Triangle LMN, with vertices L(-9,6), M(-5,7), and N(-8,9), is drawn inside a rectangle,
What is the area, in square units, of triangle LMN?

Answer:

First, we rearrange the equation to isolate the y-term on one side:

dy/dx + ytanx = secx

Then, we multiply both sides by the integrating factor, which is e^(∫tanx dx) = e^(ln|secx|) = |secx|: | secx| dy/dx + ysecx tanx = 1

Next, we can write this as the derivative of a product using the product rule: d/dx (y |secx|) = 1

Integrating both sides with respect to x, we get:  y |secx| = x + C

where C is the constant of integration. Solving for y, we have:

y = (x + C)/|secx|

Note that there is a singularity at x = (2n + 1)π/2, where the denominator |secx| is zero. At these points, the solution is not defined

Answer:

1. 17/8   2. 89/24   3. 47/12   4. 9/7

Answer:

1) 29

2) 57

3) 91

4) 15

Step-by-step explanation:

1) 7/8 + 11/4

find lcm

lcm=8

multiply through by 8

8×7/8+8×11/4

Gives: 7 + 22

 =29

2) 12/6+ 11/4

lcm=12

multiply through by 12

12× 12/6 + 12× 11/4

 24 + 33

 =57

3) 23/4 + 11/6

lcm=12

multiply through by 12

12× 23/4 + 12× 11/6

 =69 +22

 =91

4) 22/7 - 1

lcm=7

multiply through by 7

7 ×22/7 - 7 ×1

22-7

=15

Required circumference of the given diameters are 94.29 cm, 471.43 m, 377.14 ft, 62.86 cm, 251.43 m, 37.71 cm, 69.71 in, 1068.57 m, 314.29 m, 106.86 cm respectively.

What is circumference of circle?

The circumference of a circle is the distance around the edge or boundary of the circle. It is a fundamental geometric property of a circle and is defined as the product of the circle's diameter and pi (π), which is a mathematical constant approximately equal to 3.14.

The formula to calculate the circumference of a circle is C = 2πr or C = πd

where C represents the circumference, r represents the radius, and d represents the diameter of the circle,

1. Diameter = 30 cm

Circumference = π x Diameter

= 22/7 x 30

= 94.29 cm

2. Diameter = 15 m

Circumference = π x Diameter

= 22/7 x 15 x 100

= 471.43 m

3. Diameter = 40 ft

Circumference = π x Diameter

= 22/7 x 40 x 12

= 377.14 ft

4. Diameter = 20 cm

Circumference = π x Diameter

= 22/7 x 20

= 62.86 cm

5. Diameter = 8 m

Circumference = π x Diameter

= 22/7 x 8 x 100

= 251.43 m

6. Diameter = 12 cm

Circumference = π x Diameter

= 22/7 x 12

= 37.71 cm

7. Diameter = 22 in

Circumference = π x Diameter

= 22/7 x 22

= 69.71 in

8. Diameter = 34 m

Circumference = π x Diameter

= 22/7 x 34 x 100

= 1068.57 m

9. Diameter = 10 m

Circumference = π x Diameter

= 22/7 x 10 x 100

= 314.29 m

10. Diameter = 34 cm

Circumference = π x Diameter

= 22/7 x 34

= 106.86 cm

Therefore, the circumference of the given diameters are 94.29 cm, 471.43 m, 377.14 ft, 62.86 cm, 251.43 m, 37.71 cm, 69.71 in, 1068.57 m, 314.29 m, 106.86 cm.

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The graph of the system of linear equations can be seen in the image at the end.

Here we have the following system of equations:

y = -(1/3)x + 1

y = -2x - 3

To graph the system of equations, we just need to graph both of these lines in the same coordinate axis. The point where the lines intercept are the solutions of the system.

In the image at the end we can see the graph of the system of equations, there we also can see that the solution is the point (-2.4, 1.8)

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The meaning of the given statement is concept of a cyclic subgroup in group theory.

What is cyclic group?

In group theory, a cyclic group is a group that can be generated by a single element. That is, it is a group that is generated by a single element a, where any element of the group can be expressed as a power of a.

The order of a cyclic group is equal to the order of its generator. If the generator has order n, then the cyclic group has n elements. The group operation in a cyclic group can be either additive or multiplicative, depending on the notation used.

The statement defines a cyclic subgroup is a subgroup of a group that is generated by a single element. The element used to generate the subgroup is called the generator of the cyclic subgroup. The set of all powers of the generator, including the inverse powers and the identity element, forms the cyclic subgroup.

In other words, the cyclic subgroup generated by an element a of a group is the smallest subgroup that contains a. It consists of all possible combinations of a and its inverse under the group operation.

A group or subgroup is called cyclic when it can be generated by a single element. In other words, if every element of the group can be expressed as a power of a single element, then the group is cyclic.

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The three angles of the triangle are 48 degrees, 60 degrees, and 72 degrees and it is a acute triangle.

The three angles of the triangle 4x, 5x, and 6x, where x is a constant of proportionality.

We know that the sum of the angles of a triangle is always 180 degrees, so we can set up an equation:

4x + 5x + 6x = 180

Simplifying, we get:

15x = 180

Dividing both sides by 15, we get:

x = 12

So the three angles of the triangle are:

4x = 4(12) = 48 degrees

5x = 5(12) = 60 degrees

6x = 6(12) = 72 degrees

all three angles are less than 90 degrees, the triangle is an acute triangle.

Therefore, the three angles of the triangle are 48 degrees, 60 degrees, and 72 degrees and it is a acute triangle.

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12 cans of soda hold 4.26 liters of soda.

The process for determining the total volume of soda would be the same using the specific capacity and number of cans.

We need to determine how many milliliters of soda 12 cans hold. We can do this by multiplying the capacity of one can (355 mL) by the number of cans (12):

355 mL/can x 12 cans = 4,260 mL

Now we need to convert this amount to liters. We know that 1 liter is equal to 1,000 milliliters, so we can divide the total volume in milliliters by 1,000:

4,260 mL ÷ 1,000 mL/L = 4.26 L

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The probability density function (pdf) of the lifetime of a certain device is expressed as: f (x) = 2λxe^−λx² ; x > 0; λ > 0

Mean: E(x) = -2λ + C

Mode: x = 0

Median: x = ±√(-ln(0.5)/λ)

Variance: Var(x) = 0

Probability density function (PDF) describes the relative likelihood for a random variable to take on a given value. It is a continuous function that is used to represent the probability distribution of a continuous random variable.

The probability density function (pdf) of the lifetime of a certain device is expressed as:

f (x) = 2λxe^−λx² ; x > 0; λ > 0

Mean: The mean (or expected value) of the probability density function is given by:

E(x) = ∫x.f(x)dx = ∫x.2λxe^−λx²dx

= -2λe^−λx² + C

E(x) = -2λ + C

Mode: The mode of the probability density function is the value at which the maximum density occurs. This occurs at the point where the derivative of the function is equal to 0.

f′(x) = 2λxe^−λx²

= 0

x = 0

Therefore, the mode of the probability density function is 0.

Median: The median is the value of the random variable for which the cumulative distribution function is equal to 0.5.

F(x) = 1 − e^−λx² = 0.5

1 − e^−λx² = 0

e^−λx² = 0.5

−λx² = ln(0.5)

x² = -ln(0.5)/λ

x = ±√(-ln(0.5)/λ)

Therefore, the median of the probability density function is given by:

x = ±√(-ln(0.5)/λ)

Variance: The variance of the probability density function is given by:

Var(x) = E(x²) - (E(x))²

E(x²) = ∫x².f(x)dx

= ∫x^2.2λxe^−λx²dx

= -2λe^−λx² + C

E(x²) = -2λ + C

Var(x) = -2λ + C - (-2λ + C)²

= 0

Therefore, the variance of the probability density function is 0.

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Answer:

a. Compounded semiannually: $19,216.67

b. Compounded quarterly: $19,338.56

c. Compounded monthly: $19,416.32

d. Compounded continuously: $19,451.08

Step-by-step explanation:

The formula for the accumulated value (A) of an investment with an initial principal (P), an interest rate (r) and a compounding period (n) for a number of years (t) is:

A = P(1 + r/n)^(n*t)

Using this formula, we can calculate the accumulated value for each of the compounding periods given:

a. Compounded semiannually:

A = $15,000(1 + 0.065/2)^(2*5) = $19,216.67

b. Compounded quarterly:

A = $15,000(1 + 0.065/4)^(4*5) = $19,338.56

c. Compounded monthly:

A = $15,000(1 + 0.065/12)^(12*5) = $19,416.32

d. Compounded continuously:

A = $15,000e^(0.0655) = $19,451.08

Therefore, the accumulated value of the investment varies depending on the compounding period, with more frequent compounding resulting in a higher accumulated value.

Answer:

I need the rotation in degrees around the origin (flip around x axis, 90 degrees counter clockwise) or send all of the graph options

Step-by-step explanation:

The Elasticity of Demand at a price of $8 is 0.056.

Given the demand function,

D(p) = 400 - 4p²

The formula to find the elasticity of demand is,

e = p/D

Here p is the price and D is the quantity demanded.

