If they make additional payments of $3,000 every four months for the first five years, it will reduce the outstanding balance on the mortgage.
What is their monthly rate to be applied to the mortgage?To calculate the values requested, we'll need to perform various calculations based on the given information. Let's go step by step:
Monthly Interest Rate:
The mortgage rate provided is 4.9% compounded semi-annually. To calculate the monthly interest rate, we need to convert the semi-annual rate to a monthly rate. Since there are two compounding periods per year, we divide the annual interest rate by two and then convert it to a decimal:
Monthly interest rate = (4.9% / 2) / 100 = 0.0245
Monthly Payments:
To calculate the monthly payments, we can use the formula for the monthly payment of a mortgage:
Monthly Payment = (Loan Amount - Down Payment) * (Monthly Interest Rate / (1 - (1 + Monthly Interest Rate)^(-Number of Months)))
Loan Amount = $460,000 - (10% * $460,000) = $414,000
Number of Months = 25 years * 12 months/year = 300 months
Substituting these values into the formula, we can calculate the monthly payments:
Monthly Payment = ($414,000) * (0.0245 / (1 - (1 + 0.0245)^(-300)))
Amount Owed after 5 Years:
After five years, the number of months remaining on the mortgage is 25 years - 5 years = 20 years = 240 months. To find out how much they owe after the first five years, we need to calculate the remaining balance on the mortgage:
Remaining Balance = Loan Amount * (1 + Monthly Interest Rate)^Number of Months - Total Payments
In this case, the Loan Amount is $414,000, the Monthly Interest Rate is 0.0245, and the Number of Months is 240. To calculate the Total Payments, we can multiply the Monthly Payment by the number of months paid during the first five years (5 years * 12 months/year = 60 months).
Interest Paid in the First Five Years:
To determine the interest paid in the first five years, we can subtract the remaining balance after five years from the initial loan amount:
Interest Paid = Loan Amount - Remaining Balance
New Semi-Monthly Payments after Renegotiation:
If they renegotiate the mortgage at a new rate of 5.9%, compounded semi-annually, and plan to pay off the remaining balance from part c, we need to recalculate the monthly payments.
We can use a similar formula as in part b, substituting the remaining balance (from part c) as the new loan amount, and the semi-monthly interest rate based on the new mortgage rate.
Payments of $3,000 every Four Months in the First Five Years:
To calculate the new interest paid in the first five years, we need to consider the reduced balance resulting from the additional payments and then subtract this balance from the initial loan amount.
Now, let's perform the calculations and find the values for each part.
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Select the simplification that accurately explains the following statement.
Answer:
look below I got it right
Step-by-step explanation:
look carefully, for some people it’s a, for some it’s different so just look and compare to the answers
Write in standard form:
v^2 = 81
Darren scored a mark of 57 on the Miller Analogies Test. This test has a mean of 50 and a standard deviation of 5. Jennifer scored 120 on the WISC Intelligence Test. This test has a mean of 100 and a standard deviation of 15. Comparing their scores, comment on who had a better score? Explain your answer
The performance scores (each score is an x-value) of three drivers were converted to standard scores. Comment on what each of the standard z-score indicates and determine the related implication
Z = 0.03
Z = 4.2
Z = -0.49
Darren had a better score than Jennifer based on their respective test scores.
To compare their scores, we need to consider their individual test scores in relation to the mean and standard deviation of each test.
For Darren's score of 57 on the Miller Analogies Test, we can calculate the z-score using the formula:
z = (x - μ) / σ
where x is the individual score, μ is the mean, and σ is the standard deviation. Plugging in the values, we have:
z = (57 - 50) / 5 = 1.4
For Jennifer's score of 120 on the WISC Intelligence Test, we can calculate the z-score using the same formula:
z = (120 - 100) / 15 = 1.33
Comparing the z-scores, we can see that Darren's z-score of 1.4 is higher than Jennifer's z-score of 1.33. A higher z-score indicates a score that is further above the mean relative to the standard deviation. Therefore, Darren's score of 57 on the Miller Analogies Test is relatively better than Jennifer's score of 120 on the WISC Intelligence Test in terms of their respective distributions.
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Which investment choice carries the greatest price risk?
