Recall that for all [tex]z\in\Bbb C[/tex],
[tex]\displaystyle e^z = \sum_{n=0}^\infty \frac{z^n}{n!}[/tex]
Then
[tex]\displaystyle \frac{e^{z^2}}{z^3} = \frac1{z^3} \sum_{n=0}^\infty \frac{z^{2n}}{n!} = \boxed{\sum_{n=0}^\infty \frac{z^{2n-3}}{n!}}[/tex]
Suppose that y is inversely proportional to the 4th power of x, and that y=16 when x=6. What is y when x=3? Round your answer to two decimal places if necessary.
Answer:
y = 1
Step-by-step explanation:
Given
y ∝ x⁴⇒ y = kx⁴
Finding the proportionality constant, k
y = 16 and x = 316 = k (6)⁴16 = 1296kk = 16/1296k = 1/81Finding y
y = 1/81 x (3)⁴y = 1/81 x (81)y = 1Frenza is planning an $160,000 expansion to launch a new product line. Frenza currently earns $100,000 in net income, and the new product line will yield $50,000 in additional income before any interest expense. Frenza has three options: (1) do not expand, (2) expand and issue $160,000 in debt that requires payments of 8% annual interest, or (3) expand and raise $160,000 from equity financing. For each option 1, 2, and 3, compute (a) net income and (b) return on equity (Net income ÷ Equity). Ignore any income tax effects. (Round "Return on equity" to 1 decimal place.) Show less 1 2 3 Don’t Expand Debt Financing Equity Financing Income before interest expense $92,000 Interest expense 0 12,800 0 Net income $100,000 Equity $400,000 $400,000 Return on equity % % %
Based on the current income to Frenza, and the proposed expansion amount, the net income and return on equity for the three options are:
Don't Expand:
Net income = $100,000.Return on equity = 25%.Debt financing:
Net income = $137,200.Return on equity = 34.3%.Equity financing:
Net income = $150,000.Return on equity = 26.8%.What happens if Frenza doesn't expand?Net income will remain at $100,000.
Return on equity would be:
= Net income / Equity
= 100,000 / 400,000
= 25%
What happens if Frenza uses debt financing?Income goes to $150,000.
Net income:
= Income - interest
= 150,000 - (8% x 160,000)
= $137,200
Return on equity:
= 137,200 / 400,000
= $34.3%.
What happens if Frenza uses equity financing?Income goes to $150,000.
No interest payment so net income is $150,000.
Return on equity:
= 150,000 / (400,000 + 150,000 new equity)
= 26.8%
Find out more on return on equity at https://brainly.com/question/1427854.
9. An airplane is 325 miles from the airport. To get to the present positionthe plane flew 205 miles due south from the airport and then flew due westTo the nearest mile, how far west didi the plane fly?
In your own words describe how to find the area of a composite
figure? What are the steps you would take to solve a problem like
this?
HELP PLS ILL MAKE THE BRAINIEST SAY THANKS AND RATE 5 STARS JUST HELP ME IN LIKE 5 - 10 MIN PLS!
Answer:
A=LxW
Step-by-step explanation:
cut the shape into easier pieces then go to one piece and x the W with the L for example 4x5 then x them and youll get your area like this A=LxW = 20=4x5 like that then do the same for the other pieces then once you x them all add them and youll get the whole area for your shape
hoped it helped :)
Need help on one question
Answer:
write it so that we can know
now I can't see
can someone help me with this?
Answer:
f(x) = 2 -2^x
Step-by-step explanation:
The graph has a horizontal asymptote at y = 2. It has a slope that doubles in each unit interval. This tells you it is an exponential function with a base of 2, and a vertical translation of 2. The curve downward, rather than upward, means the function has been reflected across a horizontal line.
