The payment (future value), to the nearest rand, which should be made at the end of the seventh year in order to liquidate the debt, is R9,338.80.
What is the future value determined?The future payment to be made at the end of the seventh year is determined by computing the future values in two stages. The first stage computes the future value before the payment at the end of the first year. The second stage computes the future value for six years.
here, we know,
The future value is computed by compounding the present value at an interest rate.
Current debt = R6,421,00
Compound interest rate = 11% per year
Compounding period = Quarterly
Future Value in 1 Year:
N (# of periods) = 4 quarters (1 year x 4)
I/Y (Interest per year) = 11%
PV (Present Value) = R6,421.00
PMT (Periodic Payment) = R0
Results:
Future Value (FV) = R7,156.98
Total Interest = R735.98
Future Value (FV) = R7,156.98
Payment in one year's time = R2,287.00
Balance = R4,869.98
Future Value at the end of the 7th Year:
N (# of periods) = 24 quarters (6 years x 4)
I/Y (Interest per year) = 11%
PV (Present Value) = R4,869.98
PMT (Periodic Payment) = R0
Results:
Future Value (FV) = R9,338.80
Total Interest = R4,468.82
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Abstract Algebra: Let ???? be the group of all real-valued functions with domain ℝ under addition. Let H be the subset of ???? consisting of all functions that are differentiable. Determine if H is a subgroup of ????.
Yes, H is a subgroup. We can prove this by using the subgroup criterion, which states that a subset H of a group G is a subgroup if and only if it satisfies the following three conditions:
1. The identity element of G is in H.
2. If h1 and h2 are in H, then h1*h2 is in H.
3. If h is in H, then h^(-1) is in H.
Let's check if these conditions are satisfied for H:
1. The identity element of ???? is the zero function, f(x) = 0, which is differentiable. Therefore, the identity element is in H.
2. If h1 and h2 are in H, then they are both differentiable functions. The sum of two differentiable functions is also differentiable, so h1 + h2 is in H.
3. If h is in H, then it is a differentiable function. The inverse of a differentiable function under addition is its negative, which is also differentiable. Therefore,[tex]h^{-1} = -h[/tex] is in H.Since all three conditions are satisfied, H is a subgroup.
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pleaseweeee helppppp
Select the correct answer.
Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
Answer:
A
[tex]2y {}^{4} \div x {}^{4} [/tex]
Step-by-step explanation:
Divide 14 by 7 it will be 2.
Now divide the variables.
X variable will give you X{}^{-4} and y{}^{4}.
So bring X variable in the denominator to make it positive.
So your answer will be option A.
Answer:
A
Step-by-step explanation:
It was right for me
Y varies inversely as x. If x = 8 when y = 30, find x when y = 20
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=8\\ y=30 \end{cases} \\\\\\ 30=\cfrac{k}{8}\implies 240=k\hspace{9em}\boxed{y=\cfrac{240}{x}} \\\\\\ \textit{when y = 20, what's "x"?}\qquad 20=\cfrac{240}{x}\implies x=\cfrac{240}{20}\implies x=12[/tex]
I need help pls pls pls pls pls.
Answer:
G
Step-by-step explanation:
Since these triangles are similar, side lengths in one must be proportional to the other. Segment AB is similar to DE, AC similar to DF, and BC similar to EF. With that in mind, G is the only possible answer because DE/AG correspond to one another, just as DF/AC correspond to one another.
$8,374.78 $6,741.75 What are the complex solutions to the following equation? 2x^(2)+4x+6=0
The complex solutions to the given equation are -1 + i√2 and -1 - i√2.
To determine the complex solutions to the equation, we can first simplify the quadratic equation by dividing each term by 2. This gives x² + 2x + 3 = 0.
The discriminant (b² - 4ac) can be calculated to find the nature of roots.
b² - 4ac = 2² - 4(1)(3) = 4 - 12 = -8
As the discriminant is less than 0, the roots are imaginary roots. That is, the roots are complex numbers.
To find the roots of this quadratic equation, the following steps can be followed.
Since the coefficient of x² is 1, the quadratic formula can be used to solve the given quadratic equation. The quadratic formula is given by
x = [-b ± √(b² - 4ac)] / 2a
Substitute the given values into the formula.
x = [-2 ± √(-8)] / 2
On simplifying the above expression,
x = [-2 ± 2i√2] / 2= -1 ± i√2
Therefore, -1 + i√2 and -1 - i√2 are the complex roots or solutions of the given quadratic equation.
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Jiang is building a doghouse for her new puppy. The image below is what the base of the house will look like. What is the area of the dog bed that Jiang will need to make to fit the entire base of the dog house
Answer:
Step-by-step explanation:
lets take the top part as 1 and the seconds part as 2
so for the first part
1 Area= L*B
so 8*5 =40
2 Area=L*B
so 11*4=44
44+40=84cm2
Maria uses 14 beads to make a bracelet. Sarah uses 6 times as many beads as Maria to make a necklace. How many beads does Sarah use? Enter your answer in the box.
A calculator is not allowed on this question. If (mx+3)(nx+5)=8x^(2)+px+15 for all values of x, and m+n=6, what are the two possible values for p?
The answer of two possible values for p are 26 and 22
If (mx+3)(nx+5)=8x^(2)+px+15 for all values of x, and m+n=6, we can use the distributive property to expand the left side of the equation:
mnx^(2)+(5m+3n)x+15=8x^(2)+px+15
Next, we can compare the coefficients of each term to find the values of m, n, and p:
mn=8
5m+3n=p
m+n=6
Since m+n=6, we can solve for one variable in terms of the other:
n=6-m
Substituting this into the equation for p gives us:
5m+3(6-m)=p
5m+18-3m=p
2m+18=p
Now we can substitute this back into the equation for mn:
m(6-m)=8
6m-m^(2)=8
m^(2)-6m+8=0
Using the quadratic formula, we can find the two possible values for m:
m=(6±√(6^(2)-4(1)(8)))/(2(1))
m=(6±√(36-32))/2
m=(6±√4)/2
m=(6±2)/2
m=4 or m=2
If m=4, then n=6-4=2, and p=2(4)+18=26
If m=2, then n=6-2=4, and p=2(2)+18=22
Therefore, the two possible values for p are 26 and 22.
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Wite the first five terms of the sequence whose general term, a_(n), is given as a_(e)=2n-8.
The first five terms of the sequence whose general term is given as a_(n)=2n-8 are a_1=-6, a_2=-4, a_3=-2, a_4=0, and a_5=2.
To explain this in more detail, the general term for a sequence is given by an equation in the form a_(n)= some expression. In this case, the expression is 2n-8, so it can be read as “2 times the term number minus 8”.
To calculate the first term, we substitute n=1 into the equation and solve, so a_1=2*1-8=-6. To calculate the second term, we substitute n=2 into the equation and solve, so a_2=2*2-8=-4. Continuing in this manner, we calculate the third term as a_3=2*3-8=-2, the fourth term as a_4=2*4-8=0, and the fifth term as a_5=2*5-8=2.
Therefore, the first five terms of the sequence are a_1=-6, a_2=-4, a_3=-2, a_4=0, and a_5=2.
In conclusion, to find the first five terms of a sequence given by a general term a_(n)= some expression, substitute the values n=1, n=2, n=3, n=4, and n=5 into the expression and solve to get the desired terms.
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Find the period and amplitude. \[ y=-4 \sin \left(\frac{\pi x}{5}\right) \] period amplitude Need Help?
The period of the function is 10 and the amplitude is 4.
The period and amplitude of the function \[ y=-4 \sin \left(\frac{\pi x}{5}\right) \] can be found by examining the coefficients in the equation.
The amplitude is the absolute value of the coefficient in front of the sine function, which in this case is |-4| = 4. Therefore, the amplitude of the function is 4.
The period is found by dividing 2π by the coefficient in front of the x variable inside the sine function. In this case, the coefficient is \[\frac{\pi}{5}\]. So, the period is \[\frac{2\pi}{\frac{\pi}{5}} = 10\].
Therefore, the period of the function is 10 and the amplitude is 4.
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34.34. A P-value is
A. the correlation between two variables
B. the ratio between the test statistic and the standard error
C. the probability of incorrectly rejecting the null hypothesis
D. None of the above
E. the same as the significance level
The correct answer is C. the probability of incorrectly rejecting the null hypothesis.
A P-value is used in hypothesis testing to determine the likelihood of observing a test statistic as extreme as the one observed under the null hypothesis. It is a measure of the strength of evidence against the null hypothesis.
A small P-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis. A large P-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.
It is important to note that a P-value is not the same as the significance level (option E), which is the threshold used to determine whether to reject or fail to reject the null hypothesis.
The P-value is also not the same as the correlation between two variables (option A), which measures the strength of a linear relationship between two variables.
The P-value is also not the ratio between the test statistic and the standard error (option B), which is used to calculate the P-value but is not the same thing.
Therefore, the correct answer is option C, the probability of incorrectly rejecting the null hypothesis.
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Juan is deciding between two truck rental companies. Company A charges an initial fee of $65 for the rental plus $3 per mile driven. Company B charges an initial fee of $100 for the rental plus $2 per mile driven. Let A represent the amount Company A would charge if Juan drives a miles, and let B represent the amount Company B would charge if Juan drives a miles. Write an equation for each situation in terms of x, and determine the number of miles driven, x, that would make the cost of each company the same.
Answer:
35 miles.
Step-by-step explanation:
A=3x+65
B=2x+100
3x+65=2x+100
x+65=100
x=35
Write an equation for the nth term of the arithmetic seqeuence. Then find a10-
-6,-9, -12,-15, ...
an
11
a10
Given- A sequence as -6,-9,-12,-15
To find- The equation for the nth term of the arithmetic sequence and to find the value of [tex]a_{10}[/tex].
Explanation- The common difference is [tex]-9-(-6)=-3[/tex]
We know the arithmetic sequence formula is
[tex]a_n=a_1+(n-1)d\\a_n=-6+(n-1)(-3)[/tex]
When n=10
[tex]a_{10}=-6+(10-1)(-3)\\a_{10}=-6+9(-3)\\a_{10}=-6-27\\a_{10}=-33[/tex]
Final answer- The value of 10th term is -33.
HELP! PLEASE ND THANK YOU
The equation that gives the cost of each juice bottle is 24j + 2.19 = 40.83
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.
Let j represent the cost of each juice.
Sophie bought a popcorn for $2.19 and 24 juice bottles for a total of $40.83.
The equation that represents this problem is:
24j + 2.19 = 40.83
The equation is 24j + 2.19 = 40.83
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Compute the area of triangle, if x equals 3 less than 6
Answer:
C
Step-by-step explanation:
I think its c because it said x = 3 less than 6, what is three less than 6? 3 so if you were to plug in 3 for x so bc = 3 and ab = 6 you multiply those two together but when you are doing area for a triangle its 1/2 bh so how i do this is i multiply 6 and 3 and get 18 and divide that by 2 and my final answer is 9. Hope this works, let me know if it doesnt!
Solve. Check for extraneous solutions. 7y+3−6y+9=0
The solution of the given expression is y = -12 and there are no extraneous solutions.
What in algebra is a superfluous solution?A solution to an equation that appears during the solving process but does not fulfil the original problem is known as an extraneous solution. In other words, it is a solution that, when inserted back into the original equation, yields an untrue assertion. Extraneous solutions typically result from certain algebraic operations, such squaring an equation's two sides, which might introduce new solutions that don't truly satisfy the original problem.
The given expression is:
7y+3−6y+9=0
y = -12
Substitute y = -12 back into the original equation:
7y + 3 - 6y + 9 = 0
7(-12) + 3 - 6(-12) + 9 = 0
-84 + 3 + 72 + 9 = 0
The left-hand side simplifies to:
0 = 0
Hence, the solution of the given expression is y = -12 and there are no extraneous solutions.
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Cables and parallel beams are used to support a bridge. The obtuse angles formed by the beams and the bridge are 105°. The acute angle formed by the cable and the bridge is 42°.
Note: Picture is not drawn to scale.
What is the measure of angle X?
Answer:
Step-by-step explanation:
A$AP BEAN$: Khan Academy can help you. Do your work and stop cheating!!!!!
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There are 15 students in Mrs. Jones’ class who are going to the band competition. If 60% of her students are going to the competition, how many students are there in the class in all?
15 - 60%
x - 100%
1500 = 60x
x = 25
∴ There are 25 students in the class in all.
How many times as great as the value of 4 in 4,670 is the value of 4 in 5,040
The value of the digit 4 in 5,040 is 100 times more than that of the digit 4 in 4,670.
At the unit place of both numerals, there is a digit 4. The place value of a digit determines how valuable it is in a number. The position of the digit from the number's rightmost side determines its place value.
The value of the digit 4 in the tens place of the number 4,670 is 4 x 10 = 40.
The value of the digit 4 in the thousands position of the number 5,040 is 4 x 1000, or 4000.
Therefore, As 4000/40 = 100, the value of the digit 4 in 5,040 is 100 times more than that of the digit 4 in 4,670.
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What is the solution, if any, to the equation 3(x-2)+4=3x+6
Answer:
if I'm correct it's 3(4x5)
BUT RECHECK JUST INCASE
Step-by-step explanation:
HELP A GIRL OUT PLEASEEEEEEEEEE
Answer: C
Step-by-step explanation:
replace n=1 with f(n)= 5n-2 we have
f(1)=3 => remove answers B and D
f(n)= 5n-2 so f(n-1)= 5(n-1) -2=5n-7
Try with answers C and D to see if it satisfies this
f(n)= f(n-1)+5= 5n - 7+5=5n-2 => C is correct
measure the height of the tin in mm
The measure of the height of the tin in mm can be found using the steps below.
What are Measurements?
Measurement is the method of comparing the properties of a quantity or object using a standard quantity.
Measurement is essential to determine the quantity of any object.
Here, the activity is to measure the height of a tin.
Height of the tin is the vertical distance from the base of the tin to the top of the tin.
The height of the tin is the exact straight line measurement when the tin is placed upright on a flat surface.
The measurement has to be in millimeters.
So the best tool is the ruler.
Place the ruler vertically with point 0 at the baseline of the tin.
Mark the point in millimeters that the ruler coincides with the top of the tin.
Read the height to the nearest millimeter.
Hence, the height of the tin can be measured as above.
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The complete Question:
Measure the height of the tin in the mm and write down the real height in mm
Can someone help with this please?
According to the Synthetic Division, the Quotient is equal to 7x² -4x + 5 and the Remainder is equal to 8.
Synthetic Division: What is it?Synthetic division can divide two polynomials more quickly than the standard long division algorithm.
With this method, the dividend and divisor polynomials are reduced to a set of numerical numbers.
Given:
(7x³-25x² +17x -7) ÷ (x-3).
So, Synthetic Division for this is as follows:
(x-3) | (7x³-25x² +17x -7) | 7x² -4x + 5
7x³-21x²
_________
-4x² + 17x
-4x² + 12x
_______________
5x - 7
5x - 15
________
8
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HELP i have a exponential functions nd i need to know if my word problem is solve able pls
The Population of salmonella
doubles in size every 25 hours.
There are about 1.35 million
infections every year, determine
how many bacteria is present
every year.
Yes, this word problem is solvable using exponential functions.
To solve this problem, we need to use the formula for exponential growth:
P(t) = P0 * e^(rt)
where P(t) is the population after t hours, P0 is the initial population, r is the growth rate, and e is the mathematical constant approximately equal to 2.71828.
In this problem, we are given that the population doubles in size every 25 hours. This means that the growth rate is 1/25, since the population is multiplying by 2 each time.
We are also given that there are about 1.35 million infections every year. Since there are 365 days in a year, this means there are about 1.35 million/365 = 3699.18 infections per day.
We can now use this information to find the initial population:
P0 = 3699.18 / e^(1/25 * 24 * 365)
P0 ≈ 2135.05
So the initial population is about 2135.05 bacteria.
To find the population after one year, we can use the formula again:
P(365 * 24) = 2135.05 * e^(1/25 * 24 * 365)
P(365 * 24) ≈ 3.89 x 10^18
Therefore, there are approximately 3.89 x 10^18 bacteria present after one year.
A regular hexagon is a polygon that has six sides with equal length and six interior angles with equal measure. In Figure 1, regular hexagon ABCDEF has side length 2x and its vertices lie on the circle with centre O. The diagonals AD, BE and CF divide ABCDEF into six congruent equilateral triangles. (a) In terms of x, what is the radius of the circle?
radius of the circle is sqrt(3)x.
The radius of the circle can be found by using the Pythagorean Theorem. The side lengths of each equilateral triangle created by the diagonals is 2x, so the hypotenuse of the triangle is sqrt(3)x. Since the hypotenuse of each triangle is the same as the radius of the circle, the radius of the circle is sqrt(3)x.
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Evaluate. Write your answer as a fraction or whole number without exponents. 5^-4
Answer:
1 / 625
Step-by-step explanation:
To write 5^-24 without exponents, simplify.
5^-4
1 / 5^4
1 / 625 or .0016
Natalie has two number pyramids each labeled 1 to 4. Natalie is going to conduct an experiment by tossing both pyramids a total of 96 times. She will find the difference of each pair of numbers rolled by subtracting the lesser number from the greater number
a. The total number of possible outcomes is 16 x 96 = 1,536.
b. She should expect to see a difference of 1 approximately 12/16 x 96 = 72 times.
c. She should expect to see a difference of 0 approximately 8/16 x 96 = 48 times.
a) There are a total of 16 possible pairs of numbers that can be rolled on the two pyramids:
(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), and (4,4).
We can use a probability distribution to calculate the probability of each pair of numbers being rolled. Since each pyramid has four sides, there are 4 x 4 = 16 possible outcomes when both pyramids are rolled. Therefore, the probability of each outcome is 1/16.
Since Natalie is going to toss each pair of pyramids 96 times, the total number of possible outcomes is 16 x 96 = 1,536.
To calculate the difference between each pair of numbers, we can simply subtract the smaller number from the larger number.
Here is a table that shows the probability of each difference:
Difference Possible Pairs Probability
0 (1,1), (2,2), (3,3), (4,4) 4/16 = 1/4
1 (1,2), (1,3), (1,4), (2,3), (2,4), (3,4), 12/16 = 3/4
(2,1), (3,1), (4,1), (3,2), (4,2), (4,3)
2 None 0
3 None 0
Therefore, the probability of the difference being 0 is 1/4, the probability of the difference being 1 is 3/4, and the probability of the difference being 2 or 3 is 0.
Since Natalie is going to conduct the experiment a total of 96 times, we can use these probabilities to calculate the expected number of times each difference will occur:
Difference Probability Expected Number of Occurrences
0 1/4 96 x 1/4 = 24
1 3/4 96 x 3/4 = 72
2 0 96 x 0 = 0
3 0 96 x 0 = 0
b) we can expect the difference between each pair of numbers to be 0 about 24 times and
c) to be 1 about 72 times over the course of the experiment.
Differences 2 and 3 are not expected to occur.
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The correct question should be:
Natalie has two number pyramids each labeled 1 to 4. Natalie is going to conduct an experiment by tossing both pyramids a total of 96 times. She will find the difference of each pair of numbers rolled by subtracting the lesser number from the greater number.
a. How many possible outcomes are there? _________________
b. How many times should Natalie toss a difference of 1? ______________
c. How many times should Natalie toss a difference of 0?
Create a data set with 6 numbers that has a median of 12
Answer:
Median is a middle number.
Step-by-step explanation:
You can use any set of number with 12 in the middle
14, 18, 12, 12, 17, 18
Middle numbers are third and forth number added together and divided by 2
when f(x)=4 what is the of x
When f(x) = 4, then, the value of x = 2 (domain = 2, range = 4).
How did we determine the value of x?According to the mapping above, the given relationship is bijective (one-to-one and onto or one-to-one correspondence) because each element of the range is mapped to by exactly one element of the domain.
When we say a relationship is bijective, it means the satisfies both the injective (one-to-one function) and surjective function (onto function) properties. Therefore, as a result, f(x)=4 implies f(2)=4 or simply x=2.
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Michelle reads 16 pages in ¼ of an hour. How many pages will she read in one hour?
Answer:
reads 64 pages in one hour
Step-by-step explanation:
For simplicities' sake, we'll convert 1/4 of an hour into 15 minutes (60 minutes x 1/4 = 15 mins)
Since we have a ratio, of 16 pages to 15 mins, we can create the ratio by making a fraction of 16/15. Since we want to get to 1 hour, to find how many pages she read in an hour, we can multiply the top and bottom (to equalize) by 4 (because 4 x 15 = 60).
16•4/15•4
64/60
Because of this, we can see that the ratio is now 64 pages to 60 mins or one hour. Therefore, she reads 64 pages in one hour.
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Answer:
64
Step-by-step explanation:
To do this problem you have to figure out Michelle's hourly rate for reading pages. We are given that she will read 16 pages in 1/4 of an hour. This means that in 15 minutes (60 minutes in an hour / 4 for the 1/4 an hour) she will read 16 pages. We only have 15 minutes though and need 60 minutes so 60/15 gives us 4. This means that we will need 4, 15 minute periods to get to a hour. So 4*15minutes = 60 minutes or one hour and 16pages*4 = 64 pages. So in one hour she will read 64 pages.
A faster way to do this is to just multiply both sides by the recripical.
16 pages = 1/4 hour
*4/1 *4/1
64 pages = 4/4 hour
64 pages = 1 hour