Therefore , the solution of the given problem of function comes out to be g(x) (-1)ⁿ (n+2)!/n! (9ⁿ⁻²) xⁿ.
What is function?On the midterm exam, there will be a variety of questions on each topic, including questions about both made-up and actual locations as well as numerical variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.
Here,
With x = 0, we can use the formula for the geometric series to represent the function g(x) = 1/(9+x)3 as a power series:
=> 1 / (1 - t) =∑ (n = 0 to n) t
where |t| 1 and t is some integer.
In this instance, we have:
=> g(x) = 1/(9+x)³ = [tex](1/9)^{3}[/tex] [tex](1+(-x/9))^{-3}[/tex]
So, using the above calculation and the value of t = -x/9, we can write:
=> G(x) = (1/9)3 n(x/9) (n=0 to infinite)
If we condense this phrase, we get:
=> (n=0 to infinite) = g(x) [tex](-1)^{n}[/tex] (n+2)!/n! ([tex]9^{n-2}[/tex]) [tex]x^{n}[/tex]
Thus, the power series expansion for g(x) with the origin at x = 0 is as follows:
=> (n=0 to infinite) = g(x) (-1)ⁿ (n+2)!/n! (9ⁿ⁻²) xⁿ
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Use compensation to add or subtract
499+599+699
Answer: 1,797
Step-by-step explanation:
Step 1: Round Numbers Up:
500+600+700 = 1,800
Step 2: Subtract 3 to get answer (-1 for every number rounded up)
1,800-3 = 1,797
Addition using compensation method : 1800
Subtraction using compensation method : 1797
Given,
499+599+699
Here,
Compensation : Round off to the nearest number so that the calculation of addition and subtraction becomes more easy .
So,
Firstly addition,
499 + 599 + 699
Add 3 adding one to each, we get,
500 + 600 + 700 = 1800
Now,
Subtracting 3, 1800 - 3 = 1797
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(36^5-6^9)(38^9-38^8) is divisible by 30 and 37 but the answer is _ x 30 x 37
it is true that the expression (36⁴−6⁹)(38⁹−38⁸) is divisible by 30 and 37
Carl Friedrich Gauss introduced the fundamental principle of number theory in 1801, which states that any integer higher than one can be expressed as the product of prime numbers only in one way. Number theory is also referred to as arithmetic. Addition, subtraction, multiplication, and division are the four foundational operations in mathematics. Below, a quick discussion of all these operations is provided.
The expression is given as:
(36⁴−6⁹)(38⁹−38⁸)
Express 36 as 6²
(36⁴ - 6⁹) = (6²)⁴ - 6⁹
= 6⁸ - 6⁹
= 6⁷(6 - 6²)
= 6⁷(6 - 36)
= 6⁷(-30)
=(38⁹ - 38⁸)
= 38⁸(38 - 1)
= 38⁸(37)
=(36⁴−6⁹)(38⁹−38⁸)
=6⁷(-30) × 38⁸(37)
=(30)(37)(-6⁷)(38⁸)
Clearly, 30 and 37 are factors, so divisible by them.
The complete question is-
Prove that the value of the expression: b (36^5−6^9)(38^9−38^8) is divisible by 30 and 37.
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What is the measure!, in degrees in degrees, of angle x?
Answer:23 degrees
Step-by-step explanation:
Ok! I'm a high school student so this is what I can see.
Angles A and the 130 are supper- angles meaning they add up to 180.
So that means A is 50.
Next I noticed by experience that A and B are vertical angles. So that means B is 50 as well.
And since this all have to equal to 360 angles. The equation is
360= 50+130+50+107+x or X= 360- (50+130+50+107)
And that is x=23
Happy Soving
PLSSS Help
Identify the two forms of the simplified expression x^5/x^10
And if you could please give a brief description. Thank you
Both formulations convey the same meaning and represent the same equation mathematical operation: x raised to the power of 5 divided by x raised to the power of 10.
