Annabella wants to make the most economical decision so she chose the 3-year car loan so that after the loan is paid off to be able to invest in a structured saving account if Anabella put $200 into a saving account each month with an annual interest rate of 3.2% interest compounded monthly how much money would she have in her account after 2 years ​

The value of trigonometry terms sin(2x) is 120/169 and cos(2x) is 119/169 and tan(2x) is 120/119.

According to the statement

We have given that the sin(x) = 5/13 , x in quadrant iii

And we have to Find the value of cos x using the following:

So, For this purpose, we know that the trigonometry terms are:

sin2(x) + cos2(x) = 1;  

or cos2(x) = 1-sin2(x)

And

cos2(x) = 1-(-5/13)2 =

cos2(x) = 144/169;  

We know that the

In quadrant III both the sin and cos are negative so

cos(x) = -12/13 (after taking square roots).

And

Then tan(x) = sin(x)/cos(x) = (-5/13)/(-12/13) = 5/12.

Now you can use the angle addition formulas to find sin(2x), cos(2x), and tan(2x).

Now

sin(x + x) = sinx * cosx + cosx * sinx

              = (-5/13)*(-12/13) + (-12/13)(-5/13) = 120/169

And

cos(x + x) = cosX * cos(x) - sinx*sinx

               = (-12/13)(-12/13) - (-5/13)(-5/13)

               =  119/169

So,

You could use the tan double angle formula, but it is easiest to use  

tan(2x) = sin(2x)/cos(2x)  = (120/169) / (119/169)

          = 120/119.

So, The value of trigonometry terms sin(2x) is 120/169 and cos(2x) is 119/169 and tan(2x) is 120/119.

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The solution of the given expression is:

(3*5)^6 = 11,390,625

Here we have an expression with an exponent, which is:

(3*5)^6

First, we can solve the thing inside the parenthesis is:

3*5 = 15

Replacing that we get:

(3*5)^6 = (15)^6

Now, the exponent 6 means that we need to multiply the number by itself 6 times, so we get:

(15)^6 = 15*15*15*15*15*15 = 11,390,625

Then we conclude that:

(3*5)^6 = 11,390,625

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Answer:

may be like this

its 32cm³

Answer:

66/65.

Step-by-step explanation:

22/5 / 13/3

Invert the divisor and multiply.

---> 22/5 * 3/13

= 66/ 65

Based on the given parameters, the value of the printer after 9 years is $3304

The given parameters about the exponential function are

Initial value, a = $7000

Depreciation rate, r = 8%

Time, t = 9

Exponential functions are different from linear functions, and they are calculated using the following exponential function

A = a *(1 - r)^t

To calculate the value in nine years, we have:

Substitute the known values in the above equation

A = 7000 * (1 - 8%)^9

Express 8% as decimal

A = 7000 * (1 - 0.08)^9

Evaluate the difference

A = 7000 * (0.92)^9

Evaluate the exponent

A = 7000 * 0.472

Evaluate the product

A = 3304

Hence, the value of the printer after 9 years is $3304

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Answer: 5040

Step-by-step explanation

We need to find how much it will depreciate each year based of of original cost.
8% of 7000
turn the percent into a decimal
.08
multiple .08 by the 7000
.08 * 7000 = 560

The printer depreciates 560 each year , to find the total for 9 years multiply by 9

560*9 =5040

Step-by-step explanation:

the coordinates of a midpoint are

x = (x1 + x2)/2

y = (y1 + y2)/2

with (x1, y1) and (x2, y2) being the endpoints.

so, our midpoint here is

((-7 + 3)/2, (3 + -7)/2) = (-4/2, -4/2) = (-2, -2)

Answer:

[tex]y-3=-\frac{1}{2}(x-2)[/tex]

Step-by-step explanation:

The slope is

[tex]\frac{6-3}{-4-2}=-\frac{1}{2}[/tex]

So, using the point (2,3), the equation is

[tex]y-3=-\frac{1}{2}(x-2)[/tex]

Answer:

3.11%

Step-by-step explanation:

4/128.6=0.0311

multiply by 100

3.11%

The numbers which are a part of the domain for the graph are: 6, 1 and 2.

