A 20 ft ladder is leaning up against a wall. The wall forms a 90 degree angle with the floor, which has recently been waxed and is very slippery. The base of the ladder begins to slide away from the wall causing the top of the ladder to slide down the wall toward the floor. When the base of the ladder slides to 12 ft away from the wall, the base is moving at a rate of 1 ft/sec away from the wall. How quickly is the top of the ladder moving toward the floor at that moment?
Answers
Answer: The top of the ladder is moving towards the floor at a rate of 0.75 ft/sec
Step-by-step explanation: Please see the attachments below
Related Questions
Graph the line with slope 1 passing through the point (1,1)
Answers
Answer:
start at (0,0) and go up 1, right 1, and mark a point and keep doing that
Step-by-step explanation:
A big ship drops its anchor.
E represents the anchor's elevation relative to the water's surface (in meters) as a function of time t (in seconds).
E=−2.4t+75
How far does the anchor drop every 5 seconds?
Answers
The anchor drops 63 meters in the first 5 seconds.
The given function E(t) = -2.4t + 75 represents the elevation of the ship's anchor relative to the water's surface at any given time t. To find how far the anchor drops every 5 seconds, substitute t = 5 into the function:
E(5) = -2.4(5) + 75
E(5) = -12 + 75
E(5) = 63
Therefore, after 5 seconds, the anchor has dropped 63 meters relative to the water's surface. This indicates the change in elevation during this time period. The negative coefficient of t in the function implies a downward motion, and the constant term (75) represents the initial height of the anchor above the water. So, the anchor drops 63 meters in the first 5 seconds.
Suppose we conduct a hypothesis test to determine if an exercise program helps people lose weight. We measure the weight of a random sample of participants before and after they complete the exercise program. The mean number of pounds lost for the sample turns out to be 7.9 lbs. The hypotheses for the test are: H0: The program is not effective for weight loss. Ha: The program is effective for weight loss. The P-value for the test turns out to be 0.012. Which of the following is the appropriate conclusion, assuming that all conditions for inference are met and the level of significance is 0.05? (i) We reject H0---this sample does not provide significant evidence that the program is effective. (ii) We reject H0---this sample provides significant evidence that the program is effective. (iii) We fail to reject H0---this sample provides significant evidence that the program is not effective. (iv) We fail to reject H0---this sample does not provide significant evidence that the program is effective.
Answers
Answer: (ii) We reject H0---this sample provides significant evidence that the program is effective.
Step-by-step explanation:
The null hypothesis is
The program is not effective for weight loss.
The alternative hypothesis is
The program is effective for weight loss.
If the P-value for the test turns out to be 0.012, and the level of significance is 0.05, then
Alpha, 0.05 > p value, 0.012
Therefore, there is enough evidence to reject the null hypothesis. We then accept the alternative hypothesis.
The correct option is
(ii) We reject H0---this sample provides significant evidence that the program is effective.
A solid right pyramid has a square base with an edge length of x cm and a height of y cm.
A solid right pyramid has a square base with an edge length of x centimeters and a height of y centimeters.
Which expression represents the volume of the pyramid?
One-thirdxy cm3
One-thirdx2y cm3
One-halfxy2 cm3
One-halfx2y cm3
Answers
Answer:
B
Step-by-step explanation:
One-thirdx2y cm3 i got it right on edg
The volume of the pyramid with a square base of side x and height (y) is (1/3)x²y cm³
How to calculate volume?Volume is the amount of space occupied by a three dimensional shape or object.
The area of the square base = x cm * x cm = x² cm²
The volume of the pyramid = (1/3) * area of square base * height = (1/3) * x² * y = (1/3)x²y cm³
The volume of the pyramid with a square base of side x and height (y) is (1/3)x²y cm³
Find out more on volume at: https://brainly.com/question/1972490
Min's mother spent $3.96 on ground coffee that costs $0.45 per ounce. How many ounces of ground coffee did she buy?
Answers
Answer:
8.8 ounces
Step-by-step explanation:
3.96/0.45=8.8
The mean weight of an adult is 6060 kilograms with a variance of 100100. If 118118 adults are randomly selected, what is the probability that the sample mean would differ from the population mean by greater than 0.80.8 kilograms? Round your answer to four decimal places.
Answers
Answer:
The probability that the sample mean would differ from the population mean by greater than 0.8 kg is P=0.3843.
