Answer:
The objective of the confidence interval is to give a range in which the real mean of the population is placed, with a degree of confidence given by the level of significance.
The conclusion we can make is that there is 95% of probability that the mean of the population (professor's average salary) is within $99,881 and $171,172.
Step-by-step explanation:
This is a case in which, from a sample os size n=16, a confidence interval is constructed.
The objective of the confidence interval is to give a range in which the real mean of the population is placed, with a degree of confidence given by the level of significance. In this case, the probability that the real mean is within the interval is 95%.
Suppose that there are 100 MBA students in the first-year class. Of these students, 20 of them have two years of work experience, 30 have three years of work experience, 15 have four years of work experience, and 35 have five or more years of work experience. Suppose that a first-year MBA student is selected at random. (a) What is the probability that this student has at least four years of work experience
Answer:
(a)0.5
(b)0.625
Step-by-step explanation:
Out of 100 MBA students
20 of them have two years of work experience, 30 have three years of work experience, 15 have four years of work experience, and 35 have five or more years of work experience.Total Sample Space, n(S)=100
(a)Let event A be the event that an MBA student has at least four years of work experience.
n(A)=15+35=50
Therefore:
[tex]P(A)=\dfrac{n(A)}{n(S)} =\dfrac{50}{100}=0.5[/tex]
The probability that this student has at least four years of work experience is 0.5.
(b)Conditional probability that given that a student has at least three years of work experience,this student has at least four years of work experience.
P(at least 4 years|the student has at least three years of experience)
[tex]=\dfrac{50/100}{80/100} =\dfrac{5}{8}=0.625[/tex]
The probability that a randomly selected first-year MBA student has at least four years of work experience is 0.5 or 50%.
Explanation:The question involves the concept of probability in statistics, a part of Mathematics. Here, we are given that there are a total of 100 first-year MBA students. The number of students with at least four years of work experience combines the students with four years and five or more years of work experience. Thus, the students with at least four years of work experience are 15 (four years of work experience) + 35 (five or more years of work experience), which equals 50.
The probability is determined by dividing the number of favorable outcomes by the total number of outcomes. Hence, the probability that a randomly selected first-year MBA student has at least four years of work experience is calculated as 50 (students with at least four years' experience) divided by 100 (total students), which equals 0.5 or 50%.
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Suppose that a market research firm is hired to estimate the percent of adults living in a large city who have cell phones. 500 randomly selected adult residents in this city are surveyed to determine whether they have cell phones. Of the 500 people surveyed, 421 responded yes – they own cell phones. Using a 95% confidence level, compute a confidence interval estimate for the true proportion of adults residents of this city who have cell phones.
Answer:
The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).
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 = 500, \pi = \frac{421}{500} = 0.842[/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}} = 0.842 - 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.81[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 + 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.874[/tex]
The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).
The 95% confidence interval is (0.81,0.874) and this can be determined by using the confidence interval formula and using the given data.
Given :
500 randomly selected adult residents in this city are surveyed to determine whether they have cell phones. Of the 500 people surveyed, 421 responded yes – they own cell phones.95% confidence level.The formula for the confidence interval is given by:
[tex]\rm CI = p\pm z\sqrt{\dfrac{p(1-p)}{n}}[/tex] --- (1)
where the value of p is given by:
[tex]\rm p =\dfrac{421}{500}=0.842[/tex]
Now, the value of z for 95% confidence interval is given by:
[tex]\rm p-value = 1-\dfrac{0.05}{2}=0.975[/tex]
So, the z value regarding the p-value 0.975 is 1.96.
Now, substitute the value of z, p, and n in the expression (1).
[tex]\rm CI = 0.842\pm 1.96\sqrt{\dfrac{0.842(1-0.842)}{500}}[/tex]
The upper limit is 0.81 and the lower limit is 0.874 and this can be determined by simplifying the above expression.
So, the 95% confidence interval is (0.81,0.874).