Common stocks
Preferred stocks
Corporate bonds
Government bonds
The investment choice that carries the greatest price risk is common stocks. (Option-A)
Common stocks are shares of ownership in a company and their price can be very volatile, changing rapidly depending on market conditions and factors affecting the company. Their prices can be influenced by factors such as overall economic conditions, company financial performance, and investor sentiment.
On the other hand, preferred stocks and corporate bonds are typically less risky than common stocks. Preferred stocks are a type of stock that pays a fixed dividend and has a priority claim on company assets in the event of bankruptcy, while corporate bonds are debt instruments that pay a fixed interest rate.
Lastly, government bonds are considered the least risky of all of these investment choices because they are backed by the government, which has a reputation for always repaying its debts.
In summary, while all types of investments carry some level of risk, common stocks have the greatest price risk due to their volatility and sensitivity to changing market conditions.(Option-A)
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4x + 14 = 4x + 24 its to hard for me
Answer:
x=10
Step-by-step explanation:
HHHHHHHHHHHHHELLLLLPPPPPPP ME PLS PLS PLS a school wants to add a new sports team. The school sent out surveys asking for the students' favorite sport. seventeen students named swimming. Others named hockey or volleyball . Use pencil and paper. Explain how to use the circle graph and ratios to find the number of students surveyed. Then find this number.
Answer:
Total 100% or 25 students
Swimming 36% or 9 students
Lacrosse 48% or 12 students
Volleyball 16% or 4 students
Step-by-step explanation:
To do a circle graph, you draw a circle and divide it into all sections.
To know the size of each section, you need to know the total number of every category.
You could draw it with percent.
100% is total, and you know the percent of each sport.
They told you 12 students choose lacrosse so, this represents 48%.
Now, you can find the other numbers with cross-multiplication.
48%____12
100%____X=
X=(100x12)/48=25
Total students: 25
Students that named lacrosse: 12 or 48%
100%____25
16%____X=
X=(16x25)/100=4
Students that named Volleyball: 4 or 16%
100%____25
36%____X=
X=(36x25)/100=9
Students that named Swimming: 9 or 36%
To confirm: 12 + 9 + 4 = 25
Brainlist Pls!
Answer:
50
Step-by-step explanation:
¿Cuál es el valor de X en la ecuación 6(4x+1)-3(2x-3)=3(4x-5)-6(x+1)?
Using mathematical operators, the value of x in the equation is -3
What is an equation?An equation is a mathematical statement that shows that two expressions are equal. There are different types of equations based on the degree. Linear equation, quadratic equation, and cubic equation are some of the common types of equations.
Linear equations have one degree, quadratic equations have two degrees, and cubic equations have three degrees. The degree of an equation is the highest power of the variable in the equation.
In the given problem, we can find the value of x by using mathematical operators.
6(4x + 1) - 3(2x - 3) = 3(4x - 5) - 6(x + 1)
Open the brackets;
24x + 6 - 6x + 9 = 12x - 15 - 6x - 6
Collect like terms
24x - 6x + 9 + 6 = 12x - 6x - 6 - 15
18x + 15 = 6x - 21
18x - 6x = -21 - 15
12x = -36
Divide both sides by the coefficient of x;
12x/12 = -36/12
x = -3
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Assume that females have pulse rates that are normally distributed with a mean of u=72.0 beats per minute and a standard deviation of a 12.5 beats per minute. Complete parts (a) through (c) below. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 70 beats per minute The probability is (Round to four decimal places as needed.) b. If 16 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 79 beats per minute The probability is (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 307 OA. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size OB. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size OC. Since the onginal population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. OD. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 79 beats per minute The probability is (Round to four decimal places as needed.) b. I 16 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 79 beats per minute The probability is (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 309 O A Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. OB. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size OC. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample site OD. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size
The probability that a randomly selected adult female has a pulse rate less than 70 beats per minute is about 0.4371.
What is the probabilitya. To find the probability that a randomly selected adult female has a pulse rate less than 70 beats per minute, one have to calculate the z-score and use the standard normal distribution.
The z-score can be calculated as:
z = (x - μ) / σ
where:
x = the value (70 beats per minute)
μ = the mean (72.0 beats per minute)
σ = the standard deviation (12.5 beats per minute).
So putting it into the formula, it will be:
z = (70 - 72.0) / 12.5
z = -0.16
One can know probability using the z-score.