When p = $8,

D = 400 - (4 × 8²) = 144

Elasticity of demand = 8 / 144 = 0.056

Hence the elasticity of demand is 0.056.

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Answer:

400% of 2 is 8, so it would be less than 10

Step-by-step explanation:

Step-by-step explanation:

Subtract the 99 from 949 then    divide by 2

949-99= 425 dollars = price of dryer

( then washer is  425 + 99 )

We can eulerize this graph in the most efficient way possible by making these vertices have even degree through  adding  an edge between them.

We can Eulerize a graph by ensuring  to add edges to the graph in a way that preserves its connectivity while ensuring that all vertices have even degree.

A good method to do this is by  adding  edges between pairs of vertices that have odd degree until all vertices have even degree.

In the scenario above,  all the  vertices have odd degree except for the first and last vertices. To make these vertices have even degree, we go ahead and add an edge between them.

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Using Nearest Neighbor starting in Fort Worth, the route will have a total path length of 183.

Using Nearest Neighbor starting in

Foethliceth:

We take the cheapest way to travel,

19 38 41 D42 F

d+ F A 43 M

Total path length = 19 +43 +38 +41 +42 = 183

Using Repeated Nearest. Neighbor:

The repetitive nearest algorithm says. to tey each veetex as starting point I then choose the best answer.

Feam Fort Worth:

F 19 A 43 M 38 p 4D 42 F

Total path length. = 183

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Step-by-step explanation:

first, remember Pythagoras :

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle).

a and b are the legs.

so, in our case

c² = 4² + 6² = 16 + 36 = 52

c = sqrt(52) = 7.211102551... ≈ 7.21

and then remember the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides, A, B, C are the corresponding opposite angles (here also called alpha, beta. gamma would be the 90° angle).

so,

4/sin(alpha) = c/sin(90) = c

4 = c×sin(alpha)

sin(alpha) = 4/c = 4/7.211102551... = 0.554700196...

alpha = 33.69006753...° ≈ 33.69°

we don't need to do that much calculation for the third angle beta, as we know the sum of all angles in a triangle is always 180°.

so,

180 = alpha + beta + 90 = 33.69 + beta + 90

90 = 33.69 + beta

56.30993247... = beta ≈ 56.31°

Applying the circumference formula, the strip of aluminum foil should be about 38 inches long, which corresponds to answer choice D.

To determine the length of the aluminum foil strip, we need to find the circumference of the pie pan, which is the distance around the edge of the pan.

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle (which is half the diameter).

Since the pie pan has a diameter of 12 inches, the radius is 6 inches. Therefore:

C = 2π(6)

C ≈ 37.7 inches

This is approximately, D. 38 inches.

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Answer:

-4 < -2.3 < -0.43 < 69

Step-by-step explanation:

If you look at a number line,

-4 is the first to come and as we approach 0, it's -2.3 and then -0.43. After 0 is only 69 leftover.

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The height of the cone is 18 inches.

The height of the cone can be found as follows:

volume of a cone = 1 / 3 πr²h

where

Therefore,

r = 6 inches

volume of the cone = 678.24

h = ?

Hence,

678.24 = 1 / 3 × 3.14 × 6² × h

678.24 = 1 / 3 × 3.14 × 36 × h

37.68h = 678.24

divide both sides of the equation by 37.68

h = 678.24  / 37.68

h = 18 inches

Therefore,

height of the cone = 18 inches

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Answer:

57.89%

Step-by-step explanation:

Implied probability = (1 / (odds + 1)) x 100%

Using the odds of 8/11 for Hillary Clinton:

Implied probability = (1 / (8/11 + 1)) x 100% = 57.89%

There is a 57.89% chance that Hillary Clinton will win the presidency.

The initial amount of money with P was 2Q0 = 2 * 3Q0 = 6Q0.

Amount is the sum of money or quantity of something. It is usually measured in numerical values such as dollars, pounds, or euros. It is used to describe the total of something, such as how much money is in a bank account or the total cost of a purchase. Amount can also be used to describe a quantity of something such as the amount of time spent on a project or the amount of people present at an event.

Let us denote the initial amount of money with P, Q and R as P0, Q0 and R0 respectively. We know that P gave some money to Q and R such that their amounts were doubled, which implies that P0 = 2(Q0 + R0). Similarly, Q gave some money to P and R such that their amounts were doubled, which implies that Q0 = 2(P0 + R0). Finally, R gave some money to P and Q such that their amounts were doubled, which implies that R0 = 2(P0 + Q0). Substituting the value of P0 from the first equation in the third equation, we get:

2(Q0 + R0) = 2(P0 + Q0)
2Q0 + 2R0 = 2P0 + 2Q0
R0 = P0

Substituting the value of R0 in the first equation, we get:

P0 = 2(Q0 + R0)
P0 = 2(Q0 + P0)
P0 = 2Q0 + P0
P0 = 2Q0

Finally, substituting the value of P0 in the second equation, we get:

Q0 = 2(P0 + R0)
Q0 = 2(2Q0 + R0)
Q0 = 4Q0 + R0
R0 = 3Q0

Therefore, the initial amount of money with P, Q and R can be calculated as follows:
P0 = 2Q0
Q0 = 3Q0
R0 = 3Q0

Therefore, the initial amount of money with P was 2Q0 = 2 * 3Q0 = 6Q0.

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All the zeroes of the function are,

x = - 9, 5, 5

Given that;

The function is,

h (x) = (x + 9) (x² - 10x + 25)

Now, We can find all the zeroes of the function as;

h (x) = (x + 9) (x² - 10x + 25)

h (x) = (x + 9) (x² - 5x - 5x + 25)

h (x) = (x + 9) ((x - 5) - 5 (x - 5))

h (x) = (x + 9) (x - 5) (x - 5)

Thus, All the zeroes of the function are,

x + 9 = 0

x = - 9

(x - 5)² = 0

x = 5, 5

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The sum of geometric series 3+2.55+2.1675+1.842375+...

Hence, the correct option is B.

To find the sum of a geometric series, we can use the formula

S = a(1 - [tex]r^{n}[/tex]) / (1 - r)

Where

S = sum of the geometric series

a = first term of the series

r = common ratio of the series

n = number of terms in the series

In this case, we can see that the first term is 3 and the common ratio is 2.55/3 = 0.85. We can also see that there are an infinite number of terms in the series.

Using the formula for an infinite geometric series, we can simplify the formula to

S = a / (1 - r)

By putting these values we have, we get

S = 3 / (1 - 0.85) = 20.

Hence, the sum of the geometric series is 20.

Hence, the correct option is B.

The question is incomplete and the complete question is '' FIND THE SUM OF GEOMETRIC SERIES 3+2.55+2.1675+1.842375+...

A. 8

B. 20

C. 12

D. 4 ''

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When 70 to a z-score, the resulting z-score is 0

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

Mean = 70

Standard deviation = 8

Score = 70

To convert 70 to a z-score, we make use of the following equation

z = (score - mean)/Standard deviation

Substitute the known values in the above equation, so, we have the following representation

z = (70 - 70)/8

Evaluate the expression

z = 0

Hence, converting 70 to a z-score. we get 0

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The equation of the line that is perpendicular to the line passing through the points (-3, 10) and (3, 8) is y = 3x + 9.

To find a line that is perpendicular to another line, we need to use the fact that the slopes of the two lines are negative reciprocals of each other.

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the slope formula:

slope = (y₂ - y₁)/(x₂ - x₁)

Therefore, the slope of the line passing through the points (-3, 10) and (3, 8) can be found as follows:

slope = (8 - 10)/(3 - (-3)) = -1/3

Now, to find the equation of a line perpendicular to this line, we need to find the negative reciprocal of the slope -1/3, which is 3.

Therefore, the slope of the line perpendicular to the given line is 3.

Now, we can use the point-slope form of a linear equation to find the equation of the perpendicular line. The point-slope form of a linear equation is:

y - y₁ = m(x - x₁)

where m is the slope of the line, and (x₁, y₁) is any point on the line.

We know the slope of the perpendicular line is 3, and we can choose any point on the line. Let's choose the midpoint of the given points (-3, 10) and (3, 8), which is

=> ((-3+3)/2, (10+8)/2) = (0, 9).

So, using the point-slope form of the equation with m = 3 and (x1, y1) = (0, 9), we get:

y - 9 = 3(x - 0)

Simplifying this equation, we get:

y = 3x + 9

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The garment factory needs to produce an average of 126 sets per day in the next 2.5 days to complete the order of 690 sets.

We have,

The number of sets produced in the first 5 days.

= 5 x 75

= 375

The number of sets remaining.

= 690 - 375

= 315

The number of sets to be completed in the next 2.5 days.

= 315

The average number of sets to be completed per day.

= 315 / 2.5

= 126

Therefore,

The garment factory needs to produce an average of 126 sets per day in the next 2.5 days to complete the order of 690 sets.

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Answer:

Expected Value = -1(999/1000) + 499(1/1000) = -500/1000 = -50 cents

Step-by-step explanation: