Answer:
1. The 99% confidence interval is from 941.527 to 958.473
2. The 99% confidence interval is from 933.054 to 966.946
3. The 99% confidence interval is from 916.108 to 983.892
Step-by-step explanation:
The confidence interval is given by
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]
Where [tex]\bar{x}[/tex] is the sample mean and Margin of error is given by
[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]
Where n is the sample size,
s is the sample standard deviation,
[tex]t_{\alpha/2[/tex] is the t-score corresponding to some confidence level
The t-score corresponding to 99% confidence level is
Significance level = α = 1 - 0.99 = 0.01/2 = 0.005
Degree of freedom = n - 1 = 13 - 1 = 12
From the t-table at α = 0.005 and DoF = 12
t-score = 3.055
1. 99% Confidence Interval when s = 10
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{10}{\sqrt{13} } \\\\MoE = 3.055\cdot 2.7735\\\\MoE = 8.473\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 8.473\\\\\text {confidence interval} = 950 - 8.473, \: 950 + 8.473\\\\\text {confidence interval} = (941.527, \: 958.473)\\\\[/tex]
The 99% confidence interval is from 941.527 to 958.473
2. 99% Confidence Interval when s = 20
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{20}{\sqrt{13} } \\\\MoE = 3.055\cdot 5.547\\\\MoE = 16.946\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 16.946\\\\\text {confidence interval} = 950 - 16.946, \: 950 + 16.946\\\\\text {confidence interval} = (933.054, \: 966.946)\\\\[/tex]
The 99% confidence interval is from 933.054 to 966.946
3. 99% Confidence Interval when s = 40
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{40}{\sqrt{13} } \\\\MoE = 3.055\cdot 11.094\\\\MoE = 33.892\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 33.892\\\\\text {confidence interval} = 950 - 33.892, \: 950 + 33.892\\\\\text {confidence interval} = (916.108, \: 983.892)\\\\[/tex]
The 99% confidence interval is from 916.108 to 983.892
As the sample standard deviation increases, the range of confidence interval also increases.
Find the lateral area of the prism. Use the 10 by 6 rectangle as the base.
5 ft
6 ft
9 ft
Answer:
lateral area =150 square feet
Step-by-step explanation:
lateral area =(perimieter of prism base) times the height of the prism
so, the perimeter of the base is 9 ft*2 + 6 ft*2 which equals 30 ft
then you multiply the perimeter of the base by the height of the prism
so, height of prism =5 ft, so 5 ft times 30 ft =150 feet
therefor, the lateral area of the prism = 150 feet squared
Population of town was 21000 in 1980 and it was 20000 in 1990. Assuming the population is decreasing continuously at a rate proportion to the existing population, estimate the population in 2010.
Answer:
19,000
Step-by-step explanation:
Here, we are to estimate the population in the year 2010
From the question, we can see that within a period of a decade which is 10 years, 1000 was lost
So within the period of another decade, it is possible that another 1000 be lost
The estimated population in the year 2010 is thus 20,000 - 1,000 =
19,000
13 lb 14oz + 30 lb 12 oz = lb. oz
Answer:
33 lbs 10 ounces
Step-by-step explanation:
13 lb 14oz
+ 30 lb 12 oz
================
32 lbs 26 oz
But we know that 16 ounces 1 1 lb
Subtract 16 ounces and add 1 lb
32 lbs 26 oz
+1 lb - 16 ounces
==================
33 lbs 10 ounces
The first card selected from a standard 52-card deck was a king. If it is returned to the deck, what is the probability that a king will be drawn on the second selection
Answer:
[tex]\frac{1}{13}[/tex]
Step-by-step explanation:
The probability P(A) that an event A will occur is given by;
P(A) = [tex]\frac{number-of-possible-outcomes-of-event-A}{total-number-of-sample-space}[/tex]
From the question,
=>The event A is selecting a king the second time from a 52-card deck.