Check z-score in the standard normal distribution table, and the value will be 0.4371 (rounded to four decimal places).
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Consider the points A (-1, 1), B (1,5) and C (5, 1). M is the midpoint of AB, and N is the
midpoint of BC.
Show that MN is parallel to AC
Step-by-step explanation:
IN ΔAMN ΔABC
Since MN∣∣BC
∠AMN=∠ABC (Corresponding angles)
∠ANM=∠ACB (Corresponding angles)
∴ΔAMN∼ΔABC(By $$AA similarity criterion)
⇒
AB
AM
=
AC
AN
=
BC
MN
(CPST)
Since, M is mid-point of AB,
AM=
2
1
AB,or,
AB
AM
=
2
1
or,
AB
AM
=
AC
AN
=
2
1
AC
AN
=
2
1
5
AN
=
2
1
[∵AC=5cm]
AN=
2
5
cm=2.5cm
Also,
AB
AM
=
BC
MN
=
2
1
7
MN
=
2
1
[∵BC=7cm]
MN=
2
7
=3.5
Ans=AN=2.5cm and MN=3.5cm
solution
I need help with this please lol
Answer:
360 degrees
Step-by-step explanation:
The volume of a cube is 216 cubic feet. What is the length of each side of the cube?
side = ? ? ? feet
Answer:
find the cube root of 216 to get the length of one side as you get the volume of a cube by length x length x length
Step-by-step explanation:
the the cube root of 216 is 6
so the length of one side is 6 inches
Hope This Helps :)
Answer: I think it is 54 because there are four sides of a cube. So I just did 216/4 and got 54.
Step-by-step explanation:
Might be wrong but this is what I think the answer is.
If an item is on sale for 60% off, that means you actually PAY _____% of the price.
Answer:
40%
Step-by-step explanation:
100-60=40
A poker hand consists of 5 cards. A flush is a hand for which all cards are the same suit,but not of consecutive denominations (where Ace can be high or low.For example,2,3,4,5,7 of Hearts is a flush,but 2,3,4,5,6 of Hearts is not a flush. Find the probability that a poker hand from a well-shuffled deck is a flush. b Anne and Barney are playing poker. On each hand, Anne has a 20% chance of bluffing and Barney has a 30% chance of bluffing; the two players bluff in- dependently. What is the probability that Anne is bluffing,given that at least one player is bluffing?
The probability that a poker hand from a well-shuffled deck is a flush is 0.00198.
The probability that Anne is bluffing, given that at least one player is bluffing is 1.95.
a) Probability that a poker hand from a well-shuffled deck is a flush:
Consider the following points for a poker hand from a well-shuffled deck is a flush:
There are 4 suits in a deck of cards.
There are 13 denominations in each suit.
When choosing a flush hand, any of the suits can be selected.
Therefore, the probability of choosing a suit is: P(Suit) = 4/4 = 1.
Therefore, the probability of selecting a suit is 1.The first card may be of any denomination. Therefore, the probability of selecting any denomination is 1.
Since all 5 cards must have the same suit, the second card must be of the same suit as the first card. Therefore, the probability of selecting the second card of the same suit is:
P(Same Suit) = 12/51
The third card must also be of the same suit as the first card and second card. Therefore, the probability of selecting the third card of the same suit is:
P(Same Suit) = 11/50
The fourth card must also be of the same suit as the first card, second card, and third card. Therefore, the probability of selecting the fourth card of the same suit is:
P(Same Suit) = 10/49
The fifth card must also be of the same suit as the first card, second card, third card, and fourth card. Therefore, the probability of selecting the fifth card of the same suit is:
P(Same Suit) = 9/48
Multiplying all probabilities together, we have:
P(Suit) × P(Same Suit) × P(Same Suit) × P(Same Suit) × P(Same Suit)= 1 × 12/51 × 11/50 × 10/49 × 9/48= 0.00198
Therefore, the probability that a poker hand from a well-shuffled deck is a flush is 0.00198.
Ans: 0.00198.
b) Probability that Anne is bluffing, given that at least one player is bluffing:
Consider the following points for the probability that Anne is bluffing, given that at least one player is bluffing:
Anne has a 20% chance of bluffing.
Barney has a 30% chance of bluffing.
The two players bluff independently.
P(Anne is bluffing) = 20/100 = 1/5P(Barney is bluffing) = 30/100 = 3/10
Let A be the event that Anne is bluffing and B be the event that Barney is bluffing.
Let C be the event that at least one player is bluffing.
P(C) = 1 - P(none is bluffing) = 1 - (1 - P(Anne is bluffing)) × (1 - P(Barney is bluffing))= 1 - (1 - 1/5) × (1 - 3/10)= 1 - (4/5) × (7/10)= 1 - 28/50= 22/50= 11/25
Now, P(A ∩ C) = P(A) × P(C|A)
Where P(C|A) is the probability that at least one player is bluffing given that Anne is bluffing.= (3/10 + 7/10 × 4/5) / (1 - 4/5)= (3/10 + 28/50) / (1/5)= (15/50 + 28/50) / (1/5)= 43/50 × 5= 215/50
Therefore, P(A|C) = P(A ∩ C) / P(C)= 215/50 × 25/11= 1.95
Therefore, the probability that Anne is bluffing, given that at least one player is bluffing is 1.95. Ans: 1.95.
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3-6 x (34 divided by 30)2
Answer:
3-6
Step-by-step explanation:
The expression 3⁻⁶ × (3⁴ ÷ 3⁰)² value is 9 which is 3².
To simplify the given expression: 3⁻⁶ × (3⁴ ÷ 3⁰)², let's break it down step by step:
First, let's simplify the exponent expressions within the parentheses:
3⁴ = 81 (because 3⁴ = 3 × 3 × 3 × 3 = 81)
3⁰ = 1 (because any number raised to the power of 0 is 1)
Now, we can rewrite the expression with the simplified exponents:
3⁻⁶ × (81 ÷ 1)²
Next, simplify the division within the parentheses:
81 ÷ 1 = 81
Now, the expression becomes:
3⁻⁶ × 81²
Simplify the exponent:
81² = 6561 (because 81 × 81 = 6561)
Now, the expression becomes:
3⁻⁶ × 6561
1/729 × 6561
6561/729
dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 9:
729/81
We get 9 which is equal to 3².
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Michael Scott, regional manager at Dunder mifflin Scranton, bought a coin from a magic shop that is designed to flip heads much often than tails. Dwight Schrute, his employee, wants to estimate the proportion of all glips of this coin that will be heads. In 400 flips of the coin Dwight flipped 312 times. Construct and interpret the 90% confidence interval for the population proportion of flips that will be heads. show at least 2 decimal digits in your endpoints.
The 90% confidence interval for the population proportion of flips that will be heads is given as follows:
(0.746, 0.814).
The interpretation is that we are 90% sure that the true proportion of all tosses with this coin is between these two bounds.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
The parameters for this problem are given as follows:
[tex]n = 400, \pi = \frac{312}{400} = 0.78[/tex]
The lower bound of the interval is given as follows:
[tex]0.78 - 1.645\sqrt{\frac{0.78(0.22)}{400}} = 0.746[/tex]
The upper bound is given as follows:
[tex]0.78 + 1.645\sqrt{\frac{0.78(0.22)}{400}} = 0.814[/tex]
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Maths equation need help please
Answer:
I FIGURED IT OUT!
Step-by-step explanation:
a = 3
b = 3
c = 5
d = 2
give me brainliest
Inspection of a random sample of 24 aircraft showed that 16 needed repairs to fix a wiring problem that might compromise safety (a) How large a sample would be needed to estimate the true proportion of jets with the wiring problem with 90 percent confidence and an error of + 4 percent? (Enter your answer as a whole number (no decimals). Use a z. value taken to 3 decimal places in your calculations.) Sample size (b) Would the airline actually conduct further sampling, or just inspect all the planes? Conduct further sampling Inspect all the planes
The sample size required to estimate the true proportion of jets with the wiring problem with 90% confidence and an error of +4% is approximately 92 (rounded up to the nearest whole number).
