Determine how long it will take for a principal amount of $1,500 to become double its initial value when deposited into an account paying interest at a rate of 13%, continuously compounded.

guys pls help

As per the given situation, when g(x) = k · f(x), and f(x) = 2x, the value of k is 2.5.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs, where each input is related to exactly one output. Functions are often represented using function notation.

To find k, we need to know the value of g(x) for a specific value of x. Let's say we want to find k when x = 3. Then:

g(3) = k · f(3)

g(3) = k · 2(3)

g(3) = k · 6

If we know the value of g(3), we can solve for k:

g(3) = 15

15 = k · 6

k = 15/6

k = 2.5

Therefore, when g(x) = k · f(x), and f(x) = 2x, the value of k is 2.5.

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Answer:

For the Box and Whisker Plot, these are the answers for all of the parts of the plot:

Minimum:  The minimum is the lower end of the whisker which is 2

Maximum: The maximum is the upper end of the whisker which is 16

Median: The median is the thick line you see that goes down through the box plot which is the number 8

First Quartile: The lower end line of the box plot which is 4

Third Quartile: Known as the Second Quartile, this is the upper end line of the box plot which is 14

Interquartile Range: The Interquartile Range is the numbers that starts from the First Quartile to the Third Quartile which is the numbers from 4 to 14

Therefore, the answers are 2, 16, 8, 4, 14, and 4-14. Hope this helps with your homework or assignment!

-5th Grade Honors Student who learned this yesterday

Answer:

(1600 + (3200π)/3) mm²

Step-by-step explanation:

1 cm = 10mm. (1cm)² = (10²)mm = 100mm²

area of rectangle = 2 X 8 = 16cm² = 1600mm²

radius of circle = 8cm.

area of full circle would be = π r² = π (8)² = 64π cm²

360° in full circle

area of triangular sector = (60/360) X (64π) = (32π)/3 cm² = (3200π)/3 mm²

total area = (1600 + (3200π)/3) mm²

The perimeter of the figure is 9k² + 13k - 8

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

The figure

The perimeter of the figure is the sum of the side lengths

Using the above as a guide, we have the following:

Perimeter = -k + k² - 2 + 2k² + 5k + 2 + k² - 2 - k + 5k² + 10k - 6

When the expression is evaluated, we have

Perimeter = 9k² + 13k - 8

Hence, the perimeter of the figure is 9k² + 13k - 8

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Answer:

30 wats due  to electrocorrespond period of time

Step-by-step explanation:

according to plan b ratio 89 quart to a million

Power usage over time can be approximated by a Riemann sum or computed exactly by integrating the function representing the power usage. For the given 10-hour data, the total power usage can be estimated by summing up the products of the power usage and time interval.

The power use of a customer over a 30-day period is given by a continuous function P = f(t), and we are asked to find the total number of kilowatt-hours used by the customer using Riemann sums and an exact formula.

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The coordinates of A′ for the dilation with a scale factor of 1.5 and center at the origin are (3, 6).

To find the coordinates of A′, we need to apply the dilation formula:
A′ = (1.5)(A - O) + O
Where O is the center of dilation, which in this case is the origin (0, 0).
Substituting the values we have:
A′ = (1.5)(2, 4 - 0, 0) + (0, 0)
A′ = (3, 6) + (0, 0)
A′ = (3, 6)
Therefore, the coordinates of A′ for the dilation with scale factor 1.5 and center at the origin are (3, 6).
To find the coordinates of A' for the dilation with a scale factor of 1.5 and center at the origin, follow these steps:
1. Identify the given point A(2, 4) and the scale factor 1.5.
2. The center of dilation is at the origin (0, 0).
3. Multiply the x-coordinate of point A by the scale factor: 2 * 1.5 = 3.
4. Multiply the y-coordinate of point A by the scale factor: 4 * 1.5 = 6.
5. The coordinates of A' after dilation are (3, 6).
So, the coordinates of A′ for the dilation with a scale factor of 1.5 and center at the origin are (3, 6).

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Monomials are algebraic expressions that consist of a single term, whereas binomials consist of two terms.A binomial is an algebraic expression that consists of two terms.

Monomials are algebraic expressions that consist of a single term, whereas binomials consist of two terms.A binomial is an algebraic expression that consists of two terms. These terms can be added or subtracted, and they may contain variables, constants, and exponents. Binomials are commonly used in algebra to represent equations, formulas, and functions.

