A sample size of 188 would be needed to achieve a 6% margin of error at a 90% confidence level.
Used the formula for sample size calculation:
[tex]n = \dfrac{z^2 \times p (1 - p)}{E^2}[/tex]
Where: n = sample size.
Z = Z-score corresponding to the desired confidence level.
p = estimated proportion of the population that supports the candidate.
E = desired margin of error.
Here we have to give that,
90% confidence level corresponds to a Z-score of approximately 1.645.
That is, z = 1.645
p = 0.5
E = 0.06
Substituting the given values into the formula, we get:
[tex]n = \dfrac{z^2 \times p (1 - p)}{E^2}[/tex]
[tex]n = \dfrac{(1.645)^2 \times 0.5(1 - 0.5)}{0.06^2}[/tex]
[tex]n = \dfrac{0.6765}{0.0036}[/tex]
[tex]n =187.9[/tex]
Rounded to whole numbers,
[tex]n = 188[/tex]
Therefore, the size of the sample would be 188.
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In order to achieve a 6% margin of error and a 90% confidence level in a poll, the correct sample size must be determined using the error bound formula. A larger and representative sample will minimize the margin of error and improve the poll's precision and accuracy. A number of key factors, like identification of the target population and select a random sample, should be considered while conducting a poll.
Explanation:The subject matter dealt with here involves conducting a poll to gauge public opinion, with a desired accuracy defined by a 6% margin of error and a 90% confidence level. This is primarily related to Statistics, a branch of Mathematics.
To determine an appropriate sample size for a given margin of error and confidence level, the error bound formula is utilized. Although the actual formula could appear complex for some, many online calculators can complete the task. The 90% confidence level means that if we were to take multiple sets of samples, roughly 90% of the calculated confidence intervals would contain the true population mean or proportion.
Furthermore, sample size influences the margin of error; a larger sample reduces the margin of error and makes the poll result more precise and accurate. As a rule of thumb, the sample should be random and representative of the population in question to ensure the accuracy and reliability of poll results.
Take note that many criteria must be met to conduct a valid and scientifically accurate poll, some of which include: identifying the desired population of respondents, ensuring the sample is both random and representative of the wider population, and interviewing a sufficient number of citizens to achieve a reasonable sample size.
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Suppose a number is chosen at random from the set {0,1,2,3,...,1721}. What is the probability that the number is a perfect cube?
Round your answer to 6 decimal places as needed.
========================================================
Explanation:
One way to go about this is to list out all the perfect cubes. A perfect cube is the result of taking any whole number and multiplying it by itself 3 times.
1 cubed = 1^3 = 1*1*1 = 1
2 cubed = 2^3 = 2*2*2 = 8
3 cubed = 3^3 = 3*3*3 = 27
4 cubed = 4^3 = 4*4*4 = 64
and so on. We stop once we reach 1721, or if we go over. Ignore any values larger than 1721. You'll find that 11^3 = 1331 and 12^3 = 1728. So we stop here and exclude 1728 as that is larger than 1721.
A quick way to see where we should stop is to apply the cube root to 1721 and we get
[tex]\sqrt[3]{1721} = 1721^{1/3} \approx 11.98377[/tex]
The approximate result of 11.98377 tells us that 1721 is between the perfect cubes of 11^3 = 1331 and 12^3 = 1728
------------------
So effectively, we have 11 perfect cubes in the set {0, 1, 2, 3, ..., 1721} and this is out of 1722 numbers in that same set. Note how I added 1 onto 1721 to get 1722. I'm adding an extra number because of the 0. If 0 wasn't part of the set, then we would have 1721 values total inside.
In summary: There are 11 values we want (11 perfect cubes) out of 1722 values total.
Divide 11 over 1722 to get
11/1722 = 0.00638792102207
which rounds to 0.006388
The probability of randomly selecting a perfect cube from the set {0,1,2,...,1721} is calculated by finding the ratio of the number of favorable outcomes (perfect cubes in this range) to the total number of outcomes. We have 12 perfect cubes and 1722 total numbers, giving us a probability of approximately 0.006964.
