The volume of the cone, when the base area is 12 ft² and the height is 6 ft, is approximately 24 ft³.
To find the volume of the cone when the base area is 12 ft² and the height is 6 ft, we need to first determine the variation constant relating the volume, base area, and height.
Let's denote the volume of the cone as V, the base area as A, and the height as h. According to the problem, the volume varies jointly with the base area and the height.
Therefore, we can write the following equation:
V = k * A * h
Here k is the variation constant we want to find.
Given one set of values: when A = 15 ft² and h = 2 1/2 ft, V = 12.5 ft³.
Substitute these values into the equation and solve for k:
12.5 ft³ = k * 15 ft² * (2.5 ft)
Now, we can solve for k:
k = 12.5 ft³ / (15 ft² * 2.5 ft)
k = 0.3333 ft
Now that we have the value of the variation constant (k), we can find the volume when A = 12 ft² and h = 6 ft:
V = k * A * h
V = 0.3333 ft * 12 ft² * 6 ft
V = 23.9996 ft³
Therefore, the volume of the cone is 24 ft³.
Learn more about the volume of the cone here:
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The correct question is as follows:
The volume of a cone varies jointly with the base (area) and the height. The volume is 12.5 ft³ when the base (area) is 15 ft² and the height is 2 1/2 ft. Find the volume of the cone (after finding the variation constant) when the base (area) is 12 ft² and the height is 6 ft.
will give 5 stars and thanks for correct answer Richard starts high school every day at 7:45 A.M.. How many seconds is Richard in school each day of school dismissed at 2:15 P.M.
WILL GIVE BRAINLYEST AND 30 POINTS Which of the followeing can be qritten as a fraction of integers? CHECK ALL THAT APPLY 25, square root of 14, -1.25, square root 16, pi, 0.6
Answer:
25 CAN be written as a fraction.
=> 250/10 = 25
Square root of 14 is 3.74165738677
It is NOT POSSIBLE TO WRITE THIS FULL NUMBER AS A FRACTION, but if we simplify the decimal like: 3.74, THEN WE CAN WRITE THIS AS A FRACTION
=> 374/100
-1.25 CAN be written as a fraction.
=> -5/4 = -1.25
Square root of 16 CAN also be written as a fraction.
=> sqr root of 16 = 4.
4 can be written as a fraction.
=> 4 = 8/2
Pi = 3.14.........
It is NOT POSSIBLE TO WRITE THE FULL 'PI' AS A FRACTION, but if we simplify 'pi' to just 3.14, THEN WE CAN WRITE IT AS A FRACTION
=> 314/100
.6 CAN be written as a fraction.
=> 6/10 = .6
Hi Mathies, Help with this vectors excercise pls. Givan that OA (segment) = 13x+7y , OB = 5x+12y and CO = -15+12y write down each of the following vectors in its simplest form a) BA = 8x+ 5y (l got it, i ve done it) b) AC= ?? i cant find vector AC thanks in advance
Answer:
AC = 2x-19yStep-by-step explanation:
Given vector the following vector equations OA = 13x+7y , OB = 5x+12y and CO = -15x+12y, the following expression is true about vector OA, OB and OC;
OA+OB = CO (CO is the resultant since its is moving in the opposite direction compare to OA and OB)
Also BO+OA = BA and AO+OC = AC
If OB = 5x+12y, then BO = -(5x+12y)
BO = -5x-12y (BO = -OB)
Since BO+OA = BA
BA = -5x-12y + 13x+7y
BA = -5x+13x-12y+7y
BA = 8x-5y
Similarly AO+OC = AC
Since AO = -OA and OC = -CO
-OA-CO = AC
AC = -(13x+7y)-(-15x+12y)
AC = -13x-7y+15x-12y
AC = -13x+15x-7y-12y
AC = 2x-19y
Given: f(x) = x + 2 and g(x) = x2 +3, find the following:
28) f(-3)
29) f(g(2))
30) g(f(x))
31) f-1(x)
Answer:
28) -1
29) 9
30) x^2+4x+7
31) x-2
Step-by-step explanation:
Given:
f(x) = x + 2
g(x) = x^2 +3
Find:
28) f(-3)
29) f(g(2))
30) g(f(x))
31) f-1(x)
Solution:
Put the function argument values into the expression and do the arithmetic.
