GPA and study time. A survey was conducted on 218 undergraduates from Duke University who took an introductory statistics course in Spring 2012. Among many other questions, this survey asked them about their GPA and the number of hours they spent studying per week. The scatterplot below displays the relationship between these two variables. a) The explanatory variable is and the response variable is ? b) The relationship between the variables is and . c) Is this experiment or an observational study? A. Experiment B. Observational study d) Can we conclude that studying longer hours leads to higher GPAs? A. No. We cannot conclude that studying longer hours leads to higher GPA since this study is observational. B. Yes, we can conclude that studying longer hours leads to higher GPA since this study is an experiment. C. Yes, we can conclude that studying longer hours leads to higher GPA since this study this is an observational study. D. No. We cannot conclude that studying longer hours leads to higher GPA since this study is an experiment. E. We cannot draw any conclusion because the scatterplot has no distinct form.
Answers
Answer: a) The explanatory variable is hours of study per week and the response variable is GPA.
b) The relantioship between the variables seems to be positive.
c) B. Observational Study.
d) A. NO. We cannot conclude that studying loger hours leads to higher GPA since this study is observational.
Step-by-step explanation: a) Explanatory Variable is a type of independent variable, which means it is a variable that doesn't depend on the other variables. However, in explanatory variable, there is a subtle relation between variables. For that reason, Hours of Study per week is an explanatory variable. Response Variable is the dependent variable, it is the result when you change the other variable. For that reason, GPA is the response variable.
b) Observing the graphic, which is in the attachment, it can be observed that students who study more hours per week, tend to have higher GPA. For example, people who studied 60 hours per week have a GPA closer to 4.
c) Observational Studies are those experiment where the researches only observe their object of interest without changing or interfering in the outcome. Experimental Studies are the ones where the researchers introduce an interference and study their effect on the randomized groups.
Since this experiment is based on observation only, the study is an Observational Study.
d) Because it's an observational study, we can't correlate or associate the variables, since the researchers only obtain their results through observation of the behaviour of the students, without changing it.
Related Questions
Angela wants to celebrate her birthday by eating pizza with her friends. She wants to buy
one box of pepperoni pizza for $9.50 and c boxes of cheese pizza for $8.50 each. Write an
expression, in dollars, that represents the amount Angela will spend on pizzas for her
birthday celebration.
Answers
Answer:
$8.50C + $9.50 = ______
That's the expression.
A 90% confidence interval for the mean height of students
is (60.128, 69.397). What is the value of the margin of error?
Answers
Answer:
4.635
Step-by-step explanation:
A confidence interval is:
CI = μ ± ME
where μ is the sample mean and ME is the margin of error.
In other words, the margin of error is half the width of the interval.
ME = (69.397 − 60.128) / 2
ME = 4.635
How many solutions does the system have? \begin{cases} 3y =- 6x+9 \\\\ y =-6x+9 \end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 3y=−6x+9 y=−6x+9
Answers
Answer:
Exactly one answer
Step-by-step explanation:
The equations show that 3y = y and the only number that could make it equal is 0, therefore there is only one solution.
Answer:
only one
Step-by-step explanation:
Solve the problem. A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 8.9 hours.
Answers
5/6 minus what equals 1/3
Answers
Answer:
3/6 = 1/2
Step-by-step explanation:
Important: 1/3 = 2/6
5/6-?=1/3
5/6-?=2/6
3/6=?
A sales manager collected the following data on annual sales for new customer accounts and the number of years of experience for a sample of 10 salespersons. Salesperson Years of Experience Annual Sales ($1000s) 1 1 80 2 3 97 3 4 92 4 4 102 5 6 103 6 8 111 7 10 119 8 10 123 9 11 117 10 13 136(a) Write an alternative hypothesis.(b). Develop an estimated regression equation that can be used to predict annual sales given the years of experience.(c) Use the estimated regression equation to predict annual sales tor a salesperson with 9 years of experience.
Answers
Answer:
A. See diagram
B.y=80+4x
C.110000
Refer below.
Step-by-step explanation:
Refer to the pictures for complete illustration.