=> In the card deck, there are 4 king cards. After the first selection which was a king, the king was returned. This makes the number of king cards return back to 4. Therefore,
number-of-possible-outcomes-of-event-A = 4
=> Since there are 52 cards in total,
total-number-of-sample-space = 52
Substitute these values into equation above;
P(Selecting a king the second time) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]
9. A line passes through (2, –1) and (8, 4). a. Write an equation for the line in point-slope form. b. Rewrite the equation in standard form using integers.
Answer:
Step-by-step explanation:
(4+1)/(8-2)= 5/6
y + 1 = 5/6(x - 2)
y + 1 = 5/6x - 5/3
y + 3/3 = 5/6x - 5/3
y = 5/6x - 8/3
6(y = 5/6x - 8/3)
6y = 5x - 16
-5x + 6y = -16
Answer in POINT-SLOPE FORM:
Complete the point-slope equation of the line through (1,3) and (5,1) Use exact numbers!
Answer:
y - 3 = (1/2)(x - 1)
Step-by-step explanation:
As we go from (1, 3) to (5, 1), we see that x (the run) increases by 4 and y (the rise) decreases by 2. Hence, the slope is m = rise / run = 2/4, or m = 1/2.
Then the desired point slope equation is y - 3 = (1/2)(x - 1).
What are the side of triangle PWR
Answer:
PR, PW, RW
Step-by-step explanation:
The sides of a triangle are named by naming the vertices at either end.
Triangle PWR has vertices P, W, R. The sides connecting these are named ...
PW, WR, RP
Any name can have the letters reversed. That is, PR names the same segment that RP does.
Find the lateral surface area, base area of a cylinder with radius 5 cm and height 16 cm
Answer:
Lateral surface area is
≈
502.65cm²
Base area is
=
πr^2
Crane Company reports the following for the month of June.
Date
Explanation
Units
Unit Cost
Total Cost
June 1 Inventory 150 $4 $600
12 Purchase 450 5 2,250
23 Purchase 400 6 2,400
30 Inventory 80
Assume a sale of 500 units occurred on June 15 for a selling price of $7 and a sale of 420 units on June 27 for $8.
Calculate cost of goods available for sale.
Calculate Moving-Average unit cost for June 1, 12, 15, 23 & 27. (Round answers to 3 decimal places, e.g. 2.525.)
Answer:
Crane CompanyJune Financial Reports
a) Cost of goods available for sale = $5,250
b) Moving-Average unit cost for:
i) June 1: = $5
ii) 12: = $4.75
iii) 15: = $4.75
iv) 23: = $5.75
v) 27: = $5.25
Step-by-step explanation:
a) Calculations:
Date Explanation Units Unit Cost Total Cost Moving Average Cost
June 1 Inventory 150 $4 $600 $4.000
12 Purchase 450 5 2,250 4.750
15 Sale 500 7 3,500 4.750
23 Purchase 400 6 2,400 5.750
27 Sale 420 8 3,360 5.250
30 Inventory 80
Cost of goods available for sale = Cost of Beginning Inventory + Cost of Purchases = $5,250 + ($600 + 2,250 + 2,400)
b) Moving-Average unit cost for:
i) June 1: Cost of goods available/Units of goods available = $5 ($600/150)
ii) 12: Cost of goods available/Units of goods available = $4.75 ($600 + 2,250/600)
iii) 15: Cost of goods available/Units of goods available = $4.75 ($475/100)
iv) 23: Cost of goods available/Units of goods available = $5.75 ($475 + 2,400)/500
v) 27: Cost of goods available/Units of goods available = $5.25 ($420/80)
The diagram shows the first four patterns of a sequence. Find an expression for the numbers of squares in the nth pattern of the sequence.
