Answer:
y+5 = 3/4(x+8)
Step-by-step explanation:
The point slope form of the equation of a line is
y - y1 = m(x-x1) where m is the slope and ( x1,y1) is a point on the line
The slope is 3/4 and the point is (-8,-5)
y - -5= 3/4( x - -8)
y+5 = 3/4(x+8)
In one area, monthly incomes of technology-related workers have a standard deviation of $650. It is believed that the standard deviation of the monthly incomes of non-technology workers is different. 71 non-technology workers are randomly selected and it is determined that these selected workers have a standard deviation of $950. Test the claim that the non-technology workers have a different standard deviation (so different from $650). Use a 0.10 significance level.
Answer:
There is sufficient statistical evidence to prove that the standard deviation of the technology-related workers and the standard deviation of the non-technology workers are equal.
Step-by-step explanation:
Here we have our null hypothesis as H₀: σ² = s²
Our alternative hypothesis is then Hₐ: σ² ≠ s²
We therefore have a two tailed test
To test the hypothesis of difference in standard deviation which is the Chi squared test given as follows
[tex]\chi ^{2} = \dfrac{\left (n-1 \right )s^{2}}{\sigma ^{2}}[/tex]
Where:
n = Size of sample
s² = Variance of sample = 950²
σ² = Variance of population = 650²
Degrees of freedom = n - 1 = 71 - 1 = 70
α = Significance level = 0.1
Therefore, we use 1 - 0.1 = 0.9
From the Chi-square table, we have the critical value as
1 - α/2 = 51.739,
α/2 = 90.531
Plugging the values in the above Chi squared test equation, we have;
[tex]\chi ^{2} = \dfrac{\left (23-1 \right )950^{2}}{650 ^{2}} = 49.994[/tex]
Therefore, since the test value within the critical region, we do not reject the null hypothesis, hence there is sufficient statistical evidence to prove that the standard deviation of the technology-related workers and the standard deviation of the non-technology workers are equal.
Cotton On Ltd. currently has the following capital structure: Debt: $3,500,000 par value of outstanding bond that pays annually 10% coupon rate with an annual before-tax yield to maturity of 12%. The bond issue has face value of $1,000 and will mature in 20 years. Ordinary shares: $5,500,000 book value of outstanding ordinary shares. Nominal value of each share is $100. The firm plan just paid a $8.50 dividend per share. The firm is maintaining 4% annual growth rate in dividends, which is expected to continue indefinitely. Preferred shares: 45,000 outstanding preferred shares with face value of $100, paying fixed dividend rate of 12%. The firm's marginal tax rate is 30%. Required: a) Calculate the current price of the corporate bond? (4 marks) b) Calculate the current price of the ordinary share if the average return of the shares in the same industry is 9%? (3 marks) c) Calculate the current price of the preferred share if the average return of the shares in the same industry is 10% (3 marks)
Answer:
a) Calculate the current price of the corporate bond? (4 marks)
$818,18b) Calculate the current price of the ordinary share if the average return of the shares in the same industry is 9%? (3 marks)
$176.80c) Calculate the current price of the preferred share if the average return of the shares in the same industry is 10% (3 marks)
$120Step-by-step explanation:
total debt = $3,500,000 par value 10$ coupon with a YTM of 12%
YTM = [coupon + (F - P)/n] / [(F + P)/2]
0.12 = [100 + (1,000 - P)/20] / [(1,000 + P)/2]
0.12(500 + 0.5P) = 100 + 50 - 0.05P
60 + 0.06P = 150 - 0.05P
0.11P = 90
P = 90/0.11 = $818.18
total debt = $818.18 x 3,500
stock price:
Div₀ = $8.50
Div₁ = $8.50 x 104% = $8.84
g = 4%
rrr = 9%
using the perpetuity growth model:
stock price = $8.84 / (9% - 4%) = $8.84 / 5% = $176.80
preferred stock:
Div = $12
rrr = 10%
using the perpetuity formula:
preferred stock = $12 / 10% = $120
In converting 10 pounds to ounces, what unit (omit the number) would you
place in the numerator of your ratio? Use the plural form in your answer.
Remember that there are 16 ounces in 1 pound.