Explanation:The subject of this question is probability, a concept in mathematics. A perfect cube is a number that can be expressed as the cube of an integer.For instance, the numbers 1 (13), 8 (23), 27 (33), and so forth, are perfect cubes.
In this case, we need to find how many perfect cubes exist between 0 and 1721. The cube of 12 is 1728, which is greater than 1721 so, we can conclude that the largest whole number whose cube is less than 1721 is 11. This means there are 12 (perfect cubes) numbers from 0 to 1721 (0 included).
The total amount of numbers in this range is 1722 (from 0 to 1721 inclusive). Therefore, the probability of randomly selecting a perfect cube from this range is the ratio of the number of favorable outcomes (perfect cubes) to the total number of outcomes:
P(perfect cube) = Number of perfect cubes /Total numbers
P(perfect cube) = 12/1722 ≈ 0.006964.
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A 4.5 pound bag of apples cost $22.50. What is the unit price?
Answer:
The unit price is $5.
Answer:
$5.00.
Step-by-step explanation:
This is 22.5 / 4.5
= $5.00
Belsky, Weinraub, Owen, and Kelly (2001) reported on the effects of preschool childcare on the development of young children. One result suggests that children who spend more time away from their mothers are more likely to show behavioral problems in kindergarten. Using a standardized scale, the average rating of behavioral problems for kindergarten children is µ = 35. A sample of n = 16 kindergarten children who had spent at least 20 hours per week in child care during the previous year produced a mean score of M=42.7 with a standard deviation of s=6. (a) Are the data sufficient to conclude that children with a history of child care show significantly more behavioral problems than the average kindergarten child? Use a one-tail test with α = .01. (b) Compute the 90% confidence interval for the mean rating of behavioral problems for the population of kindergarten children who have a history of child care.
Answer:
Step-by-step explanation:
a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 35
For the alternative hypothesis,
µ > 35
It is a right tailed test
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 16,
Degrees of freedom, df = n - 1 = 16 - 1 = 15
t = (x - µ)/(s/√n)
Where
x = sample mean = 42.7
µ = population mean = 32
s = samples standard deviation = 6
t = (42.7 - 32)/(6/√16) = 7.13
We would determine the p value using the t test calculator. It becomes
p = 0.00001
Since alpha, 0.01 > than the p value, 0.00001, then we would reject the null hypothesis. Therefore, At a 1% level of significance, there is sufficient data to conclude that children with a history of child care show significantly more behavioral problems than the average kindergarten child
b) Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
the information given, the from population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
In order to use the t distribution,
Since confidence level = 90% = 0.95, α = 1 - CL = 1 – 0.90 = 0.1
α/2 = 0.1/2 = 0.05
the area to the left of z0.05 is 0.05 and the area to the right of z0.05 is 1 - 0.05 = 0.95
Looking at the t distribution table for t.95 and df = 15
z = 1.753
Margin of error = 1.753 × 6/√16
= 2.63
Confidence interval = 35 ± 2.63
you work in the HR department at a large franchise. you want to test whether you have set your employee monthly allowances correctly. the population standard deviation is 150. You want to test if the monthly allowances should be increased. A random sample of 40 employees yielded a mean monthly claim of $640.
1- at the 1% significance level, test if the average monthly allowances should be greater than 500(use the 5 steps hypothesis testing procedure)
2- Confirm your answer by the p value approach.
