(Number Theory) Please provide a detailed response and I
will be sure to upvote.
In plain language, answer the following questions:
(i) What is a complete residue system?
(ii) What is a primitive root

Answer:

side lengths: 12 feet, 9 feet, 4 feet

Step-by-step explanation:

Conditions for unique triangles with 3 sides:

9 + 6 = 15

As 15 < 18 this is NOT a unique triangle

9 + 4 = 13

As 13 > 12 this IS a unique triangle

3 + 2 = 5

As 5 < 6 this is NOT a unique triangle

14 + 4 = 18

As 18 < 24 this is NOT a unique triangle

answer: aiuaejaeijaeokjaea;ij;eoiroier;iijw;ije;ipjeja;eoijie;iw

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

Substitute the values

5(7) - 3(8) + 11

35 - 24 + 11

11 + 11

22

Answer:

\(\dfrac 3{10}\)

Step-by-step explanation:

\(~~~~~~\dfrac 25 + x = \dfrac 7{10}\\\\\\\implies x = \dfrac 7{10} - \dfrac 25\\ \\\\\implies x = \dfrac 7{10} - \dfrac 4{10}\\\\\\\implies x = \dfrac{7-4}{10}\\\\\\\implies x = \dfrac 3{10}\)

The degree of freedom for the t statistic, in this case, is 18.

Hi! To answer your question about testing the difference between the means of two normally distributed independent populations with sample sizes of n1 = 10 and n2 = 10, we will use the formula for degrees of freedom (df) in a two-sample t-test:

df = (n1 - 1) + (n2 - 1)

Plug in the sample sizes, n1 = 10 and n2 = 10:

df = (10 - 1) + (10 - 1)

df = 9 + 9

df = 18
The degrees of freedom for the t statistic in this case is 18.

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The two random variables from this list that are continuous are: a) The average temperature in NYC during May. b) The compensation of a Top 500 CEO.

A continuous random variable is a variable whose values are any member of an uncountable set or any uncountable combination of such members. A continuous random variable has an infinite number of possible values, which are represented by an interval (a,b), where a and b can be any value on the real number line. A continuous random variable cannot take on individual values because there are an infinite number of values between any two points.For example, temperature, length, and weight are examples of continuous random variables.

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Answer:

x=-1.837 or 1.837

Step by Step explanation:

Use the standard form,ax²+bx+c=0 , to find the coefficients of our equation, :

q = 32

b= 0

c= -108

x=-1.837 or x=1.837

I hope this is helpful

pls tag brainliest answer

Answer:

multiply the x^2 by a negative number

Step-by-step explanation:

Multiplying the x² by a negative number causes the graph of y = x2 to open downward.

It is defined as the curve which is the intersection of cone and plane. There are three major conic sections; parabola, hyperbola, and ellipse (a circle is a special of type of ellipse).

It is given that the equation is, y = x².

The given equation is of the parabola. Parabola is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

The graph of the given equation is attached below.

Thus, multiplying the x² by a negative number causes the graph of y = x² to open downward.

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Answer:

Wednesday

Step-by-step explanation:

Monday- ~5.6 as a decimal

Tuesday- 5.625 as a decimal

Wednesday- 5.375 as a decimal

Thursday- 5.8 as a decimal

therefore, Mrs.Mayes worked the least on Wednesday. Also she needs some break

Answer:

Wednesday

Step-by-step explanation:

For each of the fractions you can put them into decimals. Wednesday had the lowest decimal at 5.37

The values for numbers #21 through #26 are as follows:

#21: 2.33% or 0.0233. #22: $56.4842. #23: 1.85% or 0.0185. #24: $56.4148. #25: 3.64% or 0.0364. #26: $57.4397

#21: 2.33% (arithmetic mean as a fraction: 0.0233)

#22: $56.4842 (result of the calculation)

#23: 1.85% (geometric mean as a fraction: 0.0185)

#24: $56.4148 (result of the calculation)

#25: 3.64% (continuous mean as a fraction: 0.0364)

#26: $57.4397 (result of the calculation)

To fill out numbers #21 through #26, we need to calculate the values for each term using the given information and convert the percentages to fractions.

#21: The arithmetic mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #21 = 2.33% = 0.0233.

#22: Multiply the starting price ($53.07) by the compound factor (1 + arithmetic mean)^3. Substitute the value of #21 into the calculation. Therefore, #22 = $53.07 x (1 + 0.0233)^3 = $56.4842.

#23: The geometric mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #23 = 1.85% = 0.0185.

#24: Multiply the starting price ($53.07) by the compound factor (1 + geometric mean)^3. Substitute the value of #23 into the calculation. Therefore, #24 = $53.07 x (1 + 0.0185)^3 = $56.4148.

#25: The continuous mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #25 = 3.64% = 0.0364.

#26: Multiply the starting price ($53.07) by the continuous factor e^(continuous mean x 3). Substitute the value of #25 into the calculation. Therefore, #26 = $53.07 x e^(0.0364 x 3) = $57.4397.

Hence, the values for numbers #21 through #26 are as calculated above.

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Answer:

Multiply the two numbers and see what you get

Step-by-step explanation:

Answer:

i don't know br

Step-by-step explanation:

Sorry but this is like college stuff:(

The amount of money spent on tickets and snacks will be $39 and $20. And the total amount is $59.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Ellie is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $5 each.

The amount of tickets is given as,

Ticket's amount = 3 x $13

Ticket's amount = $39

Then the amount spent on snacks is given as,

Snack's amount = 4 x $5

Snack's amount = $20

Then the total amount is given as,

Total amount = $39 + $20

Total amount = $59

The amount of money spent on tickets and snacks will be $39 and $20. And the total amount is $59.

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Answer:

1

Step-by-step explanation:

Plug in the x value.

3(5)-14

3(5)=15

So then you do 15-14

Which equals to 1

Hope this helps! Plz mark brainliest!!

Answer:

1

Step-by-step explanation:

1. 3(5)-14     first substitute

2. 15-14

3. 1

Answer:

6k-5

Step-by-step explanation:

Answer:

k

Step-by-step explanation:

6-5=1

1*k=k

Answer:

7, 14, 14,21, and 28

Step-by-step explanation:

Only 1, 7 is pair of numbers that has 7 as its least common multiple.

Given that,
Pairs ( 1, 7 ), ( 3, 4 ), ( 7, 21), ( 14, 28).
A pair or pairs to be determined that have 7 as its least common multiple.

In mathematics, it deals with numbers of operations according to the statements.

In arithmetic, LCM is defined as the lowest common multiple of two integers X and Y, usually represented as by LCM X, Y, and is the smallest favorable integer that is dividable by both X and Y.

Since the Least common multiple of pair of numbers has 7, this is only possible for 1 * 7, because the LCM of 1 and7 is 7. So from given option 1, 7 is the required pair.

Thus, only 1, 7 is pair of numbers that has 7 as its least common multiple.

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Answer:

x= 3.096

Step-by-step explanation:

divide both sides by 5: 3^(x-1)= 10

then take the log to get log_3 (10) = x-1 = 2.096

x= 3.096

Answer:

The equation in slope-intercept form:

\(y = -3x - 4\)

Step-by-step explanation:

Use the point-slope formula:

\(y-y_{1} = m (x-x_{1})\)

Use the given slope \(-3\) and point \((0,-4)\) for the formula:

\(y + 4= -3 (x-0)\)

-Then, you solve the formula:

\(y + 4 = -3 (x-0)\)

\(y+4 - 4 = -3 (x-0) -4\)

\(y = -3x - 4\)

The equation, which is in slope-intercept form:

\(y = -3x - 4\)

Answer:

D. y = -3x - 4

Step-by-step explanation:

→You can figure this out by using the point-slope form:

\(y-y_1=m(x-x_1)\)

\(y+4=-3(x-0)\)

→Distribute the -3 to (x - 0):

y + 4 = -3x

→Subtract 4 from both sides:

y = -3x - 4

Angles of a triangle added together equal 180

A=180-143=37

B is 145 b/c like angles

C=A b/c lines are similar

D=143-85=58

E=C b/c like angles

F=90-E=53

G=48

H=180-48-G=180-48-48=84

K=180-H=96

M=180-K-D=180-96-58=26

P=180-85-M=69

R=180-P=180-69=111

S=P

We need a sample size of at least 62 to detect the alternative hypothesis with power of at least 0.80 at a 5% significance level.

To answer this question, we need to use power analysis. Power is the probability of rejecting the null hypothesis when it is false. In this case, the null hypothesis is m = 0 and the alternative hypothesis is m > 0. We want to detect the alternative hypothesis with power of at least 0.80 at a 5% significance level.

Assuming that s is 20 and we want to detect the alternative m > 4, we can use the following formula to calculate the sample size:

n = (Zα/2 + Zβ)² * σ² / δ²

where:
- Zα/2 is the critical value for the significance level α/2 (α = 0.05, so Zα/2 = 1.96)
- Zβ is the critical value for the power (power = 0.80, so Zβ = 0.84)
- σ is the standard deviation (σ = 20)
- δ is the difference between the null hypothesis and the alternative hypothesis (δ = 4)

Substituting these values into the formula, we get:

n = (1.96 + 0.84)² * 20² / 4²
n = 61.61

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Answer:

2x^2 + x + 9 + (18/(x+2))

Step-by-step explanation:

To find the result when 2x^3 - 5x^2 - 9x + 18 is divided by x + 2 using the long division method, you can follow these steps:

Divide the first term of the dividend (2x^3) by the first term of the divisor (x). The result is 2x^2.

Multiply the divisor (x + 2) by 2x^2. The result is 2x^3 + 4x^2.

Subtract this result from the dividend (2x^3 - 5x^2 - 9x + 18). The result is -x^2 - 9x + 18

Bring down the next term of the dividend (-5x^2) and add it to the result from step 3. The result is -6x^2 - 9x + 18

Divide -6x^2 by -6x and the result is x.

Multiply the divisor by x. The result is x^2 + 2x

Subtract this result from the result of step 4. The result is -9x + 18

Bring down the next term of the dividend (-9x) and add it to the result from step 7. The result is -18x + 18

Divide -18x by -18 and the result is x

Multiply the divisor by x. The result is x^2 + 2x

Subtract this result from the result of step 8. The result is 18

Therefore, the quotient is 2x^2 + x + 9 and the remainder is 18

So the result when 2x^3 - 5x^2 - 9x + 18 is divided by x + 2 is 2x^2 + x + 9 + (18/(x+2))

Answer:

Attached

Step-by-step explanation:

If you are able to utilize Excel, give it a try.

Answer:

38.4773 square inches

Step-by-step explanation:

In the above scenario, the best option would be to purchase two of the 4' x 2' x 2' oval tanks for a total cost of $280. Note that this is a decision making math prompt.

To determine which stock tank to purchase, we need to calculate the total volume of water required for the 82 calves and compare it to the volume of each tank. We can use the following formula to calculate the volume of a rectangular tank:

Volume = length x width x height

For the oval tanks, we need to break the tank down into a rectangle and two semi-circles, and then use the formula:

Volume = (length x width x height of rectangle) + (π x radius^2 x height of semi-circle)

Let's start by calculating the total water requirement for the 82 calves:

Total water requirement = 82 calves x 5 gal/head/day = 410 gallons/day

To determine the volume of each tank, we can use the formulas above and convert the result to gallons using the given conversion factor:

Using the given conversion factor, we can convert the volumes to gallons:

Based on the calculations, the 8' x 2' round tank has the largest volume and can hold enough water for the 82 calves. However, it is also the most expensive option at $500.

If cost is a consideration, we could purchase two of the 4' x 2' x 2' oval tanks for a total cost of $280, which can hold a total of 334.2 gallons, more than enough for the 410 gallons/day requirement. This would save us $220 compared to the round tank.

Therefore, the best option would be to purchase two of the 4' x 2' x 2' oval tanks for a total cost of $280.

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Therefore, the top of the ladder is sliding down the wall at a rate of 3.75 ft/sec (negative rate) when the bottom is 15 feet from the wall.

To solve this problem, we can use related rates and the Pythagorean theorem.

Let's denote the distance between the bottom of the ladder and the wall as x, and the height of the ladder (distance from the ground to the top of the ladder) as y. We are given that dx/dt = -2 ft/sec (negative because the bottom is sliding away from the wall).

According to the Pythagorean theorem, x^2 + y^2 = 17^2.

Differentiating both sides of the equation with respect to time t, we get:

2x(dx/dt) + 2y(dy/dt) = 0.

Substituting the given values, x = 15 ft and dx/dt = -2 ft/sec, we can solve for dy/dt:

2(15)(-2) + 2y(dy/dt) = 0,

-60 + 2y(dy/dt) = 0,

2y(dy/dt) = 60,

dy/dt = 60 / (2y).

To find the value of y, we can use the Pythagorean theorem:

x^2 + y^2 = 17^2,

15^2 + y^2 = 289,

y^2 = 289 - 225,

y^2 = 64,

y = 8 ft.

Now we can substitute y = 8 ft into the equation to find dy/dt:

dy/dt = 60 / (2 * 8) = 60 / 16 = 3.75 ft/sec.

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the total decrease in value of the machine in the second 5 years after it was bought is $35000. option B is correct.

To find the total decrease in value of the machine in the second 5 years after it was bought, we need to integrate the rate of change of value over that time period.

Given that the rate at which the value changes is 500(t - 12) dollars per year, we can integrate this expression over the interval t = 12 to t = 17 (second 5 years).

The integral of 500(t - 12) with respect to t is:

∫[0 to 10] 500(t - 12) dt

= 500 ∫[0 to 10] (t - 12) dt

= 500 [(t²/2 - 12t) | [0 to 10]

= 500 [(10²/2 - 12*10) - (0²/2 - 12*0)]

= 500 [(50 - 120) - 0]

= 500 [-70]

= - 350000

Therefore, the total decrease in value of the machine in the second 5 years after it was bought is $35000. option B is correct.

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the frequency of the C5+ photon is approximately 7.31 x 10^14 Hz, rounded to three significant figures.

The frequency of a photon can be calculated using the Bohr equation. In this case, we are considering a C5+ ion transitioning from energy level n=6 to n=2. The Bohr equation is given by:

ν = R_H * (1/n_f^2 - 1/n_i^2)

where ν is the frequency of the photon, R_H is the Rydberg constant (approximately 3.29 x 10^15 Hz), n_f is the final energy level, and n_i is the initial energy level.

Substituting the values into the equation, we have:

ν = 3.29 x 10^15 Hz * (1/2^2 - 1/6^2)

Simplifying the equation further, we get:

ν = 3.29 x 10^15 Hz * (1/4 - 1/36)

Calculating the value, we find:

ν = 3.29 x 10^15 Hz * (8/36)

ν ≈ 7.31 x 10^14 Hz

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Given

Arielle plans to purchase hanging baskets for her front porch. There are three businesses in her area that sell hanging baskets and she plans to purchase the baskets from one of these business.

To find: Which answer best describes the sample and population?

Explanation:

It is given that,

Arielle plans to purchase hanging baskets for her front porch. There are three businesses in her area that sell hanging baskets and she plans to purchase the baskets from one of these business.

That implies,

Sample: all available hanging baskets at one of the businesses in town that sells them.

And,

Population: all available hanging baskets at the three businesses in town that sell them.