Answer:
Emma had $62.50 in her account when she and Alexis got to the bank.
Step-by-step explanation:
Let's start by assigning variables to the unknowns in the problem. Let's call the amount of money in Emma's account before she made her deposit "E", and the amount of money in Alexis's account before she made her withdrawal "A".
From the problem, we know that:
A = 3E (because Alexis had three times as much money as Emma before making her withdrawal)
After Alexis withdrew $100 and Emma deposited $25, they had the same amount of money in their accounts. So we can set up another equation:
A - 100 = E + 25
Simplifying this equation, we get:
A = E + 125
Now we can substitute the first equation into the second equation, because we know that A is equal to 3E:
3E = E + 125
Subtracting E from both sides, we get:
2E = 125
Dividing both sides by 2, we get:
E = 62.5
So Emma had $62.50 in her account when she and Alexis got to the bank.
Answer:62.50
Step-by-step explanation:
she had 62.50
A number exceeds 20% of itself by 40. find the number.
WITH STEPS
Answer:
50
Step-by-step explanation:
Let the number = x.
20% of the number is 20% of x = 0.2x.
Since the number exceeds 20% of itself by 40, then teh number minus 20% of itself is 40.
x - 0.2x = 40
0.8x = 40
x = 40/0.8
x = 50
44 friends evenly divided up an nnn-slice pizza. One of the friends, Harris, ate 111 fewer slice than he received. How many slices of pizza did Harris eat?
Write your answer as an expression
Harris ate x - 111 slices of pizza, So the total number of slices in the pizza is n ,where x is the number of slices each of the 44 friends received, and n is the total number of slices in the pizza, which must be a multiple of 44.
Let x be the number of slices each of the 44 friends received, then the total number of slices in the pizza is 44x. Since the pizza is evenly divided, the number of slices must be a multiple of 44.
Let y be the number of slices Harris received. Then, according to the problem, Harris ate 111 fewer slices than he received, so the number of slices he ate is y - 111.
Since the total number of slices in the pizza is 44x, we have:
y + 43x = 44x
Simplifying this equation, we get:
y = x
Therefore, Harris received the same number of slices as each of the other friends. So the number of slices he ate is:
y - 111 = x - 111
Substituting y = x, we get:
x - 111
Therefore, Harris ate x - 111 slices of pizza.
To find the value of x, we need to know the total number of slices in the pizza, which must be a multiple of 44. We can express this as:
44n = 44x
Dividing both sides by 44, we get:
n = x
So the total number of slices in the pizza is n.
Putting everything together, we get: Harris ate x - 111 slices of pizza, where x is the number of slices each of the 44 friends received, and n is the total number of slices in the pizza, which must be a multiple of 44.
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) What is the measure of ∠x in the diagram below?
Answer:
Step-by-step explanation:
X+125=180 (angles on a straight line add to 180 (supplementary) ).
so x=55°
What’s a ,40,70,70 degree triangle look like?
Answer:
see attached
Step-by-step explanation:
You want a picture of an isosceles triangle with base angles of 70°.
TriangleSuch a triangle is shown in the attachment.
__
Additional comment
You can draw one of these yourself using a protractor to measure the angles.
The side lengths have the approximate ratio of 13:19:19.
Terri pays a monthly cell phone fee of $10. She pays 5 cents for each minute that she talks. If Terri does not make any calls, what would her bill be?
Answer:
$10
Step-by-step explanation:
We Know
Terri pays a monthly cell phone fee of $10. She pays 5 cents for each minute that she talks.
Let C be the total cost, and x be the number of minutes she talks; we have the equation.
C = 0.05x + 10
If Terri does not make any calls, what would her bill be?
C = 0.05(0) + 10
C = $10
So, her bill will be $10
based on the questionnaire about gap year for matrics what is a gap year a good idea?what the main reason for taking a gap year ,what the main reason against gap year what the best year gap year options ,can zanele take or not take a gap year
Answer:
Based on the questionnaire about gap year for matrics, a gap year can be a good idea for some students. The main reason for taking a gap year is to gain life experience, travel, and explore career options before committing to a specific field of study. Additionally, a gap year can provide an opportunity for personal growth and development, as well as the chance to save money and gain work experience.
