a canoe is seen floating down a creek. the canoe is first spotted 65 ft away. 7 seconds later the canoe is 40. ft away, making a 50° angle between the two settings how far did the canoe travel

Answer:

To solve the system of linear equations:

4x + 3y = 18

4x - 2y = 18

we can use the method of elimination or substitution.

Method 1: Elimination

In this method, we eliminate one of the variables by adding or subtracting the equations in a way that eliminates one of the variables. Here's how we can do it:

Multiply the first equation by 2, and the second equation by 3 to eliminate x:

8x + 6y = 36

12x - 6y = 54

Now, subtract the second equation from the first:

8x + 6y - (12x - 6y) = 36 - 54

8x + 6y - 12x + 6y = -18

-4x + 12y = -18

Divide both sides by -4 to isolate x:

-4x/(-4) + 12y/(-4) = -18/(-4)

x - 3y = 4.5

Now, we can substitute this value of x into one of the original equations, let's use the first equation:

4(4.5) + 3y = 18

18 + 3y = 18

3y = 18 - 18

3y = 0

y = 0

So, the solution to the system of equations is x = 4.5 and y = 0.

Method 2: Substitution

In this method, we solve one of the equations for one variable and then substitute that expression into the other equation to solve for the other variable. Here's how we can do it:

Solve the first equation for x:

4x + 3y = 18

4x = 18 - 3y

x = (18 - 3y)/4

Now, substitute this expression for x into the second equation:

4[(18 - 3y)/4] - 2y = 18

18 - 3y - 2y = 18

-5y = 18 - 18

-5y = 0

y = 0

Now, substitute this value of y back into the expression for x:

x = (18 - 3(0))/4

x = 18/4

x = 4.5

So, the solution to the system of equations is x = 4.5 and y = 0, which is consistent with the solution obtained using the elimination method.

Answer:

(4.5,0)

Step-by-step explanation:

The point that makes this system of equations true is (4.5,0.

When x=4.5, and y=0 both of these equations equal each other.

You can find this point either by using your calculator, or graphing the equations and seeing where they intersect.

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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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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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 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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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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Answer:

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

Step-by-step explanation:

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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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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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

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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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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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.

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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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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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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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:

-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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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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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

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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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.

Step-by-step explanation:

circular permutations of n objects =(n-1)!

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°

The total personnel costs of the cleanup would be $8,625.

Between 9AM and 5PM, a total of 8 hours, the workers are present during the interval t=0 to t=8. During this interval, the number of workers is given by:

f(t) = 30 + 10sin((2π/16)t)

We can calculate the number of workers for each hour using this formula:

f(0) = 30 + 10sin(0) = 30

f(1) = 30 + 10sin(π/8) ≈ 38.66

f(2) = 30 + 10sin(π/4) = 40

f(3) = 30 + 10sin(3π/8) ≈ 38.66

f(4) = 30 + 10sin(π/2) = 40

f(5) = 30 + 10sin(5π/8) ≈ 38.66

f(6) = 30 + 10sin(3π/4) = 30

f(7) = 30 + 10sin(7π/8) ≈ 21.34

f(8) = 30 + 10sin(π) = 20

So, during the first 8 hours, the number of workers fluctuates between 20 and 40.

Between 5PM and 9AM the next day, a total of 16 hours, the workers are present during the intervals t=8 to t=12, t=20 to t=36, and t=44 to t=48. During these intervals, the number of workers is given by:

Between t=8 and t=12, the number of workers is decreasing from 40 to 20. We can approximate this by a linear function:

f(t) = 40 - 5t

Between t=20 and t=36, the number of workers is constant at 20.

Between t=44 and t=48, the number of workers is increasing from 20 to 40. We can use the same linear function as before, but with t shifted by 44:

f(t) = 40 - 5(t-44)

We can now calculate the total personnel costs by multiplying the number of workers at each time interval by the appropriate hourly rate:

From 9AM to 5PM (8 hours): 30 workers on average, at a rate of $15 per hour:

8 × 30 × 15 = $3,600

From 5PM to 9AM the next day (16 hours):

From t=8 to t=12 (4 hours): average of 30 workers, at a rate of $22.5 per hour:

4 × 30 × 22.5 = $2,700

From t=20 to t=36 (16 hours): constant 20 workers, at a rate of $22.5 per hour:

16 × 20 × 22.5 = $7,200

From t=44 to t=48 (4 hours): average of 30 workers, at a rate of $22.5 per hour:

4 × 30 × 22.5 = $2,700

The total cost is the sum of the costs for each time interval:

$3,600 + $2,700 + $7,200 + $2,700 = $16,200

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Answer:

The height of the squirrel is 31 feet.

Step-by-step explanation:

You need to know your Right Triangle Trigonometry to do this problem.

Rt Triangle trig is all about ratios. Angles and ratios.

In your question, there is a rt triangle. The side measure given, 28 is next to the angle. The math word for "next to" is "adjacent" You know the adjacent side. The squirrel's height is the opposite side. The ratio that puts together adjacent and opposite is tangent.

tan Angle = opposite/adjacent

tan 48° = x/28

multiply both sides by 28

28•tan48° = x



You have to use a calculator that has trig functions. It will have buttons that say "sin", "cos", and "tan"



Enter 28 × tan48° =

It will return 31.0971504152

Your question asks you to round to the nearest whole.

x = 31

The squirrel's height in the tree is 31ft.

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:

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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