Give an example of a compound interest problem. Then solve the
problem.
Write me a problem about compound interest. The simple interest on a sum of money for 3 years at 6²/₃ % per annum is $ 6750. What will be the compound interest on the same sum at the same rate for the same period, compounded annually?

The y-intercept is 20 and, in the situation, it represents the initial pledge plan.

In Mathematics, the y-intercept is sometimes referred to as an initial value or vertical intercept and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Based on the information provided, an equation that describes the relationship between the money ($) received and the distance (meters) walked is given by;

M = 20 - 3d

M = 20 - 3(0)

M = 20

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In A parallelogram MNPQ with MN=12cm, MQ = 10 cm

a) The length of side PQ is equals to the 12 cm.

b) The measure of angle Q is equals to the 155°.

In a geometry, a parallelogram is a simple quadrilateral with

We have a parallelogram MNPQ, with

Side length, MN = 12cm

Other side length, MQ = 10 cm

Measure of angle M is = 25°

Also, MN|| PQ and MQ||NP

a) From the definition of parallelogram, the length of side MN is parallel to PQ and are of equal length. So, PQ = MN

= 12 cm

b) By the definition of parallelogram, opposite angles of a parallelogram are of equal measure. So, the measure of angle P = measure of angle M = 25°

Also, measure of angle N = measure of angle Q = x

Sum of all interior angles of quadrilateral

= 360°

=> m∠P + m∠N + m∠M + m∠Q = 360°

=> 25° + x + 25° + x = 360°

=> 2x + 50° = 360°

=> 2x = 310°

=> x = (310/2)° = 155°

Hence, required value of measure of angle Q is 155°.

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Complete question:

In A parallelogram MNPQ if MN=12cm , MQ = 10 cm and mZM = 25°. What is a)PQ

b) measure of angle Q

One way is to divide both numbers (the numerator and denominator) by 5. You will get 2/5.

Another way is to multiply both numbers (the numerator and denominator) 10. You will get 100/250.

The indicated trigonometric values in the specified quadrant are sec(O) = 1/3, sin(O) = sqrt(-8), and csc(O) = 1/sqrt(-8).

To find the indicated trigonometric value in the specified quadrant using the function value, we need to use the relationships between the different trigonometric functions. The given function value is cosich (C) = 3 in quadrant 2.

First, we can use the relationship between cosine and secant to find the value of secant. The relationship is:
sec(O) = 1/cos(O)

Since cosich (C) = 3, we can substitute this value into the equation and solve for sec(O):
sec(O) = 1/3

Next, we can use the relationship between cosine and sine to find the value of sine. The relationship is:
sin^2(O) + cos^2(O) = 1

Substituting the value of cosich (C) = 3 into the equation, we get:
sin^2(O) + 3^2 = 1

Solving for sin^2(O), we get:
sin^2(O) = 1 - 9 = -8

Taking the square root of both sides, we get:
sin(O) = sqrt(-8)

Since we are in quadrant 2, the value of sine will be positive. Therefore, the value of sin(O) is sqrt(-8).

Finally, we can use the relationship between sine and cosecant to find the value of cosecant. The relationship is:
csc(O) = 1/sin(O)

Substituting the value of sin(O) = sqrt(-8) into the equation, we get:
csc(O) = 1/sqrt(-8)

Therefore, the value of csc(O) is 1/sqrt(-8).

In conclusion, the indicated trigonometric values in the specified quadrant are sec(O) = 1/3, sin(O) = sqrt(-8), and csc(O) = 1/sqrt(-8).

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2 divided by 4 and 3 divided by 6 where these number can be any numbers that have the same ratio as 1:2 and under 0-6 and not repeating them.

A number is a fundamental building block of mathematics. For a range of tasks, including measuring, counting, and indexing, numbers are utilised. There are different types of numbers depending on their characteristics, such as natural numbers, whole numbers, rational and irrational numbers, integers, real numbers, complex numbers, even and odd numbers, etc. The basic integer arithmetic operations can be used to calculate the outcome number.

In the given question, we need to find two sets of three distinct numbers between 0 and 6 that have the same ratio.

One possible solution is:

2 divided by 4.

= 3 divided by 6

Here:

The ratio of the first set is 2:4 or 1:2. When we divide 2 by 4, we get 0.5.

The ratio of the second set is 3:6 or 1:2. When we divide 3 by 6, we also get 0.5.

Therefore, we have:

2 divided by 4.

= 0.5

3 divided by 6.

= 0.5

So, we can say:

2 divided by 4

= __ divided by __

where 3 and 6 can be any numbers that have the same ratio as 1:2.Similarly,

3 divided by 6

= __ divided by __

where 3 and 6 can be any numbers that have the same ratio as 1:2.

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The correct coordinates of N' is (-3, -4).    

Rotation of coordinates involves changing the orientation of a point or object in a plane about a fixed point called the center of rotation.

This process can be accomplished by applying a set of transformation rules to the original coordinates of the object.

When a point (x, y) rotated about the origin at 180° then the coordinates resultant point are (-x, -y).

Here we have

Point N has coordinates (3, 4)

Given that the point N is rotated about 180°  

As we know when the point (x, y) rotated about the origin at 180° then the resultant point is (-x, -y)

Here (3, 4) is rotated about 180°

The resultant point N' is (-3, -4)      

Therefore,

The correct coordinates of N' is (-3, -4).    

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Answer:

Step-by-step explanation:

This question doesn't say how much her lunch cost.

1. The positive x-intercept of the function f(x)= -1201(x-88)^2 + 151058 is 88 feet.

2. The y-intercept of the function f(x) = -1201(x-88)^2 + 151058 is 151058 feet.

3. The maximum height that the football reaches is 151058 feet, and the horizontal distance from Patrick Mahomes when this happens is 88 feet.

4. Yes, Travis Kelce will be able to catch the football, since it reaches a height of 10 feet or lower at the horizontal distance of 160 feet from Patrick Mahomes.

5. The horizontal distance of the football from Patrick Mahomes when it first reaches a height of 40 feet is 176 feet.

1. The positive x-intercept represents the horizontal distance from Patrick Mahomes at which the football is initially released.

2. The y-intercept of the function represents the height of the football when it is released from Patrick Mahomes.

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Answer:

5x^2+2x-7

Step-by-step explanation:

First find the common variable.

6x^2 + 10x -7 and -x^2 -8x

Add those together like any other problem.

[tex](6x^2 + 10x -7) + (-x^2 -8x)\\\\6x^2+10x-7 -x^2-8x\\\\(6x^2-x^2) + (10x-8x) - 7\\\\5x^2+2x-7[/tex]

The polynomial that 3x^(2)-22x+26 is divided by is x - 6.

To find the polynomial that 3x^(2)-22x+26 is divided by, we can use the formula:

Dividend = Quotient * Divisor + Remainder

In this case, the dividend is 3x^(2)-22x+26, the quotient is 3x-4, and the remainder is 2. We can plug these values into the formula and solve for the divisor:

3x^(2)-22x+26 = (3x-4) * Divisor + 2

Next, we can rearrange the equation to isolate the divisor:

Divisor = (3x^(2)-22x+26 - 2) / (3x-4)

Divisor = (3x^(2)-22x+24) / (3x-4)

Now, we can use polynomial long division to find the divisor:

```
3x - 4 | 3x^2 - 22x + 24
      - (3x^2 - 4x)
      -------------
           -18x + 24
          - (-18x + 24)
          -------------
                0
```

Therefore, the divisor is x - 6.

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The risk premium of L2 is $19,000 - $18,000.5 = $999.5.

The utility function u(x) = 2x + 1 represents a risk-neutral individual. This is because the utility function is a linear function, meaning that the marginal utility of wealth is constant. Therefore, the individual is indifferent between a certain outcome and a risky outcome with the same expected value.

To determine which lottery the individual prefers, we can calculate the expected utility of each lottery and compare them. The expected utility of a lottery is the sum of the probabilities of each outcome multiplied by the utility of that outcome.

The expected utility of Li is:

EU(Li) = 1 * u($20,000 - $1,000) = 1 * u($19,000) = 1 * (2 * $19,000 + 1) = $38,001

The expected utility of L2 is:

EU(L2) = 0.9 * u($20,000 + $0) + 0.1 * u($20,000 - $10,000) = 0.9 * u($20,000) + 0.1 * u($10,000) = 0.9 * (2 * $20,000 + 1) + 0.1 * (2 * $10,000 + 1) = $36,001.1

Since the expected utility of Li is greater than the expected utility of L2, the individual prefers Li.

The risk premium of L2 is the difference between the certain outcome that gives the same utility as L2 and the expected value of L2. The certain outcome that gives the same utility as L2 is $18,000.5, since u($18,000.5) = $36,001.1. The expected value of L2 is $19,000. The risk premium of L2 is $19,000 - $18,000.5 = $999.5.

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Risk premium = $900

a) Since the utility function is increasing, this means you are risk-averse as increasing your position increases your utility.

b) In this case, you would prefer Lottery Li as it has lower risk of loss compared to Lottery L2. The risk premium of L2 can be calculated by finding the expected value of the lottery and subtracting the expected value of Li.
Expected Value of Li: (.9 x $20,000) - (.1 x $1,000) = $18,900
Expected Value of L2: (.9 x $20,000) - (.1 x $10,000) = $18,000

Risk premium = $18,900 - $18,000 = $900

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I hope you're doing well and this gives a clear understanding to you.

The intercepts of the line are (-3, 0) and (0, -6/5).

What is intercepts ?

In mathematics, intercepts refer to the points at which a line or curve intersects the x-axis or the y-axis of a coordinate plane.

To find the x-intercept, we need to set y = 0 and solve for x:

2x + 5(0) = -6

2x = -6

x = -3

Therefore, the x-intercept is (-3, 0).

To find the y-intercept, we need to set x = 0 and solve for y:

2(0) + 5y = -6

5y = -6

y = -6/5

Therefore, the y-intercept is (0, -6/5).

Thus, the intercepts of the line are (-3, 0) and (0, -6/5).

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The average rate of f(x), in [4,6], is equal to 20.

To find the average rate of change of a function over an interval, we use the formula:

Average rate of change = (f(b) - f(a))/(b - a)

Where f(x) is the function, a and b are the endpoints of the interval, and f(a) and f(b) are the values of the function at those endpoints.

In this case, our function is f(x) = 2x² - 9, and our interval is [4, 6]. So, we plug in the values into the formula:

Average rate of change = (f(6) - f(4))/(6 - 4)

First, we find f(6) and f(4):

f(6) = 2(6²) - 9 = 2(36) - 9 = 72 - 9 = 63

f(4) = 2(4²) - 9 = 2(16) - 9 = 32 - 9 = 23

Now we plug these values back into the formula:

Average rate of change = (63 - 23)/(6 - 4) = 40/2 = 20

In conclusion, the average rate is worth 20.

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Answer:

FDG is 28 degrees, and x = 4

Step-by-step explanation:

We can see for angle EDG that there is a little box at the angle. This means that it is a right angle, which means it is 90 degrees. This, in turn, means that the two angles formed there (angle EDF, and angle FDG) will add up to that number, 90 degrees because they are within the initial angle.

Let us create an equation using our angles. We know one is 62 degrees and the other is 7x degrees.

62 +7x = 90

7x = 28

x =4

This means that the unknown value is 4, and since the angle was 7x, it is really 7(4) = 28 degrees, and we know the other angle is 62 degrees.

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The equivalent of the expression is w⁴z⁵/s⁶r⁵

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

s⁻⁶r⁻⁵w⁵z⁵w⁻⁹

Evaluate the like factors using the law of indices

So, we have the following representation

s⁻⁶r⁻⁵w⁴z⁵

Rewrite the expression without negative exponents.

So, we have

w⁴z⁵/s⁶r⁵

hence, the expression is w⁴z⁵/s⁶r⁵

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Answer: 55 miles per hour.

To find the unit rate, divide the miles traveled by the time taken:

275 miles ÷ 5 hours = 55 miles per hour

Step-by-step explanation:

19). The probability that a student attained a B or a C on the quiz is 0.42, or 42%. 20). The events for selecting the balls are dependent. This is because the probability of selecting the second ball is affected by the selection of the first ball.

The probability that a student attained a B or a C on the quiz can be found by adding the probabilities of the two events together. First, find the probability of attaining a B by dividing the number of students who attained a B by the total number of students. Do the same for the probability of attaining a C. Then add the two probabilities together to find the total probability.

Probability of attaining a B = (Number of students who attained a B) / (Total number of students) = 17 / 100 = 0.17
Probability of attaining a C = (Number of students who attained a C) / (Total number of students) = 25 / 100 = 0.25
Total probability = 0.17 + 0.25 = 0.42
Therefore, the probability that a student attained a B or a C on the quiz is 0.42, or 42%.

After the first ball is selected, there is one less ball in the bin, which changes the probability of selecting the second ball. Therefore, the events are dependent.

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The congruent triangles are given as follows:

DEC and BEA.

Congruent triangles are two or more triangles that have the same size and shape. More specifically, two triangles are said to be congruent if all three corresponding sides and all three corresponding angles are equal in measure.

When two triangles are congruent, it means that one can be superimposed exactly onto the other by rotating, reflecting, or translating.

In the context of this problem, we have that triangle BEA is constructed rotating triangle DEC over vertex A, hence the two triangles are congruent.

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The simplified expression is -12 and 5/12

In mathematics, an expression is a combination of symbols and/or numbers that can be evaluated or simplified to produce a certain value. Expressions can contain variables, constants, operators, and functions, and can be written in a variety of forms, such as algebraic expressions, trigonometric expressions, and exponential expressions.

Negative 4 and 2 over 3 can be written as -(4 x 3 + 2) / 3 = -14 / 3

7 and 3 over 4 can be written as 7 x 4 + 3 / 4 = 31 / 4

Next, you need to find a common denominator for the two fractions, which is 12. To convert -14/3 to a fraction with a denominator of 12, you need to multiply the numerator and denominator by 4, giving you -56/12. To convert 31/4 to a fraction with a denominator of 12, you need to multiply the numerator and denominator by 3, giving you 93/12.

Finally, you can subtract the two fractions by subtracting their numerators and keeping the denominator the same:

(-56/12) - (93/12) = -149/12

To convert this improper fraction back to a mixed number, you can divide the numerator by the denominator and get a quotient of -12 with a remainder of -5.

Therefore, the simplified expression is -12 and 5/12 or -12.41667 (rounded to five decimal places).

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The value of n for the given equation 3⁵. 3ⁿ = 3⁸ is n = 3.

Several rules of exponents are presented according to the capacities they possess. The following rule governs multiplication: Add the exponents while maintaining the base's consistency.

When bases are raised by a power of two or more, multiply the exponents while maintaining the original base.

Division Rule: When dividing similar bases, take the exponent of the denominator and divide it by the exponent of the numerator, keeping the base constant.

The given equation is:

3⁵. 3ⁿ = 3⁸

Using the product rule for exponents we have:

3⁽⁵ ⁺ ⁿ⁾ = 3⁸

The above expression can be written as:

5 + n = 8

n = 8 - 5

n = 3

Hence, the value of n for the given expression 3⁵. 3ⁿ = 3⁸ is n = 3.

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The complete question is:

Alex is currently 24 years old and Precy is currently 6 years old.

To solve this problem, we can use a system of equations.

Let A be Alex's current age and P be Precy's current age.

The first equation we can create is:

A + 3 = 3(P + 3)

The second equation we can create is:

A - 1 = 7(P - 1)

Now we can solve for one of the variables and substitute it into the other equation. From the first equation, we can isolate A:

A = 3P + 6

Substituting this value of A into the second equation:

3P + 6 - 1 = 7P - 7

Simplifying:

2P = 12 P = 6

Now we can substitute this value of P back into the first equation to find A:

A = 3(6) + 6 A = 24

So Alex is currently 24 years old and Precy is currently 6 years old.

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10⁻³ is equal to 1/1000 or 0.001.

What are Exponents?

Exponents are a shorthand way of representing repeated multiplication of a number by itself. They are indicated by a superscript number placed to the right and above the base number.

The superscript number represents the number of times the base number is multiplied by itself. For example, 2³ means 2 multiplied by itself three times, which equals 8.

Exponents are used to simplify large and small numbers, and are fundamental to algebraic and mathematical calculations. Exponents have several rules, such as the power of a power rule, product rule, quotient rule, and negative exponents rule.

10⁻³ can be evaluated as:

1 / 10^3 = 1 / 1000

Therefore, 10⁻³is equal to 1/1000 or 0.001.

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The value of x is 4 using the trigonometric function.

The term "hypotenuse" refers to a right-angled triangle's longest side as compared to the base and perpendicular lengths. The right angle, the largest angle of the three angles in a right triangle, lies opposite the hypotenuse side. In essence, only the right triangle possesses the hypotenuse feature, not any other triangles. When we study the right-angled theorem, Pythagoras Theorem, or Pythagorean Theorem, this is better understood. The main use of these ideas is in trigonometry.

The triangle is a right-triangle.

Thus, using the trigonometric functions we have:

Sin (30) = opposite / hypotenuse

sin (30) = 2 / x

1/2 = 2/x

x =2(2)

x = 4

Hence, the value of x is 4 using the trigonometric function.

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The volume of the prism would be h(60 - hp/2) cubic feet.

Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫∫ F(x, y, z) dx dy dz

Given is that the surface area of the right prism is 120 feet.

The formula for finding the surface area for the right prism is -

A = 2b + hP

2b + hp = 120

We can write the base area as -

2b = 120 - hp

b = 60 - hp/2

The volume of the prism would be -

V = base area x height

V = (60 - hp/2) x (h)

V = h(60 - hp/2)

Therefore, the volume of the prism would be h(60 - hp/2) cubic feet.

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1) 5/8

2) 15/24

3) 300/480

Answer: 5/8

10/16

15/24

Step-by-step explanation:

The polynomial equation 2x^(5)+6x^(4)-3x^(3)+x^(2)-9x-1=0 has 5 roots. This is because the degree of the equation is 5, and the number of roots of a polynomial equation is equal to its degree. Therefore, this equation has 5 roots. To find the roots of the equation, you can use the Rational Root Theorem, synthetic division, or other methods. However, finding the exact roots of a fifth-degree polynomial equation can be difficult and may require the use of a graphing calculator or computer software.

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The equation that defines "f"  for the amount of medicine in the blood stream is f(x) = 0.75ˣ * f(0).

The mathematical function known as exponential decay can be used to illustrate a quantity's progressive decline over time. The quantity that is lost or decays in each unit of time is proportionate to the amount that is still present, which is defined by a constant relative rate of change. Exponential decay is frequently seen in physical, chemical, and biological systems, where it explains the ageing of a population or the deterioration of radioactive isotopes, soil minerals, drugs, or nutrients over time.

The following equation to model the situation:

[tex]f(t) = f(0) * e^{(-kt)}[/tex]

where, f(0) is the initial amount of medicine

[tex]f(t) = f(0) * e^{(-k*1)} = 0.75\\\\f(0) * e^{-k} = 0.75\\\\[/tex]

Taking ln on both sides:

-k = ln(0.75 / f(0))

k = -ln(0.75 / f(0))

Substituting this value of "k" back into the equation for "f(x)", we get:

f(t) = f(0) * (0.75 / f(0))ˣ

Simplifying this equation further, we get:

f(t) = 0.75ˣ * f(0)

Therefore, the equation that defines "f" is f(x) = 0.75ˣ * f(0).

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The complete question is:

Hence, a 19-gram sample would contain 2.5909 x 10⁵ germs.

How come we use measure?

We can compare unknown amounts to known values with the use of measurement. We can quantify the size, length, and speed of objects with the use of measurement. The final result won't be accurate without measurement.

We may start by calculating the bacterium to dirt sample weight ratio:

bacteria per gram = 1.5 x 10⁵ / 11 = 13636.36...

We are able to employ this ratio to determine how many bacteria are present in a 19-gram specimen:

bacteria = bacteria per gram x weight of sample

bacteria = 13636.36... x 19

bacteria = 259090.91...

We must write the number in scientific notation because it is more than 10⁵. This can be achieved by adding a factor of 10⁵ and shifting the decimal place five places to a left:

bacteria = 2.5909 x 10^5

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The product of the two expressions can be set as the one in option 1.

The process of multiplying two given expressions with the aid of variables and constants is known as algebraic multiplication. The terms factors and multiplicands refer to the two expressions that make up an algebraic product, which is the combination of two expressions.

The two expressions can be set as follows:

4x³ + 0x² -3x + 4

                 2x - 5

As the x² term is not present we use the coefficient as 0.

Hence, the product of the two expressions can be set as the one in option 1.

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