Find the area of the triangle. Round your answers to the nearest tenth if necessary.
14 in
125 degrees
15 in

Answer:

b) It is false

The annual rate of return for the investment in the new oil well should approximately be 90.28%

To calculate the annual rate of return for the investment in the new oil well, we need to consider the net cash flows over its useful life. The net cash flow is the difference between the annual revenues and expenses, taking into account the initial cost and salvage value.

The net cash flow for each year is calculated as follows: Net Cash Flow = Annual Revenues - Annual Expenses - Depreciation

Using the given values, we can calculate the net cash flows for each year:

Year 1: $131,925 - $81,000 - $47,400 = $3,525

Year 2-9: $131,925 - $81,000 = $50,925

Year 10: $131,925 - $81,000 + $11,000 = $61,925

Now, we can calculate the total net cash flows over the 10-year period: Total Net Cash Flows = Year 1 + Year 2-9 + Year 10

= $3,525 + ($50,925 * 8) + $61,925

= $427,825

To determine the annual rate of return, we divide the total net cash flows by the initial investment: Annual Rate of Return = (Total Net Cash Flows / Initial Investment) * 100%

= ($427,825 / $474,000) * 100%

= 90.28%

Therefore, the annual rate of return for the investment in the new oil well is approximately 90.28%. This indicates the profitability of the investment over its useful life.

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Answer:

A function that changes the same way can be a linear function.

y = a*x + b.

Where the rate of change (this is, how much changes y when x increases or decreases) is defined by the coefficient a, that is constant.

for example, suppose that when x = x0, we have y = y0

y0 = a*x0 + b.

Now x0 increases by one unit, to (x0 + 1)

y = a*(x0 + 1) + b = (a*x0 + b) + a = y0 + a.

Then if x increases (or decreases) 1 unit, y increases (or decreases) a units.

Now, we can define the rate of change of a function as it's derivate with respect to some variable.

In this case, if we derive with respect to x, we have:

y' = a

Then the rate of change is constant.

The student with the correct answer is Dylan who says the decimal should be placed between the 8 and 0.

This is base on the estimation that 3.01 is a two decimal place number, so the product 18.06 should also be in 2 decimal place.

A decimal number is a number expressed in the decimal system (base 10).

Place value:

6 × 3.01

3.01

6 × 3.01

= 18.06

Therefore, Lucas is incorrect with his answer that the decimal should be placed between the 1 and 8.

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The perimeter of the figure with vertices D(-4, 5), E(-4, -6) and F(3, -6) is given as follows:

31.04 units.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The vertices of the polygon in this problem are given as follows:

D(-4, 5), E(-4, -6) and F(3, -6).

Hence the side lengths are given as follows:

Hence the perimeter of the polygon is given as follows:

11 + 13.04 + 7 = 31.04 units.

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Answer:

D

Step-by-step explanation:

Divide 16 by 4 to get the denominator of 4. Then divide 12 by 4 to get three. Therefore your answer is D. 3/4

Answer:

3/4

Step-by-step explanation:

All I did was divide the top and bottom number by 4. 12/4= 3 and 16/4=4

Answer:

Area = \(1\frac{7}{45}m^2\)

Step-by-step explanation:

Area of rectangle = Length * Width

'Where Length = \(2\frac{3}{5}\) and Width = \(\frac{4}{9}\)

Area = \(2\frac{3}{5}\) × \(\frac{4}{9}\)

Area = \(\frac{13}{5}\) × \(\frac{4}{9}\)

Area = \(\frac{13*4}{5*9}\)

Area = \(\frac{52}{45}\)

Area = \(1\frac{7}{45}m^2\)

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btw,, the formula you insert is incorrect:)

Answer:

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The two areas at the end of a normal curve that indicate low probability values if the null hypothesis is true are called the critical region.

Critical region: A set of values for the test statistic for which the null hypothesis is rejected is referred to as a critical region, also known as the rejection region. Specifically, we accept the alternative hypothesis and reject the null hypothesis if the observed test statistic is within the critical region.

