Bret and Kamala each begin a proof of the law of sines. Their work is shown.
B
A
Bret
sin(C) =
sin(A) =
h =
sin(A)
sin(c)
sin(A)=sin(c)
h =
sin(C) sin(A)
C
a
=
h
D
-b-
The proof was correctly completed by
The next step in the proof is to
Kamala
sin(c) = 4
sin(A) = 4
asin(C) = h
csin(A) = h
C
asin(C) = csin(A)
sin(C) sin(A)
C
a
=
and write an expression for

Rounding to the nearest decimal place, the nominal cost of trade credit is approximately 1.013. Therefore, none of the given options accurately represents the nominal cost of trade credit.

To calculate the nominal cost of trade credit, we need to determine the discount amount and divide it by the net amount due.

Given information:

Gross amount = $3,030,303

Discount rate = 1/10

Net payment period = 40 days

To calculate the discount amount:

Discount amount = Gross amount * Discount rate

Discount amount = $3,030,303 * (1/10)

Discount amount = $303,030.30

To calculate the net amount due:

Net amount due = Gross amount - Discount amount

Net amount due = $3,030,303 - $303,030.30

Net amount due = $2,727,272.70

The nominal cost of trade credit can be calculated as follows:

Nominal cost of trade credit = (Discount amount / Net amount due) * (365 / Net payment period)

Nominal cost of trade credit = ($303,030.30 / $2,727,272.70) * (365 / 40)

Nominal cost of trade credit = 0.1111 * 9.125

Nominal cost of trade credit ≈ 1.0133

Rounding to the nearest decimal place, the nominal cost of trade credit is approximately 1.013.

Therefore, none of the given options accurately represents the nominal cost of trade credit.

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The nominal cost of trade credit in this scenario is 12.12%, which is the nearest option provided. Therefore, the correct answer is option (a), "12.12%."

To calculate the nominal cost of trade credit, we need to consider the terms "1/10, net 40" provided in the question.

"1/10" refers to a cash discount of 1% if payment is made within the given period. In this case, the firm can take advantage of the discount by paying within 10 days.

"Net 40" means that the total payment is due within 40 days without any discount.

To find the nominal cost of trade credit, we need to determine the effective annual interest rate (EAR). We can use the following formula to calculate the EAR:

EAR = (1 + Discount / (1 - Discount))^(365 / Credit Period) - 1

Where:

Discount is the cash discount rate expressed as a decimal (1% in this case, so 0.01). The credit Period is the number of days until the payment is due (40 in this case)

Plugging in the values:

EAR =\([1 + 0.01 / (1 - 0.01)]^{(365 / 40) - 1}\)

EAR ≈ 0.1212 or 12.12% (rounded to two decimal places)

Therefore, the nominal cost of trade credit is approximately 12.12%.

Conclusion: The nominal cost of trade credit in this scenario is 12.12%, which is the nearest option provided. Therefore, the correct answer is option (a), "12.12%."

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Answer: ||||||| n=41° |||||| m=59° IIIII p=260° IIII

Step-by-step explanation:

Alternate angle:

<m=<59°

m=59°

<n=<41°

n=41°

______________

p+41°+59°= 360°

p+100°=360°

p=360°-100°

p=260°

Answer:

n = 49

m= 31

p= 280

Step-by-step explanation:

41 + n = 90

n= 90 -41 = 49

59 + m = 90

m = 90 - 59 = 31

Hope this helps!

p + n + m = 360

p = 360 - 49 - 31 = 280

The center of the circle will be (2, -5) and the radius of the circle will be 1 unit.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x - h)² + (y - k)² = r²

The equation is given below.

x² - 4x + y² + 10y = -28​

Then the center and the radius of the circle will be

x² - 4x + 4 + y² + 10y + 25 = -28​ + 4 + 25

               (x - 2)² + (x + 5)² = 1²

Thus, the center and the radius of the circle will be (2, -5) and 1 unit respectively.

