A gardener drew this diagram to find the area of land inside a right-triangular-shaped fence. The length of fence b is 130 feet. The measure of angle A is 42°. What is the area of land inside the fence rounded to the nearest square foot?

The 'rise' and 'run' of the line is shown in figure whose slope is:  \(\frac{11}{13.5}\)

An x-y axis graphic is a visual representation of mathematical functions or data points on a Cartesian coordinate system. The x-axis represents the horizontal or independent variable, whereas the y-axis represents the vertical or dependent variable.

As we know that, the Slope of the line in terms of 'rise' and 'run' is;

Slope =  \(\frac{rise}{run}\)

by the figure, we can take two end points are (-4, -10) and (9.5, 1) so,

rise = (y₂ - y₁) = (1) - (-10) = 1 + 10 =  11

run = (x₂ - x₁) =  (9.5) - (-4) =  9.5 + 4 =  13.5

put the values to find slope,

Slope =  \(\frac{11}{13.5}\)  =  0.8148

Therefore, the rise and run is shown in below figure whose slope is: \(\frac{11}{13.5}\)

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The sequence (Xn) is given by Xn = [10^n √7] / 10^n, where [r] represents the integral part of the real number r. The first five terms of the sequence are X1 = √7, X2 = 1.4, X3 = 1.73, X4 = 1.72, and X5 = 1.73.

The sequence (Xn) converges to √7, which is an irrational number. This means that the terms of the sequence get arbitrarily close to √7, but they never actually reach it since √7 is not a rational number. In other words, there is no rational number in the set Q that can represent the limit of the sequence (Xn).

To show that Q is not complete, we can consider the sequence (Xn) as a counterexample. If Q were complete, every convergent sequence of rational numbers would have its limit also in Q. However, since the limit of (Xn) is √7, which is not a rational number, we conclude that Q is not complete.

This demonstrates that the set of rational numbers Q is not sufficient to capture all the limits of convergent sequences of rational numbers. There exist sequences, such as (Xn) in this case, that converge to irrational numbers that are not included in Q.

This highlights the incompleteness of Q and the necessity of extending the number system to include irrational numbers to form a complete metric space.

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a. The equilibrium interest rate,  is determined by the risk-free interest rate, the probability of repayment, and the cost of default.

b. The probability of the government repaying its loan can be calculated using the loan repayment threshold and the distribution of the output.

c. If the interest rate, r, is equal to or greater than the equilibrium interest rate, the borrowing country would default.

a. To find the equilibrium interest rate,  we need to consider the risk-free interest rate, the probability of repayment, and the cost of default. The equilibrium interest rate is given by the formula: r = r + (c/p), where r is the risk-free interest rate, c is the cost of default, and p is the probability of repayment.

b. The probability that the government will repay its loan can be calculated by determining the percentage of the output distribution that exceeds the loan repayment threshold. Since 0.5 of the output is required to repay the loan, we need to calculate the probability that the output exceeds L/0.5.

c. If the interest rate, r, is equal to or greater than the equilibrium interest rate, the borrowing country would default. This can be proven by comparing the repayment threshold (L/0.5) with the loan repayment amount (L + Lr). If the repayment threshold is greater than the loan repayment amount, the borrowing country would default.

Calculations and further details would be required to provide specific numerical answers for each part of the question.

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Answer:

Explanation below

Step-by-step explanation:

(3+4)= 7

7+2 = 9

-(3-4) (Invisible one)

-3+4 add to the 9

10

10+2= 12

12-4=8

8×4 =32

Sorry if this seems a bit confusing, but its quite hard to show the process without paper.

Hope this helps! :)

Answer:

Not sure by the way the question is asked but I think the answer is x=(y-1)/4

Step-by-step explanation:

Subtract one from both sides: y-1=4x

Divide the four from both sides: (y-1)/4=x

Answer:

\( \frac{y - 1}{4} = x\)

Answer:

∠ C ≈ 73.7°

Step-by-step explanation:

using the sine ratio in the right triangle

sin C = \(\frac{opposite}{hypotenuse}\) = \(\frac{AT}{CT}\) = \(\frac{48}{50}\) , then

∠ C = \(sin^{-1}\) ( \(\frac{48}{50}\) ) ≈ 73.7° ( to the nearest tenth )

a. Phoebe's car has the greater acceleration at first.

b. The maximum distance by which the other car was ahead was approximately 0.69 feet

c. The maximum difference in velocities does not occur at the same time as the maximum distance the two cars are apart.

d. The car that was ahead at first (Calvin's car) does not regain the lead.