On the other hand, the main reason against taking a gap year is the potential delay in academic progress and the possibility of losing momentum and motivation towards pursuing further education. Additionally, some students may not have the financial means to afford a gap year and may not have access to job opportunities or travel experiences.
The best gap year options may vary depending on individual preferences and interests, but some popular options include volunteer work, internships, language immersion programs, and cultural exchanges.
As for Zanele, the decision of whether or not to take a gap year should be based on her personal goals and circumstances. If she feels that she needs time to explore her interests and gain experience before continuing with her studies, a gap year may be a good option for her. However, if she is motivated to pursue her academic goals and does not want to delay her progress, then she may choose not to take a gap year.
Step-by-step explanation:
dayna writes the integers 1,2,3,4,5,6,7,8,9,10,11,12 on a chalkboard, then she erases the integers from 1 through 6, as well as their multiplicative inverse $\mod{13}$. what is the only integer dayna does not erase?
Dayna erases the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11, and leaves only the integer 12 on the chalkboard, by the concept of multiplicative inverse and by using the extended Euclidean algorithm.
The integers from 1 through 6, as well as their multiplicative inverse [tex]$\mod{13}$[/tex], have been erased from the integers 1 through 12. We need to find the only integer that Dayna did not erase. We can find the multiplicative inverse of an integer a modulo 13 by using the extended Euclidean algorithm.
The integers from 1 through 6 are 1, 2, 3, 4, 5, and 6. We need to find their multiplicative inverses modulo 13.
The multiplicative inverse of 1 modulo 13 is 1, since
[tex]$1 \times 1 \equiv 1 \pmod{13}$[/tex].
The multiplicative inverse of 2 modulo 13 is 7, since
[tex]$2 \times 7 \equiv 1 \pmod{13}$[/tex].
The multiplicative inverse of 3 modulo 13 is 9, since
[tex]$3 \times 9 \equiv 1 \pmod{13}$[/tex].
The multiplicative inverse of 4 modulo 13 is 10, since
[tex]$4 \times 10 \equiv 1 \pmod{13}$[/tex].
The multiplicative inverse of 5 modulo 13 is 8, since
[tex]$5 \times 8 \equiv 1 \pmod{13}$[/tex].
The multiplicative inverse of 6 modulo 13 is 11, since
[tex]$6 \times 11 \equiv 1 \pmod{13}$[/tex].
Therefore, the only integer that Dayna does not erase is 12.
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find the area of a quadrilateral ABCD in each case.
The area of the quadrilateral ABCD for this case is of 4 square units.
How to obtain the area of the quadrilateral ABCD?The quadrilateral ABCD in the context of this problem represents a diamond, hence it's area is given by half the product of the diagonal lengths of the diamond.
The lengths for each diagonal of the diamond are given as follows:
Diagonal AC = 2 - 0 = 2.Diagonal BD = 4 - 0 = 4.The product of the diagonal lengths is given as follows:
AC x BD = 2 x 4 = 8 square units.
Hence half the product of these diagonal lengths, representing the area of the quadrilateral, is given as follows:
0.5 x 8 square units = 4 square units.
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A man saves Rs.7,500 in first year. In each year after the first, he saves Rs. 2,000 more than he does in the preceding year. When will he be saved the total amount Rs.1,65,000? Find it.
Answer:
aeqtq34t
Step-by-step explanation:
q34t35t134
pls answert this within 1 hour or else i will be DOOMED
In the fractions prompts given, the correct output are:
(1 ÷2) ÷ 4 = 1/8(1 ÷5) ÷ 2 = 1/10(1 ÷3) ÷ 5 = 1/15(1 ÷4) ÷ 4 = 1/16The solution to the problem for (1/2) ÷ 3 is given below.What is a fraction?A fraction represents a part of a whole. It consists of a numerator and a denominator, with the numerator indicating the number of parts and the denominator indicating the total number of parts.