Answer:
pounds
Step-by-step explanation:
pounds : ounces
10 : [tex]x[/tex]
1 : 16
[tex]x=160[/tex]
The numerator would be pounds. [tex]\frac{10 pounds}{160 ounces}[/tex]
What is the complete factorization of p(x)=32x5y−2xy5 over the integers?
Answer:
[tex]p(x)=2xy(2x-y)(2x+y)(4x^2+y^2)[/tex]
Step-by-step explanation:
[tex]p(x)=32x^5y-2xy^5=2xy(16x^4-y^4)=2xy(4x^2-y^2)(4x^2+y^2)\\\\\boxed{p(x)=2xy(2x-y)(2x+y)(4x^2+y^2)}[/tex]
__
The factoring of the difference of squares is applicable:
a^2 -b^2 = (a -b)(a +b)
Old McDonald has a farm with 36 cows and goats the number of cars he has 10 more than the number of coats how many of each animal does old McDonald have right to equations you think you solve the problem you see to represent the number of cars in on
Answer:
13 goats and 23 cows
Step-by-step explanation:
Use x to solve :) it's a hint
Answer:
g=goats
c=cows
a=cars
g + c = 36
10 + g = a
Step-by-step explanation:
the number of cows and goats together are equal to 36, so for the first equation you can write g + c = 36.
For the second equation, the number of cars he has is equal to the number of goats he has plus 10, so you can express that as 10 + g = a. (I used a since I already used c for the cows)
I think this is what you need if you need 2 equations to represent how many cars he has.
I'm not entirely sure what its asking you can comment if you need more or something else.
(AAAA HELP PLS XD WILL MARK BRAINLIEST) Nhia is setting up a marble tournament for the kids in her
apartment complex. So far, 47 kids have signed up to play. Each
player needs 10 marbles. Nhia found a discount store that sells
bags of 24 marbles. Round each amount to the nearest ten to find
a reasonable estimate for the number of bags of marbles Nhia will
have to buy to be sure to have enough marbles.
A) 18
B) 25
C) 32
D) 39
Given that we have 47 kids and each kid needs 10 marbles, find out how many bags of 24 marbles will we need.
First, we will multiply 47 by 10 to get the amount of marbles needed.
47 x 10 = 470
So, that means we need 470 marbles in total.
Then, we divide 470 by 24 to see how many bags of 24 marbles 470 marbles is.
470 / 24 = 19.5833
Since, we can't have 19.5833 bags, we have to check what it would be if we only used 19.
19 x 24 = 456
470 - 456 = 14
Since, 18 is the closest number of bags but it has less than 470 it would not be correct.
Therefore, the best answer would be B. 25 since it is better to have extra marbles but not a very wide margin.
Simplify (20!+21!+22!)/44
Answer:
11*20!
Step-by-step explanation:
(20!+21!+22!)/44=
20!(1+21+21*22)/44=
20!(22+22*21)/44=
20!*22*22/44= 11*20!
The simplified expression of (20!+21!+22!)/44 is 20! * 11
How to simplify the expression?The expression is given as:
(20!+21!+22!)/44
The factorial of a number n is:
n! = n * (n - 1)!
So, we start by expanding 22!
(20!+21!+22!)/44 = (20!+21!+22 * 21 * 20!)/44
Next, we expand 21!
(20!+21!+22!)/44 = (20!+21 * 20!+22 * 21 * 20!)/44
Factor out 20!
(20!+21!+22!)/44 = 20! * (1 + 21 + 22 * 21)/44
Evaluate the expression in the bracket
(20!+21!+22!)/44 = 20! * 484/44
Divide
(20!+21!+22!)/44 = 20! * 11
Hence, the simplified expression of (20!+21!+22!)/44 is 20! * 11
Read more about simplified expression at:
https://brainly.com/question/723406
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What is the insignificant digit in 0.09040?
Answer:
0
Step-by-step explanation:
The 0, or the last digit is the insignificant digit because it serves no purpose.
Answer:
The last zero in the number is insignificant.
Step-by-step explanation:
The 0 at the extreme right indicates that the number is accurate to the fifth decimal place, that is, one in ten thousandths.
Joe says, "I have found an interesting fact! Twenty-five percent of thirty dollars is
the same as thirty percent of twenty-five dollars." Is Joe correct? Please explain
your thinking to show that Joe is right or wrong.