Step-by-step explanation:
We have a population with mean 60 kg and a variance of 100 kg.
We take a sample of n=118 individuals and we want to calculate the probability that the sample mean will differ more than 0.8 from the population mean.
This can be calculated using the properties of the sampling distribution, and calculating the z-score taking into account the sample size.
The sampling distribution mean is equal to the population mean.
[tex]\mu_s=\mu=60[/tex]
The standard deviation of the sampling distribution is equal to:
[tex]\sigma_s=\sigma/\sqrt{n}=\sqrt{100}/\sqrt{118}=10/10.86=0.92[/tex]
We have to calculate the probability P(|Xs|>0.8). The z-scores for this can be calculated as:
[tex]z=(X-\mu_s)/\sigma_s=\pm0.8/0.92=\pm0.87[/tex]
Then, we have:
[tex]P(|X_s|>0.8)=P(|z|>0.87)=2*(P(z>0.87)=2*0.19215=0.3843[/tex]
Use Euler’s formula for exp(ix) and exp(-ix) to write cos(x) as a combination of exp(ix) and exp(-ix)
Answer = (cos(x) = (exp(ix)+exp(-ix))/2)
For real a and b, use the previous answer to find write both cos(a+b) and cos(a)cos(b) in terms of exp. Throughout the rest you will probably use exp(x+y)=exp(x)exp(y).
Answers
Answer:
[tex]cos(a+b)=\frac{e^{i(a-b)}+e^{i(-a+b)}}{2}[/tex]
Step-by-step explanation:
[tex]cos(x)=\frac{e^{ix}+e^{-ix}}{2}[/tex]
[tex]cos(a+b)[/tex]
We need to expand cos(a+b) using the cos addition formula.
[tex]cos(a+b)=cos(a)cos(b)-sin(a)sin(b)[/tex]
We know that we also need to use Euler's formula for sin, which is:
[tex]sin(x)=\frac{e^{ix}-e^{-ix}}{2}[/tex] (you can get this from a similar way of getting the first result, of simply just expanding [tex]e^{ix}=cosx+isinx[/tex] and seeing the necessary result)
We can now substitute our cos's and sin's for e's
[tex]cos(a+b)=(\frac{e^{ia}+e^{-ia}}{2})(\frac{e^{ib}+e^{-ib}}{2})-(\frac{e^{ia}-e^{-ia}}{2})(\frac{e^{ib}-e^{-ib}}{2})[/tex]
Now lets multiply out both of our terms, I'm using the exponent multiplication identity here ([tex]e^{x+y}=e^xe^y[/tex])
[tex]cos(a+b)=\frac{e^{i(a+b)} + e^{i(a-b)}+e^{i(-a+b)} + e^{i(-a-b)}}{4}-\frac{e^{i(a+b)} - e^{i(a-b)}-e^{i(-a+b)}+e^{i(-a-b)}}{4}[/tex]
Now we can subtract these two terms.
[tex]cos(a+b)=\frac{2e^{i(a-b)}+2e^{i(-a+b)}}{4}[/tex]
This is starting to look a lot tidier, let's cancel the 2
[tex]cos(a+b)=\frac{e^{i(a-b)}+e^{i(-a+b)}}{2}[/tex]
Using Euler's formula, we can write cos(x) as the average of exp(ix) and exp(-ix). Further, we demonstrated how to express cos(a+b) and cos(a)cos(b) in terms of exponential functions, utilizing the properties of Euler's formula and complex exponentials.
Using Euler's formula, exp(ix) = cos(x) + i sin(x) and exp(-ix) = cos(x) - i sin(x), we can represent cos(x) as a combination of exp(ix) and exp(-ix). By adding these two equations, we eliminate the sin(x) terms due to their opposite signs, leading us to the formula for cos(x):
cos(x) = (exp(ix) + exp(-ix)) / 2
To express cos(a+b), use the expansion:
cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
Using Euler's formula, this expands to:
cos(a+b) = [exp(ia) + exp(-ia)]/2 * [exp(ib) + exp(-ib)]/2 - [exp(ia) - exp(-ia)]/2i * [exp(ib) - exp(-ib)]/2i
Similarly, to express cos(a)cos(b), we again use the representation of cos(x) in terms of exp:
cos(a)cos(b) = [exp(ia) + exp(-ia)]/2 * [exp(ib) + exp(-ib)]/2
Consider a hypothesis test to decide whether the mean annual consumption of beer in the nation's capital is less than the national mean. Answer the following questions.
