equivalent expression to 2x7 + 2x3

The results using Fermat's little theorem are:

a. \(315 \mod 13 = 1\)

b. \(1518 \mod 17 = 1\)

c. \(4567 \mod 17 = 1\)

d. \(145102 \mod 101 = 1\)

Fermat's little theorem states that if p is a prime number and a is an integer not divisible by p, then \(a^{p-1} \equiv 1 \mod p\). We can use this theorem to find the results of the given congruences:

a. To find \(315 \mod 13\), we note that 13 is a prime number. Since 315 is not divisible by 13, we can apply Fermat's little theorem. We have \(315^{12} \equiv 1 \mod 13\). Simplifying this expression, we get \(315 \equiv 1 \mod 13\). Therefore, \(315 \mod 13 = 1\).

b. For \(1518 \mod 17\), we again use Fermat's little theorem. Since 17 is prime and 1518 is not divisible by 17, we have \(1518^{16} \equiv 1 \mod 17\). Simplifying this expression, we find \(1518 \equiv 1 \mod 17\). Hence, \(1518 \mod 17 = 1\).

c. Similarly, for \(4567 \mod 17\), we apply Fermat's little theorem. Since 17 is prime and 4567 is not divisible by 17, we have \(4567^{16} \equiv 1 \mod 17\). This simplifies to \(4567 \equiv 1 \mod 17\). Therefore, \(4567 \mod 17 = 1\).

d. Lastly, for \(145102 \mod 101\), we can once again use Fermat's little theorem. Since 101 is prime and 145102 is not divisible by 101, we have \(145102^{100} \equiv 1 \mod 101\). This simplifies to \(145102 \equiv 1 \mod 101\). Thus, \(145102 \mod 101 = 1\).

Therefore, the results using Fermat's little theorem are:

a. \(315 \mod 13 = 1\)

b. \(1518 \mod 17 = 1\)

c. \(4567 \mod 17 = 1\)

d. \(145102 \mod 101 = 1\)

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Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Answer:

x-intercept= (5,0)

y-intercept= (0,-2)

Slope= 2/5

Step-by-step explanation:

\({ \red{\boxed{ \tt{Step-by-step-explaination}}}}\)

Perimeter of a rectangle : \({ \purple{ \tt{2(l+b)}}}\)

length = \({ \red{ \tt{17cm}}}\)

breadth= \({ \red{ \tt{?}}}\)

now,

according to the rule.

perimeter = 2(l+b)

66 = 2(17+b)

66 = 34 + 2b

66 - 34 = 2b

32 = 2b

32/2 = b

16 cm = b

hence b = \({ \pink{ \sf{16cm}}}\)

Answer and Step-by-step explanation:

There are 12 coins in total, and we are told that 5 are Canadian nickels and 2 are Canadian dimes. That is 7 Canadian coins.

So, 7 out of 12.

\(\frac{7}{12}\) is the answer.

#teamtrees #WAP (Water And Plant)

Answer: Subtract 3 from both sides of the equation

simplify

divide both sides on the equation by the same term

simplify

your answer should be 4

Step-by-step explanation:

Answer:

x=-22

Step-by-step explanation:

6(x+15)=-42

6x+90=-42

6x=-132

x=-22

The price that Maura sell each scarf would be =$33. Maura sells each scarf for $33. That is option A.

To calculate the amount of money that Maura spends on each scarf the following is carried out.

The amount of money that she spends on the scarf material = $5.50

The percentage selling price of each scarf = 600% of $5.50

That is ;

= 600/100 × 5.50/1

= 3300/100

= $33.

Therefore, each price that is sold by Maura would probably cost a total of $33.

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Two sides are congruent to each other.

The third side of an isosceles triangle which is unequal to the other two sides is called the base of the isosceles triangle.

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry.

A triangle with all sides of different lengths. All angles are different, too. So no sides are equal and no angles are equal.

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Answer:

Two sides are congruent to each other.

The third side of an isosceles triangle which is unequal to the other two sides is called the base of the isosceles triangle.

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry.

A triangle with all sides of different lengths. All angles are different, too. So no sides are equal and no angles are equal.

Step-by-step explanation:

Answer:

2 1/4 square yards

Step-by-step explanation:

We have been given that Matthew and his 3 siblings are weeding a flower bed with an area of 9 square yards.    

All person weeding flower bed: .

To find the area in square yards weeded by each child, we will divide total area of flower bed by 4.

Therefore, each child weeded  square yards of flower bed.

Answer:

I believe it's going to be2 1/4 square feet

Answer:

c

Step-by-step explanation:

its one full square and 1/4

Answer:

Answer is 51+20-51+3=23.

Step-by-step explanation:

Hope you have a wonderful Christmas and New Years. Thank you this was so nice

Answer:

23

Step-by-step explanation:

51+20-51+3

= 51+20= 71

= 71+3= 74

= 74-51= 23

The gradient of the chord PQ is 2h + 8

Let's first find the coordinates of points P and Q on the curve y = 2x^2+1.