Answer:
Joe Is RightStep-by-step explanation:
Twenty-five percent of thirty dollars is $7.50
(30 x 25)/100 = $7.50
Thirty percent of twenty-five dollars is $7.50
(25 x 30)/100 = $7.50
Therefore he is right
I hope this helps
Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal place. Listed below are the systolic blood pressures (in mm Hg) for a sample of men aged 20-29 and for a sample of men aged 60-69. Group of answer choices Men aged 20-29: 4.8% Men aged 60-69: 10.6% There is substantially more variation in blood pressures of the men aged 60-69. Men aged 20-29: 4.4% Men aged 60-69: 8.3% There is substantially more variation in blood pressures of the men aged 60-69. Men aged 20-29: 4.6% Men aged 60-69: 10.2 % There is substantially more variation in blood pressures of the men aged 60-69. Men aged 20-29: 7.6% Men aged 60-69: 4.7% There is more variation in blood pressures of the men aged 20-29.
Here is the correct computation of the question given.
Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal place. Listed below are the systolic blood pressures (in mm Hg) for a sample of men aged 20-29 and for a sample of men aged 60-69.
Men aged 20-29: 117 122 129 118 131 123
Men aged 60-69: 130 153 141 125 164 139
Group of answer choices
a)
Men aged 20-29: 4.8%
Men aged 60-69: 10.6%
There is substantially more variation in blood pressures of the men aged 60-69.
b)
Men aged 20-29: 4.4%
Men aged 60-69: 8.3%
There is substantially more variation in blood pressures of the men aged 60-69.
c)
Men aged 20-29: 4.6%
Men aged 60-69: 10.2 %
There is substantially more variation in blood pressures of the men aged 60-69.
d)
Men aged 20-29: 7.6%
Men aged 60-69: 4.7%
There is more variation in blood pressures of the men aged 20-29.
Answer:
(c)
Men aged 20-29: 4.6%
Men aged 60-69: 10.2 %
There is substantially more variation in blood pressures of the men aged 60-69.
Step-by-step explanation:
From the given question:
The coefficient of variation can be determined by the relation:
[tex]coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100[/tex]
We will need to determine the coefficient of variation both men age 20 - 29 and men age 60 -69
To start with;
The coefficient of men age 20 -29
Let's first find the mean and standard deviation before we can do that ;
SO .
Mean = [tex]\dfrac{\sum \limits^{n}_{i-1}x_i}{n}[/tex]
Mean = [tex]\frac{117+122+129+118+131+123}{6}[/tex]
Mean = [tex]\dfrac{740}{6}[/tex]
Mean = 123.33
Standard deviation [tex]= \sqrt{\dfrac{\sum (x_i- \bar x)^2}{(n-1)} }[/tex]
Standard deviation =[tex]\sqrt{\dfrac{(117-123.33)^2+(122-123.33)^2+...+(123-123.33)^2}{(6-1)} }[/tex]
Standard deviation = [tex]\sqrt{\dfrac{161.3334}{5}}[/tex]
Standard deviation = [tex]\sqrt{32.2667}[/tex]
Standard deviation = 5.68
The [tex]coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100[/tex]
[tex]coefficient \ of \ variation = \dfrac{5.68}{123.33}*100[/tex]
Coefficient of variation = 4.6% for men age 20 -29
For men age 60-69 now;
Mean = [tex]\dfrac{\sum \limits^{n}_{i-1}x_i}{n}[/tex]
Mean = [tex]\frac{ 130 + 153 + 141 + 125 + 164 + 139}{6}[/tex]
Mean = [tex]\dfrac{852}{6}[/tex]
Mean = 142
Standard deviation [tex]= \sqrt{\dfrac{\sum (x_i- \bar x)^2}{(n-1)} }[/tex]
Standard deviation =[tex]\sqrt{\dfrac{(130-142)^2+(153-142)^2+...+(139-142)^2}{(6-1)} }[/tex]
Standard deviation = [tex]\sqrt{\dfrac{1048}{5}}[/tex]
Standard deviation = [tex]\sqrt{209.6}[/tex]
Standard deviation = 14.48
The [tex]coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100[/tex]
[tex]coefficient \ of \ variation = \dfrac{14.48}{142}*100[/tex]
Coefficient of variation = 10.2% for men age 60 - 69
Thus; Option C is correct.
Men aged 20-29: 4.6%
Men aged 60-69: 10.2 %
There is substantially more variation in blood pressures of the men aged 60-69.
