Answer:
The answer is "[tex]\bold{\frac{1024}{3}}[/tex]".
Step-by-step explanation:
[tex]= \int\limits^{4}_{-4} \int\limits^{4}_{0} \int\limits^{16}_{x^2} dy\ dx \ dz \\\\= 2 \int\limits^{4}_{0} \int\limits^{4}_{0} \int\limits^{16}_{x^2} dy\ dx \ dz \\\\ = 2 \int\limits^{4}_{0} \int\limits^{4}_{0} (16-x^2) dx \ dz \\\\= 2 \int\limits^{4}_{0} \int\limits^{4}_{0} 16x -\frac{x^3}{3} dx \ dz \\\\= 2 (16x -\frac{x^3}{3})^4_{0} \ dz \\\\= 2 (4) (16x -\frac{64}{3}) \\\\=8(\frac{2}{3} \times 64) \\\\=(\frac{16\times 64}{3} ) \\\\= \frac{1024}{3}[/tex]
The volume of the given solid is [tex]\frac{1024}{3}[/tex] cubic units.
In this question we must use the triple integral formula in rectangular coordinates to determine the volume of the solid ([tex]V[/tex]):
[tex]V = \iiint dy\,dx\,dz[/tex] (1)
The solid is constrained by the following intervals:
[tex]y \in [x^{2}, 16][/tex], [tex]x \in [-4, 4][/tex], [tex]z\in [0, 4][/tex]
Then, the triple integral is now described:
[tex]V = \int\limits_{0}^{4}\int\limits_{-4}^{4}\int\limits_{x^{2}}^{16} dy\,dx\,dz[/tex]
Now we proceed to integrate thrice to obtain the volume:
[tex]V = \int \limits_{0}^{4}\int \limits_{-4}^{4} (16-x^{2})\,dx\,dz[/tex]
[tex]V = \int\limits_{0}^{4} \left(16\cdot x - \frac{x^{3}}{3}\right)\left|\limits_{-4}^{4} dz[/tex]
[tex]V = \frac{256}{3} \int\limits_{0}^{4} dz = \frac{1024}{3}[/tex]
The volume of the given solid is [tex]\frac{1024}{3}[/tex] cubic units.
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Does anyone know this answer
José correctly answered 80% of the
questions on a language arts quiz. If he
answered 16 questions correctly, how ma
questions were on the language arts quiz
Answer:
20
Step-by-step explanation:
80% needs 20% more to be 100% so we devide 16 by 4 to get the awnser for 20% witch is 4 so 16+4 is equal to 80% + 20% so 20
Answer:
20
Step-by-step explanation: 16 you need to 2 more question to get 100 so if you use your brain and imagine doing a test and you get an 80 percent and answered 16 correct go back to the test to see what you have
The changes in housing prices over short time periods are in part determined by supply and demand. A real estate company in Minnesota projected an increase in its average selling prices of homes in the first quarter of 2014 over the mean 2013 selling price of $201,800. The reason for the projection was an increase in demand due to business expansion and the subsequent increase in labor. To investigate the accuracy of the projection, a sample of homes in the first quarter of 2014 was selected and the following selling prices (in $) recorded:
235,000 271,900 183,300 203,000 182,900 225,500 189,000 214,200 237,900 233,500 217,000 230,400 202,950, 216,500 209,900, 245,500
Required:
a. At 5% level of significance, is there sufficient evidence to support the real estate company's projection?
b. Which statistical distribution should be applied in this situation and why? Explain carefully.
c. Discuss the consequences of Type I and Type II errors in terms of the problem.
d. Does the management at the real estate company want a small or large value of the significance level? Explain carefully.
e. Based on a 95% confidence level, estimate the actual average selling price homes in the first quarter of 2014.
