What lump sum must be invested at 7​%, compounded​ monthly, for
the investment to grow to ​$61,000 in 13​years?

(2,1) is a solution to the system of equations 8x+7y=11 and x+y=3.

Two or more expressions with an Equal sign is called as Equation.

To check if (2,1) is a solution to the system of equations:

8x + 7y = 11

x + y = 3

We substitute x = 2 and y = 1 into both equations:

For the first equation: 8(2) + 7(1) = 16 + 7 = 23

For the second equation: 2 + 1 = 3

Hence, we can see that both equations are true when x = 2 and y = 1.

Therefore, (2,1) is a solution to the system of equations.

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 a_(n) = -12 + 100n.

The recursive formula for the sequence is a_(n) = a_(n-1) + 100. The first term of the sequence is a_(1) = -12 and the common difference is 100. The explicit form for this sequence is a_(n) = -12 + 100n.

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$600

B. $600 per week

For Activity 2, the Normal Cost is $1,000 and the Crash Cost is $4,600, so the Crash cost per week is $60.

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Solutions to Exercises 51-56:

The equation can be rewritten as: \( \cos x (2 \sin x-1)=0 \). The solutions are: \( \cos x=0 \) or \( \sin x=\frac{1}{2} \). The solutions in the interval \( [0,2 \pi) \) are: \( x=\frac{\pi}{2}, \frac{3 \pi}{2}, \frac{\pi}{6}, \frac{5 \pi}{6} \).

The equation can be rewritten as: \( \tan x (\sqrt{2} \cos x-1)=0 \). The solutions are: \( \tan x=0 \) or \( \cos x=\frac{1}{\sqrt{2}} \). The solutions in the interval \( [0,2 \pi) \) are: \( x=0, \pi, \frac{\pi}{4}, \frac{3 \pi}{4}, \frac{5 \pi}{4}, \frac{7 \pi}{4} \).

The equation can be rewritten as: \( \sin x (1-\cos x)=0 \). The solutions are: \( \sin x=0 \) or \( \cos x=1 \). The solutions in the interval \( [0,2 \pi) \) are: \( x=0, \pi, 2 \pi \).

Overall, the solutions to these exercises can be found by factoring the equations and finding the solutions to each factor in the given interval.

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The solutions in the interval \( [0,2 \pi) \) are x = 0, π, and 2π.

In Exercises 51-56, find all solutions to the equation in the interval \( [0,2 \pi) \). You do not need a calculator.

51. \( 2 \cos x \sin x-\cos x=0 \): The solutions in the interval \( [0,2 \pi) \) are x = 0, π, and 2π.

52. \( \sqrt{2} \tan x \cos x-\tan x=0 \): The solutions in the interval \( [0,2 \pi) \) are x = π/4, 3π/4, 5π/4, and 7π/4.

53. \( 2 \cos^2 x-\sin^2 x=1 \): The solutions in the interval \( [0,2 \pi) \) are x = 0, π, and 2π.

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The difference between their sound levels is 9.9W/m².

The preceding number, which is always put before a number, is referred to as the predecessor. A number's successor is the one that is written just after it. Take the list of natural numbers 1, 2, 3, 4, and 5, for instance. 1 is the precursor of 2, and 2 is the successor of 1. Consecutive numbers are those that come after one another in ascending sequence, from smallest to largest. The typical difference between every two numbers is 1.

Here, we have

Given: It is known that the sound levels of two consecutive thunderstorms in the storm are 0.1W/m² and 10W/m² respectively.

We have to find the difference between their sound levels.​

S₁ = 0.1W/m²

S₂ = 10W/m²

Difference = S₂ - S₁

Difference = 10W/m² - 0.1W/m²

Difference  = 9.9W/m²

Hence, the difference between their sound levels is 9.9W/m².

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The solution to the system of equations is (0,1).

To solve the system of equations using elimination, we need to eliminate one of the variables. In this case, we will eliminate x by multiplying the first equation by -2 and the second equation by 6.

First equation: 6x+3y=3
Second equation: 2x+7y=7

Multiply the first equation by -2: -12x-6y=-6
Multiply the second equation by 6: 12x+42y=42

Now we can add the two equations together to eliminate x:
-12x-6y=-6
+12x+42y=42
_______________
0x+36y=36

Now we can solve for y:
36y=36
y=1

Now we can plug y back into one of the original equations to solve for x:
6x+3(1)=3
6x+3=3
6x=0
x=0

So the solution to the system of equations is (0,1).

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The probability of a randomly selected tester from this group having a score between 1497 and 1819 is approximately 0.68.

Probability is the measure of how likely a certain event is to occur. It is a mathematical concept that is used to quantify the likelihood of a certain outcome from a given set of circumstances. Probability is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain. Probability is used in many fields, including mathematics, finance, and decision making.

This is because approximately 68% of the data is within one standard deviation of the mean, and the data is normally distributed. The area between the mean and the upper limit of 1819 is 0.68, which means that the graph probability of a randomly selected tester from this group having a score between 1497 and 1819 is 0.68.

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We can find g(x) for any value of x by using the function notation g(x) = f(x) + 6.

The function g is related to the parent function f by a vertical shift of 6 units. In function notation, we can write g in terms of f as:

g(x) = f(x) + 6

This means that for any value of x, we can find the corresponding value of g by first finding the value of f at that x value, and then adding 6.
For example, if x = 2, we can find g(2) by first finding f(2) and then adding 6:
f(2) = 2^(2) = 4
g(2) = f(2) + 6 = 4 + 6 = 10
So g(2) = 10.

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Answer:

Step-by-step explanation:

2b + 3d = 13.25

2b + 2d = 11.50

2b + 3d = 13.25

-2b - 2d = -11.50

d = $1.75 for one drink

2b + 3.50 = 11.50

2b = 8

b = $4 for one Big Mac

The expression x -2 y-4 3 sqrt 64xy³ can be written in the form axby as follows:

ax -2by-4c 3 sqrt 64xy³

Coefficient in mathematics is a numerical value that is used to represent the magnitude of a given quantity in an equation. It is normally the numerical factor associated with the variables in an equation that represent a certain amount of change in the equation. For example, the coefficient of x in the equation y = 5x + 7 is 5, which indicates that x is multiplied by 5 in the equation.

In this expression, a, b, and c refer to the coefficients of the x, y, and the cube of y respectively. Thus, a is equal to 1, b is equal to -2, and c is equal to -4. Therefore, the product of a, b and c is equal to 8.

To break down the expression further, the coefficient of x is a, which is equal to 1. The coefficient of y is -2b, which is equal to -2. The coefficient of the cube of y is -4c, which is equal to -4. Finally, the coefficient of the square root of 64xy³ is 3, which is equal to 3.

Thus, when written in the form axby, the expression x -2 y-4 3 sqrt 64xy³ is equal to 1 -2 -4 3 sqrt 64xy³. The product of a, b, and c in this expression is equal to 8.

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Answer:

Smaller number = 19

Larger number = 71

x + y = 90

x = 14 + 3y

Step-by-step explanation:

Let y represent the smaller number, and then represent the larger number as x, in terms of y:

Smaller number = y

Larger number = x = 3y + 14

Since the sum of the two numbers is 90, form an equation by adding them together in this notation:

y + 3y + 14 = 90

Simplify the equation:

4y + 14 = 90

4y = 76

y = 19

Therefore the smaller number is 19. Now substitute into the expression for the larger number to find its value:

x = 3(19) + 14 = 71

Now verify the two values sum to 90 like we expect:

19 + 71 = 90

Now we can use what we know to complete the equations, if x = 71:

x + y = 90 (we know they sum to 90)

x = 14 + 3y (as respresented above - multiplying by 3 and adding 14)

answer is adjacent angles

Answer:

complementary and

adjacent

Step-by-step explanation:

Complementary means the angles add up to 90°, that is, they make a right angle.