Answer:
n^2+3
Step-by-step explanation:
As we can see in the diagram
1st pattern consists from 1 square 1x1 +3 squares 1x1 each
2nd pattern consists from 1 square 2x2 +3 squares 1x1 each
3-rd pattern consists from 1 square 3x3 +3 squares 1x1 each
4-th pattern consists from 1 square 4x4 + 3 squares 1x1 each
We can to continue :
5-th pattern consists from 1 square 5x5+3 squares 1x1 each
So the nth pattern consists from 1 square nxn+3 squares 1x1 each
Or total amount of 1x1 squares in nth pattern N= n^2+3
The expression for the numbers of squares in the nth pattern of the sequence is [tex]n^{2} +3[/tex].
What is nth term of a sequence?"The nth term of a sequence is a formula that enables us to find any term in the sequence. We can make a sequence using the nth term by substituting different values for the term number(n) into it."
From the given diagram
We can see that every term is made up with a square which side is n and three small square side is 1.
So,
1st term is 1 × 1 + 3 = 4
2nd term is 2 × 2 + 3 = 4
3rd term is 3 × 3 + 3 = 12
4th term is 4 × 4 + 3 = 19
So, nth term is [tex]n^{2} +3[/tex]
Hence, The expression for the numbers of squares in the nth pattern of the sequence is [tex]n^{2} +3[/tex].
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Create a bucket by rotating around the y axis the curve y=5 ln(x-2) from y=0 to y=4. If this bucket contains a liquid with density 760 kg/m3 filled to a height of 3 meters, find the work required to pump the liquid out of this bucket (over the top edge). Use 9.8 m/s2 for gravity.
Answer:
The work will be "1909212.015 J". The further explanation is given below.
Step-by-step explanation:
The given values are:
Liquid's density
= 760 kg/m³
Height
= 3 meters
Gravity
g = 3.8 m/s²
Value of y is:
y = 5 log (x-2)
y = 0
y = 4
As we know,
⇒ [tex]\Delta V=\pi r^2 \Delta y[/tex]
⇒ [tex]y =5log(x-2)[/tex]
⇒ [tex]\frac{y}{5} =log (x-2)[/tex]
⇒ [tex]e^{\frac{y}{5}}=(x-2)[/tex]
⇒ [tex]x=e^{\frac{y}{5}}+2[/tex]
Now,
[tex]\Delta F=ma[/tex]
[tex]=760 \pi (e^{\frac{y}{5}}+2)^2(9.8)\Delta y[/tex]
So that,
⇒ [tex]\Delta W = \Delta F.distance[/tex]
[tex]=\Delta F(4-y)[/tex]
The required work will be:
⇒ [tex]W=760\times 9.8 \pi \int_{3}^{0}(e^{\frac{y}{5}}+2)^2 (\Delta-y)dy[/tex]
[tex]=760\times 9.8 \pi[{-20(y-9)^{e^{\frac{y}{5}}}-2(y-8)y}][/tex]
[tex]=760\times 9.8 \pi[81.455][/tex]
[tex]=1909212.015 \ J[/tex]
The volume of a cantaloupe is approximated by Upper V equals four thirds pi font size decreased by 5 r cubed . The radius is growing at the rate of 0.5 cm divided by week, at a time when the radius is 6.4 cm. How fast is the volume changing at that moment?
Answer:
308.67 cm ^ 3 / week
Step-by-step explanation:
A cantaloupe is approximately a sphere, therefore its approximate volume would be:
V = (4/3) * pi * (r ^ 3)
They tell us that dr / dt 0.5 cm / week and the radius is 6.4 cm
if we derive the formula from the volume we are left with:
dV / dt = (4/3) * pi * d / dr [(r ^ 3)]
dV / dt = (4/3) * pi * 3 * (r ^ 2) * dr / dt
dV / dt = 4 * pi * (r ^ 2) * dr / dt
we replace all the values and we are left with:
dV / dt = 4 * 3.14 * (6.4 ^ 2) * 0.6
dV / dt = 308.67
Therefore the volume is changing at a rate of 308.67 cm ^ 3 / week
Herschel uses an app on his smartphone to keep track of his daily calories from meals. One day his calories from breakfast were more than his calories from lunch, and his calories from dinner were less than twice his calories from lunch. If his total caloric intake from meals was , determine his calories for each meal.