Monomials:
- 9x²
- 7x
- ln x
- -3x³
- 2x
- x
- x³
- √x
- 18x14x
- √x
- 7x-1
- 1
- Sin (x)
- x³
- e*
- √x +y
- 3-x
Binomials:
- 18x14x + 14
- (x + 4)²
- - 3n+2y + 2x + 1
- x³-5
Here are the monomials and binomials from the given algebraic expressions:
Monomials:
- ln x
- x
- x³
- √x
- 1
- Sin(x)
- e*
- 3-x
Binomials:
- +9x²+7x-35
- -3x³ + 2x
- 18x¹⁴x + 14
- 7x-1
- x³-5
- (x + 4)²
- -3n+2y + 2x + 1
- √x + y

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The coordinates of the triangle after transformation are:

L′(1, −5), M′(1, 0), N′(2, −5)

There are different methods of transformation such as:

Translation

Rotation

Reflection

Dilation

Now, a rotation of 180 degrees counterclockwise about the origin is equivalent to the coordinate transformation given as (x, y) → ( −x, −y) . Meanwhile, a rotation of 270 degrees counterclockwise about the origin is equivalent to the coordinate transformation (x, y) → ( y, -x) .

Applying the rule for rotation of 180 degrees counterclockwise to the coordinates L(−1, 5), M(−1, 0), N(−2, 5) gives us:

L'(1, -5), M'(1, 0), N'(2, -5)

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Hourly growth rate parameter is 1.97%

Given,

A sample of 2,400 bacteria selected from this population reached the size of 2,489 bacteria in one and a half hours.

Let,

y = population after given time x

x = time of passage in hours

p = size of initial population

k = constant for growth rate

[tex]y = pe^{kx}[/tex]

Substitute the values of variables,

2489 = 2400 e^1.5k

1.03 = e^1.5k

Take Ln on both sides to remove the exponent,

ln(1.03) = ln(e^1.5k)

0.029 = 1.5k

k = 0.029/1.5

k = 0.0197

k = 1.97%

Thus with the help of exponent the hourly growth rate parameter can be found out.

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The length of h in the parallelogram is 17.0 units.

A parallelogram is a quadrilateral that has opposite sides equal to each

other and opposite sides parallel to each other.

Therefore, let's find the value of h in the parallelogram as follows:

Using Pythagoras's theorem,

c² = a² + b²

where

Therefore,

18² - 6² = h²

h² = 324 - 36

h = √288

h = 16.97

Therefore,

h = 17.0 units

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X must be equal to 0 for M to be singular.

For M to be singular, its determinant must be zero. So, we can set up the equation:

| 2 2 1 |

| 6 2 -x |

| 2 1 3 | = 0

Expanding the determinant along the first row, we get:

2 | 2 -x |

-6 | 1 3 | = 0

Multiplying the determinant of the 2x2 matrix by 2, we get:

4(-x - 3) - (-6)(2) = 0

Simplifying the left-hand side, we get:

-4x - 12 + 12 = 0

Solving for x, we get:

-4x = 0

x = 0

Therefore, X must be equal to 0 for M to be singular.

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Answer:

The given function h has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25, and we also know that h(8) = 19 and h(-2) = 2.

Since we know the range of h(x) is 1 ≤ h(x) ≤ 25, statement B cannot be true because it suggests a value of h(x) outside of this range.

Statement A suggests that h(8) = 21, which is outside the given range for h(x). Therefore, statement A cannot be true.

Statement C suggests that h(2) = 16, but we do not have any information about the value of h(x) at x = 2. Therefore, statement C may or may not be true.

Statement D suggests that h(13) = 18, but 13 is outside the domain of h(x). Therefore, statement D cannot be true.

Thus, the only statement that could be true for h is B. However, we cannot be certain that statement B is true without more information about the function h.

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Step-by-step explanation:

Jake hears that 60% of respondents to a recent People Magazine survey said that their favorite fast food restaurant was Taco Bell. Jake believes this is way too high, as Taco Bell just isn't that good.

An SRS of peoples' favorite fast food restaurants is conducted across multiple locations. Of the 1080 respondents, 670 say that their favorite fast food restaurant is Taco Bell.  Therefore, based on the hypothesis test, Jake does now not have enough evidence to finish that the People Magazine survey changed erroneously.

To conduct a hypothesis take a look at this situation, we can set up the following hypotheses:

Null Hypothesis (H0): The percentage of people who recall Taco Bell as their preferred speedy meal-eating place is 60% or better.

Alternative Hypothesis (H1): The share of those who recall Taco Bell as their favorite fast food restaurant is less than 60%.

We will use the binomial test to check those hypotheses. The importance level, alpha (α), is given as 0.10, which means that we need a 90% self-assurance degree for our test.

Let's calculate the p-value based on the furnished sample information and check it in opposition to our importance stage:

Sample length (n) = 1080

Number of respondents who selected Taco Bell (x) = 670

Assuming the null hypothesis is true (p = 0.6), the expected number of respondents choosing Taco Bell is n * p = 1080 * 0.6 = 648.

We can now use the binomial distribution to calculate the p-cost:

p-price = P(X ≤ x) = Σ(C(n, x) * p^x * (1-p)^(n-x)), in which Σ is the sum from 0 to x.

Calculating this sum for x = 670, we want to evaluate the p-fee against our importance stage.

Using statistical software programs or tables, we discover that the p-price is about 0.9995.

Since the p-value (0.9995) is greater than the importance degree (0.10), we fail to reject the null speculation. With this method, there isn't enough proof to conclude that the proportion of folks who don't forget Taco Bell as their favorite speedy meals eating place is less than 60%. Therefore, based on the given pattern, Jake does now not have enough evidence to finish that the People Magazine survey changed erroneously.

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The measures of angles 8 and 9 are given as follows:

m < 8 = m < 9 = 28.5º.

To obtain the angle measures, first we must consider that the sum of the measures of the internal angles of a triangle is of 180º.

Considering this, looking at the top triangle, we find the measure of angle 7 as follows:

m < 7 + 58 + 65 = 180

m < 7 = 180 - (58 + 65)

m < 7 = 57.

By the exterior angle theorem, an angle is supplementary with it's exterior angle, hence the measure of angle 6 is obtained as follows:

m < 6 = 180 - 57

m < 6 = 123º.

Triangle XWZ is an isosceles triangle, hence the measures of angles 8 and 9 are obtained as follows:

m < 8 + m < 9 + 123 = 180

m < 8 = m < 9 = (180 - 123)/2

m < 8 = m < 9 = 28.5º.

(isosceles triangle, these two angles have the same measure).

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Answer:

y = 5x - 6

Step-by-step explanation:

the equation of a line in gradient- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

here m = 5 , then

y = 5x + c ← is the partial equation

to find c substitute (3, 9 ) into the partial equation

9 = 5(3) + c = 15 + c ( subtract 15 from both sides )

- 6 = c

y = 5x - 6 ← equation of line

The equation of the straight line with gradient 5 that passes through (3,9) is y = 5x - 6.

To find the equation of a straight line with a given gradient, we can use the point-slope form of the equation: y - y1 = m(x - x1). In this case, the gradient is 5 and the given point is (3,9). Plugging in the values, we have:

y - 9 = 5(x - 3)

Expanding the equation, we get:

y - 9 = 5x - 15

Then, rearranging the equation to the form y = mx + c, we have

y = 5x - 6

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Answer (3x−2)(3x+2)^2

Step-by-step explanation:

The estimated total number of bears in 2002 will be 1060.

To estimate the population size, the mark-recapture formula is applied. This formula is used to determine the unknown population size. First, a selected sample from the population of bears has the number marked initially and the total population. The formula is: N = MC/R

In the given question,

M = 2008

C = 38

R = 72

So, N = (2008)(38)/72

= 76304/72

1059 which is estimated at 1060.

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Answer:

14

Step-by-step explanation:

angle 90° is opposite the side x. angle 45° is opposite side 7√2.

x/sin 90 = (7√2)/sin 45

multiply both sides by sin 90 (sin 90 is = 1).

x = (7√2)/sin 45

 = 14

Answer:

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

To write a linear function representing Xavier's gross income in terms of the number of hours he works, we need the slope and the y-intercept.

Let's assume that Xavier earns a constant hourly rate of $3 per hour.

The slope of the linear function represents the rate at which Xavier's income increases per hour worked. In this case, the slope is $3, as his earnings increase by $3 for every hour worked.

The y-intercept represents Xavier's income when he hasn't worked any hours. Since he earns $0 when he hasn't worked any hours, the y-intercept is 0.

Therefore, the linear function representing Xavier's gross income (G) in terms of the number of hours (x) he works can be written as:

G = 3x

This equation shows that Xavier's gross income is equal to $3 multiplied by the number of hours he works.

Mrs. Golden will not have any Fractional pieces of silver paper left over as the area of the bulletin board is exactly divisible by the area of each silver paper square.

To cover Mrs. Golden's bulletin board, we need to calculate the total area of the board and then divide it by the area of each silver paper square to get the total number of squares required.

The area of the bulletin board can be calculated by multiplying its length and width:

Area of bulletin board = 6.5 ft x 4 ft = 26 sq. ft.

Since the silver paper comes in 1 ft squares, the area of each square is 1 sq. ft.

