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a) The price (amount) of the house after 1 month = $9540

b) The price (amount) of the house after 3 months  = $10719.14

c) The price (amount) of the house after 10 months = $16117.629

a ) How to find the rental price of the house after 1 month ?

The rental price of a dacha = Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 1

Amount of a compound interest is given by,

 \(Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100}) \\\\= 9000(\frac{106}{100})\\\\= 90*106\\\\= 9540\)

The rental price of the house after 1 month = $9540

b ) How to find the rental price of the house after 3 months ?

The rental price of a dacha = Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 3

Amount of a compound interest is given by,

 \(Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^3 \\\\= 9000(\frac{106}{100})^3\\\\= 9000*(1.06)^3\\\\= 10719.14\)

The rental price of the house after 3 months = $10719.14

c ) How to find the rental price of the house after 10 months ?

The rental price of a dacha =Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 10

Amount of a compound interest is given by,

 \(Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^{10} \\\\= 9000(\frac{106}{100})^{10}\\\\= 9000*(1.06)^{10}\\\\= 9000*1.790\\\\= 16117.629\)

The rental price of the house after 10 months = $16117.629

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Chris would choose not to buy any Red Bulls if their price exceeds his willingness to pay based on his utility function and budget constraints.

(a) The tangency condition for optimal consumption occurs when the marginal rate of substitution (MRS) equals the price ratio. In this case, the MRS is the ratio of the marginal utility of chocolate bars (MUc) to the marginal utility of Red Bulls (MUr), and the price ratio is the ratio of the price of chocolate bars (pc) to the price of Red Bulls (pr). Therefore, the tangency condition is MUc / MUr = pc / pr.

(b) The demand function for chocolate bars can be derived by solving the tangency condition. Rearranging the equation from part (a), we have MUc / pc = MUr / pr. Since MUc is the derivative of the utility function with respect to chocolate bars (c), we can set this equal to the price ratio and solve for c. The resulting demand function for chocolate bars is c = (pc / pr) * r.

(c) Similarly, the demand function for Red Bulls can be derived by rearranging the tangency condition. Since MUr is the derivative of the utility function with respect to Red Bulls (r), we set this equal to the price ratio and solve for r. The resulting demand function for Red Bulls is r = (pr / pc) * ln(m / pc).

(d) Chris would choose not to buy any Red Bulls if their price (pr) exceeds his willingness to pay based on his utility function and budget constraints. In other words, if the price of Red Bulls is such that the utility derived from consuming them is less than or equal to the utility he could obtain from other goods or saving the money, he would choose not to purchase any Red Bulls.

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Answer:

2.5 x 60

Step-by-step explanation:

im pretty sure thats how you get your answer

Answer:

Step-by-step explanation:

\( speed=\frac{2.5 \:miles}{\frac{1}{3}hour}=2.5\times 3 = 7.5 miles/hour \)

The population will reach 15,000 after approximately 156.24 minutes.

To find the initial size of the culture, we can use the exponential growth formula:

\(N = N0 * e^(rt)\)

Where:

N = final count after a certain time

N0 = initial count

r = growth rate

t = time in minutes

e = Euler's number (approximately 2.71828)

We are given two data points:

At 20 minutes: N = 900

At 35 minutes: N = 1100

Using these points, we can set up two equations:

\(900 = N0 * e^(20r) ---(1)\)

\(1100 = N0 * e^(35r) ---(2)\)

To solve this system of equations, we can divide equation (2) by equation (1):

\(1100 / 900 = (N0 * e^(35r)) / (N0 * e^(20r))\)

Simplifying:

\(1.2222 = e^(35r) / e^(20r)\)

\(e^(a - b) = e^a / e^b:\)

\(1.2222 = e^((35-20)r)\)

Taking the natural logarithm (ln) of both sides:

\(ln(1.2222) = ln(e^((35-20)r))\)

ln(1.2222) = (35-20)r

Now we can solve for r:

r = ln(1.2222) / 15

Using a calculator, we find:

r ≈ 0.0461

Now we can substitute the value of r into equation (1) to find N0:

\(900 = N0 * e^(20 * 0.0461)\)

\(N0 = 900 / e^(0.922)\)

N0 ≈ 697.86

Therefore, the initial size of the culture was approximately 697.86.