Answer:
1) Null hypothesis:[tex]\mu \leq 500[/tex]
Alternative hypothesis:[tex]\mu > 500[/tex]
[tex]z=\frac{640-500}{\frac{150}{\sqrt{40}}}=5.90[/tex]
For this case since we are conducting a right tailed test we need to find a critical value in the normal standard distribution who accumulates 0.01 of the area in the right and we got:
[tex]z_{crit}= 2.33[/tex]
For this case we see that the calculated value is higher than the critical value
Since the calculated value is higher than the critical value we have enugh evidence to reject the null hypothesis at 1% of significance level
2) Since is a right tailed test the p value would be:
[tex]p_v =P(z>5.90)=1.82x10^{-9}[/tex]
If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, same conclusion for part 1
Step-by-step explanation:
Part 1
Data given
[tex]\bar X=640[/tex] represent the sample mean
[tex]\sigma=150[/tex] represent the population standard deviation
[tex]n=40[/tex] sample size
[tex]\mu_o =500[/tex] represent the value that we want to test
[tex]\alpha=0.01[/tex] represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
Step1:State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean is higher than 500, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 500[/tex]
Alternative hypothesis:[tex]\mu > 500[/tex]
Step 2: Calculate the statistic
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
We can replace in formula (1) the info given like this:
[tex]z=\frac{640-500}{\frac{150}{\sqrt{40}}}=5.90[/tex]
Step 3: Calculate the critical value
For this case since we are conducting a right tailed test we need to find a critical value in the normal standard distribution who accumulates 0.01 of the area in the right and we got:
[tex]z_{crit}= 2.33[/tex]
Step 4: Compare the statistic with the critical value
For this case we see that the calculated value is higher than the critical value
Step 5: Decision
Since the calculated value is higher than the critical value we have enugh evidence to reject the null hypothesis at 1% of significance level
Part 2
P-value
Since is a right tailed test the p value would be:
[tex]p_v =P(z>5.90)=1.82x10^{-9}[/tex]
If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, same conclusion for part 1
Reduce the following lambda-calculus term to the normal form. Show all intermediate steps, with one beta reduction at a time. In the reduction, assume that you are supplied with extra rules that allow you to reduce the multiplication of two natural numbers into the corresponding result.
(λf. λx. f (f x)) (λy. Y * 3) 2
Answer:
Step-by-step explanation:
Reduction to normal from using lambda-reduction:
The given lambda - calculus terms is, (λf. λx. f (f x)) (λy. Y * 3) 2
For the term, (λy. Y * 3) 2, we can substitute the value to the function.
Therefore, applying beta- reduction on "(λy. Y * 3) 2" will return 2*3= 6
So the term becomes,(λf. λx. f (f x)) 6
The first term, (λf. λx. f (f x)) takes a function and an argument, and substitute the argument in the function.
Here it is given that it is possible to substitute the resulting multiplication in the result.
Therefore by applying next level beta - reduction, the term becomes f(f(f(6)) (f x)) which is in normal form.
An evergreen nursery usually sells a certain shrub after 7 years of growth and shaping. The growth rate during those 7 years is approximated by dh/dt = 1.3t + 2, where t is the time in years and h is the height in centimeters. The seedlings are 17 centimeters tall when planted (t = 0). (a) Find the height after t years. h(t) = (b) How tall are the shrubs when they are sold? cm
The height of the shrubs is modeled by the function h(t) = 0.65t² + 2t + 17. After 7 years, the shrubs are 52.85 cm tall when they are sold.
Explanation:The height (h) of a shrub after t years can be found by integrating the given growth rate function dh/dt = 1.3t + 2 with respect to time t. Given the initial height (or the initial condition), h(0) = 17 cm, the function turns out to be an integral taking initial condition into account:
h(t) = ∫ (1.3t + 2) dt + h(0)
After performing the integration, the function for height turns out to be:
[tex]h(t) = 0.65t^2 + 2t + 17[/tex]
Therefore, the height of the shrubs when they are sold (at t=7 years) can be found by substituting t=7 into the height function h(t).
[tex]h(7) = 0.65 * 7^2 + 2 * 7 + 17 = 52.85 cm[/tex]
So, the shrubs are 52.85 cm tall when they are sold.
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(a). The height of the shrub after t years is given by the function h(t) = (1.3/2)[tex]t^{2}[/tex] + 2t + 17.
(b). After 7 years, the shrubs reach a height of 62.85 cm.
Let's solve the given problem step-by-step:
(a)
The growth rate of the shrub is given by the differential equation dh/dt = 1.3t + 2. To find the height function h(t), we need to integrate this equation with respect to t.
