Use Fermats Little theorem to find 23^1002 mod 41​

1.15p is the expression which  represents Daniela's Season 3 pay in terms of p

To find Daniela's Season 3 pay in terms of p, we need to calculate the pay increase for each season.

In Season 2, her pay increases by 5 percent, which means she will receive 105 percent (or 1.05) of her Season 1 pay.

In Season 3, her pay increases by 10 percent from Season 2, so she will receive 110 percent (or 1.10) of her Season 2 pay.

To express Daniela's Season 3 pay in terms of p, we multiply the Season 1 pay (p) by the pay increase factors for Season 2 and Season 3:

Season 2 pay = 1.05p

Season 3 pay = 1.10(1.05p) = (1.10)(1.05)p

Simplifying the expression, we get:

Season 3 pay = 1.155p

Therefore, 1.15p is the expression which  represents Daniela's Season 3 pay in terms of p

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Answer:

$103,875.41

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

Note: Bi-monthly means every 2 months.

Substitute the given values into the formula and solve for A:

[tex]A=240000\left(1+\dfrac{0.012}{6}\right)^{6 \cdot 30}[/tex]

[tex]A=240000\left(1.002\right)^{180}[/tex]

[tex]A=343875.406934...[/tex]

[tex]A=343875.41[/tex]

So after 30 years, Mr. and Mrs. Rainer will have paid a total of $343,875.41, which includes both the principal and the interest.

To find the amount of interest they paid, subtract the principal:

Interest paid = $343,875.41 - $240,000 = $103,875.41

Therefore, they will have paid $103,875.41 in interest over the 30-year period.

Answer:

t=3.5

Step-by-step explanation:

Divide each term in 7t=24.5 by 7 and simplify.

Some of the reasons why math is important include:

Mathematics teaches us the invaluable skills of critical thinking via logical and systematical reasoning for solving complicated problems. It is, however, essential to know that mathematics is omnipresent in our day-to-day lives but we may not be conscious about it.

Our math-related actions include computing tips, shopping, allocating time for daily tasks as well as cooking meals. With a strong foundation in Mathematics, several career paths such as engineering, finance, accounting or data analysis can materialize for perspective job-visors; hence enabling them towards professional success.

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The surface area of a three dimensional shape is the total area of all of the faces. To find the surface area of a shape, we find the area of each face and add them together. E.g. The measurements here are in centimetres so the surface area is measured in square centimetres ( c m 2 ) (cm^2) (cm2)

triangle-

Base Surface Area = 112

= 121 feet2

Lateral Surface Area =

2×11× √

( 11 )2 + 72

2

= 195.84943196241 feet2

Total Surface Area = 316.84943196241 feet2

bottom bit-

Surface Area = 2×(15×5 + 15×8 + 5×8) = 470 feet2

part 1. The job offers into a salary are:

The Adjusted Salary for Minneapolis, MN is  $220.38

The Adjusted Salary for Omaha, NE is  $322.15

part 2.

We could conclude that the job offer in Omaha, NE is better because of its the adjusted salary as it offers  a higher salary in an average USA city.

For Minneapolis, MN:

Adjusted Salary = (Offered Salary + Benefits) / Cost of Living Index

Adjusted Salary = ($21,000 + $2,400) / 106.1

Adjusted Salary = $23,400 / 106.1

Adjusted Salary =  $220.38

For Omaha, NE:

Adjusted Salary = (Offered Salary + Benefits) / Cost of Living Index

Adjusted Salary = ($27,500 + $1,200) / 89.2

Adjusted Salary = $28,700 / 89.2

Adjusted Salary = $322.15

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Answer:

The expected count of rolls to land showing a 3 is 10.00.

Answer:

The volume of the cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height:

V= πr²h = π(4cm)²(10cm) = 160π cm³

The density of the material is given by the mass per unit volume:

density = mass/volume = 500g / 160π= π(4 cm)²(10 cm)

= 160π cm³

The mass and volume are related by density (ρ), which is defined as mass per unit volume:

ρ = m/V

where m is the mass and V is the volume.

Substituting the given values, we get:

ρ = 500 g / 160π cm³

ρ ≈ 0.988 g/cm³

Therefore, the density of the material the cylinder is made of is 0.988 g/cm³.

