(-25) × [6 + 4] is not same as​

a) The amount you will repay is approximately $12,000.

b) The annual interest rate charged by the loan company is approximately 18.2715%.

To calculate the amount you will repay and the annual interest rate charged by the loan company, we can follow these steps:

Step 1: Calculate the number of $500 increments for the loan amount:

Number of $500 increments = loan amount / $500

= $1,693 / $500

≈ 3.386

Since we can't have a fraction of an increment, we round up to 4.

Step 2: Calculate the daily payment:

Daily payment = 25 © * Number of $500 increments

= 25 © * 4

= $100

Step 3: Calculate the total repayment amount:

Total repayment amount = Daily payment * number of days

= $100 * 120

= $12,000

Step 4: Calculate the annual interest rate:

Annual interest rate = (Total repayment amount - Loan amount) / Loan amount * (360 / Number of days)

= ($12,000 - $1,693) / $1,693 * (360 / 120)

Now, let's perform the calculations:

Amount you repay ≈ $12,000

Annual interest rate ≈ (($12,000 - $1,693) / $1,693) * (360 / 120)

Calculating the annual interest rate:

Annual interest rate ≈ (($10,307) / $1,693) * 3

Rounding to four decimal places:

Annual interest rate ≈ (6.0905) * 3

≈ 18.2715

Therefore,

a) The amount you will repay is approximately $12,000.

b) The annual interest rate charged by the loan company is approximately 18.2715%.

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Answer:

44

Step-by-step explanation:

This is called the Tribonacci sequence. In this sequence, you add the last 3 numbers together to get the next number in the sequence.

For example, 0+1+1=2, 1+2+4=7, 4+7+13=24 and so on.

7+13+24=44

44 is the next number in the sequence

Mr Scott paid $8664 after 3 years.

The principal of the car loan is $23,400, the interest rate of the car loan is 1.60% and the monthly payment is $375.

Given that, balance after 3 months = 22,275 and balance after 12 months = 18,900.

Average payment rate means, for any date of determination, the sum of the monthly payment rates for the prior three monthly periods divided by three.

Now, the difference of payment = 22,275 - 18,900

= $3,375

The difference of time = 12 - 3 = 9 months

So, the payment per month = 3,375 / 9

= $375 per month.

Now, 375 x 12 = $4,500

Principal amount = 4,500 + 18,900

= 23,400

Rate = 375 / 23400 × 100

= 0.016 × 100 = 1.60%

Therefore, the principal of the car loan is $23,400, the interest rate of the car loan is 1.60% and the monthly payment is $375.

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The value of x for which cos(x) = sin(14x) is x = π/30. The solution x = π/30 represents one of the possible solutions within the given range of 0 ≤ x ≤ 2π.

To find the value of x for which cos(x) = sin(14x), we can use the trigonometric identity sin(θ) = cos(π/2 - θ).

Applying this identity to the given equation, we have:

cos(x) = cos(π/2 - 14x)

Since the cosine function is equal to the cosine of the complement of an angle, the two angles must be either equal or their difference must be a multiple of 2π.

Thus, we can set the two angles inside the cosine function equal to each other:

x = π/2 - 14x

To solve for x, we can simplify the equation:

15x = π/2

Dividing both sides by 15, we get:

x = (π/2) / 15

To express the answer in radians, we can simplify further:

x = π/30

Therefore, the value of x for which cos(x) = sin(14x) is x = π/30.

It's worth noting that the equation cos(x) = sin(14x) has infinitely many solutions, as the sine and cosine functions are periodic. The solution x = π/30 represents one of the possible solutions within the given range of 0 ≤ x ≤ 2π.

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Answer:

32 markers

Step-by-step explanation:

Ty has 8 x 3 = 24 markers.

Together, they have 8 + 24 = 32 markers.

The range of the function f(x) = 2x^2 / (3x - x^2) is (-∞, 2) U (2, +∞).

To find the range of the function f(x) = 2x^2 / (3x - x^2), we need to determine the set of all possible output values.

First, we observe that the function is undefined when the denominator (3x - x^2) equals zero. This occurs when x = 0 or x = 3. Therefore, we need to consider the range for x values excluding these points.

To analyze the behavior of the function, we can examine its limits as x approaches positive or negative infinity. Taking the limit as x approaches infinity, we find that the function approaches 2. As x approaches negative infinity, the function also approaches 2.

Based on the limits and the fact that the function is continuous for all other values of x, we can conclude that the range of f(x) is the interval (-∞, 2) U (2, +∞), where (-∞, 2) represents all values less than 2 and (2, +∞) represents all values greater than 2.

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Answer:

Her allowance is $12

Equation:

1/2x + 9 = 15

Answer:

12

Step-by-step explanation:

1/2x + 9 = 15

1/2x = 6

x = 12

Answer:

Equation of the plane is 19x - 20y - 15z - 38 = 0.

Step-by-step explanation:

We can find an equation of the plane that passes through the given three points by first finding two vectors that lie in the plane and then taking their cross product to get the normal vector of the plane. Once we have the normal vector, we can use any of the three points to write the equation of the plane in point-normal form.

Let's start by finding two vectors that lie in the plane. We can take the vectors connecting (2, −1, 3) to (7, 4, 6) and from (2, −1, 3) to (−3, −3, −2), respectively:

v1 = <7-2, 4-(-1), 6-3> = <5, 5, 3>

v2 = <-3-2, -3-(-1), -2-3> = <-5, -2, -5>

Now we can find the normal vector to the plane by taking the cross product of v1 and v2:

n = v1 x v2 = det( i j k

5 5 3

-5 -2 -5 )

= < 19, -20, -15 >

Now we can use the point-normal form of the equation of a plane, which is:

n · (r - r0) = 0

where n is the normal vector, r0 is a point on the plane, and r is a generic point on the plane. We can use any of the three given points as r0. Let's use the first point, (2, −1, 3):

n · (r - r0) = < 19, -20, -15 > · ( < x, y, z > - < 2, -1, 3 > ) = 0

Expanding the dot product, we get:

19(x - 2) - 20(y + 1) - 15(z - 3) = 0

Simplifying, we get:

19x - 20y - 15z - 38 = 0

Therefore, an equation of the plane is 19x - 20y - 15z - 38 = 0.

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The future value of the loan is $18,358.16. This means that after 8 months, the loan will have grown to $18,397.54 due to the interest.

To find the future value of this loan, we can use the formula FV = PV(1 + r)^t, where FV is the future value, PV is the present value, r is the interest rate, and t is the time period in years.

In this case, we have PV = $17,592, r = 6.6%, and t = 8 months or 0.667 years (8/12).

Plugging these values into the formula, we get:
FV = $17,592(1 + 0.066)^0.667
FV = $17,592(1.066)^0.667
FV = $18,358.16

Therefore, the future value of the loan is $18,358.16. This means that after 8 months, the loan will have grown to $18,397.54 due to the interest.

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Answer:

2

Step-by-step explanation:

x + y = 10

y = 8

Substituting in equation,

x + 8 = 10

=>x = 10 - 8

=>x = 2

The graphs of the sinusoidal function for the question 1 to 4 created with MS Excel are attached

5. The function is; y = cos(θ) + 2

6. The function is; y = sin(2·θ) - 4

A sinusoidal function is a smooth periodic or repetitive function based on the sine or cosine of an angle.

The equations for the graphs in the sinusoidal function indicates that we get;

The period = 2·π/B

The horizontal shift = -C/B

The vertical shift = D

Where;

B = The coefficient of the angle, θ

C = The constant within the parenthesis

D = The constant term outside the sine or cosine function parenthesis

1. y = 2·sin(2·θ + 1)

The function indicates that the amplitude is 2, the period is 2·π/2 = π, the vertical shift is 0, and the horizontal shift is -1/2

Please find attached the graph of the function, created with MS Excel

2. y = -cos(θ) - 2

The amplitude is 1

The period is 2·π

The horizontal shift is 0

The vertical shift is -2

Please find attached the graph of the function y = -cos(θ) - 2, created with ms Excel

3. y = 4·cos(3·θ -2)

The amplitude is 4

The period is 2·π/3

The horizontal shift is 0

The vertical shift is -2

Please find attached the graph of the function y = 4·cos(3·θ -2), created with MS Excel

4. y = 3·sin(6·θ) - 1

The amplitude is 3

The period is π/3

The horizontal shift is 0

The vertical shift is -1

Please find attached the graph of the function y = 3·sin(6·θ) - 1, created with MS Excel

5. The points on the graph are;

Peak; (0, 3)

The next adjacent trough; (180, 1)

The adjacent peak; (360, 3)

Therefore;

The amplitude is 1

The period is 360°

The horizontal shift is 2

The vertical shift is 0

The peak point at θ = 0, indicates;

The function is; y = cos(θ) + 2

6. The points on the graph are;

Peak; (45, -3)

The next adjacent trough; (135, -5)

The adjacent peak; (225, -3)

Therefore;

The amplitude is 1

The period is 180 = π radians

The horizontal shift is 0

The vertical shift is -4

The function is; y = sin(2·θ) - 4

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Answer:

60 degrees

Step-by-step explanation:

The point at C is a vertical angle.

Door to door sampling is used when it is important to control where the sample is delivered and when the products are of a perishable nature.

The term sampling  selecting refers to the selection of a small proportion of the population extrapolating the results the results obtained from this small group to represent the characteristics of the entire population. This sample is chose in a manner as to reflect the properties the generality of the population.

Hence, door to door sampling is used when it is important to control where the sample is delivered and when the products are of a perishable nature.

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Answer:

237

Step-by-step explanation:

29 + 16 * 13

= 29 + 208

= 237

The probability that a randomly selected sample of 36 drivers will drive, on average, more than 12,500 miles is approximately 0.123

This problem involves the sample mean of a set of data, and we can use the central limit theorem to approximate the distribution of sample means, even if the original distribution is not normal.

Let X be the number of miles driven by a single driver in a year. We know that the population mean µ = 12,000 miles and the population standard deviation σ = 2,580 miles. We also know that the sample size n = 36.

The sample mean X is an estimator of the population mean µ. The distribution of sample means is approximately normal with a mean of µ and a standard deviation of σ/√n, according to the central limit theorem

So, the distribution of sample means can be expressed as

X ~ N(µ, σ/√n)

Substituting the given values, we get

X ~ N(12,000, 2,580/√36) = N(12,000, 430)

Now we need to find the probability that a randomly selected sample of 36 drivers will drive, on average, more than 12,500 miles. This is equivalent to finding the probability that the sample mean is greater than 12,500

P(X > 12,500) = P(Z > (12,500 - 12,000) / 430)

where Z is a standard normal random variable.

P(Z > 1.16) = 1 - P(Z < 1.16) = 1 - 0.877 = 0.123

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The given question is incomplete, the complete question is:

People drive an average of 12,000 miles per year with a standard deviation of 2,580 miles per year. what is the probability that a randomly selected sample of 36 drivers will drive, on average, more than 12,500 miles?

Answer:

False.

Step-by-step explanation:

You can put x=0 into both of the equations to justify. At the first equation, when x=0, f(x)=0. In the second equation, when x=0, f(x)=3. F(x) is the value of y. So, the function has moved 3 units up, not 3 units to the right.

Answer:  3 and 14

Step-by-step explanation:

Let the two numbers be X and Y.

"The sum of twice a number and 7 times another number is 49:"

2X + 7Y = 49

"The first number decreased by 3 times the second number is 5:"

X - 3*Y = 5

Rewrite the second equation so that either the X or Y is isolated.  I'll choose X:

X = 5+3Y

Now use this definition of X in the first equation:

2X + 7Y = 49

2(5+3Y) +7Y = 49

10 + 6Y + 7Y = 49

13Y = 39

Y = 3

Use Y = 3 to solve for X:

X - 3*Y = 5

X - 3*3 = 5

X = 5 + 9

X = 14

The values are X = 14 and Y = 3.

Check to see if these work:

2X + 7Y = 49

Does 2(14) + 7(3) = 49  ??

28 + 21 = 49  ?   YES

X - 3*Y = 5

Does 14 - 3*(3) = 5  ???

          14 - 9 = 5      YES

Answer:

the answer is probably 3/5 since its the starting one so it will be how t started

Step-by-step explanation:

Answer:3:5

Step-by-step explanation:well when you divide 6/10 it equals 3/5.when you divide 9/15 it equals 3/5 and so on.

It should be noted that the angle sector for each sport will be:

volleyball (12) = 60°

Basketball (18) = 90°

Ping Pong (8) = 40°

Softball (10) = 50°

Football (24) = 120°

From the information given, the following can be illustrated:

volleyball (12) = 12/72 × 360° = 60°

Basketball (18)= 18/72 × 360° = 90°

Ping Pong (8) = 8/72 × 360° = 40°

Softball (10) = 10/72 × 360° = 50°

Football (24) = 24/72 × 360° = 120°

Total = 72

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Answer:

A number s plus 21

Step-by-step explanation:

s+21

A number s plus 21

Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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Answer:

B. 55

Step-by-step explanation:

The angle measurements on the top are the same as the bottom, so we know  the angle next to (x+70) is 55. You then subtract 55 from 180 and you are left with 125. Then you have to subtract 70 to find x, which gives you 55. Therefore, x=55

Answer:

100+80+9+0.2+0.07+0.001

Answer:

none

Step-by-step explanation:

I just did this question and got it right.

Answer:

I think the answer would be D. 20 hope it helps

Step-by-step explanation:

To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.

To write the equation of the line with an x-intercept at -6 and a y-intercept at 2, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.

In this case, the y-intercept is given as 2, so the equation becomes y = mx + 2. To find the slope, we can use the formula (y2 - y1) / (x2 - x1) with the given points (-6, 0) and (0, 2). We find that the slope is 1/3. Thus, the equation of the line is y = (1/3)x + 2.

For the polynomial f(x) = -3x² + 6x, the degree is 2 and the leading coefficient is -3. The end behavior of the graph is determined by the degree and leading coefficient. Since the leading coefficient is negative, the graph will be "downward" or "concave down" as x approaches positive or negative infinity.

To find the zeros, we set the polynomial equal to zero and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two solutions: x = 0 and x = 2.

The x-intercept is the point where the graph intersects the x-axis, and since it occurs when y = 0, we substitute y = 0 into the polynomial and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two x-intercepts: (0, 0) and (2, 0).

To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.

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