The alternative hypothesis suggests a significant relationship between years of experience and annual sales. The estimated regression equation, derived from the given data, can be used to predict the annual sales based on years of service. For instance, a salesperson with 9 years of experience is predicted to make annual sales of $120.5k.
To begin, let's identify the variables of interest. The years of experience is the independent variable (x) and the annual sales is the dependent variable (y).
(a) Alternative Hypothesis: There is a significant linear relationship between the years of experience and the annual sales. It suggests that as the years of experience increase, the annual sales also increase.
(b) Estimated Regression Equation: To create the estimated regression equation, we first need to calculate the slope and y-intercept of the line that best fits the data. For example, using statistical software or a calculator, you might find the slope (B1) and y-intercept (B0) to be around 4.5 and 79 respectively (these numbers are hypothetical and for illustration purposes), resulting in the equation: Annual Sales = 4.5*(Years of Experience) + 79.
(c) Predicting Annual Sales: With 9 years of experience, you would plug the value 9 into the sample regression equation to predict the annual sales: Annual Sales = 4.5*(9) + 79 = $120.5 (in $1000s).
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how many 1/2 are in 7
Answers
14
All you have to do is multiply the 1/2 by the 7.
Answer:
14
Step-by-step explanation:
there are 14 1/2 in 7
The owner of the pizza chain wants to monitor the total weight of pepperoni. Suppose that for pizzas in this population, the weights have a mean of 250g and a standard deviation of 4g. Management takes a random sample of 64 of these pizzas and calculates the mean weight of the pepperoni on the pizzas. Assume that the pizzas in the sample are independent. What is the probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251g
Answers
Answer:
The probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251 g is 0.02275.
Step-by-step explanation:
We are given that the owner of the pizza chain wants to monitor the total weight of pepperoni. Suppose that for pizzas in this population, the weights have a mean of 250 g and a standard deviation of 4 g.
Management takes a random sample of 64 of these pizzas.
Let [tex]\bar X[/tex] = sample mean weight of the pepperoni.
The z score probability distribution for sample mean is given by;
Z = [tex]\frac{X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean weight = 250 g
[tex]\sigma[/tex] = standard deviation = 4 g
n = sample of pizzas = 64
Now, the probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251 g is given by = P([tex]\bar X[/tex] > 251 g)
P([tex]\bar X[/tex] > 251 g) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{251-250}{\frac{4}{\sqrt{64} } }[/tex] ) = P(Z > 2) = 1 - P(Z [tex]\leq[/tex] 2)
= 1 - 0.97725 = 0.02275
The above probabilities is calculated by looking at the value of x = 2 in the z table which has an area of 0.97725.
Hence, the probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251 g is 0.02275.
Which of the following are true if events A and B are independent? Select all that apply.
A. P(A | B) = P(A)
B. P(A | B) = P(B)
C. P(A | B) = P(A and B)
D. P(B | A) = P(A and B)
E. P(B | A) = P(A)
F. P(B | A) = P(B)
Answers
Answer:
The correct statement are (A) and (F).
Step-by-step explanation:
Events A and B are independent or mutually independent events if the chance of their concurrent happening is equivalent to the multiplication of their distinct probabilities.
That is,
[tex]P(A\cap B)=P(A)\times P(B)[/tex]
The conditional probability of event A given B is computed using the formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
And the formula for the conditional probability of event B given A is:
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]
Consider that events A and B are independent.
Then the conditional probability of event A given B will be:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
[tex]=\frac{P(A)\times P(B)}{P(B)}\\\\=P(A)[/tex]
And the conditional probability of event B given A will be:
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]
[tex]=\frac{P(A)\times P(B)}{P(A)}\\\\=P(B)[/tex]
Thus, the correct statement are (A) and (F).
In the context of independent events, the correct statements are that P(A | B) = P(A) and P(B | A) = P(B), indicating that the occurrence of one event does not affect the probability of the other event occurring. Other options presented do not accurately represent the properties of independent events in probability.
Explanation:When assessing whether events A and B are independent, it is essential to understand the criteria for independence in probability theory. Specifically, two events are independent if the probability of one event occurring does not affect the probability of the other event occurring. This can be mathematically represented as follows: P(A AND B) = P(A)P(B), P(A|B) = P(A), and P(B|A) = P(B).