The value of p when q is equal to 2 is 108

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.

This means as x increases y reduces and vice versa.

If p is inversely proportional to q, then

p = k/q

p = 18 and q = 12

18 = k/12

k = 18 × 12 = 216

When q =2

p = 216/2

p = 108

therefore the value of p is 108

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The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.

x = 3, −2+4i, −2−4i

To find the zeros of the polynomial p(x), we need to find the values of x such that p(x) = 0.

One way to do this is to use the rational root theorem, which states that if a polynomial with integer coefficients has a rational root p/q (where p and q are integers with no common factors), then p must divide the constant term and q must divide the leading coefficient.

For the polynomial, [tex]p(x) = x^3 + x^2 + 8x - 60,[/tex] the constant term is -60 and the leading coefficient is 1.

Therefore, the possible rational roots are:

±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, ±60

We can then use synthetic division or long division to check which of these roots are actually zeros of the polynomial.

Trying the possible roots, we find that x = 3 is a zero of the polynomial, since p(3) = 0.

Using long division or synthetic division, we can then divide p(x) by (x - 3) to get a quadratic factor:

[tex]x^3 + x^2 + 8x - 60 = (x - 3)(x^2 + 4x + 20)[/tex]

The quadratic factor [tex]x^2 + 4x + 20[/tex] has no real roots since its discriminant [tex](b^2 - 4ac)[/tex] is negative. Therefore, the zeros of the polynomial p(x) are:

x = 3 (with multiplicity 1)

x = -2 ± 4i (with multiplicity 1 each)

Therefore, the zeros of the polynomial p(x) are 3, -2 + 4i, and -2 - 4i.

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Answer: Hey i'd love to help you can you please provide the choices that are given?

Step-by-step explanation:

The annual deposit for John for total amount of annuity is A = $ 29,060.29

Given data ,

To determine the annual deposit amount needed for John to have a total of $500,000 by the time he retires, we can use the formula for the future value of an ordinary annuity:

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

Where FV is the future value, P is the annual deposit, r is the annual yield (interest rate), and n is the number of years.

In this case, we are given:

FV = $500,000

r = 5% = 0.05

n = 25 years

Substituting these values into the formula, we have:

$500,000 = P * [(1 + 0.05)^25 - 1] / 0.05

And , the value of P is

P = ($500,000 x 0.05) / [(1.05^25) - 1]

P ≈ ($25,000) / (1.858734... - 1)

P ≈ ($25,000) / 0.858734...

P ≈ $29,060.29

Hence , John must deposit approximately $29,060.29 into the retirement account each year to accumulate a total of $500,000 by the time he retires in 25 years

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Mia's total profit for the month is given as follows:

$200.

The profit function is obtained as the subtraction of the revenue function by the cost function, as follows:

P(x) = R(x) - C(x).

From the table given in this problem, the revenue and the costs are given as follows:

Hence the profit is given as follows:

9500 - 9300 = $200.

As the profit is positive, it is in fact a profit(gain) and not a loss.

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The positive values of the number Kofi thinks of are 1 and 2.

Let's call the number Kofi thinks of "x".

According to the problem Kofi adds 5 to this number and then multiplies the result by 3.

We can write this as:

3(x + 5)

We know that this expression cannot be greater than 21 so we can set up an inequality:

3(x + 5) ≤ 21

Simplifying the inequality, we get:

x + 5 ≤ 7

Subtracting 5 from both sides, we get:

x ≤ 2

The possible values of the number Kofi thinks of are all the positive integers less than or equal to 2 are 1 and 2.

To check that these values work can plug them back into the expression 3(x + 5) and verify that they give a result less than or equal to 21:

If Kofi thinks of 1, then 3(1 + 5) = 18 is less than 21.

If Kofi thinks of 2 then 3(2 + 5) = 21 is equal to 21 but it satisfies the condition since the problem asks for an answer that "cannot be greater than 21".

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Answer:

Yes, .023 is a rational number.

Step-by-step explanation:

A rational number is defined as any number that can be expressed as a ratio of two integers, where the denominator is not zero.

To show that .023 is a rational number, we can express it as a fraction in which the numerator and denominator are integers.

We can write:

.023 = 23/1000

Both the numerator (23) and denominator (1000) are integers, so .023 is a rational number.

The total amount of the emergency fund is A) $6,516.91

First, we need to calculate the net income after deductions:

Next, we need to calculate the amount of constant expenses:

Fixed prices = 30% of $3,425.88 = $1,027.76

The entire amount saved inside the emergency fund is 5 months' worth of fixed costs:

Emergency fund = $1,027.76 x 5 = $5,138.80

To calculate the quantity inside the 60-day CD

We need to multiply 75% of the emergency fund by means of the interest rate and divide with the aid of 12 to get the monthly interest:

Therefore, the total amount of the emergency fund is:

$5,138.80 + $160.57 + $1,284.70 = $$6,516.91

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Answer:

x = -3 + √117

x = -3 - √117

Step-by-step explanation:

So the equation is x(x+6)=108

first you gotta simplify

x*x + x*6 = 108

x^2 + 6x = 108

x^2 + 6x - 108 = 0

using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a) with a=1, b=6 and c=-108

The group does not have enough food to complete the trip with all five members. By sacrificing one member's trip to the South Pole and carefully rationing the food, the group can ensure that each person has enough food to complete the trip safely.

According to the given chart, calculate that each crate contains a total of 48000 calories. Therefore, two missing crates result in a total loss of 96000 calories (48000 x 2).

Determining whether the group has enough food to reach the South Pole and return to base camp, calculate the total number of calories required for the entire trip. Supposing a round trip of 10 days to the South Pole and back, the total number of calories required would be:

Total Calories = (6000 calories/person x 5 people x 10 days) x 2 (round trip)

Total Calories = 600,000 calories

To cover for the lost calories, the group would need to sacrifice one member's trip to the South Pole and send them directly back to base camp. This would leave four members to continue to the South Pole, where they would have to ration their food carefully to make sure they have enough for the entire trip.

Below is a plan to ensure enough food:

Day 1-2:

Day 3-5:

Day 6-7:

Day 8-10:

Add up all the total calories consumed:

60,000 + 18,000 + 180,000 + 48,000 + 90,000 = 396,000 calories

This is less than the total calories required, which was 600,000 calories. Therefore, the group does not have enough food to complete the trip with all five members. By sacrificing one member's trip to the South Pole and carefully rationing the food, the group can ensure that each person has enough food to complete the trip safely.

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Answer:

[tex]z^{2} +z-36[/tex]

Step-by-step explanation:

Multiply

Answer: The value of X is 12.

Step-by-step explanation:

K and M are parallel lines so,

6x-13 = 4x+11

Subtract 4x from both sides,

2x-13 = 11

Add the 13 to both sides,

2x = 24

Divide by 2,

x = 12

:).

Answer:

Step-by-step explanation:

6x - 13 = 4x + 11

2x = 11 + 13

2x = 24

x = 24 : 2

x = 12

The output levels that will maximize profits are Q1 = 52.5 and Q2 = 52.5.

To maximize profits, we need to find the output levels of the two goods that will maximize the difference between total revenue and total cost (i.e., profit).

The profit function can be expressed as:

π = TR - TC

  = 15Q1 + 18Q1^2 + 15Q2 + 18Q2^2 - 20 - 2Q1.Q2 - 393

Taking the partial derivative of the profit function with respect to Q1 and setting it equal to zero, we get:

∂π/∂Q1 = 15 + 36Q1 - 2Q2 = 0

Taking the partial derivative of the profit function with respect to Q2 and setting it equal to zero, we get:

∂π/∂Q2 = 15 + 36Q2 - 2Q1 = 0

Using Cramer's rule, we can solve for Q1 and Q2:

Q1 = (2(15) - (15)(36))/(-4) = 52.5

Q2 = (2(15) - (15)(36))/(-4) = 52.5

Therefore, the output levels that will maximize profits are Q1 = 52.5 and Q2 = 52.5.

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In the given figure, after applying the vertical angle and straight line angle property, the values of x and z are 5° and 116° respectively.

Four angles are created when two lines intersect. Vertical angles are those that are opposite each other and are always congruent.