28) f(-3) = (-3) +2 = -1
__
29) f(g(2)) = f((2)^2 +3) = f(7) = (7) +2 = 9
__
30) g(f(x)) = g(x+2) = (x+2)^2 +3 = x^2 +4x +7
__
31) The meaning of y = f^-1(x) is x = f(y).
x = f(y) = y+2
y = x -2
f^-1(x) = x -2
Please help. I’ll mark you as brainliest if correct!
Answer:
Children = 150
Students = 98
Adults = 75
Step-by-step explanation:
C + S + A = 323
5C + 7S + 12A = 2336
A = 1/2C
C = 150
S = 98
A = 75
Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps
west and finally 50 steps on a bearing of 3150
.
i. Sketch Musah’s movement
ii. How far west is Musah’s final point from the centre?
iii. How far north is Musah’s final point from the centre?
iv. Describe how you would guide a JHS student to find the bearing and distance of
Musah’s final point from the centre.
Answer:
ii. 75 steps
iii. 75 steps
iv. 106 steps, and [tex]315^{0}[/tex]
Step-by-step explanation:
Let Musah's starting point be A, his waiting point after taking 50 steps northward and 25 steps westward be B, and his stopping point be C.
ii. From the second attachment, Musah's distance due west from A to C (AD) can be determined as;
bearing at B = [tex]315^{0}[/tex], therefore <BCD = [tex]45^{0}[/tex]
To determine distance AB,
[tex]/AB/^{2}[/tex] = [tex]/50/^{2}[/tex] + [tex]/25/^{2}[/tex]
= 25000 + 625
= 3125
AB = [tex]\sqrt{3125}[/tex]
= 55.90
AB ≅ 56 steps
Thus, AC = 50 steps + 56 steps
= 106 steps
From ΔACD,
Sin [tex]45^{0}[/tex] = [tex]\frac{x}{106}[/tex]
⇒ x = 106 × Sin [tex]45^{0}[/tex]
= 74.9533
≅ 75 steps
Musah's distance west from centre to final point is 75 steps
iii. From the secon attachment, Musah's distance north, y, can be determined by;
Cos [tex]45^{0}[/tex] = [tex]\frac{y}{106}[/tex]
⇒ y = 106 × Cos [tex]45^{0}[/tex]
= 74.9533
≅ 75 steps
Musah's distance north from centre to final point is 75 steps.
iv. Musah's distance from centre to final point is AC = AB + BC
= 50 steps + 56 steps
= 106 steps
From ΔACD,
Tan θ = [tex]\frac{75}{75}[/tex]
= 1.0
θ = [tex]Tan^{-1}[/tex] 1.0
= [tex]45^{0}[/tex]
Musah's bearing from centre to final point = [tex]45^{0}[/tex] + [tex]270^{0}[/tex]
= [tex]315^{0}[/tex]
A certain family has a husband, wife, son, and daughter. All together they are 68 years old. The husband is 3 years older than the wife, and the son is 3 years older than the daughter. Four years ago, all together the family was 54 years old. How old is the husband now?
Answer:
32
Step-by-step explanation:
Everyone added together = 68
Four years ago, they were 68 -16 = 52
But the question told 54 years.
So there was a girl who was 2 years.
Girl = 2
Boy = 2 +3 = 5
Husband = 3 +w
Wife =w
3 +w +w + 5 + 2 = 68
10 + 2w = 68
2w = 58
w = 29
Wife = 29
Husband = 29 +3 =32
Husband = 32 years
Answer:
[tex]\large \boxed{\sf \bf \ \ 32 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
We know that "All together they are 68 years old." and "Four years ago, all together the family was 54 years old."