To find the doubling period, we can use the formula:

doubling period = ln(2) / r

doubling period = ln(2) / 0.0461

Using a calculator, we find:

doubling period ≈ 15.03 minutes

Therefore, the doubling period is approximately 15.03 minutes.To find the population after 60 minutes, we can use the formula:

\(N = N0 * e^(rt)\)

\(N = 697.86 * e^(0.0461 * 60)\)

Using a calculator, we find:

N ≈ 1579.83

Therefore, the population after 60 minutes is approximately 1579.83.

To find when the population will reach 15,000, we can rearrange the formula:

\(N = N0 * e^(rt)\)

15,000 = N0 \(* e^(0.0461 * t)\)

Dividing both sides by N0 and taking the natural logarithm:

ln(15,000/N0) = 0.0461 * t

Now we can solve for t:

t = ln(15,000/N0) / 0.0461

Substituting the value of N0 we found earlier:

t = ln(15,000/697.86) / 0.0461

Using a calculator, we find:

t ≈ 156.24 minutes

Therefore, the population will reach 15,000 after approximately 156.24 minutes.

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To determine where the function f(x) = ln(2 + sin(x)) is concave up, we need to find the second derivative of the function and then determine where the second derivative is positive.

First, we find the first derivative of f(x):

f'(x) = cos(x) / (2 + sin(x))

Then, we find the second derivative of f(x):

f''(x) = [(-sin(x))(2 + sin(x)) - (cos(x))^2] / (2 + sin(x))^2

Simplifying this expression, we get:

f''(x) = [-sin(x)^2 - cos(x)^2 - 2sin(x)cos(x)] / (2 + sin(x))^2

f''(x) = [-1 - sin(2x)] / (2 + sin(x))^2

Now, to find where f''(x) is positive, we need to solve the inequality:

f''(x) > 0

[-1 - sin(2x)] / (2 + sin(x))^2 > 0

The denominator is always positive, so we only need to consider the numerator. We can solve the inequality by considering two cases:

Case 1: -1 < sin(2x) < 0

In this case, the numerator is negative, so the inequality cannot hold. Therefore, there are no solutions in this case.

Case 2: sin(2x) < -1

In this case, sin(2x) is negative and less than -1, which means that 2x is in the third or fourth quadrant. The solutions are given by:

π/2 < x < 3π/4

5π/2 < x < 11π/4

Note that these intervals are within the given domain of the function, 0 ≤ x ≤ 2.

Therefore, the interval on which f(x) = ln(2 + sin(x)) is concave up is:

(π/2, 3π/4) U (5π/2, 11π/4)

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Rewrite the root expressions as fractional exponents:

\(\dfrac{\sqrt[3]{7}}{\sqrt[5]{7}} = \dfrac{7^{1/3}}{7^{1/5}}\)

Recall that \(\frac{a^m}{a^n} = a^{m-n}\), so that

\(\dfrac{7^{1/3}}{7^{1/5}} = 7^{1/3 - 1/5}\)

Simplify the exponent:

\(\dfrac13 - \dfrac15 = \dfrac5{15} - \dfrac3{15} = \dfrac{5-3}{15} = \dfrac2{15}\)

Then you end up with

\(\dfrac{\sqrt[3]{7}}{\sqrt[5]{7}} = 7^{2/15}\)

At this point, it is unlikely that we can find a closed-form solution for x, so we may have to resort to numerical methods or approximations.

We can start by simplifying each side of the equation using trigonometric identities:

Left side:

cosec(x)sin(x) = 1/sin(x) * sin(x) = 1

Right side:

cos(x)cot(3x-50) = cos(x) (cos(3x-50) / sin(3x-50))

= cos(x) cos(3x-50) / sin(3x-50)

= (cos(x) cos(3x) + cos(x) sin(50)) / (sin(3x) cos(50) - cos(3x) sin(50))

= (cos(x) cos(3x) + cos(x) sin(50)) / (sin(3x - 50))

So the equation becomes:

1 = (cos(x) cos(3x) + cos(x) sin(50)) / (sin(3x - 50))

Multiplying both sides by sin(3x - 50), we get:

sin(3x - 50) = cos(x) cos(3x) + cos(x) sin(50)