Sides KM and FH in the triangles below will be placed together to form a quadrilateral.
Triangle M L K. Side M L has a length of 15 and side L K has a length of 35. Angle L is 110 degrees.Triangle F G H. Side F G has a length of 35 and side G H has a length of 15. Angle G is 110 degrees.
Answer:
Parallelogram (A)
Question:
Sides KM and FH in the triangles below will be placed together to form a quadrilateral.
Triangle M L K. Side M L has a length of 15 and side L K has a length of 35. Angle L is 110 degrees. Triangle F G H. Side F G has a length of 35 and side G H has a length of 15. Angle G is 110 degrees.
Which best describes the quadrilateral that will be formed?
parallelogram
rectangle
rhombus
trapezoid
Step-by-step explanation:
Given:
∆MLK:
Side ML = 15
Side LK = 35
Angle L = 110°
∆ FGH:
Side FG = 35
Side GH = 15
Angle G = 110°
Side MK and FH placed together to form a quadrilateral.
A quadrilateral is a polygon which has 4 sides.
See attachment for diagram
From the diagram and information given:
LK is parallel to FG
ML is parallel to GH
MK = FH
∠L = ∠G (opposite angles are congruent)
Since two pairs of opposite sides are parallel and opposite angles are congruent, it is a paralellogram.
A parallelogram is a quadrilateral which has pairs of opposite sides are parallel and equal.
Answer: Option A
(A) parallelogram
Step-by-step explanation:
What’s the correct answer for this?
｡☆✼★ ━━━━━━━━━━━━━━ ☾
A tangent to a circle forms a right angle with the radius
As it is a right angled triangle, we can use Pythagoras' theorem
a^2 + b^2 = c^2
Rearrange this for a side length:
a^2 = c^2 - b^2
Sub the values in:
a^2 = 6.5^2 - 6^2
a^2 = 6.25
Square root this for the answer
a = 2.5
Thus, your answer is option D
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Answer:
2.5 ft
Step-by-step explanation:
As radius is perpendicular to tangent ,
LT [tex]\perp[/tex]KT
By pythagoras theorem:
LT² = LK² - KT²
LT² = (6.5)² - 6²
LT² = 42.25 - 36
LT² = 6.25
LT = 2.5 ft
LT = radius = 2.5 ft
PLEASE HELP I DON'T UNDERSTAND THE QUESTION. THANK YOU :)
ABC and DEC are similar, since the line segments AB and DE are parallel.
This means corresponding sides of these triangles occur in a fixed ratio with one another.
In particular, this tells us
DE/AB = DC/AC
or
7/11 = 15/(15 + x)
Solve for x:
11/7 = (15 + x)/15
11/7 = 1 + x/15
4/7 = x/15
x = 60/7
A can of StarKist tuna has a volume LaTeX: 18\pi\:cm^318 π c m 3 and a height of 2 cm. Find the area of the StarKist label below the wraps around the entire can and does not overlap. Write your answers in terms of LaTeX: \piπ.
Answer:
Area of the StarKist label around the can in terms of π = 12π cm²
Step-by-step explanation:
Given;
the volume of a can of StarKist tuna, V = 18 π cm³
height of the can of StarKist tuna, h = 2 cm
To determine the area of the StarKist label that wraps around the entire can and does not overlap, we assume the can to have a shape of a cylinder.
Volume of the can = πr²h
where;
r is radius of the can
h is height of the can
πr² x 2 = 18 π
2r² = 18
r² = 18/2
r² = 9
r = 3
Area around the can = curved surface area of the can (cylinder)
Curved surface area of the can = 2πr × h = 2πrh
Curved surface area of the can = 2πrh = 2π x 3 x 2 = 12π cm²
Area of the StarKist label around the can in terms of π = 12π cm²
Which equation represents a circle that contains the point (–2, 8) and has a center at (4, 0)?
Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot
Answer:
-3
Step-by-step explanation:
Answer:
[tex](x-4)^2 + y^2= 100[/tex]
Step-by-step explanation:
edgenuity 2020
hope this helps!
Which of the following is NOT a from AGI deduction?
A. Standard deduction
B. Itemized deduction
C. Personal exemption
D. None of these.
All of these are from AGI deductions
The relationship requirement for qualifying relative requires the potential qualifying relative to have a family relationship with the taxpayer.