If all the family was alive four years ago, it means that four years ago the sum of their ages was 68 - 4 - 4 - 4 - 4 because they are four members, so it gives 68 - 16 =52 which is different from 54, right ?
It means that we have the daughter in between, 54- 52 = 2, so the daughter's age is 2, and then the son's age is 5.
The husband is 3 years older than the wife. Let's note W the wife's age, we can write W + 3 + W + 5 + 2 = 68
2 W + 10 = 68
2 W = 68 - 10 = 58 so W = 29
and then the husband's age is 29 + 3 = 32.
And we can verify that 32 + 29 + 5 + 2 = 68, and four years ago, 28 + 25 + 1 + 0 = 54.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A manager wants to determine an appropriate learning percentage for processing insurance claims for storm damage. Toward that end, times have been recorded for completion of each of the first six repetitions:
Repetition 1 2 3 4 5 6
Time (minutes) 46 39 35 33 32 30
a. Determine the approximate learning percentage. (Round your answer to the nearest whole percent. Omit the "%" sign in your response.)
P %
b. Using your answer from part a, estimate the average completion time per repetition assuming a total of 30 repetitions are planned. (Round your answer to 3 decimal places.)
Answer:
Step-by-step explanation:
The approximate learning percentage can be estimated by using a doubling method.
If we breakdown the repetitions into three consecutive parts, we have:
1 - 2
2 - 4
3 - 6
then
1 - 2 → 46P = 39
P =39/46
P = 0.8478
P = 84.8%
2 - 4 → 39P = 33
P = 33/39
P = 0.84615
P = 84.6%
3 - 6 → 35P = 30
P = 30/35
P = 0.8571
P = 85.7%
The average value of P = (84.8 + 84.6 + 85.7)/3 = 85.03%
[tex]\simeq[/tex] 85%
From the tables of Learning Curves coefficient
The values are likened against times derived from 85% table factors at T[tex]_1[/tex] = 46
Unit 1 2 3 4 5 6
Date 46 39 35 33 32 30
Computed - 39.1 35.56 33.26 31.56 30.22
b. Using your answer from part a, estimate the average completion time per repetition assuming a total of 30 repetitions are planned. (Round your answer to 3 decimal places.)
The average completion time = [tex]\mathtt{\dfrac{T_1 \times \ Total \ time\ factor}{n}}[/tex]
At the total time factor 30, from the learning curves table , n(30) = 17.091
Thus:
The average completion time = [tex]\mathtt{\dfrac{46 \times \ 17.091}{30}}[/tex]
The average completion time = [tex]\mathtt{\dfrac{786.186}{30}}[/tex]
The average completion time = [tex]\mathtt{26.2062}[/tex]
Using the insurance company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 14-year period. Round your answer to four decimal places.
Answer: 19.2222
Step-by-step explanation:
given data;
no of tornadoes = 2,1,0 because it’s fewer than 3.
period = 14 years
probability of a tornado in a calendar year = 0.12
solution:
probability of exactly 2 tornadoes
= ( 0.12 )^2 * ( 0.88 )^11 * ( 14! / 2! * 11! )
= 0.0144 * 0.2451 * 1092
= 3.8541
probability of exac one tornado
= ( 0.12 )^1 * ( 0.88 )^12 * ( 14! / 1! * 12! )
= 0.12 * 0.2157 * 182
= 12.7109
probability of exactly 0 tornado
= ( 0.12 )^0 * ( 0.88 )^13 * ( 14! / 0! * 13! )
= 1 * 0.1898 * 14
= 2.6572
probability if fewer than 3 tornadoes
= 3.8541 + 12.7109 +2.6572
= 19.2222
9.3.2 Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of d overbar and s Subscript d. In general, what does mu Subscript d represent? Temperature (degrees Upper F )at 8 AM 98.1 98.8 97.3 97.5 97.9 Temperature (degrees Upper F )at 12 AM 98.7 99.4 97.7 97.1 98.0 Let the temperature at 8 AM be the first sample, and the temperature at 12 AM be the second sample. Find the values of d overbar and s Subscript d.
Answer:
[tex]\frac{}{d}[/tex] = −0.26
[tex]s_{d}[/tex] = 0.4219
Step-by-step explanation:
Given:
Sample1: 98.1 98.8 97.3 97.5 97.9
Sample2: 98.7 99.4 97.7 97.1 98.0
Sample 1 Sample 2 Difference d
98.1 98.7 -0.6
98.8 99.4 -0.6
97.3 97.7 -0.4
97.5 97.1 0.4
97.9 98.0 -0.1
To find:
Find the values of [tex]\frac{}{d}[/tex] and [tex]s_{d}[/tex]
d overbar ( [tex]\frac{}{d}[/tex]) is the sample mean of the differences which is calculated by dividing the sum of all the values of difference d with the number of values i.e. n = 5
[tex]\frac{}{d}[/tex] = ∑d/n
= (−0.6 −0.6 −0.4 +0.4 −0.1) / 5
= −1.3 / 5
[tex]\frac{}{d}[/tex] = −0.26
s Subscript d is the sample standard deviation of the difference which is calculated as following:
[tex]s_{d}[/tex] = √∑([tex]d_{i}[/tex] - [tex]\frac{}{d}[/tex])²/ n-1
[tex]s_{d}[/tex] =
√ [tex](-0.6 - (-0.26))^{2} + (-0.6 - (-0.26))^{2} + (-0.4 - (-0.26))^{2} + (0.4-(-0.26))^{2} + (-0.1 - (-0.26))^{2} / 5-1[/tex]
= √ (−0.6 − (−0.26 ))² + (−0.6 − (−0.26))² + (−0.4 − (−0.26))² + (0.4 −
(−0.26))² + (−0.1 − (−0.26))² / 5−1
= [tex]\sqrt{\frac{0.1156 + 0.1156 + 0.0196 + 0.4356 + 0.0256}{4} }[/tex]
= [tex]\sqrt{\frac{0.712}{4} }[/tex]
= [tex]\sqrt{0.178}[/tex]
= 0.4219
[tex]s_{d}[/tex] = 0.4219
Subscript d represent
μ[tex]_{d}[/tex] represents the mean of differences in body temperatures measured at 8 AM and at 12 AM of population.
What does the tape measure say Measurement # 3 is? *
Answer:
5 and 3/32 of an inch.
When a sender and receiver belonging to the same group want to transmit technical information more efficiently, they should use:___________.
Answer:
Jargon that they both understand will be used.
Step-by-step explanation:
Jargon that they both understand will be used.
Jargon is a literary term that is defined as the use of specific phrases and words in a particular situation, profession, or trade. The use of jargon becomes important in prose or verse or some technical pieces of writing, when the writer plans to convey something only to the readers who are aware of these terms. Some of such examples are:
Due diligence: This is a business term, which refers to the research that should be done before making an important business decision.
AWOL: Short for "absent without leave," AWOL is military jargon used to describe a person whose whereabouts is unknown.
Suppose a 99% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$34,393, $47,207]. The population standard deviation used for the analysis is known to be $14,900.
Required:
a. What is the point estimate of the mean salary for all college graduates in this town?
b. Determine the sample size used for the analysis.
Answer: a. $40,800 b. 36
Step-by-step explanation:
Given : a 99% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$34,393, $47,207].
[tex]\sigma= \$14,900[/tex]
a. Since Point estimate of of the mean = Average of upper limit and lower limit of the interval.
Therefore , the point estimate of the mean salary for all college graduates in this town = [tex]\dfrac{34393+47207}{2}=\dfrac{81600}{2}[/tex]
= 40,800
hence, the point estimate of the mean salary for all college graduates in this town = $40,800
b. Since lower limit = Point estimate - margin of error, where Margin of error is the half of the difference between upper limit and lower limit.