The probability of rejecting H0, or the Null Hypothesis, is represented by the alpha level. The critical region is the set of z values on a graph that result in the null hypothesis being rejected.

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The pair that has a positive correlation (relationship) between them, in general, is the years of experience of an employee and the salary of an employee. So, the correct answer is A).

A positive correlation indicates that as one variable increases, the other variable tends to increase as well. In the given pairs, the years of experience of an employee and the salary of an employee are likely to have a positive correlation.

This is because, in many job settings, employees with more experience often receive higher salaries. As individuals gain more experience and develop their skills, they become more valuable to employers, leading to increased compensation.

However, it is important to note that correlation does not imply causation, and other factors may also influence salary apart from just years of experience.  So, the correct option is A).

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Answer:

The horizontal cross-sections of the prisms at the same height must have the same area.

Step-by-step explanation:

A pyramid and a cone are both 12 centimeters tall and have the same volume.... What is the volume?

Volume is the quantification of the three-dimensional space a substance occupies.

We have to determine the true statement, and it is

The horizontal cross-sections of the prisms at the same height must have the same area cone and given pyramid are looks like same in two-dimensional.

The horizontal cross-sections of the prisms at the same height must have the same area thus the correct option is A.

A pyramid and a cone are both 12 centimeters tall and have the same volume, we know that Volume is the quantification of the three-dimensional space a substance occupies.

We have to determine the true statement, and it is the horizontal cross-sections of the prisms at the same height must have the same area cone and given pyramid are looks like same in two-dimensional.

If we cross-section the figures at the same height, it won't get the same shape but we should get the same area, as the area of the cross-section will be proportional to the base area, and the base area of both figures are the same.

Thus, the correct option is A.

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The vector triple product relation A×(B×C) = (A⋅C)B - (A⋅B)C can be proven using vector algebra. The scalar triple product of three vectors is zero if any two of them are equal, due to the properties of the cross product and dot product.

To prove the vector triple product relation A×(B×C) = (A⋅C)B - (A⋅B)C, we start by expanding the expression B×C using the cross product formula: B×C = B × (C × C) - (B ⋅ C)C. Since the cross product of a vector with itself is zero, the first term on the right side becomes zero: B × (C × C) = 0.

Substituting this into A×(B×C), we get A×(B×C) = -(B ⋅ C)C + (A ⋅ C)B. By rearranging terms, we obtain A×(B×C) = (A⋅C)B - (A⋅B)C, which proves the vector triple product relation. Moving on to the scalar triple product, let's consider A⋅(B×C).

If any two vectors, such as B and C, are equal, their cross product B×C will be zero since the cross product of two parallel vectors is zero. Hence, the scalar triple product A⋅(B×C) will also be zero. Moreover, if all three vectors A, B, and C are equal, then A⋅(B×C) equals A⋅0, which is zero.

Thus, if any two vectors are equal, the scalar triple product is always zero. This can be attributed to the properties of the cross product (resulting in zero for parallel vectors) and the dot product (resulting in the square of the magnitude for a vector dotted with itself).

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Answer:

the roots must be (x-3)^2 and (x+5)^2

That is (x2-6x+9) (x^2+10x+25)

That is

x^4+10x^3+25x^2-150x+225

-6x^3-60x^2+90x

+9x^2

===

x^4+4x^3-26x^2-60x+225

Answer:

2 , 8 , - 1

Step-by-step explanation:

substitute x = 0, 2, - 1 into f(x)

f(x) = 3x + 2

(a)

f(0) = 3(0) + 2 = 0 + 2 = 2

(b)

f(2) = 3(2) + 2 = 6 + 2 = 8

(c)

f(- 1) = 3(- 1) + 2 = - 3 + 2 = - 1

If a line parallel to one side of a triangle contacts the other two sides of the triangle, the line proportionally splits these two sides. If DE = BC, then ADDB=AEEC.