1. "The mean annual consumption of beer in the nation's captial is less than the national mean and the result of the hypothesis test does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean" is a:________
a. Correct decision
b. Type II error
c. Type I error
2. "The mean annual consumption of beer in the nation's captial is less than the national mean and the result of the sampling leads to the conclusion that the mean annul consumption of beer in the nation's capital is less than the national mean" is a:_________
a. Correct decision
b. Type II error
c. Type I error
3. "The mean annual consumption of beer in the nation's captial is less than the national mean but the result of the sampling does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean" is a:________
4. Correct decision
b. Type II error
c. Type I error
d. "The mean annual consumption of beer in the nation's captial is not less than the national mean and the result of the sampling does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean" is a:________
a. Correct decision
b. Type II error
c. Type I error
Answers
Answer:
Step-by-step explanation:
Type I error occurs when the null hypothesis is rejected even when it is true.
Type II error occurs when the null hypothesis is not rejected even when it is false.
The null hypothesis is
The mean annual consumption = the national mean
The alternative hypothesis is
The mean annual consumption < the national mean
1) it is a type II error because the null hypothesis was not rejected even when it is false
2) it is a correct decision because the decision corresponds to the outcome
3) it is also a type II error
d) it is a correct decision because the null hypothesis is accepted when it is true
By interpreting the various scenarios related to hypothesis testing, it is determined that scenarios 1 and 3 represent Type II errors, while scenarios 2 and 4 represent correct decisions. This shows an understanding of statistical hypothesis tests.
Explanation:This problem falls within the discipline of statistical hypothesis testing, a method used to make statistical decisions using data. In the context of this problem, the null hypothesis states that the mean annual consumption of beer in the nation's capital is not less than the national mean.
'The mean annual consumption of beer in the nation's capital is less than the national mean and the result of the hypothesis test does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean' is a Type II error. This is because the reality is that the consumption in the nation's capital is indeed less, but the test results failed to conclude this.'The mean annual consumption of beer in the nation's capital is less than the national mean and the result of the sampling leads to the conclusion that the mean annul consumption of beer in the nation's capital is less than the national mean' is a correct decision. This is because the reality and the test conclusion are in agreement.'The mean annual consumption of beer in the nation's capital is less than the national mean but the result of the sampling does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean' is a Type II error. Even though in reality the consumption in the nation's capital is less, the test results failed to detect it.'The mean annual consumption of beer in the nation's capital is not less than the national mean and the result of the sampling does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean' is a correct decision. This is because both reality and test results agree that the nation's capital's consumption is not below the national mean.Learn more about statistical hypothesis testing here:https://brainly.com/question/34698067
#SPJ3
Use StatKey or other technology to generate a bootstrap distribution of sample proportions and find the standard error for that distribution. Compare the result to the standard error given by the Central Limit Theorem, using the sample proportion as an estimate of the population proportion p.
Proportion of peanuts in mixed nuts, with n=94 and P =0.52
Round your answer for the bootstrap SE to two decimal places, and your answer for the formula SE to three decimal places.
Answers
Answer:
0.0515
Step-by-step explanation:
By the central limit theorem
when n increase distribution when data follows normal
Standard Error, SE of P is
[tex]SE = \sqrt{\frac{p(1-p)}{n} }[/tex]
Bootstrap Standard Error = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
where n = 94 and p = 0.52
hence,
SE of Bootstrap = [tex]\sqrt{\frac{0.52(1-0.52)}{94} }[/tex]
[tex]=\sqrt{\frac{0.2496}{94} }\\\\=0.0515[/tex]
SE and the SE of Bootstrap are the same
Factor 16p^4 - 24p^3.
Answers
Answer:
8p^3(2p - 3) is the factor
Step-by-step explanation:
Owen has completed his education and is looking for a job. He received three different offers. He researched each job, and what he learned is shown in the table.
A 4-column table with 3 rows. Column 1 has entries Salary, benefits, average monthly rent at job location. Column 2 is labeled Job A with entries 46,650 dollars, 14,000 bonus and health insurance and 401 k, 850 dollars. Column 3 is labeled Job B with entries 38,750 dollars, 15,000 dollar bonus and health insurance and 401 k, 790 dollars. Column 4 is labeled Job C with entries 52,880 dollars, 8,000 dollar bonus and health insurance and 401 k, 950 dollars.