Point P has an abscissa of 2, so its coordinates are (2, 2(2)^2+1) = (2, 9).

Point Q has an abscissa of 2+h, so its coordinates are (2+h, 2(2+h)^2+1) = (2+h, 2(4+4h+h^2)+1) = (2+h, 8+8h+2h^2+1) = (2+h, 2h^2+8h+9).

The gradient of the chord PQ is given by:

(m) = Δy /Δx

(m) = (2h^2+8h+9 - 9) / (2+h - 2)

(m) = (2h^2+8h) / (h)

(m) = 2h + 8

As h approaches zero, the gradient of the chord PQ approaches 8, because the term 2h becomes negligible compared to 8 when h is small. Therefore, the gradient of the tangent to the curve at point P is 8.

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Answer:

i think its d

Step-by-step explanation:

Answer:

I think it is the second one

Step-by-step explanation:

Answer:

slope=-2/5

Step-by-step explanation:

rise -2

run 5

Answer:

The Forth Answer

Step-by-step explanation:

I Think That Is correct

The graph of g is Transformation up 7 units.

what is Transformation?

A graph transformation is a method for altering an existing graph or graphed equation to create a different version of the graph that follows. The modification of algebraic equations is a typical form of algebraic issue.

solution:

From the question, we have the following parameters that can be used in our computation:

g(x) = f(x) + k

Also, we have the value of k to be

k = 7

From the question, we can interpret g(x) = f(x) + k as f(x) is shifted up by k units

This means that

g(x) = f(x) + k

So, we have

g(x) = f(x) + 7

Hence, the transformation is (a) translated up 7 units

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Answer:

b)

Step-by-step explanation:

There must be both left and right side.

To test whether a data model is biased, one can compute the average difference between a predicted result and an actual result using the bias() function.

Unreasonably supporting or opposing someone or something because you allowed your opinions to cloud your judgement: The senator accused the media of being biased. Journalists need to be objective and free of political prejudice. Cognitive biases are systematic thinking errors that are often learned from cultural and personal experiences.

They lead to perceptional distortions when people make decisions. Even though data may appear to be objective, it can still be biased because it is gathered and handled by humans. We are not objective in the way we perceive things. Biases can be deliberate or unintentional. If given the choice between three shirts, a person might choose the one in their preferred hue above the other two.

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Correct Question:

A data analyst wants to find out how much the predicted outcome and the actual outcome of their data model differ. what function can they use to quickly measure this?

Answer:

193

Step-by-step explanation:

Algebraic expressions are expressions that use variables and combination of terms.

1. Addition

The addition expression is:

\(5x^2 - \frac 13x + \frac 52 - \frac 12x^2 + \frac 12x - \frac 13 -2x^2 + \frac 15x - \frac 16\)

Collect like terms

\(5x^2 - \frac 12x^2 -2x^2 - \frac 13x + \frac 12x + \frac 15x + \frac 52 - \frac 13 - \frac 16\)

Evaluate the like terms

\(\frac 52x^2 + \frac{11}{30}x + 2\)

2. Subtraction

The subtraction expression is:

\(7x^2 -2x + 10 - (-2x^2 + \frac 12x - 3)\)

Open the bracket

\(7x^2 -2x + 10 + 2x^2 - \frac 12x +3\)

Collect like terms

\(7x^2 + 2x^2 -2x - \frac 12x+ 10 +3\)

Evaluate the like terms

\(9x^2- \frac 52x+ 13\)

3. Simplify

The expression is given as:

\((\frac 13x^2 - \frac 47x + 11) - (\frac 17x - 3 -2x^2) - (\frac 27x - \frac 23x^2 + 2)\)

Rewrite as:

\((\frac 13x^2 - \frac 47x + 11) - ( -2x^2 + \frac 17x - 3) - (- \frac 23x^2 + \frac 27x + 2)\)

Open the brackets

\(\frac 13x^2 - \frac 47x + 11 + 2x^2 - \frac 17x + 3+ \frac 23x^2 - \frac 27x - 2\)

Collect like terms

\(\frac 13x^2 + 2x^2 + \frac 23x^2 - \frac 47x - \frac 17x - \frac 27x + 11 + 3 - 2\)

Evaluate the like terms

\(3x^2 - x + 12\)

4. Products

The expression is given as:

\((x-\frac 1x)(x + \frac 1x)(x^2 + \frac 1{x^2})(x^4 + \frac 1{x^4})\)

Apply the difference of two squares

\((x^2-\frac 1{x^2})(x^2 + \frac 1{x^2})(x^4 + \frac 1{x^4})\)

Apply the difference of two squares

\((x^4-\frac 1{x^4})(x^4 + \frac 1{x^4})\)

Apply the difference of two squares

\(x^8 - \frac 1{x^8}\)

5. Formula

The expression is given as:

\((\frac 32m + \frac 23n)(\frac 32m - \frac 23n)\)

Apply the difference of two squares

\(\frac 94m^2 - \frac 49n^2\)

6. Identity

The expression is given as:

\((m + 3)(m + 2)\)

The identity used to solve the above expression is:

\((x + a)(x + b)\)

7. Identity

The expression is given as:

\((4x + y)^2\)

Expand

\(16x^2 + 8xy + y^2\)

Rewrite as:

\(16x^2+ y^2 + 8xy\)

8. Difference of two squares

The expression is given as:

\((a + b)(a - b)\)

Apply the difference of two squares

\(a^2 - b^2\)

9. Evaluate

The expression is given as:

\(a^2 + b^2\)

Apply the sum of two squares

\((a + b)^2 - 2ab\)

So, we have:

\(5^2 - 2 * 6\)

Evaluate

\(13\)

10. Coefficient

The expression is given as:

\(\frac x2 +\frac y2 - xy\)

The coefficient of xy in the expression is -1

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The officer can conclude the driver exceeded the speed limit because, based on the given information, the car traveled a distance of 30 miles in 26 minutes, which corresponds to an average speed of 69.23 miles per hour.

The officer observed the car starting from rest at a highway on-ramp and radioed ahead to another officer 30 miles along the highway.

The car reached the location of the second officer 26 minutes later, and it was clocked going 60 miles per hour at that point.

To determine if the driver exceeded the speed limit, we need to calculate the average speed of the car between the two officers.

We can use the formula: average speed = total distance / total time.

The total distance traveled by the car is 30 miles, and the total time taken is 26 minutes.

To convert the time to hours, we divide 26 minutes by 60 (1 hour = 60 minutes), resulting in 0.4333 hours.

Substituting the values into the formula, we get average speed = 30 miles / 0.4333 hours ≈ 69.23 miles per hour.

Since the average speed between the two officers is greater than the speed limit of 60 miles per hour, the officer can conclude that the driver exceeded the speed limit.

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Answer:

\( 5x + 12y = -78 \)

or

\( y = -\dfrac{5}{12}x - \dfrac{13}{2} \)

Step-by-step explanation:

\( y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) \)

\( y - (-4) = \dfrac{-9 - (-4)}{6 - (-6)}(x - (-6)) \)

\( y + 4 = \dfrac{-9 + 4}{6 + 6}(x + 6) \)

\( y + 4 = \dfrac{-5}{12}(x + 6) \)

\( 12y + 48 = -5x - 30 \)

\( 5x + 12y = -78 \)

\( 12y = -5x - 78 \)

\( y = -\dfrac{5}{12}x - \dfrac{13}{2} \)

Answer:

\( 5x + 12y = -78 \)

or

\( y = -\dfrac{5}{12}x - \dfrac{13}{2} \)

Answer:

for number 1

x=-1 y=-5

for number 2

x=1 y=2

for number 3

x=1 y=8

Step-by-step explanation:

for number 1  

x=-1 y=-5

for number 2

x=1 y=2

for number 3

x=1 y=8

a) 0 fraudulent records need to be resampled if we would like the proportion of fraudulent records in the balanced data set to be 20%.

b) 1600 non-fraudulent records need to be set aside if we would like the proportion of fraudulent records in the balanced data set to be 20%?

(a) How many non-fraudulent records need to be set aside if we would like the proportion of fraudulent records in the balanced data set to be 20%

Ans - 0

(b) How many non-fraudulent records need to be set aside if we would like the proportion of fraudulent records in the balanced data set to be 20%?

Ans 1600

Therefore, fraudulent records is 400 which 4% of 10000 so we will not resample any fraudulent record.

To balance in the dataset with 20% of fraudulent data we need to set aside 16% of non-fraudulent records which is 1600 records and replace it with 1600 fraudulent records so that it becomes 20% of total fraudulent records

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Complete Question:

6. Suppose we are running a fraud classification model, with a training set of 10,000 records of which only 400 are fraudulent.

a) How many fraudulent records need to be resampled if we would like the proportion of fraudulent records in the balanced data set to be 20%?

b) How many non-fraudulent records need to be set aside if we would like the proportion of fraudulent records in the balanced data set to be 20%?

To order the given expressions from least to greatest, we need to find the values of each expression. However, since we do not have the function p(x), we cannot find the values of p′(1), p′(3), p′(6), p′(7), p′(9), and p′(10). Therefore, we cannot order the expressions from least to greatest.

It is important to note that the sign of each expression will depend on the function p(x) and its derivative p′(x). If p′(x) is positive, then the function p(x) is increasing at that point. If p′(x) is negative, then the function p(x) is decreasing at that point. Without the function p(x), we cannot determine the sign of each expression and therefore cannot order them from least to greatest.

In conclusion, without the function p(x), we cannot order the expressions p′(1), p′(3), p′(6), p′(7), p′(9), and p′(10) from least to greatest.

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