The sequence converges to 0.
To determine the convergence or divergence of the given sequence, we can use the limit comparison test.
Let's consider the series a_n = -8n^6 + sin^2(7n) and b_n = n^7 + 9.
Since sin^2(7n) is always between 0 and 1, we have 0 ≤ sin^2(7n) ≤ 1 for all n. Therefore,
-8n^6 ≤ -8n^6 + sin^2(7n) ≤ -7n^6
Dividing all terms by n^7 + 9, we get
-8n^-1/(n^7+9) ≤ (-8n^6 + sin^2(7n))/(n^7 + 9) ≤ -7n^-1/(n^7+9)
Now, taking the limit as n approaches infinity, we have
lim n→∞ -8n^-1/(n^7+9) = 0
lim n→∞ -7n^-1/(n^7+9) = 0
Since both the upper and lower bounds go to 0, the limit comparison test tells us that the series a_n and b_n have the same convergence behavior.
Since the series b_n = n^7 + 9 is a p-series with p = 7 > 1, it converges. Therefore, the given sequence
(-8n^6 + sin^2(7n))/(n^7 + 9)
also converges by the limit comparison test.
To evaluate its limit, we can use algebraic manipulation and the squeeze theorem.
-8n^6 ≤ -8n^6 + sin^2(7n) ≤ -7n^6
Dividing all terms by n^7 + 9 and taking the limit as n approaches infinity, we get
lim n→∞ (-8n^6)/(n^7 + 9) ≤ lim n→∞ (-8n^6 + sin^2(7n))/(n^7 + 9) ≤ lim n→∞ (-7n^6)/(n^7 + 9)
Using the squeeze theorem, we know that
lim n→∞ (-8n^6)/(n^7 + 9) = lim n→∞ (-7n^6)/(n^7 + 9) = 0
Therefore,
lim n→∞ (-8n^6 + sin^2(7n))/(n^7 + 9) = 0
Hence, the sequence converges to 0.
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6. Let S : [0, 1] →R be defined by f(x) = x if x ∈ Q
x² if x ∉ Q
Show that is continuous at 0 and at 1 but it is not continuous at any point in (0,1).
S is not continuous at c, and since this is true for any irrational number in (0,1), S is not continuous at any point in (0,1).
To show that S is continuous at 0 and at 1, we need to show that the limit of S(x) as x approaches 0 and 1 exists and is equal to S(0) and S(1), respectively.
First, let's consider the limit as x approaches 0. We have:
lim x→0 S(x) = lim x→0 x² = 0² = 0
Since S(0) = 0, we have lim x→0 S(x) = S(0), and thus S is continuous at 0.
Now let's consider the limit as x approaches 1. We have:
lim x→1 S(x) = lim x→1 x² = 1² = 1
Since S(1) = 1, we have lim x→1 S(x) = S(1), and thus S is continuous at 1.
To show that S is not continuous at any point in (0,1), we need to find a point c in (0,1) such that S is not continuous at c. One way to do this is to show that the limit of S(x) as x approaches c does not exist.
Let c be any irrational number in (0,1), and let {r_n} be a sequence of rational numbers in (0,1) that converges to c. Then we have:
lim n→∞ S(r_n) = lim n→∞ r_n = c
On the other hand, since c is irrational, S(c) = c². Therefore, we have:
lim x→c S(x) = c²
Since lim n→∞ S(r_n) ≠ lim x→c S(x), the limit of S(x) as x approaches c does not exist. Therefore, S is not continuous at c, and since this is true for any irrational number in (0,1), S is not continuous at any point in (0,1).
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The water pressure on Mustafa as he dives is increasing at a rate of
0. 992
0. 9920, point, 992 atmospheres
(
atm
)
(atm)left parenthesis, start text, a, t, m, end text, right parenthesis per meter
(
m
)
(m)left parenthesis, start text, m, end text, right parenthesis. What is the rate of increase in water pressure in
atm
km
km
atm
start fraction, start text, a, t, m, end text, divided by, start text, k, m, end text, end fraction?
The rate of increase in water pressure in atmospheres 0.000992 atm/km.
To find the rate of increase in water pressure in atm/km, we need to convert the given rate of increase from atm/m to atm/km.
[tex]1 km = 1000 m[/tex]
So, we can convert the given rate of increase as follows:
[tex]0.992 atm/m = (0.992 atm/m)[/tex] × [tex](1000 m/km)[/tex]
[tex]= 992 atm/km[/tex]
Therefore, the rate of increase in water pressure in atm/km is 992 atm/km.