1. We have:
dh/dt = 1.3t + 2
2. Integrating both sides with respect to t,
∫(dh) = ∫(1.3t + 2) dt
h(t) = (1.3/2)[tex]t^{2}[/tex]+ 2t + C
3. Where C is the constant of integration. To find C, we use the initial condition: h(0) = 17.
So:
17 = (1.3/2)[tex]0^{2}[/tex] + 2(0) + C
C = 17
4.Thus, the height function is:
h(t) = (1.3/2)[tex]t^{2}[/tex] + 2t + 17
(b)
To find the height after 7 years, we substitute t = 7 into the height function:
h(7) = (1.3/2)[tex]7^{2}[/tex] + 2(7) + 17
h(7) = (1.3/2)(49) + 14 + 17
h(7) = 31.85 + 14 + 17
h(7) = 62.85
Therefore, the shrubs are 62.85 cm tall when they are sold.
Given: g ∥ h and ∠2 ≅ ∠3
Prove: e ∥ f
Horizontal and parallel lines e and f are intersected by diagonal and parallel lines g and h. At the intersection of lines g and e, the bottom right angle is angle 2. At the intersection of lines h and e, the bottom right angle is angle 1. At the intersection of lines f and h, the top left angle is angle 3.
Statements Reasons
1. g || h 1. given
2. ∠1 ≅ ∠2 2. corresponding angles theorm
3. ∠2 ≅ ∠3 3. given
4. ∠1 ≅ ∠3 4. transitive property
5. e || f 5. ?
What is the missing reason in the proof?
vertical angles theorem
alternate exterior angles theorem
converse corresponding angles theorem
converse alternate interior angles theorem
Answer:
In the image, you can observe a diagram representing this problem.
We know by given that [tex]g \parallel h[/tex] and [tex]\angle 2 \cong \angle 3[/tex].
From the parallelism between line g and line h, we deduct several congruence between angles.
[tex]\angle 2 \cong \angle 1[/tex], by corresponding angles (same side of the transversal, one interior, the other exterior to parallels).
Now, to demonstrate [tex]e \parallel f[/tex], we must demonstrate a congruence between angle 2 and an angle on the intersection between line g and line f.
In the parallelogram formed, we know
[tex]\angle 2 + \angle 3+ 180-\angle 1 + x =360[/tex]
Where [tex]x[/tex] is the angle at the intersection line g and line f.
But, we know [tex]\angle 2 \cong \angle 3[/tex] and [tex]\angle 2 \cong \angle 1[/tex], so
[tex]\angle 2 + \angle 2 +180 - \angle 2 +x=360\\\angle 2 + x=180[/tex]
Notice that we don't have a congruence, however there's theorem which states that the same-side interior angles of parallels are supplementary.
In this case, we use the corolary of that theorem, which states if two same-side interior angles are supplementary, then the lines are parallels.
[tex]\therefore e \parallel f[/tex]
However, according to the choices of the problem, the missin proof is "converse alternate interior angles theorem", because the problem was demonstrate using transitive property, to show that angles 1 and 3 are congruent, there by converse alternate interior angles theorem, lines e and f are parallels.
This is the same case we used, but using converse alternate interior angles theorem.
Answer:
the answer is c-
Step-by-step explanation:
converse alternate interior angles theorem
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On Friday a local hamburger shop sold a combined total of 564 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold?
Answer:
I believe it's 188
Step-by-step explanation:
If there was a total of 564 and the cheeseburgers was three times the amount, you need to divide 564 by 3. 564 divided by 3 equals to 188. I am pretty sure this could be the correct answer!
Prove that the diagonals of a parallelogram bisect each other.
Name the coordinates for point C.
A: (2a, 2b + 2c)
B: (2a, 2b)
C: (2a, 2c)
D: (2a + 2b, 2c)
Answer:2a + 2b, 2c
Step-by-step explanation:
B / 3 - 6 equals 9.
Answer:
B = 45
Step-by-step explanation:
B/3 - 6 = 9
B/3 = 15
B = 45
Tell me if I am wrong.