Based on the information in the table, which job should Owen take?
Job
Answers
Job A is the correct answer! :)
Based on the information in the table, Owen should take Job A with total earnings of $50,400 before tax.
What determines job acceptance?The factors that should determine if a job should be accepted or not include:
Base salaryBenefits (e.g. 401(K)Working hoursResidential /transportation costsCareer advancement.Data and Calculations:Job A Job B Job C
Salary $46,650 $38,750 $52,880
Benefits 14,000 15,000 8,000
Average monthly rent 850 790 950
Annual rent $10,200 $9,480 $11,400 ($950 x 12)
Earnings before tax $50,400 $44,270 $49,480
Thus, based on the information in the table, Owen should take Job A with total earnings of $50,400 before tax.
Learn more about accepting jobs at https://brainly.com/question/6747675
#SPJ2
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:
Also SSR (X1 ∣ X2) = 36400.6326 and SSR (X2 ∣ X1) = 3297.7917
What fraction of the variability in house size is explained by income and size of family?
A. 84.79%
B. 71.89%
C. 17.56%
D. 70.69%
Answers
Answer:
Correct option: (B) 71.89%.
Step-by-step explanation:
R-squared is a statistical quantity that measures, just how near the values are to the fitted regression line. It is also known as the coefficient of determination.
The coefficient of determination R² specifies the percentage of the variance in the dependent variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent variable).
The coefficient of determination R² can be computed by the formula,
[tex]R^{2}=\frac{SSR}{SST}[/tex]
Here,
SSR = sum of squares of regression
SST = sum of squares of total
From the output attached below the value of SSR and SST are:
SSR = 37043.3236
SST = 51531.0863
Compute the value of R² as follows:
[tex]R^{2}=\frac{SSR}{SST}[/tex]
[tex]=\frac{37043.3236 }{51531.0863}[/tex]
[tex]=0.7188539\\\approx 0.7189[/tex]
Thus, the fraction of the variability in house size is explained by income and size of family is 71.89%.
The correct option is (B).
To find the fraction of the variability in house size that is explained by family income and size, we sum the two SSR values and express this as a fraction or percentage of the total variability in house size. The actual value could not be determined from the provided information as it appears to be missing.
Explanation:The question focuses on understanding the impact of family income and family size (the independent variables) on the house size (the dependent variable). The builder calculated the Sum of Squares for Regression (SSR) considering each independent variable given other independent variables constant. These calculations provide crucial insights into the contribution made by each independent variable to the variation in the dependent variable.
The total SSR (from both variables) can be calculated by summing the SSRs given: SSR(X1 ∣ X2) = 36400.6326 and SSR(X2 ∣ X1) = 3297.7917, which gives 39698.4243. This total variability is a representation of the entire variability in house size that is accounted for by both family income and family size. Express this as a fraction or percentage of total variability in house size to determine the proportion of variability explained by the two predictors.
Note: The Excel output and the options (A. 84.79%, B. 71.89%, C. 17.56%, D. 70.69%) should contain the exact proportion but in the provided information, these values are missing.
Learn more about Multiple Regression here:https://brainly.com/question/3737733
#SPJ12
a table cost 5 times as much as a chair. for $40000 a trader can buy 20 more chairs than tables. find the cost of a chair and number of tables.
Answers
Answer:
Chair is $1600
Table are 5 pieces
Step-by-step explanation:
Let the cost of a chair be x then for a table, it will be 5x since table cost 5 times as much as a chair.
For $40000, chairs alone will be 40000/x while tables will be 40000/5x=8000/x
The difference between these numbers is 20 hence
40000/x-8000/x=20
32000/x=20
X=32000/20=1600
The cost of a chair is $1600
Table will be 5*1600=$8000
The number bought will be proved as follows
Chairs=40000/1600=25 pieces
Tables=40000/8000=5 pieces
Difference in number is 25-5=20
Fast-food restaurants spend much time studying the amount of time cars spend in their drive-thrus. Certainly, the faster the cars get service, the more opportunity for making money. According to a recent study by QSR magazine, Wendy’s has the best time, with a mean time spent in the drive thru of 138.5 seconds. Assuming drive-thru time is normally distributed with a standard deviation of 29 seconds, what proportion of cars spends between 120 and 180 seconds in Wendy's drive-thru? Write answer as decimal rounded to the thousandth.