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9514 1404 393

Answer:

  (3/2)√2 ≈ 2.1213 units

Step-by-step explanation:

The distance d from point (x, y) to line ax+by+c = 0 is given by ...

  d = |ax +by +c|/√(a^2 +b^2)

We can write the equation of the line as ...

  x + y -4 = 0

so the distance is ...

  d = |x + y - 4|/√(1^2 +1^2)

For point (x, y) = (2, -1), the distance is ...

  d = |2 +(-1) -4|/√2 = 3/√2 = (3√2)/2

The distance from A(2, -1) to the line y = -x +4 is (3√2)/2 units.

Answers in bold

\(\begin{array}{|c|c|} \cline{1-2}\text{number of rolls} & \text{number of people}\\\cline{1-2}1 & \boldsymbol{0.5}\\\cline{1-2}6 &3\\\cline{1-2}10 & \boldsymbol{5}\\\cline{1-2}16 & \boldsymbol{8}\\\cline{1-2}25 & \boldsymbol{12.5}\\\cline{1-2}n & \boldsymbol{0.5n}\\\cline{1-2}\end{array}\)

========================================================

Explanation:

The given table looks like this

\(\begin{array}{|c|c|} \cline{1-2}\text{number of rolls} & \text{number of people}\\\cline{1-2}1 & \\\cline{1-2}6 & 3\\\cline{1-2}10 & \\\cline{1-2}16 & \\\cline{1-2}25 & \\\cline{1-2}n & \\\cline{1-2}\end{array}\)

Focus on the row that has two values in it.

x = number of rolls = 6

y = number of people 3

k = constant of proportionality

y = kx

k = y/x = 3/6 = 0.5

The constant of proportionality is k = 0.5 which gives the direct variation equation of y = 0.5x

If x = 1, then y = 0.5*1 = 0.5 meaning that 1 roll feeds 0.5 people. This means we need 2 rolls to feed one person.

If x = 10, then y = 0.5x = 0.5*10 = 5 people can be fed with those 10 rolls. This process is continued until we finish filling out the table.

Answer:

$1.10

explanation:

Answer:

In total that is $1.10

Step-by-step explanation:

Answer:

Step-by-step explanation:

The Quadratic Formula uses the "a", "b", and "c" from "ax2 + bx + c", where "a", "b", and "c" are just numbers; they are the "numerical coefficients" of the quadratic equation they've given you to solve

True. Exception reports show a greater level of detail than is included in routine reports.

Exception reports are reports that help in identifying data that does not conform to expected patterns. Exception reports show information about an exception in the data set.

This helps to identify irregularities or anomalies in data or system operations.Exception reports are used to analyze system performance, monitor resource consumption, and to detect unusual activity.

This type of report is important to identify issues or errors, where the routine reports or standard reports would not provide enough detail or insight to do so.

It provides detailed information on any unusual event or anomaly that occurred beyond the usual course of events or processes.Exception reports are generated and distributed when the data is not expected or when an event occurs that is outside of what is considered typical.

For example, a financial system might generate an exception report if a transaction is entered that exceeds the maximum allowed amount. This report would show the details of the transaction and highlight the exception.

The purpose of exception reports is to provide users with a higher level of detail than they would find in routine reports. Exception reports are used to highlight significant data, which will be used for further analysis or action.

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Answer:f8

Step-by-step explanation:

The statement is proven that mn is a perfect square then m and n are perfect squares for each m>=1 and n>=1.

The given statement is "For each m>=1 and n>=1, if mn is a perfect square, then either m or n is a perfect square."

Let's prove this statement by using a direct proof method.

Suppose mn is a perfect square.

Then there exists an integer k such that mn=k^2.

By the fundamental theorem of arithmetic, each positive integer greater than one can be uniquely represented as a product of prime numbers. Hence we can write,

m=p1^(a1) * p2^(a2) * ... * pk^(ak)

where p1, p2, ... , pk are distinct prime numbers and a1, a2, ... , ak are positive integers.

Therefore, mn = p1^(a1) * p2^(a2) * ... * pk^(ak) * p1^(a1) * p2^(a2) * ... * pk^(ak) = p1^(2a1) * p2^(2a2) * ... * pk^(2ak).

As k is the number of prime factors, it must be a positive integer.

Therefore, 2a1, 2a2, ... , 2ak are also positive integers.

By the definition of a perfect square, mn is a perfect square as well.