If a line parallel to one side of a triangle contacts the other two sides, the two sides are proportionately divided.

The formula for a proportional equation is y = kx. The letters y and x denote the variables in the equation. The letter k represents the proportionality constant, which is fixed.

Because matching angles produce the AA similarity shortcut, when a line is drawn parallel to one side of a triangle, two similar triangles are generated. Because the triangles are comparable, the parallel line segments are proportionate segments.

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The square miles that was burned if one square mile is 640 acres is 840.625 square miles.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

Square miles that was burned = 538,000 / 640 = 840.625 square miles

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There are 840.625 square miles did the fire burn.

Division is the process of sharing a collection of items into equal parts and is one of the basic arithmetic operations in maths.

The wallow fire of 2011 burned 538,000 acres in eastern Arizona.

The area of square miles did the fire burned is;

\(\rm Area =\dfrac{538,000}{640}\\\\Area =840.625 \ square \ miles\)

Hence, there are 840.625 square miles did the fire burn.

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To sketch the curve with the given vector equation r(t) = t, 6 − t, 2t and indicate with an arrow the direction in which t increases, we need to find the points on the curve and then connect those points.

1. Let's put t = 0 in the given vector equation r(t) = t, 6 − t, 2t to find the first point on the curve.

r(0) = 0, 6, 0

Thus, the point on the curve is (0,6,0).

2. Let's select some values of t and put them in the given vector equation to find some additional points on the curve.

When t = 1,r(1) = 1, 5, 2

When t = 2,

r(2) = 2, 4, 4

When t = 3,

r(3) = 3, 3, 6

When t = 4,

r(4) = 4, 2, 8

When t = 5,

r(5) = 5, 1, 10

When t = 6,

r(6) = 6, 0, 12

Thus, we have found some points on the curve, which are (0,6,0), (1,5,2), (2,4,4), (3,3,6), (4,2,8), (5,1,10), and (6,0,12).

3. Now, we can connect these points to sketch the curve.

4. Finally, we indicate with an arrow the direction in which t increases.

We can see that as t increases, the curve moves in the direction of the arrow, which is along the positive x-axis. Thus, we can conclude that the direction in which t increases is along the positive x-axis.

Answer:

Therefore, the curve and the direction in which t increases are shown below in the image.

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Answer:

x < -3 and x > 5

Step-by-step explanation:

x² - 2x - 8 > 7

~Rewrite in standard form

x² - 2x - 15 > 0

~Factor

(x + 3)(x - 5) = 0

~Solve for both factors

x + 3 = 0

x = -3

x - 5 = 0

x = 5

Best of Luck!

The expression does not have any variable term (n) in it, the sequence converges to a constant value. The limit of the sequence as n approaches infinity is: Limit = 1/(sqrt(80))

To find the limit of the sequence n/(sqrt(16n^2 5)), we can simplify the expression by dividing both the numerator and denominator by n:

n/(sqrt(16n^2 5)) = 1/(sqrt(16*5/n^2)) = 1/(4sqrt(5/n^2))

As n approaches infinity, 5/n^2 approaches zero. Therefore, the denominator of the expression approaches infinity, and the whole expression approaches zero.

Therefore, the limit of the sequence is 0.
To find the limit of the given sequence n/(sqrt(16n^2 * 5)), we'll apply some algebraic simplification and use the properties of limits.

First, simplify the expression:

n/(sqrt(16n^2 * 5)) = n/(sqrt(80n^2))

Now, divide both the numerator and denominator by n:

n/(sqrt(80n^2)) = 1/(sqrt(80))

Since the expression does not have any variable term (n) in it, the sequence converges to a constant value. The limit of the sequence as n approaches infinity is:

Limit = 1/(sqrt(80))

This is the final answer.

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Answer

Number of students Total cost

0 $800

20 $1160

30 $1340

40 $1520

50 $1700

Explanation

Given

Cost per student = $18

The cost of the bus = $800

Step-by-step solution:

The total cost for food, admission, and the bus can be calculated using;

18a + b

Where a is the number of students and b is the cost of the bus.

For 30 students:

$18(30) + $800 = $540 + $800 = $1340

For 40 students:

$18(40) + $800 = $720 + $800 = $1520

For 50 students:

$18(50) + $800 = $900 + $800 = $1700

The most pieces of fabric that can be used is 144 pieces, making a quilt with 12 pieces on each side.

The square is a term to refer to a geometric figure that is characterized by being a type of parallelogram with four sides of equal length. A square is a regular polygon that has all its sides equal, and its interior angles measure 90º.

To identify the number of square pieces that I can use to make a square quilt, I must keep in mind that to create a square quilt I must put the same number of pieces on each side of the quilt so that it forms a perfect square.

To identify the maximum number of pieces needed, we can try taking the square root of 150, 149, 148, 147... until the result is a integer number (no decimals). In this case the first integer that appears is 12 by taking the square root of 144 as shown below.

\(\sqrt[2]{144} = 12\)

This means that to make a square quilt we must use 144 pieces in total and place 12 pieces on each side of the square. Additionally we can state that the side length of this quilt is 48 inches because each piece measured 4 inches on a side.

4 inches × 12 = 48 inches.

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Answer:

$8.72

Step-by-step explanation:

Since the tax rate is 9% of the lunch cost, the tax for this lunch is .72 dollars since 9% of 8 is 0.72(see math below). You add the 0.72 to 8 and the total cost is $8.72.

8 x (9/100) = tax

8 x 0.09 = 0.72

8+0.72 = $8.72

Answer:

The side lengths will form a triangle because 6+4 > 7

Step-by-step explanation:

For side lengths, the two smallest sides (ex. 6 and 4) must have a greater sum than then highest side length. Since 6+4 is greater than 7, it creates a triange. If it would have been 5+2 it would not have worked because it needs to be greater than, not less than or equal to.

Answer:1/6

Step-by-step explanation:

Answer:

1 / (x+5)

Step-by-step explanation:

Factor the denominator

(x+1)/ (x+5)(x+1)

Cancel both (x+1)

=1/(x+5)

Equation of circle G: \(\bold{(x-3)^{2} + (y-4)^{2} = 49}\)

"An equation of a circle with center (p, q) and radius r is:\((x-p)^{2}+ (y-q)^{2}=r^{2}\) "

"The coordinates of the midpoint M of two points (a, b) and (x, y) :

\(M(\frac{a+x}{2} ,\frac{b+y}{2} )\) "

"The distance between two coordinate points (a, b), (m, n):

\(d=\sqrt{(n-b)^{2} +(m-a)^{2} }\) "

"A diameter of a circle is the straight line that from one side of a circle to other side and passes through the center."

For given question,

The line segment connecting the two points B(-4,4) and D (10,4) is a diameter of the circle.

This means, the midpoint of the diameter BD would be the center of a circle G.

Let M represents the center of the circle.

First we find the coordinates of the center of the circle.

Using midpoint formula,

⇒ M = \((\frac{-4+10}{2} ,\frac{4+4}{2} )\)

⇒ M = (6/2 , 8/2)

⇒ M = \((3,4)\)

Now, we find the distance between points B(-4,4) and D (10,4) to determine the diameter of a circle G.

Using distance formula,

⇒ \(d=\sqrt{(4-4)^{2} +(10-(-4))^{2} }\)

⇒ \(d=\sqrt{0+(14)^{2} }\)

⇒ \(d=14\) units

So, the radius of the circle r would be,

r = d/2

⇒ r = 14 / 2

⇒ r = 7 units

Now, we find the equation of circle with center M(3, 4) and radius r = 7 units.

Using center - radius form equation of circle would be,

\((x-3)^{2} + (y-4)^{2} = 7^{2}\)

⇒ \(\bold{(x-3)^{2} + (y-4)^{2} = 49}\)

Therefore, option (A) is the correct answer.

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