the answer is C. 3(2k + 7) i hope this helps! :)
Step-by-step explanation:
trying to find 6k + 21
given 3(2k + 6)
distribute the 3 to both inside the parenthesis 6k + 18
given 3(k + 6)
distribute the 3 to both inside the parenthesis 3k + 18
given 3(2k + 7)
distribute the 3 again to both inside of the parenthesis 6k + 21
Answer:
C. 3(2k+7)
Step-by-step explanation:
you should mark me brainliest lol
Based on the graph of an exponential function f(x)=b^x, for b >0, describe how you can verify that the output of the function can NEVER be equal to zero.
Answer:
see the explanation
Step-by-step explanation:
we know that
The equation of a exponential growth function is given by
[tex]f(x)=a(b^x)[/tex]
where
a is the initial value or y-intercept
b is the factor growth (b>0)
In this problem
a=1
so
[tex]f(x)=b^x[/tex]
we know that
The graph of the function has no x-intercept
Remember that the x-intercept of a function is the value of x when the value of the function is equal to zero
That means ----> The output of the function can NEVER be equal to zero
Verify
For f(x)=0
[tex]0=b^x[/tex]
Apply log both sides
[tex]log(0)=xlog(b)[/tex]
Remember that
log 0 is undefined. It's not a real number, because you can never get zero by raising anything to the power of anything else.
Final answer:
Exponential functions with a positive base can never output zero due to their growth pattern.
Explanation:
Exponential functions of the form f(x) = b^x, where b is greater than 0, never output zero.
To verify this, consider that any positive number raised to any power will never result in zero, as it will approach zero but never reach it. For example, 2^x will grow rapidly but never touch zero. This property holds true for all exponential functions with a positive base.
You are given the parametric equations x=2cos(θ),y=sin(2θ). (a) List all of the points (x,y) where the tangent line is horizontal. In entering your answer, list the points starting with the smallest value of x. If two or more points share the same value of x, list those points starting with the smallest value of y. If any blanks are unused, type an upper-case "N" in them. Point 1: (x,y)= ( , )
Answer:
The solutions listed from the smallest to the greatest are:
x: [tex]-\sqrt{2}[/tex] [tex]-\sqrt{2}[/tex] [tex]\sqrt{2}[/tex] [tex]\sqrt{2}[/tex]
y: -1 1 -1 1
Step-by-step explanation:
The slope of the tangent line at a point of the curve is:
[tex]m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]
[tex]m = -\frac{\cos 2\theta}{\sin \theta}[/tex]
The tangent line is horizontal when [tex]m = 0[/tex]. Then:
[tex]\cos 2\theta = 0[/tex]
[tex]2\theta = \cos^{-1}0[/tex]
[tex]\theta = \frac{1}{2}\cdot \cos^{-1} 0[/tex]
[tex]\theta = \frac{1}{2}\cdot \left(\frac{\pi}{2}+i\cdot \pi \right)[/tex], for all [tex]i \in \mathbb{N}_{O}[/tex]
[tex]\theta = \frac{\pi}{4} + i\cdot \frac{\pi}{2}[/tex], for all [tex]i \in \mathbb{N}_{O}[/tex]
The first four solutions are:
x: [tex]\sqrt{2}[/tex] [tex]-\sqrt{2}[/tex] [tex]-\sqrt{2}[/tex] [tex]\sqrt{2}[/tex]
y: 1 -1 1 -1
The solutions listed from the smallest to the greatest are:
x: [tex]-\sqrt{2}[/tex] [tex]-\sqrt{2}[/tex] [tex]\sqrt{2}[/tex] [tex]\sqrt{2}[/tex]
y: -1 1 -1 1
Using derivatives of the parametric curves and the solving a trigonometric equation, it is found that the points (x,y) are:
[tex]x = 2\cos{\left(\frac{k\pi}{4}\right)}, k = 1, 3, 5, \cdots[/tex]
[tex]y = \sin{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]
Given two parametric curves x(t) and y(t), the slope of the tangent line is given by:
[tex]m = \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]
The tangent line is horizontal for:
[tex]\frac{dy}{dt} = 0, \frac{dx}{dt} \neq 0[/tex]
In this problem, since we are working with trigonometric functions sine and cosine, they will never be simultaneously 0, hence, the equation of interest is:
[tex]\frac{dy}{dt} = 0[/tex]
Then:
[tex]y(t) = \sin{2\theta}[/tex]
[tex]\frac{dy}{d\theta} = 2cos{2\theta}[/tex]
Hence:
[tex]2\cos{2\theta} = 0[/tex]
[tex]\cos{2\theta} = 0[/tex]
[tex]\cos{2\theta} = \cos{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]
[tex]2\theta = \frac{k\pi}{2}[/tex]
[tex]\theta = \frac{k\pi}{4}, k = 1, 3, 5, \cdots[/tex]
Hence, the points (x,y) are:
[tex]x = 2\cos{\left(\frac{k\pi}{4}\right)}, k = 1, 3, 5, \cdots[/tex]
[tex]y = \sin{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]
A similar problem is given at https://brainly.com/question/13442736
i need points please if i have 0 and you give me 10 then how much do i have?
Answer:
10 :/
Step-by-step explanation:
If you have 0 and I give you 10, then you have 10 because 0+10 is 10.
(Photo attached) Trig question. Please explain and thanks in advance! :)
Answer:
0.2036
Step-by-step explanation:
u = arcsin(0.391) ≈ 23.016737°
tan(u/2) = tan(11.508368°)
tan(u/2) ≈ 0.2036
__
You can also use the trig identity ...
tan(α/2) = sin(α)/(1+cos(α))
and you can find cos(u) as cos(arcsin(0.391)) ≈ 0.920391
or using the trig identity ...
cos(α) = √(1 -sin²(α)) = √(1 -.152881) = √.847119
Then ...
tan(u/2) = 0.391/(1 +√0.847119)
tan(u/2) ≈ 0.2036
__
Comment on the solution
These problems are probably intended to have you think about and use the trig half-angle and double-angle formulas. Since you need a calculator anyway for the roots and the division, it makes a certain amount of sense to use it for inverse trig functions. Finding the angle and the appropriate function of it is a lot easier than messing with trig identities, IMO.