What is the expression?In this format, the expression is shown using exponent notation. The denominator (bottom) of the fraction is x raised to the power of 10, while the numerator (top) of the fraction is x raised to the power of 5. The phrase can therefore be written as x⁵/x¹⁰.
In this method, the division symbol serves to represent the expression. The denominator (bottom) of the fraction is x raised to the power of 10, while the numerator (top) of the fraction is x raised to the power of 5. The expression is therefore (x⁵)/. (x¹⁰).
Therefore, the same mathematical operation is represented by both formulations, which both express the same meaning: x to the power of 5 divided by x to the power of 10.
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Ten years into your 15-year $600,000 mortgage begun in October 2015, you inherit your rich uncle's estate and decide to pay off the outstanding principal on your mortgage. What is that amount? (Do not round the payment amount to the nearest cent. Round the final outstanding principal to the nearest cent.)
You need to pay mortgages of $6370 monthly.
What is mortgage?A mοrtgage is an agreement between yοu and a lender that gives the lender the right tο take yοur prοperty if yοu fail tο repay the mοney yοu've bοrrοwed plus interest. Mοrtgage lοans are used tο buy a hοme οr tο bοrrοw mοney against the value οf a hοme yοu already οwn
In this case,
P = $600000
r = 13.10 % = 0.131 [Credit card rate fοr Octοber 2015]
t = 15years
n = 12 [Cοmpοunded mοnthly]
Monthly payment = [tex]$ \rm \frac{r \times P}{n} \times \left[1 - (1 +\frac{r}{n}) - nt \right][/tex]
= [tex]$ \rm \frac{0.131 \times 600000}{12} \times \left[1 - (1 +\frac{0.131}{12}) - 12 \times 15 \right][/tex]
= 6550 - 180
= 6550 - 180
= 6370
Thus, You need to pay mortgages of $6370 monthly.
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solve with explanation
2(12)-(-4)
Answer:
28
Step-by-step explanation:
2×12-(-4) - and - = +
24+4 + and + = +
28 + and - = -
- and + = -
A bank has fixed the rate of interest 10% p.a. semi-annually compound interest in account A and 12% per annum annually compound interest in account B. If you are going to deposit Rs. 30,000 for 2 years in the same bank in which account will you deposit and why? Give your reason with calculation.
As the calculations show, account B will yield a bigger total sum after two interest years than account A. As a result, we should deposit our funds in account B.
what is interest ?In mathematics, interest is the amount of money earned or payable on an original investment or loan. You can use either simple or compound interest. Simple interest is calculated as a percentage of the initial amount, whereas compound interest is calculated on the principal amount plus any previously earned interest. If you invest $100 at a 5% annual simple interest rate, you will get $5 in interest every year for three years, for a total of $15.
Account A: Semi-annual interest rate = 10% divided by two equals 5%.
2 years multiplied by 2 equals 4 compounding periods.
Total interest earned Equals Rs. 30,000 multiplied by (1 + 5%/2).
4 - Rs. 30,000 = Rs. 6,380.
13 After two years, the total sum is Rs. 30,000 plus Rs. 6,380.
13 = Rs. 36,380.
13
About Account B:
12% annual interest rate
The number of compounding periods is equal to two.
Total interest earned = Rs. 30,000 multiplied by (1 + 12%)
2 - Rs. 30,000 = Rs. 7,440
After two years, the total payment is Rs. 30,000 + Rs. 7,440 = Rs. 37,440.
As the calculations show, account B will yield a bigger total sum after two years than account A. As a result, we should deposit our funds in account B.
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can somebody please help me with this asap!!
The relative frequency of music downloads that were regional, either tropic or urban, were not urban are 42%,16% and 89% respectively.
What is relative frequency?Relative frequency is a statistical concept that refers to the proportion or percentage of times a particular event or category occurs in relation to the total number of events or categories. It is calculated by dividing the frequency of the event or category by the total number of events or categories
Equation:(a) The relative frequency of music downloads that were regional is:
230/550 = 0.42 or 42%
(b) The relative frequency of music downloads that were either tropical or urban is:
(80+10)/550 = 0.16 or 16%
(c) The relative frequency of music downloads that were not urban is:
(230+170+80)/550 = 0.89 or 89%
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Which right does the Fair Debt Collection Practices Act (FDCPA) give
borrowers?