Answers
Answer:
0.663
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 = 138.5, \sigma = 29[/tex]
What proportion of cars spends between 120 and 180 seconds in Wendy's drive-thru?
This is the pvalue of Z when X = 180 subtracted by the pvalue of Z when X = 120. So
X = 180
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{180 - 138.5}{29}[/tex]
[tex]Z = 1.43[/tex]
[tex]Z = 1.43[/tex] has a pvalue of 0.924
X = 120
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{120 - 138.5}{29}[/tex]
[tex]Z = -0.64[/tex]
[tex]Z = -0.64[/tex] has a pvalue of 0.261
0.924 - 0.261 = 0.663
Final answer:
0.662 when rounded to three decimal places.
Explanation:
To determine the proportion of cars that spend between 120 and 180 seconds in Wendy's drive-thru, we can use the properties of the normal distribution. Given that the mean time is 138.5 seconds and the standard deviation is 29 seconds, we can calculate the corresponding z-scores for both 120 seconds and 180 seconds.
Firstly, calculate the z-score for 120 seconds:
z = (X - µ) / σ = (120 - 138.5) / 29 ≈ -0.6379.
Next, calculate the z-score for 180 seconds:
z = (X - µ) / σ = (180 - 138.5) / 29 ≈ 1.4310.
By looking up these z-scores in a standard normal distribution table, we find that:
P(Z < 1.4310) ≈ 0.9236
P(Z < -0.6379) ≈ 0.2616.
To find the proportion of times between 120 and 180 seconds, we subtract the smaller probability from the larger:
P(120 < X < 180) = P(Z < 1.4310) - P(Z < -0.6379) ≈ 0.9236 - 0.2616 = 0.6620.
An agricultural researcher plants 25 plots with a new variety of yellow corn. Assume that the yield per acre for the new variety of yellow corn follows a Normal distribution with unknown mean LaTeX: \mu and standard deviation LaTeX: \sigma = 10 bushels per acre.Q: Which of the following would produce a confidence interval with a smaller margin of error than the 90% confidence interval?A) Plant only 5 plots rather than 25, because 5 are easier to manage and control.B) Plant 10 plots rather than 25, because a smaller sample size will result in a smaller margin of error.C) Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error.D) Plant 100 plots rather than 25, because a larger sample size will result in a smaller margin of error.
Answers
Answer:
Correct Answer: CA larger sample size results in a smaller margin error, i.e. with a plant of 100 plots instead of 25, the margin error will be smaller.
Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
An agricultural researcher plants 25 plots with a new variety of yellow corn.
Assume that the yield per acre for the new variety of yellow corn follows a Normal distribution with unknown mean and standard deviation of 10.
We need to find a confidence interval with a smaller margin of error than the 90% confidence interval
n=25, x=150,s=10,a=0.95
Unknown mean u means we use t table.
[tex]150 ± t_{0.975} \frac{10}{\sqrt{25}}[/tex]
150±[tex]t_{0.975}[/tex]×2
Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error
Hence, option C is correct. Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error
To learn more on Statistics click:
https://brainly.com/question/29093686
#SPJ5
Two numbers have a sum of 23 and a difference of 9. Find the two numbers
Answers
Answer:
The numbers are 16 and 7
Step-by-step explanation:
Let the numbers be x and y
x+y = 23
x-y = 9
Add the two equations together
x+y = 23
x-y = 9
-------------------
2x = 32
Divide each side by 2
2x/2 = 32/2
x = 16
Now subtract the two equations
x+y = 23
-x +y = -9
-------------------
2y = 14
Divide by 2
2y/2 = 14/2
y = 7
Final answer:
The two numbers with a sum of 23 and a difference of 9 are 16 and 7. Solved by setting up equations for the sum and difference, then solving for the two unknowns.
Explanation:
To find the two numbers with a sum of 23 and a difference of 9, we can set up two equations based on the given information:
x + y = 23 (Equation for sum)x - y = 9 (Equation for difference)Adding the two equations together, we get:
2x = 32
Dividing both sides by 2:
x = 16
Now, substituting x back into one of the original equations, for example, x + y = 23:
16 + y = 23
y = 23 - 16
y = 7
Therefore, the two numbers are 16 and 7.
The average annual inflation rate in the United States over the past 98 years is 3.37% and has a standard deviation of approximately 5% (Inflationdata). In 1980, the inflation rate was above 13%. If the annual inflation rate is normally distributed, what is the probability that inflation will be above 13% next year
Answers
Answer:
2.68% probability that inflation will be above 13% next year
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 = 3.37, \sigma = 5[/tex]
If the annual inflation rate is normally distributed, what is the probability that inflation will be above 13% next year
This is the pvalue of Z when X = 13. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{13 - 3.37}{5}[/tex]
[tex]Z = 1.93[/tex]
[tex]Z = 1.93[/tex] has a pvalue of 0.9732
1 - 0.9732 = 0.0268
2.68% probability that inflation will be above 13% next year
Answer:
[tex]P(X>13)=P(\frac{X-\mu}{\sigma}>\frac{13-\mu}{\sigma})=P(Z>\frac{13-3.37}{5})=P(Z>1.926)[/tex]
And we can find this probability using the complement rule and the normal standard distirbution table or excel:
[tex]P(Z>1.926)=1-P(Z<1.926)=1-0.9729=0.0271[/tex]
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 annual inflation of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(3.37,5)[/tex]
Where [tex]\mu=3.37[/tex] and [tex]\sigma=5[/tex]
We are interested on this probability
[tex]P(X>13)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(X>13)=P(\frac{X-\mu}{\sigma}>\frac{13-\mu}{\sigma})=P(Z>\frac{13-3.37}{5})=P(Z>1.926)[/tex]
And we can find this probability using the complement rule and the normal standard distirbution table or excel:
[tex]P(Z>1.926)=1-P(Z<1.926)=1-0.9729=0.0271[/tex]
How many times larger is 4 x 10^8 than 2 x 10^-5
Answers
Answer:The answer is 8x10^7
Step-by-step explanationi took the thing
figure out what 100 times 1000 equals?
Answers
Answer:
100,000 lol
Step-by-step explanation:
Which are solutions of the linear equation?
Select all that apply.
3x + y = 10
(1, 6)
(2, 4)
(3, 1)
(4, –1)
(5, –5)
Answers
Explanation: if you input the X values from the options for X and Y values for Y and it equals to 10 then it is a solution:)
The solutions of the linear equation are; (2, 4), (3, 1) and (5, –5)
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
The given linear equation is;
3x + y = 10
For (1, 6)
3x + y = 10
y = 10 - 3x
y = 10 - 3(1)
y = 10 -3 = 7
So, this is not the solution of the linear equation.
For (2, 4)
y = 10 - 3x
y = 10 - 3(2)
y = 10 -6 = 4
So, this is the solution of the linear equation.
For (3, 1)
y = 10 - 3x
y = 10 - 3(3)
y = 10 -9 = 1
So, this is the solution of the linear equation.
For (4, –1)
y = 10 - 3x
y = 10 - 3(4)
y = 10 -12 = -2
So, this is not the solution of the linear equation.
For (5, –5)
y = 10 - 3x
y = 10 - 3(5)
y = 10 -15 = -5
So, this is the solution of the linear equation.
Learn more about linear equations;
https://brainly.com/question/10413253
#SPJ2
What is the area of a circular cardboard piece needed for the base of a model of a volcano that’s is 20 centimeters tall and has a volume of 960 cubic centimeters
Answers
Answer: 144 square centimeters
Answer:
the answer is 144 centimeters
The value of a gold coin picturing the head of the Roman Emperor Vespasian is increasing at the rate of 5% per year. If the coin is worth $105 now, what will it be worth in 11 years?
Answers
Answer:
255.75
Step-by-step explanation:
Answer:
$179.59
Step-by-step explanation:
Step 1 Write the exponential growth function for this situation.
y = a(1 + r)t Write the formula.
= 105(1 + 0.05)t Substitute 105 for a and 0.05 for r.
= 105(1.05)t Simplify.
Step 2 Find the value in 11 years.
y = 105(1.05)t Write the formula.
= 105(1.05)11 Substitute 11 for t.
≈ 179.59 Use a calculator and round to the nearest hundredth.