Adjacent means they are next to each other.

Both of these are the correct answer.

(since the question has boxes on the answers, you can mark more than one correct answer)

As a result, the circle's precise size is (529/4)π³  square centimetres.

A circle is a closed, two-dimensional shape where every point in the surface is equally spaced from a central point. The line of mirror symmetry is formed by all lines that traverse the circle. Additionally, every point has circular symmetry around the centre.

The circumference of a circle is given by the formula:

C = 2πr

where r is the radius of the circle. We can rearrange this formula to solve for the radius:

r = C / 2π

When we substitute the circumference's specified number, we obtain:

r = (23r) / (2π)

Simplifying:

r = (23/2)π

Now that we know the radius, we can use the formula for the area of a circle:

A = πr²

Substituting the value we found for the radius, we get:

A = π[(23/2)π]²

Simplifying:

A = π(529/4)π²

A = (529/4)π³

Therefore, the exact area of the circle is (529/4)π³ square cm.

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Answer:

y = 129°

Step-by-step explanation:

the figure has opposite sides congruent and is therefore a parallelogram.

• consecutive angles are supplementary , that is

y + 51° = 180° ( subtract 51° from both sides )

y = 129°

This is our final answer in terms of n.

The given sum is n Σ (3k – 3) = ____ , where k=1. To express this sum in closed form, we can use the formula for the sum of an arithmetic series. The formula is:

S = n/2 (a1 + an)

where S is the sum, n is the number of terms, a1 is the first term, and an is the last term.

In this case, the first term is 3(1) - 3 = 0 and the last term is 3(n) - 3 = 3n - 3. Plugging these values into the formula, we get:

S = n/2 (0 + 3n - 3)

Simplifying the equation gives us:

S = n/2 (3n - 3)

S = (3n^2 - 3n)/2

S = (3n^2)/2 - (3n)/2

S = (3/2)n^2 - (3/2)n

Therefore, the sum in closed form is:

n Σ (3k – 3) = (3/2)n^2 - (3/2)n

This is our final answer in terms of n.

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The quadratic equations are solved and the value of x are 1 and -7 respectively

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

a)

x² + 6x = 7

Adding 9 on both sides of the equation , we get

x² + 6x + 9 = 16

On simplifying the equation , we get

( x + 3 )² = ( 4 )²

Taking square roots on both sides , we get

x + 3 = ±4

Subtracting 3 on both sides , we get

x = 1 and x = -7

Therefore , the value of x are 1 and -7 respectively

Hence , the quadratic equations is solved

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Answer:

P'(1,2) S'(2,5)

Step-by-step explanation:

P(3,-2) S(4,-5) glode translation (x-2,y)

-2 -2

P(1,-2) S(2,-5) reflect over x-axis

P'(1,2) S'(2,5) ----> answer

hope this helpzzz

Answer:

0.011

Step-by-step explanation:

Answer:9.05

Step-by-step explanation: uh why? its easy

John must score 286 on his 8th game to achieve an average score of 215.

What is an Average?

Average, also known as the mean, is a mathematical concept that represents the central value of a set of numbers. It is found by dividing the sum of the numbers by the total count of the numbers.

To find out what John must score on his 8th game to achieve an average score of 215, we need to use the formula for calculating the average or mean:

Average = (Sum of Scores) / (Number of Scores)

We can use this formula to solve for the unknown score:

215 = (159 + 182 + 225 + 240 + 198 + 200 + 230 + x) / 8

Multiplying both sides by 8, we get:

1720 = 159 + 182 + 225 + 240 + 198 + 200 + 230 + x

Simplifying, we get:

1720 = 1434 + x

Subtracting 1434 from both sides, we get:

x = 286

Therefore, John must score 286 on his 8th game to achieve an average score of 215.

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Answer: VA: x = 2

Step-by-step explanation: In order to find the verticle asymtote you have to substitute values for x in order to get zero. Look in the denominator and see which value minus or plus the value next to it will equal zero. In this case, 2-2 is 0 so your verticle asymtote is 2. Keep in mind you want 0 in the denominator because that would mean the value on a graph is undefined, showing your asymtote.

Answer: 2

Step-by-step explanation:

The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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The maximum height reached by the baII is 9 meters.

In mathematics, a functiοn is a relatiοn between twο sets, typically called the dοmain and range, that assigns tο each element οf the dοmain a unique element οf the range. In οther wοrds, a functiοn is a rule οr a set οf rules that assοciates each input value with exactly οne οutput value.

Tο find the maximum height reached by the ball, we need to find the vertex of the parabolic functiοn [tex]h = -t^2 + 6t[/tex]. The vertex of a parabola in the form[tex]y = ax^2 + bx + c[/tex] is located at the point [tex](-b/2a, c - b^2/4a)[/tex].

In this case, the functiοn is[tex]h = -t^2 + 6t[/tex]t, which has a=-1, b=6, and c=0. Therefοre, the vertex οf the parabοla is located at:

t = -b/2a = -6/(-2) = 3

Tο find the maximum height, we substitute t = 3 into the functiοn:

[tex]h = -t^2 + 6t = -3^2 + 6(3) = 9 meters[/tex]

Therefοre, the maximum height reached by the baIl is 9 meters.

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(1) The distance from the starting point to the final point is 589.5 km and  the bearing from the starting point to the final point is 16.7° north of east

(2) The distance from the ship to the port is 126.49 km and the bearing of the port from the ship is  18.4° south of west.

To solve this problem, we can use the law of cosines to find the distance from the starting point to the final point. We can also use trigonometry to find the bearing (angle) between the starting point and final point.

See the diagram attached:

We want to find the distance and bearing from the starting point (x) to the final point.

Using the law of cosines, we have:

c² = a² + b² - 2abcos(C)

c² = 500² + 150² - 2x500x150xcos(120°)

c² = 250,000 + 22,500 + 75,000

c² = 347,500

c = √347,500

c = 589.5 km

To find the bearing, we can use trigonometry. Let θ be the angle between the line from the starting point to the final point and due east.

tan(θ) = (150 km) / (500 km)

θ = tan⁻¹(0.3)

θ = 16.7°

2. To solve this problem, we can use the Pythagorean theorem to find the distance from the ship to the port. We can also use trigonometry to find the bearing (angle) between the ship and the port.

We want to find the distance and bearing of the port (P) from the ship (S).

Using the Pythagorean theorem, we have:

d² = 120² + 40²

d² = 14400 + 1600

d² = 16000

d = √(16000)

d = 126.49 km

To find the bearing, we can use trigonometry. Let θ be the angle between the line from the ship to the port and due west.

tan(θ) = (40 km) / (120 km)

θ = tan⁻¹ (1/3)

θ = 18.4°

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The actual area of the lake 64000 square meters.

When two numbers are compared, the ratio between them shows how often the first number contains the second. As an illustration, the ratio of oranges to lemons in a dish of fruit is 8:6 if there are 8 oranges and 6 lemons present.

In this given question, we are first of all going to use the given ratio of the on map measurements to the actual measurements, that is 1:20000 to calculate the actual measurements as follows:

[tex]1.6cm^2=1\times 1.6cm^2[/tex]------->1

Using the ratio 1:20000 in 1.1, we get,

[tex]1.6\times1 cm^2= 1.6\times (20000)^2 cm^2 = 1.6\times 400000000 cm^2 = 640000000cm^2[/tex]-----> 2

As the actual measurement of the area of the lake.

So, 1m = 100 cm

=> [tex](1m)^2=(100cm)^2[/tex]

=> [tex]1m^2 = 10000cm^2[/tex]-------> 3

So, using equation 3 in the value obtained 2, we get,

=> [tex]640000000cm^2 = \frac{640000000}{10000} = 64000m^2[/tex]

Hence the actual area of the lake is 64000 square meters.

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The value of y that satisfies the equation is y = -11.

An equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two sides, separated by an equals sign (=), with each side containing one or more terms that may include variables, constants, and mathematical operators.

We can start by setting up the equation:

(y+1)/(y-5) + 10/(y+5) = (y+1)/(y-5) × 10/(y+5)

To solve for y, we need to simplify and manipulate the equation:

Multiply both sides by (y-5) × (y+5) to eliminate the denominators:

(y+1)(y+5) + 10(y-5) = 10 × (y+1)

Expand and simplify:

y² + 6y - 15 + 10y - 50 = 10y + 10

Combine like terms:

y² + 16y - 55 = 0

Factor the quadratic:

(y + 11)(y - 5) = 0

Solve for y:

y = -11 or y = 5

However, we need to check if either solution makes the denominators of the original equation equal to zero, since division by zero is undefined:

For y = -11, the denominators are -16 and -6, respectively, which are both nonzero. Therefore, y = -11 is a valid solution.

For y = 5, the denominator of the first fraction is 0, which is not allowed. Therefore, y = 5 is an extraneous solution and should be discarded.

Therefore, the value of y that satisfies the equation is y = -11.

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The scale factor is 11.

Scale factor is a numerical value used to proportionally enlarge or reduce a size of an object or image. It is also used to compare two similar shapes or objects. When the scale factor is greater than 1, it indicates an increase in size and when the scale factor is less than 1, it indicates a decrease in size. Scale factors are usually expressed as a ratio, such as 1:2, which means that the object has been doubled in size.

To calculate it, divide the first number by the second number and multiply by the third number: (35/42) x 11 = 10.714. Therefore, the scale factor is 11.

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The best estimate of the volume of the stack once it has been bumped/shifted is 4πt³ cubic centimeters.

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases connected by a curved surface. The volume of a cylinder is the amount of space occupied by the shape and is given by the formula:

Volume = πr²h

where π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the circular base, and h is the height of the cylinder.

Assuming that the coins have the same dimensions and are perfectly circular, the original stack of 15 coins formed a cylinder with a height of 15 times the thickness of a single coin, and a radius equal to the radius of a single coin.

The volume of this cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height.

Since the volume of the original stack is 8 cubic centimeters, we can set up the equation:

8 = πr²(15t)

where t is the thickness of a single coin.

Solving for r, we get:

r = √(8/15πt)

When the stack is bumped and shifts to a leaning position, the new shape will still be a cylinder, but the height will be shorter than before. Let's say that the new height is h2. We can calculate the new volume using the same formula:

V2 = πr²h2

To estimate the new height, we can use the fact that the coins are now leaning against each other, so the new height will be less than 15t. Let's say that the new height is approximately 12t.

Substituting in the values, we get:

V2 = π(√(8/15πt))²(12t)

Simplifying, we get:

V2 = 4πt³

Therefore, the best estimate of the volume of the stack once it has been bumped/shifted is 4π³ cubic centimeters.

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Fraction in simplest form is (3)/(4).

To add or subtract fractions with the same denominator, you simply add or subtract the numerators and keep the same denominator. Then, simplify the fraction if possible.

In this case, the fractions have the same denominator of 8, so we can simply add the numerators:

(1)/(8) + (5)/(8) = (1 + 5)/(8) = (6)/(8)

Now, we need to simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator. The GCF of 6 and 8 is 2, so we can divide both the numerator and denominator by 2 to get:

(6)/(8) = (6/2)/(8/2) = (3)/(4)

So the final answer is (3)/(4).

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