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Outdoor Luggage, Inc., makes high-end hard-sided luggage for sports equipment. Data concerning three of the company’s most popular models appear below. Ski Guard Golf Guard Fishing GuardSelling price per unit $ 270 $ 350 $ 185 Variable cost per unit $ 155 $ 210 $ 65 Plastic injection molding machine processingtime required to produce one unit 7 minutes 9 minutes 12 minutes Pounds of plastic pellets per unit 11 pounds 15 pounds 13 pounds Required:1. If we assume that the total time available on the plastic injection molding machine is the constraint in the production process, how much contribution margin per minute of the constrained resource is earned by each product? 2. Which product offers the most profitable use of the plastic injection molding machine?3. If we assume that a severe shortage of plastic pellets has required the company to cut back its production so much that its new constraint has become the total available pounds of plastic pellets, how much contribution margin per pound of the constrained resource is earned by each product? 4. Which product offers the most profitable use of the plastic pellets?5. Which product has the largest contribution margin per unit?
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Leah has a 22 ounce coffee. she drinks 7 ounces. enter the percentage of ounces Leah has left of her coffee. round your answer to the nearest hundredth.
Answer:
The percentage of ounces Leah has left of her coffee is 68.18%.
Step-by-step explanation:
The decrease percentage is computed using the formula:
[tex]\text{Decrease}\%=\frac{\text{Original amount - Decrease}}{\text{Original amount}}\times 100[/tex]
It is provided that Leah originally had 22 ounce coffee.
Then she drinks 7 ounces of coffee.
Decrease = 7 ounces
Original = 22 ounces
Compute the percentage of ounces Leah has left of her coffee as follows:
[tex]\text{Decrease}\%=\frac{\text{Original amount - Decrease}}{\text{Original amount}}\times 100[/tex]
[tex]=\frac{22-7}{22}\times 100\\\\=\frac{15}{22}\times 100\\\\=68.1818182\%\\\\\approx 68.18\%[/tex]
Thus, the percentage of ounces Leah has left of her coffee is 68.18%.
WILL GIVE BRAINLIEST ANSWER TO CORRECT ANSWER I need help with questions 2 part a,b,c and question 3 part a,b,c. Please, thank you !
Answer:
Q2
a) total sweets: 5 + 3 = 8
i) P(red) = 5/8
ii) P(yellow) = 3/8
b) for the second one:
4 red and 3 yellow left
i) P(red) = 4/7
ii) P(yellow) = 3/7
c) for the second one:
5 red and 2 yellow left
i) P(red) = 5/7
ii) P(yellow) = 2/7
Q3
a) total probability is 1
⅙ + ¼ + ⅓ + x = 1
x = 1 - (⅙ + ¼ + ⅓)
x = ¼
b) most likely is the color with highest probability, which is green
c) P(not red) = 1 - P(red)
= 1 - ⅙ = ⅚
You are building a play area for the children. It will be 20 feet long. The total perimeter is 50 feet. What is the width of the play area?
Answer:
5
Step-by-step explanation:
20+20=40
50-40=10
10/2=5
To check our work we find the perimeter with our new width. 20+20+5+5=50
So we are right!!!
Suppose that the money demand function takes the form If output grows at rate and the nominal interest rate is constant, at what rate will the demand for real balances grow
Complete Question
Suppose that the money demand function takes the form
(M/P)^d = L(i,Y) = Y/(5i)
a. If output grows at rate and the nominal interest rate is constant, at what rate will the demand for real balances grow
b. What is the velocity of money in this economy
Answer:
a. See explanation below
b. Velocity = 5i
Step-by-step explanation:
a. Suppose that the nominal interest rate remains constant, the demand for real balances will grow at the same rate at which the output grows.
b.
Given that (M/P)^d = L(i,Y) = Y/(5i)
Money equation is written as;
Total Spending = MV
Where M = Amount of Money..
V = Velocity of Circulation
Total Spending = PY;
So, PY = MV --- Make V the subject of formula
PY/M = V --- Rearrange
V = PY/M ---- (1)
Also,
M/P = Y/5i --- Cross Multiply
M * 5i = P * Y --- Make 5i the subject of formula
5i = PY/M ---- (2)
Compare 1 and 2
5i = V = PY/M
So, 5i = V
V = 5i
Hence, Velocity = 5i
An article reported that for a sample of 52 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO2 level (ppm) was 654.16, and the sample standard deviation was 164.55.
a) calculate and interpret a 95% confidence interval for true average CO2 level in the population of all homes from which the sample was selected .
b) Suppose the investigators had made a rough guess of 175 for the value of s before collecting data .What sanple size would be necessary to obtain an interval width of 50 ppm for confidence level of 95% ?