We must convert the stated rate of increase in water pressure from atm/m to atm/km in order to determine the rate of increase in atm/km.
We are aware that 1000 metres make up 1 kilometre. As a result, we can translate the supplied water pressure rise rate from atm/m to atm/km as follows:
[tex]0.000992 atm/km = 0.992 atm/m[/tex] × [tex](1 km/1000 m)[/tex]
0.000992 atm/km is the rate of rise in water pressure as a result.
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Complete Question:
The water pressure on Mustafa as he dives is increasing at a rate of
0. 992, atmospheres left parenthesis, start text, a, t, m, end text, right parenthesis per meter left parenthesis, start text, m, end text, right parenthesis. What is the rate of increase in water pressure in atmospheres?
Let X count the number of suits in a 5-card hand dealt from a standard 52-card deck. 4 a) Complete the following table: value of X 1 2 3 4probablity 0. 00198 b) Compute the expected number of suits in a 5-card hand. Probability
a) The table of probability is given below.
b) The expected number of suits in a 5-card hand dealt from a standard 52-card deck is 2.345.
We have to choose from four suits, so there are 4 ways to choose which suit we will get. After we have chosen a suit, we need to select 5 cards from that suit. We can choose any combination of 5 cards from 13 cards as there are 13 cards in each suit. We can calculate this by formula for combinations: C(13,5) = 1287.
We can choose any 5 cards from the 52 cards. This can also be calculated by the formula for combinations: C(52,5) = 2598960.
The probability of getting exactly one suit in a 5-card hand will be
= 4 * C(13,5) / C(52,5) = 0.198.
We can fill the table for all possible values of X using similar calculations
value of X probability
1 | 0.198
2 | 0.422
3 | 0.308
4 | 0.071
We need to multiply each possible value of X by its probability and then add up the results to compute the expected number of suits in a 5-card hand.
E(X) = Σ (X * P(X))
Here Σ denotes the sum over all possible values of X, and P(X) is the probability of getting X suits. When we apply this formula to the table above, we get:
E(X) = 1 * 0.198 + 2 * 0.422 + 3 * 0.308 + 4 * 0.071
= 2.345
This means that if we were to draw many 5-card hands from the deck, we would expect the average number of suits to be around 2.345.
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You have measured the systolic blood pressure of an SRS of 25 company employees. A 95% confidence interval for the mean systolic blood pressure for the employees of this company is (122,138). Which of the following statements gives a valid interpretation of this interval?
(a) 95% of the sample employees have systolic blood pressure between 122���138.
(b) 95% of the population of employees have systolic blood pressure between 122���138.
(c) If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.
(d) The probability that the population mean blood pressure is between 122���138 is 0.95.
(e) If the procedure were repeated many times, 95% of the sample means would be between 122���138.
Your answer: (c) If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.
The correct interpretation of the given confidence interval is (b) 95% of the population of employees have systolic blood pressure between 122-138. This means that if we take multiple samples of the same size from the population, 95% of the confidence intervals we construct from those samples will contain the true population mean systolic blood pressure.
Option (a) is incorrect as it only talks about the sample employees, not the population.
Option (c) is also incorrect as it talks about repeating the procedure of constructing confidence intervals, not the actual population mean systolic blood pressure.
Option (d) is incorrect as it talks about the probability of the population mean, which is not a valid interpretation of a confidence interval.
Option (e) is also incorrect as it talks about the sample means, not the population mean.
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A research center claims that 63% of U.S. adults support using more surveillance cameras in public places. In a random sample of 300 U.S. adults, 210 say that they support using more surveillance cameras in public places. At 0.10 level of significance, is there enough evidence to reject the research center's claim? Select the correct answer below: A. At the 0.10 level of significance there is enough evidence to reject the research center's claim that 63% of U.S. adults support more surveillance cameras in public places.
B. At the 0.10 level of significance there is not enough evidence to reject the research center's claim that 63% of U.S. adults support more surveillance cameras in public places.
The correct answer is: A. At the 0.10 level of significance there is enough evidence to reject the research center's claim that 63% of U.S. adults support more surveillance cameras in public places.
To test whether the research center's claim is supported by the sample data, we need to perform a hypothesis test.
The null hypothesis is that the true proportion of U.S. adults who support using more surveillance cameras in public places is equal to 63%, i.e. H0: p = 0.63. The alternative hypothesis is that the true proportion is different from 63%, i.e. H1: p ≠ 0.63.