That means, z° = (12x + 56)° ---------- (1)

On a straight line, the angles add up to 180°.

That means, z° + (8x + 24)° = 180° ---------- (2)

Substituting value of z from (1) in (2),

(12x + 56) + (8x + 24) = 180

20x + 80 + 180

20x = 100

x = 5°

Substituting x = 5 in (2),

z + (8*2 + 24) = 180

z + 64 = 180

z = 116°

Therefore, x = 5° and z = 116°.

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Answer:

y=3x−9

Step-by-step explanation:

The area of Curtis's triangular frame is 36 square feet. The Option C is correct.

To get area of the frame, we will use formula for the area of a triangle which is [tex]A = 1/2 * b * h[/tex]

B = length of the base

H = perpendicular distance from the base to the vertex.

Substituting the values, we get:

A = 1/2 * 12 feet * 6 feet

A = 1/2 * 72 feets

A = 36 square feet

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The measure of angle θ is 210°. Therefore, the value of the cos θ will be -√3 / 2.

Given that:

sin θ = -0.5

The angle θ lies in the third quadrant.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The angle θ is calculated as,

sin θ = -0.5

θ = 210°

The value of the cosine of anlge θ is calculated as,

cos θ = cos 210°

cos θ = -√3 / 2

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Answer:

a)  Very strong positive correlation (r = 0.99).

b)  y = 299.46 + 1.74x

c)  $1,709 per month

Step-by-step explanation:

Linear regression is a statistical technique used to model the relationship between a dependent variable and an independent variable by fitting a linear equation to the observed data points. It aims to find the line of best fit that minimizes the overall distance between the observed data and the predicted values based on the linear equation.

We can use a statistical calculator to perform linear regression analysis on the given data.

The explanatory (independent) variable is the square footage (x-values).

The response (dependent) variable is monthly rent (y-values).

After entering the data into a statistical calculator we get:

The r-value, also known as the correlation coefficient, is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It ranges between -1 and 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

In this case, an r-value of 0.99 suggests that there is a very strong positive linear relationship between between square footage and monthly rent. As the square footage increases, the monthly rent tends to increase as well.

This high correlation indicates that square footage is a strong predictor of monthly rent. However, it is important to note that the correlation coefficient alone does not imply causation or provide information about the underlying factors influencing the relationship.

[tex]\hrulefill[/tex]

To determine the regression equation, substitute the found values of a and b into the regression line formula, y = a + bx.

Round the values of a and b to the nearest hundredth:

Therefore, the regression equation is:

[tex]\boxed{y = 299.46 + 1.74x}[/tex]

where:

[tex]\hrulefill[/tex]

To determine the monthly rent that we might expect to pay for an 810 square foot apartment, substitute x = 810 into the regression equation found in part (b), and solve for y:

[tex]\begin{aligned}y &= 299.46 + 1.74(810)\\&=299.46+1409.4\\&=1708.86\\&=1709\end{aligned}[/tex]

Therefore, we would expect to pay approximately $1,709 per month for an 810 square foot apartment.

Answer:

∠ BCA = 25°

Step-by-step explanation:

the inscribed angle BCA is half the measure of the central angle BOA , so

∠ BCA = [tex]\frac{1}{2}[/tex] × 50° = 25°

The correct statement about the relationship between the IRR and the MIRR is that a typical firm’s IRR will be less than its MIRR.

To calculate the MIRR, we need to find the future value of the positive cash flows at the end of year 4, using the reinvestment rate equal to the WACC. We can then find the discount rate that equates the present value of the initial investment with the future value of the negative cash flows and the positive future value of the positive cash flows.

Using the financial calculator or spreadsheet software, we can find that the future value of the positive cash flows is $698,711.27, and the MIRR is 27.46%.

Therefore, the MIRR is 27.46%, and based on the MIRR criterion, the project should be accepted if the required rate of return is less than 27.46%.

The correct statement about the relationship between the IRR and the MIRR is that a typical firm’s IRR will be less than its MIRR. This is because the IRR assumes that positive cash flows are reinvested at the IRR, which may not be realistic, while the MIRR assumes that positive cash flows are reinvested at the WACC, which is usually more realistic.

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