Answer:
a) [tex]654.16-2.01\frac{164.55}{\sqrt{52}}=608.29[/tex]
[tex]654.16+2.01\frac{164.55}{\sqrt{52}}=700.03[/tex]
And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm
b) [tex]n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189[/tex]
Step-by-step explanation:
Part a
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=52-1=51[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,51)".And we see that [tex]t_{\alpha/2}=2.01[/tex]
Replacing we got:
[tex]654.16-2.01\frac{164.55}{\sqrt{52}}=608.29[/tex]
[tex]654.16+2.01\frac{164.55}{\sqrt{52}}=700.03[/tex]
And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm
Part b
The margin of error is given by :
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
The desired margin of error is ME =50/2=25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex] (b)
The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got [tex]z_{\alpha/2}=1.960[/tex], and we use an estimator of the population variance the value of 175 replacing into formula (b) we got:
[tex]n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189[/tex]
Suppose shirts are one of 3 colors (red, blue and green) and pants are either black or brown. An outfit consists of a shirt and pants. What is the minimum number of people that need to be in a room together to guarantee that at least two of them are wearing same-colored outfits
You solve this question by finding the maximum possible number of different combinations, then adding one extra person.
3 possible shirts * 2 possible pants for each shirt = 6 combinations of pants and shirts.
6 + 1 = 7
Therefore, the minimum is:
7 People
The annual energy consumption of the town where Camilla lives in creases at a rate that is onal at any time to the energy consumption at that time. The town consumed 4.4 trillion ually after 5 years. British thermal units (BTUs) initially, and it consumed 5.5 trillion BTUs ann What is the town's annual energy consumption, in trillionso f BTUs, after 9 years?
Answer:
6.575 trillion BTUs
Step-by-step explanation:
Let represent the annual energy consumption of the town as E
The rate of annual energy consumption * energy consumption at time past
dE/dt * E
dE/dt =K
k = the proportionality constant
c= the integration constant
(dE/dt=) kdt
lnE = kt + c
E(t) = e^kt+c ⇒ e^c e^kt e^c is a constant, and e^c = E₀
E(t) = E₀ e^kt
The initial consumption of energy is E(0)=4.4TBTU
set t = 0 then
4.4 = E₀ e⇒ E₀ (1)
E₀ = 4.4
E (t) = 4.4e^kt
The consumption after 5 years is t = 5, e(5) = 5.5TBTU
so,
E(5) = 5.5 = 4.4e^k(5)
e^5k = 5/4
We now take the log 5kln = ln(5/4)
5k(1) = ln(5/4)
k = 1/5 ln(5/4) = 0.04463
We find the town's annual energy consumption, after 9 years
we set t=9
E(9) = 4.4e^0.04463(9)
= 4.4(1.494301) = 6.5749TBTUs
Therefore the annual energy consumption of the town after 9 years is
= 6.575 trillion BTUs
What is (f+g)(x)?
f(x)=-x
g(x)=3x+3
Write your answer as a polynomial or a rational function in simplest form.
Answer:
There u go
Step-by-step explanation:
(-x+3x+3)×x=2x^2+3x
2x^2+3x=x(2x+3)
The sum of the functions f(x) = -x and g(x) = 3x + 3 is computed as (f+g)(x) = f(x) + g(x), which simplifies to 2x + 3. This denotes a polynomial in simplest form.
Explanation:The question is asking to compute the sum of two functions, f(x) = -x and g(x) = 3x+3 and to express it as a polynomial or a rational function in simplest form.
The sum of the two functions can be computed by adding together the outputs of the individual functions. In mathematical bricolage, this is known as function addition. The function sum (f+g)(x) can be calculated as f(x) + g(x).
If f(x) = -x and g(x) = 3x + 3, then (f+g)(x) can be calculated as follows:
(-x) + (3x + 3) = (-1x + 3x) + 3 = 2x + 3
So, (f+g)(x), in this case, is 2x + 3 which is a polynomial function in simplest form.
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Which of the following it true about the graph below?