__
vertical shiftAn exponential function of the form ...
y = a·b^x
will have a horizontal asymptote at y=0. The asymptote here is y=2, so 2 has been added to the function value.
base valueThe slope of the above function (y=a·b^x) will be multiplied by a factor of 'b' when x increases by 1. Your graph has a slope (rise/run) of -1 for x between 0 and 1, a slope of -2 for x between 1 and 2, and a slope of -4 between x=2 and 3. This behavior indicates that b=-2/-1 = -4/-2 = 2.
scale factorThe function so far looks like ...
y = a·2^x +2
Using x=0, we can find the value of 'a'.
1 = a·2^0 +2
-1 = a . . . . . . . . subtract 2
Then the function is ...
f(x) = -2^x +2
If the area of the rectangle is twenty-four-and-thirty-two-hundredths square inches, what’s the measurement of the width?
Answer:
Can't answer this without knowing the height of the rectangle ...
Step-by-step explanation:
Answer: 3.2
Step-by-step explanation: Trust me, I got it right.
Solve the following quadratic equation: x^2-10x+25=51
please show steps i don’t understand
1. Simplify the quadratic equation into its standard form
Formula : ax^2+bx+c=0
Subtract from both sides:
x^2-10x+25=51
x^2-10x+25-51=0
x^2-10x-26=0
Use the standard form, ax^2+bx+c=0, to find the coefficients of our equation.
x^2-10x-26=0
a=1
b=-10
c=-26
The quadratic formula gives us the roots for ax^2+bx+c=0, in which a, b and c are numbers (or coefficients), as follows :
x=(-b±sqrt(b^2-4ac))/(2a)
to get the result :
x=(10±sqrt(204))/2
Simplify 204 by finding its prime factors:
The prime factorization of 204 is 2^2*3*17
x_2=-2.141
Answer:
x = 5 ± √51
Step-by-step explanation:
x² - 10x + 25 = 51
x² - 10x + 25 - 51 = 51 - 51
x² - 10x - 26 = 0
Factors with a product of -26 and a sum of -10:
NONE! Solve by completing the square (see attachment)
Step 1: Rearrange
x² - 10x + 25 = 51
x² - 10x = 26
Step 2: Add (b/2)² to both sides
x² - 10x + (-10/2)² = 26 + (-10/2)²
x² - 10x + 25 = 51
Step 3: Factor and solve
(x - 5)² = 51
x - 5 = √51
x = 5 ± √51
BRAINLIEST please if this helped!Course challenge
You might need: Calculator
Figure A is a scale image of figure B.
Figure A
Figure B
16
Figure A maps to figure B with a scale factor of 4/9
What is the value of X?
Answer:
x=36
Divide the corresponding side (16) by 4/7
Answer:
x=36
Divide the corresponding side (16) by 4/7
Step-by-step explanation:
x=16×9/4=36
Solve the following problems.
Given: IL Perpendicular EJ at M
Prove: mEL + mll = 180°
Just need the proof!
Goran is running for president of the chess club, and he received 24 votes. There are 40 members in the club. What percentage of the club members voted for Goran?
Answer:
60%
Step-by-step explanation:
[tex]\sf Percentage=\left(\dfrac{Value}{Total\:value}\right) \times 100[/tex]
Given:
value = 24 votesTotal value = 40 membersSubstituting these into the formula:
[tex]\implies \sf \left(\dfrac{24}{40}\right) \times 100=0.6 \times 100 = 60 \%[/tex]
Therefore, 60% of the club members voted for Goran.
Keith is the owner of a cafe. He bought 28.6 pounds of apples for making pies. Apples cost$1.75 per pound. He also bought a can of chocolate syrup for $27.75. What was the amount that Keith spent?
Answer:
$77.514
Step-by-step explanation:
28.6 x 1.74 + 27.75 = 77.514
Write (5 – 8i)2 in simplest a + bi form.
Answer:
10-16i
Step-by-step explanation:
use distrubutive property and treat i like a variable
Which pieces of information may be found on a person's credit report?