1. True
2. False
In year 1, the Bennetts' 25-year-old daughter, Jane, is a full-time student at an out-of-state university but she plans to return home after the school year ends. In previous years, Jane has never worked and her parents have always been able to claim her as a dependent. In year 1, a kind neighbor offers to pay for all of Jane's educational and living expenses. Which of the following statements is most accurate regarding whether Jane's parents would be allowed to claim an exemption for Jane in year 1 assuming the neighbor pays for all of Jane's support?
A. No, Jane must include her neighbor's gift as income and thus fails the gross income test for a qualifying relative.
B. Yes, because she is a full-time student and does not provide more than half of her own support, Jane is considered her parent's qualifying child.
C. No, Jane is too old to be considered a qualifying child and fails the support test of a qualifying relative.
D. Yes, because she is a student, her absence is considered as "temporary." Consequently she meets the residence test and is a considered a qualifying child of the Bennetts.
Answer:
1) D. None of these.
2) False
3) C. No, Jane is too old to be considered a qualifying child and fails the support test of a qualifying relative.
Step-by-step explanation:
1) AGI deductions are subtracted from the gross income to calculate the taxable income. Not all the individual's earnings are subject to taxation, therefore some expenses are deducted to calculate the Adjusted Gross Income, the one that will be taxed.
All of the three options listed ( Standard deduction, Itemized deduction, and personal exemption) are AGI deductions.
2) False
The potential qualifying relative does not have to be family/biologically related with the taxpayer. The IRS condition states that he/she is either family related or have lived in the taxpayer's abode for a whole year to be a qualified relative of the taxpayer. So far any of the two conditions are met, it is fine.
C. For a student to be regarded as a qualifying relative of her parents, she must not be up to 24 years at the end of the year according to IRS. Jane is already 25, she is too old and fails the test as a qualifying relative.
There are 560 third- and fourth-grade students in King Elementary School. If there are 80 more third-graders than fourth-graders, how many third-graders are there in the school? work has to be shown
Answer:
There are 200 4th grades and 360 third graders
Step-by-step explanation:
560/2=280-80=200 280+80=360
12. Jeremy got quote from iVan to move him into his new home. One quote was for a weekday move which is
for 8 hours of loading/unloading and 6 hours of packing/unpacking for $890. The other quote was for a
weekend move which is for 5 hours of loading/unloading and 3 hours of packing/unpacking for $515. If
iVan has set hourly rates for loading/unloading and packing/unpacking, what are these hourly rates?
Answer:
Loading/unloading hourly rate: $70
Packing/unpacking hourly rate: $55
Step-by-step explanation:
We can write this as a system of linear equations.
We define L as the loading/unloading hourly rate, and P as the packing/unpacking hourly rate.
"One quote was for a weekday move which is for 8 hours of loading/unloading and 6 hours of packing/unpacking for $890":
[tex]8L+6P=890[/tex]
"The other quote was for a weekend move which is for 5 hours of loading/unloading and 3 hours of packing/unpacking for $515":
[tex]5L+3P=515[/tex]
If we express L in function of P in the first equation, and then replace this value in the second equation, we have:
[tex]8L+6P=890\\\\8L=890-6P\\\\L=\dfrac{890-6P}{8}[/tex]
[tex]5L+3P=515\\\\5\cdot \dfrac{890-6P}{8}+3P=515\\\\556.25-3.75P+3P=515\\\\-0.75P=515-556.25=-41.25\\\\P=41.25/0.75=55[/tex]
Then, L is:
[tex]L=\dfrac{890-6P}{8}=\dfrac{890-6(55)}{8}=\dfrac{890-330}{8}=\dfrac{560}{8}=70[/tex]
Question 1
Pogo sells shirts for $14.99 each. Baja Coast has a special deal: buy 2 and
get the third at 30% off the least expensive shirt. There are 3 shirts you want
to buy. At Baja Coast, the 3 shirts you want are $16.99, $15.99, and $15.50.
What is the least amount you can pay for all 3 shirts?
Note - Use the calculator above for help,
Answer:
the cheapest for the 3 shirts you can get is 43.83 (Baja Coast)
Step-by-step explanation:
For the three shirts at Pogo it costs $44.97. However, at the Baja Coast it costs $43.83. So the least amount you pay is $43.87.
Find the value of y.