Answer:
The data given is
235,000 271,900 183,300 203,000 182,900 225,500 189,000 214,200 237,900 233,500 217,000 230,400 202,950, 216,500 209,900, 245,500
The sample size is n = 16
The population is [tex]\mu = \$201,800[/tex]
The sample mean is mathematically represented as
[tex]\= x =\frac{\sum x_i}{n}[/tex]
=> [tex]\= x =\frac{235,000 + 271,900 + \cdots + 245,500 }{16}[/tex]
=> [tex]\= x = 218653.125[/tex]
Generally the sample standard deviation is mathematically represented as
[tex]s = \sqrt{\frac{\sum (x_i - \= x)^2}{n} }[/tex]
=> [tex]s = \sqrt{\frac{ (235,000 - 218653.125)^2+ (271,900 - 218653.125)^2 + \cdots + (245,500 - 218653.125)^2}{16} }[/tex]
=> [tex]s = 23946.896 [/tex]
The null hypothesis is [tex]H_o : \mu = \$201,800[/tex]
The alternatively hypothesis is [tex]H_o : \mu > \$201,800 [/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{s}{\sqrt{n} } }[/tex]
=> [tex]t = \frac{218653.125 - 201800 }{ \frac{23946.896 }{\sqrt{16} } }[/tex]
=> [tex]t = 2.82[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n - 1[/tex]
=> [tex]df = 16 - 1[/tex]
=> [tex]df = 15[/tex]
Generally the probability of [tex]t = 2.82[/tex] at a degree of freedom of [tex]df = 15[/tex] from the t - distribution table is
[tex]p-value = P( t >2.82 ) =0.00646356[/tex]
The
From the values obtained we see that [tex]p-value < \alpha[/tex]
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the real estate company's projection is true
Given that the population variance is unknown then the best statistical distribution to be applied is the t -distribution
Type I Error
The type 1 error occur when the null hypothesis is wrongfully rejected
The consequence in this case is the company will assume that the average selling price has increase and this will lead the company to start expanding the business while in the real sense the average selling price is still $201,800
Type II Error
The type 11 error occur when the null hypothesis is wrongfully accepted(i.e wrongfully failed to reject the null hypothesis)
The consequence in this case is that the company will assume that the average selling price is still $201,800 and will not make plans to increase the business while in the real sense the average selling price has increased
Given that resource is scare the management of the company will want a smaller significance level in order not to commit type I error which will lead to wrongly expanding the business and wastes of resources
generally the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E =Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{n} }[/tex]
=>[tex]E =1.96* \frac{23946.896}{\sqrt{16} }[/tex]
=>[tex]E = 11733.96[/tex]
Generally the 95% confidence interval is mathematically represented as
[tex]218653.125 - 11733.96 < \mu < 218653.125 + 11733.96[/tex]
=> [tex]206919.165 < \mu < 230387.085[/tex]
Generally there is 95% confidence that the actual average selling price is within this interval
Step-by-step explanation:
Ok so If and anchor descends -17.5 meters down in the ocean in 5 seconds, how much does it descend in 1 second?
The school band is in charge of a new set of uniforms made with a new logo. A local
business charges $140 to set up the logo with the design and $0.25 in materials per
logo printed. The function C(x) = 140+0.25x / x
represents the average cost per logo if x
uniforms are printed by this business.
a. What is the average cost per uniform to get the logo printed on 25 uniforms?
b. What is the average cost per uniform to get the logo printed on 100 uniforms?
C. How many uniforms should be printed to have an average cost of $1 per logo?
d. What will happen to the price as the number of uniforms printed increases?
Answer:
a. [tex]C(25) = 146.25[/tex]
b. [tex]C(100) = 165[/tex]
c. [tex]x = 187[/tex]
d. Increment in number of uniform causes an increment in price
Step-by-step explanation:
Given
[tex]C(x) = 140 + 0.25x[/tex]
Solving (a)
[tex]x = 25[/tex]
This gives:
[tex]C(x) = 140 + 0.25x[/tex]
[tex]C(25) = 140 + 0.25 * 25[/tex]
[tex]C(25) = 140 + 6.25[/tex]
[tex]C(25) = 146.25[/tex]
Solving (b):
[tex]x = 100[/tex]
This gives:
[tex]C(x) = 140 + 0.25x[/tex]
[tex]C(100) = 140 + 0.25 * 100[/tex]
[tex]C(100) = 140 + 25[/tex]
[tex]C(100) = 165[/tex]
Solving (c):
Average cost = $1 per logo
For x logos,
Average cost = $1 * x
Average cost = $x
So, we have:
[tex]C(x) = 140 + 0.25x[/tex]
[tex]x = 140 + 0.25x[/tex]
Collect Like Terms
[tex]x - 0.25x = 140[/tex]
[tex]0.75x = 140[/tex]
Solve for x
[tex]x = 140/0.75[/tex]
[tex]x = 187[/tex] ---- Approximated
Solving (d): What happens when number uniform increases.
