The statement that correctly describes the expression |x^3|+5 is 5 more than the absolute value of the cube of a number.
Given this expression: |x^3|+5
| | = This sign means Absolute value,
x^3 = x³ = x × x × x
Hence, the statement that correctly describes the expression |x^3|+5 is : 5 more than the absolute value of the cube of a number.
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[tex]\frac{v-2}{2v^2+10v} + \frac{1}{2v+10}=\frac{1}{2}[/tex]
Show all steps
The value of variable 'v' in the expression ( v - 2 ) / (2v² + 10v ) + 1 / ( 2v + 10 ) = 1 / 2 is equal to -4.
The expression is equal to,
( v - 2 ) / (2v² + 10v ) + 1 / ( 2v + 10 ) = 1 / 2
Simplify the expression we have,
⇒ ( v - 2 ) / 2v ( v + 5 ) + 1 / 2( v+ 5 ) = 1 / 2
Take the least common multiple of the denominator we have,
⇒ [( v - 2 ) + 2 ] / 2v( v+ 5 ) = 1 / 2
⇒ v / 2v( v+ 5 ) = 1 / 2
Multiply both the sides of the expression by 2 we get,
⇒ 1 / 2( v+ 5 ) = 1 / 2
⇒ 1 /( v + 5 ) = 1
Cross multiply the expression we get,
⇒ v + 5 = 1
Subtract 5 from the both the sides of the equation we get,
⇒ v = -4
Therefore , the value of v in the given expression is equal to -4.
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A basket contains 3 green, 4 yellow, 5 blue and 6 red tickets, one of which is randomly selected.
Giving your answer in its simplest form, what's the theoretical probability of not drawing a yellow ticket?
Probability of not drawing a yellow ticket =
Again using theoretical probability, determine the chance of getting a green or red ticket. Give your answer as a fraction in its simplest form.
Probability of drawing a green or red ticket =
The theoretical probability of drawing a green or red ticket is 1/2 or 0.5.
We have,
There are a total of 3 + 4 + 5 + 6 = 18 tickets in the basket.
The probability of drawing a yellow ticket.
= 4/18
Since there are 4 yellow tickets out of 18 total tickets.
The probability of not drawing a yellow ticket is equal to the probability of drawing a green, blue, or red ticket.
There are 3 + 5 + 6 = 14 tickets that are not yellow.
The probability of not drawing a yellow ticket.
= 14/18
= 7/9
To find the probability of drawing a green or red ticket, we need to add the probabilities of drawing a green ticket and a red ticket.
The probability of drawing a green ticket.
= 3/18
The probability of drawing a red ticket.
= 6/18
Now,
The probability of drawing a green or red ticket is
= 3/18 + 6/18
= 9/18
= 1/2
Thus,
The theoretical probability of drawing a green or red ticket is 1/2 or 0.5.
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if I made a profit of $3,250 after selling stocks for $10,500 after 4 years what was my average annual percentage game.
Answer:
To calculate the average annual percentage gain, we need to use the formula:
Average annual percentage gain = ((Ending value / Beginning value)^(1/n) - 1) x 100%
where:
- Ending value = the value of the investment at the end of the period
- Beginning value = the value of the investment at the beginning of the period
- n = the number of years
In this case, the beginning value of the stocks is not given, so we cannot calculate the exact average annual percentage gain. We only know the profit and the ending value. However, we can make an estimate assuming that the profit is equal to the gain, i.e., there were no transaction costs or other fees.
If the profit was $3,250 and the ending value was $10,500, then the beginning value was:
Beginning value = Ending value - Profit
Beginning value = $10,500 - $3,250
Beginning value = $7,250
The number of years is given as 4.
Using the formula above, we can estimate the average annual percentage gain as:
((10,500 / 7,250)^(1/4) - 1) x 100%
= (1.1267^(0.25) - 1) x 100%
= (1.0266 - 1) x 100%
= 0.0266 x 100%
= 2.66%
Therefore, the estimated average annual percentage gain is 2.66%.
Step-by-step explanation:
What is the meaning of "the equation ax = b has a solution for every b ∈ H"?
In the given image, H is a non-empty set of complex numbers, a and b are complex numbers, and x is a variable.
"The equation ax = b has a solution for every b ∈ H" means that for any complex number b in the set H, there exists a complex number x such that the product of a and x is equal to b.
In other words, for every numbers of b in H, there exists a solution for x that satisfies the equation ax = b.
This statement has important implications in linear algebra and functional analysis, where it is used to define the concept of a surjective linear transformation in numbers. It also has applications in many areas of mathematics and science, including engineering, physics, and computer science.
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m/1 = x and m/2 = 2x. Find
the value of 'x'.
Answer:
-m = x is the answer hope it helps
Ayuda por favor es para mañana, fracciones equivalentes. Doy coronita
These fractions are equivalent fractions by algebraic property:
Case 1: YES
Case 2: NO
Case 3: YES
Case 4: NO
Case 5: YES
Case 6: YES
Case 7: NO
Case 8: YES
Case 9: YES
Case 10: YES
Case 11: NO
Case 12: YES
Case 13: NO
Case 14: YES
Case 15: YES
Case 16: YES
Case 17: NO
Case 18: YES
How to determine if two fractions are equivalent
In this question we must check 18 cases of equivalent fractions, two fractions are equivalent if the following algebraic property is met:
a / b = (a · c) / (b · c), where a, b, c are integers and c is nonzero.
Now we proceed to determine if each pair is equivalent:
Case 1
2 / 3 = (2 · 2) / (3 · 2)
2 / 3 = 4 / 6 (YES)
Case 2
2 / 6 = (2 · 3) / (6 · 3)
2 / 6 = 6 / 18 (NO)
Case 3
9 / 9 = (9 · 4) / (9 · 4) = 36 / 36 (YES)
Case 4
3 / 11 = (3 · 3) / (11 · 3) = 9 / 33 (NO)
Case 5
7 / 8 = (7 · 2) / (8 · 2) = 14 / 16 (YES)
Case 6
4 / 6 = (4 · 5) / (6 · 5) = 20 / 30 (YES)
Case 7
5 / 6 = (5 · 2) / (6 · 2) = 10 / 12 (NO)
Case 8
2 / 7 = (2 · 4) / (7 · 4) = 8 / 28 (YES)
Case 9
6 / 12 = (6 · 2) / (12 · 2) = 12 / 24 (YES)
Case 10
4 / 9 = (4 · 5) / (9 · 5) = 20 / 45 (YES)
Case 11
9 / 10 = (9 · 3) / (10 · 3) = 27 / 30 (NO)
Case 12
1 / 5 = (1 · 5) / (5 · 5) = 5 / 25 (YES)
Case 13
12 / 12 = (12 · 3) / (12 · 3) = 36 / 36 (NO)
Case 14
8 / 11 = (8 · 4) / (11 · 4) = 32 / 44 (YES)
Case 15
5 / 5 = (5 · 4) / (5 · 4) = 20 / 20 (YES)
Case 16
6 / 9 = (6 · 4) / (9 · 4) = 24 / 36 (YES)
Case 17
3 / 7 = (3 · 8) / (7 · 8) = 24 / 56 (NO)
Case 18
10 / 12 = (10 · 4) / (12 · 4) = 40 / 48 (YES)
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Here are two similar solid shapes.
and
A
surface area of shape A: surface area of shape B = 3:4
The volume of shape B is 10 cm³
Work out the volume of shape A.
Give your answer correct to 3 significant figures.
B
Step-by-step explanation:
Let the volume of shape A be V. Since the surface area of shape A is 3/4 times that of shape B, the surface area of shape A is 3/7 times the total surface area of the two shapes combined.
Therefore, the surface area of shape A is:
3/7 (surface area of shape A + surface area of shape B) = 3/7 (4/3 surface area of shape B) = 12/21 surface area of shape B
We know that the volume of shape B is 10 cm³, and we can find the volume of shape A by using the ratio of the volumes to the ratio of the surface areas:
V/10 = 3/4
V = 7.5 cm³ (to 3 significant figures)
Therefore, the volume of shape A is 7.5 cm³.
Thanks to an initiative to recruit top students, an administrator at a college claims that this year's entering
class must have a greater mean IQ score than that of entering classes from previous years. The
administrator tests a random sample of 17 of this year's entering students and finds that their mean IQ score
is 114, with a standard deviation of 15. The college records indicate that the mean IQ score for entering
students from previous years is 113.
Is there enough evidence to conclude, at the 0.05 level of significance, that the population mean IQ score, μ,
of this year's class is greater than that of previous years? To answer, assume that the IQ scores of this year's
entering class are approximately normally distributed.
Perform a one-tailed test. Then complete the parts below.
(If Rococcan consult a list of
Answer: The answer is B and im 100% correct
Step-by-step explanation:
(1 point) (a) Find a vector parametric equation for the part of the saddle = z = x y inside the cylinder 2+2=9 x 2 + y 2 = 9 .
(Time limit) Tell if the graph is a function or not.
Give me the domain and range.
The graph is a function: yes.
The domain of this function is: x ≥ -3.
The range of this function: all real numbers.
What is a range?In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.
Furthermore, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left-hand side of the graph to the right-hand side.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-3, ∞}, x ≥ -3, or -3 ≤ x ≤ ∞.
Range = {-∞, ∞} or all real numbers.
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In an election, the median number of votes a candidate received in 6 towns was 250. Which statement MUST be true about this election?
OA. The total number of votes the candidate received in the election was 1500.
OB. The candidate received at least 250 votes in half of the 6 towns.
OC. The candidate received exactly 250 votes in at least two of the towns.
O D. The total number of votes received by all the candidates in the election was 1500.
Answer:
B. The candidate received at least 250 votes in half of the 6 towns.
This is because the median number of votes is the middle value when all the vote counts are put in order. This means that at least three towns gave the candidate more than 250 votes, and at least three towns gave the candidate fewer than 250 votes. So, the candidate received at least 250 votes in half of the 6 towns. The total number of votes the candidate received in the election cannot be determined from this information. Similarly, the number of votes received in individual towns cannot be determined.
SVM & Kernel Methods Problem 1 (10 points) In this problem we would like to compare the solutions of hard and soft SVMs on a linearly seperable dataset. Let n > 1 be a fixed number. Is it true that there exists C > 0 such that for every sample S of n training examples with binary label, which are linearly separable, the hard-SVM and the soft-SVM (with parameter C) solutions will return exactly the same weight vector. Justify your answer. (Hint: consider n = 2, d = 1 and S = {(x1, yı), (x2, y2)}. Let a > 0 and consider x1 = a, yı = 1, X2 = –a, y2 = -1. Derive the optimal solution for hard and soft SVM and compare the results.)
It is not true that there exists a C > 0 such that for every sample S of n training examples with binary label, which are linearly separable, the hard-SVM and the soft-SVM (with parameter C) solutions will return exactly the same weight vector.
This can be shown by considering the case where n = 2, d = 1 and S = {(x1, yı), (x2, y2)}. Let a > 0 and consider x1 = a, yı = 1, X2 = –a, y2 = -1.
For the hard-SVM, the optimal solution is to find the weight vector w that maximizes the margin between the two classes while ensuring that all training examples are classified correctly. In this case, the margin is 2a and the weight vector is w = (0, 1) or w = (0, -1), depending on the choice of the positive and negative class labels.
For the soft-SVM with parameter C, the optimal solution is to find the weight vector w and the slack variables ξi that minimize the objective function:
min ||w||^2 + CΣξi
s.t. yi(wT xi) ≥ 1 - ξi, ξi ≥ 0
In this case, since the data is linearly separable, the slack variables will be zero for all training examples and the optimal solution will be the same as for the hard-SVM. However, if C is chosen to be a large value, the soft-SVM may allow some misclassifications by penalizing them with the slack variables. In this case, the optimal solution will be different from the hard-SVM.
Therefore, it is not always true that the hard-SVM and soft-SVM solutions will return exactly the same weight vector for linearly separable data, but they may be the same if the parameter C is chosen appropriately.
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how much cardboard is needed to make the single slice pizza box shown
that would be 5 pieces of cardboard needed
Which function has a domain where x is not equal to 3 and a range where y is not equal to 2?
Domain where x is not equal to 3 and a range where y is not equal to 2 for function (x+5)/(x-3)
Domain = Set of all input values of a function.
range = set of all output values of a function.
Given: Domain: x≠3 ; range = y≠2
We do not include a value for domain if it makes the expression indeterminant .
Since all the functions in options are fractions, here the denominator does not equal to 0.
But in option C and D, the denominator can be zero if x=3.
So , domain for then it x ∈ R-3
for option C if 2=2(x+5)/(x-3)
x-3=x+5
-3=5 which is not possible
Where as in option D, 2=(x+5)/(x-3)
2x-6=x+5
x=11
Hence, domain where x is not equal to 3 and a range where y is not equal to 2 for function (x+5)/(x-3)
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Which function has a domain where x does not =3 and a range where y does not =2? A. f(x)=(x-5)/(x+3) B. f(x)=2(x+5)/(x+3) C. 2(x+5)/(x-3) D. (x+5)/(x-3)
When working for a District Attorney, an investigator analyzed the leading digits of the amounts from 784 checks issued by seven suspect insurance companies. The frequencies were found to be 0, 12, 0, 73, 482, 186, 8, 23, and 0, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford's Law, the check amounts appear to result from fraud. Use a 0.05 significance level to test for goodness-of-fit with Benford's Law. What is the value of the test statistic? Does it appear that the checks are the result of fraud?
Using chi-squared goodness-of-fit test with Benford's Law, observed check frequencies were found to be significantly different, indicating possible fraud. The test statistic was 756.153, exceeding the critical value of 15.51.
Using chi-squared goodness-of-fit test with Benford's Law, observed check frequencies were found to be significantly different, indicating possible fraud. The test statistic was 756.153, exceeding the critical value of 15.51.
To test for goodness-of-fit with Benford's Law, we can use the chi-squared goodness-of-fit test. The null hypothesis is that the observed frequencies follow Benford's Law, while the alternative hypothesis is that they do not.
We can start by calculating the expected frequencies for each leading digit based on Benford's Law. According to Benford's Law, the expected proportion of leading digits is
P(d) = log10(1 + 1/d), where d is the leading digit (1, 2, ..., 9).
Then, we can calculate the expected frequencies by multiplying the proportion by the sample size
Expected frequency for digit d = P(d) * sample size.
Using this formula, we can calculate the expected frequencies for each digit
Expected frequencies: 3.542, 2.019, 1.518, 1.221, 1.028, 0.886, 0.778, 0.697, and 0.643.
We can use these expected frequencies and the observed frequencies to calculate the chi-squared statistic
chi-squared = Σ (observed frequency - expected frequency)² / expected frequency
We can then compare this value to the chi-squared distribution with 8 degrees of freedom (since there are 9 digits and one constraint, which is that the frequencies must add up to the sample size). Using a significance level of 0.05 and a chi-squared distribution table or calculator, the critical value is 15.51.
Plugging in the observed and expected frequencies, we get
chi-squared = (0 - 3.542)²/3.542 + (12 - 2.019)²/2.019 + (0 - 1.518)²/1.518 + (73 - 1.221)²/1.221 + (482 - 1.028)²/1.028 + (186 - 0.886)²/0.886 + (8 - 0.778)²/0.778 + (23 - 0.697)²/0.697 + (0 - 0.643)²/0.643
chi-squared = 756.153
Since the calculated chi-squared statistic (756.153) is greater than the critical value (15.51), we reject the null hypothesis and conclude that the observed frequencies are not consistent with Benford's Law. This suggests that the check amounts are the result of fraud.
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Consider the line y=8x-7
Find the equation of the line that is parallel to this line and passes through the point (5,-3)
Find the equation of the line that is perpendicular to this line and passes through the point (5,-3)
Answer:
Parallels lines:
y = 8x - 43
Perpendicular line:
y = [tex]\frac{-1}{8}[/tex]x - [tex]\frac{19}{8}[/tex]
Step-by-step explanation:
y = 8x -7
Parallel lines have the same slope.
The slope will be 8. We will use the x from the point (5,-3) and the y from the point (5,-3) to find the y-intercept (b)
y = mx + b Substitute in -3 for y, 8 for m, and 5 for x.
-3 = 8(5) + b
-3 = 40 + b Subtract 40 from both sides
-3 - 40 = 40 - 40 + b
-43 = b
Substitute in 8 for m and -43 for b to write the equation
y = mx + b
y = 8x - 43
Perpendicular slope are opposite reciprocals of each other, so the perpendicular slope is [tex]\frac{-1}{8}[/tex]
Substitute [tex]\frac{-1}{8}[/tex] doe m, -3 for y and 5 for x.
y = mx + b
-3 = [tex]\frac{-1}{8}[/tex](5) + b
-3 = [tex]\frac{-5}{8}[/tex] + b add [tex]\frac{5}{8}[/tex] from both sides
-3 + [tex]\frac{5}{8}[/tex] = [tex]\frac{-5}{8}[/tex] + [tex]\frac{5}{8}[/tex] + b
[tex]\frac{-24}{8}[/tex] + [tex]\frac{5}{8}[/tex] = b
[tex]\frac{-19}{8}[/tex] = b
Substitute [tex]\frac{-1}{8}[/tex] for m and [tex]\frac{-19}{8}[/tex] for b
y = mx + b
y = [tex]\frac{-1}{8}[/tex]x - [tex]\frac{19}{8}[/tex]
Helping in the name of Jesus.
[8 points] Find the y-intercept and graph the equation by
making a table of values with three points,
2) y=-3x+2
SEENE
Answer:
The answer is (0,2) (1,-1) (2,-4)
Step-by-step explanation:
The slope is -3.
Because of this, you go down 3 and to the side 1 (it's also called rise/run).
I REALLY HOPE THIS HELPS!!!!
6-Tel, Inc. is a telecommunication services provider looking to expand to a new territory Z; it is analyzing whether it should install its own telecom towers or lease them out from a prominent tower-sharing company T-share, Inc.
Leasing out 100 towers would involve payment of $5,000,000 per year for 5 years. Erecting 100 news towers would cost $18,000,000 including the cost of equipment and installation, etc. The company has to obtain a long-term secured loan of $18 million at 5% per annum. Owning a tower has some associated maintenance costs such as security, power and fueling, which amounts to $10,000 per annum per tower.
The company's tax rat is 40% while its long-term weighted average cost of debt is 6%. The tax laws allow straight-line depreciation for 5 years. Determine whether the company should erect its own towers or lease them out.
Answer:
The present value of leasing the towers is $19,576,000 while the present value of erecting new towers is $20,273,000. Therefore, the company should lease the towers.
Step-by-step explanation:
What is 2x-5y=9 in slope intercept form?
Round to the nearest whole number, then find the sum. 15.43 + 12.85 + 21.3 = ___ pls i will give 60 points!!!!!!!!!!
Answer:
15.43 + 12.85 + 21.3 = 49.58
Rounding to the nearest whole number, the sum is 50.
Step-by-step explanation:
Answer:
15.43 + 12.85 + 21.3 = 49.58
Step-by-step explanation:
I need explanation for example 8.
Thankyou
There is a probability of 94/315 that the problem will be solved.
We are given that P has a chance of solving the problem of 2/7, Q has a chance of solving the problem of 4/7, and R has a chance of solving the problem of 4/9. To find the probability that the problem is solved, we need to consider all possible scenarios in which the problem can be solved.
The probability of this scenario is 2/7. If P solves the problem, then it does not matter whether Q or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 2/7.
The probability of this scenario is 4/7. If Q solves the problem, then it does not matter whether P or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/7.
The probability of this scenario is 4/9. If R solves the problem, then it does not matter whether P or Q solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/9.
The probability of this scenario is (1-2/7) * (1-4/7) * (1-4/9) = 3/35. This is because the probability of P not solving the problem is 1-2/7, the probability of Q not solving the problem is 1-4/7, and the probability of R not solving the problem is 1-4/9. To find the probability of none of them solving the problem, we multiply these probabilities together.
To find the probability of the problem being solved, we need to add the probabilities of all the scenarios in which the problem is solved. Therefore, the probability of the problem being solved is:
2/7 + 4/7 + 4/9 = 94/315
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Circle the students error in the problem below and rewrite what correct step should be
The students error is in step 3 and the correct solution is g(x) = 2x² + 4x - 4
Circling the students errorFrom the question, we have the following parameters that can be used in our computation:
The steps to solve the expression
From step 2 to step 3, we have
g(x) = 2(x + 1)(x + 1) - 6
g(x) = 2(x² + 1x + 1) - 6
The step 3 is incorrect
Because when the expression is expanded, we have
g(x) = 2(x² + 2x + 1) - 6
This gives a solution of
g(x) = 2x² + 4x - 4
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Luciana bought a total of 7 textbooks at the bookstore. She bought four more textbooks than journals. How many journals did she buy
Find the multiplying integers -2x24=
The multiplying integers -2x24= -48
Multiplication of Integers:Here is some rules of multiplication of integers:
1. Positive integer × negative integer = negative.
2. Positive integers × Positive integers = positive.
3. Negative integers × Negative integers = positive.
Here, To find the the multiplying integers
-2x24 = -48
When you multiply integers :
Negative x Positive = Negative
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Look at the picture
According to the information, we can infer that the area of the triangle is: 19 1/4ft²
How to calculate the area of the triangle?To calculate the area of the triangle, we need to use the formula for the area of a triangle:
Area = (1/2) x base x heightwhere,
Base = 5 1/2 ftHeight = 7 ft.How to find the height of the triangle?To find the height of the triangle, we need to use the Pythagorean theorem, which relates the slant height, height, and half the base:
(slant height)^2 = (height)^2 + (1/2 base)^2Substituting the given values, we get:
(1/3)^2 = (7)^2 + (1/2 x 5 1/2)^2(1/9) = 49 + (15/4)(1/9) = (196/4 + 15/4)(1/9) = (211/4)Multiplying both sides by 36, we get:
4 = 844.44...So the height of the triangle is approximately 2.04 ft.
Now we can plug in the values for the base and height into the formula for the area:
Area = (1/2) x 5 1/2 x 7Area = 19.25 square feetArea = 19 1/4ft²Therefore, the area of the triangle is approximately 19.25 square feet.
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PLEASE HELP ME !!! I NEED THIS TO GRADUATE
Find the surface area
The surface area of the prism is 70.44 yd²
What is surface area of prism?A prism is a solid shape that is bound on all its sides by plane faces. There are different types of prism, triangular prism, rectangular prism e.t.c
The surface area of a prism is expressed as;
SA = 2B +pH
where B is the base area and p is the perimeter of the base and h is the height of the prism
Base area = 1/2 bh
= 1/2 × 3 × 3 = 4.5 yd²
The hypotenuse of the triangle = √3²+3²
= √9+9 = √18 = 4.24
perimeter of the base = 4.24+3+3 = 10.24yds
Therefore,
SA = 2×4.5 + 10.24 × 6
SA = 9 + 61.44
SA = 70.44 yd²
therefore the surface area of the prism is 70.44yd²
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In a normal distribution, what percentage of the data falls within 2 standard
deviations of the mean?
A. 99.7%
B. 68%
C. 34%
D. 95%
The percentage of the data that falls within 2 standard deviations of the mean is B. 68%
Calculating the percentage of dataFrom the question, we have the following parameters that can be used in our computation:
Percentage = 2 standard deviations
As a general rule:
The percentage of the data that falls within 2 standard deviations of the mean is 68%
This means that the correct option is (b) 68%
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PLEASE HELP (WILL GIVE BRAINLIEST)
Answer:d
Step-by-step explanation:
Anna took a job that paid $116 the first week. She was guaranteed a raise of 7% each week. How much money will she make in all over 10 weeks? Round the answer to the nearest cent, and number answer only.
Anna will make $1602.71 in all over 10 weeks.
Here, the first week salary of Anna = $116
i.e., the initial salary a = $116
She was guaranteed a raise of 7% each week.
so, her salary in the next week would be,
116 + 7% of 116
7 percent of 116 is:
116 × 7/100 = 8.12
so, her salary will be $124.12
So, the equation for the salary after 'm' weeks would be,
[tex]n = 116\times (1 + 0.07)^{m - 1}\\\\n = 116\times (1 .07)^{m - 1}[/tex]
Using this equation , the salary in the second week m = 2 would be,
n = 124.12
Salary in the third week m = 3 would be,
n = 116 × [tex](1.07)^{3-1}[/tex]
n = 132.81
Salary in the fourth week m = 4 would be,
n = 116 × [tex](1.07)^{4-1}[/tex]
n = 142.11
Salary in the fifth week m = 5 would be,
n = 116 × [tex](1.07)^{5-1}[/tex]
n = 152.05
Salary in the sixth week m = 6 would be,
n = 116 × (1.07)⁶⁻¹
n = 162.7
Salary in the seventh week m = 7 would be,
n = 116 × (1.07)⁷⁻¹
n = 174.08
Salary in the eighth week m = 8 would be,
n = 116 × (1.07)⁸⁻¹
n = 186.27
Salary in the nineth week m = 9 would be,
n = 116 × (1.07)⁹⁻¹
n = 199.31
And the salary after the tenth week m = 10 would be,
n = 116 × (1.07)¹⁰⁻¹
n = 213.26
The total money after 10 weeks would be,
T = 116 + 124.12 + 132.81+ 142.11 + 152.05 + 162.7 + 174.08 + 186.27 + 199.31 + 213.26
T = $1602.71
This is the required amount.
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