OA. The right to negotiate debt
OB. The right to declare bankruptcy
C. The right to verify the amount owed
OD. The right not to receive phone calls
Answer: prohibits debt collection companies from using abusive, unfair or deceptive practices to collect debts from you.
Step-by-step explanation:
prohibits debt collection companies from using abusive, unfair or deceptive practices to collect debts from you.
The right to verify the amount owed is the right the Fair Debt Collection Practices Act (FDCPA) give borrowers The correct option is C.
What is FDCPA?The Fair Debt Collection Practices Act (FDCPA) is a federal law that governs the conduct of third-party debt collectors who attempt to collect debts on creditors' behalf.
Borrowers who are being pursued by debt collectors have several rights under the FDCPA.
One of the rights granted to borrowers by the FDCPA is the right to verify the amount owed.
This means that borrowers have the right to ask the debt collector for written confirmation of the debt, including the amount owed and the creditor's name.
The debt collector is required to provide this information within a reasonable time after receiving the request.
Thus, the correct option is C.
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If o=12, find the sample size to estimate the mean with an error of +4 and 95 percent confidence (rounded to the next higher integer).
Multiple Choice
75
35
58
113
URGENT
We need to round up to the next higher integer, the sample size required to estimate the mean with an error of +4 and 95 Percent confidence is 170.
To find the sample size to estimate the mean with an error of +4 and 95 percent confidence, we need to use the formula:
n = [(z*sigma)/E]^2
Where:
n = sample size
z = z-score for 95% confidence level (which is 1.96)
sigma = standard deviation (unknown in this case)
E = maximum allowable error (which is +4 in this case)
We are given that o=12, which is the population standard deviation. Since we do not have any information about the sample standard deviation, we can use the population standard deviation as an estimate. Therefore, we can substitute o=12 in the above formula to get:
n = [(1.96*12)/4]^2
n = 169.64
Since we need to round up to the next higher integer, the sample size required to estimate the mean with an error of +4 and 95 percent confidence is 170.
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What is the additive inverse of the polynomial?
The additive inverse of the polynomial -7y² + x²y -3xy - 7x² include the following: A. 7y² - x²y + 3xy + 7x².
What is an additive inverse?In Mathematics and Geometry, an additive inverse can be defined as a number (n) which when added to another number (a) makes it equal to zero (0). This ultimately implies that, an additive inverse is the opposite of another number (a).
Mathematically, an additive inverse can be represented by the following equations:
a + n = 0
a = -n
-7y² + x²y - 3xy - 7x² = -(-7y² + x²y - 3xy - 7x²)
-7y² + x²y - 3xy - 7x² = 7y² - x²y + 3xy + 7x²)
In this context, we can reasonably infer and logically deduce that an additive inverse of -7y² + x²y -3xy - 7x² is 7y² - x²y + 3xy + 7x².
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Mark was working on the long jump
competition, and he was able to
jump 9 3
4 feet. Chris jumped 7
8
as far as Mark. Write and solve the
equation that will help you figure
out how far Chris jumped.
Explain the steps you took to solve
Chris has jumped 85/8 feet.
What is the distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or an estimate based on other factors in common usage.
Here, we have
Given: Mark was working on the long jump competition, and he was able to jump 9 3/4 feet. Chris jumped 7/8 as far as Mark.
The distance jumped by Mark = 9 3/4 feet
The distance jumped by Chris = 9 3/4 + 7/8
The total distance covered by Chris would be:
= 9 3/4 + 7/8
= 7/8 + 39/4
= 85/8
Hence, Chris has jumped 85/8 feet.
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YZ is tangent to the circle at Z. Find the measure of minor arc WX
.