Can I get brainliest
suppose that y is directly proportional to x and y = 150 when x = 15 what is the constant of proportional
Answer:
10
Step-by-step explanation:
hope it helps
A procurement specialist has purchased 23 resistors from vendor 1 and 30 resistors from vendor 2. Let represent the vendor 1 observed resistances, which are assumed to be normally and independently distributed with mean 120 ohms and standard deviation 1.7 ohms. Similarly, let represent the vendor 2 observed resistances, which are assumed to be normally and independently distributed with mean 125 ohms and standard deviation of 2.0 ohms. What is the sampling distribution of ? What is the standard error of ? The sampling distribution of is What is thesampling distribution of X1 − X2? What is the standard errorof X1 − X2?
Answer:
The standard error( X1 − X2 ) = 0.547
Step-by-step explanation:
Step:-(1)
Given a procurement specialist has purchased 23 resistors
Given normally and independently distributed with mean 120 ohms and standard deviation 1.7
mean of the Population of the vendor 1 is μ₁ = 120 ohms
Standard deviation of the Population the vendor 1 is σ₁ = 1.7 ohms
similarly represent the vendor 2 observed resistances, which are assumed to be normally and independently distributed with mean 125 ohms and standard deviation of 2.0
mean of the Population of the vendor 2 is μ₂ = 120 ohms
Standard deviation of the Population the vendor 2 is σ₂ = 1.7 ohms
The standard error of the difference of two means
Se( X1 − X2) = [tex]\sqrt{\frac{σ^2_{1} }{n_{1} } +\frac{σ^2_{2} }{n_{1} } }[/tex]
Here σ₁ = 1.7 ohms and σ₂ = 2 ohms and n₁=n₂ =n = 23 resistors
se(X1 − X2) = [tex]\sqrt{\frac{1.7^2}{23 } +\frac{2^2 }{23} }[/tex]
se(X1 − X2) = √0.2995
= 0.547
Conclusion:-
The standard error of X1 − X2 = 0.547
Final answer:
Explains the standard error of sample means for two vendors and the distribution of sample means.
Explanation:
The standard error of the sample mean in this scenario, rounded to two decimal places, is calculated as follows:
For vendor 1: standard error = 1.7 / sqrt(23)
For vendor 2: standard error = 2.0 / sqrt(30)
The distribution of the sample mean X: Since the sample means are normally distributed, the sampling distribution of X is approximately normal.
The standard error of X1 − X2: The standard error of the difference between sample means X1 and X2 is calculated using the formula for the standard error of the difference between two independent sample means.
A surveyor wishes to lay out a square region with each side having length L. However, because of measurement error, he instead lays out a rectangle in which the north-south sides both have length X and the east-west sides both have length Y. Suppose that X and Y are independent and that each is uniformly distributed on the interval [L − A, L + A] (where 0 < A < L). What is the expected area of the resulting rectangle?
Step-by-step explanation:
Area, A = Length,x × Breadth,y
A=xy
When x and y are independent, E(xy) = E(x)E(y)
As x and y have the same distribution, U[L-A,L+A], they have the same mean.
We could argue by symmetry that E(x) = L and E(y) + L, also.
We can also reason this from the fact that, if X ~ U[L-A, L+A], f(x) = 1/(2A) from L-A to L+A
Therefore
[tex]E(x)= \int\limits {f(x)} \, dx \\\\=\int\limits^{(L+A)}_{(L-A)} {\frac{1}{2A}x } \, dx[/tex]
[tex]=\int\limits^{(L+A)}_{(L-A)} {\frac{1}{2A}x } \, dx \\\\=[\frac{1}{4A}x^2 ]\limits^{(L+A)}_{(L-A)}[/tex]
=1/(4A)(L+A)2 - 1/(4A)(L-A)2
= 1/(4A)(L2 + 2AL + A2) - 1/(4A)(L2 - 2AL + A2)
=1/(4A)(2AL+2AL)
= 1/(4A)(4AL)
= L
Thus, E(xy) = E(x)E(y) = L×L = L²
Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 10 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following results were obtained: SST = 10,800. SSTR = 4560. Set up the ANOVA table for this problem. Using alpha = .05. test for any significant difference in the means for the three assembly methods.
Answer:
During the test for any significant difference in the means for the three assembly methods, there is significant evidence to reject the claim of equal population means
Step-by-step explanation:
Let;
SS be sum of square
MS be Mean Square
d.f be degree of freedom
trt be treatment
w be workers
Pls see attached files for detail step by step solutions as typing the explanation is not possible because of tables involved.
Using a one-way ANOVA test, it is determined that at least one of the assembly methods differs significantly from the others in terms of units assembled correctly by the randomly assigned workers.
Explanation:The question involves the use of a one-way Analysis of Variance (ANOVA) to explore any significant difference in the means of the three proposed assembly methods. The given data are: SST (Total Sum of Squares) = 10800, SSTR (Sum of Squares between groups) = 4560. We can calculate SSE (Sum of Squares within groups) using the formula: SSE = SST - SSTR, which gives 10800 - 4560 = 6240.
The degrees of freedom (df) for between groups is k - 1 = 3 - 1 = 2 (where k is the number of groups). Similarly, the total degrees of freedom is n - 1 = 30 - 1 = 29 (where n is the total number of observations). The within groups degrees of freedom is df(total) - df(between) = 29 - 2 = 27.
Next, calculate Mean Square Between (MSB) = SSTR/df(between) = 4560/2 = 2280 and Mean Square Error (MSE) = SSE/df(within) = 6240/27 = 231.112. The F-statistic is given by F = MSB/MSE = 2280/231.112 = 9.869.
For a one-way ANOVA test at alpha = .05 with df(between) = 2 and df(within) = 27, checking an F distribution table, the critical value of F is approximately 3.354. Since our calculated F(9.869) > F critical(3.354), there is evidence to reject the null hypothesis. This indicates that at least one assembly method has a significantly different mean than the others.
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Which of the following is not an example of primary data?
A. Financial data tapes that contain data compiled from the New York Stock Exchange
B. Data published by the New York Stock Exchange
C. Data published by the U.S. Census Bureau
D. Data published by Statistics Canada
Answer:
A. Financial data tapes that contain data compiled from the New York Stock
Step-by-step explanation:
Primary data is data that is collected by a researcher from first-hand sources. Data published by the New York Stock Exchange is primary data, which inherently makes the data tapes secondary data, because they contain the data from a source other than original source.
shareholdings in Tazon Insurance by Country ( As of April in Year 1) Total number of shares: 45 million. Germany 15% France 10% Switzerland 8% Other 14% Treasury Stock 5% IS 30% UK 18% if each share had a market value of $30 in April year 1, what was the total value of the German shareholding?
The total value of the German shareholding is 202500 million dollars.
Given that, the total number of shares is 45 million.
We need to find the total value of the German shareholding.
How to calculate the total value of share holding?Determine the company's earnings per share.Add the company's stock price to its EPS to determine your shareholder value on a per-share basis.Multiply the per-share shareholder value by the number of shares in the company you own.Germany holds 15% of the shares, which is 15% of 45 million
=15/100×45000000=67,50,000
Number of shares Germany holds=67,50,000
Now, the total value of the German shares=67,50,000×30=$20,25,00,000
Therefore, the total value of the German shareholding is 202500 million dollars.
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Final answer:
The total value of the German shareholding in Tazon Insurance is $202.5 million as of April in Year 1.
Explanation:
The student is asking for the calculation of the total value of German shareholdings in Tazon Insurance when each share is valued at $30. To find this, we need to calculate the number of shares held by Germany and then multiply by the share price.
Calculate the number of shares held by Germany: 45 million shares * 15% = 6.75 million shares.Multiply the number of shares by the market value: 6.75 million shares * $30/share = $202.5 million.Therefore, the total value of the German shareholding in Tazon Insurance is $202.5 million as of April in Year 1.
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Step-by-step explanation:
R'(x) = 5x³ − 60x²
A) R"(x) = 15x² − 120x
0 = 15x² − 120x
0 = 15x (x − 8)
x = 0 or 8
B) R"(-1) = 135
R"(1) = -105
R"(x) changes signs around x = 0, so x = 0 is an inflection point.
R"(7) = -105
R"(9) = 135
R"(x) changes signs around x = 8, so x = 8 is an inflection point.
Which two figures have the same number of lateral faces?
Answer:
Cube and cuboid
Both have 6 faces
Answer:
Cube and cuboid
Both have 6 faces
Complete the recursive formula of the arithmetic sequence 1, 15, 29, 43, ....
a(1) =
a(n) = a(n − 1)+
Answer:
a(1)=1
a(n)=a(n-1)+14
Step-by-step explanation:
The first term is 1, so a(1) = 1
Now, the second term, n=2 which means a(2)=a(1)+x
a(2)=1+x
also a(2)=15, then 1+x=15, and x=14
We can also check using a(3), a(4), and it fits.
The recursive formula of the arithmetic sequence is a(n) = a(n − 1) + 14.
What is an arithmetic sequence?There are two definitions for an arithmetic sequence. It is a "series where the differences between every two succeeding terms are the same" or "each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term."
Given arithmetic sequence 1, 15, 29, 43, ....
the first term of the sequence is 1
a(1) = 1
and formula a(n) = a(n − 1) + x
the second term is 15
a(2) = 15 and n = 2
substitute in formula
a(n) = a(n − 1) + x
a(2) = a(2 - 1) + x
15 = a(1) + x
15 = 1 + x
x = 14
so formula is a(n) = a(n − 1) + 14
check for n = 3
a(3) = a(3 - 1) + 14
a(3) = a(2) + 14
a(3) = 15 + 14 = 26
Hence the formula is a(n) = a(n − 1) + 14
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You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately σ = 79.5 σ=79.5 dollars. You would like to be 90% confident that your estimate is within 4 dollar(s) of average spending on the birthday parties. How many parents do you have to sample?
Answer:
We need to sample at least 1069 parents.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
How many parents do you have to sample?
We need to sample at least n parents.
n is found when [tex]M = 4, \sigma = 79.5[/tex]. So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]4 = 1.645*\frac{79.5}{\sqrt{n}}[/tex]
[tex]4\sqrt{n} = 1.645*79.5[/tex]
[tex]\sqrt{n} = \frac{1.645*79.5}{4}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.645*79.5}{4})^{2}[/tex]
[tex]n = 1068.92[/tex]
Rounding up
We need to sample at least 1069 parents.
Answer:
[tex]n=(\frac{1.64(79.5)}{4})^2 =1062.43 \approx 1063[/tex]
So the answer for this case would be n=1063 rounded up to the nearest integer
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=79.5[/tex] represent the population standard deviation
n represent the sample size
Solution to the problem
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =4 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} \sigma}{ME})^2[/tex] (b)
The critical value for 90% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.05;0;1)", and we got [tex]z_{\alpha/2}=1.64[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.64(79.5)}{4})^2 =1062.43 \approx 1063[/tex]
So the answer for this case would be n=1063 rounded up to the nearest integer
A circle has a diameter that measures 8 inches What is the area of the circle to the nearest 10th use 3.14 for pi
The area of a circle can be calculated by formula πr^2...
radius(r)=4inches
therefore,
Area(A)=3.14×4
=12.56
Final answer:
To calculate the area of a circle with an 8-inch diameter using 3.14 for π, the formula A = πr² gives us 50.24 square inches, which rounds to 50.2 square inches to the nearest tenth.
Explanation:
The student is asking for the area of a circle with a diameter of 8 inches using 3.14 for π (Pi). The area of a circle is given by the formula A = πr², where 'r' is the radius of the circle. Since the diameter is twice the radius, we have that the radius 'r' is 4 inches (half of 8 inches). Plugging this into the formula we get A = 3.14 × 4².
