Answer:
Correct option:
The 95% confidence interval is wider than the 90% confidence interval.
Step-by-step explanation:
The (1 - α)% confidence interval for the population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The width of this interval is:
[tex]W=UL-LL\\=2\times z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The width of the interval is directly proportional to the critical value.
The critical value of a distribution is based on the confidence level.
Higher the confidence level, higher will be critical value.
The z-critical value for 95% and 90% confidence levels are:
[tex]90\%: z_{\alpha /2}=z_{0.05}=1.645\\95\%: z_{\alpha /2}=z_{0.025}=1.96[/tex]
*Use a z-table.
The critical value of z for 95% confidence level is higher than that of 90% confidence level.
So the width of the 95% confidence interval will be more than the 90% confidence interval.
Thus, the correct option is:
"The 95% confidence interval is wider than the 90% confidence interval."
a study examined the effectiveness of an ear molding technique used to correct ear deformities in newborns without the need for surgery. a plastic mold was placed around the deformed ear shortly after birth for about 2 weeks. the study reports that 152 of 158 procedures were successful. what is the sample proportion of successful procedures
Answer:
The sample proportion of successful procedures is 0.962.
Step-by-step explanation:
The sample proportion of successful procedures is the number of successfiç procedures divided by the total number of procedures.
In this problem:
158 procedures, of which 152 were successful. So
p = 152/158 = 0.962
The sample proportion of successful procedures is 0.962.
The sample proportion is the ratio of the number of successes to the total number of samples or trials, Hence, the sample proportion is 0.962
Given the Parameters :
Number of successful procedures, x = 152 Total number of procedures, n = 158The sample proportion can be calculated using the relation :
Sample proportion = x/nSample proportion = 152/158 = 0.962
Hence, the sampling proportion of successful procedures is 0.962.
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If [infinity] cn8n n = 0 is convergent, can we conclude that each of the following series is convergent? (a) [infinity] cn(−3)n n = 0 When compared to the original series, [infinity] cnxn n = 0 , we see that x = here. Since the original for that particular value of x, we know that this . (b) [infinity] cn(−8)n n = 0 When compared to the original series, [infinity] cnxn n = 0 , we see that x = here. Since the original for that particular value of x, we know that this
Answer:
a) we know that this is convergent.
b) we know that this might not converge.
Step-by-step explanation:
Given the [tex]\sum^\infty_{n=0}C_n8^n[/tex] is convergent
Therefore,
(a) [tex]\sum^\infty_{n=0}C_n(-3)^n[/tex] The power series [tex]\sum C_nx^n[/tex] has radius of convergence at least as big as 8. So we definitely know it converges for all x satisfying -8<x≤8. In particular for x = -3
∴ [tex]\sum^\infty_{n=0}C_n(-3)^n[/tex] is convergent.
(b) [tex]\sum^\infty_{n=0}C_n(-8)^n[/tex] -8 could be right on the edge of the interval of convergence, and so might not converge
The convergence of the series ∑ cn(−3)^n and ∑ cn(−8)^n depends on whether the original power series, ∑ cnxn, converges for these specific values of x i.e. x = -3 and x = -8. To determine this, one must apply the Ratio Test or Root Test.
Explanation:This is a question about the convergence of a series in mathematics, particularly power series. For a power series like ∑ cnxn (from n = 0 to infinity), the series converges absolutely for certain values of x. When dealing with the two series in the question, ∑ cn(−3)^n and ∑ cn(−8)^n, we can observe that they are similar to the original power series, with x = -3 and x = -8, respectively.
Now, whether these series will converge or not, strictly depends on the radius of convergence of the original series. If the original series converges for x = -3 and x = -8, then these two series will also converge. Otherwise, they won't.
To determine the range or radius of convergence, you have to use the Ratio Test or Root Test in most cases. These are some standard mathematical methods used to determine whether a given series is convergent or not.
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Find X: 5x=45
A) 9
B) 2
C) 12
D) 0
Answer: [tex]x=9[/tex]
Divide both side by 5
[tex]5x/5=45/5\\x=9[/tex]
Answer:
[tex]x = 9[/tex]
Step-by-step explanation:
[tex]5x = 45 \\ \frac{5x}{5} = \frac{45}{5} \\ x = 9[/tex]
hope this helps you.....
