find the consecutive even integers such that three times the larger number is 30 more than the smaller one. help :')

The outstanding balance right after the 12th payment has been made is approximately $17,752.60.

To find the loan amount L, we can calculate the present value of the future payments using the given interest rate and payment schedule.

First, let's calculate the present value of the first 16 payments of $1,000 each. These payments occur at the end of each month. We'll use the formula for the present value of an ordinary annuity:

\(PV = P * [1 - (1 + r)^(-n)] / r\)

Where:

PV = Present value

P = Payment amount per period

r = Interest rate per period

n = Number of periods

Using the given interest rate of 12% per year compounded monthly (1% per month) and 16 payments, we have:

PV1 = $1,000 * [1 - (1 + 0.01)^(-16)] / 0.01

Calculating this expression, we find that PV1 ≈ $12,983.67.

Next, let's calculate the present value of the final 8 payments of $2,000 each. Again, using the same formula, but with 8 payments, we have:

PV2 = $\(2,000 * [1 - (1 + 0.01)^(-8)] / 0.01\)

Calculating this expression, we find that PV2 ≈ $14,148.70.

The loan amount L is the sum of the present values of the two sets of payments:

L = PV1 + PV2

≈ $12,983.67 + $14,148.70

≈ $27,132.37

Therefore, the loan amount L is approximately $27,132.37.

Next, to find the outstanding balance right after the 12th payment has been made, we can calculate the present value of the remaining payments. Since 12 payments have already been made, there are 12 remaining payments.

Using the same formula, but with 12 payments and the loan amount L, we can calculate the present value of the remaining payments:

Outstanding Balance = L * [1 - (1 + 0.01)^(-12)] / 0.01

Substituting the value of L we found earlier, we have:

Outstanding Balance ≈ $27,132.37 * [1 - (1 + 0.01)^(-12)] / 0.01

Calculating this expression, we find that the outstanding balance right after the 12th payment has been made is approximately $17,752.60.

Therefore, the outstanding balance right after the 12th payment has been made is approximately $17,752.60.

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Answer:

$0.65

Step-by-step explanation:

2.40-1.10=1.3

1.3/2=.65

The simplified expression for f(x) after expanding the polynomials is:

f(x) = 2x³ - 5x² + 10x - 25

And the derivative of function f(x) is f'(x) = 6x² - 10x + 10

Consider a function f(x) = (x² + 5)(2x - 5)

We need to find the derivative of f(x) by first expanding the polynomials.

First we simplify expression for f(x) after expanding the polynomials.

f(x) =  (x² + 5)(2x - 5)

f(x) = x²(2x - 5) + 5(2x - 5)

f(x) = 2x³ - 5x² + 10x - 25

Now we find the defivative of f(x)

We know that the derivative of \(x^n\) is \(nx^{n-1}\)

Using above formula,

f'(x) = 2(3x³⁻¹) - 5(2x²⁻¹) + 10(x¹⁻¹) + 0   .....(as derivative of constant is zero)

f'(x) = (2 × 3)x² - (5 × 2)x + 10

f'(x) = 6x² - 10x + 10

Therefore, the derivative of function f(x) is f'(x) = 6x² - 10x + 10

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(1) An example of a strict preference relation that is negatively transitive and asymmetric can be defined on the set X = {a, b, c, d, e} by listing all the pairs in the relation.
(2) An example of a choice structure (B, C(·)) on the set X = {a, b, c, d} can be provided, along with a collection of budget sets and a choice correspondence that satisfies the weak axiom of revealed preference. The pairs contained in the revealed preference relation can be listed, but whether the relation is transitive or not does not need to be shown.
(3) Given the utility function u(x1, x2) = x1 + x2, a graph can be drawn to represent the indifference curves passing through the consumption bundles (1,1) and (2,2). The axes should be labeled clearly.
(4) The properties of the given preferences, such as nondecreasing, increasing, strictly increasing, locally nonsatiated, convex, or strictly convex, should be described, but it is not necessary to prove these properties.

(1) An example of a strict preference relation that is negatively transitive and asymmetric on the set X = {a, b, c, d, e} can be defined as follows:

Pairs in the relation:

(a, b), (a, c), (a, d), (a, e), (b, c), (b, d), (b, e), (c, d), (c, e), (d, e)

This preference relation is negatively transitive because if a is preferred to b, and b is preferred to c, then a is not preferred to c. Additionally, it is asymmetric because if a is preferred to b, then b is not preferred to a.

(2) Let (B, C(·)) be a choice structure defined on the set X = {a, b, c, d}. An example of a collection of budget sets and a choice correspondence that satisfies the weak axiom of revealed preference (WARP) can be as follows:

Budget sets:

B1 = {a}, B2 = {b}, B3 = {c}, B4 = {d}, B5 = {a, b}, B6 = {a, c}, B7 = {b, c}, B8 = {a, b, c}, B9 = {a, b, d}

Choice correspondence:

C(a) = {a, b}

C(b) = {a}

C(c) = {c}

C(d) = {a, d}

The revealed preference relation, which is derived from the choice correspondence, can be listed as follows:

Pairs in the relation:

(a, b), (b, a), (a, c), (c, a), (a, d), (d, a), (b, c), (c, b), (b, d), (d, b), (c, d), (d, c)

The revealed preference relation is not transitive because, for example, (a, b) and (b, c) are both in the relation, but (a, c) is not.

(3) The utility function u(x1, x2) = x1 + x2 represents the consumer's preferences. The indifference curves for this utility function will be straight lines with a slope of -1.

Graphically, the indifference curves through the consumption bundles (1,1) and (2,2) will be diagonal lines passing through those points. The x-axis represents the quantity of good 1, the y-axis represents the quantity of good 2. The graph will have a 45-degree angle, and the indifference curves will be evenly spaced parallel lines.

(4) The preferences represented by the utility function u(x1, x2) = x1 + x2 are:

Nondecreasing: The preferences are nondecreasing because as the consumption of either good 1 or good 2 increases, the utility also increases.

Increasing: The preferences are increasing because more of both goods is preferred to less of both goods.

Strictly increasing: The preferences are not strictly increasing because the utility function is linear, and the marginal utility of each good is constant.

Locally nonsatiated: The preferences are locally nonsatiated because the consumer always prefers more of both goods.

Convex: The preferences are convex because the utility function is linear, and any convex combination of two consumption bundles on an indifference curve will also be on the same indifference curve.

Strictly convex: The preferences are not strictly convex because the utility function is linear and not strictly concave.

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1.5·10⁸ kilometers

As a result, the Earth Sun distance is 150 million kilometers. To use scientific notation, pick a value between 1 and 10, then multiply it by 10ˣ.

So the number between 1 and 10 in 150,000,000 is 1.5, with 8 decimal points.

As a result, the solution is 1.5·10⁸

The benefits of Earth's prime placement in the solar system are numerous. We are just far enough away from the Sun for life to thrive.

Venus is excessively hot. Mars is quite chilly. Scientists refer to our region of space as the "Goldilocks Zone" because it looks to be ideal for life.

As previously stated, Earth's average distance from the Sun is around 93 million miles (150 million kilometers). That's one AU.

On this hypothetical scale, these so-called "linebackers" resemble minuscule specks rather than the massive linebackers of the NFL.

If all of the known asteroids in our solar system were combined, their total mass would be less than 10% that of Earth's moon.

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Answer: A. 2/3 B. 8/9 C. 3/10 D. 9/11 E. 3/4 F. 1/5

Step-by-step explanation:

The current required to produce metal at a rate of 5.00 g/min is 274A

The electrolyte ion equation is;

Ni²⁺ (aq)  +  2e⁻   →   Ni (s)

Faradays constant = 9.65 * 10⁴ C/mol

Molar mass of Nickel = 58.69 g/mol

Number of moles of nickel; n_ni = 5 g/min * 1 mol/58.69 g/mol = 0.0852 mol

n_e = 0.0852 mol * 2/1

n_e = 0.170 mol

I = nF/t

where;

t is in minutes

F is faradays' constant

Thus;

I = (0.17 * 9.65 * 10⁴)/(1 * 60)

I = 274 A

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Answer

y = 3/2x -8

Step-by-step explanation:

The first thing you should do is change the equation into slope intercept form. Subtract 2x from both sides to get: 3y = -2x + 18. Divide all parts of the equation by 3 to get your equation in slope intercept: y = -2/3x + 6. One thing you should know when finding the slope of a perpendicular line is that it is the opposite reciprocal. So, the slope is going to be 3/2. This is your current equation: y = 3/2x + b. Plug in the point to the equation, it should look like this: 1 = 3/2(6) + b. Multiply 3/2 by 6 to get 9. This is what it should look like: 1 = 9 + b. Then, subtract 9 from both sides of the equation to get your y-intercept of -8. Go back to your other equation and plug in -8 for b. This is your final equation: y = 3/2x -8.

The volume of the solid generated when the region R is revolved about the y-axis is 0 cubic units. This indicates that the region R does not enclose a solid when revolved around the y-axis in the first quadrant.

To find the volume of the solid generated when the region R is revolved about the y-axis using the shell method, we'll follow these steps:

Sketch the region R: The curve y = 4 - x^2 intersects the x-axis at x = -2 and x = 2, and the y-axis at y = 4. The region R lies in the first quadrant.

Determine the limits of integration: Since we are revolving the region about the y-axis, the limits of integration will be the y-values that define the region R. In this case, the limits of integration are y = 0 and y = 4.

Set up the integral: The volume of the solid can be calculated using the formula V = ∫(2πr * h) dy, where r is the distance from the y-axis to the curve, and h is the height of the shell.

Express r and h in terms of y: Since we are revolving the region about the y-axis, the distance r is simply the x-coordinate of the curve at a given y-value. In this case, r = x = √(4 - y).

The height h of the shell can be calculated as the difference between the upper and lower y-values of the region. In this case, h = 4 - 0 = 4.

Evaluate the integral: The integral setup becomes:

V = ∫(2π√(4 - y) * 4) dy

V = 8π∫(√(4 - y)) dy

Integrate and evaluate the integral: We integrate with respect to y, using the power rule for integration.

V = 8π * (2/3)(4 - y)^(3/2) |[0, 4]

V = 16π * [(4 - 4)^(3/2) - (4 - 0)^(3/2)]

V = 16π * [0 - 0]

V = 0

The volume of the solid generated when the region R is revolved about the y-axis is 0 cubic units. This indicates that the region R does not enclose a solid when revolved around the y-axis in the first quadrant.

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The absolute value is:

Work/explanation:

First, we will evaluate 2-7.

It evaluates to -5.

Now, let's find the absolute value of -5 by using these rules:

\(\sf{\mid a\mid=a}\)

\(\sf{\mid-a \mid=a}\)

Similarly, the absolute value of -5 is:

\(\sf{\mid-5\mid=5}\)

Therefore,  The pdf of e^(−x) for x ∼ expo(1) is f(x) = e^(−x) for x ≥ 0. The pdf is a decreasing function that approaches zero as x increases.

The probability density function (pdf) of an exponential distribution with parameter λ is f(x) = λe^(−λx) for x ≥ 0. In this case, λ = 1, so the pdf of e^(−x) for x ∼ expo(1) is f(x) = e^(−x) for x ≥ 0. This means that the probability of observing a value of e^(−x) between a and b is given by the integral of e^(−x) from a to b, which is equal to e^(−a) − e^(−b). The graph of this pdf shows that it is a decreasing function that approaches zero as x increases.

Therefore,  The pdf of e^(−x) for x ∼ expo(1) is f(x) = e^(−x) for x ≥ 0. The pdf is a decreasing function that approaches zero as x increases.

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b. and d.

Step-by-step explanation:

the sentence is true

Answer:

$10

Step-by-step explanation:

Since 6 cost four dollars 3 would cost 2 dollars multiply 3 to get 15 bananas and 2 to get $10

Answer:

$10

Step-by-step explanation:

Make proportion:

?= cost  of bananas

6  -  4

15  -  ?

?= 15×4÷6=10

The value of c that makes the equation true is c = 64, when x = 6 and y = 3.

To find the value of c that makes the equation true, we can start by simplifying both sides of the equation using exponent rules and canceling out common factors.

First, we can simplify 3√(x^3) to x√x, and 3√y to y√y, giving us:

x√x/cy^4 = x/4y(y√y)

Next, we can simplify x/4y to 1/(4√y), giving us:

x√x/cy^4 = 1/(4√y)(y√y)

We can cancel out the common factor of √y on both sides:

x√x/cy^4 = 1/(4)

Multiplying both sides by 4cy^4 gives us:

4x√x = cy^4

Now we can solve for c by isolating it on one side of the equation:

c = 4x√x/y^4

We can substitute in the values of x and y given in the problem statement (x>0 and y>0) and simplify:

c = 4x√x/y^4 = 4(x^(3/2))/y^4

c = 4(27)/81 = 4/3 = 1.33 for x = 3 and y = 3

c = 4(64)/81 = 256/81 = 3.16 for x = 4 and y = 3

c = 4(125)/81 = 500/81 = 6.17 for x = 5 and y = 3

c = 4(216)/81 = 64 for x = 6 and y = 3

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Answer:

x=3 means draw a vertical line at 3 on the x-axis

Answer:

Keith paid $0.25 less than Tony paid.

Step-by-step explanation:

Tony paid ($48 - 10%) = $43.2

Keith paid $42.95.

The difference is Tony paid $0.25 more, or Keith paid $0.25 less.

Answer:

Keith paid $0.25 less than Tony.

Step-by-step explanation:

Tony: 48 x 0.10 = 4.8

48 - 4.8 = $ 43.20 (Tony)

Keith: $ 42.95

43.20 - 42.95 = 0.25

The system of inequalities that represents the number of quarters, x, and the number of dimes, y, that Mai could have is given by:

x + y ≥ 10 and 0.25x + 0.1y < 2

These are the two systems of inequalities that represent the number of quarters, x, and the number of dimes, y, that Mai could have.

Let x be the number of quarters and y be the number of dimes that Mai has. Then, the system of inequalities can be represented as:

Thus, the first inequality is x + y ≥ 10.

Also, Mai has less than $2.00, therefore, the second inequality is 0.25x + 0.1y < 2. The value of x and y are assumed to be non-negative integers.+

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Answer:

standard form:   y = x² - 2x - 8

vertex form:  y = (x − 1)² - 9

factorized form:  y = (x + 2)(x - 4)

Step-by-step explanation:

From inspection of the graph:

Standard quadratic form:   y = ax² + b x + c

Vertex form of a quadratic equation:   y = a(x − h)² + k

If a > 0 then the parabola opens upwards

If a < 0 then the parabola opens downwards

(h, k) is the vertex

c is the y-intercept

Inputting the vertex into the vertex form gives:

y = a(x − 1)² - 9

  = a(x² - 2x + 1) - 9

  = ax² - 2ax - 8

Using the x-intercepts to create a quadratic equation:

y = a(x + 2)(x - 4)

  = a(x² - 2x - 8)

  = ax² - 2ax - 8a

Comparing the y-intercepts:

-8 = -8a  ⇒  a = 1

Therefore,   y = x² - 2x - 8

The answer is m = -59/42

Step by step explanation is in the image below.

Answer:

first, you can go to the doctor

Step-by-step explanation:

Answer:

Step-by-step explanation:

Try doing something active!

Answer:

  x = -2, x = 2

Step-by-step explanation:

The denominator factors as ...

  x^2 -4 = (x -2)(x +2)

The numerator has no factors that cancel either of these, so the function will have vertical asymptotes where the denominator is zero: at x = -2 and x = 2.

Answer:

add 3, add 5, add 7, add 9

Step-by-step explanation:

1+3=4

4+5=9

9+7=16

16+9=25

add by odd numbers, for a simpler answer

Answer:

The perpendicular line has a slope of -2/3

Step-by-step explanation:

Perpendicular lines have a slope that multiplies to -1

3/2 * m = -1

Multiply each side by 2/3

3/2 * 2/3 *m = -1 * 2/3

m = -2/3

Answer: -2/3

Step-by-step explanation: The key to understanding this problem is to understand what it means when slopes are perpendicular.

To most students, perpendicular lines are simply

lines that meet  at a 90 degree angle.

However, when dealing with these kinds of problems, it's important

to think about perpendicular lines in terms of their slopes.

As a rule, the slopes of two perpendicular

lines are always negative reciprocals.

So if we know that the slope of one line is 3/2, we can find the slope of the other line by finding the negative reciprocal of 3/2.

So we take the fraction and flip it, then we change the sign.

So the negative reciprocal of 3/2 is -2/3.

On solving the provided question, we can say that the spherical balloon's initial radius is 7 cm.; the final radius is 14 cm. ratio =  (7/14) ^2 = 1:4

The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle.

The spherical balloon's initial radius is 7 cm.

The final radius is 14 cm.

ratio =

(7/14) ^2 = 1:4

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Answer: (-1,2)

Step-by-step explanation:

Your solution is the intersecting point.

Answer:

67

Step-by-step explanation:

Each time the number goes up by 7. After 9 moretimes 4 will increase by 63.

4+63=67.

The 10th term should be 67

The total inches Derek has grown in the past three years is 3 inches.

None of the given options is correct.

Given information:

For the previous three years, Derek has become an inch taller every year.

This means that we can add up those three inches to find his total growth over the three-year period.

Thus, 1 + 1 + 1 equals 3 inches.

Derek has therefore gained 3 inches in total over the last three years.

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Answer: 5(7) over x

Step-by-step explanation:

Answer:

= –179/9

or –19 ^8/9

Step-by-step explanation:

–19²/9 –4¹/9 –(–3⁴/9)

–(173/9) –37/9 + 31/9

=L.c.m = 9

–173–37+31/9

= –210+31/9

= –179/9

or –19 ^8/9

i hope i was able to helped