To find the area to the nearest tenth, we perform the calculation: A = 3.14 × 16 = 50.24. Therefore, the area of the circle is 50.2 square inches when rounded to the nearest tenth.
A box contains a red shirt, a blue shirt, a black trouser, and a red trouser. What is the probation choosing the black trouser and the red shirt without replacement?
Answer:
1/12
Step-by-step explanation:
Probability is the result of the number of possible outcome divided by the number of total outcome.
Given that the box contains a red shirt, a blue shirt, a black trouser, and a red trouser, the number of total outcome is
= 1 + 1 + 1 + 1
= 4
The possibility of picking;
a black trouser is
= 1/4
then a red (without replacement, the total outcome drops to 3)
= 1/3
Hence, the probation choosing the black trouser and the red shirt without replacement
= 1/4 * 1/3
= 1/12
Light travels at a speed of about 186,000 miles per second. How far does light travel in 5 second? Use repeated addition to solve.
Answer:
Step-by-step explanation:
The speed of light in a vacuum is 186,282 miles per second (299,792 kilometres per second), and in theory nothing can travel faster than light. In miles per hour, light speed is, well, a lot: about 670,616,629 mph. If you could travel at the speed of light, you could go around the Earth 7.5 times in one second.
186 ,282 x 5 = 931 , 410 for 5 seconds
7/15+(-5/6)
What is the answer and how do I get it?
Answer:
-0.36666666666...
Step-by-step explanation:
not sure how to explain, that's a repeating number.
how much more is 3/8 gallon than 1/4?
Answer: 1/8
Step-by-step explanation: If you convert 1/4 to eighths, it becomes 2/8. 3/8-2/8 is 1/8
A Starbucks coffee costs $4.50. What is the total price if the sales tax rate is 7%?
Answer:
$4.815
Step-by-step explanation:
4.50 x 7/100=0.315
then add 4.50+0.315=4.815
An electronics store is selling a pair of headphones for $82.00. If there is a 7% sales tax, what is the actual cost of the headphones?
Answer:
87.74
Step-by-step explanation:
Please help with this easy 5th grade math! Tysm!
Answer:
5000m
12/3 = 4yd
2kg
8x16 = 128oz
9000ml
20qt
120+23 =143mins
Answer:
5000m
4yd
2kg
128oz
9000ml
20qt
143min
The normal model N(58, 21) describes the distribution of weights of chicken eggs in grams. Suppose that the weight of a randomly selected chicken egg has a z-score of 1.78. What is the weight of this egg in grams
Answer:
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(58,21)[/tex]
Where [tex]\mu=58[/tex] and [tex]\sigma=21[/tex]
The z score for this case is given by this formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
We know that the value of z = 1.78 and we want to estimate the value of X. If we solve for X from the z formula we got:
[tex] X= \mu +1.78 \sigma= 58 +1.78*21= 95.38[/tex]
So the corresponging weight for a z score of 1.78 is 95.38 grams
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(58,21)[/tex]
Where [tex]\mu=58[/tex] and [tex]\sigma=21[/tex]
The z score for this case is given by this formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
We know that the value of z = 1.78 and we want to estimate the value of X. If we solve for X from the z formula we got:
[tex] X= \mu +1.78 \sigma= 58 +1.78*21= 95.38[/tex]
So the corresponging weight for a z score of 1.78 is 95.38 grams
A chicken egg with a z-score of 1.78 in a normal distribution model N(58, 21) will weigh approximately 95.38 grams.
Explanation:The normal model N(58, 21) describes that weights of chicken eggs are normally distributed with a mean of 58 grams and a standard deviation of 21. Given a z-score of 1.78 for a randomly selected egg, we can calculate the egg's weight according to the Z-score formula, 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 z-score.
Let's apply the z-score value to the formula and solve for X:
X = Z.σ + µX = 1.78 * 21 + 58X = 37.38 + 58X = 95.38 grams.
Therefore, the weight of the egg with the z-score of 1.78 is approximately 95.38 grams.
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find the value of two numbers if their sum is 23 and their difference is 1