Expanding the right side using the product-to-sum formula, we have:

sin(3x - 50) = cos(x) (cos(3x) + sin(50))

Dividing both sides by cos(x) (which is nonzero since cosec(x) is defined), we get:

sin(3x - 50) / cos(x) = cos(3x) + sin(50)

Using the identity tan(a) = sin(a)/cos(a), we can write:

tan(3x - 50 + 90°) = cos(3x) + sin(50)

Simplifying the left side using the angle addition formula for tangent, we get:

tan(3x + 40°) = cos(3x) + sin(50)

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Answer:

Step-by-step explanation:

Given,

7+5(x-3)=27+5(x−3)=22

(Taking one of the equation)

=> 7 + 5(x - 3) = 22

=> 7 + 5x - 15 = 22

=> 5x = 22 + 15 - 7

=> 5x = 30

\( = > x = \frac{30}{5} \)

=> x = 6 (Option c)

Answer:

Solve the equation for x:

Correct choice is c

If 14 inches of wire cost 42 cents, with 21 cents can be bought  7 inch of wire

Information about the problem:

Calculating how much 1 inch cost, we have:

1 inch cost= Inches bought cost  / Inches bought

1 inch cost= 42 cents / 14 inches

1 inch cost= 3 cent/inch

Calculating how much can be bought with 21 cents:

Inches of wire= Amount / 1 inch cost

Inches of wire= 21 cent / 3 cent/inch

Inches of wire= 7 inch

Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.

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Answer:

one hosta=$6

one ornamental grass=$10

Step-by-step explanation:

6 10?

6*6+3*10

36+30

66

12*6+8*10

72+80=152

Answer:

$ 375 / month

Step-by-step explanation:

$ 18 000 / 48 months = 375 /month

The minimum amount he should save per month to achieve his goal is $375.00. Thus, option 2 is correct.

Given that:

Number of months = 48

Monthly savings = $18,000

The minimum amount to save per month can be calculated by dividing the total amount by the number of months:

Minimum monthly savings goal = Total amount to save / Number of months

Minimum monthly savings goal = $18,000 / 48

Minimum monthly savings goal ≈ $375.00

Therefore, the minimum amount he should save per month to achieve his goal is $375.00. Thus, option 2 is correct.

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For the first loan, the final payment is $1,576.25. For the second loan, the final payment is $0. The calculations consider the given interest rates and compounding periods.



To determine the final payment for the first loan, we need to calculate the accumulated value of the loan after six years. For the first year, interest is compounded quarterly at a rate of 10% per annum. The accumulated value after one year is $10,000 * (1 + 0.10/4)^(4*1) = $10,000 * (1 + 0.025)^4 = $10,000 * 1.1038125.For the next three years, interest is compounded semi-annually at a rate of 8% per annum. The accumulated value after four years is $10,000 * (1 + 0.08/2)^(2*4) = $10,000 * (1 + 0.04)^8 = $10,000 * 1.3604877.

Finally, for the remaining two years, interest is compounded annually at a rate of 7.5% per annum. The accumulated value after six years is $10,000 * (1 + 0.075)^2 = $10,000 * 1.157625.To find the final payment, we subtract the payments made so far ($5,000 and $6,000) from the accumulated value after six years: $10,000 * 1.157625 - $5,000 - $6,000 = $1,576.25.For the second loan, we calculate the accumulated value after six years using the given interest rates and compounding periods for each period. The accumulated value after two years is $5,000 * (1 + 0.09/4)^(4*2) = $5,000 * (1 + 0.0225)^8 = $5,000 * 1.208646.

The accumulated value after four years is $5,000 * (1 + 0.10/12)^(12*2) = $5,000 * (1 + 0.0083333)^24 = $5,000 * 1.221494.Finally, the accumulated value after six years is $5,000 * (1 + 0.10)^2 = $5,000 * 1.21.To find the final payment, we subtract the payments made so far ($2,500 and $2,500) from the accumulated value after six years: $5,000 * 1.21 - $2,500 - $2,500 = $0.

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Answer:

The answer is 13.6

a^2+b^2=c^2

so 13^2+4^=c^2

169+16=c^2

square root of 185 is 13.6

so the answer is 13.6 or 14 if you round

Answer:

1.6

Step-by-step explanation:

12.8/8 = 1.6

15.2/9.5 = 1.6

Scale factor = 1.6

Answer:

Around 73.68

Step-by-step explanation:

Write it as an equation

OF= multiplication (in this scenario)

IS= equal sign

14=.19x

Isolate x

x= Approx 73.68

Answer:

Anything from 0.31 - 0.34 rounds to 0.3

The equation of the line that passes through (-6,-13) and is parallel to the x-axis is y = -13.

A line parallel to the x-axis has a slope of 0 because it does not change in the vertical direction. The general equation of a line is y = mx + b, where m represents the slope and b represents the y-intercept.

Since the line is parallel to the x-axis, its slope is 0. Therefore, the equation becomes y = 0x + b, which simplifies to y = b.

To find the value of b, we can substitute the coordinates of the given point (-6,-13) into the equation. Plugging in x = -6 and y = -13, we get -13 = b.

Hence, the equation of the line that passes through (-6,-13) and is parallel to the x-axis is y = -13. This equation indicates that regardless of the value of x, the y-coordinate will always be -13, creating a horizontal line parallel to the x-axis.

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Answer:

61

Step-by-step explanation:

Let's see what to do buddy...

_________________________________

KJI = KJR + RJI

So :

172° = ( 6x -5 )° + ( 12x -3 )°

172° = 18x - 8°

Subtract the sides of the equation plus 8°

180° = 18x

Divided the sides of the equation by 18

x = 180/18

x = 10°

_________________________________

So we have :

KJR = 6x -5 = 6(10) - 5 = 60 - 5 = 55°

KJR = 55°

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

Answer:

Step-by-step explanation:

H(3,2)  & J(4, 1)

\(Slope = \dfrac{y_{2} -y_{1}}{x_{2}-x_{1}}\\\\=\dfrac{1-2}{4-3}\\\\\\=\dfrac{-1}{1}\\\\= -1\)

K(-2,-4)  & M(-1 , -5)

\(Slope =\dfrac{-5-[-4]}{-1-[-2]}\\\\=\dfrac{-5+4}{-1+2}\\\\= \dfrac{-1}{1}\\\\\\= -1\)

Line HJ and KM have same slopes. So, they are parallel

Answer:

3x-7y

Step-by-step explanation:

9x^2 - 49y^2

find the square root of a values

=3x-7y

Answer: b + 24 = 68

Step-by-step explanation:

we are told the zoo has 68 different species of birds so the equation will be = 28. The answers showing = 24 are already wrong.

transported means they are taken away, so we have to subtract 24 (animals that stayed in the zoo) to find b which are the remaining species moved to the barn.

b + 24 = 68
  -  24    -24

b = 44 (transported to the barn)
     24 ( stayed in the zoo)
    68 ( total number of species of birds)

The correct expression to show the species of transported birds will be;

⇒ b + 24 = 68

Where, b is the number of transported birds.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Total number of birds in Roaring Zoo = 68

Number of stayed birds in Zoo = 24

Let number of transported birds = b

Then, We can formulate;

Total number of birds = Stayed birds + Transported birds

Substitute all the values, we get;

⇒ 68 = 24 + b

Therefore,

The correct expression to show the species of transported birds will be;

⇒ b + 24 = 68

Where, b is the number of transported birds.

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A. The compound amount of $1,200 at 4.5% compounded quarterly for 10 years is approximately $1,810.52.

B. To find the compound amount, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the compound amount

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times interest is compounded per year

t = the number of years

In this case, the principal amount is $1,200, the annual interest rate is 4.5% (or 0.045 as a decimal), interest is compounded quarterly (n = 4), and the time period is 10 years.

Substituting these values into the formula:

A = 1200(1 + 0.045/4)^(4*10)

Simplifying the equation:

A = 1200(1 + 0.01125)^40

A = 1200(1.01125)^40

A ≈ 1200(1.551029)

A ≈ $1,810.52

Therefore, the compound amount of $1,200 at 4.5% compounded quarterly for 10 years is approximately $1,810.52.