We can use the normal approximation to the binomial distribution to calculate the test statistic:
z = (p - p) / sqrt(p(1-p)/n)
where p is the sample proportion, p is the hypothesized proportion, and n is the sample size.
Plugging in the values, we get:
p = 210/300 = 0.7
p = 0.63
n = 300
z = (0.7 - 0.63) / sqrt(0.63*0.37/300)
= 2.24 (rounded to two decimal places)
Using a standard normal distribution table or calculator, we find that the p-value for a two-tailed test at the 0.10 level of significance is approximately 0.025 (rounded to three decimal places). Since this p-value is less than 0.10, we reject the null hypothesis.
Therefore, the correct answer is: A. At the 0.10 level of significance there is enough evidence to reject the research center's claim that 63% of U.S. adults support more surveillance cameras in public places.
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Often, there is more than one set of sequences that will take a preimage to an image. Determine one or two other sequences to create FGHIJ from ABCDE.
The one or two other sequence to create FGHIJ from ABCDE are:
1. F, B+5=G, C+5=H, D+5=I, E+5=J.
2. Reverse ABCDE to get EDCBA
What is a sequence?A sequence refers to an ordered list of items. It may be letters, numbers, or any other objects arranged in a particular order.
A sequence of rigid motions and dilations is a combination of transformations that preserve the original shape and size of a figure, but change its position, orientation, and scale.
To create the sequence FGHIJ from ABCDE, there are many possible sequences that can be used. Here are two:
Sequence 1:
Add 5 to each letter in ABCDE to get FGHIJ: A+5=F, B+5=G, C+5=H, D+5=I, E+5=J.
Sequence 2:
Reverse the order of the letters in ABCDE to get EDCBA.
Add 5 to each letter in EDCBA to get JIHGF: E+5=J, D+5=I, C+5=H, B+5=G, A+5=F.
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if you give me new answer i will give you like
Generate demand for 100 SKUs such that the average number of weeks with zero demand during the two-year span is between 20 and 40, and the square of the coefficient of variation is between 0.30 and 0.85. also ansure that the mean demand for each sku is between 3000 and 8000
The given conditions, we can use them to simulate inventory levels, forecast sales, and make production and procurement decisions.
To generate demand for 100 SKUs that satisfies the given conditions, we can use a random number generator in Excel.
First, we can generate a random demand value for each SKU using the following formula: =NORM.INV(RAND(),(8000-3000)/2+3000,(8000-3000)/6)
This generates a random demand value from a normal distribution with mean = (8000-3000)/2+3000 = 5500 and standard deviation = (8000-3000)/6 = 833.33, ensuring that the mean demand is between 3000 and 8000.
Next, we can calculate the coefficient of variation (CV) for each SKU using the formula: =STDEV.P(A1:A104)/AVERAGE(A1:A104)
Then, we can use Excel's Goal Seek function to adjust the random demand values until the average number of weeks with zero demand and the square of the CV fall within the specified ranges.
For example, we can set up a table with columns for SKU, demand, CV, and weeks with zero demand. Then, we can use the following steps:
Enter random demand values for each SKU using the formula above.
Calculate the CV for each SKU using the formula above.
Calculate the number of weeks with zero demand for each SKU using the formula: =SUM(IF(A1:A104=0,1,0))
Calculate the average number of weeks with zero demand for all SKUs using the formula: =AVERAGE(D1:D104)
Calculate the square of the CV for all SKUs using the formula: =VAR.P(C1:C104)/AVERAGE(B1:B104)^2
Use Excel's Goal Seek function to adjust the demand values until the average number of weeks with zero demand falls between 20 and 40 and the square of the CV falls between 0.30 and 0.85.
To use Goal Seek, we can go to Data > What-If Analysis > Goal Seek, and set up the following:
Set "Set Cell" to the cell containing the average number of weeks with zero demand.
Set "To Value" to a value between 20 and 40.
Set "By Changing Cell" to the range of cells containing the demand values.
Click OK.
Excel will then adjust the demand values until the average number of weeks with zero demand falls within the specified range. We can repeat this process for the square of the CV until it also falls within the specified range
Once we have generated demand values that satisfy the given conditions, we can use them to simulate inventory levels, forecast sales, and make production and procurement decisions.
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if three of the interior angles of a convex quadrilateral measure 98, 139, and 80 degrees what is the measure of the fourth
Answer:
The sum of the interior angles of any quadrilateral is 360 degrees.