Answer:
B
Step-by-step explanation:
choose brainliest
Rearrange this to make a the subject
Answer:
w = 3(2a + b) - 4
w = 6a + 3b - 4
a = (w - 3b + 4) / 6
Answer:
[tex]a = \frac{w + 4 - 3b}{6} [/tex]
Step-by-step explanation:
[tex]w = 3(2a + b) - 4 \\ w + 4 = 6a + 3b \\ w + 4 - 3b = 6a \\ \frac{w + 4 - 3b }{6} = \frac{6a}{6} \\ \\ a = \frac{w + 4 - 3b}{6} [/tex]
3. The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = .17 and a sample of 800 households will be selected from the population. a. Show the sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries. b. What is the probability that the sample proportion will be within ±.02 of the population proportion? c. Answer part (b) for a sample of 1600 household
Answer:
A)sample proportion = 0.17, the sampling distribution of p can be calculated/approximated with normal distribution of sample proportion = 0.17 and standard error/deviation = 0.013281
B) 0.869
C)0.9668
Step-by-step explanation:
A) p ( proportion of population that spends more than $100 per week) = 0.17
sample size (n)= 800
the sample proportion of p = 0.17
standard error of p = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex] = 0.013281
the sampling distribution of p can be calculated/approximated with
normal distribution of sample proportion = 0.17 and standard error/deviation = 0.013281
B) probability that the sample proportion will be +-0.02 of the population proportion
= p (0.17 - 0.02 ≤ P ≤ 0.17 + 0.02 ) = p( 0.15 ≤ P ≤ 0.19)
z value corresponding to P
Z = [tex]\frac{P - p}{standard deviation}[/tex]
at P = 0.15
Z = (0.15 - 0.17) / 0.013281 = = -1.51
at P = 0.19
z = ( 0.19 - 0.17) / 0.013281 = 1.51
therefore the required probability will be
p( -1.5 ≤ z ≤ 1.5 ) = p(z ≤ 1.51 ) - p(z ≤ -1.51 )
= 0.9345 - 0.0655 = 0.869
C) for a sample (n ) = 1600
standard deviation/ error = 0.009391 (applying the equation for calculating standard error as seen in part A above)
therefore the required probability after applying
z = [tex]\frac{P-p}{standard deviation}[/tex] at p = 0.15 and p = 0.19
p ( -2.13 ≤ z ≤ 2.13 ) = p( z ≤ 2.13 ) - p( z ≤ -2.13 )
= 0.9834 - 0.0166 = 0.9668
The sampling distribution of the sample proportion can be approximated by a normal distribution. The probability of the sample proportion being within a certain range can be calculated using z-scores.
Explanation:a. The sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries, can be approximated by a normal distribution with a mean of p and a standard deviation of √[(p(1-p))/n], where p is the population proportion and n is the sample size.
b. To find the probability that the sample proportion will be within ±0.02 of the population proportion, we calculate the z-scores for both values and find the area under the normal curve between those z-scores.
c. The probability of the sample proportion being within ±0.02 of the population proportion will remain the same for a sample of 1600 households, as long as the population proportion remains the same.
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f(x) = 10x-4 and g(x) = . What is the value of f(g(-4))?
This is a composite function problem in high school mathematics. To solve the problem, first evaluate g(-4), then substitute that result into the function f(x). Using these steps, the composite function f(g(-4)) equals -114.
Explanation:First, it is crucial to identify that this is a question involving composite functions, specifically applying the function f(g(x)). In this case, the function g(x) is not provided in the question, so I'll assume we have a typo. If g(x) has been given as 3x + 1, then g(-4) would equal -11. We substitute -11 into the function f(x)=10x-4, we get f(-11)=10*(-11)-4, which results in f(-11)=-114.
The composite function f(g(-4)) is thus -114.
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At 12.5 mph how long will it take her to go 4.5 miles
Answer:
asdasd
Step-by-step explanation:
miles ÷ miles/hour = hours
Just divide the miles by the mph
4.5/12.5 = 0.36 hours
(0.36 hours)(60 min/hour) = 21.6 minutes
(0.6 minutes)(60 seconds/minute) = 36 seconds
Time: 21 minutes 36 seconds
Answer:
0.36 hours
Step-by-step explanation:
Miles ÷ Miles/hour = hours
4.5 miles ÷ 12.5 mph = 0.36 hours
A town has a population of 17000 and grows at 4% every year. What will be the population after 12 years?
Final answer:
To find the population of a town after 12 years with an initial population of 17,000 and an annual growth rate of 4%, use the exponential growth formula. After the calculations, the town's estimated future population would be around 26,533 residents.