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We have to find the value of  `(sinθ+cosθ−tanθ)/(secθ+cscθ−cotθ)`

Let's find all trigonometric ratios:

We can say that:

\($$\tan \theta= \frac{opp}{adj}= \frac{-4}{3}$$$$\text\)

{Using the Pythagorean Theorem we can find the hypotenuse }

\($$$$\text{Hypotenuse = } \sqrt{(-4)^2+(3)^2}\)

\(= \sqrt{16+9}\)

= \(\sqrt{25}\)

=\(5$$$$\)

Substituting the values of sinθ, cosθ and tanθ in `

\(= \frac{\frac{3}{5} + \frac{-4}{5} - \frac{-4}{3}}{\frac{-4}{5} + \frac{5}{3} - \frac{-3}{4}}$$$$\)

\(=\frac{\frac{9}{15} + \frac{-12}{15} + \frac{20}{15}}{\frac{-16}{20} + \frac{25}{12} + \frac{3}{4}}$$$$\)

\(=\frac{\frac{17}{15}}{\frac{-14}{15}}$$$$\)

\(=-\frac{17}{14}$$\)

Therefore, \(`(sinθ+cosθ−tanθ)/(secθ+cscθ−cotθ)\)` is equal to

`-17/14` when `tanθ=−43` (Quadrant II).

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Dividing two polynomials may produce another polynomial only when the divisor has a lower degree than the dividend. Otherwise, it will generally result in a rational function.

No, dividing two polynomials may not result in another polynomial. It can produce a rational function.

A polynomial is an algebraic expression consisting of terms with non-negative integer exponents. When two polynomials are divided, the result is not always a polynomial.

If the degree of the polynomial being divided (dividend) is higher than the degree of the polynomial dividing (divisor), then the result can be a polynomial with a lower degree. However, if the degree of the divisor is equal to or greater than the degree of the dividend, the result will generally be a rational function, which is a ratio of two polynomials.

A rational function has the form P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) is not equal to zero. The division can introduce terms with negative or fractional exponents, making the result a rational function rather than a polynomial.

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The remainder of the polynomial using the remainder theorem and factor theorem is 6.

Apply the remainder theorem,

When we divide a polynomial

f(x) by (x − c)

f(x) = (x − c)q(x) + r

f(c) = 0 + r

Here,

f(x)=(x−c)q(x)+rf(c)=0+r

and (x−c) is (x−(−2))

Therefore,

f(−2) = \((-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2\)

= 16 + 8 − 12 − 8 + 2

= 6

Hence, the remainder of the polynomial using the remainder theorem is 6.

Whereas using the factor theorem and doing synthetic division, we get,  

x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide

the coefficients of the polynomial as follows -

         -2   |   1  -1    -3     4      2

                      -2   6    -6      4

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

                    1   -3   3    -2     6

Hence, we get that 6 is the remainder when (\(x^4-x^3-3x^2+4x+2\)) ÷ (x+2), using the factor theorem.

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The complete question is -

Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, \(x^4-x^3-3x^2+4x+2\) ÷ (x+2)

Answer:

its 24

Step-by-step explanation:

because it is the biggest answer and its bigger than the other variable

Considering the situation described, the classification of the elections is given as follows, according to their order of finish:

David, Greg, Victor, Mac, Bill.

We take the situation that is described, and build the classification from it. The classification has the following format:

P1 - P2 - P3 - P4 - P5

With P1 being the first placed candidate, P2 being the second placed candidate, and so on until P5 which is the fifth placed candidate.

From the text given in this problem, we have that:

Hence the classification of the election is given by:

David, Greg, Victor, Mac, Bill.

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Answer

I believe B.)8in3 is the right answer according to the square-cube law.

Step-by-step explanation:

Answer:

horizontal shift 1 unit left

vertical shift  down two units

Domain of graph g is x≥ -1 or [-1,∞)

Range y ≥ -2 [-2,∞)

minimum (-1,-2)

2- h(x)=√x+3 is horizontally translation to the left and not the right it has to be √x-3.

3- f(1)= 4*1 = 4  y1

 f(4)= 4*4 =16    y2

step 2 : f(4)-f(1)/4-1 = y2-y1/x2-x1 = 16-4/4-1=12/3=4

the average rate of f(x)=√4x is 4