Margin of error[tex]=\dfrac{47207-34393}{2}=6407[/tex]
Also, margin of error = [tex]z\times\dfrac{\sigma}{\sqrt{n}}[/tex], where z= critical z-value for confidence level and n is the sample size.
z-value for 99% confidence level = 2.576
So,
[tex]6407=2.576\times\dfrac{14900}{\sqrt{n}}\\\\\Rightarrow\ \sqrt{n}=2.576\times\dfrac{14900}{6407}=5.99\\\\\Rightarrow\ n=(5.99)^2=35.8801\approx 36[/tex]
The sample size used for the analysis =36
Vhat is the volume of the right rectangular prism?
Will mark brainliest
Answer:
432 mm³
Step-by-step explanation:
Volume of a Rectangular Prism: V = lwh
Step 1: Define variables
l = 8
w = 6
h = 9
Step 2: Plug into formula
V = 8(6)(9)
Step 3: Evaluate
V = 48(9)
V = 432
And we have our answer!
HELP PLEASE!! (math)
Answer:
Hey there!
We can write: -2+9=7.
Let me know if this helps :)
Answer:
[tex]\large \boxed{{-2+9=7}}[/tex]
Step-by-step explanation:
-2 is also 0-2
The arrow goes from 0 to -2.
-2 + 9 = 7
The arrow goes from -2 to 7.
What is meant by the term "90% confident" when constructing a confidence interval for a mean? Group of answer choices
Answer:
The question is not complete, below is the complete question:
What is meant by the term 90% confident? when constructing a confidence interval for a mean?
a. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.
b. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the sample mean.
c. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.
d. If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples.
Answer:
The correct answer is:
If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean. (c)
Step-by-step explanation:
a 90% confidence level means that if repeated samples were taken, 9 out of 10 times, the confidence intervals of the sample chosen will be close to the mean (true value), which is a true representation of the population parameter. when using confidence intervals, there are always margins of allowable accuracy, and this is suggested by using standard diviations snd variances.
I attached a simple document to this answer that will give you more insight into confidence intervals used in statistics.
Write 8:18 as a fraction in simplest form.
Ratio as a Fraction:
Fraction in Simplest Form:
Answer:
[tex]\text{Ratio as a fraction - \: \boxed{\frac{8}{18}}}[/tex]
[tex]\text{Fraction in simplest form - \boxed{\frac{4}{9}}}[/tex]
Step-by-step explanation:
Part 1: Writing a ratio as a fraction
A fraction and a ratio are the same thing - just a different name. Therefore, the colon in a ratio is the same as a divisor line in a fraction. Therefore, to write a ratio as a fraction,
Replace the colon with a divisor line or the divisor line with a colon (use the first portion to transform a ratio into a fraction and the second form to transform a fraction into a ratio).Therefore, 8:18 as a fraction is 8/18.
Part 2: Fraction in simplest form
To put a fraction in simplest form, first divide the numerator by the denominator. If it contains a remainder, you cannot use this step to verify it.
8 only goes into 18 twice and leaves a 2 as a remainder, so this method does not work.
Instead, if both numbers are even, divide by 2.
8/2 = 4
18/2 = 9
Check to see if the new numerator and denominator can reduce any further.
4/9 = 4/9
The fraction in simplest form is 4/9.
A die is rolled five times and the number of fours that come up is tallied. Find the probability of getting the given result. Exactly 3 fours.
A. 0.161
B. 0.002
C. 0.116
D. 0.216
Answer:
0.0321
Step-by-step explanation:
This can be found by binomial probability distribution as the probability of success is constant. There are a given number of trials. the successive tosses are independent.
