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Answer: For Damian's investment:

The interest rate is 3%, compounded quarterly, which means the interest rate per quarter is 3%/4 = 0.75%.

The number of quarters in 16 years is 16*4 = 64.

Using the formula for compound interest, the balance after 16 years is:

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

where:

P = the principal (initial investment) = $81,000

r = the interest rate per quarter = 0.75%

n = the number of times the interest is compounded per year = 4 (quarterly)

t = the number of years = 16

A = 81000*(1 + 0.0075/4)^(4*16) = $157,222.39

For Marques's investment:

The interest rate is 2%, compounded continuously.

Using the formula for continuous compound interest, the balance after 16 years is:

A = Pe^(rt)

where:

P = the principal (initial investment) = $81,000

r = the interest rate per year = 2%

t = the number of years = 16

A = 81000e^(0.0216) = $131,518.16

Therefore, Damian would have $157,222.39 - $131,518.16 = $25,704.23 more than Marques in his account after 16 years. Rounded to the nearest dollar, this is $25,704.

Step-by-step explanation:

Damian would have approximately $351 more in his account than Marques after 16 years.

Interest rate is the percentage of a loan or deposit that is charged as interest or earned as interest over a period of time. It is expressed as a percentage of the principal amount borrowed or deposited, and it represents the cost of borrowing or the reward for saving money.

We can use the compound interest formula to calculate the future value of each investment after 16 years and then subtract to find the difference.

For Damian's investment, the interest rate is 3% per year, compounded quarterly. This means that the quarterly interest rate is r = 0.03/4 = 0.0075, and the number of compounding periods is n = 16 x 4 = 64. The future value of Damian's investment is:

F = 81000 * [tex](1 + r)^n[/tex]

  = 81000 * [tex](1.0075)^64[/tex]  

  = 129,535.28

For Marques's investment, the interest rate is 2% per year, compounded continuously. This means that the continuously compounded interest rate is r = 0.02, and the number of compounding periods is n = 16 x 1 = 16. The future value of Marques's investment is:

F = 81000 * [tex]e^(rn)[/tex]

  = 81000 * [tex]e^(0.0216)[/tex]

  = 129,183.81

The difference between the two investments is:

129,535.28 - 129,183.81 = 351.47

So Damian would have approximately $351 more in his account than Marques after 16 years. Rounded to the nearest dollar, the difference is $351.

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Answer: To simplify the expression, we need to follow the order of operations, which is to perform the division first, then addition.

1/3 ÷ 7/6 + 1/5

To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction:

1/3 ÷ 7/6 = 1/3 × 6/7 = 2/7

Now we can substitute this value back into the original expression:

2/7 + 1/5

To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 35:

2/7 × 5/5 = 10/35

1/5 × 7/7 = 7/35

Now we can add the two fractions:

10/35 + 7/35 = 17/35

Therefore, the simplified expression is 17/35.

Step-by-step explanation:

The probability that a conversation lasts longer than 6 minutes is approximately 0.0764 or 7.64%.

What is probability?

The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place.

We can use the standard normal distribution to solve this problem by standardizing the variable using the formula:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

In this case, we want to find the probability that a conversation lasts longer than 6 minutes, so x = 6, μ = 5, and σ = 0.7. Substituting these values into the formula, we get:

z = (6 - 5) / 0.7 = 1.43

Next, we can use a standard normal distribution table or a calculator to find the probability that a standard normal random variable is greater than 1.43. Using a standard normal distribution table, we find that this probability is approximately 0.0764.

Therefore, the probability that a conversation lasts longer than 6 minutes is approximately 0.0764 or 7.64%.

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Answer:

Step-by-step explanation:

The sequence starts with 4 and each subsequent term is obtained by multiplying the previous term by -3. Therefore, the equation to describe the sequence is:

aₙ = 4(-3)^(n-1)

where aₙ represents the nth term in the sequence.

Using this equation, we can find the values of the first few terms in the sequence as follows:

a₁ = 4(-3)^(1-1) = 4(1) = 4

a₂ = 4(-3)^(2-1) = 4(-3) = -12

a₃ = 4(-3)^(3-1) = 4(9) = 36

and so on.

Note that the index n starts at 1, but in some contexts it may start at 0, in which case we would need to adjust the exponent accordingly.

Answer:

[tex]x = 4 \frac{2}{3} [/tex]

[tex]y = 5[/tex]

Step-by-step explanation:

Multiply the second equation by -5 to eliminate 15x:

{15x - 4y = -50,

{3x - 2y = -16; / × (-5)

+ {15x - 4y = -50,

{-15x + 10y = 80;

----------------------------

6y = 30 / : 6

y = 5

Make x the subject from the 2nd equation (it doesn't matter, you can do it from the 1st one instead):

15x = -50 + 4y / : 15

[tex]x = 3 \frac{1}{3} + \frac{4}{15} y[/tex]

[tex]x = 3 \frac{1}{3} + \frac{4}{15} \times 5 = \frac{14}{3} = 4 \frac{2}{3} [/tex]

Rolle’s Theorem can be applied to the closed interval and the value of x = (12 ±√12)/3

Rolle's theorem states that "If a function f is defined in the closed interval [a, b] in such a way that it satisfies the following condition: If is continuous οn [a, b], ii) f is differentiable οn (a, b), and iii) f (a) = f (b), then there exists at leastοne value οf x, let us assume this value to be c, which lies between a and b i.e. (a < c < b) in such a way that f'(c) = 0.".

Here, we have

Given: f(x) = (x-1)(x-2)(x-3), [1,3]

We have to determine whether Rolle’s Theorem can be applied to the closed interval.

This function is continuous in [1, 3] and is differentiable everywhere except at the points x = 1, 2, 3.

This point is in the interval [1, 3], and since Rolle's Theorem requires that the function must be differentiable on the open interval (1, 3).

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

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

f'(x) = x² - 5x + 6 + x² - 4x + 3 + x² -3x + 2

f'(x) = 3x² -12x + 11

f'(x) = 0

3x² -12x + 11 = 0

x = (12 ±√12)/3

Hence, Rolle’s Theorem can be applied to the closed interval.

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Answer: For x < -2.5:

y = |2x + 5| - |2x - 5|

y = -(2x + 5) - (-(2x - 5)) (since 2x - 5 < 0 and 2x + 5 < 0 for x < -2.5)

y = -2x - 5 + 2x - 5

y = -10

For x > 2.5:

y = |2x + 5| - |2x - 5|

y = 2x + 5 - (2x - 5) (since 2x - 5 < 0 and 2x + 5 > 0 for x > 2.5)

y = 10

For -2.5 ≤ x ≤ 2.5:

y = |2x + 5| - |2x - 5|

y = 2x + 5 - (-(2x - 5)) (since 2x - 5 < 0 and 2x + 5 > 0 for -2.5 ≤ x ≤ 2.5)

y = 4x

Step-by-step explanation:

Answer:

9.6 / 0.91 ≈ 10.55

Step-by-step explanation:

I used a calculator

Answer:

The slope of a line represents the rate of change, which in this case is the rate at which the skydiver is falling. The rate of falling is 4,800 feet in 4 seconds, which simplifies to 1,200 feet per second, therefore, the graph that has a slope of 1,200 best represents this rate.

The answer is 369,072. This is the total number of copies sold to date.

An expression that uses symbols to represent the relationship between two or more values.

This is calculated by solving the equation 9.7% × x = 35,800, where x is the total number of copies sold to date.

To solve this equation, we first need to convert the percentage to a decimal.

To do this, we divide 9.7 by 100, giving us 0.097.

We can then multiply both sides of the equation by this decimal, giving us 0.097x = 35,800.

We can then solve for x by dividing both sides of the equation by 0.097. This gives us x = 369,072. This is the total number of copies sold to date.

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The product of 3.18 × 16 is 50.88 in decimal form.

A number system is a way to represent numbers using symbols or digits. The most commonly used number system is the decimal or base-10 system, which uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) to represent any quantity.

Other common number systems include:

Binary or base-2 system, which uses two digits (0 and 1) to represent numbers

Octal or base-8 system, which uses eight digits (0, 1, 2, 3, 4, 5, 6, 7) to represent numbers

Hexadecimal or base-16 system, which uses sixteen digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F) to represent numbers

Knowing that;

3.18 × 16

After multiplying, we now have;

3.18 × 16 = 50.88

Thus, the product of 3.18 × 16 is 50.88 in decimal form.

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The balances and the running total, given the checking account record is :

The balance on the 14 th of February would be:

= Balance forward - Amount of check

= 299. 88 - 90. 48

= $ 209. 40

The balance on 2 / 15 :

= 209. 40 - 65

= $ 144. 40

The balance on 2 / 17 :

= 144. 40 + 381.33 which is a deposit

= $ 525.73

The balance and running total on 2 / 22 :

= 525. 73 - 54.47

= $ 471.26

The balance on 2 / 22 after the National Mortgage deduction is:

= 471. 26 - 375.99

= $ 95.27

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Answer:

Got you bro

Step-by-step explanation:

The two-dimensional shape appears to be a semi-circle, and it is being rotated about a line to form a three-dimensional shape. The resulting shape is a sphere.

Answer:

Step-by-step explanation:

The two-dimensional shape appears to be a semi-circle, and it is being rotated about a line to form a three-dimensional shape.

The resulting shape is a sphere.

Answer:

√3/2

Step-by-step explanation:

sin(10°) • cos(50°) + cos(10°) • sin(50°)

= sin(10 + 50)

sin(60°) = √3/2

PEMDAS is an acronym used to mention the order of operations to be followed while solving expressions having multiple operations.

PEMDAS rule states that the order of operation starts with the parentheses first or the calculation, which is enclosed in brackets. Then, the operation is performed on exponents(degree or square roots), and later, we do operations on multiplication & division and at last addition and subtraction.

PEMDAS is the order that you solve a problem.

PEMDAS stands for:

Parenthesis

Exponents

Multiplication and Division

Addition and Subtraction

If you have an equation or expression that you need to solve, you solve it in this order. You do the parenthesis first, then you solve the exponents, then you do the multiplication and division from left to right, and last you do addition and subtraction from left to right.

In the equation

2 + 3 * 5,

first you would do 3 * 5 because multiplication is before addition.

2 + 15

Then you would do the addition to get the answer:

17.

Please give brainliest

The tangent of 60° is √3, so the coterminal angle of tan(780°) is √3.

Coterminal angles are angles that have the same initial and terminal sides in standard position.

To find the coterminal angle of tan(780°), we need to add or subtract multiples of 360° to 780° until we get an angle between 0° and 360°, because angles that differ by a multiple of 360° have the same trigonometric function values.

First, we can subtract 360° from 780°:

780° - 360° = 420°

This is not yet between 0° and 360°, so we can subtract another 360°:

420° - 360° = 60°

Now we have an angle between 0° and 360° that is coterminal with 780°.

The tangent function has a period of 180°, which means that the tangent function has the same value for angles that differ by a multiple of 180°. Since 60° is an acute angle, we can use the tangent of 60° to find the tangent of 780°:

tan(780°) is equivalent to tan(780° - 720°) = tan(60°)

The tangent of 60° is √3, so the coterminal angle of tan(780°) is √3.

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[tex]\textit{Law of sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(B)}{7}=\cfrac{\sin(30^o)}{6}\implies \sin(B)=\cfrac{7\sin(30^o)}{6} \\\\\\ B=\sin^{-1}\left[ \cfrac{7\sin(30^o)}{6} \right]\implies B\approx 35.69^o[/tex]

Make sure your calculator is in Degree mode.

The product of 3 and 10v√40 in simplest radical form is 30v(2√5).

What is product?

To find the product of 3 and 10v√40 in simplest radical form, we can simplify the radical first.

First, we can simplify 40 by finding its prime factorization:

40 = 2 × 2 × 2 × 5

Next, we can rewrite 10v√40 as 10v√(2 × 2 × 2 × 5) to separate out the perfect squares:

10v√(2 × 2 × 2 × 5) = 10v(√2 × √2 × √2 × √5)

We can then simplify the perfect squares under the radical:

10v(√2 × √2 × √2 × √5) = 10v(2√5)

Now we can multiply 3 and 10v(2√5):

3 × 10v(2√5) = 30v(2√5)

So the product of 3 and 10v√40 in simplest radical form is 30v(2√5).

What is prime factorization?

Prime factorization is the process of expressing a composite number as a product of its prime factors. In other words, it is finding the prime numbers that can be multiplied together to get the original number. For example, the prime factorization of 24 is 2 x 2 x 2 x 3 or 2³ x 3, since 24 can be expressed as a product of the prime numbers 2 and 3, and each of these primes is repeated as many times as necessary to get the original number. Prime factorization is an important concept in mathematics and has many practical applications, including in cryptography, number theory, and computer science.

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The population will exceed 2458 after approximately 10.1465 units of time, where the time unit depends on the context of the problem (e.g., hours, days, etc.).

A statement proving the equality of two expressions is known as an equation. It can include variables, integers, and mathematical operations like addition, subtraction, multiplication, and division. It also incorporates mathematical symbols. In mathematics and science, equations are frequently used to illustrate connections between quantities. The equals sign (=) is typically used in equations to denote that the expressions on each side of the sign have the same value. For instance, the formula 2 + 3 = 5 demonstrates that the total of 2 and 3 equals 5. Equations can be solved to determine a variable's value or to determine if a certain value meets the connection that the equation describes.

To estimate when the population will exceed 2458, we can set up an inequality using the equation for the population growth:

p(t) > 2458

Substituting the given equation for p(t), we get:

[tex]1100e^0.12t[/tex] > 2458

Dividing both sides by 1100, we get:

[tex]e^0.12t > 2.23545[/tex]

Taking the natural logarithm of both sides, we get:

0.12t > ln(2.23545)

Solving for t, we get:

t > ln(2.23545)/0.12

Using a graphing calculator to evaluate this expression, we get:

t > 10.1465

Therefore, the population will exceed 2458 after approximately 10.1465 units of time, where the time unit depends on the context of the problem (e.g., hours, days, etc.).

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Answer:

$67,000 after 15 years.

Step-by-step explanation:

You deposit $6000 in an account earning 7% interest compounded monthly. How much will you have in the account in 15 years? account will have $67,000 in it after 15 years

Therefore, the absolute maximum value of f(x) over (-2, 3) is 201 and it occurs at x = -2. The absolute minimum value of f(x) over (-2, 3)is -98 and it occurs at x = 3.

We must identify the crucial points of the function within the period in order to determine the function's absolute maximum and minimum values.

Define critical point?

The critical points are those where the function's derivative is zero or undefinable. The function is then assessed at these pivotal points as well as the interval's endpoints.

Absolute maximum and lowest values are represented by the largest and smallest values, respectively.

The derivative of f(x) = 3x⁴ - 4x³ - 12x² + 1 over (-2, 3) is initially found as follows:

f'(x) = 12x³ - 12x²- 24x

If we set f'(x) to 0, we obtain:

12x³ - 12x² - 24x = 0

By multiplying both sides of this equation by 12x, we may simplify it to:

x²- x - 2 = 0

The answer to this quadratic equation is:

x = -1, x = 0, x = 2

Now we evaluate f(x) at these critical points and at the endpoints of the interval:

f(-2) = 201

f(-1) = -6

f(0) = 1

f(2) = 49

f(3) = -98

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The required statement is "The sky is clear if and only if the plane is on time."

The statement "Q<->P" is a logical statement that uses the biconditional operator "<->" which means "if and only if." This operator connects two propositions in such a way that both propositions are true or false together.

In this case, the propositions are "Q" and "P" which are defined as "The sky is clear" and "The plane is on time," respectively. Therefore, the statement "Q<->P" can be translated into words as "The sky is clear if and only if the plane is on time."

This means that the truth of the proposition "Q" (the sky is clear) is dependent on the truth of proposition "P" (the plane is on time) and vice versa.

If the plane is on time, then the sky must be clear, and if the sky is clear, then the plane must be on time. If either of these propositions is false, then the bi-conditional statement is false as well.

Thus, required statement is "The sky is clear if and only if the plane is on time."

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Therefore , the solution of the given problem of equation comes out to be  rounded to three decimal places, is 17.483 grams.

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Think about the information that y + 7 provides. When accompanied by generate y + 7, increasing results in b + 7 in this case rather than another method that could split 12 into two separate components.

Here,

We must enter t = 110 into the equation for y and solve for y in order to determine how much of the original mass is still present after 110 years:

=> y = 20(1 - 2^(-t/30))

=> y = 20(1 - 2^(-110/30))

=> y ≈ 2.517

As a result, there are roughly 2.517 grams of cesium-137 left after 110 years. We can deduct this amount from the original mass of 20 grams to determine how much of the initial mass is still present:

=> 20 - 2.517 ≈ 17.483

Thus, roughly 17.483 grams of the original 20 grams of cesium-137 are still present after 110 years.

The number, rounded to three decimal places, is 17.483 grams.

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The inverse of the function f(x) is f⁻¹(x) = √(x) - 8

To find the inverse of the function f(x) = (x + 8)², we need to solve for x in terms of y:

y = (x + 8)²

Taking the square root of both sides, we get:

±√(y) = x + 8

Solving for x, we get:

x = ±√(y) - 8

Since we want the inverse function to be a function (i.e., have a unique output for each input), we must choose the positive square root. Therefore, the inverse function is:

f⁻¹(x) = √(x) - 8

The domain of f⁻¹ is the range of f, which is [0, ∞). Therefore, the domain of f⁻¹ is [0, ∞).

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Using the Pythagorean theorem we know that the value of x in the given situation is 15 units respectively.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

So, the Pythagorean formula is as follows:

c = √a² + b²

Now, insert values as follows:

c = √a² + b²

c = √12² + 9²

c = √144 + 81

c = √225

c = 15 units

Therefore, using the Pythagorean theorem we know that the value of x in the given situation is 15 units respectively.

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Answer:A complex number will, in general, have five(5) fifth complex roots./

Step-by-step explanation:

Two events are dependent since the probability of getting a perfect square is affected by the fact that we already know that we got an even number.

Probability is a measure of the likelihood of an event occurring. It 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. For example, the probability of rolling a 6 on a fair dice is 1/6, or approximately 0.167.

In probability theory, events are often expressed as sets of possible outcomes, and probabilities are calculated based on the number of outcomes in the event relative to the total number of possible outcomes. For example, the probability of rolling an even number on a fair dice is 3/6, or 0.5, because there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.

Since the event E is the event of getting an even number, the possible outcomes are 2, 4, 6, or 8.

Out of these, only 4 is a perfect square. Therefore, P(S/E) = 1/4.

These two events are dependent since the probability of getting a perfect square is affected by the fact that we already know that we got an even number.

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After solving for side a, we have come to know that a = 2.2. Thus, option A is correct.

The law of cosines is a trigonometrical rule that links the lengths of a triangle's sides to the cosines of one of its angles, whether the triangle is spherical or flat. When two sides and the angle between them are known, it can be used to determine the length of a side or the angle of a triangular. There are two versions of the law of cosines: one for spherical triangles and one for planar triangles.

We can use the Law of Cosines to solve for the length of BC (denoted by a) in triangle ABC, since we know two sides and the included angle.

[tex]\rm a=\sqrt{c^{2}+b^{2}-2 c b \cdot \cos A}[/tex]

[tex]\rm a=\sqrt{4^{2}+3^{2}-2(4)(3) \cdot \cos(32^{\circ})}[/tex]

[tex]\rm a=\sqrt{16+9-24\cdot \cos(32^{\circ})}[/tex]

[tex]\rm a=\sqrt{1 \cdot \cos(32^{\circ})}[/tex]

a = 2.155654

a ≈ 2.2

Thus, After solving for side a, we have come to know that a = 2.2. Thus, option A is correct.

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The parabola's equation is as follows, with the directrix at y = 5 and the focus at (-4, 3). [tex](x + 4)^2 = 4y - 16[/tex]

A hyperbolic is a U-shaped symmetry curve that is created when a plane and a cone collide. The parabola has the characteristic that the distance between any point on the curve and a fixed point (referred to as the focus) is identical to the distance between that point and a telephone service (called the directrix). Equation y = ax2 + bx + c, at which a, b, and c are constants, gives the conventional form of a parabola. The parabola opens either upwards or downwards depending on the sign of coefficient a. The arc opens upwards if an is positive and downwards if an is negative.

given

A parabola with a vertex at (h, k) and a vertical axis of symmetry has the following standard form equation:

[tex](x - h)^2 = 4p(y - k) (y - k)[/tex]

where p is the separation between the vertex and the directrix or focus.

In this instance, the vertex's coordinates are (h, k) = since it is located halfway between the focus and directrix (-4, 4). As the directrix is a horizontal line with the coordinates y = 5, the separation between it and the vertex is p = 1.

When we enter these values into the equation in standard form, we obtain:

[tex](x + 4)^2 = 4(1)(y - 4) (y - 4)[/tex]

If we simplify, we get:

[tex](x + 4)^2 = 4y - 16[/tex]

The parabola's equation is as follows, with the directrix at y = 5 and the focus at (-4, 3). [tex](x + 4)^2 = 4y - 16[/tex] .

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