The value of f(5) is e^5 + 5/3, which is exactly 150.0798257693, and the value of f(11) is e^11 + 11/3, which is approximately 59877.808.
The function is f(x)= e^x + 1/3x
To find the value of f(5), put the value of x = 5 in the function f(x)= e^x + 1/3x. Which is equal to f(5) = e^5 + 5/3.
Similarly, to find the value of f(11), put the value of x = 11 in the function f(x)= e^x + 1/3x.
Which is equal to f(11) = e^11 + 11/3
f(11) = 59874.141715198 + 3.6666666667
f(11) = 59877.808381865
f(11) ≈ 59877.808
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How do I solve for this arclength problem? I am gto an intigral of sqrt(1+cos2x) and when i solve for it it should be 1 but that wont work
Length of the curve is 1
What is arc length?Arc length or length of a curve is the distance travelled by a point it follows the graph of a function along a some particular interval.
Given,
[tex]y=\int\limits^0_x {\sqrt{cost2t} } \, dt[/tex]
Let find the derivative of the function,
[tex]\frac{dy}{dt} =\frac{d}{dt} (\int\limits^0_x {\sqrt{cost2t} } \, dt)[/tex]
[tex]\frac{dy}{dt} = \sqrt{cos2t}[/tex]
Now using arc length formula,
[tex]L= \int\limits^0_\frac{\pi }{4} {\sqrt{1+(\sqrt{cos2t})^{2} } } \, dt[/tex]
[tex]L= \int\limits^0_\frac{\pi }{4} {\sqrt{1+cos2t} } \, dt[/tex]
Using trigonometric identities, [tex]cos^{2} t+sin^{2} =1[/tex] and[tex]cos2t = cos^{2}t-sin^{2} t[/tex][tex]L= \int\limits^0_\frac{\pi }{4} {\sqrt{cos^{2} t+sin^{2} + cos^{2}t-sin^{2} t } } \, dt[/tex][tex]L= \int\limits^0_\frac{\pi }{4} {\sqrt{2cos^{2} t} } \, dt[/tex]
[tex]L= \sqrt{2} \int\limits^0_\frac{\pi }{4} cos t} } \, dt = \sqrt{2} sint[/tex]
Apply limits we get, L=1.
Hence, length of the curve , L=1.
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Consider the following two systems.
(a)
4x−2yx+5y==−3
x+5y = 1
(b)
4x−2yx+5y=2
X+5y = 3
(i) Find the inverse of the (common) coefficient matrix of the two systems.
(ii) Find the solutions to the two systems by using the inverse, i.e. by evaluating A^{-1} B where B represents the right hand side (i.e.
B =
−3
1
for system (ii) Find the solutions to the two systems by using the inverse, i.e. by evaluating A^{-1} B where B represents the right hand side (i.e. B =
−3
1
for system (a) and B =
2
3
for system (b)).
and B =
2
3
for system (b)).
To the inverse, use the formula A−1=1/ad−bc[d −b]
[ −c a]
when the system (ii) By applying the inverse, that is, by calculating A-1 B where B represents the right-hand side (i.e. B = ), the solutions to the two systems-:
−3
1
for system (a) and B =
2
3
for system (b)).
and B =
2
3
for system (b)).
The coefficient matrix is
[4−2
1 5]
To find the inverse, use the formula
A−1=1/ad−bc[d −b
−c a]
The solutions can then be obtained by multiplying this inverse matrix by the vectors. (For example, use writing to solve the equation Ax=b.
x=A⁻¹b)
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The full question
Consider the following two systems.
(a)
4x−2yx+5y==−31
(b)
4x−2yx+5y==23
(i) Find the inverse of the (common) coefficient matrix of the two systems.
(ii) Find the solutions to the two systems by using the inverse, i.e. by evaluating A^{-1} B where B represents the right-hand side (i.e.
B =−31
help!! needed quickly!
On solving the provided question we can say that The coordinates are = ( 9 , - 6 ); the slope intercept will be y + 6 = 9xm - m
what is slope intercept?In mathematics, the intersection point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are emphasised in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten such that they seem to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.
The coordinates are = ( 9 , - 6 )
the slope intercept will be y + 6 = 9xm - m
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The function f(x) = x^3 is transformed to f(x) = 4x^3. Which statement describes the graph of the transformed function?
A. The graph was translated up by 4 units.
B. The graph was stretched horizontally by a factor of 4.
C. The graph was translated down by 4 units.
D. The graph was stretched vertically by a factor of 4.
Answer:
D
Step-by-step explanation:
You just multiplied it times 4 ....it is four times taller
Determine the factor by which g (a) grows over the interval from 14 to 16.
The factor by which g(x) grows over the interval from 14 to 16 is 64/56 = 1.1429.
What is interval?An interval is a specific range of values within a set of data. It is the difference between the maximum and minimum values of the data set, and is used to measure the spread of the data. Intervals can be used in a variety of ways, from measuring the distribution of data over time to help identify trends in the data. Intervals can also be used to find outliers or unusually high or low values in a data set. Interval data is often used in statistics to measure the variability of data.
The factor by which g(x) grows over the interval from 14 to 16 can be determined by dividing the value of g(16) by the value of g(14).
The value of g(14) is 56, and the value of g(16) is 64.
Therefore, the factor by which g(x) grows over the interval from 14 to 16 is 64/56 = 1.1429.
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A cylinder has a height of 5 centimeters and a radius of 5 centimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answer:
below
Step-by-step explanation:
First find the area ( pi r^2) of the endcaps...then multiply by the height
pi r^2 h = 3.14 (5^2)(5) = 392.50 cm^3
Given the quadratic function x2+5x-24=0,mark on the graph where the solution[s]exit
The solutions exist at x=-8 and x=3, so the graph will have points at (-8,0) and (3,0).
Quadratic FormulaThe solutions to the equation x2+5x-24=0 can be found by using the Quadratic Formula, which is x = [-b ± √(b2-4ac)]/2a. In this case, a = 1, b = 5, and c = -24.This results in x = {8, -3}.These solutions can be represented graphically on a coordinate plane.There are two points of intersection at (8, 0) and (-3, 0).These points represent the two solutions to the equation.This type of graph is called a parabola.It is a U-shaped curve that consists of all points that satisfy the equation.The vertex is the point at which the parabola changes direction and is located at the point (5, -24).To learn more about Quadratic Formula refer to:
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a) If 12 quintals of weight is equal to 1200 kg, how many kilograms are there in 1 quintal?
Answer:
12q=1200
12q/12=1200/12
q=100
1 quintal has 100 kg. The equation above was to show how to solve it with a variable. Hope this helps!
Step-by-step explanation:
suppose the probability of an irs audit is 3.4 percent for u.s taxpayers who file form 1040 and earn $100,000 or more
I am struggling in Statistics
How many ways are there to fill the four commuter positions
Answer:
69 ways.
Step-by-step explanation:
What value of x would make KM ∥ JN?
Triangle J L N is cut by line segment K M. Line segment K M goes from side J L to side L N. The length of J K is x minus 5, the length of K L is x, the length of L M is x + 4, and the length of M N is x minus 3.
Complete the statements to solve for x.
By the converse of the side-splitter theorem, if JK/KL =
, then KM ∥ JN.
Substitute the expressions into the proportion: StartFraction x minus 5 Over x EndFraction = StartFraction x minus 3 Over x + 4 EndFraction.
Cross-multiply: (x – 5)(
) = x(x – 3).
Distribute: x(x) + x(4) – 5(x) – 5(4) = x(x) + x(–3).
Multiply and simplify: x2 – x –
= x2 – 3x.
Solve for x: x =
To solve for the value of x that would make KM ∥ JN, we can use the converse of the side-splitter theorem.
What value of x would make KM ∥ JN?This theorem states that if the ratio of the lengths of any two sides of a triangle are equal to the ratio of any two corresponding sides of another triangle, then the two triangles are similar.This means that if we determine the ratio of JK/KL, then this ratio must be equal to the ratio of LM/MN for KM to be parallel to JN. To find the ratio of JK/KL, we must first substitute the given expressions into the proportion: JK/KL = (x – 5)/x. We can then cross-multiply to get (x – 5)(x) = x(x – 3).We can then distribute and simplify to get x2 – x – 20 = x2 – 3x. Solving for x, we get x = 20. Thus, the value of x that would make KM ∥ JN is 20.To solve for x, both sides of the equation x2 – x – 20 = x2 – 3x can be set equal to zero. This yields a quadratic equation of the form ax2 + bx + c = 0, where a = 1, b = -1, and c = -20.To solve this equation, one can use the quadratic formula, which states that the solutions to a quadratic equation of the form ax2 + bx + c = 0 are given by x = (-b ± √(b2 - 4ac)) / (2a). In this case, the solutions are x = 21 and x = -1. This problem is called solving a quadratic equation.To learn more about the side-splitter theorem refer to:
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Which expression is equivalent to the given expression? (ab^2)^3 divided by b^5
The solution to the algebraic expression (ab²)³/b⁵ using laws of exponents is; ab
How to divide Algebra Expressions?The algebraic expression we are trying to solve is;
(ab²)³/b⁵
Now, according to laws of exponents, we have that;
1) Product Law of exponents: To multiply two expressions with the same base, add the exponents while keeping the base the same
2) Quotient Law of Exponents: To divide two expressions with the same base, subtract the exponents while keeping the base same
3) Zero Law of exponents: Any number (other than 0) raised to 0 is 1
4) Power of a power law of exponents: It states that when we have a single base with two exponents, just multiply the exponents.
We will first apply the power of a power law to get;
(ab²)³/b⁵ = ab⁶/b⁵
= ab
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Suppose /(x)= x. Find the graph of f(x) + 4
Click on the correct answer.
The function's value is f(x). The line's slope is m.When x is equal to 0, the function's value is equal to b, which is also the coordinate at where the line in the coordinate plane crosses the y-axis.
Find the graph ?The function's value is f(x). The line's slope is m.
When x is equal to 0, the function's value is equal to b, which is also the coordinate at where the line in the coordinate plane crosses the y-axis.
The x-value coordinate's is given by x.
Graph Rules for Derivatives
The graph of f'(x) will be below the x-axis if f(x) has a negative slope.
The graph of f'(x) will be above the x-axis if f(x) has a positive slope.
The x-intercepts of f' will be all relative extrema of f(x) (x).
Given that ;
f(x)= x³
f(x)-4 = x³- 4
See attached graph using the graph tool
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Can someone help
Please
The journal entry for the transaction will be:
Debit Cash $617,500
Credit Preferred stock $475,000
Credit Paid up Capital in excess of Par 142,500
(Issued Preferred Stock in Cash)
What is a journal entry?A journal entry is the act of recording any transaction, whether one that is economic or not. An accounting diary that displays the debit and credit balances of a corporation lists transactions.
4,750 Preferred Stock issued at 100 Par Value at $ 130
Means $ 30($ 130-$ 100) Paid up Capital in excess of Par
Total amount Received :
Preferred Stock Par Value = 4,750 Shares at 100 = $475,000
Paid up Capital in excess of Par = 4,750 Shares at 30 = $ 142,500
Total Received = $ 617,500
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Complete the table below
For exponential function g(x)=10ˣ, the table is given below.
What are exponential functions?An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
Exponential Growth
In Exponential Growth, the quantity increases very slowly at first, and then rapidly. The rate of change increases over time. The rate of growth becomes faster as time passes. The rapid growth is meant to be an “exponential increase”. The formula to define the exponential growth is:
y = a ( 1+ r )ˣ
Where r is the growth percentage.
Exponential Decay
In Exponential Decay, the quantity decreases very rapidly at first, and then slowly. The rate of change decreases over time. The rate of change becomes slower as time passes. The rapid growth meant to be an “exponential decrease”. The formula to define the exponential growth is:
y = a ( 1- r )ˣ
Where r is the decay percentage.
Now given function
g(x)=10ˣ
then function g(x-1)=10^(x-1)ˣ⁻¹
So, g(x)/g(x-1)=10*10ˣ⁻¹=10ˣ⁻¹=10
Therefore, the table will be as
x g(x) g(x)/g(x-1)
2 100 10
3 1000 10
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I need help with This question I’ll give you brainliest
Please help!
Solve the equation using the steps:
2(x + 8)= 2x + 8
Step 1: __________ to get _________
Step 2: _________ to get _________
There is ________ solution(s).
Word bank
Distribute
Combine Like Terms
2x+16=2x+8
2x+8 =2x+8
Subtract x on both sides
Add x to both sides
x+16=8
x = 2
x = -8
16 = 8
x + 8 = 8
One
No
Infinite
2x + 8 = x
Subtract 2x on both sides
8 = -x or x = -8
Add 2x to both sides
The equation, 2(x + 8) = 2x + 8 has no solution because 16 = 8.
How to Solve an Equation?To solve an equation, you find the value of the variable that makes the equation true. This can involve using inverse operations (such as addition and subtraction, multiplication and division, or exponentiation and logarithms) to isolate the variable on one side of the equation, and then using properties of equality to simplify the equation.
Given the following, 2(x + 8) = 2x + 8:
Step 1: Distribute 2(x + 8) = 2x + 8 to get 2x + 16 = 2x + 8
Step 2: Subtract 2x from both sides to get 16 = 8
2x + 16 = 2x + 8
2x + 16 - 2x = 2x + 8 - 2x
16 = 8
There is no solution.
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Hi, image is shown below. Please help if able to.. thank you.
Answer:
50 days
Step-by-step explanation:
Grace=3x+200
Joseph=6x+50
3x+200=6x+50
3x=150
x=50
a confidence interval is an interval calculated from the population data, where we strongly believe the true value of the population parameter lies. A.True B.False
As a range of values that are bound above and below the statistic's mean, a confidence interval is likely to contain an unidentified population parameter. So the statement is true.
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.
In statistics, confidence is another word for probability. For many different statistical estimates, such as proportions, population means, differences between population means or proportions, and estimates of variation among groups, confidence intervals can be calculated.
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How do I show work for 27x 506
506 is 27 times the value of 18.74 because the sum of the two numbers is 506.
506 is 27 times as much as what?We divide both sides by 27 to get x on its own, and then we can solve for x. The math is illustrated below:
27 • x = 506
27x = 506
27x/27 = 506/27
x = 18.74
Every day, we deal with decimals while calculating length, weight, and other variables. When whole numbers are insufficient to offer the level of precision needed, decimal numbers are utilized. For instance, we don't always find that our weight is equal to a whole number on the scale when we calculate it on the weighing machine.
Simply said, round down the preceding digit if the last digit is less than 5. The previous digit should be rounded up if the number is five or higher.
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Complete Question is :How do I show work for 27x is 506 and Find the value of x?
Please help me with the following question.
The probability of a single value greater than 134 is given as follows:
P(X > 134) = 0.6844 = 68.44%.
The probability of the sample mean greater than 134 is given as follows:
P(M > 134) = 0.9641 = 96.41%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 155, \sigma = 43.7[/tex]
The probability of a single value above 134 is one subtracted by the p-value of Z when X = 134, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (134 - 155)/43.7
Z = -0.48
Z = -0.48 has a p-value of 0.3156.
Hence:
1 - 0.3156 = 0.6844 = 68.44%.
For the sample of 14, the standard error is given as follows:
[tex]s = \frac{43.7}{\sqrt{14}} = 11.68[/tex]
Hence:
Z = (134 - 155)/11.68
Z = -1.8
Z = -1.8 has a p-value of 0.0359.
Hence:
1 - 0.0359 = 0.9641 = 96.41%.
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50 POINTS!!! 6TH GRADE MATH ANSWER THIS BEFORE 30 MINS FOR BRINLIST 5 STAR AND A THANK YOU!!
(EXPLAINATION REQUIERD OTHERWISE YOUR AWNSER WILL BE TAKEN DOWN THANKS SO MUCH!!)
The heights of 11 plants, in inches, are listed.
14, 15, 15, 16, 16, 16, 17, 17, 18, 19, 20
If another plant with a height of 17 inches is added to the data, how would the range be impacted?
The range would stay the same value of 6 inches.
The range would stay the same value of 16 inches.
The range would increase to 17 inches.
The range would decrease to 6 inches.
Answer:
The range is the difference between the largest and smallest values in a set of data. In this case, the heights of the 11 plants are listed as:
14, 15, 15, 16, 16, 16, 17, 17, 18, 19, 20
The smallest height is 14 inches and the largest height is 20 inches, so the range is 20 - 14 = 6 inches.
If another plant with a height of 17 inches is added to the data, the smallest and largest values do not change, so the range would still be 6 inches.
Answer:
Answer to the question posted: The range would stay the same value of 6 inches.
Answer to the question in the comments: The mean would decrease in value to about 16.8 inches.
Step-by-step explanation:
Answer to the question posted:
First, to figure out if the range increases, decreases, or stays the same, we need to find the range. The range is siply the difference between the largest ans smallest number. In this problem, the smallest plant height is 14 while the largest plant height is 20. Since the difference between the smallest and largest plant is 20-14, or 6, inches, the range is 6 inches.
Now, let's figure out what would happen if we added a plant with a height of 17 inches. Well, since our smallest plant height and largest plant height would not be changed, the range would stay the same value of 6 inches.
Answer to the question in the comments:
The first step is to find the mean of the plant heights. To find mean, you need to add up all the plant heights and divide it by the number of plants. Since 13+14+15+15+16+16+16+17+17+18+19+20+22+23=241 and there are 14 plants, we can divide 241 by 14 to find the original mean of the plant heights. When we solve 241/14, we get 17.2142857143.
Now, let's figure out what would happen to the mean if we added a plant with a height of 11 inches. Again, we would need to total up all the plant heights, and it should be 11 inches larger than last time, as we are adding 11 inches to the total plant height. Since our original total height was 241, or new total height, adding in the 11 inch plant, would be 252 inches. Now that we have our total plant height including the 11 inch plant, we need to figure out how many total plants we have. If we started with 14 plants and add another plant into the data set, then the total number of plants, including the 11 inch plant, must be 15. Now that we know the new total plant height and new amount of plants, we can find the new mean, The new mean is 252/15, or 16.8.
So, if our mean went from 17.2142857143 to 16.8 when we added the 11 inch plant, the mean would decrease in value to about 16.8 inches.
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The Stable Matching Problem, as discussed in the text, assumes that all men and women have a fully ordered list of preferences. In this problem we will consider a version of the problem in which men and women can be indifferent between certain options. As before we have a set M of n men and a set Wof n women. Assume each man and each woman ranks the members of the opposite gender, but now we allow ties in the ranking. For example (with n- 4), a woman could say that m1 is ranked in first place; second place is a tie between m2 and m3 (she has no preference between them); and m4 is in last place. We will say that w prefers m to m' if m is ranked higher than m' on her preference list (they are not tied) With indifferences in the rankings, there could be two natural notions for stability. And for each we can ask about the existence of stable matchings, as follows. (a) A strong instability in a perfect matching S consists of a man m and a woman w, such that each of m and w prefers the other to their partner in S. Does there always exist a perfect matching with no strong instability? Either give an example of a set of men and women with preference lists for which every perfect matching has a strong instability; or give an algorithm that is guaranteed to find a perfect matching with no strong instability. (b) A weak instability in a perfect matching S consists of a man m and a woman w, such that their partners in S are w and m', respectively, and one of the following holds: m prefers w to w', and w either prefers m to m' or is indifferent between these two choices; or w prefers m to m', and m either prefers w to w' or is indifferent between these two choices. In other words, the pairing between m and w is either preferred by both, or preferred by one while the other is indifferent. Does there always exist a perfect matching with no weak instability? Either give an example of a set of men and women with preference lists for which every perfect matching has a weak instability; or give an algorithm that is guaranteed to find a perfect matching with no weak instability.
Yes, there always exists a perfect match with no weak instability.
For part (a), an example of a set of men and women with preference lists for which every perfect matching has a strong instability would be if all members of one gender ranked all members of the opposite gender equally.
This would mean that no matter which pairing was chosen, one member of the pairing would prefer to be with another member.
As for part (b), an example of a set of men and women with preference lists for which every perfect matching has a weak instability would be if some members of one gender ranked all members of the opposite gender equally, while others had a strict preference.
In this case, the members with strict preferences would always have an alternative that was preferred by one or both members of the pairing, leading to weak instability.
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use deductive reasoning to show that the following procedure always produces the number 8. procedure: pick a number. add 5 to the number and multiply the sum by 3. subtract 7 and then decrease this difference by the triple of the original number.
After using the deductive reasoning the procedure always produces the number 8.
Procedure:
Let the number be x.
We have to add 5 to the number x.
So the expression is x + 5.
We have to multiply the sum by 3.
Now the expression is 3(x + 5).
Now we have to subtract 7.
Now the expression is 3(x + 5) - 7.
Then we have to decrease this difference by the triple of the original number.
The triple of original number is 3x.
Now the expression is {3(x + 5) - 7} - 3x.
Now solving this expression
= {3(x + 5) - 7} - 3x.
First simplify the bracket
= 3x + 15 - 7 - 3x.
= 8
Now we can se that the after following the whole procedure the answer is 8.
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A 20-year mortgage of $50, 000 has monthly payments with 12.5% interest convertible semi-annually. After making the 60th payment, the borrower decides to renegotiate the loan so that he will repay the outstanding amount by making a lump sum payment of $10000, and clearing the balance by means of monthly instalments of $x for 10 years at 11% interest convertible semi-annually. Find x to 2 decimal places.
Answer:
$490.36
Step-by-step explanation:
We can start solving the problem by using the formula for compound interest:
A = [tex]P(1+\frac{R}{n})^{nt}[/tex]
Where A is the final amount, P is the initial principal, R is the interest rate, n is the number of times the interest is compounded in a year, and t is the number of years.
First, we need to calculate the outstanding amount after 60 payments. Since the interest is 12.5% convertible semi-annually, we can use the following formula:
A = [tex]P(1+\frac{R}{2})^{2t}[/tex]
Where P = $50,000 (initial principal), R = 12.5/100 = 0.125, n = 2 (convertible semi-annually), t = 60/12 = 5 years.
A =$ [tex]$50,000(1+\frac{0.125}{2*5})[/tex]
= $ [tex]$50,000(1.0625)^{10}[/tex]
= $50,000(1.7440312)
= $87,201.56
So, the outstanding amount after 60 payments is $87,201.56
Next, we need to calculate the remaining balance after paying $10,000 as a lump sum, which is $87,201.56 - $10,000 = $77,201.56
Now, we need to calculate the monthly payments for 10 years at 11% interest convertible semi-annually. Using the formula above:
A =[tex]P(1+\frac{R}{n})^{nt}[/tex]
Where P = $77,201.56, R = 11/100 = 0.11, n = 2 (convertible semi-annually), t = 10 years.