A random telephone survey of 1,091 adults (aged 18 and older) was conducted by an online tax preparation and e-filing service. The survey results showed that 634 of those surveyed planned to file their taxes electronically. (Round your answers to the nearest whole number.) (a) Develop a descriptive statistic that can be used to estimate the percentage of all taxpayers who file electronically. % (b) The survey reported that the most frequently used method for preparing the tax return is to hire an accountant or professional tax preparer. If 60% of the people surveyed had their tax return prepared this way, how many people used an accountant or professional tax preparer
Answers
Answer:
a. The percentage of all taxpayers who file electronically is 58%
b. 654 people used an accountant or professional tax preparer preparing the tax return
Step-by-step explanation:
According to the given data, in order to estimate the percentage of all taxpayers who file electronically, we would have to make the following calculation:
percentage of all taxpayers who file electronically=634×100%=0.58
1,091
Hence, the percentage of all taxpayers who file electronically is 58%
In order to calculate how many people used an accountant or professional tax preparer for preparing the tax return, we would have to make the following calculation:
people used an accountant or professional tax preparer= 60%×1,091=654
100%
654 people used an accountant or professional tax preparer preparing the tax return.
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 4.0 minutes. It is known that the standard deviation of the checkout time is one minute. The 98% confidence interval for the average checkout time of all customers is Group of answer choices 3.02 to 4.98 3.00 to 5.00 3.795 to 4.205 3.767 to 4.233
Answers
Answer:
[tex]4-2.326\frac{1}{\sqrt{100}}=3.767[/tex]
[tex]4+2.326\frac{1}{\sqrt{100}}=4.233[/tex]
So on this case the 98% confidence interval would be given by (3.767;4.233)
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=4[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=1[/tex] represent the population standard deviation
n=100 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
Since the Confidence is 0.98 or 98%, the value of [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that [tex]z_{\alpha/2}=2.326[/tex]
Now we have everything in order to replace into formula (1):
[tex]4-2.326\frac{1}{\sqrt{100}}=3.767[/tex]
[tex]4+2.326\frac{1}{\sqrt{100}}=4.233[/tex]
So on this case the 98% confidence interval would be given by (3.767;4.233)
Ice-cream palace has received an order for 3 gallons of ice cream the shop packages its ice cream in 1 quart containers
Answers
2x + 3y = 12 is an equation in slope intercept form.
True
False
Answers
The amount in milligrams of a drug in the body t hours after taking a pill is given by A(t) = 25(0.85)t a. What is the initial dose given? b. What percent of the drug leaves the body each hour? c. What is the amount of drug left after 10 hours? (Write answer using function notation)
Answers
Answer:
(a)25 Milligrams
(b)15%
(c)[tex]A(10) = 25(0.85)^{10}[/tex]
Step-by-step explanation:
The amount in milligrams of a drug in the body t hours after taking a pill is given by the model:
[tex]A(t) = 25(0.85)^t[/tex]
(a)Comparing this with the exponential decay model, [tex]A(t)=A_0(\frac{1}{2})^{\frac{t}{t_{1/2}} }[/tex], the initial dose given is 25 milligrams.
(b)From the model,
[tex]A(t) = 25(0.85)^t\\A(t) = 25(1-0.15)^t[/tex]
We can also use this method:
[tex]r = a - 1 = 0.85 - 1 = -0.15=-15\%[/tex]
We can see that for every hour, 15% of the drug leaves the body.
(c)After 10 hours
When t=10
[tex]A(10) = 25(0.85)^{10}[/tex]
The amount of drug left after 10 hours is given above in function notation.
a. The initial dose given is 25 milligrams. b. 85(0.85)^t percent of the drug leaves the body each hour. c. The amount of drug left after 10 hours is 0.2147 milligrams.
Explanation:a. The initial dose given can be found by substituting t = 0 into the function A(t) = 25(0.85)^t. This gives A(0) = 25(0.85)^0 = 25(1) = 25 milligrams.
b. To find the percent of the drug that leaves the body each hour, we need to find the rate of change of A(t) with respect to time. Taking the derivative of A(t) gives dA/dt = 25(0.85)^t * ln(0.85) = 21.25(0.85)^t. This represents the rate of change of A(t) with respect to time. To find the percent, we can divide this rate by the initial dose and multiply by 100: (21.25(0.85)^t / 25) * 100 = 85(0.85)^t percent.
c. To find the amount of drug left after 10 hours, we substitute t = 10 into the function A(t) = 25(0.85)^t: A(10) = 25(0.85)^10 = 25(0.0859) = 0.2147 milligrams.