Step-by-step explanation:
the angle at Y = 1/2 × (arc angle WZ - arc angle ZX).
so,
42 = (arc angle WZ - 51)/2
84 = arc angle WZ - 51
135° = arc angle WZ
the arc angle WX is the remainder of the whole circle to the sum of the arc angles WZ and ZX :
arc angle WX = 360 - 135 - 51 = 174°
A bookstore manager will randomly select 1 of 5 newly
arrived fiction books and 1 of 4 newly arrived nonfiction
books for a window display. What is the probability that
the manager will select the shortest of the newly arrived
fiction books and the longest of the newly arrived
nonfiction books?
A. 5%
B. 10%
C. 20%
D. 45%
Answer:
Step-by-step explanation:
number of books are 5 so you will have to do 5 by hundred which will lead to twenty percent
The likelihood that the manager will choose the longest just-received nonfiction book and the shortest recently arrived fiction book is 1/20, or 5%.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
The probability of selecting the shortest fiction book is 1/5 and the probability of selecting the longest nonfiction book is 1/4. Since these events are independent, we can multiply their probabilities to find the probability of both events happening:
P(shortest fiction book and longest nonfiction book) = P(shortest fiction book) x P(longest nonfiction book) = 1/5 x 1/4 = 1/20
So the probability that the manager will select the shortest of the newly arrived fiction books and the longest of the newly arrived nonfiction books is 1/20, which is equivalent to 5%.
Therefore, the answer is option A.
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Bus A stops at a certain bus stop every 25 minutes. Bus B stops at the same stop every 40 minutes. If both buses are at the bus stop at 9:30 a.m., when is the next time they will be there together again?
A. 12:20 p.m.
B. 12:50 p.m.
C. 1:10 p.m.
D. 1:30 p.m.
SHOW YOUR WORK!!
Answer:
B
Step-by-step explanation:
Bus A
1. 9:55
2. 10:20
3.10:45
4.11:10
5.11:35
6.12:00
7.12:25
8.12:50
Bus B
1. 10:10
2.10:50
311:30
4. 12:10
5. 12:50
Evan sold half his story books and then bought 17 more. He now has 32 books. With how many did he begin?
Evan sold half his story books and then bought 17 more. Evan had thirty bucks.
What is equivalent?
A mathematical statement is known as an equation, and the equal sign ('=') connects two expressions. At least one unknown variable must be determinable. For instance, an equation is 3x - 8 = 16. We achieve x = 8.
We will sοlve the prοblem by fοrming a οne variable equatiοn.
Let's say Evan started out with a lot of problems. Evan gave up half of his regular wares. He split two separate cakes.
He now has (x-x/2)=x/2 straight numbers.
He then gained 17 pounds.
Sο subsequent to purchasing 17 bοοks he has nοw (x/2+17) story bοοks
Given number οf stοry bοοks he has right nοw is 32.
By equating the two, we can construct a equation for one variable.
(x/2+17) = 32 Solving for x will be the equation:
(x/2+17) = 32; x/2 = 32- 17; x/2 = 15; x = 152; x = 30.
According to the initial equation, Evan had 30 books.
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A collection of 50 buttons is in a jar. The probability of reaching into the jar and retrieving a black button is 0.64. What is the probability that you will reach in the jar and retrieve a button that is not black?
Answer: The probability of reaching into the jar and retrieving a black button is 0.64. Therefore, the probability of reaching into the jar and retrieving a button that is not black is the complement of this probability, which is 1 - 0.64 = 0.36.
In other words, the probability of not getting a black button is the same as the probability of getting a non-black button, which includes all the other colored buttons in the jar. Since there are no other details given in the problem regarding the number of non-black buttons or the probability of retrieving each non-black button, we assume that they are all equally likely to be retrieved and simply calculate the probability of not getting a black button as the complement of the probability of getting a black button.
Therefore, the probability of reaching in the jar and retrieving a button that is not black is 0.36 or 36%.
Step-by-step explanation:
HElp plsssssssssssssss
A ramp is being built to ga up a vertical increase of 10 feet. Codes require the angle the
ramp makes with the ground to be no more than 15
. At least how long will the actual
ramp need to be to pass code?
The length of the ramp we need to build should be at least 38.61 feet to pass code.