So, let x be the measure of the fourth angle. Then we can write the equation:
98 + 139 + 80 + x = 360
Simplifying this equation gives:
317 + x = 360
Subtracting 317 from both sides gives:
x = 43
Therefore, the measure of the fourth interior angle of this convex quadrilateral is 43 degrees.
Step-by-step explanation:
The measure of the fourth interior angle of the convex quadrilateral is 43 degrees. To find the measure of the fourth interior angle of a convex quadrilateral, we'll use the following terms: interior, angles, quadrilateral, and measure.
Step 1: Remember that the sum of interior angles of a quadrilateral is always 360 degrees.
Step 2: Add the three given interior angles: 98 + 139 + 80 = 317 degrees.
Step 3: Subtract the sum of the three angles from the total sum of quadrilateral angles (360 degrees) to find the measure of the fourth angle: 360 - 317 = 43 degrees.
The measure of the fourth interior angle of the convex quadrilateral is 43 degrees.
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Using FT properties, Compute Fourier transform of the following signals
(a)×(t)=δ(t-1)
(b)×(t)=δ(t-1)
The Fourier transform of x(t) is zero for all frequencies.
(a) x(t) = δ(t-1)
Using the time-shifting property of the Fourier transform, we have:
F{δ(t-a)} = e^{-j2πf a}
Therefore,
F{x(t)} = F{δ(t-1)} = e^{-j2πf (1)}
The Fourier transform of x(t) is a complex exponential at frequency f = 1:
F{x(t)} = e^{-j2π} = cos(2π) - j sin(2π) = -1
(b) x(t) = δ(t-1) + δ(t+1)
Using the linearity property of the Fourier transform and the time-shifting property, we have:
F{x(t)} = F{δ(t-1)} + F{δ(t+1)} = e^{-j2πf (1)} + e^{j2πf (1)}
The Fourier transform of x(t) is a sum of two complex exponentials at frequencies f = ±1:
F{x(t)} = e^{-j2π} + e^{j2π} = cos(2π) - j sin(2π) + cos(2π) + j sin(2π) = 0
Therefore, the Fourier transform of x(t) is zero for all frequencies.
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#1 BRAINLIST
SHow all steps pls it was due yesterday!
Answer:
Step-by-step explanation:
The number of combinations on n items taken 3 at a time is 6 times the number of combinations of n items taken 2 at the time. Find the value of the constant n.
To solve this problem, we can use the formula for combinations, which is:
C(n, k) = n! / (k! * (n-k)!)
where C(n,k) represents the number of combinations of n items taken k at a time.
Using this formula, we can write the given information as an equation:
6 * C(n, 3) = C(n, 2)
Substituting the formula for combinations, we get:
6 * (n! / (3! * (n-3)!)) = (n! / (2! * (n-2)!))
Simplifying this equation, we get:
6 * (n * (n-1) * (n-2)) / 6 = n * (n-1) / 2
Multiplying both sides by 2, we get:
2 * n * (n-1) * (n-2) = 6 * n * (n-1)
Simplifying further, we get:
n * (n-1) * (n-2) = 3 * n * (n-1)
Dividing both sides by n * (n-1), we get:
n-2 = 3
n = 5
Therefore, the value of the constant n is 5.
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There are 31 fish in a tank. The fish are either orangr or red. There are 7 more orange fish than half the number of red fish. How many fish are orange? How many fish are red?
There are 19 orange fish and 12 red fish in the tank. This was found by setting up and solving a system of equations based on the given information.
We can set up a system of equations. Let x be the number of red fish in the tank. We know that the total number of fish is 31, so the number of orange fish must be 31 - x.
We also know that there are 7 more orange fish than half the number of red fish, which can be written as: 31 - x = 7 + 0.5x. Solving for x, we get: 1.5x = 24. x = 16
Hence, there are 16 red fish in the tank. To find the number of orange fish, we can substitute x = 16 into the equation we derived earlier: 31 - 16 = 15. 15 = 7 + 0.5(16). 15 = 15. Hence, there are 15 orange fish in the tank.
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Partition each whole number interval into fourths. Label 7/4 and 9/4
We can see that 7/4 is located between 3/4 and 1 on the first interval, and 9/4 is located between 2 and 5/2 on the second interval.
To partition each whole number interval into fourths, divide each interval by 4. Label 7/4 between 3/4 and 1 and label 9/4 between 2 and 5/2 on an extended scale from 0 to 3.