The calculations are given as follows;
1 )
= (1/2) x (1/4) [dividing by a number is the same as multiplying by its reciprocal]
= 1/8
2) (1/5) ÷ 2
= (1/5) x (1/2)
= 1/10
3)
(1/3) ÷ 5
= (1/3) x (1/5)
= 1/15
4) (1/4) ÷ 4
= (1/4) x (1/4)
= 1/16
5) One day, Amy baked a cake and wanted to divide it equally among 3 of her friends. She realized she only had half a cake left, so she decided to divide it into equal parts. Each friend received 1/6 of a cake. To check her calculation, she multiplied 1/6 by 3 and got 1/2. Thus, (1/2) ÷ 3 = 1/6, since dividing by 3 is the same as multiplying by 1/3.
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Automobiles arrive at a vehicle equipment inspection station according to a Poisson process with rate α = 10 per hour. Suppose that with probability .5 an arriving vehicle will have no equipment violations. a. What is the probability that exactly ten arrive during the hour and all ten have no violations?
b. For any fixed y ≥ 10, what is the probability that y arrive during the hour, of which ten have no violations?
c. What is the probability that ten "no-violation" cars arrive during the next hour? [Hint: Sum the probabilities in part (b) from y =10 to [infinity].]
a. The probability that exactly ten arrive during the hour and all ten have no violations is given by the Poisson distribution, P(X=10) = (e-α*(α10)/(10!) = 0.024
b. The probability that y arrive during the hour, of which ten have no violations is given by the Binomial distribution, P(Y=y) = (y!/(10!*(y-10)!))*(0.510)*(0.5y-10)
c. The probability that ten "no-violation" cars arrive during the next hour is given by summing the probabilities in part (b) from y=10 to [infinity]. This is given by P(Y≥10) = Σy=10 to ∞P(Y=y) = 1 - Σy=0 to 9P(Y=y).
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there are black, blue, and white marbles in a bag. the probability of choosing a black marble is 0.36 . the probability of choosing a black and then a white marble is 0.27 . to the nearest hundredth, what is the probability of the second marble being white if the first marble chosen is black?
There are black, blue, and white marbles in a bag. The probability of choosing a black marble is 0.75.
Let's assume that there are 100 marbles in the bag. If the probability of choosing a black marble is 0.36, there are 36 black marbles in the bag. Therefore, there are 64 marbles of other colors (white and blue) in the bag.
Using the same method, we can say that the probability of choosing a white marble after drawing a black one is [tex]\frac{0.27}{0.36}= 0.75[/tex] (rounded to the nearest hundredth). It means that there are 75 white marbles for every 100 black marbles in the bag.
Therefore, the probability of the second marble being white if the first marble chosen is black is
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suppose the average gmat score of one university is 600 and such scores has a standard deviation of 100. what percentage of students has gmat scores between 400 and 800?
In conclusion, 95.4% of students have GMAT scores between 400 and 800.
Calculate z score need to find the proportion of scores that fall within the range of 400 to 800.
[tex]z=\frac{x- mean}{standard deviation}[/tex]
This formula tells us how many standard deviations away from the mean a given score is.
Given:
Mean= 600
Standard deviation = 100.
For the 400 scores:-
[tex]z=\frac{400-600}{100} \\z= -2[/tex]
For the 800 scores:-
[tex]z=\frac{800-600}{100} \\z=2[/tex]
Now we will use the standard normal distribution table to find the percentage of values between -2 and 2.
According to the standard normal distribution table, the percentage of values between -2 and 2 is approximately 95.45%.
Therefore, approximately 95.45% of students have GMAT scores between 400 and 800.
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when performing a hypothesis test based on a 95% confidence level, what are the chances of making a type ii error?
When performing a hypothesis test based on a 95% confidence level, the chances of making a type II error are 5%.