In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles.
We can use trigonometry to solve the problem. Let x be the length of the ramp we need to build. Then, the angle the ramp makes with the ground is given by:
sin(theta) = opposite/hypotenuse
where theta is the angle the ramp makes with the ground, opposite is the vertical increase of 10 feet, and hypotenuse is the length of the ramp x.
Solving for x, we get:
x = opposite/sin(theta) = 10/sin(15)
Using a calculator, we can evaluate sin(15) to be approximately 0.2588. Then, we can divide 10 by 0.2588 to get:
x ≈ 38.61
Therefore, the length of the ramp we need to build should be at least 38.61 feet to pass code.
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Hellpppppp due soon
Answer:21.33 is the right answer for x
WILL GIVE BRAINLIEST
Defense mechanisms
please just check my work, see if u can spot out any errors… thanks :)
Answer:
the is no error in your work
There are 37 erasers in the receptacle. Each day the students loose 3 erasers. How many erasers are in the receptacle for each of the first 6 days
There will be 34,31,28,25,22,19 erasers after Day 1,2,3,4,5,6respectively.
Define daysDays are units of time that are used to measure the duration of a complete rotation of the Earth on its axis. One day is defined as the time it takes for the Earth to complete one full rotation on its axis, which is approximately 24 hours long.
Starting with 37 erasers, if 3 erasers are lost each day, then the number of erasers in the receptacle for each of the first 6 days can be calculated as follows:
After Day 1: 37 - 3 = 34 erasers
After Day 2: 34 - 3 = 31 erasers
After Day 3: 31 - 3 = 28 erasers
After Day 4: 28 - 3 = 25 erasers
After Day 5: 25 - 3 = 22 erasers
After Day 6: 22 - 3 = 19 erasers
Therefore, there will be 34 erasers after Day 1, 31 erasers after Day 2, 28 erasers after Day 3, 25 erasers after Day 4, 22 erasers after Day 5, and 19 erasers after Day 6.
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A fast-food restaurant promotes certain food items by giving a game piece with each item.
Advertisements proclaim that "25% of the game pieces are Instant Winners!" To test this claim, a frequent diner collects 20 game pieces and gets only 3 instant winners.
1. Identify the population, the parameter, the sample, and the statistic in this context.
The correct answer of population is all the game pieces and sample is 20.
How to find the percentage of winners?
As we know that a fast-food restaurant promotes certain food items by giving a game piece with each item, and proclaims that 25% of the game pieces are instant winners.
Population is all the game pieces.
Parameter is true proportion of all the game pieces that are winner.
Sample is 20, the game pieces that is collected.
Statistics is the proportion of the sample that are winners i.e. [tex]\frac{3}{20}[/tex]
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sample is the 20 and the statistic is 3/20 .
What is sample space ?A random experiment's sample space is the collection of all possible outcomes. A portion of the sample space is an event that is associated with a random experiment. Any outcome has a probability that is between 0 and 1. All outcomes have probabilities that add up to 1.
he population is all the game pieces that the fast-food restaurant produces.
The parameter is the proportion of game pieces that are instant winners in the population.
The sample is the 20 game pieces that the frequent diner collected.
The statistic is the proportion of instant winners in the sample. In this case, the statistic is 3/20 or 0.15 (15%).
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A store sells 12 oranges for 4 dollars how many oranges can you buy for 1 dollar?
A) 2 B) 3 c) 4 D) 6
Answer:
B) 3
Step-by-step explanation:
Divide 12 and 4 then you will get 3 as your answer.
Answer:
You can Buy 3 oranges from 1 dollar.
Given- A Store sells 12 Oranges for 4 dollars
let dollar = x (equation 1)
Now,
12 oranges = 4x (Equation 1)
Taking 4 to the other side of equals sign, it divides 12 : -
12/4 oranges = x
3 oranges = x
Thus we get the value of x which is 3 oranges. As we know that x = dollar, we get to know that each dollar will get us 3 oranges.