If events A and B are independent, the correct statements among the choices provided are:
Option A is true because if A and B are independent, the probability of A occurring given that B has occurred is the same as the probability of A occurring on its own.
Option F is also correct for the same reason applied to event B; the probability of B occurring given that A has occurred is the same as the probability of B occurring on its own.
The remaining options are incorrect because they do not align with the definition of independent events:
amy wants to frame a poster that has a wdith of 8 inches and a lenghth of 1 foot. What is the permiter of the poster?
Answers
To find the perimeter of Amy's poster, convert all measurements to inches, resulting in a length of 12 inches and a width of 8 inches. Then use the formula for the perimeter of a rectangle, which is 40 inches in this case.
To calculate the perimeter of a poster, we must first have all dimensions in the same units. Amy's poster has a width of 8 inches and a length of 1 foot. Since there are 12 inches in a foot, the length is 12 inches. The perimeter of a rectangle is calculated by adding together the lengths of all the sides, or using the formula 2 * (length + width).
Using Amy's measurements, the perimeter of her poster would be:
2 * (12 inches + 8 inches) = 2 * 20 inches = 40 inches.
Therefore, the poster has a perimeter of 40 inches.
PLEASE HELP WILL MARK BRAINLIEST!
For the function below, is the discriminant positive, negative, zero
y=x^2 + 4x + 4
Answers
For this question it would
4^2-4(1)(4) = 0 so the discriminant is zero.
Location is known to affect the number, of a particular item, sold by an automobile dealer. Two different locations, A and B, are selected on an experimental basis. Location A was observed for 18 days and location B was observed for 13 days. The number of the particular items sold per day was recorded for each location. On average, location A sold 39 of these items with a sample standard deviation of 8 and location B sold 49 of these items with a sample standard deviation of 4. Does the data provide sufficient evidence to conclude that the true mean number of sales at location A is fewer than the true mean number of sales at location B at the 0.01 level of significance? Select the [Alternative Hypothesis, Value of the Test Statistic].
Answers
Final answer:
The question involves hypothesis testing for the difference in mean sales between two car dealership locations, using a t-test at the 0.01 level of significance. We would compare the p-value to 0.01 and if the p-value is less, we can conclude there's evidence supporting fewer mean sales at location A.
Explanation:
The student is asking whether the data from the two car dealership locations provide sufficient evidence to conclude that the true mean number of sales at location A is fewer than the true mean number of sales at location B at the 0.01 level of significance. This question pertains to hypothesis testing, specifically testing the difference between two means.
To test the hypothesis, we would set up the null hypothesis (H0): μA ≥ μB (mean sales at A are greater than or equal to those at B) and the alternative hypothesis (H1): μA < μB (mean sales at A are less than those at B). We can use a t-test for the difference in means since the population standard deviations are not known and the sample sizes are small.
The test statistic is calculated using the sample means, sample standard deviations, and sample sizes from both locations. Since we are performing a hypothesis test at a 0.01 significance level, we would compare the p-value of our test statistic to 0.01 to determine whether to reject the null hypothesis. If the calculated p-value is less than 0.01, we can conclude that there is sufficient evidence at the 1% significance level to support the claim that location A has fewer mean sales than location B.
What is the following product? RootIndex 5 StartRoot 4 x squared EndRoot times RootIndex 5 StartRoot 4 x squared EndRoot 4 x squared RootIndex 5 StartRoot 16 x Superscript 4 Baseline EndRoot 2 (RootIndex 5 StartRoot 4 x squared EndRoot) 16 x Superscript 4
Answers
Answer:
[tex](B)\sqrt[5]{16x^4}[/tex]
Step-by-step explanation:
We are required to evaluate:
[tex]\sqrt[5]{4x^2} X \sqrt[5]{4x^2}[/tex]
By laws of indices: [tex]\sqrt[n]{x}=x^{^\frac{1}{n} }[/tex]
Therefore: [tex]\sqrt[5]{4x^2} =(4x^2)^{^\frac{1}{5}[/tex]
Thus:
[tex]\sqrt[5]{4x^2} X \sqrt[5]{4x^2}=(4x^2)^{1/5}X(4x^2)^{1/5}\\$Applying same base law of indices:a^mXa^n=a^{m+n}\\(4x^2)^{1/5}X(4x^2)^{1/5}=(4x^2)^{1/5+1/5}=(4x^2)^{2/5}\\$Now, by index product law: a^{mn}=(a^m)^n\\(4x^2)^{2/5}=[(4x^2)^2]^{1/5}=[16x^4]^{1/5}\\[/tex]
[tex][16x^4]^{1/5}=\sqrt[5]{16x^4} \\$Therefore:\\\sqrt[5]{4x^2} X \sqrt[5]{4x^2}=\sqrt[5]{16x^4}[/tex]
Answer:
b in edge
Step-by-step explanation:
Multiply 5 2/5 x 9 2/10 show your work.