To find the value of x, we can set up the equation:
$77,201.56 = [tex]x*(1+\frac{0.11}{2})^{2*120}[/tex] - $10,000
Solving for x gives:
x ≈ $490.36 is the monthly instalment for 10 years at 11% interest convertible semi-annually.
To know about compound interest refer:
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Derrick would like to explore his area. He estimates that his walking speed is 3.5 mph in the difficult terrain he has been given. If Derrick leaves at around 12 pm, and the sun sets at 4:45 pm, how far can he explore and still make it back by sunset?
Answer:
wassup my mf jsbhdhdbsidhdbududbdbdishdbjdudhdbd
add the fraction 2 3/10+7 2/3
WILL MARK BRAINLYST IF RIGHT ANSWER
You work for a company that rents out inflatable tents for birthday parties. A customer has asked you for the typical length of time a tent will stay inflated. For recent events, your data show the following inflation times, in hours: 24, 27, 27, 24, 27, 24, 24, 27, 24, 24, 24, and 27.
What is the best measure to describe the typical length of time that a tent will stay inflated?
spread
mode
mean
median
none of the above
Answer:
Mean
Step-by-step explanation:
You need to find the average amount of time that tents stay inflated. You could argue Mode but then you'd only get 24 when it could be 27
we know that triangle dfe is isosceles with base fe and that segment fb is congruent to segment ec because . segment df is congruent to segment by the definition of isosceles triangle. since these segments are congruent, the base angles, angles , are congruent by the isosceles triangle theorem. therefore, triangles are congruent by sas.
In a Isosceles triangle, DEF , ∆DFB is congruent to ∆DEC by SAS Congruence criteria, i.e., ∆DFB ≅ ∆DEC.
SAS congruance Criteria : If two sides and the angle between these two sides of one triangle are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent. We have a triangle DFE with base FE, see in above figure. The EC congruent to FB, i.e., FB ≅ EC. We have to prove ∆DFB ≅ ∆DEC.
Proof : It is known that ∆DEF is isocles triangle with base FE. So, two sides of triangle are equal.
In ∆DFB and ∆DEC,
=> DF = D E ( by definition of Isoceles triangle)
Also, base FB≅ EC ( since, we have)
Now, ∠DFE = ∠DEF => ∠DFB = ∠DEC ( because DE = DF in ∆DEF , corresponding angles of equal sides are equal) .
So, Two sides and the angle between the sides of one triangle, ∆DFB is congruent to the corresponding sides and angle of another triangle, ∆DEC. Therefore, by SAS Congruence criteria, Triangle DFB is congruent to triangle DEC, i.e., ∆DFB≅ ∆DEC. Hence proved..
To learn more about SAS Congruence rule, refer:
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Complete question:
Given: ΔDFE is isosceles with base FE; FB ≅ EC. Prove: ∆DFB ≅ ∆DEC.Complete the missing parts of the paragraph proof. We know that triangle DFE is isosceles with base FE and that segment FB is congruent to segment EC because . Segment DF is congruent segment by the definition of isosceles triangle. Since these segments are congruent, the base angles, angles , are congruent by the isosceles triangle theorem. Therefore, triangles are congruent by SAS
The length of a side of a triangle is in the extended ratio of 3:5:7. The perimeter of the triangle is 120cm. What are the lengths of the sides?
Answer:
56cm
Step-by-step explanation:
Ratio = 3 : 5 : 7
Perimeter = 120 cm
Process
# of parts = 3 + 5 +7 = 15
Divide 120 by 15 = 120 / 15
Number of parts = 8
First side = 3 x 8 = 24 cm
Second side = 5 x 8 = 40 cm
Third side = 7 x 8 = 56 cm
Perimeter = 24 + 40 + 56 = 120 cm