A random sample of 16 students selected from the student body of a large university had an average age of 25 years. We want to determine if the average age of all the students at the university is significantly different from 24. Assume the distribution of the population of ages is normal with a standard deviation of 2 years. At a .05 level of significance, it can be concluded that the mean age is:
Answer:
[tex]z=\frac{25-24}{\frac{2}{\sqrt{16}}}=2[/tex]
[tex]p_v =2*P(Z>2)=0.0455[/tex]
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the true mean differs from 24 at 5% of significance
Step-by-step explanation:
Data given and notation
[tex]\bar X=25[/tex] represent the sample mean
[tex]\sigma=2[/tex] represent the sample population deviation for the sample
[tex]n=16[/tex] sample size
[tex]\mu_o =24[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean is different from 24, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 24[/tex]
Alternative hypothesis:[tex]\mu \neq 24[/tex]
If we analyze the size for the sample is < 30 but we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]z=\frac{25-24}{\frac{2}{\sqrt{16}}}=2[/tex]
P-value
Since is a two sided test the p value would be:
[tex]p_v =2*P(Z>2)=0.0455[/tex]
Conclusion
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the true mean differs from 24 at 5% of significance
A hypothesis test is used to determine if the average age of all the students at the university is significantly different from 24. The test statistic does not fall within the critical region, so we fail to reject the null hypothesis. There is not enough evidence to conclude that the mean age is significantly different from 24.
Explanation:In order to determine if the average age of all the students at the university is significantly different from 24, we can perform a hypothesis test.
Step 1: State the hypotheses:
Null hypothesis (H0): The mean age is 24.Alternate hypothesis (Ha): The mean age is not equal to 24.Step 2: Set the significance level (α): α = 0.05.
Step 3: Calculate the test statistic:
Standard error (SE) = standard deviation / √sample size = 2 / √16 = 2 / 4 = 0.5.T-test statistic = (sample mean - population mean) / SE = (25 - 24) / 0.5 = 2.Step 4: Determine the critical value(s): Since the test statistic follows a t-distribution, we need to find the critical values from the t-table. With a sample size of 16 and a significance level of 0.05, we have 15 degrees of freedom. The critical values are t = ±2.131.
Step 5: Make a decision: Since the test statistic (2) does not fall within the critical region (±2.131), we fail to reject the null hypothesis. There is not enough evidence to conclude that the mean age is significantly different from 24.
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A study of long-distance phone calls made from General Electric's corporate headquarters in Fairfield, Connecticut, revealed the length of the calls, in minutes, follows the normal probability distribution. The mean length of time per call was 3.6 minutes and the standard deviation was 0.40 minutes.
(a) What fraction of the calls last between 3.6 and 4.2 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)
(b) What fraction of the calls last more than 4.2 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)
(c) What fraction of the calls last between 4.2 and 5 minutes? (Round z-score computation to 2 decimal places and final answer to 4 decimal places.)
(d) What fraction of the calls last between 3 and 5 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)
(e) As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 4% of the calls. What is this time? (Round z-score computation to 2 decimal places and your final answer to 2 decimal places.)
Answer:
a) 0.4332 = 43.32% of the calls last between 3.6 and 4.2 minutes
b) 0.0668 = 6.68% of the calls last more than 4.2 minutes
c) 0.0666 = 6.66% of the calls last between 4.2 and 5 minutes
d) 0.9330 = 93.30% of the calls last between 3 and 5 minutes
e) They last at least 4.3 minutes
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 3.6, \sigma = 0.4[/tex]
(a) What fraction of the calls last between 3.6 and 4.2 minutes?
This is the pvalue of Z when X = 4.2 subtracted by the pvalue of Z when X = 3.6.
X = 4.2
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4.2 - 3.6}{0.4}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a pvalue of 0.9332
X = 3.6
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.6 - 3.6}{0.4}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
0.9332 - 0.5 = 0.4332
0.4332 = 43.32% of the calls last between 3.6 and 4.2 minutes
(b) What fraction of the calls last more than 4.2 minutes?
This is 1 subtracted by the pvalue of Z when X = 4.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4.2 - 3.6}{0.4}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a pvalue of 0.9332
1 - 0.9332 = 0.0668
0.0668 = 6.68% of the calls last more than 4.2 minutes
(c) What fraction of the calls last between 4.2 and 5 minutes?
This is the pvalue of Z when X = 5 subtracted by the pvalue of Z when X = 4.2. So
X = 5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 3.6}{0.4}[/tex]
[tex]Z = 3.5[/tex]
[tex]Z = 3.5[/tex] has a pvalue of 0.9998
X = 4.2
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4.2 - 3.6}{0.4}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a pvalue of 0.9332
0.9998 - 0.9332 = 0.0666
0.0666 = 6.66% of the calls last between 4.2 and 5 minutes
(d) What fraction of the calls last between 3 and 5 minutes?
This is the pvalue of Z when X = 5 subtracted by the pvalue of Z when X = 3.