Answers
Answer: [tex]49\frac{7}{10}[/tex]
Turn 5 2/5 into an Improper Fraction
Multiply 5*5 and get 25. Now add 2 and get 27.
5 2/5=27/5
Turn 9 2/10 into an Improper Fraction
Multiply 9*10 and get 90. Now add 2 and get 92.
9 2/10=92/10
New problem: 27/5×92/10
Multiply
[tex]27/5*92/10=2484/50[/tex]
Divide
[tex]2485/50=49.7[/tex]
Turn 49.7 into a Mixed Number
[tex]49.7=49\frac{7}{10}[/tex]
Answer:
[tex] = 49.68[/tex]
Step-by-step explanation:
[tex]5 \frac{2}{5} \times 9 \frac{2}{10} \\ \frac{27}{5} \times \frac{92}{10} \\ \frac{2484}{50} \\ = 49.68[/tex]
11,235,000,000 in scientific notation
Answers
Answer:
the answer in scientific notation is 1.1235x10^10
what is 4/7 divded by 10/21
Answers
Answer:
6/5
Step-by-step explanation:
(4/7) divided by (10/21) = (4/7) * (21/10) = (3*4)/10= 6/5
Hope this helps
The ratio of Jane's age to her daughter's age is 9:2.
The sum of their ages is 44. How old is Jane?
A. 22
B. 33
C. 35
D. 36
E. 40
Answers
Jane is of 36. Hence the option D. 36 is correct.
The ratio of Jane's age to her daughter's age is 9:2.
The sum of their ages is 44.
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
The ratio of age is 9:2
now total = 11
jane age can be given as = 44 x9/11
jane age = 36
Thus, the required age of jane is 36.
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Which of the following explains how ΔAEI could be proven similar to ΔDEH using the AA similarity postulate?
Quadrilateral ABDC, in which point F is between points A and C, point G is between points B and D, point I is between points A and B, and point H is between points C and D. A segment connects points A and D, a segment connects points B and C, a segment connects points I and H, and a segment connects points F and G. Segments AD, BC, FG, and IH all intersect at point E.
∠AEI ≅ ∠DEH because vertical angles are congruent; reflect ΔHED across segment FG, then translate point D to point A to confirm ∠IAE ≅ ∠HDE.
∠AEI ≅ ∠DEH because vertical angles are congruent; rotate ΔHED 180° around point E, then translate point D to point A to confirm ∠IAE ≅ ∠HDE.
∠AEI ≅ ∠DEH because vertical angles are congruent; rotate ΔHED 180° around point E, then dilate ΔHED to confirm segment ED ≅ segment EA.
∠AEI ≅ ∠DEH because vertical angles are congruent; reflect ΔHED across segment FG, then dilate ΔHED to confirm segment ED ≅ segment EI.
Answers
Answer:
∠AEI ≅ ∠DEH because vertical angles are congruent; rotate ΔHED 180° around point E, then translate point D to point A to confirm ∠IAE ≅ ∠HDE.
Step-by-step explanation:
tbh im not suuper sure but my educated guess is that by looking at it. Good Luck!
Two triangles are said to be similar by AA if two angles of both triangles are equal. The explanation that proves the similarity of [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex] by AA is option (a)
Given that: [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex]
To prove that [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex] are similar by AA, it means that two corresponding angles of both triangles must be congruent. So, the following must be true:
The angle at point E in both triangles must be equal. i.e. [tex]\angle AEI \cong \angle DEH[/tex]. This is so because the angle at E is a vertical angle to both triangles, and vertical angles are congruent.The angle at A and D of both triangles must be equal, i.e. [tex]\angle IAE \cong HDE[/tex]. This is so because a 180 degrees rotation of [tex]\triangle DEH[/tex] around the center E will give a similar (but larger) triangle to [tex]\triangle AEI[/tex]. Point D can then be shifted to A.Hence, (a) is true
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Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t ≥ 0. Then the integral ℒ{f(t)} = [infinity] e−stf(t) dt 0 is said to be the Laplace transform of f, provided that the integral converges. to find ℒ{f(t)}. (Write your answer as a function of s.) f(t) = te9t ℒ{f(t)} = (s > 9)
Answers
Answer:
e^-s/s + e^-s/s^2
Step-by-step explanation:
See the attachment please
The question asks for the Laplace transform of f(t) = te^9t using the given definition of the Laplace Transform. This can be calculated using the integral ℒ{f(t)} = ∫ (from 0 to ∞) e^{-st} te^9t dt and likely requires the technique of integration by parts for evaluation.
Explanation:The question is asking for the Laplace transform of the function f(t) = te9t, using the definition of the Laplace transform. The Laplace Transform is a method that can be used to solve differential equations. In general, the Laplace Transform of a function f(t) is defined as ℒ{f(t)} = ∫ (from 0 to ∞) e-st f(t) dt, provided that the integral converges.
In this case, f(t) is equal to te9t so the integral becomes ℒ{f(t)} = ∫ (from 0 to ∞) e-st te9t dt. To find the integral, you would generally need to use integration by parts, which is a method of integration that is typically taught in a calculus course. Note that the given condition (s > 9) will affect the convergence of the integral.
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The National Center for Health Statistics interviewed 5409 adults smokers in 2015, and 2636 of them said they had tried to quit smoking during the past year. Consider this to be a random sample. a) Find a 95% confidence interval for the proportion of smokers who have tried to quit within the past year.
Answers
Answer:
0.4740<p<0.5006
Step-by-step explanation:
-Given [tex]n=5409, \ x=2636 , \ CI=0.95[/tex]
#we calculate the proportion of trial quitters;
[tex]\hat p=\frac{2636}{5409}\\\\=0.4873[/tex]
For a confidence level of 95%:
[tex]z_{\alpha/2}=z_{0.025}\\\\=1.96[/tex]
The confidence interval is calculated as follows:
[tex]Interval= \hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\\\\\=0.4873\pm 1.96\times\sqrt{\frac{0.4873(1-0.4873)}{5409}}\\\\\\\\=0.4873\pm0.0133\\\\\\=[0.4740,0.5006][/tex]
Hence, the 95% confidence interval is 0.4740<p<0.5006
The 95% confidence interval for the proportion of smokers who have tried to quit within the past year is (0.4738, 0.5004), calculated using the sample proportion and the z-score for the 95% confidence level.
Explanation:To find the 95% confidence interval for the proportion of smokers who have tried to quit within the past year, we use the formula for a confidence interval for a population proportion:
CI = p± z*(√p(1-p)/n)
Where:
CI = Confidence Interval
p = Sample proportion (successes/sample size)
z = z-score associated with the confidence level
n = Sample size
Given:
p = 2636/5409
n = 5409
And for a 95% confidence level, the z-score is typically about 1.96.
Step 1: Calculate the sample proportion (p):
2636/5409 = 0.4871
Step 2: Calculate the standard error (SE):
SE = √[0.4871*(1-0.4871)/5409] = 0.0068
Step 3: Calculate the margin of error (ME):
ME = z * SE = 1.96 * 0.0068 = 0.0133
Step 4: Calculate the confidence interval:
Lower bound = p - ME = 0.4871 - 0.0133 = 0.4738
Upper bound = p + ME = 0.4871 + 0.0133 = 0.5004
So, the confidence interval is (0.4738, 0.5004).
An inverted pyramid is being filled with water at a constant rate of 35 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 6 cm, and the height is 8 cm. Find the rate at which the water level is rising when the water level is 3 cm.
Answers
Final answer:
The rate at which the water level is rising when the water level is 3 cm is approximately 2.92 cm/s.
Explanation:
To find the rate at which the water level is rising, we need to consider the volume of water being added per unit time and how that volume relates to the change in water level. The volume of a pyramid can be calculated using the formula V = (1/3)b*h, where b is the area of the base and h is the height. In this case, the base is a square with sides of length 6 cm, so the area is 6*6 = 36 cm^2. Substituting this into the formula, the volume of the pyramid is V = (1/3)*36*8 = 96 cm^3. Since the water is being filled at a rate of 35 cm^3/s, we can find the rate of the water level rising by taking the derivative of the volume equation with respect to time:
dV/dt = (1/3)*b*dh/dt
where dV/dt is the rate of change of volume, b is the area of the base, and dh/dt is the rate of change of the height (which is the same as the rate of change of the water level).
Substituting in the known values:
35 = (1/3)*36*(dh/dt)
dh/dt = (35*3)/(36) = 35/12 ≈ 2.92 cm/s
A fish in an aquarium with flat sides looks out at a hungry cat. To the fish, the distance to the cat appears to be A fish in an aquarium with flat sides looks out at a hungry cat. To the fish, the distance to the cat appears to be Equal to the actual distance. Less than the actual distance. More than the actual distance.
Answers
Answer:
Hence A fish in an aquarium see the cat more than actual distance.
Step-by-step explanation:
Given:
A fish in aquarium with flat silde looks out to cat .
To find :
Appearance of fish to the cat.
Solution:
Now this problem is related to the refractive index of 2 mediums
So cat is in air medium and a fish in water i.e. aquarium
R.I of water =1.33
R.I of air =1.00
We know the incident ray ,reflected ray,refracted ray and normal .
When a incident ray enter in denser medium it bends towards normal.
But it diverges outward direction and goes beyond the actual object.
(Refer the Attachment).
Hence A fish in an aquarium see the cat more than actual distance.
Please help!!!
If the area of a rectangle is 42m^2, find value x
Answers
Answer:
Give me more fees back on your equation
Step-by-step explanation:
Area of the base = 75 square inches and
height is 15 inches
Answers
The question pertains to calculating the volume of a triangular prism using the given area of the base and height. The volume is found by multiplying the area of the base (75 square inches) by the height (15 inches) to yield an answer of 1125 cubic inches.
Explanation:The question provided relates to the concept of finding the volume of a geometric shape, specifically a triangular prism, as it gives the area of the base and the height of the prism. In geometry, to find the volume of a triangular prism, we use the formula V = Area of base imes Height. Given that the area of the base provided is 75 square inches and the height is 15 inches, we can calculate the volume of the triangular prism.
To calculate volume:
Multiply the area of the base (75 square inches) by the height of the prism (15 inches).Volume = 75 in2 imes 15 in = 1125 cubic inches.Thus, the volume of the triangular prism is 1125 cubic inches.
A cylindrical can, open at the top, is to hold cm3 of liquid. Find the height, , and the radius, , that minimize the amount of material needed to manufacture the can. Enter the exact answers.
Answers
Answer:
[tex]r=4\ cm,\ h=4\ cm[/tex]
Step-by-step explanation:
Minimization
Optimization is the procedure leading to find the values of some parameters that maximize or minimize a given objective function. The parameters could have equality and inequality restrictions. If only equality restrictions hold, then we can use the derivatives to find the possible maximum or minimum values of the objective function.
The problem states we need to minimize the amount of material needed to manufacture the cylindrical can. The material is the surface area of the can. If the can has height h and radius r on the base, then the surface area is
[tex]A=2\pi rh+\pi r^2[/tex]
Note there is only one lid at the bottom (open at the top), that is why we added only the surface area of one circle.
That is our objective function, but it's expressed in two variables. We must find a relation between them to express the area in one variable. That is why we'll use the given volume (We'll assume the volume to be [tex]64\pi cm^3[/tex] because the question skipped that information).
