What is the value of tan(-284°24') to the nearest ten-thousandth?

Answer:

Step-by-step explanation:

You want to know the monthly payment on a 30-year loan of $99,000 at 8%, and the total interest paid.

The monthly payment is given by the amortization formula ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where P is the loan amount, r is the annual interest rate, and t is the loan period in years

  A = $99000(0.08/12)/(1 -(1 +0.08/12)^(-12·30)) ≈ 726.42692814058

The monthly payment is $726.43.

The total of monthly payments is about 360 times the "exact" value of the monthly payment. There is always a slight adjustment made in the last payment to account for the fact that the payment value is always rounded. We can approximate that adjustment by using the "exact" monthly payment amount: $726.42693

The interest paid is the difference between the total of payments and the original loan amount:

  I = 360×$726.42693 -99000 ≈ $162,513.69

The total interest paid is about $162,513.69.

__

Additional comment

If you use 360 times the monthly payment of $726.43, you will compute the interest paid as $162,514.80.

If you compute the future value of the loan after 360 payments of $726.43, you will find it is $4.58. This means the last payment will be $726.43 -4.58 = $721.85, and the total of payments will be $261,510.22, which includes $162,510.22 in interest.

If you make an amortization schedule, where interest is rounded every month (as in "real life"), the result will be different from any of these values. It is $162,510.63. (The last payment is $722.26.)

The upshot is that the amount you determine for total interest paid will depend on the method you use to determine it.

The point (3, 7) lies on the circle with center (-1, 4) and containing the point (-1, 9).

The distance formula is a mathematical formula used to calculate the distance between two points in a two or three-dimensional space. It is derived from the Pythagorean theorem and is given by:

d = √((x2 - x1)² + (y2 - y1)²)

Where d represents the distance between the two points, (x1, y1) and (x2, y2) represent the coordinates of the two points in a two-dimensional space.

To determine if the point (3, 7) lies on the circle with center (-1, 4) and containing the point (-1, 9), we need to calculate the distance between the center of the circle and the point (3, 7), and compare it to the radius of the circle.

Let's first find the radius of the circle. Since the circle contains the point (-1, 9), the distance between the center of the circle and (-1, 9) is equal to the radius. Using the distance formula, we get:

radius = √[(9 - 4)² + (-1 - (-1))²] = √[25] = 5

Now let's find the distance between the center of the circle (-1, 4) and the point (3, 7):

distance = √[(7 - 4)² + (3 - (-1))²] = √[3² + 4²] = 5

We see that the distance between the center of the circle and the point (3, 7) is equal to the radius of the circle. Therefore, the point (3, 7) lies on the circle with center (-1, 4) and containing the point (-1, 9).

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Answer:

the perimeter of the paperboard that remains after the semicircle is removed is 82.84 inches.

Step-by-step explanation:

The perimeter of the paperboard that remains after the semicircle is removed is equal to the sum of the four sides of the rectangular portion of the paperboard plus half the circumference of the semicircle.

The rectangle has dimensions of length = 20 inches and width = 12 inches. Therefore, the sum of the four sides of the rectangular portion of the paperboard is:

2(20) + 2(12) = 64 inches

The semicircle has a diameter equal to the width of the rectangle, which is 12 inches. Therefore, the radius of the semicircle is half the diameter, or 6 inches. The circumference of a full circle with a radius of 6 inches is:

2 * 3.14 * 6 = 37.68 inches

Half of the circumference of the semicircle is:

(1/2) * 37.68 = 18.84 inches

Therefore, the perimeter of the paperboard that remains after the semicircle is removed is:

64 + 18.84 = 82.84 inches

Thus, the perimeter of the paperboard that remains after the semicircle is removed is 82.84 inches.

Rounding to the nearest foot, the distance from point A to point B is approximately 182 feet.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

Let's assume that the distance from point A to the lighthouse is x feet and the distance from point B to the lighthouse is y feet. Also, let's assume that the height of the boat's crew's eye level is h feet above the water.

From point A, we can use tangent function to find x:

tan(5°) = (119 + h) / x

From point B, we can use tangent function again to find y:

tan(18°) = (119 + h) / y

We want to find the distance between point A and point B, which is the difference between x and y:

distance AB = y - x

We need to eliminate h from these equations to solve for x and y. We can do this by solving for h in one equation and substituting it into the other equation:

h = x tan(5°) - 119

tan(18°) = (119 + x tan(5°) - 119) / y

tan(18°) = x tan(5°) / y

y = x tan(5°) / tan(18°)

distance AB = y - x = x (tan(5°) / tan(18°) - 1)

Now we can plug in the values and use a calculator to find the distance:

distance AB = x (tan(5°) / tan(18°) - 1)

distance AB = x (0.107 - 1)

distance AB = -0.893 x

Since the distance cannot be negative, we know that x must be greater than zero. Therefore, we can ignore the negative sign and solve for x:

x = distance AB / -0.893

Using a calculator, we get:

x ≈ 181.74 feet

Rounding to the nearest foot, the distance from point A to point B is approximately 182 feet.

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Step-by-step explanation:

As a salesperson at Scrapbooks and Treasures, Alysse receives a monthly base pay plus commission on all that she sells. If she sells $400 worth of merchandise in one month, she is paid $292. If she sells $800 of merchandise in one month, she is paid $384.

Here is the salary function used to represent this situation in terms of the amount of merchandise sold:

s(x) = 0.23x + 200

Find Alysse's salary when she sells $2,200 worth of merchandise.

The point estimate for the proportion parameter for this population is A)0.305.

What is probability?

Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

In a random sample of 892 college students in the United States, 272 say they skip at least one class per week.

From the given information then,

Sample size n = 892

No of favorable outcomes (i.e successes) x=272

We know ,

The point estimate for the population parameter [tex]\hat P[/tex]=x/n.

Where n=sample size , x=number of success.

Here x = 272 ,n=892 then

The point estimate for the proportion parameter for this population then,

=> [tex]\hat p[/tex] = 272/892 = 0.305.

Hence  the point estimate for the proportion parameter for this population is A)0.305.

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7) ∠1≅∠4 on the basis of opposite angles.

8) ∠1≅∠3 on the basis of opposite angles.

9) ∠5≅∠7 on the basis of opposite angles.

Opposite angles in geometry are equal in measure. This is known as the "vertical angles theorem." In other words, if two lines intersect, the opposite angles formed by those lines will have the same degree of measurement.

7) since ∠1 = ∠2

and ∠3 = ∠4, then by the rule of the congruence of opposite angles, ∠1≅∠4

8) In the above shape, we can see that ∠1 and ∠3 are a opposite angles, hence, they are both equal or congruent.

9) The logic is the same for ∠5 and ∠7. The are opposites hence they are equal.

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Answer:

The two points (4, 5) and (-4, 5) have the same y-coordinate, which means they lie on a horizontal line. This horizontal line is the x-axis. So, the points are related in that they both lie on the x-axis, with a distance of 8 units between them.

Step-by-step explanation:

Put both of the equations into   y = mx + b form to compare them

                   m = slope    if they have the same slope they are parallel and do not intersect

                    b = y axis intercept

                  if m and b are equal in each of the equations , they are the same line

2x+y = 0   ======>   y =  - 2x + 0

2y = -4x + 6  ====>   y =  - 2x + 3

The both have the same slope = -2   so they are parallel

   but they have different  b  values so they are not the same lines

No intersection means no solution :   parallel  lines do not intersect  

Answer:

I think it will be

y=1/3x+0

The inequality that models the amount of weight the forklift can carry is: 45x + 70y ≤ 3000

An inequality is a mathematical statement that indicates a relationship between two expressions that are not equal. It uses comparison symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to) to show the relationship between the two expressions.

The total number of boxes that a forklift can carry is x + y.

The total weight that the forklift can carry is equal to 45x + 70y pounds, which is less than or equal to 3000 pounds.

Therefore, the inequality that models the number of boxes the forklift can carry is:

x + y ≤ 60

The inequality that models the amount of weight the forklift can carry is:

45x + 70y ≤ 3000.

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The probability of having no 1 and no 5 among the rolls is approximately 0.131 or 13.1%.

According to the First Principle of Probability, the outcomes of one chance occurrence have no bearing on those of succeeding chances occurrences. Thus, the chance of getting heads the second or third time you flip it stays at 1 in 2. The chances of getting heads on the sixth flip, even if you got five consecutive heads, stay at 12.

The Bayes Theorem asserts that the likelihood of a second tournament given the first occurrence multiplied by the odds of the first event equals the conditional event's likelihood depending on the presence of another event.

The probability of rolling a number other than 1 or 5 on a fair die is 4/6 or 2/3, since there are four favorable outcomes (2, 3, 4, 6) out of six possible outcomes.

To find the probability of rolling no 1 and no 5 in five rolls, we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.

So, for each roll, the probability of rolling a number other than 1 or 5 is 2/3. Therefore, the probability of rolling no 1 and no 5 in five rolls is:

(2/3) * (2/3) * (2/3) * (2/3) * (2/3) = (2/3)⁵ ≈ 0.131

Rounding to three decimal places, the probability is approximately 0.131.

Therefore, the probability of having no 1 and no 5 among the rolls is approximately 0.131 or 13.1%.

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The equatiοn has nο sοlutiοn.

An equatiοn is defined as a mathematical statement in algebra that prοves the equality οf twο mathematical expressiοns. Fοr example, the fοrmula 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the wοrd "equal."

Here the given equatiοn is ,

=> |4x-4(x+1)|=4

Nοw simplifying the equatiοn then,

=> 4x-4(x+1)=± 4

=> 4x-4x-4=±4

=>-4=±4

Hence the given equatiοn has nο sοlutiοn.

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Answer: The Silo is 44 meters tall

Step-by-step explanation:

To find the height of the silo, first you have to divide the drawing height (33cm) by 1.5 to get the unit rate. Then multiply the 22 by 2 to get 44 meters (The height of the silo)

Answer:

B

Step-by-step explanation:

5280 yards does not equal one mile

Answer

B.5,280

Step-by-step explanation:

Im just smart like that

Answer:

The function is shifted 1 unit to the right and then flipped over the x-axis. So the correct result is:

[tex]y = - f(x - 1)[/tex]

option D is correct answer  As we can see, the graph is a parabola for x <= 0 and an exponential curve for x > 0. The function is continuous, but not differentiable at x = 0

what is exponential curve?

An exponential curve is a mathematical curve that rises or falls at an increasing rate as its values get larger. The curve is defined by an exponential function

In the given question,

To graph this function, we can start by plotting the points for different values of x. Since the function behaves differently for x <= 0 and x > 0, we will plot the points separately for each region.

For x <= 0:

x     g(x)

-2     4

-1     1

0     0

For x > 0:

x          g(x)

0.5     e⁰⁵ = 1.65

1        e = 2.72

2       e²= 7.39

        x <= 0     x > 0

As you can see, the graph is a parabola for x <= 0 and an exponential curve for x > 0. The function is continuous, but not differentiable at x = 0 because the derivative from the left and the derivative from the right do not match.

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On an 8-question multiple-choice test, where each question has 2 answers,  the probability of getting at least one question wrong is [tex]\frac{1023}{1024}[/tex]

Probability is a way to gauge how likely something is to happen1. It is expressed as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty for the event.

In an 8-item multiple-choice test with 2 possible answers for each, the likelihood of getting at least one question wrong can be computed as follows:

P(at least one mistake) = 1 - P (none wrong)

P(at least one wrong) [tex]=1-(\frac{1}{2})^{10[/tex]

P(at least one wrong) [tex]=1-\frac{1}{1024}\\\\=\frac{1023}{1024}[/tex]

On an 8-question multiple-choice test, where each question has 2 answers,  the probability of getting at least one question wrong is [tex]\frac{1023}{1024}[/tex]

The complete question is-

On an 8-question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?

Give your answer as a fraction

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473,615 rounded to the nearest hundred is D. 473,600.

Number rounding or approximation is the adjustment of the digits (up or down) to make rough calculations easier.

The result of number rounding is an estimated value rather than a precise one.

Number rounding or approximation are useful when the precise information is not required for decision-making.

473,615 = 473,600

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201.5 is the smallest average of 200 different positive and odd integers.

Let's first consider the set of the first 200 odd positive integers: {1, 3, 5, ..., 397, 399, 401}.

The average of this set is (1+3+5+...+397+399+401)/200 = 201.

Now, we want to find a set of 200 distinct positive and odd integers that has a smaller average than 201.

One way to do this is to remove the largest element from the first set (401) and replace it with the smallest odd positive integer that is greater than 401, which is 403.

The new set is {1, 3, 5, ..., 397, 399, 403}.

The average of this set is (1+3+5+...+397+399+403)/200 = 201.5.

Hence, 201.5 is the smallest average that can be calculated from 200 different positive and odd integers.

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The calculated value of the expression 2x - y for the given values of x and y is 9/2.

We are given that 2x = 7 and 2y = 5, and we are asked to find the value of 2x - y.

This means that

x = 7/2 and y = 5/2

We can start by substituting the given values into the expression:

2x - y = 2(7/2) - (5/2)

Notice that since 2x = 7, then x = 7/2.

Similarly, since 2y = 5, then y = 5/2. Substituting these values into the expression, we get:

2x - y = 2(7/2) - (5/2) = 7 - 5/2 = 9/2

Therefore, the value of 2x - y is 9/2.

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The probability that both students selected are males is 0.46.

The multiplication rule of probability for independent events states that the probability of two or more independent events occurring together is the product of their individual probabilities.

If event A has probability P(A) and event B has probability P(B), and A and B are independent events, then the probability of both A and B occurring  

P(A and B) = P(A) x P(B)

Here we have

There are 13 males and 6 females in the class, for a total of 19 students.

The probability of selecting a male on the first draw is 13/19.

After one male has been selected,

There are 12 males and 6 females left in the class.

The probability of selecting another male on the second draw = 12/18

[ Since there is one less student in the class and one less male]

The probability of selecting two males in a row is the product of the probabilities of each individual event:

P(male and male) = P(male on the first draw) x P(male on the second draw | male on the first draw)

= (13/19) x (12/18)

= 0.456 or approximately 0.46 (rounded to two decimal places).

Therefore,

The probability that both students selected are males is 0.46.

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The x-intercept is 21/5 and the y-intercept is -7/2 of the given line.

What is the x and y-intercept of a line?

In a two-dimensional Cartesian coordinate system, the x-intercept of a line is the point where the line crosses the x-axis, which means the value of y is zero at that point. The x-intercept can be found by setting y = 0 in the equation of the line and solving for x.

Given that we have to find the y-intercept and x-intercept

The given equation is:

5x - 6y = 21

The x-intercept is the point at which the line crosses the x-axis. At this point, the y-coordinate is zero.

The y-intercept is the point at which the line crosses the y-axis. At this point, the x-coordinate is zero

Finding x-intercept:

To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'.

Substitute y = 0 in a given equation

5x - 6(0) = 21

x = 21/5

Thus x-intercept is 21/5.

Finding y-intercept:

To find the y-intercept, plug 0 in for 'x' and solve for 'y'

Substitute x = 0 in a given equation

5(0) - 6y = 21

-6y = 21

-2y = 7

y = -7/2

Thus y-intercept is   -7/2

hence, the x-intercept is 21/5 and the y-intercept is -7/2 of the given line.

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Complete question:

Find the y-intercept and x-intercept of the line. 5x-6y=21

The values of the composite function are (f + g)(x) = 2x² + 3x - 2, (f - g)(x) = -2x² + 3x - 8, (f . g)(x) = 6x³ + 4x² - 15x - 15, (f o g)(x) = 6x² + 4, (g o f)(x) = 18x² - 60x + 53, (f o g)(3) = 58

To determine the values of the composite functions, we have to evaluate or simplify each as

7. (f + g)(x) = f(x) + g(x) = (3x - 5) + (2x² + 3) = 2x² + 3x - 2

8. (f - g)(x) = f(x) - g(x) = (3x - 5) - (2x² + 3) = -2x² + 3x - 8

9. (f . g)(x) = f(x) * g(x) = (3x - 5) * (2x² + 3) = 6x³ + 4x² - 15x - 15

10. (f o g)(x) = f(g(x)) = f(2x² + 3) = 3(2x² + 3) - 5 = 6x² + 4

11. (g o f)(x) = g(f(x)) = g(3x - 5) = 2(3x - 5)² + 3 = 18x² - 60x + 53

12. (f o g)(3) = f(g(3)) = f(2(3)² + 3) = f(21) = 3(21) - 5 = 58

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It will take Allan approximately 38 months (rounded up) to repay the loan with monthly payments of $100 at an interest rate of 9.5% per year, compounded monthly.

Interest rate refers to the percentage of the principal amount charged by a lender to a borrower for the use of money over a certain period of time.

To calculate the time it takes for Allan to repay the loan, we can use the formula for the present value of an annuity:

PV = PMT x (1 - [tex](1 + r)^-n[/tex]) / r

where:

PV = present value

PMT = monthly payment

r = monthly interest rate (9.5% per year / 12 months = 0.00791667)

n = number of months

Plugging in the given values, we get:

3000 = 100 x (1 - (1 + 0.00791667)[tex]^-n[/tex]) / 0.00791667

Simplifying and solving for n, we get:

n = -ln(1 - (3000 x 0.00791667 / 100)) / ln(1 + 0.00791667)

n = 37.4 months

Therefore, it will take Allan approximately 38 months (rounded up) to repay the loan with monthly payments of $100 at an interest rate of 9.5% per year, compounded monthly.

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Nicky had $73 initially. Since Abby had the same amount, Abby also had $73 initially.

Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.

After Abby spent $37, she had A - 37 dollars left. After Nicky spent $61, she had N - 61 dollars left. We also know that after Abby spent $37, she had 3 times as much money as Nicky. So we can set up an equation:

A - 37 = 3(N - 61)

Substituting A = N from the earlier equation, we get:

N - 37 = 3(N - 61)

Expanding the brackets, we get:

N - 37 = 3N - 183

Simplifying and solving for N, we get:

2N = 146

N = 73

Therefore, Nicky had $73 initially. Since Abby had the same amount, Abby also had $73 initially.

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Answer:

f(x) = -(x-3)+7

Step-by-step explanation:

To satisfy the equation y = -3x - 4, we need to substitute the given values of x and y in the equation and check if it holds true.

For the ordered pair (-4, y):

y = -3(-4) - 4

y = 12 - 4

y = 8

So, the ordered pair (-4, 8) satisfies the equation y = -3x - 4.

For the ordered pair (x, 2):

2 = -3x - 4

6 = -3x

x = -2

So, the ordered pair (-2, 2) satisfies the equation y = -3x - 4.