Notice that in (a) & (b).
x increases from 25 to 100
Price also increases from $146.25 to $165.
Hence:
Increment in number of uniform causes an increment in price
In order to compare the durability of four different brands of golf balls (ALPHA, BEST, CENTURY, and DIVOT), the National Golf Association randomly selects five balls of each brand and places each ball into a machine that exerts the force produced by a 250-yard drive. The number of simulated drives needed to crack or chip each ball is recorded. The results are given in the following table.
Alpha Best Century Divot
281 270 218 364
220 334 244 302
274 307 225 325
242 290 273 337
251 331 249 355
Provide the EXCEL printout of ONEWAY ANOVA using either DATA ANALYSIS or PTSTAT2 to determine whether the mean number of stimulated drives differs by brand of golf ball.
Use the ANOVA printout to write-up the six step hypothesis testing procedure for determining whether the average number of simulated drives differs by brand of golf ball. What is the p-value for this problem and what does it mean? Assume alpha =.05.
Answer:
As our computed test statistic falls in critical region, so we reject our null hypothesis. Also p-value=0.0009 is less than significance level, so we reject our null hypothesis and conclude that the average number of simulated drives differs by brand of golf ball at 5% significance level.
Step-by-step explanation:
Excel output print out
Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Alpha 5 1268 253.6 609.3
Best 5 1532 306.4 740.3
Century 5 1209 241.8 469.7
Divot 5 1583 316.6 1235.3
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 20960.4 3 6986.8 9.149217573 0.000925804 3.238871517
Within Groups 12218.4 16 763.65
Total 33178.8 19
The six steps of hypothesis are
1. Null hypothesis: The average number of simulated drives are same by brand of golf ball
Alternative hypothesis: The average number of simulated drives differs by brand of golf ball
2. Significance level: α=0.05
3. Test statistic: F-ratio for one way anova
4. Computations
F=9.149
5. Critical region: F>3.239
6. Conclusion:
As our computed test statistic falls in critical region, so we reject our null hypothesis. Also p-value=0.0009 is less than significance level, so we reject our null hypothesis and conclude that the average number of simulated drives differs by brand of golf ball at 5% significance level.
working through this one. An airplane cuts through the morning sky. For every 1,000 feet that it climbs, the outside temperature drops 20 degrees Fahrenheit What is the rate of temperature change in degrees Fahrenheit per foot? In the following activity, you'll use what you know about dividing rational numbers to find the solution. Complete the steps below to answer the question. write the change in elevation and the temperature as rational number.
Answer:
Step-by-step explanation:
The air plane is rising so the change in elevation is +1000 feet. The temp dropped and is -20 degrees ferhenhite.
Please help me ..................
The answers are shown below:
What is square root?The square root of a number is that factor of a number which when multiplied by itself gives the original number. Squares and square roots are special exponents.
Consider the number 9. When 3 is multiplied by itself, it gives 9 as the product. This can be written as 3 × 3 or 32. Here, the exponent is 2, and we call it a square. Now when the exponent is 1/2, it refers to the square root of the number. For example, √n = n^1/2, where n is a positive integer.
a) point E represent √47 ( 6.855)b) point D represent √27 ( 5.19)
c) point A represent √11 ( 3.316)
√13(3.6050 lies between 3 and 4.-√150 (12.247) lies between (-12 and -13)side = √area= √30 = 5.477 inch√90=9.48 ( option b)The incorrect statement is √12 lies between 4 and 5Learn more about square root here:
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Factorise fully
-14x - 8
ease do quick, will mark brainiest!
Answer:
-2( 7x+4)
Step-by-step explanation:
-14x - 8
Factor out -2
-2*7x -2*4
-2( 7x+4)
Answer:
2(-7x -4)Step-by-step explanation:
[tex] - 14x - 8[/tex]
Write -8 as -4×2
[tex] - 14x + 2 \times 4[/tex]
Factor out common term : 2
[tex]2( - 7x - 4)[/tex]
Find the selling price of each item original plate price of gold fish at $7.65 discount 10%
Answer:
6.88 is what I think you're looking for
Step-by-step explanation:
is 10 15 18 equal to a right triangle
Answer:
no
Step-by-step explanation:
Right triangles follow the Pythagorean theorem:
[tex]a^2+b^2=c^2\\c=\sqrt{a^2+b^2}\\18=\sqrt{10^2+15^2} \\18=\sqrt{325} \\18 != 18.0277\\[/tex]
Because this statement isn't true, the side lengths are not for a right triangle.
Simplify this radical.
Square root 84
Answer: 9.16515139
Answer 2: 2√21
According to Wine-Searcher, wine critics generally use a wine-scoring scale to communicate their opinions on the relative quality of wines. Wine scores range from to , with a score of indicating a great wine, indicating an outstanding wine, indicating a very good wine, indicating a good wine, indicating a mediocre wine, and below indicating that the wine is not recommended. Random ratings of a pinot noir recently produced by a newly established vineyard in follow:
87 91 86 82 72 91
60 77 80 79 83 96
Required:
a. Develop a point estimate of mean wine score for this pinot noir (to decimals).
b. Develop a point estimate of the standard deviation for wine scores received by this pinot noir (to decimals).
Answer:
a
[tex]\= x = 82 [/tex]
b
[tex]s = 9.64 [/tex]
Step-by-step explanation:
From the question we are told that
The data is 87 91 86 82 72 91 60 77 80 79 83 96
Generally the point estimate for the mean is mathematically represented as
[tex]\= x = \frac{\sum x_i }{n}[/tex]
=> [tex]\= x = \frac{87 +91 + 86 + \cdots + 96}{12}[/tex]
=> [tex]\= x = 82 [/tex]
Generally the point estimate for the standard deviation is mathematically represented as
[tex]s = \sqrt{\frac{ \sum ( x_i - \= x )^2 }{ n -1 } }[/tex]
=> [tex]s = \sqrt{\frac{ ( 87 - 82 )^2 +( 91 - 82 )^2 + \cdots + ( 96 - 82 )^2 }{ 12 -1 } }[/tex]
=> [tex]s = 9.64 [/tex]
Part(a): The required mean is 82
Part(b): The required standard deviation is 9.639
Mean:
The mean is one of the measures of central tendency.
Part(a):
The formula for finding the mean is,
[tex]\bar{x}=\frac{\sum x_i}{n}[/tex]
Now, calculating the mean for the [tex]n=12[/tex] observation
[tex]\bar{x}=\frac{87+91+86+82+72+91+60+77+80+79+83+96}{12}\\ \bar{x}=82[/tex]
Part(b):
The formula for the standard deviation is,
[tex]S=\sqrt{\frac{\sum (x_i-\bar{x})^2}{n-1} }[/tex]
Substituting the given values into the above formula we get,
[tex]S=\sqrt{\frac{((87-82)^2+(91-82)^2)+(86-82)^2+(82-82)^2+(72-82)^2+(91-82)^2+(60-82)^2+(77-82)^2+...+(96-82)^2}{12-1} } \\S=9.639[/tex]
Learn more about the topic Mean:
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Write the decimal represented by each shaded square.
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
The decimal would be .70 because there's 70 squares that are shaded.
HELP MEE ;-;
2/3a - 7= 1/3 Round your answer to the nearest tenth.
Answer:
a=11
Step-by-step explanation:
Answer:
a = 11
Step-by-step explanation:
PLEASE HELP ME What is the amount of rain fall for the 1M 6 months of the year in Kennedale Texas
Arlington Texas Rainfall Amounts
Month
January
February
March
April
May
June
Rainfall Amount
+0.5 inches
-1.26 inches
+0.32 inches
+3.71 inches
- 1.27 inches
-2.40 Inches
A 2 inches
B. -0.4 inches
C 0.8 inches
D. -1.3 inches
Loo
Answer:
.5
Step-by-step explanation:
during a sale, 20 cent bars of soap were sold at the rate of 3 for 50 cents. how much is saved on 9 bars?
Answer:
30 is saved
Step-by-step explanation:
20 x 3 = 60 - 50 = 10, you get 10 three times because of 9 / 3 = 3 you get 10 x 3 = 30
Solve for x: y=3mx-2b
Answer:
x=(y+2b)/3m
Step-by-step explanation:
y+2b=3mx
(y+2b)/3m=x
Help, please I need it. I am horrible at math.
Using exponential maths what is 2x = 1/128
6 hours and 30 minutes after 11;00 is what time
Answer:
5:30
Step-by-step explanation:
you go ahead and add the 30 minutes so you then have 11:30 plus 6 hours is 5:30 because it only goes to 12:00 and repeats.
Answer ASAP: What is the smallest positive number that can be added to 55 so that the resulting number and 45 have 9 as their greatest common factor?
Answer:
55 + 45 = 90
90 divided by 45 = 2
90 divided by 9 = 10
Step-by-step explanation:
Eight individuals are candidates for positions of president, vice president, and treasurer of an organization. How many possibilities of selections exist
Answer:
336
Step-by-step explanation:
It is given that,
Total number of individuals are 8
They are candidates for positions of president, vice president, and treasurer of an organization.
It is a based on permutations. We need to find P(8,3). It can be calculated as follows :
[tex]P(n,r)=\dfrac{n!}{(n-r)!}[/tex]
So,
[tex]P(8,3)=\dfrac{8!}{(8-3)!}\\\\=\dfrac{8!}{5!}\\\\=\dfrac{8\times 7\times 6\times 5!}{5!}\ [\because n!=n(n-1)!]\\\\=8\times 7\times 6\\\\=336[/tex]
Hence, there are 336 possibilities of selections.
You come from a large, dysfunctional family. You learn of this year’s upcoming reunion, and dread the very thought of being around those people for any length of time. However, you’ve been intrigued by your introductory statistics course, and decide you will have some fun with the reunion by using it as an opportunity to study your family. As a preliminary project, you want to keep track of how many times each family member verbally assaults another person throughout the first 24 hours.
After 24 hours, you review your notes:
Family Member # Verbal Assaults
Stew (Dad) 5
Marge (Mom) 7
Betsy 18
Fred 11
Gracie 4
Jorge 10
Kim 5
Ferdinand 15
Hal 6
You 19
Find the mean, median, and mode of your distribution:
1. Mean
2. Median
3. Mode
4. Which measure of central tendency do you think is most appropriate for this dataser? Why?
5. What is the range of your dataset? Show how you figured it out.
6. Define, as specifically as necessary, the population in which you are interested for this research. In other words, how do you decide whether a person would be appropriate to include in your study?
7-9. Find the standard deviation for the data in the table on the first page. Showing your work is how you earn points for this part
10. What is the standard deviation of your dataset?
Answer:
Explained below.
Step-by-step explanation:
The data provided is for the number of times each family member verbally assaults another person throughout the first 24 hours.
Use Minitab to compute the descriptive statistics.
Go to Stat → Basic Statistics → Display Basic Statistics
A dialog box will open.
Select the variable.
Select 'Statistics'.
Another dialog box will open.
Select the statistics required.
Press OK.
Select "Graphs'.
Select Histogram.
Press OK
The output is attached below.
(1)
The mean of the data is, Mean = 10.
(2)
The median of the data is, Median = 8.50.
(3)
The mode of the data is, Mode = 5.
(4)
The inequality statement for the mean, median and mode is:
Mean > Median > Mode
A distribution is known as to be skewed to the right, or positively skewed, when maximum of the data are collected on the left of the histogram of the distribution.
Also if the Mean > Median > Mode then the distribution is skewed to the right.
For a skewed distribution the best of central tendency is the median.
So, the measure of central tendency that is most appropriate for this dataset is, Median = 8.50.
(5)
The range of the data set is:
Range = Maximum - Minimum
= 19 - 4
= 15
Thus, the range is 15.
(6)
The population of interest is the number of times the family members verbally assaults another person throughout the first 24 hours.
(7)
Consider the Minitab output.
The standard deviation of the data set is, SD = 5.60.
Chris has 12 sweets. He has 3 red, 6 blue, 1 yellow and 2 green sweets what fraction of his sweets is red
Answer:
He has had a quarter of the red one
Step-by-step explanation:
3/12 is 1/4 when simplified
Which expression is equivalent to |-5| + |3|?
Answer:
5+3 =8
Step-by-step explanation:
absolute value
Please find the area
Answer:
the answer is 6cm like its really obvious
Name the points which satisfy the conditions. The ordinate is zero.
9514 1404 393
Answer:
G
Step-by-step explanation:
The one point with a y-value of 0 is the one on the x-axis: G.
Simplify. 32v2 the power of 4/ 8v to the power of 6
1/4(-16x+8)? simplify or expand the expression
Answer:
-4x+2
Step-by-step explanation: