helpFind the fourth derivative of f(x) = 2 + In (2) - 179x Enclose arguments of functions in parentheses For example, sin (2x).

Answer:

(2,14)

Step-by-step explanation:

so i solved this with substitution but there are other methods to solve this!

equation 1 : y = -x + 16
equation 2 : y = x + 12

solve for y in equation 1 !!
y = -x + 16
(add x on both sides)
y + x = 16
(subtract y on both sides)
x = -y + 16

equation 1 now equals : x = -y + 16

substitute equation 1 into equation 2 :)

y = (-y + 16) + 12
(add 16 + 12)
y = -y + 28
(add y on both sides)

2y = 28
(divide 2 on both sides)
y = 14

now to solve for x you can insert y !
you can use equation 1 or equation 2 to solve for x.

i'm using equation 2 :
y = x + 12
(14) = x + 12
(subtract 12 on both sides)
x = 2

therefore, the answer is (2, 14).

hope this helps :p

Answer:

3/1 or 3

Step-by-step explanation:

It rises up three and to the side one

Answer: The slope is 3.

The number of different orders of top-three finishers in the free throw contest depends on the total number of participants. The specific number of participants is not provided in the given information.

To determine the number of different orders of top-three finishers, we need to know the total number of participants in the free throw contest. The order of finishers can be calculated using the concept of permutations, where the order matters.

If there are "n" participants, the number of different orders of top-three finishers can be calculated using the formula nP3, which represents the number of permutations of "n" objects taken 3 at a time. However, since the total number of participants is not provided in the given information, we cannot determine the exact number of different orders of top-three finishers.

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Answer:

40 feet

Step-by-step explanation:

4+4+8+4+12+8

= 40 ft.

Answer:

The random variable in given problem is "x" . The possible values of random variable x are 0,1,2 and 3..

All possible values of random variable is numrical in nature.

We have a table to right lists probabilities for the corresponding number of girls in three live births.

from the table we cleary see that the random variable is x which represents the number of girls in three live births.

Random variable is a variable whose value is unknown or a variable which assigns a numerical value to each trials in Sample Space.

Also, we can see in list that the number of girls in three live birth values are 0, 1 ,2 and 3 ( 3 live birth)

So, the possible values of random variable x is 4 i.e., 0, 1, 2 and 3..

From data we get a result that all possible values of random variable and it's probabilities are numrical in nature.

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Answer:

Step-by-step explanation:

Equation representing the relationship between the calories from Protein and fat is,

6p + 9f = 60

1). A). If p = 5 grams  and f = 2 grams,

        Number of calories = (6×5) + (9×2)

                                         = 30 + 18

                                         = 48 calories

  B). If p = 10.5 grams  and f = 2 grams,

        Number of calories = (6×10.5) + (9×2)

                                         = 63 + 18

                                         = 81 calories

  C). If p = 8 grams and f = 4 grams

        Number of calories = (6×8) + (9×4)

                                         = 48 + 36

                                         = 84 calories

(2). If f = 6 grams, then we have to calculate the grams of protein from the given equation.

    4p + (9×6) = 60

    4p + 54 = 60

    4p = 60 - 54

    p = \(\frac{6}{4}=1.5\) grams

(3). Combination of 6 grams of fat and 1.5 grams of protein in a snack gives 60 calories of energy.

The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.

First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17

Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40

Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65

Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92

Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.

The present value of the dividends can be calculated as follows:

PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)

where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:

PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)

PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5

PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59

PV ≈ $16.22

Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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Answer: x = -3/13.

Step-by-step explanation: Start by subtracting 3x from both sides of the equation to isolate the x terms on one side:

16x + 6 - 3x = 3x + 3 - 3x

Simplifying the equation:

13x + 6 = 3

Next, subtract 6 from both sides of the equation:

13x + 6 - 6 = 3 - 6

Simplifying the equation:

13x = -3

Finally, divide both sides of the equation by 13 to solve for x:

(13x)/13 = (-3)/13

Simplifying the equation:

x = -3/13

First, we use the method of reduction of order to find the general solution of the differential equation.

Given that y1(x) = e^x is a solution of the above equation, we want to find another solution y2(x) of the form y2(x) = u(x)e^x, where u(x) is an unknown function of x. We obtain the first and second derivatives of y2(x) as follows: y2(x) = u(x)e^x

dy2/dx = (u'(x) + u(x))e^x d²y2/dx² = (u''(x) + 2u'(x) + u(x))e^x.