To determine the sample size needed to estimate the true proportion of jets with the wiring problem, we can use the formula for sample size calculation for proportions:
n = ([tex]Z^2 * p * q[/tex]) / [tex]E^2[/tex]
Where:
n = sample size
Z = Z-score corresponding to the desired confidence level (90% confidence corresponds to a Z-score of 1.645)
p = estimated proportion (16/24 = 0.6667)
q = 1 - p
E = maximum error tolerance (4% = 0.04)
Let's calculate the sample size:
p = 0.6667
q = 1 - p = 0.3333
E = 0.04
Z = 1.645
n = ([tex]1.645^2[/tex] * 0.6667 * 0.3333) / [tex]0.04^2[/tex]
n ≈ 91.62
Regarding the decision to conduct further sampling or inspect all the planes, it depends on the context and resources available. If inspecting all the planes is feasible and does not require excessive time or cost, it might be preferred to ensure the safety of all aircraft.
However, if conducting further sampling is a practical and reliable way to estimate the proportion while saving time and resources, the airline might choose to conduct additional sampling.
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It costs $4.95 to professionally dryclean a pair of slacks. Marcie uses a product that allows her to dry-clean clothes in her own dryer. For about $12, she can dry-clean 16 garments. 1. How much would it cost to have the slacks professionally dry-cleaned 16 times? 2. How much would she save by doing the job herself?
A cylinder has a height of 16 meters and a diameter of 26 meters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answer:
V= 5224.96
Step-by-step explanation:
To find the volume for a cylinder, you need to use the formula
V=(pi)r^2h.
The question gives is the diameter. The radius is half of the diameter, so you would divide by 2.
16/2 = 8.
Now we plug in the numbers and solve.
V= (pi) 8^2(26)
V= (pi)(64)(26)
V=(pi)(1664)
V= 5224.96
Express your answer in scientific notation. 6.4 * 10^5 + 36,000 =
Answer:
6.76x10^5
^ represents to the 5th power
Step-by-step explanation:
A store owner offers a discount of 20% off the regular price of all jackets. Jessica has a coupon that gives her an additional 5% off the discounted price. The original price of the jacket Jessica buys is $84. What is the price of the jacket after the discount and Jessica's coupon?
Answer:
21
Step-by-step explanation:
I haven't done this in a long time but this is what I know: the discount would overall be 25%. So, you set it up by .25(84) = 21. Therefore the jacket would cost $21.
I hope this is right and helps!
2
A = 2.5 km
b= 5 km
h =
Answer:
First of all, we have to make area km by multiplying 10 then solve, the answer is 5
are all vertical lines parallel?
Answer: Yes
Step-by-step explanation: All vertical lines have the same slope and because of that they are always parallel.
convert (badfaced)16 from its hexadecimal expansion to its binary expansion
The binary expansion of (badfaced)16 is 10111010111111011010111110101101 2.
In order to convert (badfaced)16 from its hexadecimal expansion to its binary expansion, we need to follow the steps below:
Step 1: Write down the hexadecimal number (badfaced)16
Step 2: Write the binary equivalent of each hexadecimal digit (use the table below)
Step 3: Combine all the binary digits to get the answer
Table showing the binary equivalent of each hexadecimal digit Binary Equivalentb00001011a00001010d00001101f00001111a00001010c00001100e00001110d00001101
Step 2: Writing the binary equivalent of each hexadecimal digit(badfaced)16 = b a d f a c e d
Step 3: Combining all the binary digits to get the answer(badfaced)16 = 10111010111111011010111110101101 2
Thus, the binary expansion of (badfaced)16 is 10111010111111011010111110101101 2.
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A container in the shape of a cylinder has a volume of 60 cubic meters. Its base has an area of 15 square units. What is the height of the container?
options
3m
2m
4m
5m
The answer would be 4m
BRAINLIST. BRAINLIST. BRAINLIST. PLS HELP.
Answer:
Mild- 5x=50 4x=40
Medium- 90- 48=42, 42/2=21 so, 2x=21
Spicy- 90-25=65, 65+18=83
Step-by-step explanation:
I'm gonna guess that this is the angle measurement so.....
A grain silo is shown below:
Grain silo formed by cylinder with radius 6 feet and height 168 feet and a half sphere on the top
What is the volume of grain that could completely fill this silo, rounded to the nearest whole number? Use 22 over 7 for pi.
Answer: 13750+262=14,012 ft^3
Step-by-step explanation:
Hello!!!
Find the volume of the bottom and top separately and then add them. Cylinder volume is the area of the bottom times the height (22/7)(5^2)•175=13750 ft^3
The volume of a sphere isV=(4/3)(22/7)r^3where r is the radius. also 5 since it fits on the cylinder. Also we only want half the sphere so useV=(2/3)(22/7)•5^3=261.9 ft^3 round upto 262. Now add together 13750+262=14,012 ft^3
Hope this helps~!!!!!