Answer:
let the number of calories from lunch be called L. As such, breakfast is then L + 128, and dinner is 2L - 400. We can then sum the three meals and equate it to the total caloric intake, the known value of 1932.
So: 1932 = L + L + 128 + 2L - 400 = 4L - 272.
Lunch = 551
Breakfast = 551 + 128 = 679
Dinner = 2*551 - 400 = 702
What is the measure of
Answer:
C. 35
55 degrees + 35 degrees= 90 degrees
If AB= X and x=4, then the transitive property states
Answer:
AB=4
Step-by-step explanation:
The transitive property states if A=B and B+C than A+C Next substitute
AB=x and x=4 so AB=4
Hope this helps, if it did, please give me brainliest, it helps me a lot. :)
Have a good day!
Uncle Louise is at least 1 inch shorter than Miriam, and at least 2 inches taller than Jeffery. Jeffery's height is 64 inches. Miriam is not more than 5 inches taller than Jeffery. Which answer could be Uncle Louise's height? Please answer!!!
Answer:
67 inches
Step-by-step explanation:
Let's call the height of Louise 'L', the height of Miriam 'M' and the height of Jeffery 'J'.
Then, we can write the following equations and inequations:
[tex]L \leq M - 1[/tex]
[tex]L \geq J + 2[/tex]
[tex]J = 64[/tex]
[tex]M \leq J + 5[/tex]
Substituting J in the second and four inequations, we have:
[tex]L \geq 66[/tex]
[tex]M \leq 69[/tex]
If we assume the maximum value for M, in the first inequation we have that:
[tex]L \leq 68[/tex]
So the height of Uncle Louise is greater than or equal 66, and lesser than or equal 68, so his height could be 67 inches for example.
which of these is a ratio table?
Answer:
The last graph.
Step-by-step explanation:
The last graph is the only one that has a constant pattern that can have a rule, which is every number is multiplied by two.
Hope this helped ! good luck :)
xpress 8/(1 - 2x)2 as a power series by differentiating the equation below. What is the radius of convergence? 4 (1 - 2x) = 4(1 + 2x + 4x2 + 8x3 + ...) = 4 [infinity] Σ n=0 (2x)n SOLUTION Differentiating each side of the equation, we get 8 (1 - 2x)2 = 4(2 + Correct: Your answer is correct. + 24x2 + ...) = 4 [infinity] Σ n=1 Incorrect: Your answer is incorrect. If we wish, we can replace
Recall that for |x| < 1, we have
[tex]\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]
Replace x with 2x, multiply 4, and call this function f :
[tex]f(x)=\dfrac4{1-2x}=\displaystyle4\sum_{n=0}^\infty(2x)^n[/tex]
Take the derivative:
[tex]f'(x)=\dfrac8{(1-2x)^2}=\displaystyle8\sum_{n=0}^\infty n(2x)^{n-1}=\boxed{8\sum_{n=0}^\infty (n+1)(2x)^n}[/tex]
By the ratio test, the series converges for
[tex]\displaystyle\lim_{n\to\infty}\left|\frac{(n+2)(2x)^{n+1}}{(n+1)(2x)^n}\right|=|2x|\lim_{n\to\infty}\frac{n+2}{n+1}=|2x|<1[/tex]
or |x| < 1/2, so the radius of convergence is 1/2.
Which are not changed after a rotation? Check all that apply. angle measures orientation size shape position of center of rotation
Answer:
1 3 4 5
Step-by-step explanation:
The rotation does not change the angle measure, the side lengths and the shape of the shape that is being rotated.
What is an angle?
An angle measure the size, the shape, and the position of center of rotation do not change after rotation.
Which are not changed after rotation?
If one thing is rotated then it will not change the angle measures, the side lengths and shape of the body. The rotation does not change the center of object.
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help asap!! will get branliest.
Answer:
C
Step-by-step explanation:
A reflection is when the original diagram or picture is fliped exactly over the x axis.
HEYA!!