The volume of a cylinder is
[tex]V=\pi r^2h[/tex]
We can solve it for h and replace the formula into the formula for the area:
[tex]\displaystyle h=\frac{V}{\pi r^2}[/tex]
Substituting into the area
[tex]\displaystyle A=2\pi r\cdot \frac{V}{\pi r^2}+\pi r^2[/tex]
Simplifying
[tex]\displaystyle A=\frac{2V}{ r}+\pi r^2[/tex]
Now we take the derivative
[tex]\displaystyle A'=-\frac{2V}{ r^2}+2\pi r[/tex]
Equating to 0
[tex]\displaystyle \frac{-2V+2\pi r^3}{ r^2}=0[/tex]
Since r cannot be 0:
[tex]-2V+2\pi r^3=0[/tex]
[tex]\displaystyle r=\sqrt[3]{\frac{V}{\pi}}[/tex]
Since [tex]V=64\pi[/tex]
[tex]\displaystyle r=\sqrt[3]{\frac{64\pi}{\pi}}=4[/tex]
[tex]r=4\ cm[/tex]
And
[tex]\displaystyle h=\frac{64\pi}{\pi 4^2}=4[/tex]
[tex]h=4\ cm[/tex]
Summarizing:
[tex]\boxed{r=4\ cm,\ h=4\ cm}[/tex]
The point Z(3,−3) is rotated 180°counterclockwise around the origin. What are the coordinates of the resulting point, Z'?
Answers
The coordinates of point Z(3, -3) after a 180° counterclockwise rotation around the origin are Z'(-3, 3).
The student has asked about the result of a 180° counterclockwise rotation around the origin for a point with given coordinates. When a point (x, y) is rotated 180° around the origin, both the x-coordinate and y-coordinate flip signs, which is a standard transformation in coordinate geometry.
For the point Z(3,−3), performing this rotation results in the point Z' having the coordinates (-3, 3).
This transformation follows the rule that (x, y) becomes (-x, -y) upon a 180° rotation about the origin.
Brian has reduced his cholesterol level by 13% after his last check up. If his original level was 200, what is his cholesterol level now?
Answers
174
Explanation
Because Brian reduces his cholesterol level by 13%, he now has 87% of his original cholesterol level. Multiply his original cholesterol level by the percentage of his original cholesterol level he has left (.87) to get his current cholesterol level.
200 * 0.87 = 174
A fence on a hill uses vertical posts L and M to hold parallel rails N and P. ∠10 and ∠14 are alternate interior angles. What is the transversal?
A. M
B. N
C. P
D. L
Answers
Line P exists the common transversal of parallel lines L and M.
What is the transversal?Let, L and M exists vertical posts,
⇒ L and M exists parallel to one another,
Given: ∠10 and ∠14 are alternative interior angles of the parallel lines L and M.
Since, the alternative interior angles on the parallel line exists created by a common transversal.
Consider to the diagram,
Line P creates the angles 10 and 16 on the parallel lines L and M.
Line P exists the common transversal of parallel lines L and M.
Therefore, the correct answer is option C. P.
To learn more about transversal
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simplest form 8/10 - 2/10 =
Answers
Answer:
3/5, 0.6
Step-by-step explanation:
8/10 - 2/10 = 6/10
6/10/2= 3/5
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Step-by-step explanation:
8/10-2/10
it will be 6/10 both numbers arre divisible by 2 so 3/5
Final ANSWER
3/5
In the figure below, BD and EC are diameters of circle P.
What is the arc measure of AE in degrees?
Answers
Answer:
27°Step-by-step explanation:
We know by given
[tex]m \angle APB = 90\°[/tex]
[tex]m \angle DPE=63\°[/tex]
According to the given circle,
[tex]m\angle DPE + m\angle EPA + m\angle APB=180\°[/tex], by supplementary angles.
Replacing each value, we have
[tex]63\° + m\angle EPA + 90\° = 180\°\\m \angle EPA = 180\° - 153\°\\m \angle EPA = 27\°[/tex]
Now, the angle EPA subtends the arc AE, and this angle is a central angle. So, according to its defintion, the arc AE is equal to its central angle.
[tex]arc(AE)= m\angle EPA = 27\°[/tex]
Therefore, the answer is 27°