The process of hypothesis testing is used to determine whether or not a given statistical hypothesis is valid. The objective of this method is to determine whether the null hypothesis can be accepted or rejected based on the sample data obtained.
Hypothesis testing can be used to evaluate two hypotheses. The null hypothesis is the one that must be accepted or rejected, while the alternative hypothesis is the one that must be supported. In other words, hypothesis testing is a way of determining whether the null hypothesis is reasonable or not.
The Type II error is defined as the error that occurs when the null hypothesis is not rejected even though it is incorrect. In hypothesis testing, this type of error is referred to as a beta error or a false-negative error. The chances of making a Type II error depend on several factors, including the sample size, the level of significance, and the power of the test. When the level of significance is lowered to 0.05, the chances of making a Type II error are 5%.
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Please help, as it is greatly appreciated
Solve 2log 12 (-8x)=6
The solution to the logarithmic equation [tex]2log12(-8x) = 6[/tex] is [tex]x = -9/32[/tex] .
What are logarithmic properties ?
Logarithmic properties are the rules that govern the behavior of logarithmic functions. These properties are important in simplifying logarithmic expressions and solving logarithmic equations. Some of the commonly used logarithmic properties include:
Product property: [tex]logb(xy) = logb(x) + logb(y)[/tex]
This property allows us to simplify the logarithm of a product of two numbers into the sum of logarithms of the individual numbers.
Quotient property: [tex]logb(x/y) = logb(x) - logb(y)[/tex]
This property allows us to simplify the logarithm of a quotient of two numbers into the difference of logarithms of the individual numbers.
Power property:[tex]logb(x^y) = ylogb(x)[/tex]
This property allows us to simplify the logarithm of a power of a number by bringing the exponent outside of the logarithm and multiplying it with the logarithm of the base.
Change of base formula: [tex]logb(x) = logc(x) / logc(b)[/tex]
This property allows us to change the base of a logarithm by dividing the logarithm of the number by the logarithm of the base in a different base.
Solving the given logarithmic equation :
The equation can be solved by using logarithmic properties and basic algebraic manipulation.
We can begin by using the property that states [tex]loga(b^n) = nloga(b)[/tex] for any base a and any positive real number b. Applying this property, we can rewrite the left side of the equation as:
[tex]log12((-8x)^2) = log12(64x^2)[/tex]
Next, we can use the property that states [tex]loga(b) = c[/tex] is equivalent to [tex]a^c = b[/tex]. Applying this property, we can rewrite the equation as:
[tex]12^{2log12(64x^2)} = 12^6[/tex]
Simplifying the left side, we get:
[tex]64x^2 = 12^6 / 12^2[/tex]
[tex]64x^2 = 144[/tex]
Dividing both sides by 64, we get:
[tex]x^2 = 144/64[/tex]
[tex]x^2 = 9/4[/tex]
Taking the square root of both sides, we get:
[tex]x=\pm 3/2[/tex]
However, we need to check the solutions for extraneous roots since the original equation has a logarithm with a negative argument. We can see that the solution x = 3/2 is extraneous since it results in a negative argument for the logarithm. Therefore, the only valid solution is x = -9/32.
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The population of a city was 20000. The next year it increased by 2% find the new population
The city had 20,000 residents. The next year, it went up by 2%. The new population of the city after a 2% increase is 20400.
To find the new population of the city after a 2% increase from 20000, we need to use the following formula:
New population = Old population + (Percentage increase x Old population)
Substituting the given values into the formula, we get:
New population = 20000 + (2/100 x 20000)
New population = 20000 + 400
New population = 20400
It is important to note that this calculation assumes that the increase in population is the only factor affecting the total population. In reality, there may be other factors that affect the population, such as migration, birth rates, and mortality rates.
Additionally, this calculation only gives the estimated population based on the percentage increase, and the actual population may differ due to various factors.
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Factor completely.
