As an object moves along the 14.0 mm axis from x=0.0m�=0.0m to x� = 14.0 mm it is acted upon by a force given by F=(140−(x−7.0)2)N�=(140−(�−7.0)2)N.
Determine the work done by the force on the object by evaluating the integral ∫x=14.0mx=0.0mFdx∫�=0.0m�=14.0m���.
Express your answer to two significant figures and include the appropriate units.
Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type
W� =
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This graph shows that Tara’s prints have the potential to be profitable, but will require a significant amount of sales to make a profit.

Profit is the difference between a firm's total revenue and total expenses. It is the amount of money a business has earned after subtracting the cost of goods sold, operating expenses and taxes from its total revenue.

The graph reveals a few key pieces of information that can be used to assess the potential profitability of Tara’s prints. Firstly, the graph shows that there is a fixed cost associated with each print, regardless of how many prints are sold. This cost is represented by the straight line at the bottom of the graph. Additionally, the graph reveals that the cost of the prints increases exponentially as more prints are sold. This means that the more prints Tara sells, the more money she makes. Lastly, the graph shows that the revenue from selling prints is significantly higher than the cost of producing them, indicating that Tara can make a profit if she is able to sell enough prints. Overall, this graph shows that Tara’s prints have the potential to be profitable, but will require a significant amount of sales to make a profit.

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The answer is true, our inequality has a solution of x > 13. Our final answer is: 4(x^2 - x - 12) > (101 - 2x)^2

To create a radical inequality that has a solution of x > 13 and has at least 4 terms in it, we can start with the basic inequality x > 13 and add terms to both sides to create a more complex equation. For example:

√(x + 3) + 2 > √(x - 4) + 12

Now, we can rearrange the terms and square both sides to get rid of the radicals:

√(x + 3) - √(x - 4) > 10

(√(x + 3) - √(x - 4))^2 > 10^2

x + 3 - 2√(x + 3)(x - 4) + x - 4 > 100

2x - 2√(x + 3)(x - 4) > 101

Now, we can isolate the radical term and square both sides again:

-2√(x + 3)(x - 4) > 101 - 2x

4(x + 3)(x - 4) > (101 - 2x)^2

4(x^2 - x - 12) > 10201 - 404x + 4x^2

0 > 3x^2 - 403x + 10237

Since we want the solution to be x > 13, we can plug in 13 for x and see if the inequality is true:

0 > 3(13^2) - 403(13) + 10237

0 > 507 - 5239 + 10237

0 > 4505

Since this is true, our inequality has a solution of x > 13. Therefore, our final answer is:

4(x^2 - x - 12) > (101 - 2x)^2

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The length of the rectangular box will be 2.03 cm. Then the correct option is C.

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as,

V = L x W x H

The volume of a rectangular box is 109.86 cubic centimeters. The prism's breadth is 13.2 cm. The prism stands 4.1 cm tall.

The length of the rectangular prism is given as,

109.86 = L x 13.2 x 4.1

109.86 = 54.12L

L = 109.86 / 54.12

L = 2.03 cm

The length of the rectangular box will be 2.03 cm. Then the correct option is C.

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The perimeter of the regular octagon with an apothem of 4 units will be 26.51 units.

All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.

P = (Side length) x n

The Apothem of a regular octagon is 5 units. Then the side length of the regular octagon is given as,

tan (360° / (2 × 8)) = (n/2) ÷ 4

tan 22.5° = n / 8

n = 3.3137

Then the perimeter is given as,

P = 8 x 3.3137

P = 26.51 units

The perimeter of the regular octagon with an apothem of 4 units will be 26.51 units.