X = 5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 3.6}{0.4}[/tex]
[tex]Z = 3.5[/tex]
[tex]Z = 3.5[/tex] has a pvalue of 0.9998
X = 3
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3 - 3.6}{0.4}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
0.9998 - 0.0668 = 0.9330
0.9330 = 93.30% of the calls last between 3 and 5 minutes
(e) As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 4% of the calls. What is this time?
At least X minutes
X is the 100-4 = 96th percentile, which is found when Z has a pvalue of 0.96. So X when Z = 1.75.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.75 = \frac{X - 3.6}{0.4}[/tex]
[tex]X - 3.6 = 0.4*1.75[/tex]
[tex]X = 4.3[/tex]
They last at least 4.3 minutes
There are six multiple-choice questions on an exam, each with three possible answers. (a) Determine the number of possible answer sequences for the six questions. (b) Only one of the sets can contain all six correct answers. If you are guessing, so that you are as likely to choose one sequence of answers as another, what is the probability of getting all six answers correct
Answer:
a) 729
b)0.0014
Step-by-step explanation:
(a) In order to determine number of possible answers, we'll use combination method
nPr= [tex](n)^{r}[/tex]
where,
n=3 and r=6
number of possible answers= [tex]3^{6}[/tex] => 729
(b) If Only one of the sets can contain all six correct answers.
probability of getting all five answers correct = 1/ 729 => 0.0014
The total number of possible answer sequences for the six questions is 729. The probability of guessing and getting all six answers correct is 1/729 or approximately 0.00137.
Explanation:This question requires knowledge from probability and combinatorics, specific branches of Mathematics.
(a) Given that there are six questions on an exam and each question has three possible answers, the total number of possible answer sequences will be 3^6, also based on the rule of multiplication in probability theory. That gives us 729 possible answer sequences.
(b) If only one set of answers is correct, guessing each answer independently, the chances of getting the correct sequence is 1 in 729.
So, the probability of randomly guessing and getting all six answers correctly is 1/729, which is approximately 0.00137, or 0.137%.
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Square
Move the active vertex to change the shape of the quadrilateral and
check all properties that apply.
Square
All sides congruent
Opposite sides congruent
All angles congruent
Opposite angles congruent
Diagonals congruent
Diagonals bisect
Check
Answer:
Step-by-step explanation: All of the answers are correct for a square.
Opposite sides are congruent, all angles are congruent, opposite angles are congruent, diagonals congruent, and diagonals bisect are the correct answers for a rectangle.
Opposite sides are congruent, opposite angles are congruent, and diagonals bisect are the correct answers for a parallelogram.
All sides congruent, Opposite sides congruent, All angles congruent, Opposite angles congruent, Diagonals congruent and Diagonals bisect are the properties of square.
What is Quadrilateral?A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles
A square is a special type of quadrilateral that has the following properties:
All sides are congruent.
Opposite sides are parallel and congruent.
All angles are congruent and equal to 90 degrees.
Opposite angles are congruent.
Diagonals are congruent and bisect each other at right angles.
Hence, All sides congruent, Opposite sides congruent, All angles congruent, Opposite angles congruent, Diagonals congruent and Diagonals bisect are the properties of square.
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A study was recently conducted to estimate the mean cholesterol for adult males over the age of 55 years. The following random sample data were observed: 245 304 135 202 300 196 210 188 256 390 Given this information, what is the point estimate for the population mean? Question 2 options: About 242.6 ±102 About 73.35 Can't be determined without knowing the confidence level.
Final answer:
The point estimate for the population mean cholesterol level for adult males over the age of 55 years is 242.6 mg/dL, calculated by averaging the values from the given sample data.
Explanation:
The point estimate for the population mean is the average of the sample data. Here are the steps to calculate it:
Add all the sample values together to get the sum: 245 + 304 + 135 + 202 + 300 + 196 + 210 + 188 + 256 + 390 = 2,426.Divide the sum by the number of data points to find the mean: 2,426 / 10 = 242.6.So, the point estimate for the population mean cholesterol level for adult males over the age of 55 years is 242.6 mg/dL. This value is the best estimate for the mean cholesterol level based on the sample given.