A) p^2-x^2+6x-9
B)b^2-c^2-10(b-c)
Thank you :DD
An expression is a combination of numbers, variables, and operations that can be evaluated to produce a value. Expressions can be simple or complex and can involve arithmetic, logical, or comparison operations.
What is the expression?A) To factor [tex]p^2-x^2+6x-9[/tex] first notice that the expression inside the parentheses is the difference of two squares, so we can use the formula:
[tex]p^2 - x^2 = (p + x)(p - x)[/tex]
Therefore, we can write the expression as:
[tex](p + x + 3)(p - x + 3)[/tex]
To check this, you can use FOIL to expand the expression:
[tex](p + x + 3)(p - x + 3) = p^2 - px + 3p + px - x^2 + 3x + 3p - 3x + 9 = p^2 - x^2 + 6x + 9[/tex]
B) To factor b^2-c^2-10(b-c), notice that the first two terms form a difference of squares, so we can use the formula again:
[tex]b^2 - c^2 = (b + c)(b - c)[/tex]
The expression can then be written as:
[tex](b + c)(b - c) - 10(b - c) = (b - c)(b + c - 10)[/tex]
To check this, we can use FOIL again:
[tex](b - c)(b + c - 10) = b^2 - bc - 10b - cb + 10c = b^2 - c^2 - 10(b - c)[/tex]
Therefore, the factored form of the expression is [tex](b - c)(b + c - 10)[/tex].
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5 x _ = -35
Topic: Multiplying and Dividing Integers
Given:
5× ______ = - 35
• -35/5
• -7
Answer:5 x -7 = -35
Answer:
The answer is 7
Step-by-step explanation:
Divide each term in 5x=-35 by 5 and simplify.x=−7
The perimeter of a square is 8 root 2x units. The area of a square is 56 units square. Find the value of x
According to the perimeter, the value of x is 7/2.
The problem tells us that the perimeter of a square is 8√2x units. We can use this information to set up an equation. Since all four sides of a square are equal, we can let s represent the length of one side of the square. Then, we know that:
Perimeter of square = 4s = 8√2x
We can simplify this equation by dividing both sides by 4:
s = 2√2x
Now, we can use this expression for s to find the area of the square. The area of a square is simply the length of one side squared. So, we have:
Area of square = s² = (2√2x)² = 8x
The problem tells us that the area of the square is 56 units square, so we can set up another equation:
8x = 56
Solving for x, we get:
x = 7/2
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What is the slope in the equation y=2× + 3?
Answer:
Use the slope-intercept form to find the slope and y-intercept.
Slope: 2y-intercept: (0,3)
Step-by-step explanation:
Answer:
(0,3).
Step-by-step explanation:
for example, y=2x+3 tells us that the slope of the line is 2 and the y-intercept is at (0,3).
The following information presents financial results for the two models from last year:
Private Label Branded Total
Sales revenue $ 768,000 $ 480,000 $ 1,248,000
Direct material 216,000 156,000 372,000
Direct labor 144,000 96,000 240,000
Manufacturing overhead
Department A-101 $ 201,600
Department A-102 230,400
Total overhead $ 432,000
The product costing system at EA allocates manufacturing overhead on the basis of direct labor costs. Required:
Compute the profit or loss for each product using plantwide allocation. Compute the profit or loss for each product using department allocation
a) The profit or loss for the private label product is $223,714 and the profit or loss for the branded product is $125,143 using plantwide allocation.
b) The profit or loss for the private label product is $159,114 and the profit or loss for the branded product is $132,171 using department allocation.
a) Using plantwide allocation, the total manufacturing overhead of $432,000 is allocated based on the total direct labor cost of $336,000 (sum of direct labor costs for both products). The overhead rate is calculated as $432,000 / $336,000 = $1.2857 per dollar of direct labor cost. The overhead cost for each product is then calculated by multiplying the overhead rate by the direct labor cost for that product.