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What is the solution of 3x+8/x-4>0
Answer:
Solve the inequality for
x
by finding
a
,
b
, and
c
of the quadratic then applying the quadratic formula.
All real numbers
Interval Notation:
(
−
∞
,
∞
)
Step-by-step explanation:
how do i find these I’m so confused
Triangles BIG and MOP are similar so, the values of v, w, x, y are 36 cm, 156°, 46.7°, 43.2° respectively.
Describe Triangles?A triangle is a two-dimensional geometric shape that is formed by three line segments that connect three non-collinear points in a plane. These points are called the vertices of the triangle, and the line segments connecting them are called sides.
Triangles are characterized by several properties, including their side lengths, angles, and areas. Based on the lengths of their sides, triangles can be classified into three types:
Scalene triangle: A triangle in which all three sides have different lengths.
Isosceles triangle: A triangle in which two sides have the same length.
Equilateral triangle: A triangle in which all three sides have the same length.
Since triangles BIG and MOP are similar, we know that their corresponding angles are equal and their corresponding sides are proportional.
Let's first find the value of w in triangle BIG. We know that the sum of angles in a triangle is 180 degrees. Therefore, we can find angle BIG as follows:
angle BIG = 180 - angle BGI
= 180 - 24
= 156 degrees
Now we can use the fact that the corresponding sides of similar triangles are proportional to set up the following ratios:
v/42 = 48/v (since BI/IG = GB/BI)
v^2 = 4248
v = sqrt(4248)
v = 36
In triangle MOP, we can use the law of cosines to find the value of angle MOP:
cos(MOP) = (60^2 + 72^2 - y^2) / (26072)
cos(MOP) = (3600 + 5184 - y^2) / 8640
cos(MOP) = (8784 - y^2) / 8640
MOP = acos((8784 - y^2) / 8640)
MOP = 46.7 degrees (approximately)
Now we can use the fact that the corresponding sides of similar triangles are proportional to set up the following ratios:
v/60 = y/72 (since BI/MO = IG/MP)
y = (v/60)*72
y = (36/60)*72
y = 43.2 cm
Lastly, we can use the fact that the sum of angles in a triangle is 180 degrees to find the value of angle POM in triangle MOP:
angle POM = 180 - angle MOP - 126
= 180 - 46.7 - 126
= 7.3 degrees (approximately)
Therefore, we have:
v = 36 cm
w = 156 degrees
x = 46.7 degrees (approximately)
y = 43.2 cm
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High temperatures in a certain city for the month of August follow a uniform distribution over the interval 65°F to 87°F. What is the probability that a randomly selected August day has a high temperature that exceeded 70°F?
Probability that a randomly selected August day has a high temperature that exceeds 70°F is approximately 0.7727, or 77.27%.
Assuming that the range of high temperatures in a specific city throughout the month of August is uniform, the probability density function (pdf) of the distribution is as follows:
[tex]f(x) = 1 / (b - a) = 1 / (87 - 65) = 1 / 22[/tex]
where the temperature interval's lower and higher bounds are set at 65 and 87, respectively.
We must determine the area under the pdf curve to the right of x = 70°F in order to determine the likelihood that a randomly chosen August day will have a high temperature that is higher than 70°F. This can be done by integrating the pdf from 70 to 87:
[tex]P(x > 70) = ∫(70 to 87) (70 to 87) f(x) dx = ∫(70 to 87) (70 to 87) 1/22 dx = [1/22 * (x)] (70 to 87) = (1/22) * (87 - 70) = 0.7727[/tex]
As a result, there is a 77.27% probability that an August day chosen at random would have a high temperature above 70 degrees Fahrenheit. This suggests that out of 100 randomly selected August days, we may expect roughly 77 days to have a high temperature surpassing 70°F.
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The entire group of individuals we want information about is called the sample.
The statement is False. The entire group of individuals we want information about is called the population, not sample.
What is sample?In statistics, a sample is a subset of individuals or observations taken from a larger population, which is used to estimate characteristics or parameters of the population.
The goal of statistical analysis is often to make inferences about a population based on information gathered from a representative sample. Therefore, it is important to carefully select a sample that is truly representative of the population of interest.