A computer manufacturer is testing a batch of processors. They place a simple random sample of processors from the batch under a stress test and record the number of failures, their guidelines specify the percentage of failures should be under 4%. Of the 300 processors tested, there were 54 failures.
a. State the hypotheses for the test. Assume the manufacturer wants to assume there is a problem with a batch, that is, they will only accept that there are fewer than 4% failures in the population if they have evidence for it.
b. Calculate the test statistic and p-value. Your test statistic should be either a z-value or a t-value, whichever is appropriate for the problem
Answer:
a)We need to conduct a hypothesis in order to test the claim that the true proportion is lower than 0.04 or no.:
Null hypothesis:[tex]p \leq 0.04[/tex]
Alternative hypothesis:[tex]p > 0.04[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
b) We need to use a z statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.135 -0.04}{\sqrt{\frac{0.04(1-0.04)}{300}}}=8.396[/tex]
Since is a right tailed test the p value would be:
[tex]p_v =P(z>8.396) \approx 0[/tex]
Step-by-step explanation:
Data given and notation
n=400 represent the random sample taken
X=54 represent the number of failures
[tex]\hat p=\frac{54}{400}=0.135[/tex] estimated proportion of adults that said that it is morally wrong to not report all income on tax returns
[tex]p_o=0.04[/tex] is the value that we want to test
[tex]\alpha[/tex] represent the significance level
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Part a: Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is lower than 0.04 or no.:
Null hypothesis:[tex]p \leq 0.04[/tex]
Alternative hypothesis:[tex]p > 0.04[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Part b: Calculate the statistic
We need to use a z statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.135 -0.04}{\sqrt{\frac{0.04(1-0.04)}{300}}}=8.396[/tex]
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a right tailed test the p value would be:
[tex]p_v =P(z>8.396) \approx 0[/tex]
So the p value obtained was a very low value and using the significance level for example [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of defectives is significantly higher than 0.04 or 4%
Factor x3+x2+x+1 by grouping. What is the resulting expression
Answer:
(x+1) (x^2+1)
Step-by-step explanation:
x^3+x^2+x+1
Factor by grouping
x^3+x^2 +x+1
Factor out x^2 from the first group and 1 from the second group
x^2( x+1) + 1( x+1)
Factor out (x+1)
(x+1) (x^2+1)
what are some of the characteristics of the graph of a cube root functions
Answer:
I)One to three roots.
ii)Two or zero extrema.
iii)One inflection point.
iv)Point symmetry about the inflection point.
v)Range is the set of real numbers.
vi)Three fundamental shapes.
vii)Four points or pieces of information are required to define a cubic polynomial function.
Roots are solvable by radicals.
Final answer:
The graph of a cube root function has several characteristics such as its domain, range, starting point, and symmetry.
Explanation:
A cube root function is represented by the equation y = ∛x. The graph of a cube root function has several characteristics:
The domain of the function is all real numbers because the cube root can be taken of any number.The range of the function is also all real numbers because the cube root of any number will give a real number.The graph starts in the fourth quadrant and passes through the origin.The graph is continuous, meaning there are no breaks or holes in the line.The graph is decreasing for negative values of x and increasing for positive values of x.The graph is symmetric about the origin, meaning if a point (x, y) lies on the graph, then (-x, -y) also lies on the graph.Peanuts cost $12.00 for 2.5 pounds.How much for 1 pound
Answer:
$4.80
Step-by-step explanation:
Make a proportion
$12 for 2.5 pounds, and $x for 1 pound
12/2.5=x/1
x/1 is equivalent to x
12/2.5=x
Divide
x=4.8
So, one pound of peanuts costs $4.80
Answer:
4.8
Step-by-step explanation:
divide 12.00 by 2.5 to find the unit rate which is 4.8.
What is the answer ?
Answer:
its d
Step-by-step explanation:
A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a one-hour flight is 0.037.What is the probability that both will fail? .0014What is the probability that neither will fail?What is the probability that at least one fails?
Answer:
Probability (Both fail) = 0.001369
Probability (None fails) =0.927369
Probability (at least one fails) = 0.072631
Step-by-step explanation:
given data
Probability (fail) P = 0.037
two alternators is independent
solution
we get here first probability that both will fail will be
Probability (Both fail) = 0.045² ................1
Probability (Both fail) = 0.001369
and
now we get probability that neither will fail
Probability (None fails) = (1-0.037)² ...............2
Probability (None fails) =0.927369
and
now we get probability that at least one fails
Probability (at least one fails) = 1 - Probability (non fails) .................3
Probability (at least one fails) = 1 - 0.927369
Probability (at least one fails) = 0.072631
Kathy and her brother Clay recently ran in a local marathon. The distribution of finishing time for women was approximately normal with mean 259 minutes and standard deviation 32 minutes. The distribution of finishing time for men was approximately normal with mean 242 minutes and standard deviation 29 minutes.
(a) The finishing time for Clay was 289 minutes. Calculate and interpret the standardized score for Clay’s marathon time. Show your work.
(b) The finishing time for Kathy was 272 minutes. What proportion of women who ran the marathon had a finishing time less than Kathy’s? Show your work.