Private Label Branded Total
Sales revenue $768,000 $480,000 $1,248,000
Direct material 216,000 156,000 372,000
Direct labor 144,000 96,000 240,000
Manufacturing 184,286 122,857 307,143
Total cost 544,286 354,857 899,143
Profit (loss) $223,714 $125,143 $348,857
The profit or loss for the private label product is $223,714 and the profit or loss for the branded product is $125,143 using plantwide allocation.
b) Using department allocation, the manufacturing overhead of $432,000 is allocated based on the direct labor costs for each department. The overhead rate for department A-101 is $201,600 / $144,000 = $1.4014 per dollar of direct labor cost, and the overhead rate for department A-102 is $230,400 / $96,000 = $2.4000 per dollar of direct labor cost. The overhead cost for each product is then calculated by multiplying the overhead rate by the direct labor cost for that product in each department.
Private Label Branded Total
Sales revenue $768,000 $480,000 $1,248,000
Direct material 216,000 156,000 372,000
Direct labor 144,000 96,000 240,000
Manufacturing overhead
Department A-101 $201,600 $64,400 $266,000
Department A-102 46,286 31,429 77,714
Total overhead $247,886 $95,829 $343,715
Total cost 608,886 347,829 956,715
Profit (loss) $159,114 $132,171 $291,285
The profit or loss for the private label product is $159,114 and the profit or loss for the branded product is $132,171 using department allocation.
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It says to determine whether the following symbolized arguments are valid or invalid by constructing the truth table for each?
The valid symbolized arguments is HS-valid. (option e).
Now let's focus on the symbolized arguments presented in this question. To determine their validity, we need to identify the form of each argument. In some cases, we may need to rewrite the argument using double negation or commutativity before assigning a name to its form.
The argument form known as Hypothetical Syllogism (HS) is represented as follows:
P⊃Q
Q⊃R
P⊃R
The given argument can be rewritten using double negation as follows:
H⊃~M
M⊃H
H⊃~H
Then, we can see that the argument follows the form of HS, where if H implies not M, and not M implies not H, then we can conclude that H implies not H. This conclusion is always true because it is a contradiction. Therefore, the argument is valid.
Hence the correct option is (e).
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Complete Question:
Determine whether the following symbolized arguments are valid of invalid by identifying the form of each. In some cases the argument must be rewritten using double negation or commutativity before it has a named for. Those arguments without a specific name are valid.
H⊃~M
M
______
~H
a. DA-Invalid.
b. MP-valid.
c. AC-invalid.
d. MT-valid.
e. HS-valid.
Given the functions f(x) = 1/x-1 + 1 and g(x)=1/x+2 +4 describe the transformation of the graph of function f onto the graph of function g
Transformation of the graph from parent function f(x) to g(x) is:
there is shift of 3 units towards the right to reach from -1 to 2 along x axis.there is a shift of 3 units upward to reach from 1 to 4 on y axis.Explain about the transformation of coordinates?That whenever a figure is relocated from one place to another without affecting its dimension, shape, or orientation, a transition known as translation takes place. If we are aware of the direction and magnitude of the figure's movement, we may draw the translation in the coordinate plane.
The x - axis and y values are reversed. 180° rotation about the origin Every x and y value reverses from what it was. Each current value becomes the counterpart of what it was after a 270° rotation of the origin. The two x and y values are reversed.
The given function:
f(x) = 1/x-1 + 1 and g(x)=1/x+2 +4
g(x) is obtained function after transformation:
transformation:
there is shift of 3 units towards the right to reach from -1 to 2 along x axis.there is a shift of 3 units upward to reach from 1 to 4 on y axis.Know more about the transformation of coordinates
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Looking for an answer to this: Every non zero number can be used twice, between two same non zero numbers is as many zeros as how large is the non zero number example is 40001041 and 300103100. How many 7 digit numbers are there that have two 1s and two 2s and not defined number 0s?
Thank you for any responses.
Answer:
50000
Step-by-step explanation:78473294724829384739284732984739824
Please Help ASAP
Help would be greatly appreciated
Answer: A
Step-by-step explanation: i thing its wrigth
4) Ella drives 60 miles per hour. How far will she drive in 2% hours?