The sample is a subset of the population that is selected for analysis in order to make inferences about the population.
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The complete question is : The entire group of individuals we want information about is called the sample.
a. True
b. False
What value of x makes this equation true 0.6x-5=0.1x+7
Step-by-step explanation:
To solve for x, we'll first need to simplify the equation by combining like terms:
0.6x - 5 = 0.1x + 7
0.6x - 0.1x = 7 + 5
0.5x = 12
x = 12 / 0.5
x = 24
Therefore, the value of x that makes the equation true is 24.
Enterprise A is considering a new production line project with 100% equity financing. The expected operational life of the project is 6 years. Investment value in equipment is 1,500 million VND, which is paid once in 0. Working capital is spent 2 times in the first 2 years of the project (year 0 and year 1), with the amount respectively 300 million VND and 100 million VND. Working capital is fully recovered once at the end of the project (year 6). The production line is depreciated evenly over 6 years, with negligible liquidation value.
Year
1
2
3
4
5
6
Revenue
860
920
1.050
1.200
880
820
Million VND
Variable costs are 40% of net sales. Fixed costs (excluding depreciation of fixed assets) are VND 250 million/year. The corporate income tax rate is 20%. Corporate discount rate is 15%/year. Determine the NPV of the project. If the project is selected according to NPV criteria, will the project be approved?
To calculate the NPV of the project, we need to find the cash inflows and outflows for each year and discount them back to their present value using the corporate discount rate of 15%.
Year 0:
Initial investment = 1,500 million VND
Working capital = -300 million VND
Year 1:
Revenue = 860 million VND
Variable costs = -344 million VND (40% of net sales)
Fixed costs = -250 million VND
Depreciation = -250 million VND (1,500 million VND / 6)
Operating income before taxes = 16 million VND (860 - 344 - 250 - 250)
Taxes = -3.2 million VND (20% of operating income before taxes)
Operating income after taxes = 12.8 million VND (16 - 3.2)
Add back depreciation = 250 million VND
Net cash flow = 262.8 million VND
Discounted cash flow = 228 million VND (262.8 / 1.15)
Year 2:
Revenue = 920 million VND
Variable costs = -368 million VND (40% of net sales)
Fixed costs = -250 million VND
Depreciation = -250 million VND (1,500 million VND / 6)
Operating income before taxes = 52 million VND (920 - 368 - 250 - 250)
Taxes = -10.4 million VND (20% of operating income before taxes)
Operating income after taxes = 41.6 million VND (52 - 10.4)
Add back depreciation = 250 million VND
Net cash flow = 291.6 million VND
Discounted cash flow = 231.9 million VND (291.6 / 1.15^2)
Year 3:
Revenue = 1,050 million VND
Variable costs = -420 million VND (40% of net sales)
Fixed costs = -250 million VND
Depreciation = -250 million VND (1,500 million VND / 6)
Operating income before taxes = 130 million VND (1,050 - 420 - 250 - 250)
Taxes = -26 million VND (20% of operating income before taxes)
Operating income after taxes = 104 million VND (130 - 26)
Add back depreciation = 250 million VND
Net cash flow = 354 million VND
Discounted cash flow = 255.3 million VND (354 / 1.15^3)
Year 4:
Revenue = 1,200 million VND
Variable costs = -480 million VND (40% of net sales)
Fixed costs = -250 million VND
Depreciation = -250 million VND (1,500 million VND / 6)
Operating income before taxes = 220 million VND (1,200 - 480 - 250 - 250)
Taxes = -44 million VND (20% of operating income before taxes)
Operating income after taxes = 176 million VND (220 - 44)
Add back depreciation = 250 million VND
Net cash flow = 426 million VND
Discounted cash flow = 286.6 million VND (426 / 1.15^4)
Year 5:
Revenue = 880 million VND
Variable costs = -352 million VND (40% of net sales)
Fixed costs = -250 million VND
Depreciation = -250 million VND (1,500 million VND / 6)
Operating income before taxes = 28 million VND