(c) The standard deviation of finishing time is greater for women than for men. What does this indicate about the finishing times of the women who ran the marathon compared to the finishing times of the men who ran the marathon?
Answer:
a) Clay's marathon time is 1.62 standard deviations above the mean finishing time for men.
b) 69.51% of those who ran the marathon has a finishing time less than 272.
c) The spread in the distribution of women's finishing time is greater as compared to the spread in the distribution of men's finishing time.
Step-by-step explanation:
Part a) It was given that, the finishing time for Clay's marathon time is 289 minutes.
To calculate the standardized test score for Clay's marathon time, we use the formula:
[tex]z = \frac{x - \mu}{ \sigma} [/tex]
where
[tex]x = 289[/tex]
[tex] \mu = 242[/tex]
and
[tex] \sigma = 29[/tex]
We substitute the values into the formula to get:
[tex]z = \frac{289 - 242}{29} = 1.62[/tex]
Interpretation: Clay's marathon time is 1.62 standard deviations above the mean finishing time for men.
b) To calculate the proportion of women that had a finishing time less than Kathy , we again need to calculate the z-score for x=272, with mean for women being 259 minutes and standard deviation 32 minutes.
We substitute to get:
[tex]z = \frac{272 - 259}{32} = 0.41[/tex]
From the standard normal distribution table, P(z<0.41)=0.6951
Therefore 69.51% of those who ran the marathon has a finishing time less than 272.
c) The standard deviation measures the variation of a distribution. This means the standard deviation measures how far away the data set of a distribution are from the mean.
If the standard deviation of finishing time is greater for women than for men, then it indicates that, women's finishing time are far away from the mean finishing time as compared to men's finishing time.
Is the square root of 95 less than 10
Answer:
Yes,it is
Step-by-step explanation:
95's square root is 9.7467943448
10 is greater than 9.7 and so forth.
So the square root of 95 is less than 10.
The square root of 95 is approximately 9.74679434, thus the square root of 95 is less than 10. The question pertains to the mathematical operation of finding square roots that are indeed pivotal while solving various mathematical problems.
The student question asks if the square root of 95 is less than 10. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the square root of 95 is approximately 9.74679434, which is indeed less than 10. The concept of square roots comes from the realm of Mathematics, more specifically Algebra. It's crucial to understand this mathematical operation as it is frequently encountered in various mathematical problems, especially ones involving quadratic equations where an unknown variable is squared. Usually, these equations will yield two solutions, as both a positive and a negative number squared gives the same result. However, the context of a problem can sometimes restrict the solution to only one value, typically the positive.
As an example, let's consider an equation like x² = 49. The solutions to this are x = -7 and x = 7 because both (-7)² and 7² equals 49. But if this equation was describing a real-world scenario where negative values could not apply (like time or distance), the meaningful solution would only be x = 7.
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Dr. Cawood's class is presented with a large bin that contains small plastic beads. The beads in the box are either purple or white. Dr. Cawood states that 25% of the beads are purple but Oliver, a student in Dr. Cawood's class believes that more than a quarter of the beads in the model box are purple. Select both a null and alternative hypothesis that represent this situation. Be careful of notation.
Answer:
Step-by-step explanation:
The null hypothesis is the hypothesis that is assumed to be true. It is an expression that is the opposite of what the researcher predicts.
The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected.
From the given situation,
Dr. Cawood states that 25% of the beads are purple. This is the null hypothesis.
Oliver, a student in Dr. Cawood's class believes that more than a quarter of the beads in the model box are purple. This is the alternative hypothesis.
Therefore, the correct null and alternative hypotheses are
H0: p = 0.25 and HA: p > 0.25
The null hypothesis, [tex]\(H_0\)[/tex], is that the proportion of purple beads in the bin is 25%, which can be written as [tex]\(H_0: p = 0.25\)[/tex]. The alternative hypothesis, [tex]\(H_1\)[/tex], is that the proportion of purple beads is greater than 25%, which can be written as [tex]\(H_1: p > 0.25\)[/tex].
In hypothesis testing, the null hypothesis represents the default position or the status quo, which in this case is Dr. Cawood's claim that 25% of the beads are purple. This is represented by the symbol [tex]\(H_0\)[/tex] and is often a statement of no effect or no difference. Here, it is stated as [tex]\(H_0: p = 0.25\)[/tex], where p is the proportion of purple beads in the bin.
The alternative hypothesis, denoted by [tex]\(H_1\)[/tex], represents the claim that is being tested against the null hypothesis. It is the hypothesis that the researcher or the student, in this case Oliver, believes to be true. Since Oliver believes that more than a quarter of the beads are purple, the alternative hypothesis is that the proportion of purple beads is greater than 25%. This is represented as [tex]\(H_1: p > 0.25\)[/tex].
It is important to note that the alternative hypothesis can also be one-sided (as in this case) or two-sided, depending on the context of the claim being tested. If Oliver believed that the proportion of purple beads was different from 25% (either more or less), the alternative hypothesis would be [tex]\(H_1: p \neq 0.25\)[/tex], indicating a two-sided test. However, since the claim specifies ""more than,"" a one-sided alternative hypothesis is appropriate.
A real estate appraiser is developing a regression model to predict the market value of single family residential houses as a function of heated area, number of bedrooms, number of bathrooms, age of the house, and central heating (yes, no). The response variable in this model is _______.
a. heated area
b. number of bedrooms
c. market value
d. central heating
e. residential houses
The response variable in this model is: Market value .
Hence the correct option is C.
Given, that a regression model is developed.
A real estate appraiser is developing a regression model to predict the market value of single family residential houses as a function of heated area, number of bedrooms, number of bathrooms, age of the house, and central heating (yes, no). The response variable in this model is market value .
Therefore the correct option is C .
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In the regression model being developed by the real estate appraiser, the response variable is the market value of the single-family residential houses.
Explanation:In the regression model described by the question, the market value of single-family residential houses is being predicted based on several predictive variables (heated area, number of bedrooms, number of bathrooms, age of the house, and presence of central heating). Therefore, the response variable or the dependent variable in this model is the market value of the houses.
A response variable is the feature or quantity that the model outputs. In this context, the real estate appraiser is trying to produce a model that will tell him how changes in the variables like heated area, bedrooms etc. will change the output, which is the market value.
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The temperature at a point (x, y) on a flat metal plate is given by T(x, y) = 31/(3 + x^2 + y^2), where T is measured in °C and x, y in meters.
(a) Find the rate of change of temperature with respect to distance at the point (3, 9) in the x- direction.
(b) Find the rate of change of temperature with respect to distance at the point (3, 9) in the y- direction.
Answer:
Find the rate of change of temperature with respect to distance at the point (3, 9) in the x- direction.
(b) Find the rate of change of temperature with respect to distance at the point (3, 9) in the y-
Step-by-step explanation:
because 3 9 t 2 x y where t
The sum of number times 3 and 15
Answer:
45?
Step-by-step explanation:
How would you not know this?
Two candidates are running for mayor in a small town. The campaign committee for candidate A has been conducting weekly telephone polls to assess the progress of the campaign. Currently, there are 16,000 registered voters, 43% of whom are planning to vote. Of those planning to vote, 59% will vote for candidate A. Candidate B has begun some serious mudslinging, which has resulted in increasing public interest in the election and decreasing support for candidate A. Polls show that the percentage of people who plan to vote is increasing by 5 percentage points per week, and the percentage who will vote for candidate A is declining by 4 percentage points per week. How rapidly is the number of votes that candidate A will receive increasing at this moment? (Answer in the nearest integer.)
Answer:
a) 6,880
b) 4,059
c) Check Explanation
The number of expected votes for candidate A increases only in the first 3 weeks of mudslinging. The rate of weekly increase in those 3 weeks, is provided in the explanation. The number changes weekly for those 3 weeks with an average increase of 101 new votes per week.
Step-by-step explanation:
a. If the election were held today, how many people would vote?
b. How many of those would vote for candidate A?
c. How rapidly is the number of votes that candidate A will receive increasing at the moment?
There are 16,000 registered voters, 43% of whom are planning to vote, with 59% planning to vote for candidate A.
a) Number of registered voters planning to vote = 43% × 16000 = 6880
b) Number of registered voters that will vote and vote for candidate A
= 59% of registered voters planning to vote
= 59% × 6880 = 4059.2 ≈ 4059 people
c) Polls show that the percentage of people who plan to vote is increasing by 5 percentage points per week, and the percentage who will vote for candidate A is declining by 4 percentage points per week.
Since, the 'moment' isn't specified, we will check how much the number is increasing for the first 4 weeks after the mudslinging by candidate B began
Normally, 43% of registered voters want to vote, but now it is increasing at a rate of 5% per week. So, the percentage of registered voters that want to vote is now
43% + 5x% (where x = number of weeks after the mudslinging by candidate B started)
And the percentage of voting, registered voters that want to vote for candidate A is now (59% - 4x%)
After a week, percentage of registered voters that will vote = 48%
Number of registered voters that will vote = 48% × 16000 = 7680
percentage of voting, registered voters that want to vote for candidate A = 55%
Number of voting, registered voters that want to vote for candidate A = 55% × 7680 = 4224
Difference between the initial number of expected votes for candidate A between the beginning of the mudslinging and end of week 1
= 4224 - 4059 = 165
After week 2,
percentage of registered voters that will vote = 53%
Number of registered voters that will vote = 53% × 16000 = 8480
percentage of voting, registered voters that want to vote for candidate A = 51%
Number of voting, registered voters that want to vote for candidate A = 51% × 8480 = 4324.8 = 4325
Difference between the number of expected votes for candidate A between week 1 and week 2
= 4325 - 4224 = 101
After week 3,
percentage of registered voters that will vote = 58%
Number of registered voters that will vote = 58% × 16000 = 9280
percentage of voting, registered voters that want to vote for candidate A = 47%
Number of voting, registered voters that want to vote for candidate A = 47% × 9280 = 4361.6 = 4362
Difference between the number of expected votes for candidate A between week 2 and week 3
= 4362 - 4325 = 37
After week 4,
percentage of registered voters that will vote = 63%
Number of registered voters that will vote = 63% × 16000 = 10,080
percentage of voting, registered voters that want to vote for candidate A = 43%
Number of voting, registered voters that want to vote for candidate A = 43% × 10080 = 4334
Difference between the number of expected votes for candidate A between week 3 and week 4
= 4334 - 4362 = -28
The number of expected votes for candidate A begins to decline after the 4th week of mudslinging.
So, the required 'moment' should be within the first 3 weeks of mudslinging. And the rate of increase weekly is provided above with an average increase of 101 new voters per week.
Hope this Helps!!!
At the current moment, the number of votes that candidate A will receive is increasing at a rate of approximately 197 votes per week.
To determine how rapidly the number of votes that candidate A will receive is changing at this moment, we need to take into account the rate at which both the number of voters planning to vote and the percentage of voters supporting candidate A are changing.
Initial Conditions:
Registered voters: 16,000Percentage planning to vote: 43%Percentage supporting candidate A: 59%Weekly Changes:
Increase in voters planning to vote: 5 percentage points per weekDecrease in support for candidate A: 4 percentage points per weekCalculations:
Initial number of voters planning to vote:⇒ 16,000 × 0.43 = 6,880
Initial number of votes for candidate A:⇒ 6,880 × 0.59 = 4,059.2 (approximately 4059)
Rate of change of voters planning to vote:⇒ 16,000 × 0.05 = 800 voters/week
Rate of change of support for candidate A:⇒ (800 × 0.59) + (16,000 × 0.43 × -0.04) = 472 - (6,880 × 0.04)
⇒ 472 - 275.2 = 196.8 voters/week
Thus, the number of votes that candidate A will receive is initially increasing at a rate of approximately 197 votes per week.
A rectangle has a height of 3c4 and a width of c2– 4c + 3.
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
+
-4c
+
3
3c4
Answer: 3c^6 - 12c^5 + 9c^4
Step-by-step explanation:
The area of the rectangle is found by multiplying the height (3c^4) and the width (c^2 - 4c + 3), resulting in 3c^6 - 12c^5 + 9c^4.
Explanation:To find the area of a rectangle, you use the formula Area = length x width. From your question, we are told that the height of the rectangle is 3c4, and the width is c2 - 4c + 3. So, to find the area, we need to multiply the height and the width. That will give us:
Area = 3c4(c2 - 4c + 3)
Which, upon multiplication, yields Area = 3c6 - 12c5 + 9c4.
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Find the product
(9x2 – 4).
An expression can be written in rational form by
writing it as a fraction with a denominator
of |
Answer:
14/1
Step-by-step explanation:
Answer:
The answer is 1. The next part of that same question should be 12n+8.
The exponential model Upper A equals 925.2 e Superscript 0.027 t describes the population, A, of a country in millions, t years after 2003. Use the model to determine when the population of the country will be 1504 million.
Answer:
In 2021 , the population of the country will be 1504 million
Step-by-step explanation:
We are given that
[tex]A=925.2e^{0.027t}[/tex]
Where A(in millions)
Time,t=After 2003
We have to find the population of the country will be 1504 million.
Substitute the values
[tex]1504=925.2e^{0.027t}[/tex]
[tex]e^{0.027t}=\frac{1504}{925.2}[/tex]
[tex]e^{0.027t}=1.626[/tex]
[tex]0.027t=ln(1.626)[/tex]
[tex]0.027t=0.486[/tex]
[tex]t=\frac{0.486}{0.027}[/tex]
[tex]t=18[/tex]
After 18 years means=2003+18=2021
In 2021 , the population of country will be 1504 million.
find the value of x and tan x in the given trigonometric equation:
sin 2x= cos(3x+10)
Answer:
x = 16°, tan x = 0.3
Step-by-step explanation:
[tex]sin \: 2x = cos \: (3x + 10) \\ cos(90 - 2x) = cos \: (3x + 10) \\ 90 - 2x = 3x + 10 \\ 90 - 10 = 3x + 2x \\ 80 = 5x \\ x = \frac{80}{5} \\ \huge \red{ \boxed{x = 16 \degree }}\\ \\ tan \: x = tan \: 16 \degree \\ = 0.2867453858 \\ = 0.3[/tex]
In triangle ABC, the angles, angle A, angle B, angle C form an arithmetic sequence. If angle A = 23 degrees, then what is angle C, in degrees?
Angle C in triangle ABC, where the angles form an arithmetic sequence with angle A at 23 degrees, is 97 degrees.
Explanation:If the angles in triangle ABC form an arithmetic sequence and angle A = 23 degrees, then we can denote the angles of the triangle as A, A+d, A+2d, where d is the common difference between the terms of the arithmetic sequence. Since we know that the sum of angles in a triangle is 180 degrees, we can set up the equation:
23 + (23 + d) + (23 + 2d) = 180
Combining like terms, we get:
69 + 3d = 180
Subtracting 69 from both sides, we find:
3d = 111
Dividing by 3 gives us the common difference d:
d = 37 degrees
Therefore, angle C, being the third term in our arithmetic sequence, is:
angle C = A + 2d = 23 + (2 * 37) = 23 + 74 = 97 degrees
What is the approximate length of the missing side in the triangle below?
18 miles
15 miles
80 degrees
[Not drawn to scale]
Answer: 21.3 miles
Step-by-step explanation:
Families USA, a monthly magazine that discusses issues related to health and health costs, surveyed 20 of its subscribers. It found that the annual health insurance premiums for a family with coverage through an employer averaged $10,979. The standard deviation of the sample was $1,000.a. Based on this sample information, develop a 90 percent confidence interval for thepopulation mean yearly premium.b. How large a sample is needed to find the population mean within $250 at 99 percentconfidence?
Answer:
(a) The 90 percent confidence interval for the population mean yearly premium is ($10,974.53, $10983.47).
(b) The sample size required is 107.
Step-by-step explanation:
(a)
The (1 - α)% confidence interval for population mean is:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]
Given:
[tex]\bar x=\$10,979\\s=\$1000\\n=20[/tex]
Compute the critical value of t for 90% confidence level as follows:
[tex]t_{\alpha/2, (n-1)}=t_{0.10/2, (20-1)}=t_{0.05, 19}=1.729[/tex]
*Use a t-table.
Compute the 90% confidence interval for population mean as follows:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]
[tex]=10979\pm 1.729\times \frac{1000}{\sqrt{20}}\\=10979\pm4.47\\ =(10974.53, 10983.47)[/tex]
Thus, the 90 percent confidence interval for the population mean yearly premium is ($10,974.53, $10983.47).
(b)
The margin of error is provided as:
MOE = $250
The confidence level is, 99%.
The critical value of z for 99% confidence level is:
[tex]z_{\alpha/2}=z_{0.01/2}=z_{0.005}=2.58[/tex]
Compute the sample size as follows:
[tex]MOE= z_{\alpha/2}\times \frac{s}{\sqrt{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\times s}{MOE} ]^{2}[/tex]
[tex]=[\frac{2.58\times 1000}{250}]^{2}[/tex]
[tex]=106.5024\\\approx107[/tex]
Thus, the sample size required is 107.
What is -14=k+9?
I tried several different answers but none work?
It would help a lot because then I will know for next time
Answer:
k = -23
Step-by-step explanation:
-14=k+9
Subtract 9 from each side
-14-9 = k+9-9
-23 = k
Answer: k=23
Step-by-step explanation:
50 POINTS!!!
PLEASE SOLVE WITH STEPS.
THANK YOU!
Step-by-step explanation:
G(x) = (16x − 7) cos³(4x) − 9 sin⁻¹(x)
A) Use product rule, power rule, and chain rule to take the derivative.
G'(x) = (16x − 7) (3 cos²(4x) (-4 sin(4x))) + 16 cos³(4x) − 9 / √(1 − x²)
G'(x) = (-192x + 84) cos²(4x) sin(4x) + 16 cos³(4x) − 9 / √(1 − x²)
Evaluate at x = 0.
G'(0) = (0 + 84) cos²(0) sin(0) + 16 cos³(0) − 9 / √(1 − 0)
G'(0) = 16 − 9
G'(0) = 7
B) Use point-slope form of a line to write the equation.
y − (-7) = 7 (x − 0)
y + 7 = 7x
y = 7x − 7