Answer:
Your Answer of the Question is C
if you want to prove it you can do the same thing in real life by drawing a 'W' on a paper and see its reflection on the mirror
HOPE IT MATCHES!!
which of the following statements is false?
Answer:
A.
Step-by-step explanation:
It's the first one. The angles are supplementary not complementary.
Answer:
I would have to say A
Step-by-step explanation:
NEED UGANT HELP pls help me
An event that is impossible has a probability of 0
An event that is certain to happen has a probability of 1
The probability scales from 0 to 1, referring from no chance to will happen.
16. How much money will I need to have at retirement so I can withdraw $60,000 a year for 20 years from an account earning 8% compounded annually? a. How much do you need in your account at the beginning b. How much total money will you pull out of the account? c. How much of that money is interest?
Answer:
starting balance: $636,215.95total withdrawals: $1,200,000interest withdrawn: $563,784.05Step-by-step explanation:
a) If we assume the annual withdrawals are at the beginning of the year, we can use the formula for an annuity due to compute the necessary savings.
The principal P that must be invested at rate r for n annual withdrawals of amount A is ...
P = A(1+r)(1 -(1 +r)^-n)/r
P = $60,000(1.08)(1 -1.08^-20)/0.08 = $636,215.95
__
b) 20 withdrawals of $60,000 each total ...
20×$60,000 = $1,200,000
__
c) The excess over the amount deposited is interest:
$1,200,000 -636,215.95 = $563,784.05
Write an equation:
For every 2 apples there
are 6 bananas
Answer:
[tex]2a=6b\\a=3b[/tex]
Step-by-step explanation:
Let [tex]a[/tex] equal the amount of apples and [tex]b[/tex] equal the amount of bananas.
[tex]2a=6b\\a=3b[/tex]
Answer:
every 2 apples there
are 6 bananas
Step-by-step explanation:
2a=6b
If x is a binomial random variable with n trials and success probability p , then as n gets smaller, the distribution of x becomes
Answer:
If the value of n gests smaller then the distribution of X would be more skewed, that's a property of the binomial distribution
Step-by-step explanation:
For this problem we are assumeing that the random variable X is :
[tex] X \sim Bin(n,p)[/tex]
If the value of n gests smaller then the distribution of X would be more skewed, that's a property of the binomial distribution and if we don't satisfy this two conditions:
[tex] n p>10[/tex]
[tex]n(1-p) >10[/tex]
Then we can't use the normal approximation
Hello, can someone help me with this problem?
Answer:
Area of Rectangle A
[tex]Area = 4x^2[/tex]
Area of Rectangle B
[tex]Area = 2x^2[/tex]
Fraction
[tex]Fraction =\frac{2}{3}[/tex]
Step-by-step explanation:
From the attached, we understand that:
The dimension of rectangle A is 2x by 2x
The dimension of rectangle B is x by 2x
Area of rectangle is calculated as thus;
[tex]Area = Length * Breadth[/tex]
Area of Rectangle A
[tex]Area = 2x * 2x[/tex]
[tex]Area = 4x^2[/tex]
Area of Rectangle B
[tex]Area = x * 2x[/tex]
[tex]Area = 2x^2[/tex]
Area of Big Rectangle
The largest rectangle is formed by merging the two rectangles together;
The dimension are 3x by 2x
The Area is as follows
[tex]Area = 2x * 3x[/tex]
[tex]Area = 6x^2[/tex]
The fraction of rectangle A in relation to the largest rectangle is calculated by dividing area of rectangle A by area of the largest rectangle;
[tex]Fraction = \frac{Rectangle\ A}{Biggest}[/tex]
[tex]Fraction =\frac{4x^2}{6x^2}[/tex]
Simplify
[tex]Fraction =\frac{2x^2 * 2}{2x^2 * 3}[/tex]
[tex]Fraction =\frac{2}{3}[/tex]
Find the value of x. Then find the measure of each labeled angle. x = 37.5; the labeled angles are 77.5º and 102.5º. x = 37.5; the labeled angles are 37.5º and 142.5º. x = 15; both labeled angles are 55º. x = 25; both labeled angles are 65º.