To partition each whole number interval into fourths, we can divide each interval by 4. For example, the interval from 0 to 1 can be divided into fourths as follows:
0 -------- 1/4 -------- 1/2 -------- 3/4 -------- 1
Now, to label 7/4 and 9/4 on this scale, we can extend it by adding another interval from 1 to 2 and dividing it into fourths as well. This would give us the following scale:
0 -------- 1/4 -------- 1/2 -------- 3/4 -------- 1 -------- 5/4 -------- 3/2 -------- 7/4 -------- 2 -------- 9/4 -------- 5/2 -------- 11/4 -------- 3
So we can see that 7/4 is located between 3/4 and 1 on the first interval, and 9/4 is located between 2 and 5/2 on the second interval.
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Audra rolled a six-sided number cube with sides numbered 1 through 6 multiple times. Her results are shown below. Based on the data, what is the experimental probability that the next time Audra rolls the number cube, she will roll a 2? A. 1/25 B. 3/22 C. 3/25 D. 2/3
The experimental probability that the next time Audra rolls the number cube, she will roll a 2 is 3/22.
Experimental probability is the ratio of the number of times an event occurs to the total number of trials conducted. In this case, we want to find the experimental probability of rolling a 2.
Looking at the data provided, we can see that Audra rolled a 2 three times out of the total 22 rolls. So, the experimental probability of rolling a 2 can be calculated as:
Experimental probability = number of times the event occurred / total number of trials
Experimental probability of rolling a 2 = 3 / 22
Therefore, the correct option is (B) 3/22. This means that based on Audra's experiment, the probability of rolling a 2 is approximately 0.136 or 13.6%. It is important to note that this is the experimental probability based on a small sample size, and the actual probability of rolling a 2 in a large number of rolls may differ.
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Amaya used these steps to solve the equation 8x+4=9+4(2x−1)
. Which choice describes the meaning of her result, 4=5?
the choices are :
Amaya made a mistake because 4
is not equal to 5
.
No values of x
make the equation true.
.
All values of x
make the equation true.
.
The solution is x=4
or 5
.
Amaya made a mistake because 4 is not equal to 5. She incorrectly wrote 4=5 in the final step of solving the equation 8x+4=9+4(2x-1). So, the correct answer is A).
In step 1, Amaya sets up the equation 8x+4=9+4(2x-1).
In step 2, she simplifies the right side of the equation to 9+8x-4=5+8x.
In step 3, she subtracts 8x from both sides of the equation to get 4=5.
In step 4, she simplifies the equation to 4=9-4.
In step 5, she mistakenly writes that 4=5, which is incorrect.
Therefore, the correct choice is that Amaya made a mistake because 4 is not equal to 5. So, the correct option is A).
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At a photography contest, entries are scored on a scale from 1 to 100. At a recent contest with 1,000 entries, a score of 68 was at the 77th percentile of the distribution of all the scores. Which of the following is the best description of the 77th percentile of the distribution?a. There were 77% of the entries with a score less than 68.b. There were 77% of the entries with a score greater than 68.c. There were 77% of the entries with a score equal to 68.d. There were 77 entries with a score less than 68.
Answer:
The correct answer is:
a. There were 77% of the entries with a score less than 68.
Step-by-step explanation:
The 77th percentile of the distribution of all the scores means that 77% of the entries had a score lower than 68, and 23% had a score equal to or greater than 68.
So option a is the best description of the 77th percentile. Option b is incorrect because it describes the complement of the 77th percentile (i.e., the percentage of entries with a score greater than 68). Option c is incorrect because it describes a single score,
whereas the percentile refers to a percentage of the distribution. Option d is incorrect because it provides a specific number of entries with a score less than 68, which may or may not be true,
but it doesn't address the percentile of the distribution.
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Hello, can someone answer this for me?
If Amy wants to go to the place that has the highest typical temperature and the least variability, she should visit C. Destin.
Why should she visit Destin?Destin has one of the highest temperatures as it reaches about 95 degrees. This is the second highest of all the places and so can be one of the places to visit.
Destin has a variability (using range) of :
= 95 - 83
= 12 degrees
Pensacola Beach on the other hand, is:
= 98 - 80
= 18 degrees
Destin has the lower variability.
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What is the Y-coordinate of the
point that partitions segment AC
into a 1:2 ratio?
10
9
8
7
6
5
4
3
2
1
A
2 3
5
9
с
7 8
00
The Y-coordinate would be:
B
10
x
The y-coordinate of the point that partitions segment AC into a 1:2 ratio is given as follows:
y = 5.
How to obtain the y-coordinate?The y-coordinate of the point that partitions segment AC into a 1:2 ratio is obtained applying the proportions in the context of the problem.
The segment AC is partitioned into a 1:2 ratio, hence the equation for the coordinates of P are given as follows:
P - A = 1/3(C - A).
The coordinates of A and C are given as follows:
A(1,3) and C(6,9).
Hence the y-coordinate of B is obtained as follows:
y - 3 = 1/3(9 - 3)
y - 3 = 2
y = 5.
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"please answer to one decimal place. 2nd time asking
question
Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 15.7 years and a standard deviation of 1.2 years. If the company wants to provide a warranty so that only 1.5% of the quartz time pieces will be
replaced before the warranty expires, what is the time length of the warranty?
warranty=
years
Enter your answer as a number accurate to 1 decimal place.
The mean replacement time for the quartz timepieces produced by Company XYZ is 15.7 years with a standard deviation of 1.2 years. The company wants to provide a warranty so that only 1.5% of the quartz timepieces will be replaced before the warranty expires.
To find the time length of the warranty, we can use the formula for z-score:
z = (x - μ) / σ
where x is the value, we want to find, μ is the mean, σ is the standard deviation and z is the corresponding z-score.
We can use a z-score table or calculator to find that the z-score corresponding to 1.5% is approximately -2.33.
-2.33 = (x - 15.7) / 1.2
Solving for x gives:
x = 13.9 years (rounded to one decimal place)
Therefore, Company XYZ should provide a warranty of 13.9 years so that only 1.5% of the quartz timepieces will be replaced before the warranty expires.
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WILL GIVE BRAINLIEST PLS ANSWER QUICKLY
Jackson added new baseball cards to his collection each year. The table below shows how many cards Jackson has in his collection over time.
Years Number of cards
2 32
3 48
5 80
7 ?
At this rate, how many cards will Jackson have in 7 years?
82 cards
96 cards
108 cards
112 cards
Jackson will have 112 cards in his collection after 7 years. The Option D is correct.
Howw many cards will Jackson have in 7 years?The difference between the number of cards in year 2 and year 3 is:
= 48 - 32
= 16
Note: Its covers a span of 3 - 2 = 1 year. Therefore, the average number of cards added per year between years 2 and 3 is 16/1 = 16.
Now we can estimate the number of cards Jackson will have in year 7 by stating the following formula:
= Number of cards in year 5 + (Average number of cards added per year) x (Number of years from year 5 to year 7)
= 80 + 16 x (7 - 5)
= 80 + 32
= 112 cards
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his has stock $2,435.51. nts to sell nvest in priced at Bruno is ed $25 by his proker every he buys or stock. How new shares runo buy by ng in his old ? EXAMPLE Step 1 Geraldo has $1,000.00 to invest. He likes a stock selling for $52.50. How many shares could he purchase? Find the cost. Estimate. $52.50 = $50 1,000 $20 50 About 20 shares Step 2 Divide $1,000.00 by the cost per share. Discard the remainder. Step 3 Multiply the cost $ 52.50 Cost per share per share by the X 19 number of shares $997.50 purchased. Number of shares Total cost Money Available 1. $1,000.00 2. $1,500.00 3. $800.00 4. $600.00 5. $3,000.00 6. $1,800.00 7. $4,000.00 8. $100.00 9. $75.00 19. 52.5.)1000.0 525 Exercise F For each amount available, compute the number of shares that can be purchased. Then compute the total cost. Cost Total per Share Cost $20.25 $12.75 $9.75 $1.63 475 0 -472 5 25 Number of Shares $3.25 $16.75 $26.12 $4.25 $0.63
Answer:
Step-by-step explanation:
a = b - 7000
0.05a + 0.07b = 1690
Since we have a "value" for a, we can substitute that "value" in place of a.
0.05(b - 7000) + 0.07b = 1690
0.05b - 350 + 0.07b = 1690
0.12b = 2040
b = $17,000
troy has an album that holds 900 stamps . Each page of the album holds 9 . If 72% of the album is empty, how many pages are filled with stamps ?
The pages that are filled with stamps are 252
How many pages are filled with stamps ?From the question, we have the following parameters that can be used in our computation:
Stamps = 900
Empty = 72%
Using the above as a guide, we have the following:
Filled = (1 - Empty) * Stamps
So, we have
Filled = (1 - 72%) * 900
Evaluate
Filled = 252
Hence, 252 are filled
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Algo An economist would like to estimate the 99% confidence interval for the average real estate taxes collected by a small town in California. In a prior analysis, the standard deviation of real estate taxes was reported as $1,330. (You may find it useful to reference the z table.) What is the minimum sample size required by the economist if he wants to restrict the margin of error to $480? (Round up final answer to nearest whole number.)