Learn more about Drug dosage and elimination here:https://brainly.com/question/8728922
#SPJ3
The dot plot shows how many hours this week students in the band practiced their instruments.
A dot plot titled Hours of Band Practice going from 0 to 4. 0 has 1 dot, 1 has 2 dots, 2 has 3 dots, 3 has 4 dots, 4 has 3 dots.
How many observations were used for the dot plot?
Hope you get it right so you can get brainlest
Answers
Answer:
the answer is 13!
Step-by-step explanation:
hope this helps
Answer:
the answer is 13
Step-by-step explanation:
A recent report estimated that 25% of all college students in the United States have a sexually transmitted disease (STD). Due to the demographics of the community, the director of the campus health center believes that the proportion of students who have a STD is lower at his college. He tests H0: p = 0.25 versus Ha: p < 0.25.
The campus health center staff select a random sample of 50 students and determine that 18% have been diagnosed with a STD.
a) Is the sample size condition for conducting a hypothesis test for a population proportion satisfied?
Answers
Answer:
The sample size condition for conducting a hypothesis test for a population proportion is satisfied for this question.
Step-by-step explanation:
a) The sample size condition for conducting a hypothesis test for a population proportion is satisfied is when
np > 5 and n(1 - p) > 5
n = sample size = 50
p = proportion that have STD = 18% = 0.18
np = 0.18 × 5 = 9 > 5
n(1 - p) = 0.82 × 50 = 41 > 5
Hope this Helps!!!
Answer:
Step-by-step explanation:
Given :
Which of these statements is best? The errors in a regression model are assumed to have an increasing mean. The regression model assumes the error terms are dependent. The errors in a regression model are assumed to have zero variance. The regression model assumes the errors are normally distributed.
Answers
Answer:
[tex] \epsilon = Y -X\beta[/tex]
And the expected value for [tex] E(\epsilon) = 0[/tex] a vector of zeros and the covariance matrix is given by:
[tex] Cov (\epsilon) = \sigma^2 I[/tex]
So we can see that the error terms not have a variance of 0. We can't assume that the errors are assumed to have an increasing mean, and we other property is that the errors are assumed independent and following a normal distribution so then the best option for this case would be:
The regression model assumes the errors are normally distributed.
Step-by-step explanation:
Assuming that we have n observations from a dependent variable Y , given by [tex] Y_1, Y_2,....,Y_n[/tex]
And for each observation of Y we have an independent variable X, given by [tex] X_1, X_2,...,X_n[/tex]
We can write a linear model on this way:
[tex] Y = X \beta +\epsilon [/tex]
Where [tex]\epsilon_{nx1}[/tex] i a matrix for the error random variables, and for this case we can find the error ter like this:
[tex] \epsilon = Y -X\beta[/tex]
And the expected value for [tex] E(\epsilon) = 0[/tex] a vector of zeros and the covariance matrix is given by:
[tex] Cov (\epsilon) = \sigma^2 I[/tex]
So we can see that the error terms not have a variance of 0. We can't assume that the errors are assumed to have an increasing mean, and we other property is that the errors are assumed independent and following a normal distribution so then the best option for this case would be:
The regression model assumes the errors are normally distributed.
Final answer:
The best statement is that the regression model assumes the errors are normally distributed. In regression analysis, it is essential that the errors are independent, normally distributed, and have constant variance, which supports the validity of the model's predictions.
Explanation:
The correct statement among the provided options is that the regression model assumes the errors are normally distributed. This is a fundamental assumption of linear regression analysis, where it's assumed that the residuals or errors of the regression model are randomly distributed about an average of zero. These error terms must be independent, normal, and have constant variance (homoscedasticity) across all levels of the independent variables.
According to the theoretical foundation of regression, it is not assumed that errors have an increasing mean, nor that they have zero variance, as some diversity in errors is expected. Additionally, the assumption that errors are indeed dependent would violate the principles of ordinary least squares (OLS) regression, making the model invalid.
Normality, independence, and equal variance are key premises in regression analysis to ensure the validity of the model's inferences. Indeterminate errors that affect the dependent variable 'y' are assumed to be normally distributed and independent of the independent variable 'x'. This maintains the integrity of the regression model.