Substituting y1(x) = e^x, y2(x), and their first two derivatives into the differential equation (2 - x)d³y/dx³ + (2x - 3)d²y/dx² - xdy/dx + y = 0, we get: (2 - x)[(u''(x) + 2u'(x) + u(x))e^x] + (2x - 3)[(u'(x) + u(x))e^x] - x[u(x)e^x] + u(x)e^x = 0.

Expanding the brackets and collecting like terms, we get: [u''(x) + (2 - x)u'(x) + (2x - 3)u(x)]e^x = 0.Since e^x ≠ 0 for all x, we can divide both sides by e^x to get: u''(x) + (2 - x)u'(x) + (2x - 3)u(x) = 0. This is a second-order linear homogeneous ordinary differential equation with variable coefficients, which we can solve using the method of undetermined coefficients.

We guess that u(x) = Ax + B, where A and B are constants to be determined. We obtain the first and second derivatives of u(x) as follows: u'(x) = A, u''(x) = 0. Substituting u(x), u'(x), and u''(x) into the differential equation, we get: 0 + (2 - x)A + (2x - 3)(Ax + B) = 0. Expanding the brackets and collecting like terms, we get: (2A - A)x + (4B - 3A) = 0. Equating the coefficients of x and the constant terms to zero, we get the following system of linear equations: 2A - A = 0, 4B - 3A = 0. Solving for A and B, we get: A = 0, B = 0. Therefore, u(x) = 0, and the general solution of the differential equation is: yh(x) = C1e^x. Now, we consider the inhomogeneous ordinary differential equation (2 - x)d³y/dx³ + (2x - 3)d²y/dx² - xdy/dx + y = (x - 2)², x < 2. We first find the general solution of the corresponding homogeneous equation, which is given by yh(x) = C1e^x. We then use the method of variation of parameters to find a particular solution yp(x) of the inhomogeneous equation of the form yp(x) = u1(x)e^x + u2(x)xe^x + u3(x)x²e^x, where u1(x), u2(x), and u3(x) are unknown functions of x to be determined. We obtain the first derivatives of u1(x), u2(x), and u3(x) as follows: du1/dx = -[p₂(x)y₂(x) + p₃(x)y₃(x)]yp/dx + f(x)/W(y1,y2,y3) du2/dx = [p₁(x)y₁(x) + p₃(x)y₃(x)]yp/dx - x f(x)/W(y1,y2,y3) du3/dx = -[p₁(x)y₁(x) + p₂(x)y₂(x)]yp/dx + x²f(x)/W(y1,y2,y3),

where p₁(x) = (2 - x),

p₂(x) = (2x - 3), p₃(x) = -x, and W(y1,y2,y3) is the Wronskian of

y1(x) = e^x, y2(x), and y3(x).

The Wronskian is given by W(y1,y2,y3) = e^x[y2(x)x² - y3(x)x + y3(x) - y2(x)]. Substituting y1(x) = e^x,

y2(x) = xe^x,

y3(x) = x²e^x,

and f(x) = (x - 2)² into the above equations, we get:

du1/dx = -(2 - x)xe^x(x²e^x)² + (x - 2)²/[(xe^x)

(x²e^x - x²e^x)] = -(2 - x)x(x²e^x) + (x - 2)²/

[x³e^x] du2/dx = (2x - 3)x²e^x(x²e^x)² - x(x - 2)²/[(e^x)

(x²e^x - x²e^x)] = (2x - 3)x²(x²e^x) - (x - 2)²/[xe^x] du3/dx = -x²e^xxe^x(x - 2)² + (x - 2)²/[e^x(x²e^x - xe^x)] = -x²(x - 2)² + (x - 2)²/[x(x - 1)].

Therefore, the first-order derivatives of u1(x), u2(x), and u3(x) are given by: du1/dx = -x³e^x(2 - x) + (x - 2)²/[x³e^x] du2/dx = 2x³e^x(2x - 3) - (x - 2)²/[xe^x] du3/dx = -(x - 2)² + (x - 2)²/[x(x - 1)].