Here n= 5
The probability of getting a four in a roll of a die = 1/6
The probability of not getting a four in a roll of a die = 5/6
The probability of getting exactly three 4s in five throws is given by
5C3 (1/6)³ (5/6)² = 10 (0.0046) (0.694)= 0.0321
During April of 2013, Gallup randomly surveyed 500 adults in the US, and 47% said that they were happy, and without a lot of stress." Calculate and interpret a 95% confidence interval for the proportion of U.S. adults who considered themselves happy at that time. 1 How many successes and failures are there in the sample? Are the criteria for approximate normality satisfied for a confidence interval?
A What is the sample proportion?
B compute the margin of error for a 95% confidence interval.
C Interpret the margin of error you calculated in Question 1
C. Give the lower and upper limits of the 95% confidence interval for the population proportion (p), of U.S. adults who considered themselves happy in April, 2013.
D Give an interpretation of this interval.
E. Based on this interval, is it reasonably likely that a majority of U.S. adults were happy at that time?
H If someone claimed that only about 1/3 of U.S. adults were happy, would our result support this?
Answer:
number of successes
[tex]k = 235[/tex]
number of failure
[tex]y = 265[/tex]
The criteria are met
A
The sample proportion is [tex]\r p = 0.47[/tex]
B
[tex]E =4.4 \%[/tex]
C
What this mean is that for N number of times the survey is carried out that the which sample proportion obtain will differ from the true population proportion will not more than 4.4%
Ci
[tex]r = 0.514 = 51.4 \%[/tex]
[tex]v = 0.426 = 42.6 \%[/tex]
D
This 95% confidence interval mean that the the chance of the true population proportion of those that are happy to be exist within the upper and the lower limit is 95%
E
Given that 50% of the population proportion lie with the 95% confidence interval the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time
F
Yes our result would support the claim because
[tex]\frac{1}{3 } \ of N < \frac{1}{2} (50\%) \ of \ N , \ Where\ N \ is \ the \ population\ size[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 500[/tex]
The sample proportion is [tex]\r p = 0.47[/tex]
Generally the number of successes is mathematical represented as
[tex]k = n * \r p[/tex]
substituting values
[tex]k = 500 * 0.47[/tex]
[tex]k = 235[/tex]
Generally the number of failure is mathematical represented as
[tex]y = n * (1 -\r p )[/tex]
substituting values
[tex]y = 500 * (1 - 0.47 )[/tex]
[tex]y = 265[/tex]
for approximate normality for a confidence interval criteria to be satisfied
[tex]np > 5 \ and \ n(1- p ) \ >5[/tex]
Given that the above is true for this survey then we can say that the criteria are met
Given that the confidence level is 95% then the level of confidence is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha =0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p (1- \r p}{n} }[/tex]
substituting values
[tex]E = 1.96 * \sqrt{ \frac{0.47 (1- 0.47}{500} }[/tex]
[tex]E = 0.044[/tex]
=> [tex]E =4.4 \%[/tex]
What this mean is that for N number of times the survey is carried out that the proportion obtain will differ from the true population proportion of those that are happy by more than 4.4%
The 95% confidence interval is mathematically represented as
[tex]\r p - E < p < \r p + E[/tex]
substituting values
[tex]0.47 - 0.044 < p < 0.47 + 0.044[/tex]
[tex]0.426 < p < 0.514[/tex]
The upper limit of the 95% confidence interval is [tex]r = 0.514 = 51.4 \%[/tex]
The lower limit of the 95% confidence interval is [tex]v = 0.426 = 42.6 \%[/tex]
This 95% confidence interval mean that the the chance of the true population proportion of those that are happy to be exist within the upper and the lower limit is 95%
Given that 50% of the population proportion lie with the 95% confidence interval the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time
Yes our result would support the claim because
[tex]\frac{1}{3 } < \frac{1}{2} (50\%)[/tex]
Question 3 Rewrite in simplest rational exponent form √x • 4√x. Show each step of your process.
Answer:
4x
Step-by-step explanation:
Given:
√x • 4√x
Required:
Simplify in rational exponent form
SOLUTION:
Recall => [tex] \sqrt{a} = a^{\frac{1}{2}} [/tex]
Thus,
[tex] \sqrt{x}*4\sqrt{x} [/tex] can be expressed in exponent form as [tex] x^{\frac{1}{2}}*4x^{\frac{1}{2} [/tex]
When multiplying 2 bases having exponents together, their exponents should be added together, while you multiply the bases. I.e. [tex]x^m*x^n = x^{m+n }[/tex]
[tex] = x*4^{\frac{1}{2}+\frac{1}{2} [/tex]
[tex] = 4x^{1} = 4x [/tex]
The answer is 4x
Consider a pair of random variables X; Y with constant joint density on the quadrilateral with vertices (0; 0), (2; 0), (2; 6), (0; 12). a) Find the expected value E(X). b) Find the expected value E(Y ).
The given quadrilateral (call it Q) is a trapezoid with "base" lengths of 6 and 12, and "height" 2, so its area is (6 + 12)/2*2 = 18. This means the joint density is
[tex]f_{X,Y}(x,y)=\begin{cases}\frac1{18}&\text{for }(x,y)\in Q\\0&\text{otherwise}\end{cases}[/tex]
where Q is the set of points
[tex]Q=\{(x,y)\mid0\le x\le 2\land0\le y\le12-3x\}[/tex]
(y = 12 - 3x is the equation of the line through the points (0, 12) and (2, 6))
Recall the definition of expectation:
[tex]E[g(X,Y)]=\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\infty g(x,y)f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy[/tex]
(a) Using the definition above, we have
[tex]E[X]=\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\infty xf_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=\int_0^2\int_0^{12-3x}\frac x{18}\,\mathrm dy\,\mathrm dx=\frac89[/tex]
(b) Likewise,
[tex]E[Y]=\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\ifnty yf_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=\int_0^2\int_0^{12-3x}\frac y{18}\,\mathrm dy\,\mathrm dx=\frac{14}3[/tex]
What is the slope of the line showed?
Answer:
2
Step-by-step explanation:
The formula for the slope of a line is rise over run. We know that the slope of the line will be positive because the line is going up from left to right.
Rise is the change on the y-axis, going up and down. Run is the change on the x-axis, going from left to right.
Let's start from the origin (0,0). To reach the next point on the line, we have to go up two points (rise) and over one point (run).
Slope = rise/run
Slope = 2/1
Slope = 2
Hope that helps.
Answer:
slope=2
Step-by-step explanation:
take two points from graph (0,0) and (1,2)
m=y2-y1/x2-x1
m=2-0/1-0
m=2
a sample of 25 workers with employer provided health insurance paid an average premium of $6600 eith a sample standard deviation of $800. Construct a 95% confidence interval for the mean premium amount paid by all workers who have employer provided health insurance g
Answer:
$6284.4≤μ≤$6313.6
Step-by-step explanation:
Using the formula for calculating confidence interval as shown:
CI = xbar ± Z×S/√n
xbar is the average premium
Z is the z-score at 95% confidence
S is the standard deviation
n is the sample size
Given parameters
xbar = $6600
Z score at 95% CI = 1.96
S = $800
n = 25
Substituting this parameters in the formula we have;
CI = 6600±1.96×800/√25
CI = 6600±(1.96×800/5)
CI = 6600±(1.96×160)
CI = 6600±313.6
CI = (6600-313.6, 6600+313.6)
CI = (6284.4, 6913.6)
Hence the 95% confidence interval for the mean premium amount paid by all workers who have employer provided health insurance is $6284.4≤μ≤$6313.6
You have 9kg of oats and cup scales that gears of 50g and 200g. How − in three weighings− can you measure 2kg of the oats?
Answer: You will need 8 cup scales
Step-by-step explanation:
kg=1000 grams
2000/250=8
Question 1 (5 points)
The line segment AB with endpoints A(-3, 6) and B(9, 12) is dilated with a scale
factor 2/3 about the origin. Find the endpoints of the dilated line segment.
OA) (-2, 4), (6,8)
B) (2, 4). (6,8)
OC) (4, -2), (6,8)
OD) (-2,4), (8,6)
Answer: A) (-2, 4), (6,8)
Step-by-step explanation:
When a point (x,y) is dilated by a scale factor of k , then the new points is given by (kx,ky).
Given: The line segment AB with endpoints A(-3, 6) and B(9, 12) is dilated with a scale factor [tex]\dfrac23[/tex] about the origin.
Let A' and B' b the endpoints of the dilated line segment.
Then, [tex]A'(\dfrac{2}{3}(-3), \dfrac23(6))=A'(-2,4)[/tex]
[tex]B'(\dfrac{2}{3}(9), \dfrac23(12))=B'(6,8)[/tex]
Hence, the correct option is A) (-2, 4), (6,8)
Varia is studying abroad in Europe. She is required pay $3,500 (in US dollars) per year to the university; however, she must pay in euros. How many euros can Varia expect to pay per month to the university?
Answer: 247.92 euros
Step-by-step explanation:
Given: Varia is required pay $3,500 (in US dollars) per year to the university.
So, [tex]$3500\div 12 \approx\$291.67[/tex]
i.e. She will pay $ 291.67 per month.
Recent currency value: 1 US dollar = 0.85 euro
∴ $291.67 = ( 0.85 ×291.67) euros
= 247.92 euros [Round to the nearest cent]
∴ She can expect 247.92 euros to pay per month to the university.
Write the equations, after translating the graph of y = |x+2|: one unit up,
Answer:
y = |x + 2| + 1
Step-by-step explanation:
Parent Graph: f(x) = a|bx + c| + k
a is vertical stretch/shrink
b is horizontal stretch/shrink
c is horizontal movement left/right
k is vertical movement up/down
Since we are given an equation and we want to move it 1 unit up (vertical movement up), we only manipulate k:
y = |x + 2| + k
k = 1
y = |x + 2| + 1
Answer:
y = |x+2| + 1
Step-by-step explanation:
The equation will be y = |x+2| + 1.
By translating the graph one unit up, the equation will simply change by adding +1 to the graph, outside of the absolute value part.
How many cubic inches of a milkshake can you fit up to the brim of this cup without letting it overflow? The
cup is 10 inches tall, and the rim of the cup is 4 inches across. (Hint: the radius is half of the diameter.)
Assuming the cup is a right circular cylinder, it's volume is [tex]V=\pi r^2 h[/tex]
$h=10$, $r=\frac 42$
So the volume is $\pi\cdot(2)^2\cdot10=125.66$
hence you can fill up to 125.66 cubic Inches of milkshake
.
The scores for all the Algebra 1 students at Miller High on a test are normally distributed with a mean of 82 and a standard deviation of 7. What percent of students made scores above 89?
Answer:
15.7% of students made above an 89.
Step-by-step explanation:
If the data is normally distributed, the standard deviation is 7, and the mean is 82, then about 68.2% of students made between 75 and 89. 13.6% made between 90 and 96, and 2.1% made over 96. 13.6+2.1=15.7%
A study was conducted to explore the effects of ethanol on sleep time. Fifteen rats were randomized to one of three treatments. Treatment 1 got only water (control). Treatment 2 got 1g of ethanol per kg of body weight, and treatment 3 got 2g/kg. The amount of REM sleep in a 24hr period was recorded, in minutes: Treatment 1: 63, 54, 69, 50, 72 Treatment 2: 45, 60, 40, 56 Treatment 3: 31, 40, 45, 25, 23, 28
A) Graph the data. Why did you choose the graph that you did and what does it tell you?B) Create an ANOVA table for the data using the formulas provided in class. C) Evaluate the ANOVA assumptions graphically. Was ANOVA appropriate here?D) Based on the ANOVA table, make a conclusion in the context of the problem.E) Create 95% CIs for all pairwise comparisons of means using the Tukey method.
Answer: Find answer in the attachment
Step-by-step explanation:
