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Suppose that you deposit $6500 into a bank account that pays 4% annual interest compounded continuously. Assuming that you make no other deposits or withdrawals, how long will it take before your account balance reaches $10,000?


Round your answer to the nearest tenth.

In order to translate a figure 2 units right and 2 units down, these steps should be followed:

Initially, draw the original figure.

Subsequently, sketch a vector from the origin (0,0) leading towards the point (2,2). By doing so, you parallelly instigate defining an amount of how you desire to transform said figure.

Create a novel focal point by augmenting the vector to each central point within the pre-existing image. Hence, if the prime pictorial contains, for instance, points (x,y), then this fresh peak will exist as (x+2,y+2).

Interconnect aforementioned new points in accordance with the formation that is desirable for the translated rendering of the initial diagram.

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The formula for the variable r is r = √A/π

The subject of formula can be defined as the variable that is allowed to alone in an equation.

The variables is made to be written on one end of the equality sign.

It is also described as the variable that is worked out in an equation.

From the information given, we have that;

the formula for the area of the circular pool is;

A = πr²

Such that;

We then have;

r = √A/π

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Answer:

A

Step-by-step explanation:

sqrt 5 ( 4pi - 2pi) =   2 pi sqrt 5  for the numerator

then     2 pi sqrt (5)  / 3 sqrt (5)      the sqrt (5) 's cancel out and you have

          2pi / 3

Answer:

Step-by-step explanation:

picture?

The correct statements regarding the scatter plot are given as follows:

The scatter plot, as shown by the image given in the problem is a series of points of the data-set in the following format:

(SAT score, GPA).

There is a positive association between the data, as the line of best fit, which gives the best approximation between the SAT score and the GPA, and can be used to predict the GPA based on the SAT score, is increasing.

For a SAT score of 1700, an expected GPA is of about 3.1, considering the intersection of y = 3.1 with the line of fit when x = 1700.

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Answer:

These are all the 3D shapes ;cone, cylinders, cuboid,cubes, sphere, rectangular prism, pyramid

The Value of x in the equation x^2+2x=6 is 1.645 or -3.654.

Rearranging the Given equation and Putting all values on other side of Zero.

x^2+2x=6

x^2+2x-6=0 ____________(1)

It can be seen that we can not have the multiples that counts of 6 so that they have a subtraction value 2. therefore, Using the Quadratic Formula for the above equation,

x=(-b±√(b²-4ac))/(2a)  ___________(2)

where

a=1

b=2

c=-6

putting the values of a,b,c in the equation (2)

x=(-2±√(4²-4*1*(-6)))/(2*1)

x=(-2±2√7)/2

x=(-1±√7)/2

Solving the Values of x in simplified form, we get x=1.645 and -3.654.

Therefore, The Value of x in the equation x^2+2x=6 is 1.645 or -3.654.

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The total cost of SE Company's advertising campaign will be $14,436.23.

The first step is to calculate the cost of the half-page ad for one week:

65.5 column inches × $24.55 per column inch = $1604.025

Since the ad will run for nine weeks, the total cost of the campaign is:

$1604.025 × 9 = $14,436.225

Therefore, the total cost of SE Company's advertising campaign will be $14,436.23.

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The range is the difference between the maximum and minimum values in the data set. From the box plot, we can see that the maximum value is 52 and the minimum value is 16, so the range is:

Range = Maximum value - Minimum value

Range = 52 - 16

Range = 36

The IQR (interquartile range) is the difference between the first and third quartiles of the data set, which is represented by the length of the box in the box plot. From the box plot, we can see that the length of the box is:

Box length = Upper quartile - Lower quartile

Box length = 45 - 27

Box length = 18

Therefore, the range is 36, and the IQR is 18.

So the correct answer is:

The range is 36, and the IQR is 18.

Answer: 15 square units

Step-by-step explanation:

Area of a triangle is 1/2bh

x = b = 6

H=5

1/2(6)(5)

1/2(30)

Area = 15 square units

The necessary information to carry out the hypothesis are given below.

For carrying out a hypothesis examination on the information, we need to do the following steps:

Step 1: Express the null and alternative hypotheses

Step 2: Pick the pertinent measure of value and significance level

Step 3: Compute the test statistic

Step 4: Estimate the p-value

Step 5: Draw a conclusion and interpret the results

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The regression equation is:

y = 20.85 + 0.735 * x

Year Motor registration (000 nos.) No. of tyres sold (000 nos.)

2 62 65

3 65 70

4 48 53

5 53 73

6 60 68

7 68 60

8 60 8

9 9 10

10 65 82

11 72 62

12 62 80

13 40 52

(a) In order to ascertain the coefficient of correlation between the registration of the motor and the number of tires sold, we can apply the following formula:

r = Σ[(xi - x_mean)(yi - y_mean)] / √[Σ(xi - x_mean)^2 * Σ(yi - y_mean)^2].

To do this, we need to determine the mean values for the motor registration (x) and the number of tyres purchased (y).

[tex]x_m_e_a_n = (62 + 65 + 48 + 53 + 60 + 68 + 60 + 9 + 65 + 72 + 62 + 40) / 12 = 664 / 12 = 55.33\\y_m_e_a_n = (65 + 70 + 53 + 73 + 68 + 60 + 8 + 10 + 82 + 62 + 80 + 52) / 12 = 733 / 12 = 61.08[/tex]

Now, we can calculate the required sums for the correlation formula:

Σ(xi - x_mean) = -39

Σ(yi - y_mean) = -39

Σ(xi - x_mean)^2 =3543

Σ(yi - y_mean)^2 = 6649

Σ[(xi - x_mean)(yi - y_mean)] = 2604

Now, we can calculate the correlation coefficient:

r = 2604 / √(3543 * 6649) ≈ 0.556

(b) Interpret your result:

With a correlation coefficient, r, between -1 and 1 going up to 0.556, it shows up as a significant positive relationship.

So when the number of car registrations augments, the sales of tires will also go up.

(c) Test the significance of the result:

As the t-statistic is listed as 1.934, we can analyze it using the critical t-value from a t-distribution table which is around 2.228.

Consequently, since the t-statistic (1.934) is lower than the critical t-value (2.228), the correlation between them is not statistically significant at the 0.05 level.

(d) Compute the two regression coefficients:

The two regression coefficients can be calculated using the following formulas:

b1 = Σ[(xi - x_mean)(yi - y_mean)] / Σ(xi - x_mean)^2

b0 = y_mean - b1 * x_mean

Using the previously calculated values:

b1 = 2604 / 3543 ≈ 0.735

b0 = 61.08 - 0.735 * 55.33 ≈ 20.85

The regression equation is:

y = 20.85 + 0.735 * x

(e) Estimate the number of tyres to be sold when the expected motor registration is 92,000:

Using the regression equation, we can predict the number of tyres to be sold when the expected motor registration is 92,000 (92 in thousands):

y = 20.85 + 0.735 * 92 ≈ 87.81

We estimate that when the expected motor registration is 92,000, approximately 87,810 tyres will be sold.

It should be stated that the relationship was not considered to be statistically relevant so care is advised.

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According to the information, the interest earned on the annuity over the 20-year period is $78,066.89.

To find the value of the annuity, we can use the formula:

where:

In this case, PMT = $7,000, r = 6.5% per year compounded annually, and n = 20 years.

First, we need to convert the annual interest rate to a periodic interest rate. Since the interest is compounded annually, the periodic interest rate is the annual rate divided by the number of periods in a year:

i = r / m

where,
m = number of compounding periods per year.

In this case, since the interest is compounded annually, m = 1, so:

i = 6.5% / 1 = 0.065

Now we can plug in the values and solve for V:

V = $7,000 x [(1 + 0.065)^20 - 1] / 0.065

V = $218,066.89

Therefore, the value of the annuity is: $218,066.89.

To find the interest earned on the annuity over the 20-year period, we can subtract the total amount deposited from the total value of the annuity:

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Step-by-step explanation:

Notice how we have 3 relative extrema , this means our equation has a degree of 4.

Notice how at root 1, our graph bounces off the curve.

This means we have a multiplicity of 2 there so one of our roots are

[tex](x - 1) {}^{2} [/tex]

For roots -3, and 4, our graph just passes through the x axis so those are roots with a multiplicity of 1.

[tex](x + 3)[/tex]

[tex](x - 4)[/tex]

So our equation is

[tex]y = (x - 1) {}^{2} (x + 3 )(x - 4)[/tex]

The graph passes through(-1,-2) so let see if we need any constant

[tex] - 2 = a( - 2) {}^{2} (2)( - 5)[/tex]

[tex] - 2 = - 40a[/tex]

[tex] \frac{1}{20} = a[/tex]

So our equation now is

[tex] \frac{1}{20} (x - 1) {}^{2} (x + 3)(x - 4)[/tex]

The equation that best represents the graph is p(x) = (x + 3)(x - 4)(x - 1)²

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

The graph

On the graph, we have the following properties

So, the base equation of the function is

p(x) = a(x + 3)(x - 4)(x - 1)²

Set a = 1

So, we have

p(x) = (x + 3)(x - 4)(x - 1)²

Hence the function is p(x) = (x + 3)(x - 4)(x - 1)²

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The values of the composite functions are f(g(2)) = 5.5, h(f⁻¹(5)) = 1, x = 5 for f(h(x)) = 7, R(4) = 4 and k(x) = 2

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

The functions f(x), g(x) and h(x)

Solving the composite functions, we have

f(g(2)) = f(3) i.e. g(2) = 3

This gives

f(g(2)) = 5.5

Next, we have

h(f⁻¹(5))

Here, we have

f⁻¹(5) = 4

So, we have

h(f⁻¹(5)) = h(4)

Evaluate

h(f⁻¹(5)) = 1

Next, we have

f(h(x)) = 7

From the graph, we have

f(0) = 7

This means that

h(x) = 0

From the table, we have

h(5) = 0

This means that

x = 5 for f(h(x)) = 7

Evaluating R(x) at x = 4. we have

R(x) = 2f(x) - 3g(x) + h(x)

This means that

R(4) = 2f(4) - 3g(4) + h(4)

So, we have

R(4) = 2 * 9 - 3 * 5 + 1

R(4) = 4

Evaluating k(x) at x = 5. we have

k(x) = h⁻¹(g(f⁻¹(x)))

This means that

k(x) = h⁻¹(g(f⁻¹(5)))

From the graph, f⁻¹(5) = 4

So, we have

k(x) = h⁻¹(g(4))

Next, we have

g(4) = 5

So, we have

k(x) = h⁻¹(5)

From the table, we have

h⁻¹(5) = 2

This means that

k(x) = 2

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The correct answer is,

C. 60(x - 3) = 45x.

This equation is based on the information that the 45 expensive wood costs $3.00 more than the 60 cheap wood. In other words, if the price of the 60 cheap wood is x, the price of the 45 expensive wood is x + 3.

Since,  Algebra involves working with numbers, equations, and variables to solve real-world problems and understand abstract relationships.

Now, To solve this equation, we must use algebra and solve for x.

First, we multiply both sides of the equation by 4/5. This gives us:

48x + 36 = 45x

-36 = 3x

Finally, we divide left side of the equation by 3, giving us the final solution:

x = -12

Therefore, the price of the 60 cheap wood is $12, and the price of the 45 expensive wood is $15.

that is, 60 (x - 3) = 45x

This equation shows the correct relationship between the two types of wood that the contractor purchased.

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Answer:

We can use the transformations of the graph of y=1/x to graph the rational function r(x) = 2x-9/x-4.

First, we will shift the graph of y=1/x to the right by 4 units to get the graph of y=1/(x-4). Next, we will stretch the graph vertically by a factor of 2 to get the graph of y=2/(x-4). Finally, we will shift the graph down by 9 units to get the graph of r(x) = 2x-9/x-4.

The domain of r(x) is all real numbers except x=4, since that would make the denominator zero. The range of r(x) is also all real numbers except y=2, since that would make the numerator zero.

Here is a rough sketch of the graph of r(x), using the transformations:

| ----------

| / \

| / \

| -- --

| | |

-- -- -- -- -- -- -- -- -- -- -

| | |

| | |

| | |

| | |

| | |

| | |

x=4 y=2

Note: This graph is not to scale and is intended to show the general shape of the graph.

The solution is : The price per unit is $48, when 30 units are demanded.

Here, we have,

Since we have given that

At price of $12 per unit, the number of units demanded = 40 units

At price of $18 per unit, the number of units demanded = 25 units.

So, the coordinates would be

(40,12) and (25,18)

As we know that x- axis denoted the quantity demanded.

y-axis denoted the price per unit.

So, the slope would be

m = -2/5

So, the equation would be

5y + 2x = 140

So, if 30 units are demanded, the price per unit would be

y = $48

Hence, the price per unit is $48, when 30 units are demanded.

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complete question:

Suppose consumers will demand 40 units of a product when the price is $12 per unit and 25 units when the price is $18 each. Find the demand equation assuming that it is linear. Find the price per unit when 30 units are demanded.

The statements of description are true about function h as:

The horizontally compressed by a factor of 1/2.

The vertically shifted up 4 units.

The period of function h is half the period of the parent function.

The given function h(x) = -3cos(2x-π)+4 and compare it with the parent cosine function f(x) = cos(x).

First, let's look at the expression: -3cos(2x-π).

The factor of -3 represents a vertical compression by a factor of 3 from the parent function, which means the amplitude is three times smaller.

The argument 2x-π represents a horizontal compression by a factor of 2 and a phase shift to the right by π/2 units.

The period of the cosine function is 2π, but the period of -3cos(2x-pi) is π. Therefore, the period of h(x) = -3cos(2x-π)+4 is half that of the parent function.

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Answer:a

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is a A

The recursive formula is 5/6

You should know that a recursive formula is an equation used to describe a sequence in which terms are defined using one or more previous terms along with an initial condition.

The given parameters are

aₓ = a(n-1) + 2

Where aₓ = 2aₓ₋1

= 2*5(₃₋₁) = 5(3-1) + 2

= 10₂ = 10 + 2

Taking the log of both sides

Log₂10 - Log12 = 0

Dividing by 10 we have

10/12 = 5/6

therefore the recursive formula is  5/6

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Answer:

a. The mean of the data set is:

(146 + 153 + 155 + 160 + 161) / 5 = 155

b. The deviation from the mean for each data item is:

146 - 155 = -9

153 - 155 = -2

155 - 155 = 0

160 - 155 = 5

161 - 155 = 6

c. The sum of the deviations from the mean is:

-9 + (-2) + 0 + 5 + 6 = 0

Note that the sum of the deviations from the mean is always zero, since the positive deviations cancel out the negative deviations.

The value of the expression l/2 when l=50 is 25.

Given information:

The expression l/2 means "half of l".

The expression is l/2 where l is variable.

In this case, the value of l is given as 50. So to calculate the expression, you just need to substitute 50 for l in the expression and simplify:

If l = 50, then

l/2 = 50/2 = 25

Therefore, the value of the expression l/2 when l=50 is 25.

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a.) [tex]135 + 89 + \text{C} \geq 325[/tex]

[tex]224 + \text{C} \geq 325[/tex]

b.) [tex]224 + \text{C} \geq 325[/tex]

[tex]\text{C} \geq 325 - 224[/tex]

[tex]\text{C} \geq 101[/tex]

Answer:

v = 8.6

Step-by-step explanation:

The first step to solve for x in the equation v + 1.26 = 9.86​  is to isolate the variable (v) on one side of the equation.

Looking at the equation, this can be done by subtracting 1.26 from both sides of the equation.

Shown below:

v + 1.26 - 1.26 = 9.86​ - 1.26      

v  = 8.6

As a result, v = 8.6

xKavinsky

Answer:

Step-by-step explanation:

[tex]\mathrm{v + 1.26 = 9.86}[/tex]

Subtract -1.26 to both sides:-

[tex]\mathrm{v + 1.26-1.26 = 9.86-1.26}[/tex]

Simplify :-

[tex]\mathrm{v=8.6}[/tex]

_____________________

Hope this helps!

The area of the square given in the diagram is: 25 square units.

Pythagoras Theorem is defined as the way in which we find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

Using Pythagoras theorem, we can find the length of a side of the square:

AB = √(3² + 4²)

AB = √(9 + 16)

AB = √25

AB = 5

Area of a square is given by the formula:

A = side * side

Thus:

A = 5 * 5

A = 25

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$48.07 would be the monthly payments on the loan.

We must first determine the total amount of interest charged over the course of the 4-year term in order to determine the monthly payments on a basic interest add-on loan.

The formula for simple interest is:

I = P * r * t

where I is the interest charged, P is the principal (the amount borrowed), r is the annual interest rate as a decimal, and t is the time period in years.

In this case, P = $1,426.25, r = 0.1545 (15.45% expressed as a decimal), and t = 4 years. So, the total amount of interest charged is:

I = $1,426.25 * 0.1545 * 4

I = $881.25

Adding the interest to the principal, we get the total amount paid over the 4-year term:

Total amount = $1,426.25 + $881.25

Total amount = $2,307.50

We must divide the sum by the number of months left in the loan term in order to get the monthly installments. As the loan period is 4 years long, there are 48 months:

Monthly payment = Total amount / Number of months

Monthly payment = $2,307.50 / 48

Monthly payment = $48.07

Therefore, the monthly payments on the loan would be $48.07.

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The equation of the line in point-slope form that passes through (1, -7) and has a slope of -2/3 is y + 7 = -2/3(x-1). Correct option is B.

The point-slope form of a linear equation is given by:

y - y₁ = m(x - x₁)

where m is the slope of the line and (x₁, y₁) is a point on the line.

We are given a point (1, -7) that the line passes through and a slope of -2/3. Therefore, we can substitute these values into the point-slope form equation to obtain:

y - (-7) = (-2/3)(x - 1)

Simplifying this equation, we get:

y + 7 = (-2/3)x + (2/3)

Taking 2/3 common from right sides, we get:

y + 7 = -2/3(x-1)

Therefore, Correct option is B.

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