Select each correct answer.
credit card balance
late payments
person's address
income
household size
age
Answer:
credit card balance
late payments
income
Answer:
See below ~
Step-by-step explanation:
On a person's credit report, the following information may be found :
credit card balancelate paymentsperson's addressMatt and Mindy each built a rectangular prism that has a length of 5 units, a width of 2 units, and a height of 4 units. Matt used cubes that are 1 cm on each side. Mindy used cubes that are 1 in. on each side. What is the volume of each prism?
Answer:Matt’s is 40cm^3 and Mindy’s is 40in^3
Step-by-step explanation:5x2x4=40units^3
Answer:volume of rectangular prism is = whl= 2*4*5=40 unit³
the prism of the matt built will have the volume of 40cm³
where as Mindy will have 40in³
therefore,
1in=2.54cm
Mindy built volume= 40*2.54cm³= 101.6cm³
Dad is getting food ready for my birthday party! Including
me, there will be 18 people at the party. Dad is baking
cookies for us! He can bake 24 cookies per batch.
How many batches should I tell Dad to make so we can each
have 4 cookies?
Answer: Dad is getting food ready for my birthday party! Including
me, there will be 18 people at the party. Dad is baking
cookies for us! He can bake 24 cookies per batch.
How many batches should I tell Dad to make so we can each
have 4 cookies?
Step-by-step explanation:
Answer:
3 batches and a half = 84 cookies
Step-by-step explanation:
24 x 3= 84
84 divided by 19= 4.4
HGD
please help be answer this
Answer:
D
Step-by-step explanation:
[tex](2x +12)(2x + 8)[/tex]
[tex]4 {x}^{2} + 16x + 24x + 96[/tex]
[tex]4 {x}^{2} + 40x + 96[/tex]
If a point P is moving such that the lengths of the tangents drawn from P to the circles
[tex]x^2+y^2-4x-6y-12=0[/tex]
and
[tex]x^2+y^2+6x+18y+26=0[/tex]
are in the ratio 2:3 then find the equation of the locus of P.
Hello ~
My name is Irxdscent, and I will be answering your question today! :D
→ Answer :-[tex]\sf{(x_{1} \: - y_{1})[/tex]
→ Explanation :-[tex]\sf{Equations \: of \: the \: circles \: are:}[/tex][tex]\sf{S = x^2 \: + \: y^2 \: - \: 4x \: - \: 6y \: - \: 12 = 0}[/tex]
[tex]\sf{S_{1} = y^2 \: + \: y^2 \: + \: 6x \: + \: 18y \: + \: 26 = 0}[/tex]
[tex]\sf{P(x_{1}, \: y_{1}) \: is \: any \: point \: on \: the \: locus \: and \: PT_{1,} \: PT_{2} \: are \: the \: tangents \: from \: P \: to \: the \: two \: circles.[/tex]
[tex]\sf{Given \: condition \: is:}[/tex][tex]\sf{\frac{PT_{1}}{PT_{2}} = \frac{2}{3}[/tex][tex]\sf{3PT_{1} \: = \: 2PT_{2}[/tex][tex]\sf{3(x^2 \: + \: y^2 \: - \: 4x \: - \: 6y \: - \: 12) = 2(x^2 \: + \: y^2 \: + \: 6x \: + \: 18y \: + 26)[/tex]
[tex]\sf{3x^2 \: + \:3 y^2 \: - \: 12x \: - \: 18y \: - \: 36 = 2x^2 \: + \: 2y^2 \: + \: 12x \: + \: 36y \: + 52}[/tex]
[tex]\sf{x^2 \: + \: y^2 \: - \: 24x \: - \: 54y \: - \: 88 = 0}[/tex]
[tex]\sf{This \: is \: the \: locus \: P \: \sf{(x_{1} \: - y_{1})[/tex]
Hope It Helps! ~
~ Learn With Lrxdscent ~
[tex]\underline{Answer :}[/tex]
ɪ ʀ x ᴅ ꜱ ᴄ ᴇ ɴ ᴛ
Help please please WILL MARK BRAINIEST
Let's consider the information given:
states that this is a regular polygon⇒ means that all the side lengths are equal
this is a hexagon since it has six sidesTo calculate the area of the hexagon:
⇒ must know the formula
[tex]Area = \frac{3\sqrt{3} }{2} s^2[/tex]
s: length of one side --> 7 unitsLet's solve: (remember we need to round the final answer to the nearest hundredth)
[tex]Area = \frac{3\sqrt{3} }{2} *7^2=73.5\sqrt{3} =127.306[/tex] ≈ 127.31 square units
Answer: 127.31 square units
Hope that helps!
Someone please help!
Step-by-step explanation:
<1 = 180°-102° = 78° (the extended angle is 180°)
<2 = <5 = 58°
<3 = 180° - 78° - 58° = 44° (the sum of the angles inside of a triangle is 180°)
<4 = 180° - 44° - 58° = 78° = <1 (the extended angle is 180°)
Find the value of p if the mean of the following distribution is 20.
X:- 15 17 19 20+p 23
F:- 2 3 4 5p 6
Answer:
X:-15 17 19 20+p 23 there is a difference of 2 between each number so p=1 .
F:-2 3 4 5p 6 there is a difference of one so p needs to be 1 .
You recently discovered that your job provides a 30% matching towards your retirement. If you deposit $300 each month into a retirement account with an APR of 5.50%, what would you type in Excel to find the balance after 25 years?
Answer:
Total amount of every money dat I have deposited
What is 1/2 of 0.45x-1/4?
Answer:
0.45x−0.125
Step-by-step explanation:
0.45x-1/4
0.45x - 0.25 ÷ 2
0.45x−0.125
504,047 written in expanded form
Answer:
500,000 + 4,000 + 40 + 7
BRAINLIEST please if this helped!Write the mixed number as an improper fraction 2 3/10
Answer:
23/10
Step-by-step explanation:
and put the denominator as it is
[tex]\boxed{\rm{pls\:refer\:to\:explanation}}[/tex]
Step-by-step explanation:
First multiply the whole part (2) times the denominator (10) :
20
Add the numerator (3) :
23
That's the numerator of our improper fraction .
The denominator stays the same .
So the answer is :[tex]\boxed{\frac{23}{10}}[/tex]
[tex]\footnotesize\text{hope\:helpful}[/tex]
(12-3)\times6+(3\times7)
Answer:
The answer is 75
Step-by-step explanation:
Subtract: 12 - 3 = 9Help?? um i can’t select multiple pics so..the other two Drop down menus say ..
A) (x - 5)(x - 1)
B) (x + 5)(x + 1)
C) x-1
D) x-5
—-
A) -1
B) 5
C) 2
D) -5
Answer:
Step-by-step explanation:
[tex]\frac{x^2 -3x-10}{x^2 -6x+5}[/tex] × [tex]\frac{x-2}{x-5}[/tex] = [tex]\frac{(x-5)(x+2)}{(x-5)(x-1)}[/tex] × [tex]\frac{x-2}{x-5}[/tex] = [tex]\frac{(x+2)(x-2)}{(x-1)(x-5)}[/tex] ( Domain is x ≠ 1 and x ≠ 5 )
The expression has an excluded value of x = 5
37+6x-33-7x
i need help i cant find the answer
Answer:
By simplifiying the expression we get
−x+4
Answer:
-x+4
Step-by-step explanation:
Subtract: 37-33
Combine like terms: 6x-7
Rearrange terms: -x+4
12. In a language survey of students, it is found that 80 students know English, 60 know
French, 50 know German, 30 know English and French, 20 know French and German, 15 know English and German and 10 students know all the three languages. How many students know at least one language ?
Answer:
190 students
Step-by-step explanation:
Just focus on the first half of the problem: 80 english, 60 French, and 50 German. Added together this gives you 190
"I have a 40% chance of being selected as the captain of the volleyball team and a 75% chance of being elected student body president." What is the probability that Cara will be selected as the captain of the volleyball team and will be elected student body president?
Answer:
30% chance of them both happening
Answer:
thats going to be and exact 85%!
I used the probability calculater on cal.net