Therefore, the total number of silver paper squares required to cover the bulletin board can be calculated by dividing the area of the bulletin board by the area of each square:

Total number of squares required = Area of bulletin board / Area of each square

= 26 sq. ft / 1 sq. ft

= 26 squares

So, Mrs. Golden will need 26 silver paper squares to cover her bulletin board.

As the area of the bulletin board is not exactly divisible by the area of each silver paper square, there will be some fractional pieces of silver paper left over. The leftover fractional area will be equal to the remainder obtained when the area of the bulletin board is divided by the area of each square. In this case, the remainder is 0 sq. ft since the area of the bulletin board is exactly divisible by the area of each square.

Therefore, Mrs. Golden will not have any fractional pieces of silver paper left over as the area of the bulletin board is exactly divisible by the area of each silver paper square.

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Answer:

[tex]y \leqslant x[/tex]

The number in the mathematical statemnent is 1 1/2

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

The sum of a number, 1/6 of that number, 2 1/2 that number, and 7 is 12 1/2

Represent the number with x

So, we have the following equation

x + x/6 + 5x/2 + 7 = 12 1/2

So, we have

x + x/6 + 5x/2 = 5 1/2

Multiply through by 6

This gives

6x + x + 15x = 33

Evaluate the like terms

22x = 33

Divide through by 22

So, we have

x = 33/22

This gives

x = 1 1/2

Hence, the number is 1 1/2

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The value of the number is 1.5

First, we have that;

Let the number be x

From the information given, we have that;

The sum of a number, 1/6 of that number, 2 1/2 that number, and 7 is 12 1/2. Find the number

This is represented as;

x + 1/6x + 5/2x + 7 = 25/2

find the LCM, we get;

42x + 7x + 105x + 294  /42 = 25/2

collect the like terms, we have;

154x + 294/42 = 25/2

cross multiply the values, we have;

(154x + 294) = 25 × 21

154x = 231

Divide both sides by the coefficient

x = 1. 5

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Hello

        S        a         T

2a + 6  /            /
          /             /       a + 17
        /             /
   V          a         U

you want ST = VU (it's good) and SV = TU (not good)

2a + 6 = a + 17

2a - a = 17 - 6

a = 9

The expected  of your  account to be worth when you retire at 67 years old is $1,118,473.61.

To calculate the future value of your savings account, we can use the formula for compound interest:

FV = PV * (1 + r/n)^(n*t)

Where:

FV = Future Value of the account

PV = Present Value of the account

r = Annual interest rate (as a decimal)

n = Number of times the interest is compounded per year

t = Number of years

In this case, the present value (PV) is zero because you haven't started saving yet. The interest rate (r) is 7% per year, or 0.07 as a decimal. You will be depositing $200 every 2 months, which means 6 times a year (n=6). You have 45 years until you retire (t=45), and want to find the future value (FV) of the account.

We can start by calculating the total number of deposits you will make:

45 years * 12 months/year / 2 months/deposit = 270 deposits

Each deposit will be for $200, so the total amount you will deposit is:

270 deposits * $200/deposit = $54,000

Now we can use the formula for compound interest to calculate the future value of the account:

FV = $0 * (1 + 0.07/6)^(645) + $54,000 * (1 + 0.07/6)^(645)

FV = $0 + $1,118,473.61

So, you can expect your savings account to be worth approximately $1,118,473.61 when you retire at 67 years old, assuming you make regular deposits of $200 every 2 months and earn an annual interest rate of 7%.

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The maximum area of the patio is, 450 feet²

Now, Lets remove the brackets from the function's expression

A(x) = -2x² + 60x

So we got the quadratic function and we have to find the x that corresponds to function's maximum. Let it be X max

As we know ,

X (max) = (X₁ + X₂)/2 ,

where X₁ and X₂ are the roots of the function A(x)

Lets find X₁ and X₂

x (60 - 2x) = 0

Hence, x₁ = 0  

And, 60 - 2X₂=0

x₂ = 30

So, X max= (0 + 30)/2 = 15

So A max= A(15) = 15 (60-2 x 15) = 15 (60 - 30) = 15 x 30 = 450 feet²

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Answer:

You will approximately have about 48,297.74

Step-by-step explanation:

The length FE in the circle is 6 units

The arc AE has a measure of 64 degrees

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

The circle

Given that the lengths from the center to either chords are equal

This means that

FE = 6 units

For the other circle, we have

BC = 58 degrees

AB = ED

The arc AE is calculated as

AE = 180 - BC - ED

Where

AB = ED = BC = 58 degrees

So, we have

AE = 180 - 58 - 58

Evaluate

AE = 64

Hence, the arc AE is 64 degrees

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