Answer:
x = 25; both labeled angles are 65º
Step-by-step explanation:
To find the value of x, recall that the angles formed by two parallel lines on the same line are equal if they correspond to each other.
In the figure given above, we have two parallel line given. The angle formed by each parallel line is corresponding to the other. Therefore, both angles formed are equal.
Thus,
(3x - 10)° = (x + 40)°
Solve for x
3x - 10 = x + 40
Subtract x from both sides
3x - 10 - x = x + 40 - x
3x - x - 10 = x - x + 40
2x - 10 = 40
Add 10 to both sides
2x - 10 + 10 = 40 + 10
2x = 50
Divide both sides by 2
2x/2 = 50/2
x = 25
*Plug in the value of x to find the measure of each labelled angles:
(3x - 10)° = 3(25) - 10 = 75 - 10 = 65°
(x + 40)° = 25 + 40 = 65°
In a certain online dating service, participants are given a 4-statement survey to determine their compatibility with other participants. Based on the questionnaire, each participant is notified if they are compatible with another participant. Each question is multiple choice with the possible responses of "Agree" or "Disagree," and these are assigned the numbers 1 or −1, respectively. Participant’s responses to the survey are encoded as a vector in R4, where coordinates correspond to their answers to each question. Here are the questions:
The question is incomplete. Here is the complete question.
In a certain online dating service, participants are given a 4-statement survey to determine their compatibility with other participants. Based on the questionnaire, each particpant is notified if they are compatible with another participant. Each question is multiple choice with the possible responses of "Agree" or "Disagree", and these are assigned the numbers 1 or -1, respectively. pArticipnat's responses to the survey are encoded as a vector in R4, where coordinates coreespond to their answers to each question. Here are the questions:
Question #1: I prefer outdoor activities, rather than indoor activities.
Question #2: I prefer going out to eat in restaurants, rahter than cooking at home.
Question #3: I prefer texting, rather than talking on the phone.
Question #4: I prefer living in a small town, rather than in a big city.
Here are the results for the questionaire, with a group of 5 participants:
Question1 Question2 Question3 Question4
participant A 1 1 -1 -1
participant B -1 1 1 1
participant C -1 -1 1 1
participant D 1 -1 -1 -1
participant E 1 -1 1 1
Two participants are considered to be "compatible" with each other if the angle between their compatibility vectors is 60° or less. Participants are considered to be "incompatible" if the angle between their compatibility vectors is 120° or larger. For angles between 60° or 120°, pairs of participants are warned that they "may or may not be compatible".
(a) Which pairs of paricipants are compatible?
(b) Which pairs of participants are incompatible?
(c) How would this method of testing compatibility change if the questionnaire also allowed the answer "Neutral", which would correspond to the number zero in a participant's vector? Would this be better than only
allowing "Agree" or "Disagree"? Could anything go wrong if we allowed "Neutral" as an answer?
Answer: (a) Participants A and D; B and C; C and E.
(b) Participants A and B; A and C; A and E; B and D; C and D;
Step-by-step explanation: Vectors in R4 are vectors in a 4 dimensional space and are determined by 4 numbers.
Vectors form angles between themselves and can be found by the following formula:
cos α = [tex]\frac{A.B}{||A||.||B||}[/tex]
which means that the cosine of the angle between two vectors is equal the dot product of these vectors divided by the product of their magnitude.