The minimum sample size required by the economist, if he wants to restrict the margin of error to $480, is 37.
To determine the minimum sample size required to estimate the 99% confidence interval for the average real estate taxes collected by a small town in California with a margin of error of $480, we can use the formula:
[tex]n = \frac{[(z-value)^2 (standard deviation)^2] }{(margin of error)^2}[/tex]
The z-value for a 99% confidence interval is 2.576 (using the z table), and the standard deviation of real estate taxes is $1,330.
Plugging in these values, we get:
[tex]n = \frac{[(2.576)^2 (1,330)^2] }{(480)^2}[/tex]
n = 36.54
Rounding up to the nearest whole number, the minimum sample size required is 37.
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keegan has 30 dollars to spend on pita wraps and bubble tea pita is 6 bubble tea is 3 what is keegans optimal consumption bundle
To find Keegan's optimal consumption bundle of pita wraps and bubble tea, we need to determine the combination that maximizes his utility while staying within his budget of $30. The price of a pita wrap is $6, and the price of a bubble tea is $3.
Step 1: Calculate the maximum quantity of each item Keegan can buy with his budget.
- Pita wraps: $30 / $6 = 5 wraps
- Bubble teas: $30 / $3 = 10 bubble teas
Step 2: List all possible combinations of pita wraps and bubble teas within the budget.
1. 0 wraps and 10 bubble teas
2. 1 wrap and 8 bubble teas
3. 2 wraps and 6 bubble teas
4. 3 wraps and 4 bubble teas
5. 4 wraps and 2 bubble teas
6. 5 wraps and 0 bubble teas
Step 3: Determine the optimal consumption bundle.
Without information about Keegan's preferences, we cannot definitively determine his optimal consumption bundle. However, these six combinations represent all possible bundles that Keegan can purchase with his $30 budget. Keegan's optimal consumption bundle would depend on his personal preferences for pita wraps and bubble teas.
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i need help i have to get it done by 11:00 pleasee!!
The area of each of the semicircle is approximately:
a. 9.82 in.² b. 16.08 in.²
What is the Area of a Semicircle?A semicircle is half of a full circle. Therefore, the formula to find the area of a semicircle would be:
Area = 1/2(πr²), where r is the radius of the semicircle.
a. The parameters given are:
Diameter = 5 in.
Radius (r) = 5/2 = 2.5 in.
Area of the semicircle = 1/2(π * 2.5²) ≈ 9.82 in.²
b. The parameters given are:
Diameter = 6.4 in.
Radius (r) = 6.4/2 = 3.2 in.
Area of the semicircle = 1/2(π * 3.2²) ≈ 16.08 in.²
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one-way anova is applied to independent samples taken from three normally distributed populations with equal variances. which of the following is the null hypothesis for this procedure?
One-way ANOVA is applied to independent samples taken from three normally distributed populations with equal variances. The null hypothesis for this procedure is:
H0: μ1 = μ2 = μ3
This means that there are no significant differences between the means of the three normally distributed populations.
One-way ANOVA: One-way ANOVA is a statistical test used to compare the means of three or more independent groups.
Null hypothesis: The null hypothesis for one-way ANOVA is that the means of all the groups are equal.
Alternative hypothesis: The alternative hypothesis, which is accepted if the null hypothesis is rejected, is that at least one of the population means is different from the others.
In this case, the alternative hypothesis is: Ha: At least one of the means is different Test statistic: The test statistic used in one-way ANOVA is the F-statistic.
A small p-value (usually less than 0.05) indicates strong evidence against the null hypothesis.
Decision: If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that at least one of the population means is different from the others.
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prove the average degree in a tree is always less than 2. more specifically express this average as a function of the number of vertices in tree.
we have proven that the average degree in a tree is always less than 2.
To prove that the average degree in a tree is always less than 2, we need to first understand what a tree is. A tree is an undirected graph that is connected and acyclic, meaning it does not contain any cycles. Each node in a tree has exactly one parent, except for the root node, which has no parent. The degree of a node in a tree is the number of edges that are connected to it. For the root node, its degree is equal to the number of edges that are connected to its children.
Now, let's consider a tree with n vertices. The total number of edges in a tree is always n-1, since each node except the root node has exactly one incoming edge, and the root node has no incoming edges. Therefore, the sum of the degrees of all the nodes in a tree with n vertices is equal to 2(n-1), since each edge is counted twice, once for each of the nodes it connects.