Acceleration is the rate at which an object changes its velocity. In other words, it's the amount of change in velocity per unit of time. The standard unit of acceleration is meters per second squared (m/s²).

a Since \(e^{t}\) is always positive and increasing, while 3\(t^{2}\) is positive but increasing at a slower rate, we can conclude that Phoebe's car has the greater acceleration at first.

b We can do this by taking the derivative of the difference and setting it equal to zero:

(su(t) - sp(t))' = 3\(t^{2}\) - \(e^{t}\) = 0

Solving for t, we get t ≈ 0.85 seconds. Plugging this value back into the distance functions, we find that at this time Phoebe was ahead of Calvin by approximately 0.69 feet.

c. The maximum difference in velocities does not occur at the same time as the maximum distance the two cars are apart.

d. Yes, the car that was ahead at first does eventually regain the lead, since both cars have unbounded distance functions.

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Answer:

its C

Step-by-step explanation:

Answer:

0.36

Step-by-step explanation:

So the first step is to count up all the socks which is 18. Then I took 2 (because you can't just wear one sock) and multiplied it by 18 and got 36. The question asked for decimal form so I divided it by 100 and got 0.36.

I hope this helps you :)

\(2 * 18 = 36\\\\36/100 = 0.36\)

John earned $400 interest at a rate of 6% for 3 years. Therefore, the amount of money John originally invested was $2,222.22.

We are able to use the Simple interest formula to resolve this problem:

Simple interest is a simple concept in finance that is used to calculate the interest earned or paid on a essential amount over a positive time period.

Simple interest = (principal x charge x time)

Given that John earned $400 in interest at a price of 6% for three years, we are able to set up the equation as:

400 = (P x 0.06 x 3)

In which P is the principal (the original amount invested).

Simplifying this equation, we get:

400 = 0.18P

Dividing both facets through 0.18, we get:

P = $2,222.22

Thus, John originally invested $2,222.22.

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Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Market risk premium: 8%, After-tax cost of debt: 5.94%, Cost of equity: 9.6%, and the Company's Rwacc: 7.97%.

Market risk premium: The market risk premium is the difference between the expected market return and the risk-free rate. In this case, the market risk premium is 12% - 4% = 8%.

After-tax cost of debt: The after-tax cost of debt is calculated by multiplying the pretax cost of debt by (1 - tax rate). In this case, the after-tax cost of debt is 9.0% * (1 - 34%) = 5.94%.

Cost of equity: The cost of equity can be calculated using the Capital Asset Pricing Model (CAPM) formula, which takes into account the risk-free rate, the company's beta, and the market risk premium. In this case, the cost of equity is 4% + (0.70 * 8%) = 9.6%.

Rwacc (Weighted Average Cost of Capital): The company's Rwacc is calculated by weighting the cost of debt and the cost of equity based on the market values of debt and equity.

In this case, assuming the total market value of the company is $110 million ($60 million equity + $50 million debt), the weights would be 60/110 = 0.5455 (equity) and 50/110 = 0.4545 (debt). Therefore, the Rwacc is (0.5455 * 9.6%) + (0.4545 * 5.94%) = 7.97%.

In summary, the market risk premium is 8%, the after-tax cost of debt is 5.94%, the cost of equity is 9.6%, and the company's Rwacc is 7.97%.

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The correct Excel function that returns the sample correlation coefficient is b. CORREL.

In Excel, the CORREL function is used to calculate the correlation coefficient between two sets of data. It is specifically designed to calculate the sample correlation coefficient when working with a sample dataset. The syntax of the CORREL function is as follows:

CORREL(array1, array2)

The function takes two arrays or ranges of data as input and returns the correlation coefficient between them. It uses the formula for the sample correlation coefficient, which measures the strength and direction of the linear relationship between two variables in a sample.

The other options listed, a. CORRELATION, c. CORRELS, and d. COVARIANCE.S, are not valid Excel functions for calculating the sample correlation coefficient. CORREL is the appropriate function to use when you want to compute the sample correlation coefficient in Excel.

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Answer:

1 / (Ryan's rate + Shawn's rate)

72 minutes

Step-by-step explanation:

Given that :

Ryan's time = 2 hours ; rate = 1 /2

Shawn's time = 3 hours ; rate = 1/3

A.)

Working together :

Take the reciprocal of the sum of Ryan and Shawn's rate

1 / (Ryan's rate + Shawn's rate)

B.) 1/ (1/2 + 1/3)

(1/2 + 1/3) = (3 + 2) / 6 = 5/6

Rate working together = 5/6

Time taken = 1 ÷ (5/6)

= 1 * 6/5

= 6/5 hours = 1.2 hours = (1.2 * 60) = 72 minutes

Answer:

Set your calculator to degree mode.

sin(C)/8 = sin(49°)/35

sin(C) = 8sin(49°)/35 = .1725

C = 9.9°

A = 180° - (9.9° + 49°) = 121.1°

35/sin(49°) = a/sin(121.1°)

a = 35sin(121.1°)/sin(49°) = 39.7 feet

The length of the fence in feet if he uses all 72 feet of material is 33 feet.

Perimeter = 2(length + width)

72 = 2(x + 3)

72 = 2x + 6

72 - 6 = 2x

68 = 2x

x = 68/2

x = 33 feet

Therefore, the length of the fence in feet if he uses all 72 feet of material is 33 feet.

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Answer:

Step-by-step explanation:

h(x) = 3x - 3

To find h(3) , substitute the value of x that's 3 into h(x). That is for every x in f (x) replace it with 3

We have

h(3) = 3(3) - 3

= 9 - 3

We have the final answer as

Hope this helps you

The value of h(3) is 6 from the equation h(x) = 3x - 3

A function notation is a method used for expressing functions for easy understanding and solution. A function notation usually has:

Here;

Now,

h(x) = 3x - 3

we will replace x with 3 for h(3)

h = 3(3) - 3

h = 9 -3

h = 6

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The random variable x, which represents the amount of rain (in inches) that fell this spring, is a continuous random variable.

In this context, a continuous random variable is one that can take on any value within a certain range. The amount of rain can be measured with different levels of precision, such as 2.5 inches or 2.5342 inches, indicating that there is an infinite number of possible values between any two given points.

On the other hand, a discrete random variable would involve countable outcomes or a finite number of possible values. For example, if we were counting the number of rainy days during the spring, the random variable would be discrete since it can only take whole number values.

In the case of measuring the amount of rain, there can be infinitely many possible values within any given range, and therefore, it is considered a continuous random variable. So, the correct answer is option A.

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The complete question is:

Decide whether the random variable x is discrete or continuous. Explain your reasoning Let x represent the amount of rain (in inches) that fell this spring. Is the random variable x discrete or continuous? Choose the correct answer below.

A. Continuous, because x is a random variable that cannot be counted.

B. Discrete, because x is a random variable that can be counted.

Answer:

3/4    or    75/100

Step-by-step explanation:

75/100 simplified is 3/4

Answer:

\(\frac{75}{100}\)

The system can be written as a vector equation as [5, 1, -3] [x1, x2, x3]^T = [8, 0]^T and as a matrix equation as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].

To write the given system as a vector equation, we group the variables and the constants into vectors and write the equations in a matrix form. Thus, the system can be written as [5x1 + x2 - 3x3; 2x2 + 4x3] = [8; 0], which is a vector equation.

To write the system as a matrix equation, we can write the coefficients of the variables in a matrix A, the variables in a vector X, and the constants in a vector B. Thus, the system can be written as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].

We can then solve for X by finding the inverse of A and multiplying both sides of the equation by it.

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The equation for split times is 4x= 198.608  and the value of x is 49.652

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Let x be the split time

all 4 of the split times were the same.

4x= 198.608

=> x= 198.608/4 = 49.652

The equation for split times is 4x= 198.608  and the value of x is 49.652

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Answer:

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Step-by-step explanation:

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

The given trianagle FAN is an acute triangle.

Step-by-step explanation:

There are three types of triangles on the basis of angle:

(As shown in image attached)

Given:

A triangle FAN with an angle measurement of each angke.

To find:

The name adjoining triangle FAN on the  basis of angle.

Solution:

In ΔFAN

∠A=55°, ∠F=85° ,and ∠C=45​°

∠A<90°, ∠F<90° ,and ∠C<90°

All the given three angles of triangle FAN are less than 90°, which imolies that the given trianagle FAN is an acute triangle.

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The answer is "false". The interval [1, 2] contains all the real numbers between 1 and 2 including the endpoints.

An interval notation is used for representing the continuous set of real values. This is the shortest way of writing inequalities.

Intervals are represented within the brackets such as square brackets or open brackets(parenthesis).

The given interval is [1, 2]

The given statement is - 'the interval [1, 2] contains exactly two numbers - the numbers 1 and 2'

The given statement is 'false'.

This is beacuse, an interval consists set of all the real values in between the two values given.

So, according to the definition, there are not only the end values but also many real values in between them.

Thus, the answer is "false". The interval [1, 2] consists of all the real values between 1 and 2 including 1 and 2.

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Online calculator of variable cost is used to Total Variable Cost = Total Cost-Fixed Costs to calculate the Total Variable Cost.

A variable cost is an expense that changes as a company's production output rises and falls. Variable expenses vary according on the amount of output produced. Basic variable costs include, in large part:

Variable costs are frequently employed in business and are a crucial component of the analysis of the company's break-even point. The revenue or unit that must be sold to cover all costs is examined using the break-even approach.

The following calculation is the break-even point:

Break-even point in units = Fixed costs/(Sales price per unit – Variable cost per unit)

Variable costs are crucial for successful investors because they help them calculate the proportion of the set price and predict how the company will respond to various operational scenarios.

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The point where the triangle's three altitudes connect is known as the orthocentre.

The circumcentre is the center of a triangle's circumcircle. It can be found as the point of intersection of the perpendicular bisectors of the triangle.

The letter H is frequently used to denote the orthocentre.

The kind of triangle determines where the orthocentre is.

The orthocentre will be located inside an acute triangle.

The orthocentre will be outside of an acute triangle.

Finally, the orthocentre will be the vertex at the correct angle if the triangle is right.

Thus, The point where the triangle's three altitudes connect is known as the orthocentre.

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Answer: 2.5 is the constant

Step-by-step explanation: a constant is the number before the variable so if 2.5 comes before "x" than 2.5 is the constant

Answer:

the answer is 5... 5- (-10) and 6-3 and divide the change by 15 and 3 and you'll get 5

Step-by-step explanation:

The linear function or equation in the slope-intercept form will be y = 5x - 25.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

The linear function is given as,

y = mx + c

Here, m is the slope while c is the y-intercept.

Slope m = (5 + 10)/(6 - 3)

m = 5

Put m = 5, (6,5)

5 = 5(6) + c

c = -25

Thus, y = 5x - 25

Hence "The linear function or equation in the slope-intercept form will be y = 5x - 25".

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Answer:

b= 50

Step-by-step explanation:

the entire angle equals 80 degrees and a portion of it equals 30. therefore the portion that equals b = 50 because 30+50=80 hope this helps.

The following solutions with regard to resolving or simplifying the radii of circular ponds are given below.

Part A: 5√100 + √164 meters = 5 × 10 + 2√41 meters

Part B: 5 × 10 + 2√41 meters = 50 + 2√41 meters
Part C: The radius of Pond B is 10√2 meters.
Part D: the radius of Pond B is greater than the radius of Pond A.

Part A: The mistake is in Step 1. To simplify the square root of 164, we need to find its prime factors:

164 = 2 × 2 × 41

So, we can write:

√164 = √(2 × 2 × 41) = 2√41

Using this, we can rewrite Step 1 as:

5√100 + √164 meters = 5 × 10 + 2√41 meters

Part B: Using the corrected step from Part A, we can simplify the radius of Pond A as:

5 × 10 + 2√41 meters = 50 + 2√41 meters

So, the radius of Pond A is 50 + 2√41 meters.

Part C: The radius of Pond B is already simplified, so we don't need to do any additional steps. It is:

25√200/5 meters = 5√200 meters

We can simplify this further by finding the prime factorization of 200:

200 = 2 × 2 × 2 × 5 × 5

So, we can write:

√200 = √(2 × 2 × 2 × 5 × 5)

= 2 × 5√2

Using this, we can rewrite the expression for the radius of Pond B as:

5 × 2 × √2 meters

= 10√2 meters

Thus, the radius of Pond B is 10√2 meters.

Part D: We can compare the radii of the ponds using the original expressions by writing:

√164 < 25√200/5

Simplifying both sides:

2√41 < 10√2

Dividing both sides by 2:

√41 < 5√2

Squaring both sides (since both sides are positive):

41 < 25 × 2

41 < 50

So, the inequality is true. Therefore, the radius of Pond B is greater than the radius of Pond A.

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Full Question:

Two circular ponds at a botanical garden have the following radii:

Pond A: Sqrt(164) meters;

Pond B: 25Sqrt(200)/5 meters:

Todd simplified the radius of pond A this way:

5sqrt(164)

Step 1: 5sqrt(100) + Sqrt(164) meters

Step 2: 5(10 + 8)

Step 3: 5(18)

Step 4: 90

One of the steps above is incorrect.

Part A: Rewrite the steps so that it is correct

Part B: Using the corrected step from Part A, simplify the radius of Pond A.

Part C: Simplify the expression for the radius of pond B.

Part D: Write an inequality to compare the radii of the ponds, using the original expressions.