Answer:
60°
Step-by-step explanation:
The value of y is half the measure of the arc the chord subtends:
y = 120°/2
y = 60°
A rectangle has a base length of 12 inches and an unknown height, h. The area of the rectangle is less than 60 square inches. Which inequality can be used to model the problem?
12h < 60
12h > 60
12 + h < 60
12 + h > 60
Answer:
12h < 60
Step-by-step explanation:
A rectangle, with height h and base length l, has the following area.
[tex]A = l*h[/tex]
In this question:
[tex]l = 12, A < 60[/tex]
So
[tex]A < 60[/tex]
[tex]l*h < 60[/tex]
[tex]12h < 60[/tex]
So the correct answer is:
12h < 60
Answer:
12h < 60
hope this helps, its right because i took the test and it shows
Eric’s average income for the first 4 months of the year is $1,450.25, what must be his
average income for the remaining 8 months so that his average income for the year is
$1,780.75?
Answer:
$1946
Step-by-step explanation:
Eric’s average income for the first 4 months of the year is $1,450.25
Therefore, his total earning in the first four months
= 4 X $1,450.25
=$5,801
Let the average income for the remaining 8 months= x
Then:
[tex]\text{Eric's Yearly Average Income}=\dfrac{5801+8x}{12} \\1,780.75=\dfrac{5801+8x}{12} \\$Cross multiply\\12*1,780.75=5801+8x\\21369=5801+8x\\8x=21369-5801\\8x=15568\\Divide both sides by 8\\x=\$1946[/tex]
Therefore, to get an average income for the year of $1,780.75, Eric must earn an average income of $1946 for the remaining 8 months.
Dan earns £388 over the course of a five-day week. How much is that per day?
Answer:
£77.6 per day
Step-by-step explanation:
388/5 = 77.6
Answer:
£77.60
Step-by-step explanation:
388/5=77.6
but remember that this is money so add the 0.
Consider the transformation T: x = \frac{56}{65}u - \frac{33}{65}v, \ \ y = \frac{33}{65}u + \frac{56}{65}v
A. Computer the Jacobian:
\frac{\partial(x, y)}{\partial(u, v)} =
B. The transformation is linear, which implies that ittransforms lines into lines. Thus, it transforms the squareS:-65 \leq u \leq 65, -65 \leq v \leq 65 into a square T(S) with vertices:
T(65, 65) =
T(-65, 65) =
T(-65, -65) =
T(65, -65) =
C. Use the transformation T to evaluate the integral\int \!\! \int_{T(S)} \ x^2 + y^2 \ {dA}
Answer:
Step-by-step explanation:
[tex]T: x = \frac{56}{65}u - \frac{33}{65}v, \ \ y = \frac{33}{65}u + \frac{56}{65}v[/tex]
A)
[tex]\frac{d(x,y)}{d(u,v)} =\left|\begin{array}{ccc}x_u&x_v\\y_u&y_v\end{array}\right|[/tex]
[tex]=(\frac{56}{65} )^2+(\frac{33}{65} )^2\\\\=\frac{(56)^2+(33)^2}{(65)^2} \\\\=\frac{4225}{4225} \\\\=1[/tex]
B )
[tex]S:-65 \leq u \leq 65, -65 \leq v \leq 65[/tex]
[tex]T(65,65)=(x=\frac{56}{65} (65)-\frac{33}{65} (65),\ \ y =\frac{33}{65} (65)+\frac{56}{65} (65)\\\\=(23,89)[/tex]
[tex]T(-65,65)=(-56-33,\ \ -33+56)\\\\=(-89,23)[/tex]
[tex]T(-65,-65) = (-56+33,-33-56)\\\\=(-23,-89)[/tex]
[tex]T(65,-65)=(56+33, 33-56)\\\\=(89,-23)[/tex]
C)
[tex]\int \!\! \int_{T(S)} \ x^2 + y^2 \ {dA}[/tex]
[tex]=\int\limits^{65}_{v=-65} \int\limits^{65}_{u=-65}(x^2+y^2)(\frac{d(x,y)}{d(u,v)} du\ \ dv[/tex]
Now
[tex]x^2+y^2=(\frac{56}{65} u-\frac{33}{65} v)^2+(\frac{33}{65} u+\frac{56}{65} v)^2[/tex]
[tex][(\frac{56}{65} )^2+(\frac{33}{65}) ^2]u^2+[(\frac{33}{65} )^2+(\frac{56}{65}) ^2]v^2[/tex]
[tex]=\frac{(65)^2}{(65)^2} u^2+\frac{(65)^2}{(65)^2} v^2=u^2+v^2[/tex]
[tex]\int \!\! \int_{T(S)} \ x^2 + y^2 \ {dA}[/tex]
[tex]=\int\limits^{65}_{v=-65} \int\limits^{65}_{u=-65}(u^2+v^2) du\ \ dv[/tex]
[tex]=\int\limits^{65}_{-65}\int\limits^{65}_{-65}u^2du \ \ dv+\int\limits^{65}_{-65}\int\limits^{65}_{-65}v^2du \ \ dv[/tex]
By symmetry of the region
[tex]=4\int\limits^{65}_0 \int\limits^{65}_0u^2 du \ \ dv + u\int\limits^{65}_0 \int\limits^{65}_0v^2 du \ \ dv[/tex]
[tex]= 4(\frac{u^3}{3} )^{65}_{0}(v)_0^{65}+(\frac{v^3}{3} )^{65}_{0}(u)_0^{65}\\\\=4[\frac{(65)^4}{3} +\frac{(65)^4}{3} ][/tex]
[tex]=\frac{8}{3} (65)^4[/tex]
Can someone help me with this is the hardest one by far
Answer:
10 units
Explanation:
Create a right triangle, determine the a and b side lengths of the triangle by looking at the graph. (See image)
Then use the Pythagorean theorem to find c.
a² + b² = c²
(8)² + (6)² = c²
64 + 36 = c²
100 = c²
Square root both sides to get c.
[tex]\sqrt{100}[/tex] = c
10 = c
Let mu denote the true average number of minutes of a television commercial. Suppose the hypothesis H0: mu = 2.1 versus Ha: mu > 2.1 are tested. Assuming the commercial time is normally distributed, give the appropriate rejection region when there is a random sample of size 20 from the population and we would like to test at the level of significance 0.01. Let T be the appropriate test statistic.
A, T > 2.539
B. > 2.845
C. T> .528D. T >2.861
Answer:
A. T > 2.539
Step-by-step explanation:
We have a hypothesis test of the mean, with unknown population standard deviation.
The hypothesis are:
[tex]H_0: \mu = 2.1 \\\\H_a: \mu > 2.1[/tex]
From the hypothesis we can see that the test is right-tailed, so the critical value of t should be a positive value.
The degrees of freedom can be calculated as:
[tex]df=n-1=20-1=19[/tex]
The significance level is 0.01, so the critical value tc should be the one that satisfies:
[tex]P(t>t_c)=0.01[/tex]
Looking up in a t-table, for 19 degrees of freedom, this critical value is tc=2.539.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. x - 3
Step-by-step explanation:
Set it up like this:
(3x - 2) - (2x + 1)
Combine like terms:
3x - 2 - 2x - 1
3x - 2x = x
-2 - 1 = -3
Put it together:
x - 3
What is the sum 2/x^2 + 4/x^2
What is the range of the function f(x) = -2(64) + 3?
Answer:
Step-by-step explanation:
f(x) = -2(64) + 3 is not a function of x; it's a constant with the single value -125.
Ensure that you have copied down this problem correctly.
Answer: -2 multiply 64 add 3 equals -125
Step-by-step explanation:
-2 multiply 64 add 3
then multiply 2 and 64 which is 128
then add/subtract: -128 add 3 which is -125
Then final answer -2 multiply 64 add 3 equals -125
In Seaton Park school, 60% of the boys play baseball and 24% of the boys play baseball and football. What percentage of those that play baseball also play football?
Answer:
[tex]0.4\%[/tex]
Step-by-step explanation:
Given: 60% of the boys play baseball and 24% of the boys play baseball and football in Seaton Park School
To find: percentage of those that play baseball also play football
Solution:
Let B denotes boys who play baseball and F denotes boys who play football.
[tex]P(B)=60\%[/tex]
[tex]P(F\cap B)=24\%[/tex]
Percentage of those that play baseball also play football = [tex]P\left ( F|B \right )=\frac{P(F\cap B)}{P(B)}=\frac{24}{60}=\frac{2}{5}=0.4\%[/tex]