Integrating these equations with respect to x, we get: u1(x) = (x - 2)³/6 - x² + C1 u2(x) = (x - 2)²/2 + x³ - C2

u3(x) = -x² + x - 2 + C3,

where C1, C2, and C3 are constants of integration. Therefore,

the particular solution of the inhomogeneous equation is given by: yp(x) = (x - 2)³/6 - x² + C1e^x + (x - 2)²/2 + x³ - C2xe^x - x² + x - 2 + C3x²e^x = (x - 2)³/6 + (x - 2)²/2 + x³ + (C1 - C2)x + (C3 - 1)x² - x²e^x.

Therefore, the general solution of the inhomogeneous equation is given by: y(x) = yh(x) + yp(x) = C1e^x + (x - 2)³/6 + (x - 2)²/2 + x³ + (C1 - C2)x + (C3 - 1)x² - x²e^x.

We are given the third-order linear homogeneous ordinary differential equation with variable coefficients as(2-x) d³y/dx³+ (2x-3). d²y/dy - x dy/dx +y=0, x < 2.

We are to find the general solution using the method of reduction of order. Given that y₁(x) = e^x is a solution of the above equation, we want to find another solution y₂(x) of the form y2(x) = u(x)e^x, where u(x) is an unknown function of x. We obtain the first and second derivatives of y2(x) as follows:y2(x) = u(x)e^x.

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Answer:

the answer is the product of 3 and 4 because 3x is a multipulcation problem

a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

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Answer:

84%

Step-by-step explanation:

2940+560=3,500

\(\frac{2940*100}{3500} =\)\(\frac{84}{100}\)

=84%

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

Answer:

(-1.732,0) and (1.732,0)

Step-by-step explanation:

Ignore f(x). The solutions are also called x-intercepts and zeros. So the solutions would be where the parabola crosses the x axis. In my answer ignore the 0 in the coordinates. Just put in the -1.732 and 1.732.

The algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y). (Option D)

A dilation is a type of transformation that changes the size of the shape or object.  It refers to a process of changing an object’s size by decreasing or increasing its dimensions by a scaling factor. A dilation produces an image that has the same shape as the original image but is a different size.

A dilation that results in a larger image is called an enlargement while a dilation that generates a smaller image is called a reduction. A dilation is described using the scale factor and the center of the dilation (which is a fixed point in the plane).

For a scale factor > 1, the image is an enlargement; for a scale factor < 1 and  > 0, the image is a reduction; and for a scale factor = 1, the figure and the image are congruent. Hence, for a point (x,y), algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y) as the scale factor is greater than 1. For the remaining options, the scale factor is between 0 and 1, hence they are reduction.

Note: The question is incomplete. The complete question probably is: Which of the following algebraic representation shows a dilation that is an enlargement? A) (1/3 x,1/3 y) B) (0.1x, 0.1y) C) (5/6 x,5/6 y) D) (5/2 x,5/2 y)

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Answer:

172.2 = 250.5

Step-by-step explanation:

6³− 43.5 = 250.5

Follow PEMDAS (Parenthesis Exponents Multiplication Division Addition Subtraction)

216 − 43.5 = 250.5

172.2 = 250.5

Answer:

The answer is false.

6³− 43.5 ≠ 250.5

6³− 43.5 = 172.5

Step-by-step explanation:

I hope this helps.

The probability of selecting a human character randomly in the game is \(\frac{1}{3}\)

The probability that a human character will be chosen when the player selects a character randomly can be calculated by dividing the number of human characters by the total number of available characters.

There are 8 animal characters and 4 human characters, making a total of 12 characters to choose from. Therefore, the probability of selecting a human character randomly is:

P(Human) = Number of human characters / Total number of characters

P(Human) = 4 / 12

Simplifying this fraction, we find:

P(Human) = 1 / 3

Therefore, the probability of selecting a human character randomly is 1/3 or approximately 0.333.

In the given scenario, there are a total of 8 animal characters and 4 human characters, making a total of 12 characters to choose from. When a player selects a character randomly, each character has an equal chance of being chosen. Since there are 4 human characters, the probability of selecting one of them is determined by dividing the number of human characters (4) by the total number of characters (12).

When we simplify the fraction 4/12, we find that it is equal to 1/3.

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Answer:

None of them but for the actual question on the picture it is x < -3

Step-by-step explanation:

Answer:

the x-coordinate and y-coordinate change places.

Step-by-step explanation: so you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).

The equation, (x - 10)² + (y - 5)² = 144, represents a circle with center (10, 5) and radius 12.

From the question, we are to determine the center and radius of the circle represented by the given equation

From the given information, the given equation is

(x - 10)² + (y - 5)²= 144

To determine the center and the radius of the circle we will compare the given equation to the standard form of the equation of a circle:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

The equation

(x - 10)² + (y - 5)²= 144

can be written as

(x - 10)² + (y - 5)²= 12²

By comparison,

h = 10, k = 5 and r = 12

Hence, the center of the circle is (10, 5) and the radius is 12

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Answer:

There are 17 natural numbers divisible.

There are 17 natural numbers between 150 and 300 that are divisible by 9.

To find the number of natural numbers between 150 and 300 that are divisible by 9, we need to find the count of multiples of 9 within this range.

The first multiple of 9 greater than or equal to 150 is 153 (9 x 17), and the last multiple of 9 less than or equal to 300 is 297 (9 x 33).

Now, we can calculate the number of multiples of 9 between 153 and 297 (inclusive):

Number of multiples of 9 = (Last multiple - First multiple) / 9 + 1

Number of multiples of 9 = (297 - 153) / 9 + 1

Number of multiples of 9 = 144 / 9 + 1

Number of multiples of 9 = 16 + 1

Number of multiples of 9 = 17

So, there are 17 natural numbers between 150 and 300 that are divisible by 9.

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The correct answers are: The test is statistically significant. We have observed something unusual if the null hypothesis is true. The other statements are not necessarily true on the given p-value of 1.5%.

Based on the information provided, we can determine the following:

The test is statistically significant: A p-value of 1.5% indicates that the observed result is unlikely to have occurred by chance, given the null hypothesis.

We have observed something unusual if the null hypothesis is true: A small p-value suggests that the observed data is unlikely to be a result of random chance, which implies that the data is unusual if the null hypothesis is true.

The null hypothesis is not necessarily false: The p-value alone does not provide direct information about the truth or falsehood of the null hypothesis. It only indicates the level of evidence against the null hypothesis.

The alternative hypothesis is not necessarily true: Similarly, the p-value does not provide evidence for the alternative hypothesis being true. It only indicates the strength of evidence against the null hypothesis.

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a) The effective rate of interest on a mortgage at 8.15 percent compounded semi-annually is 8.23 percent.

b) It will take approximately 54.4 years to save $1,000,000 for retirement with $200 monthly deposits at 6 percent interest compounded monthly.

a) To find the effective rate of interest, we use the formula: Effective Rate = (1 + (Nominal Rate / Number of Compounding Periods))^Number of Compounding Periods - 1.

For a mortgage at 8.15 percent compounded semi-annually, the nominal rate is 8.15 percent and the number of compounding periods is 2 per year.

Plugging these values into the formula, we get Effective Rate = (1 + (0.0815 / 2))^2 - 1 ≈ 0.0823, or 8.23 percent. Therefore, the effective rate of interest on the mortgage is 8.23 percent.

b) To determine how long it will take to save $1,000,000 for retirement with $200 monthly deposits at 6 percent interest compounded monthly, we can use the formula for the future value of an ordinary annuity: FV = P * ((1 + r)^n - 1) / r, where FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of periods.

Rearranging the formula to solve for n, we have n = log(FV * r / P + 1) / log(1 + r). Plugging in the values $1,000,000 for FV, $200 for P, and 6 percent divided by 12 for r, we get n = log(1,000,000 * (0.06/12) / 200 + 1) / log(1 + (0.06/12)) ≈ 54.4 years.

Therefore, it will take approximately 54.4 years to save $1,000,000 for retirement under these conditions.

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Answer:

Correct, good job!

Step-by-step explanation:

45% of $450:

$450 × 0.45 = $202.50

Add the 45% of $450 to $450

$202.50 + $450 = $652.50

I used a different method to double check your work

It will take 12 seconds until Hudson and Knox have run the same number of feet.

Let's denote the time it takes until Hudson and Knox have run the same number of feet as "t" (in seconds).

The distance Hudson runs can be calculated by multiplying his speed (8.8 feet/second) by the time "t". Thus, the distance Hudson covers is 8.8t feet.

Knox, on the other hand, had a head start of 30 feet. So the distance Knox covers can be calculated by multiplying his speed (6.3 feet/second) by the time "t" and adding the head start of 30 feet. Thus, the distance Knox covers is 6.3t + 30 feet.

To find the time when both runners have covered the same distance, we set their distances equal to each other:

8.8t = 6.3t + 30

Simplifying the equation:

2.5t = 30

Dividing both sides by 2.5:

t = 30 / 2.5

t = 12

Therefore, it will take 12 seconds until Hudson and Knox have run the same number of feet.

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Answer:

80 degrees

Step-by-step explanation:

What we see in this drawing is a triangle formed by three lines. In order to solve this problem, we need to know that when two lines intersect, the two angles formed are supplementary (meaning they add up to 180 degrees). For example, the 150-degree angle, and the angle right next to it (the angle on the left side of the triangle) add up to 180 degrees. This means that the left-most angle of the triangle is 180-150, which is 30 degrees

We can figure out the topmost angle of the triangle using the same method. We know that the angle outside the triangle is 130 degrees, so the angle right next to it (in this case, right below it), is 180-130, or 50 degrees.

Next, we use the fact that triangles are 180 degrees on the inside to figure out the third angle (the one on the right, right next to angle 1). We know that the other two angles are 30 and 50 degrees, and if you add that up, you get 80 degrees. The last angle, then, is 180-80, or 100 degrees.

Lastly, we know that the rightmost angle of the triangle and angle 1 add up to 180 degrees. In other words, 100+Angle1=180. Therefore, Angle 1 is 180-100 or 80 degrees.

The answer to the simplified expression 4⁹/4³ in index form is derived to be equal to 4⁶

To simplify a fraction written in index form, you can first express the numbers in prime factorization form by writing both the numerator and denominator as a product of prime factors. Identify common prime factors in the numerator and denominator and cancel them out. Then write the remaining factors as a product in index form.

Given the fraction 4⁹/4³, we can simplify as follows:

4⁹/4³ = (4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4)/(4 × 4 × 4)

we can cancel out (4 × 4 × 4) from both the numerator and denominator, living us with;

4⁹/4³ = 4 × 4 × 4 × 4 × 4 × 4

4⁹/4³ = 4⁶

Therefore, the answer to the simplified expression 4⁹/4³ in index form is derived to be equal to 4⁶

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When  3.68086257145 divided by 6.533 * 4,085,0811 we get 1.379228624370833401829E-8

The methods of division are of three types according to the difficulty level. These are the chunking method or division by repeated subtraction, short division method or bus stop method and long division method.

The division of two numbers can be calculated using the following formula:

Dividend / Divisor = Quotient + Remainder.

The number that is being divided in this case is known as the dividend. The number that divides the number (dividend) into equal parts is known as the divisor.

The quotient is the result of the division operation.

The remainder is the leftover number in the division operation.

We have been given that

3.68086257145 divided by 6.533× 4,085,0811

First we simplify multiplication part

6.533× 4,085,0811  = 266878348.263

Now

3.68086257145 divided by 266878348.263

3.68086257145 ÷ 266878348.263

= 1.379228624370833401829E-8

Hence , 1.379228624370833401829E-8 is the result of the 3.68086257145 divided by 6.533× 4,085,0811 .

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For given average temperatures and °C=5/9°F-32 C represents temperature unit in celsius.

What is average?

In Maths, an average of a list of data is the expression of the central value of a set of data. Mathematically, it is defined as the ratio of summation of all the data to the number of units present in the list. In terms of statistics, the average of a given set of numerical data is also called mean. For example, the average of 2, 3 and 4 is (2+3+4)/3 = 9/3 =3. So here 3 is the central value of 2,3 and 4.  Thus, the meaning of average is to find the mean value of a group of numbers.

Average = Sum of Values/Number of Values

Also

Suppose, we have given with n number of values such as x1, x2, x3 ,….., xn. The average or the mean of the given data will be equal to:

Average = (x1+x2+x3+…+xn)/n

Now,

Given formula

°C=5/9°F-32, C represents  where °c is temperature unit in Celsius and

°F represents unit of temperature in Fahrenheit.

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