Prove the The Argument principle for meromorphic functions i.e. calculate the integral 1 f' L 2πi where does not hit zeroes or poles of f.(meromorphic: locally a quotient of two holomorphic functions).
The Argument Principle for meromorphic functions states that the integral of the logarithmic derivative of a meromorphic function around a closed curve is equal to 2πi times the sum of the winding numbers of the curve around its zeros and poles. This result is derived using the Residue Theorem and the properties of zeros and poles.
To prove the Argument Principle for meromorphic functions, we start by considering a meromorphic function f(z) on a closed curve C, where f(z) is holomorphic except at a finite number of isolated singularities (poles and/or removable singularities) within the region enclosed by C. We assume that C is positively oriented.
The Argument Principle states that the integral of the logarithmic derivative of f(z) along the curve C is equal to 2πi times the sum of the winding numbers of the curve around the singularities of f(z) within the region enclosed by C. Mathematically, it can be expressed as:
∮C (f'(z)/f(z)) dz = 2πi (N - P)
where N is the sum of the winding numbers of C around the zeros of f(z) and P is the sum of the winding numbers of C around the poles of f(z).
To prove this, we can use the Residue Theorem. First, we write f(z) as a product of its zeros and poles:
f(z) = (z - z₁)^(n₁) (z - z₂)^(n₂) ... (z - z_N)^(n_N) / (z - w₁)^(m₁) (z - w₂)^(m₂) ... (z - w_P)^(m_P)
where z₁, z₂, ..., z_N are the zeros of f(z) with respective multiplicities n₁, n₂, ..., n_N, and w₁, w₂, ..., w_P are the poles of f(z) with respective multiplicities m₁, m₂, ..., m_P.
Taking the logarithmic derivative of f(z), we get:
(f'(z)/f(z)) = ∑ (n_j/(z - z_j)) - ∑ (m_k/(z - w_k))
Now, we consider the integral of (f'(z)/f(z)) dz along the closed curve C. By the Residue Theorem, this integral can be evaluated as the sum of the residues of the function (f'(z)/f(z)) at its isolated singularities within the region enclosed by C.
The residues at the zeros z_j of f(z) are given by n_j, and the residues at the poles w_k of f(z) are given by -m_k. Therefore, the integral becomes:
∮C (f'(z)/f(z)) dz = ∑ (n_j) - ∑ (m_k) = N - P
where N is the sum of the winding numbers of C around the zeros of f(z), and P is the sum of the winding numbers of C around the poles of f(z).
Finally, using the fact that the integral of (f'(z)/f(z)) dz is equal to 2πi times the sum of the residues, we arrive at:
∮C (f'(z)/f(z)) dz = 2πi (N - P)
which proves the Argument Principle for meromorphic functions.
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find the surface area of the figure below
Answer:
64
Step-by-step explanation:
square= 16
triangle= 12
12*4 = 48+16 = 64
Answer:
64 m²
Step-by-step explanation:
Hello There!
The surface area is the total area of the figure
So in order to find the area we need to find the area of each shape
For the square:
the square has a length of 4 so we can simply find the area by squaring it
4 * 4 = 16
so the area of the square is 16 square meters
Now we need to find the area of the triangles
The formula for area of a triangle is
[tex]A=\frac{bh}{2}[/tex]
where b = base and h = height
The triangles dimensions are:
base - 4m
height - 6m
having found these dimensions we plug them in into the formula
[tex]A=\frac{4*6}{2} \\4*6=24\\\frac{24}{2} =12[/tex]
so the area of one of the triangles is 12 square meters
We want to find the total area of all of the triangles
To do so we multiply the area of one triangle by 4 (because there are four triangles)
12 * 4 = 48
So the total area of the four triangles is 48 square meters
Finally we add the two areas
48 + 16 = 64
so we can conclude that the total surface area of the pyramid is 64 m²
find the volume of the 2 dice if the length of the base of the cube is 4cm
A) 64cm cubed
B) 96cm cubed
C) 108cm cubed
D) 128cm cubed
Answer:
I think the answer is A 64cm cubed