Explanation:
To calculate the future population of a town that currently has 17,000 residents and grows at a rate of 4% per year, we can use the formula for exponential growth: future population = current population × [tex](1 + growth \ rate)^n,[/tex] where n is the number of years the population is growing. In this case, the formula becomes [tex]17000 \times (1 + 0.04)^n[/tex], because we're looking to find the population after 12 years.
Calculating this, we have: future population = [tex]17,000 \times (1.04)^{12}[/tex]. Using a calculator, we get approximately 26,533, meaning after 12 years, the population of the town is expected to be around 26,533 residents.
Consider a sampling distribution with p equals 0.15p=0.15 and samples of size n each. Using the appropriate formulas, find the mean and the standard deviation of the sampling distribution of the sample proportion. a. For a random sample of size n equals 5000n=5000. b. For a random sample of size n equals 1000n=1000. c. For a random sample of size n equals 500n=500.
Answer:
[tex]a.\ \mu_p=750\ \ , \sigma_p=0.005\\\\b.\ \mu_p=150\ \ , \sigma_p=0.0113\\\\c.\ \mu_p=75\ \ , \sigma_p=0.0160[/tex]
Step-by-step explanation:
a. Given p=0.15.
-The mean of a sampling proportion of n=5000 is calculated as:
[tex]\mu_p=np\\\\=0.15\times 5000\\\\=750[/tex]
-The standard deviation is calculated using the formula:
[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\=\sqrt{\frac{0.15(1-0.15)}{5000}}\\\\=0.0050[/tex]
Hence, the sample mean is μ=750 and standard deviation is σ=0.0050
b. Given that p=0.15 and n=1000
#The mean of a sampling proportion of n=1000 is calculated as:
[tex]\mu_p=np\\\\=1000\times 0.15\\\\\\=150[/tex]
#-The standard deviation is calculated as follows:
[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\\\=\sqrt{\frac{0.15\times 0.85}{1000}}\\\\\\=0.0113[/tex]
Hence, the sample mean is μ=150 and standard deviation is σ=0.0113
c. For p=0.15 and n=500
#The mean is calculated as follows:
[tex]\mu_p=np\\\\\\=0.15\times 500\\\\=75[/tex]
#The standard deviation of the sample proportion is calculated as:
[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\\\=\sqrt{\frac{0.15\times 0.85}{500}}\\\\\\=0.0160[/tex]
Hence, the sample mean is μ=75 and standard deviation is σ=0.0160
1 third plus 1/2 -1/5 equals
Answer: 0.63333333333
Step-by-step explanation: Use a calculator.
Answer: 19/30
Step-by-step explanation:
You want to find a common denominator that works for all fractions and add a subtract them and the simplify
Solve the following expression using order of operations 58-2x3+1
uppose a 95% confidence interval for the average forearm length of men was (24cm, 27cm). How would we then interpret this interval? 95% of all men have a forearm length between 24cm and 27cm. In confidence intervals calculated from many random samples, 95% would contain a sample average forearm length between 24cm and 27cm. The average forearm length of all men is between 24cm and 27cm 95% of the time. 95% of men in this sample of 9 men have a forearm length between 24cm and 27cm. In confidence intervals calculated from many random samples, 95% would contain the average forearm length for all
Answer:
in many random samples, 95% of the confidence intervals will contain a sample average between 24cm and 27cm.
Step-by-step explanation:
We then interpret this interval that 95% would contain a sample average forearm length between 24cm and 27cm.
What is average?The average is defined as the mean equal to the ratio of the sum of the values of a given number to the total number of values in the set.
The formula for finding the average of given numbers or values is very simple. We just need to add all the numbers and divide the result by the given number of values. So the formula for mean in mathematics is given as follows:
Mean = sum of values/ number of values
Suppose we have given n as number of values like x1, x2, x3 ,..., xn. The average or mean of the given data is equal to:
Mean = (x1 x2 x3 … xn)/n
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Choose the function that represents the data in the table.
A.Y= 0.5x^2+6
B. Y= 0.5^x+6
C. Y= 0.5x+ 6
D. Y= x^0.5+ 6
Given:
It is given that the function represents the data in the table.
We need to determine the function.
Slope:
The slope can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let us substitute the coordinates (1,6.5) and (4,8) in the above formula, we get;
[tex]m=\frac{8-6.5}{4-1}[/tex]
[tex]m=\frac{1.5}{3}[/tex]
[tex]m=0.5[/tex]
Thus, the slope is 0.5
y - intercept:
The y - intercept is the value of y when x = 0.
Thus, from the table, when x = 0 the corresponding y value is 6.
Therefore, the y - intercept is [tex]b=6[/tex]
Equation of the function:
The equation of the function can be determined using the formula,
[tex]y=mx+b[/tex]
Substituting the values [tex]m=0.5[/tex] and [tex]b=6[/tex], we get;
[tex]y=0.5x+6[/tex]
Thus, the equation of the function is [tex]y=0.5x+6[/tex]
Hence, Option C is the correct answer.
Solve the equation (y-10)^2=0
Answer:
y=10
Step-by-step explanation:
(y-10)^2=0
Take the square root of each side
sqrt((y-10)^2)=sqrt(0)
y-10 =0
Add 10 to each side
y-10+10=0+10
y = 10
(please break it down for me to understand):)
*I got 0.00040404 on calculator but I need fraction not decimal trying to understand how to get the fraction*
[tex] \frac{1}{50} \times \frac{2}{99} = \frac{1}{2475} [/tex]
Answer:
1/50 times 2/99 = 2/4950
divide numerator and denominator by 2 and the answer you should get is 1/2475 and in decimal form it equals 0.00040404040404040
Step-by-step explanation:
I need to Simplify (3mn)^4
9514 1404 393
Answer:
81m^4·n^4
Step-by-step explanation:
"Simplify" in this context means "remove parentheses." The applicable rule of exponents is ...
(ab)^c = (a^c)(b^c)
__
[tex](3mn)^4=3^4m^4n^4=\boxed{81m^4n^4}[/tex]
Between the years of 1947 and 1956 earthenware jars containing what are known as the Dead Sea scrolls were found in caves along the coast of Jerusalem in the Dead Sea. Upon radiometric testing it was found that the scrolls were wrapped in material that contained about 79 percent of the original carbon-14.archeologists estimated that the scrolls are about 1900 years old. Are they right ?
Answer:
The scroll is 1949 years old, thus the archeologists are right.
Step-by-step explanation:
The decay equation of ¹⁴C is:
[tex] A = A_{0}e^{-\lambda*t} [/tex] (1)
Where:
A₀: is the initial activity
A: is the activity after a time t = 79%*A₀
λ: is the decay rate
The decay rate is:
[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex] (2)
Where [tex]t_{1/2}[/tex]: is the half-life of ¹⁴C = 5730 y
By entering equation (2) into equation (1) we can find the age of the scrolls.
[tex] A = A_{0}e^{-\lambda*t} = A_{0}e^{-\frac{ln(2)}{t_{1/2}}*t} [/tex]
Since, A = 79%*A₀, we have:
[tex]\frac{79}{100}A_{0} = A_{0}e^{-\frac{ln(2)}{t_{1/2}}*t}[/tex]
[tex]ln(\frac{79}{100}) = -\frac{ln(2)}{t_{1/2}}*t[/tex]
Solving the above equation for t:
[tex]t = -\frac{ln(79/100)}{\frac{ln(2)}{t_{1/2}}}[/tex]
[tex]t = -\frac{ln(75/100)}{\frac{ln(2)}{5730 y}} = 1949 y[/tex]
Hence, the scroll is 1949 years old, thus the archeologists are right.
I hope it helps you!
Answer:
The hypothesis is correct.
Step-by-step explanation:
Using the half-life equation, the number of years (1,900) can be substituted for t and the half-life (5,730) can be substituted for h. Since the original amount is not known but the percent remaining is known, any value can be used for the original amount. Using 100 will be the easiest. Plugging these values into the equation gives 79.47 remaining. If 79.47 of the original 100 units are left, that is 79.47 percent. Since radiometric dating gives an estimate of age, the archeologists’ hypothesis is correct.
Vitamins in Milk - Milk is a good source of many vitamins that can help us stay healthy. FDA recommends that the average vitamin A concentration for whole milk should be 202 micrograms per liter.
A first study in 2016 collected a sample of 35 whole milk bottles and found the average vitamin A concentration was 206.83 micrograms per liter with a standard deviation of 10 micrograms per liter.
A medical researcher wants to determine if the mean vitamin A concentration in whole milk is more than 202 micrograms per liter. The null and alternative hypothesis are given by
H0 : μ = 202 vs HA: μ > 202.
The effect size for this first study is 0.483 and the p-value is 0.0036.
1. A new study of 100 whole milk bottles reports a p-value of 0.00056 and an effect size of 0.4342. Does the new study confirm or conflict with the results of the first study?
O Conflict, because the effect size is smaller.
O Conflict, because the p-value is much smaller.
O Confirm, because the effect size is comparable.
O Confirm, because the p-value is much smaller.
Answer:
O Confirm, because the p-value is much smaller.
Step-by-step explanation:
The p-value is the probability used to determine whether to accept or reject an null hypothesis. Higher p-value means that there is evidence in favour of the null hypothesis while smaller p-value means that there is stronger evidence in favour of the alternative hypothesis. For the case above, the p-value is smaller which means that the new study confirms the results of the first study which also have a small p-value.
A random sample of n = 4 scores is selected from a population with a mean of 50 and a standard deviation of 12. If the sample mean is 56, what is the z-score for this sample mean?
The z-score for the sample mean in this case is 0.5, which is calculated using the z-score formula, Z = (X - μ) / σ, where X is the sample mean, μ is the population mean, and σ is the standard deviation.
Explanation:The subject here pertains to the calculation of a z-score, which is a statistical measurement describing a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean.
Given the sample mean (56), population mean (50), and standard deviation (12), and the formula for the z-score, which is Z = (X - μ) / σ, we can compute for the z-score as follows:
- X is the raw score which is 56- μ is the population mean which is 50- σ is the population standard deviation which is 12Substituting these values into the equation, we have: Z = (56 - 50) / 12 = 0.5. Hence, the z-score of the sample mean is 0.5.
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The accompanying technology output was obtained by using the paired data consisting of foot lengths (cm) and heights (cm) of a sample of 40 people. Along with the paired sample data, the technology was also given a foot length of 15.2 cm to be used for predicting height. The technology found that there is a linear correlation between height and foot length. If someone has a foot length of 15.2 cm, what is the single value that is the best predicted height for that person?
Answer:
76 inches
Step-by-step explanation:
It should be understood that 15.2cm is equal to 5 inches.
Since the height = 5 * size of the foot
= 5 * 15.2 = 76
Therefore, a person with 15.2cm as the size of the foot will have the height of 76 inches.
Using the regression model produced by the technology output. The best predicted value for the person's height would be 123.288 cm.
Using the Regression equation produced by the technology used :
Height = 52.0 + 4.69(foot length)For a foot length of 15.2 cm :
The predicted height value can be calculated by substituting the foot length value into the equation thus :
Height = 52.0 + 4.69(15.2)
Height = 52.0 + 71.288
Height = 123.288 cm
The best predicted value for the person's height would be 123.288 cm.
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Suppose a simple random sample of size nequals36 is obtained from a population with mu equals 74 and sigma equals 6. (a) Describe the sampling distribution of x overbar. (b) What is Upper P (x overbar greater than 75.9 )? (c) What is Upper P (x overbar less than or equals 71.95 )? (d) What is Upper P (73 less than x overbar less than 75.75 )?
Final answer:
The Central Limit Theorem explains the sampling distribution of the sample mean. We calculate probabilities using z-scores in the normal distribution for different scenarios. Understanding the concepts of sampling distributions and z-scores is essential for handling such questions in statistics.
Explanation:
The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the population distribution.
(a) The mean of the sampling distribution of x equals the population mean, which is 74, and the standard deviation of the sampling distribution σ/√n equals 6/√36 = 1.
(b) To find Upper P(x > 75.9), we standardize the value: z = (75.9 - 74) / 1 = 1.9. Consulting a z-table, we find P(z > 1.9) ≈ 0.0287.
(c) For Upper P(x< 71.95), we standardize: z = (71.95 - 74) / 1 = -2.05. From the z-table, P(z < -2.05) ≈ 0.0202.
(d) To find Upper P(73 < x < 75.75), we standardize both values, giving z(73) = (73 - 74) / 1 = -1 and z(75.75) = (75.75 - 74) / 1 = 1.75. Then, P(-1 < z < 1.75) = P(z < 1.75) - P(z < -1) ≈ 0.9599 - 0.1587 = 0.8012.