Therefore, we can write, mn = (p1^(a1) * p2^(a2) * ... * pk^(ak))^2.

Since p1, p2, ... , pk are distinct primes, they do not share any common factor. Therefore, the only way mn can be a perfect square is if each ai in the prime factorization of m or n is even.

Let's assume m=p1^(b1) * p2^(b2) * ... * pk^(bk) and n=p1^(c1) * p2^(c2) * ... * pk^(ck).

Since mn=k^2 and each ai is even, it follows that k is also even.

Therefore, k=2d for some positive integer d.

So,mn = p1^(b1+c1) * p2^(b2+c2) * ... * pk^(bk+ck) = (p1^(b1) * p2^(b2) * ... * pk^(bk)) * (p1^(c1) * p2^(c2) * ... * pk^(ck)) = m * n = (2d)^2 = 4d^2.

Therefore, mn is a perfect square if and only if m and n are perfect squares.

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Answer:

Step-by-step explanation:

to make 3255 a perfect square subtract 6 from 3255

3255 - 6 = 3249

3249 is a perfect square

Answer:

The cost of a sheet metal per square foot is $30

Step-by-step explanation:

Given

Size of Sheet Metal = 8.2ft squared

Used Sheet Metal = 3.5ft squared

Worth of leftover sheet = $141

Equation: \(8.2x - 3.5x = 141\)

Required

Find the cost per square foot of the sheet metal

Solving for x in the above equation will give the cost per square foot of the sheet metal.

\(8.2x - 3.5x = 141\)

\(4.7x = 141\)

Divide both sides by 4.7

\(\frac{4.7x}{4.7} = \frac{141}{4.7}\)

\(x = \frac{141}{4.7}\)

\(x = 30\)

Hence, the cost of a sheet metal per square foot is $30

6 minutes per mile.

As in, 30/5= 6

Answer:

Deandre can run 1 mile in 6 min

Step-by-step explanation:

Answer:

-3, 5/2

Step-by-step explanation:

What are the roots of the function y = 4x2 + 2x – 30?

To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x – 30.

Factor out the GCF of : 2, so the equation becomes 0 = 2(2x2+x-15)

Next, factor the trinomial completely. The equation becomes: 0=2(x+3)(2x-5)

Use the zero product property and set each factor equal to zero and solve.

x+3=0      2x-5 = 0

x = -3, 5/2

The roots of the function are -3, 5/2.

Hope this helped!

The roots of the function y = 4x² + 2x - 30 are -3, 5/2 after using the zero product property.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

y = 4x² + 2x - 30

To find the roots of the quadratic equation plug y = 0

4x² + 2x - 30 = 0

4x² + 12x - 10x - 30 = 0

4x(x + 3) - 10(x + 3) = 0

(x + 3)(4x -10) = 0

x + 3 = 0  or  4x - 10 = 0

x = -3 or x = 10/4 = 5/2

Thus, the roots of the function y = 4x² + 2x - 30 are -3, 5/2 after using the zero product property.

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Answer:

The explicit rule of the geometric sequence

 aₙ   = 187.5 (0.8)ⁿ⁻¹

Step-by-step explanation:

Step(i):-

Given that the third term of the sequence = 120

        tₙ = a rⁿ⁻¹  

       t₃  = a r³⁻¹ = ar²

        120 = ar² ..(i)

Given that the fifth term of the given geometric sequence = 76.8

        tₙ = a rⁿ⁻¹  

       t₅  = a r⁵⁻¹ = a r⁴

   76.8  = a r⁴...(ii)

Step(ii):-

 Dividing (ii) and (i)

         \(\frac{ar^{4} }{ar^{2} } = \frac{76.8}{120}\)

        r²   = 0.64

       r    =√ 0.64 = 0.8

Substitute r= 0.8 in equation (i)

         120 = ar²

       120 = a(0.8)²

⇒      \(a = \frac{120}{0.64} =187.5\)

Step(iii):-

The explicit rule of the geometric sequence

                 aₙ  = a rⁿ⁻¹

put a= 187.5  and r = 0.8

                aₙ   = 187.5 (0.8)ⁿ⁻¹

Answer:

a

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

60 because a regular hexagon has a exterior angle measure of 60.