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The following are solutions to the given problems given f(x)=x²- 5x+7 and g(x)=3x² + 4x - 2;

(f- g)(x) = -2x² - 9x + 9

(g-f)(x) = 2x² + 9x - 9

(f + g)(x) = 4 x² - x + 5

A function can be defined as a relation between a set of inputs having one output each. In other words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain (range). A function is generally denoted by f(x) where x is the input.

here, we have,

The general mathematical representation of a function is y = f(x).

f(x)=x²- 5x+7

g(x)=3x² + 4x - 2

so, we get,

(f- g)(x) = x²- 5x+7 - (3x² + 4x - 2)

(f- g)(x) = x²- 5x+7 - 3x² - 4x + 2

(f- g)(x) = -2x² - 9x + 9

(g-f)(x) = 3x² + 4x - 2 - (x²- 5x+7)

(g-f)(x) = 3x² + 4x - 2 - x² + 5x - 7

(g-f)(x) = 2x² + 9x - 9

(f + g)(x) = x²- 5x+7 + 3x² + 4x - 2

(f + g)(x) = 4 x² - x + 5

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(a) Each row represents a different individual and Each column represents a different variable or characteristic. (b) Identifying the relationship between different variables and the likelihood of a person having a heart attack, this problem can be solved using this data table.

(a) The table is organized into rows and columns. Each row represents a different individual and includes information about their age, gender, weight category, cholesterol level, marital status, stress level, and anxiety trait. Each column represents a different variable or characteristic, such as age, gender, weight category, etc. The rows and columns are used to organize the data and make it easier to read and understand.

(b) The problem that can be solved using this data table is identifying the relationship between different variables and the likelihood of a person having a heart attack. For example, the table can be used to determine if there is a correlation between age, gender, weight category, cholesterol level, marital status, stress level, and anxiety trait and the likelihood of a person having a heart attack.

(c) Decision table for the above table:

| Age | Gender | Weight Category | Cholesterol Level | Marital Status | Stress Level | Anxiety Trait | Heart Attack |
|-----|--------|-----------------|-------------------|----------------|--------------|---------------|--------------|
| 60  | Female | Overweight      | 150               | Yes            | High         | Yes           | Yes          |
| 69  | Male   | Overweight      | 170               | Yes            | Normal       | Yes           | Yes          |
| 52  | Female | Normal          | 174               | No             | High         | Yes           | No           |
| 66  | Male   | Overweight      | 169               | Yes            | Normal       | No            | Yes          |
| 70  | Female | Overweight      | 237               | Yes            | Normal       | No            | Yes          |
| 52  | Female | Normal          | 174               | No             | High         | Yes           | No           |
| 58  | Male   | Normal          | 140               | Yes            | Normal       | No            | No           |

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Therefore , expression problem solution is during the run, the adults covered a distance of 24 metres, and it took them 8 seconds to catch up to the children.

There is a need for mathematical operations like multiplying, splitting, combining, and now even deleting. If they were combined, it would be said that: A mathematical formula, some data, and an equation A declaration of truth is composed of values, elements, and mathematical operations like additions, subtractions, missteps, algebraic formulas, and divisions. It is possible to evaluate and analyse words and phrases.

Here,

Distance is determined by rate and duration.

for the distances that children and adults travel, two equations should be made up:

=> (d - 16) = 1t (for the youngsters) (for the kids)

=> d = 3t (for the males) (for the adults)

where "t" represents the amount of time that has elapsed since the competition began.

We can set the distances between the children and adults to be equal because we know that they were side-by-side at some time during the race:

=> d - 16 = 3t - 16

When we simplify this solution, we obtain:

=> d = 3t

When we add this to the prior solution, we obtain:

=> 3t - 16 = 1t

To solve for "t," we obtain:

=>  t = 8 sec.

Now that we know how far the grownups travelled:

D=3t=3x8=24 metres.

As a result, during the run, the adults covered a distance of 24 metres, and it took them 8 seconds to catch up to the children.

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The graphs when classified are decay and growth functions

The complete solution is shown below

A graph that represents an exponential growth would increase as the input value (x) increases, while graphs of exponential decay would decrease with increment in x

This means that:

An exponential function is represented as

y = abˣ

If b > 1, then it is a growth function, otherwise it is a decay function

This means that:

For the equation y = abˣ, we have

Initial value = a

Decay rate (if b < 0) = 1 - b

Growth rate (if b > 0) = b - 1

This means that

Function (12) is unclear

13. f(x) = 11(0.4)ˣ:

Initial value = 11

Decay factor = 0.4

Decay rate = 6%

14. f(x) = (1/4)ˣ:

Initial value = 1

Decay factor = 1/4

Decay rate = 75%

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The correct answer is d. 9.9498.

To find the standard deviation of a distribution, we use the formula:

Standard deviation = √[(∑(x - mean)2)/n]

First, we need to find the mean of the distribution. The mean is the sum of all the values divided by the number of values. In this case, the mean is:

mean = (35 + 250)/5 = 57

Next, we need to find the sum of the squared differences between each value and the mean. This is:

∑(x - mean)2 = (35 - 57)2 + (250 - 57)2 = 485 + 37249 = 37734

Finally, we divide this sum by the number of values and take the square root to get the standard deviation:

Standard deviation = √(37734/5) = √7546.8 = 9.9498

So the standard deviation of the distribution is 9.9498.

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The 6th term of the sequence is -97.65625

From the question, we have the following parameters that can be used in our computation:

A(n) = -2.5^(n-1)

In the sixth term, we have

n = 6

Substitute the known values in the above equation, so, we have the following representation

A(6) = -2.5^(6-1)

Evaluate

A(6) = -97.65625

Hence, the 6th term is -97.65625

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The area in square miles (rounded to the nearest integer) is:

area = 2,492 square miles.

Here we need to perform a change of units from acres to square miles. We know the relation:

1 square mile = 640 acres.

And we want to find the area of a park with 1,505,011 acres in square miles.

We can rewrite the relation above as:

1 acre = (1/604) square miles.

Then the area of the park will be:

Area = 1,505,011 acres  = 1,505,011*(1/604) square miles

Area = 2,491.74 square miles.

Rounding to the nearest integer we will get:

area = 2,492 square miles.

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The correct answer to this question is 7/220. To calculate this answer, divide the number of students who preferred the turkey club (7) by the total number of seventh-grade students (220). The fraction form of this answer is 7/220, the decimal form is 0.0318, and the percentage form is 3.18%.

Proportion is a mathematical concept that compares two values, which can be the same or different, using division. It is used to identify the relationship between two or more values. It can also be used to compare the parts of a whole or to compare two different wholes. Proportions can be expressed as a fraction, a decimal, or a percentage.

This answer can be used to estimate the number of students who preferred the turkey club. To do this, multiply the total number of seventh-grade students (220) by the proportion (7/220). This calculation results in 7 students. In other words, approximately 7 of the 220 seventh-grade students preferred the turkey club.

The proportion 7/220 can also be used to estimate the number of students who preferred the turkey club if the total number of seventh-grade students changes. For example, if the total number of seventh-grade students increases to 250, the estimated number of students who preferred the turkey club can be calculated by multiplying the new total (250) by the proportion (7/220). This calculation results in 8 students.

Therefore, the correct answer to the question is 7/220.

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For subspace (a.1) basis for Col(A) is the first four columns of A and dimension is 4. For (a.2) basis for Row(A) is the first four rows of A and dimension is 4. A basis for (a.3) Nul(A) is the set of vectors obtained by setting one free variable to 1 and the others to 0 and dimension is 7.

A basis for a subspace is a set of vectors that are linearly independent and span the subspace. The dimension of a subspace is the number of vectors in a basis for that subspace.

(a.1) Col(A) is the subspace of R^4 spanned by the columns of A. To find a basis for Col(A), we can reduce A to its reduced row echelon form (RREF) and find the columns of A that correspond to the pivot columns in the RREF. The RREF of A is:

1 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0

The pivot columns are the first four columns, so a basis for Col(A) is the first four columns of A:

{[1, 1, 1, 1], [1, 1, -1, -1], [1, -1, 1, -1], [1, -1, -1, 1]}

The dimension of Col(A) is the number of vectors in the basis, which is 4.

(a.2) Row(A) is the subspace of R^11 spanned by the rows of A. To find a basis for Row(A), we can reduce A to its RREF and find the nonzero rows. The RREF of A is the same as above, so a basis for Row(A) is the first four rows of A:

{[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 1, -3, 3, 0, 0]}

The dimension of Row(A) is the number of vectors in the basis, which is 4.

(a.3) Nul(A) is the subspace of R^11 consisting of all vectors x such that Ax = 0. To find a basis for Nul(A), we can reduce A to its RREF and find the solutions to the homogeneous equation Ax = 0. The RREF of A is the same as above, and the general solution to Ax = 0 is:

x1 = 0
x2 = 0
x3 = 0
x4 = 0
x5 = free
x6 = free
x7 = free
x8 = free
x9 = free
x10 = free
x11 = free

A basis for Nul(A) is the set of vectors obtained by setting one free variable to 1 and the others to 0:

{[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]}

The dimension of Nul(A) is the number of vectors in the basis, which is 7.

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Answer:

1+1= 2

Step-by-step explanation:

im a genuis

Answer:

Step-by-step explanation:

pamela:  j - 6 years = juri's age.

juri: j + 6 years.

sum of pamela and juri = 94 years.

  j +(j - 6) = 94

  2j - 6 = 94

  2j = 94 - 6

  2j = 88

  j = 44

juri age: 44years and pamela age: 44years - 6years = 38years.

The solutions to this 3x^(2)-4x=-2  are x=(2/3)+i*√(2/9) or x=(2/3)-i*√(2/9).

To solve this equation by completing the square, we need to first rearrange the equation and then complete the square for the x terms. Here are the steps:

1. Rearrange the equation:
3x^(2)-4x=-2 becomes 3x^(2)-4x+2=0

2. Divide the entire equation by the coefficient of the x^(2) term:
(3x^(2)-4x+2)/3=0/3 becomes x^(2)-(4/3)x+(2/3)=0

3. Complete the square by adding the square of half the coefficient of the x term to both sides of the equation:
x^(2)-(4/3)x+(2/3)+(4/3)^(2)/4=(4/3)^(2)/4 becomes x^(2)-(4/3)x+(4/9)=(4/3)^(2)/4-(2/3)

4. Simplify the right side of the equation:
(4/3)^(2)/4-(2/3)=(16/9)/4-(2/3)=(4/9)-(2/3)=(4/9)-(6/9)=-(2/9)

5. Factor the left side of the equation:
(x-(2/3))^(2)=-(2/9)

6. Take the square root of both sides of the equation:
x-(2/3)=+/-sqrt(-(2/9))

7. Solve for x:
x=(2/3)+/-sqrt(-(2/9)) becomes x=(2/3)+i*sqrt(2/9) or x=(2/3)-i*sqrt(2/9)

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The exponential function that is equivalent to the geometric sequence, aₙ = 9.5 × 5ⁿ is A. f(n) = (0.95)5ⁿ.

An exponential function is a mathematical function that calculates the exponential growth or decay of a data set.

There are two types of exponential functions: exponential growth and exponential decay.

The function f(x) = bx where b > 1 represents exponential growth function while f(x) = bx when 0 < b < 1, represents an exponential decay function.

Thus, the equivalent exponential function is Option A.

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Answer:

Yes they are similar since it is a regular shape

Yes, the red outer shape is a regular hexagon. the hexagons are similar. red outer shape is a regular hexagon can be seen as regular hezagon, whereby the hezagon are been considered to be similar.

NOTE; We can see that from the given two regular hexagon, all the interior angle are equal, hence the are similar.

A regular hexagon is a polygon with six equal sides and six equal angles. All the interior angles of a regular hexagon are 120 degrees, and the sum of all interior angles of a regular hexagon is 720 degrees. The regular hexagon is a highly symmetrical shape and is often used in geometry and design.

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1. HP price for Susie is R 282600 and David is R 179300

2. The difference between the total price paid by Susie and David  is R 103300

3. The interest that Susie and David have to pay as a percentage of the cash price​ is 117.38% and 37.92%

The HP price, also known as the hire purchase price, is the total amount that a buyer pays for a product when purchasing it through a hire purchase agreement.

It includes the cash price of the product plus any interest and fees charged by the lender.

Here we have

3.1.1, For Susie:

The cash price of the car is R 130000.

She pays a 10% deposit, which is:

= [10/100] × 130000 = R 13000

=> HP price =  the cash price - the deposit

=>  130000 -  13000 = R 117000

She will pay monthly installments of R 4600 for 3 years,

which is 36 months.

Therefore, the total amount she will pay is:

36 x 4600 = R 165600

Therefore, the total amount she will pay is R 165600

The HP price for Susie is,  

117000 + 165600 = R 282600

For David:

The cash price of the car is R 130000. He pays a 35% deposit, which is:

=> [ 35/100] × 130000 = R 45500

The HP price = 130000 - 45500 = 84500

He will pay monthly installments of R 3950 for 2 years, which is 24 months. Therefore, the total amount he will pay is:

24 × 3950 = 94800

The HP price for David is, therefore:

=> 84500 + 94800 = R 179300

3.1.2, The difference between the total price paid by Susie and by David  

=  282600 - 179300 = R 103300

3.1.3

For Susie:

The total interest she has to pay is the difference between the HP price and the cash price, which is:

=> 282600 - 130000 = R 152600

The interest rate as a percentage of the cash price is:

=> (152600/130000) × 100% = 117.38%

For David:

The total interest he has to pay is the difference between the HP price and the cash price, which is:

=> 179 300 - 130 000 = R 49 300

The interest rate as a percentage of the cash price is:

=> (49 300/130000) × 100% = 37.92%

Therefore,

1. HP price for Susie is R 282600 and David is R 179300

2. The difference between the total price paid by Susie and David  is R 103300

3. The interest that Susie and David have to pay as a percentage of the cash price​ is 117.38% and 37.92%

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I apologize, but it seems that the question is incomplete or has not been properly formatted. Please provide the full question and any additional details or context so that I can accurately and effectively answer it. Thank you.

The effective annual IRR (internal rate of return) is 8%. If the dollars invested and withdrawn and the inflation rate for the 19-year time span of the investment is 9% per year the inflation-free IRR is -0.92%.

To calculate this, we need to use the IRR formula: IRR = [Sum of cash flows / (-initial investment)]1/n - 1, where n is the number of periods.

a. To find the effective annual IRR earned on this investment, we can use the following formula:

0 = -10,000/(1+IRR) - 10,000/(1+IRR)^2 - 10,000/(1+IRR)^3 - 10,000/(1+IRR)^4 + 10,000/(1+IRR)^5 + 10,000(1-0.05)/(1+IRR)^6       + 10,000(1-0.05)^2/(1+IRR)^7 + ... + 10,000(1-0.05)^14/(1+IRR)^18

The effective annual IRR earned on this investment to the nearest percent is 8%.

b. To find the inflation-free IRR earned on this investment, we can use the following formula:

Inflation-free IRR = (1 + IRR)/(1 + inflation rate) - 1

Plugging in the values we found in part (a), we get:

Inflation-free IRR = (1 + 0.08)/(1 + 0.09) - 1 = -0.0092

So the inflation-free IRR earned on this investment is approximately -0.92%.

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we can reject the null hypothesis

Null Hypothesis (H₀): μ ≥ 50

Alternative Hypothesis (H₁): μ < 50

Assumptions:
- A normal distribution for the population of LCBO stores
- A random sample of 20 stores
- A significance level of 0.05

Critical-value approach:

First, calculate the test statistic using the formula:

Test statistic = (Sample Mean - Population Mean) / (Standard Deviation / √Sample Size)

= (41.3 - 50) / (12.2 / √20)

= -2.6

Then, compare this test statistic to the critical-value.

The critical-value is the value that divides the acceptance and rejection regions of the distribution. The critical-value for a two-tailed test with a significance level of 0.05 is ±1.96.

Since -2.6 is less than -1.96, the test statistic falls into the rejection region and we reject the null hypothesis.

p-value approach:

Calculate the p-value using the formula:

p-value = 1 - CDF(test statistic)

Where CDF is the cumulative distribution function.

= 1 - CDF(-2.6)

= 0.004

Since 0.004 is less than 0.05, we reject the null hypothesis.

In conclusion, based on the critical-value approach and the p-value approach, we can reject the null hypothesis and conclude that the population mean sales increase is less than 50 cases.

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The value οf the annuity after 120 depοsits is $1,059,780.64.

Cοmpοund interest is interest that is earned nοt οnly οn the principal amοunt but alsο οn any interest earned οn that principal amοunt οver time.

Tο determine the value οf the annuity, we can use the fοrmula fοr the future value οf an annuity:

[tex]A = P \times \dfrac{(1 + r/n)^{(nt)} - 1)}{(r/n)}[/tex]

where A is the future value οf the annuity, P is the mοnthly depοsit amοunt, r is the annual interest rate, n is the number οf times the interest is cοmpοunded per year, and t is the tοtal number οf depοsits.

In this case, P = $100, n = 2 (since interest is cοmpοunded semi-annually), t = 120, and r is the interest rate per year, sο we need tο find r. Tο dο this, we can use the fοrmula:

[tex]A = P\times (1 + r/n)^{(nt)[/tex]

where A is the future value of the annuity after t depοsits.

Substituting the given vaIues, we have:

[tex]\$100 \times (1 + r/2)^{(2\cdot120)[/tex] = A

SimpIifying, we get:

[tex](1 + r/2)^{240} = A/100[/tex]

Taking the natural lοgarithm of both sides, we get:

[tex]ln(1 + r/2)^{240} = ln(A/100)[/tex]

240*ln(1 + r/2) = ln(A/100)

ln(1 + r/2) = ln(A/100)/240

Solving for r, we get:

[tex]$r = 2 \times \frac{e^{(ln(A/100)}}{240) - 1}[/tex]

Substituting the given vaIues, we get:

r = 0.4902 or 49.02%

Now we can plug in all the values into the original fοrmula for the future value οf the annuity:

[tex]A = $100\times \dfrac{(1 + 0.4902/2)^{(2\cdot 120) - 1)}}{0.4902/2}[/tex]

SimpIifying, we get:

A = $1,059,780.64

Therefοre, the value οf the annuity after 120 depοsits is $1,059,780.64.

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Answer:

Let the base of the triangle and parallelogram be denoted by 'b' and their respective altitudes be denoted by 'h1' and 'h2'.

Given that the area of the triangle is equal to the area of the parallelogram, we have:

Area of triangle = (1/2)bh1 Area of parallelogram = b*h2

Since the areas are equal, we have:

(1/2)bh1 = b*h2

Simplifying the above equation, we get:

h1 = 2*h2

Substituting the given value of h2 as 100 m, we get:

h1 = 2*100 = 200 m

Therefore, the altitude of the triangle is 200 meters

The solution to the compound inequality 3u-2<=-14 or 4u+4<28 is u<=-4 or u<6.

A compound inequality is an equation that combines two inequalities with the word "and" or "or".

To solve a compound inequality, we need to solve each inequality separately and then combine the solutions.

For the compound inequality 3u-2<=-14 or 4u+4<28, we will solve each inequality separately.

First, we will solve 3u-2<=-14: 3u-2<=-14 3u<=-14+2 3u<=-12 u<=-4

Next, we will solve 4u+4<28:

4u+4<28 4u<28-4 4u<24 u<6

Now, we will combine the solutions.

Since the word "or" is used in the compound inequality, the solution is the union of the two solutions. This means that the solution is any value of u that satisfies either inequality.

The solution is u<=-4 or u<6. This can also be written in interval notation as (-∞,-4] U (-∞,6).

So, the solution to the compound inequality 3u-2<=-14 or 4u+4<28 is u<=-4 or u<6.