For the compatibility test, find the angle between vectors:
1) The vectors magnitude:
Magnitude of a vector is given by:
||x|| = [tex]\sqrt{x_{i}^{2} + x_{j}^{2}}[/tex]
Since all the vectors have value 1, they have the same magnitude:
||A|| = [tex]\sqrt{1^{2} + 1^{2} + (-1)^{2} + (-1)^{2}}[/tex] = 2
||A|| = ||B|| = ||C|| = ||D|| = ||E|| = 2
2) The dot product of vectors:
A·B = 1(-1) + 1(1) + (-1)1 + (-1)1 = -2
cos [tex]\alpha_{1}[/tex] = [tex]\frac{-2}{4}[/tex] = [tex]\frac{-1}{2}[/tex]
The angle that has cosine equal -1/2 is 120°, so incompatible
A·C = 1(-1) + 1(-1) + (-1)1 + (-1)1 = -4
cos [tex]\alpha _{2}[/tex] = -1
Angle = 180° --------> incompatible
A·D = 1(1) + 1(-1) + (-1)(-1) + (-1)(-1) = 2
cos [tex]\alpha _{3}[/tex] = 1/2
Angle = 60° ---------> COMPATIBLE
A·E = 1.1 + 1(-1) + (-1)1 + (-1)1 = -2
cos [tex]\alpha_{4}[/tex] = -1/2
Angle = 120° --------> incompatible
B·C = (-1)(-1) + 1(-1) + 1.1 + 1.1 = 2
cos [tex]\alpha _{5}[/tex] = 1/2
Angle = 60° -------------> COMPATIBLE
B·D = (-1)1 + 1(-1) + 1(-1) + 1(-1) = -4
cos[tex]\alpha_{6}[/tex] = -1
Angle = 180° -----------> incompatible
B·E = (-1)1 + 1(-1) + 1.1 + 1.1 = 0
cos[tex]\alpha _{7}[/tex] = 0
Angle = 90° -------------> may or may not
C·D = (-1)1 + (-1)(-1) + 1(-1) + 1(-1) = -2
cos[tex]\alpha_{8} =[/tex] -1/2
Angle = 120° ---------------> Incompatible
C·E = (-1)1 + (-1)(-1) + 1.1 + 1.1 = 2
cos [tex]\alpha_{9}[/tex] = 1/2
Angle = 60° ---------------> COMPATIBLE
D·E = 1.1 + (-1)(-1) + (-1)1 + (-1)1 = 0
cos [tex]\alpha_{10}[/tex] = 0
Angle = 90° -----------------> may or may not
(c) Adding zero (0) as a component of the vectors would have to change the method of compatibility because, to determine the angle, it is necessary to calculate the magnitude of a vector and if it is a zero vector, the magnitude is zero and there is no division by zero. So, unless the service change the method, adding zero is not a good option.
Suppose that the number of square feet per house are normally distributed with an unknown mean and standard deviation. A random sample of 22 houses is taken and gives a sample mean of 1500 square feet and a sample standard deviation of 151 square feet. 1. The EBM, margin of error, for a 95% confidence interval estimate for the population mean using the Student's t. distribution is 66.96.2. Find a 95% confidence interval estimate for the population mean using the Student's t-distribution.
Answer:
1. The margin of error is of 66.96 square feet.
2. The 95% confidence interval estimate for the population mean using the Student's t-distribution is between 1433.04 square feet and 1566.96 square feet
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 22 - 1 = 21
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 21 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.08
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.08*\frac{151}{\sqrt{22}} = 66.96[/tex]
In which s is the standard deviation of the sample.
The margin of error is of 66.96 square feet.
The lower end of the interval is the sample mean subtracted by M. So it is 1500 - 66.96 = 1433.04 square feet
The upper end of the interval is the sample mean added to M. So it is 1500 + 314 = 1566.96 square feet
The 95% confidence interval estimate for the population mean using the Student's t-distribution is between 1433.04 square feet and 1566.96 square feet
11. If 4 < x < 14, what is the range for -x - 4?
Answer:
-18 < -x-4 < -8
Step-by-step explanation:
We start with the initial range as:
4 < x < 14
we multiplicate the inequation by -1, as:
-4 > -x > -14
if we multiply by a negative number, we need to change the symbols < to >.
Then, we sum the number -4, as:
-4-4> -x-4 > -14-4
-8 > -x-4 > -18
Finally, the range for -x-4 is:
-18 < -x-4 < -8