If we let d_i denote the degree of the i-th node in the tree, then the average degree of the tree can be expressed as:
(1/n) * sum(d_i) = (1/n) * 2(n-1)
Simplifying the right-hand side, we get:
(1/n) * 2(n-1) = 2 - (2/n)
As n approaches infinity, the average degree approaches 2, but for any finite value of n, the average degree is always less than 2. Therefore, we have proven that the average degree in a tree is always less than 2.
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Sandstone Middle School installed new lockers over the summer. The lockers are shaped like rectangular prisms. Each one has a volume of 7 and one over two
cubic feet and is 1 foot deep and 6 feet tall.
Which equation can you use to find the width of each locker, w?
What is the width of each locker?
Write your answer as a whole number, proper fraction, or mixed number.
The width of each locker is 1 1/4 foot.
We have,
Length = 1 foot
Volume = 7 1/2 cubic feet
Height = 6 foot
So, Volume of Prism = l w h
7 1/2 = (1) w (6)
15/2 = 6w
w= 15/(2 x 6)
w = 5/4
w= 1 1/4 foot
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A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%.
The p-value is
A. 0.2112
B. 0.05
C. 0.025
D. 0.1251
The correct answer is D. 0.1251.
To determine the p-value, we need to perform a hypothesis test.
Step 1: State the null and alternative hypotheses.
The null hypothesis is that the proportion of the population in favor of Candidate A is 75%.
H0: p = 0.75
The alternative hypothesis is that the proportion of the population in favor of Candidate A is significantly more than 75%.
Ha: p > 0.75
Step 2: Determine the level of significance (alpha).
We are not given a level of significance in the problem statement, so we will assume a level of significance of 0.05.
Step 3: Calculate the test statistic.
We will use the sample proportion, P, to calculate the test statistic:
P = 80/100 = 0.8
The sample size is n = 100, so the standard error of the sample proportion is:
SE = sqrt[p(1-p)/n]
SE = sqrt[0.75(1-0.75)/100]
SE = 0.0433
The test statistic is:
z = (P - p) / SE
z = (0.8 - 0.75) / 0.0433
z = 1.15
Step 4: Calculate the p-value.
We will use the standard normal distribution to calculate the p-value:
p-value = P(Z > 1.15)
p-value = 0.1251
Step 5: Make a decision and interpret the results.
Since the p-value (0.1251) is greater than the level of significance (0.05), we fail to reject the null hypothesis. This means that we do not have sufficient evidence to conclude that the proportion of the population in favor of Candidate A is significantly more than 75%.
Therefore, the correct answer is D. 0.1251.
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In a study of brain wave activity, the group of 14 students that did not consume any wine had an average brain wave activity of 6.857 (Hz) with a standard deviation of 3.367 (Hz). Assume that the simple conditions apply. 3 pts. a) Construct a 99% confidence interval for the average brain wave activity 1 pt.
b) Compute the margin of error for this interval. 1 pt. c) Interpret this interval in context of the problem.
The margin of error is approximately 3.281 Hz, which means that if we were to repeat this study many times, we would expect the sample mean to be within 3.281 Hz of the true population mean in 99% of the studies.
a) The 99% confidence interval can be calculated as:
lower bound = x - t(α/2, n-1) * s/√n
upper bound = x + t(α/2, n-1) * s/√n
where x is the sample mean, s is the sample standard deviation, n is the sample size, and t(α/2, n-1) is the t-score for the given confidence level and degrees of freedom.
Substituting the given values, we get:
lower bound = 6.857 - t(0.005, 13) * 3.367/√14 ≈ 3.576
upper bound = 6.857 + t(0.005, 13) * 3.367/√14 ≈ 10.138
Therefore, the 99% confidence interval for the average brain wave activity is (3.576, 10.138).
b) The margin of error is given by the formula:
margin of error = t(α/2, n-1) * s/√n
Substituting the given values, we get:
margin of error = t(0.005, 13) * 3.367/√14 ≈ 3.281
Therefore, the margin of error for this interval is approximately 3.281.
c) We can interpret this interval as follows: we are 99% confident that the true average brain wave activity of the population of students who did not consume any wine is between 3.576 Hz and 10.138 Hz. The margin of error is approximately 3.281 Hz, which means that if we were to repeat this study many times, we would expect the sample mean to be within 3.281 Hz of the true population mean in 99% of the studies.
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