The domain of a graph is a set of all possible input, x-values. Consequently, since the domain of the graph given ranges over intergers, 1 to 10, it follows that numbers which are part of the domain are; 6, 2, and 1.

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The domain of the ellipse is [-4. 6] and the range of the ellipse is [-4. 0]

The equation of the ellipse is given as:

4x^2 + 25y^2 – 8x + 100y + 4 = 0

Next, we plot the graph of the ellipse

See attachment for the graph of the ellipse

The domain

From the attached graph the minimum and the maximum values of x are:

Minimum = -4

Maximum = 6

So, the domain of the ellipse is [-4. 6]

The range

From the attached graph the minimum and the maximum values of y are:

Minimum = -4

Maximum = 0

So, the range of the ellipse is [-4. 0]

Hence the domain of the ellipse is [-4. 6] and the range of the ellipse is [-4. 0]

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A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.

In this exercise, you're required to plot a graph for the data (velocity and time) recorded for an object that is falling from rest.

Based on the graph for the data (see attachment), we can logically deduce the following points:

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Complete Question:

Plot a graph for the following data recorded for an object falling from rest

a. What kind of a curve did you obtain?

b. What is the relationship between the variables?

c. What do you expect the velocity to be after 4.5 s?

d. How much time is required for the object to attain a speed of 100 ft/s?

The five number summary can be calculated as follows:

lower quartile(Q₁) = 54 + 56 / 2 = 55

Median = 63.5

Upper quartile(Q₃) = 74

Maximum = 80

Interquartile range = Q₃ - Q₁ = 74 - 55 = 19

The five number summary can be found as follows;

48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80

minimum = 48

lower quartile(Q₁) = 54 + 56 / 2 = 55

The median is the middle number when the data is arranged in ascending or descending order.

Median = 63 + 64 / 2 = 127 / 2 = 63.5

Upper quartile(Q₃)= 74 + 74 / 2 = 148 / 2 = 74

Maximum = 80

Interquartile range = Q₃ - Q₁ = 74 - 55 = 19

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There are 10 common characteristics attributed to servant leadership: active listening, empathy, healing, awareness, persuasion, conceptualization, foresight, stewardship, commitment to the growth of people, and community-building.

A Scrum Master is a servant-leader whose focus is on the needs of the team members and those they serve (the customer), with the goal of achieving results in line with the organization's values, principles, and business objectives.

1.  Active listening: Active listening is the practice of preparing to listen, observing what verbal and non-verbal messages are being sent.

2.  Empathy:  the ability to understand and share the feelings of another.

3.  Healing:  the process of making or becoming sound or healthy again.

4.  Awareness:  knowledge or perception of a situation or fact.

5.  Persuasion:  A belief or set of beliefs, especially religious or political ones.

6.  Conceptualization:  The action or process of forming a concept or idea of something.

7. Foresight: The ability to predict or the action of predicting what will happen or be needed in the future.

8. stewardship: The job of supervising or taking care of something, such as an organization or property.

9. Commitment: The state or quality of being dedicated to a cause, activity, etc.

10. Community-building: Community building is a field of practices directed toward the creation or enhancement of community among individuals within a regional area or with a common need or interest.

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Since [tex]a_1,a_2,a_3,\cdots[/tex] are in arithmetic progression,

[tex]a_2 = a_1 + 2[/tex]

[tex]a_3 = a_2 + 2 = a_1 + 2\cdot2[/tex]

[tex]a_4 = a_3+2 = a_1+3\cdot2[/tex]

[tex]\cdots \implies a_n = a_1 + 2(n-1)[/tex]

and since [tex]b_1,b_2,b_3,\cdots[/tex] are in geometric progression,

[tex]b_2 = 2b_1[/tex]

[tex]b_3=2b_2 = 2^2 b_1[/tex]

[tex]b_4=2b_3=2^3b_1[/tex]

[tex]\cdots\implies b_n=2^{n-1}b_1[/tex]

Recall that

[tex]\displaystyle \sum_{k=1}^n 1 = \underbrace{1+1+1+\cdots+1}_{n\,\rm times} = n[/tex]

[tex]\displaystyle \sum_{k=1}^n k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]

It follows that

[tex]a_1 + a_2 + \cdots + a_n = \displaystyle \sum_{k=1}^n (a_1 + 2(k-1)) \\\\ ~~~~~~~~ = a_1 \sum_{k=1}^n 1 + 2 \sum_{k=1}^n (k-1) \\\\ ~~~~~~~~ = a_1 n +  n(n-1)[/tex]

so the left side is

[tex]2(a_1+a_2+\cdots+a_n) = 2c n + 2n(n-1) = 2n^2 + 2(c-1)n[/tex]

Also recall that

[tex]\displaystyle \sum_{k=1}^n ar^{k-1} = \frac{a(1-r^n)}{1-r}[/tex]

so that the right side is

[tex]b_1 + b_2 + \cdots + b_n = \displaystyle \sum_{k=1}^n 2^{k-1}b_1 = c(2^n-1)[/tex]

Solve for [tex]c[/tex].

[tex]2n^2 + 2(c-1)n = c(2^n-1) \implies c = \dfrac{2n^2 - 2n}{2^n - 2n - 1} = \dfrac{2n(n-1)}{2^n - 2n - 1}[/tex]

Now, the numerator increases more slowly than the denominator, since

[tex]\dfrac{d}{dn}(2n(n-1)) = 4n - 2[/tex]

[tex]\dfrac{d}{dn} (2^n-2n-1) = \ln(2)\cdot2^n - 2[/tex]

and for [tex]n\ge5[/tex],

[tex]2^n > \dfrac4{\ln(2)} n \implies \ln(2)\cdot2^n - 2 > 4n - 2[/tex]

This means we only need to check if the claim is true for any [tex]n\in\{1,2,3,4\}[/tex].

[tex]n=1[/tex] doesn't work, since that makes [tex]c=0[/tex].

If [tex]n=2[/tex], then

[tex]c = \dfrac{4}{2^2 - 4 - 1} = \dfrac4{-1} = -4 < 0[/tex]

If [tex]n=3[/tex], then

[tex]c = \dfrac{12}{2^3 - 6 - 1} = 12[/tex]

If [tex]n=4[/tex], then

[tex]c = \dfrac{24}{2^4 - 8 - 1} = \dfrac{24}7 \not\in\Bbb N[/tex]

There is only one value for which the claim is true, [tex]c=12[/tex].

Answer:

8/11

Step-by-step explanation:

In the given scenario was cannot calculate P(B) directly. As it depends on what happened first, by itself we don’t know what was drawn first. Thus it becomes a conditional probability question:

P( B | A ) ← reads as the probability of “B” happening “given that” “A” has already happened — in this case the probability that the second marble drawn is a blue marble given that the first was a red marble.

The amount of money that you will have to save to buy a car at the $9,500 price is $556.11 ($9,500 - $8,943.89).

The amount of money needed can be determined by calculating the future value of $7,500 invested at 4.5% for 4 years.

Then, the result, which is the future value, $8,943.89, is deducted from the $9,500 price, to determine the additional savings required.

The future value of an investment can be calculated using the future value formula, A = P (1 + i)^n.

Where:

A = future value

P = Present value of investment

i = interest rate

n = number of periods.

The future value can also be determined using an online finance calculator, as follows.

N (# of periods) = 4 years

I/Y (Interest per year) = 4.5%

PV (Present Value) = $7,500

PMT (Periodic Payment) = $0

Results:

FV = $8,943.89

Total Interest = $1,443.89

Thus, the amount of money that you will have to save to buy a car at the $9,500 price is $556.11.

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The solutions to the quadratic equation -t² + 7t = 0 are 7 and 0.

Hence, x = 7, 0.

Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;

ax² + bx + c = 0

Where x is the unknown

To solve for x, we use the quadratic formula

x = (-b±√(b² - 4ac)) / (2a)

Given the equation;

-t² + 7t = 0

Comparing with the standard form.

We substitute into the quadratic formula.

x = (-b±√(b² - 4ac)) / (2a)

x = (-7±√( (7)² - ( 4 × -1 × 0) ) / (2 × -1)

x = (-7±√( 49 - 0) ) / (-2)

x = (-7±√49 ) / (-2)

x = (-7±7 ) / (-2)

x = (-7-7 ) / (-2), (-7+7 ) / (-2)

x = -14/(-2), 0/(-2)

x = 7, 0

The solutions to the quadratic equation -t² + 7t = 0 are 7 and 0.