A regular hexagon has 6 sides you divide 360 by 6 which is 60

Ans: 60

Answer:

(x+3)(y+2)

Step-by-step explanation:

(xy+2x)+(3y+6)

x(y+2)+3(y+2)

(x+3)(y+2)

Answer:

80 degrees

Step-by-step explanation:

angle c=50

this is an isoceles triangle in which both base angles are same

so, angle e=50

now we will use angle sum.property which states that the sum of all the interior angles of a triangle is equal to 180

so, 50+50+angle d=180

100 + angle d = 180

angle d =180-100

angle d = 80 degrees

When the person is 42 feet away from the jetski, the sound intensity is approximately 87.1 decibels.

To answer this question, we need to use the inverse square law of sound intensity, which states that the intensity of a sound decreases with the square of the distance from the source.
1. Identify the initial distance (D1) and initial decibel level (L1): In this case, D1 = 12 feet and L1 = 100 decibels.
2. Identify the final distance (D2): In this case, D2 = 42 feet.
3. Calculate the ratio of the initial distance to the final distance: \(R = (D1 / D2)^2\)

\(= (12 / 42)^2\)

\(= (2 / 7)^2\)

\(= 4 / 49.\)
4. Convert the initial decibel level to intensity (I1): The intensity of a sound is proportional to \(10^(L1/10).\)

\(So, I1 = 10^(100/10) = 10^10.\)
5. Calculate the final intensity (I2) using the ratio of distances: I2 = I1 * R

\(= 10^10 * (4 / 49).\)
6. Convert the final intensity back to decibels (L2): L2 = 10 * log10(I2) = \(10 * log10(10^10 * 4 / 49).\)
7. Calculate the final decibel level: L2 ≈ 10 * (10 - log10(49/4)) = 10 * (10 - 1.29)

= 87.1 decibels.

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A)  (-infinity,1) U (1,infinity).

b)  There is a horizontal asymptote at y=1.

c)  The derivative is always negative (except at x=1 where it is undefined), so the function is decreasing on the interval (-infinity,1) and increasing on the interval (1,infinity).

d)   The function has no local maximum or minimum values

e)   The function is concave up on the interval (-infinity,1) U (1,infinity).

f) This has no real solutions, so there are no inflection points.

(a) The domain of f(x) is all real numbers except x = 1. Thus, the domain can be expressed as (-infinity,1) U (1,infinity).

(b) There is a vertical asymptote at x=1 since the denominator becomes zero at x=1. To find the horizontal asymptote, we can use the fact that as x approaches infinity or negative infinity, the function approaches the value of its leading term. In this case, the leading term is x/x, which simplifies to 1. Therefore, there is a horizontal asymptote at y=1.

(c) To find the intervals of increase and decrease, we can take the derivative of the function:

f'(x) = -2/(x-1)^2

The derivative is always negative (except at x=1 where it is undefined), so the function is decreasing on the interval (-infinity,1) and increasing on the interval (1,infinity).

(d) The function has no local maximum or minimum values since it does not change direction.

(e) To find the intervals of concavity, we can take the second derivative of the function:

f''(x) = 4/(x-1)^3

The second derivative is positive for all x except x=1 where it is undefined, so the function is concave up on the interval (-infinity,1) U (1,infinity).

(f) To find the inflection points, we can set the second derivative equal to zero:

4/(x-1)^3 = 0

This has no real solutions, so there are no inflection points.

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The best measure of variability for the given data is the range, and its value is 10.

The measure of variability for the data would be the range.

The range is the difference between the largest and smallest value in the dataset. In this case, the largest value is the single dot above 10, and the smallest value is zero.

Therefore, the range is 10-0 = 10.
The interquartile range (IQR) is another measure of variability that is useful when dealing with skewed data or outliers. It is the difference between the upper quartile and lower quartile.

However,

In this case, there is not enough information to calculate the quartiles, and the data does not appear to be skewed or have any outliers.
Therefore, the range is the most appropriate measure of variability for this particular line plot. It tells us the spread of the data and how much variation there is in the number of roses purchased per day.