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The value of angle A and C is 68° respectively

The sum of angle In a triangle is 180°. This means that A+B+C = 180°.

An isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as havingat least two sides of equal length.

Since AB = BC, then the triangle is an isosceles triangle.

The sum of angle in a triangle is 180. This means that A+B+C = 180

Since AB = BC , then angle A = angle C

therefore , substitute C for A

C +B + C = 180

2C + 44 = 180

2C = 180-44

2C = 136

divide both sides by 2

C = 136/2

C = 68°

then A= C = 68°

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The augmented matrix for the given system of equations is [[-2, 5, 2, 0], [3, 4, -8, 6], [-6, -6, 3, 0]]

An augmented matrix is a matrix that includes the coefficients of the variables and the constants in a system of equations. Each row of the matrix corresponds to one equation, and each column corresponds to one variable or the constant.

To write the augmented matrix for the given system of equations, we can start by rearranging the equations so that the variables are on the left side and the constants are on the right side:

5x + 2z = 2
3x + 4y - 8z = -6
-6x + 6y - 3z = 0

Next, we can write the coefficients of the variables and the constants in a matrix, with each row corresponding to one equation:

[5, 0, 2, 2]
[3, 4, -8, -6]
[-6, 6, -3, 0]

Finally, we can combine these rows into a single matrix to get the augmented matrix:

[[-2, 5, 2, 0], [3, 4, -8, 6], [-6, -6, 3, 0]]

This is the augmented matrix for the given system of equations.

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The vectors v1 = {1,2,0}, v2 = {1,0,1}, and v3 = {1,a,4} are linearly independent if a = 8/3, t and  linearly dependent for a = 2, and linearly independent for a = 8/3.

For the vectors to be linearly independent, we need to check if the following system of equations has a unique solution:

c1v1 + c2v2 + c3v3 = 0

where c1, c2, c3 are constants, and 0 is the zero vector.

Substituting the given vectors, we get the following system of equations:

c1 + c2 + c3 = 0 (1)

2c1 + ac3 = 0 (2)

c2 + 4c3 = 0 (3)

If we can find values of a for which this system of equations has a non-trivial solution, then the vectors are linearly dependent. Otherwise, they are linearly independent.

To find such values of a, we need to solve the system of equations and find the conditions under which it has non-trivial solutions.

From equations (2) and (3), we get:

c2 = -4c3 (4)

2c1 + ac3 = 0 (5)

Substituting equations (1) and (4) into equation (5), we get:

2(-c2 - c3) + ac3 = 0

Simplifying, we get:

(-2 + a)c3 - 2c2 = 0

Substituting equation (4), we get:

(-2 + a)c3 + 8c3 = 0

Solving for c3, we get:

c3 = 0 if a = 2

c3 = 0 if a = 8/3

For a = 2, the system reduces to:

c1 + c2 = 0

2c1 = 0

c2 + 4c3 = 0

This system has a non-trivial solution: c1 = 0, c2 = 1, c3 = -1/4.

Therefore, the vectors are linearly dependent for a = 2.

For a = 8/3, the system reduces to:

c1 + c2 + c3 = 0

(8/3)c3 = 0

c2 + 4c3 = 0

This system has only the trivial solution: c1 = c2 = c3 = 0.

Therefore, the vectors are linearly independent for a = 8/3.

In summary, the given vectors are linearly dependent for a = 2, and linearly independent for a = 8/3.

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Answer:

x=6

My best attempt

Step-by-step explanation:

The ratio is 4:5.6 from top to bottom.

We have a ratio of x:8.4

We will make an equation.

4:5.6=x:8.4

Cross multiply:

5.6x=4x8.4

5.6x=33.6

Divide both sides by 5.6:

x=6

Answer:

B

Step-by-step explanation:

2 is hundred = 2x100

0 is tens =0x10

4 is unit =4 x 1

All numbers after the decimal point to the right are fractions

0 is tenth = 0/10 =0

1 is hundredth =1/100

7 is thousandth 7/1000

Now you can choose the right answer