Answer: 1.2 miles
Step-by-step explanation:
1 hour = 60 min
60 x 0.02 = 1.2 1 minute and 20 seconds has elapsed
60 miles/ every 60 minutes or 1 mile a minute
1 x 1.2 = 1.2
she has traveled 1.2 miles
Answer: The answer is 120 mph (miles per hour)
Step-by-step explanation:
The one thing you need to do is to figure out how many mph did Ella drive for 2 hours.
So, you need to do 60 x 2, and you will get the answer 120.
And there's your answer!
Let a function f be analytic everywhere in a domain D. Prove that if f(z) is real-valued for all z in D, then f(z) must be constant throughout D.
Let a function f be analytic everywhere in a domain D. Prove that if f(z) is real-valued for all z in D, then f(z) must be constant throughout D. Suppose a function f(z) is analytic and real-valued throughout a domain D. Assume that there are two different points in D, say w and z, so that f(z) ≠ f(w). Therefore, we have a closed path consisting of the line segment from z to w and the line segment from w to z. Now let γ be any closed path in D that encloses the path from z to w. Since f(z) ≠ f(w), f(z) - f(w) ≠ 0, so f(z) - f(w) / z - w ≠ 0. This makes the function 1 / (f(z) - f(w)) analytic throughout D. Thus, by Cauchy's theorem, $\oint_{\gamma } \frac{1}{f(z)-f(w)}dz = 0$.where gamma is a function.
frac stands for fraction. This leads to $\int_{w}^{z} \{1}/{f(z)-f(w)}dz + \int_{z}^{w} \{1}/{f(z)-f(w)}dz = 0$. But by substituting f(w) = f(z) and reversing the direction of integration in the second integral, we get, $\int_{w}^{z} \frac{1}{f(z)-f(w)}dz - \int_{w}^{z} \frac{1}{f(w)-f(z)}dz = 0$ . This results in the integral$\int_{w}^{z} \frac{f'(w)}{f(z)-f(w)}dz - \int_{w}^{z} \frac{f'(z)}{f(w)-f(z)}dz = 0$. Now it is time to simplify and evaluate each of the integrals. The first integral has value $\ln|f(z)-f(w)|$ and the second integral has value $\ln|f(z)-f(w)|$. Therefore, $f'(z)/f(z)-f(w) = f'(w)/(f(w)-f(z))$. This equation, however, is not possible unless $f(z) = f(w)$. Hence, we conclude that the function f(z) is constant throughout D.
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Given the triangle, find the length of z. Give your answer in simpliest radical form.
Frankie's dad made scrambled eggs for the family's breakfast. He started with a full carton of 12 eggs he used 8 of the eggs. What fraction of the carton of eggs did he use write at least two equivalent fractions
Frankie's dad used 2/3 of the carton of eggs for their breakfast. Two equivalent fractions are 16/24 and 24/36.
Frankie's dad used 8 out of 12 eggs from a full carton. To express this as a fraction, we can write it as 8/12. However, this fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which in this case is 4. Thus, we get:
8/12 = (8 ÷ 4)/(12 ÷ 4) = 2/3
Alternatively, we can also express this fraction in different forms. One way to do this is by multiplying both the numerator and denominator by the same number. For example, if we multiply both by 2, we get:
8/12 = (8 × 2)/(12 × 2) = 16/24
Similarly, we can multiply by 3 to get:
8/12 = (8 × 3)/(12 × 3) = 24/36
Both of these fractions are equivalent to 2/3, and we can find infinitely many other equivalent fractions by multiplying both numerator and denominator by different numbers.
In summary, when Frankie's dad made scrambled eggs using 8 eggs from a full carton of 12 eggs, he used 2/3 of the carton. This fraction can be expressed in different forms that are equivalent to 2/3 by dividing both numerator and denominator by their greatest common factor or by multiplying both numerator and denominator by the same number.
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