The value of the range is 10 indicating that the number of roses purchased per day can vary greatly with a maximum of 10 rose bouquets sold in a single day.
The  more accurate representation of variability in the number of rose bouquets purchased per day.

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To calculate the probability that at least two people in a class of 30 share the same birthday, we can use the complement rule, which states that the probability of an event happening is equal to one minus the probability of the event not happening.

If we assume that birthdays are uniformly distributed throughout the year (i.e., each day is equally likely to be someone's birthday), then the probability that no two people in the class share the same birthday is:

365/365 * 364/365 * 363/365 * ... * 336/365

This is because the first person can have any birthday (probability of 365/365), the second person must have a different birthday (probability of 364/365), the third person must have a different birthday than the first two (probability of 363/365), and so on, up to the 30th person, who must have a different birthday than the first 29 (probability of 336/365).

Calculating this probability gives us:

(365/365) * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937

So the probability that no two people in the class share the same birthday is approximately 0.2937.

Using the complement rule, the probability that at least two people in the class share the same birthday is:

1 - 0.2937 = 0.7063

Therefore, the probability that at least two people in a class of 30 share the same birthday is approximately 0.7063, or 70.63%.

Stem-and-leaf plots contain original data values where histograms do not. Therefore, option B is the correct answer.

The "stem" values are listed down, and the "leaf" values go right (or left) from the stem values.

The "stem" is used to group the scores and each "leaf" shows the individual scores within each group.

The advantage of a stem leaf diagram is it gives a concise representation of data. The advantage of a frequency histogram is, that it is visually strong. Histograms are usually preferable to stem and leaf diagrams in large data sets. The disadvantage of a stem leaf diagram is not visual.

Therefore, option B is the correct answer.

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Answer:

|x+3|>8

Step-by-step explanation:

x is positive, so remove the absolute value signs. Adding a number greater than 5 to 3 will result in a number greater than 8.

The output of this code will be a signal that starts at zero and gradually increases to three. After five seconds, the signal starts decreasing to zero, with an exponential decay rate. The output plot will look like a ramp that rises linearly and falls exponentially after five seconds.

The term "son of a mention" is not familiar in mathematics. The correct term might be "son of a gun" or "son of a function."A differential equation used to model your specific engineering course is called an engineering differential equation. Such equations are used to predict, control, and monitor various physical processes, ranging from the dynamics of mechanical systems to the motion of fluids and gases, and electrical and electronic circuits. It's essential to know the form of the differential equations, the initial and boundary conditions, and the physical meaning of the parameters to use them effectively in modeling physical systems.

The following MATLAB code represents a simple for loop with a nested if-else statement and a plotting command. The code generates a signal with two segments: a rising ramp from zero to three and a falling ramp from three to zero. The signal has a total duration of 10 seconds, a sampling interval of 0.05 seconds, and a plotting delay of 0.002 seconds.

01 t=0 02 while t<10 03

if

(t<5) 04 y=3*(1-exp(-t)); 05 else if

(t>=5) 06 y=3*exp(-t+5); 07 ends 08 end 09

t = t + 0.05 10 pauses (0.002)

The output of this code will be a signal that starts at zero and gradually increases to three. After five seconds, the signal starts decreasing to zero, with an exponential decay rate. The output plot will look like a ramp that rises linearly and falls exponentially after five seconds.

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Therefore, the answer of the given question of the equation maximum value is 41 .

What is equation?

The equal sign is used between numerical or changeable expressions to create an equation, such as 3x+5=11.

A number that can be entered as the variable's replacement in an equation serves as the solution.

According to the given question:

Correct option is D)

f(x)=  3+9x+17 /  3+9x+7

=> 3+9x+7+10 / 3+9x+7

=> 1 +  10 / 3+9x+7

f(x) = 0 for maximum value

f(x)= 10 (6x+9) / (3x2+9x+7)2

6x+9=0

X=-3/2

Given that x is real, the highest value of f(x) is => 1 +

=> 1 +

=> 1 + 40/1 = 41

Therefore, the answer of the given question of the equation is 41 .

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A proof competition is held annually by Contradiction Club, with special prizes awarded for first, second, third, and fourth place. If 16 students participate in the competition this year, the awards can be allocated among the students in 120 different ways.

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