Hence, x = 7, 0.

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The value of expression 9/9/3-6/10-6/10 is 9/5.

Given an expression 9/9/3-6/10-6/10.

We are required to simplify the expression 9/9/3-6/0-6/10.

Expression is combination of numbers,fraction, coefficients, determinants,indeterminants, symbols.It is mostly not found in equal to form. It also includes algebraic operations also.

Expressions: 9/9/3-6/10-6/10

This is present in fraction which is combination of two numbers one is numerator and denominator. The numbers above division sign are known as numerator and the numbers below division sign are known as denominator.

Invert the fraction which is given in denominator.

=(9*3)/9-6/10-6/10

=27/9-6/10-6/10

Taking LCM now.

=(270-54-54)/90

=(270-108)/90

=162/90

=9/5

Hence the value of expression 9/9/3-6/10-6/10 is 9/5.

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The minimum value of f(8) - f(3) is 20.

The maximum value of f(8) - f(3) is 25.

In the question, we are given that, 4 ≤ f'(x) ≤ 5 for all values of x.

Taking the given inequality as (i).

We are asked to find the minimum and maximum possible values of f(8) - f(3).

We multiply (i) by dx throughout, to get:

4dx ≤ f'(x)dx ≤ 5dx.

To find this, we integrate (i) in the definite interval [8, 3] with respect to dx, to get:

[tex]\int_{3}^{8}4dx \leq \int_{3}^{8}f'(x)dx \leq \int_{3}^{8}5dx\\\Rightarrow [4x]_{3}^{8} \leq [f(x)]_{3}^{8} \leq [5x]_{3}^{8}\\\Rightarrow 4*8 - 4*3 \leq f(8)-f(3) \leq 5*8 - 5*3\\\Rightarrow 20 \leq f(8) -f(3) \leq 25[/tex]

Thus, the minimum value of f(8) - f(3) is 20.

The maximum value of f(8) - f(3) is 25.

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Answer: Step 1

Step-by-step explanation: The order of operations states that multiplication must be done before addition. However, in step 1, 3x3-2 turns into 3x1 which is wrong. It should be 9-2 because you need to do the multiplication first.

Using a quadratic regression equation, it is found that the prediction of y when x = 6 is of -154.70.

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, we have that the function initially increases, then it decreases, which means that it is a quadratic function. The points (x,y) to  be inserted into the calculator are given as follows:

(-1, -2.75), (0, 2.15), (1, -1.60), (2, -13.85), (3, -34.55).

Inserting these points into the calculator, the prediction of y for a value of x is given as follows:

y = -4.721428571x² + 1.482857143x + 3.201428571

Hence, when x = 6, the prediction is:

y = -4.721428571 x 6² + 1.482857143 x 6 + 3.201428571

y = -154.70

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The cofactors of each entry in the first row of the matrix exist

[tex]$$Ac_{11 }= -13[/tex]

[tex]Ac_{12} = 44[/tex]

[tex]Ac_{13} = 27[/tex]

We have to estimate the cofactors of each entry in the first row of the matrix.

A set of numbers exists arranged in rows and columns to create a rectangular array. The numbers exist named the elements, or entries, of the matrix.

Thus the cofactors of each entry in the first row of the matrix exist

[tex]$$Ac_{11 }= -13[/tex]

[tex]Ac_{12} = 44[/tex]

[tex]Ac_{13} = 27[/tex]

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An inequality greater than (-3) but less than or equal to 3 is as follows:

- 3 < x ≤ 3

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.

An inequality have the following signs:

Therefore, an inequality greater than (-3) but less than or equal to 3 can be represented as follows:

Note the value we are comparing is x.

Hence,

- 3 < x ≤ 3

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The original price of the laptop is calculated as $545

We are given;

Sales Price of Laptop = $299.75

Now, the laptop is on sale for 45% off regular price.

If original price is x, then we can express that;

(100% - 45%) * x = 299.75

Thus;

55%x = 299.75

0.55x = 299.75

x = 299.75/0.55

x = $545

Thus, the original price of the laptop is calculated as $545

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Answer:

Step-by-step explanation: I did the test and the answer should be A

hope this helps :)