Can I get help with number 15 am stuck

To find a primitive root modulo a given integer, we can use Corollary 5.15 and Proposition 5.17. For (a) 7, a common primitive root r can be found by using these results. Similarly, for (b) 11m, (c) 13m, and (d) 17m, the same approach can be applied to find primitive roots modulo each integer.

(a) To find a primitive root modulo 7 and 72, we can use Corollary 5.15, which states that if r is a primitive root modulo n, then r is also a primitive root modulo any power of n. Since 7 is a prime number, we can easily find a primitive root modulo 7. Let's say r is a primitive root modulo 7. Using Proposition 5.17, which guarantees that a primitive root modulo a prime number remains a primitive root modulo any positive integral power of the prime, we can conclude that r is a primitive root modulo 7 for all positive integral m.

(b) Similarly, for 11m, we can find a primitive root modulo 11 and use Proposition 5.17 to prove that it is a primitive root modulo 11m for all positive integral m.

(c) The same approach can be applied to find a primitive root modulo 13m.

(d) Finally, for 17m, we can find a primitive root modulo 17 and use Proposition 5.17 to prove its primitiveness modulo 17m for all positive integral m.

By using Corollary 5.15 and Proposition 5.17, we can find a common primitive root for all the given integers modulo their corresponding powers.

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a) The GCD of 27,720 and 58,212 is 1.

b) Integers r = 3 and s = -1 satisfy the equation 27720r + 58212s = GCD(27720, 58212).

(a) To find the greatest common divisor (GCD) of 27,720 and 58,212, we can use the Euclidean Algorithm.

Divide 58,212 by 27,720.

58,212 ÷ 27,720 = 2 remainder 2

Divide the previous divisor (27,720) by the remainder (2).

27,720 ÷ 2 = 13,860

Divide the previous remainder (2) by the new remainder (2).

2 ÷ 2 = 1

Since the remainder is now 1, the GCD is found.

Therefore,  the greatest common divisor (GCD) of 27,720 and 58,212 is 1.

(b) To find integers r and s such that 27720r + 58212s = GCD(27720, 58212), we can use the Extended Euclidean Algorithm.

Using the Euclidean Algorithm from part (a), we can backtrack to find the coefficients r and s:

2 = 27,720 - 13,860

Substituting the values:

2 = 27,720 - (58,212 - 2 * 27,720)

Simplifying:

2 = 3 * 27,720 - 58,212

Comparing with the form 27720r + 58212s = GCD(27720, 58212):

r = 3

s = -1

Therefore, we substitute r = 3 and s = -1 into the equation 27720r + 58212s, it will result in the greatest common divisor (GCD) of 27720 and 58212.

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After considering the given data we conclude that one tailed test can be utilised for this claim.

To test the claim about the proportion of students involved in extracurricular activities, we would employ a one-tailed test.
A one-tailed test is applied when the alternative hypothesis is directional, which projects the it predicts the direction of the difference between the sample proportion and the claimed proportion. For the given case, the alternative hypothesis will be that the proportion of attending students involved in at least one extracurricular activity is greater than 70%.
Hence, we would use a one-tailed test to test this claim.
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Answer:

DO you go to a connexus school? I do and i have this same project im trying to find answers to!

Step-by-step explanation:

For the first box the volume, surface area, and cost of materials are 180 cubic inches, 258 square inches, and $12.9, for the second box 192 cubic inches, 224.4 square inches, and $11.22 for the third box 235.61 cubic inches, 227.76 square inches, and $11.38.

It is defined as a three-dimensional space enclosed by an object or thing.

For the first cereal box:

Volume = L×W×H

Here L = 7.5 in, W = 2 in, and H = 12 in

Volume = 7.5×2×12 = 180 cubic inches

Surface area = 2(L×B+B×H+H×L)

= 2(7.5×2+2×12+12×7.5)

= 2(15+24+90)

= 258 square inches

Cost for this cereal box = 258×0.05 = $12.9

For the second cereal box:

[tex]\rm Volume = \frac{1}{3} bh[/tex]

b is the area and h, is the height of the pyramid.

b = 8×6 = 48 square inches, h = 12 inches

[tex]\rm Volume = \frac{1}{3} \times48\times12[/tex]

Volume = 192 cubic inches

[tex]\rm Surface \ area = b+\frac{1}{2} ps[/tex]

p is the perimeter of the base = 2(8+6) = 28 in

Slant height s = 12.6 in

[tex]\rm Surface \ area = 48+\frac{1}{2} (28)(12.6)[/tex] = 224.4 square inches

Cost of this cereal box = 224.2×0.05 = $11.22

For the third box:

Volume = πr²h

r = 2.5 in and h = 12 in

Volume = π(2.5)²(12) = 235.61 cubic inches

Surface area = 2πr(h+r) = 2π(2.5)(12+2.5) = 227.76 square inches

Cost of this cereal box = 227.76×0.05 = $11.38

Thus, for the first box the volume, surface area, and cost of materials are 180 cubic inches, 258 square inches, and $12.9, for the second box 192 cubic inches, 224.4 square inches, and $11.22 for the third box 235.61 cubic inches, 227.76 square inches, and $11.38.

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Answer:

.9 g/cm^3

Step-by-step explanation:

density formula is mass divided by volume.

d=m/v

d=18g/20cm^3

d=0.9

(a) R4= 61.4626 and (b) L4= 61.4626.

In order to estimate the area under the graph of f(x) = 10 sqrt x from x = 0 to x = 4 using four approximating rectangles and right endpoints, we need to use the formula:

Rn = Δx [f(x1) + f(x2) + f(x3) + ... + f(xn)], where Δx is the width of each rectangle and f(xi) is the height of the rectangle at the right endpoint of the ith interval.

Step 1: Calculation of ∆x.∆x = (4 - 0)/4 = 1

Step 2: Calculation of xi for i = 1, 2, 3 and 4.x1 = 1, x2 = 2, x3 = 3, x4 = 4

Step 3: Calculation of f(xi) for i = 1, 2, 3 and 4.f(x1) = 10√(1) = 10f(x2) = 10√(2) ≈ 14.1421f(x3) = 10√(3) ≈ 17.3205f(x4) = 10√(4) = 20

Step 4: Calculation of R4.R4= ∆x [f(x1) + f(x2) + f(x3) + f(x4)]R4= 1[10 + 14.1421 + 17.3205 + 20]= 61.4626Area ≈ 61.4626 square units.

Step 5: Calculation of L4.Ln = ∆x [f(x0) + f(x1) + f(x2) + ... + f(xn-1)]

Where x0 is the initial value.

Here, we can find the value of L4 by using the left endpoints.

So, x0 = 0L4 = ∆x [f(x0) + f(x1) + f(x2) + f(x3)]L4 = 1 [f(0) + f(1) + f(2) + f(3)]L4 = 1 [10 + 14.1421 + 17.3205 + 20]L4 = 61.4626

Therefore, (a) R4= 61.4626 and (b) L4= 61.4626.

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(a) The area under the curve is 154 square units.

(b) The exact area of the region between the curve y= f(x) and the x-axis is (118 / 3) square units.

(a) The given function is f(x) = 25 - x² .

We need to estimate the area under the graph between x = - 3 and x = 5 by dividing the interval [-3, 5] into 4 subintervals each of the same length by using left-hand and midpoint approximation and sketch the 4 rectangles that approximates the area under the curve.

The width of each rectangle is given by Δx, where Δx = (b - a) / n = (5 - (-3)) / 4 = 2.

The height of each rectangle is determined by either left-hand approximation or midpoint approximation.

1. Left-hand approximation: In the left-hand approximation method, the height of each rectangle is taken from the left endpoint of each subinterval. We have:

Left endpoint of the 1st subinterval is x₁ = -3 Left endpoint of the 2nd subinterval is x₂ = -1 Left endpoint of the 3rd subinterval is x₃ = 1 Left endpoint of the 4th subinterval is x₄ = 3

Thus, the heights of the four rectangles are: f(x₁) = f(-3) = 16f(x₂) = f(-1) = 24f(x₃) = f(1) = 24f(x₄) = f(3) = 16

We sketch the four rectangles as follows:

The total area of the four rectangles is the sum of the individual areas of the rectangles.

We have: Area ≈ [f(-3) + f(-1) + f(1) + f(3)] Δx= [16 + 24 + 24 + 16] × 2= 80 square units.2.

Midpoint approximation: In the midpoint approximation method, the height of each rectangle is taken from the midpoint of each subinterval.

We have: Midpoint of the 1st subinterval is x₁* = -2 Midpoint of the 2nd subinterval is x₂* = 0 Midpoint of the 3rd subinterval is x₃* = 2 Midpoint of the 4th subinterval is x₄* = 4

Thus, the heights of the four rectangles are: f(x₁*) = f(-2) = 21f(x₂*) = f(0) = 25f(x₃*) = f(2) = 21f(x₄*) = f(4) = 9

We sketch the four rectangles as follows:

The total area of the four rectangles is the sum of the individual areas of the rectangles.

We have:

Area ≈ [f(-2) + f(0) + f(2) + f(4)] Δx= [21 + 25 + 21 + 9] × 2= 154 square units.

(b) The exact area of the region between the curve y = f(x) and the x-axis on the interval [-3, 5] is given by the limit of a Riemann sum as the number of subintervals n approaches infinity.

We have:

Area = ∫[(-3, 5)] f(x) dx= ∫[-3, 5] (25 - x²) dx

= [25x - (x³ / 3)]|[-3, 5]

= [125 - (125 / 3)] - [-75 + (27 / 3)]

= (100 / 3) + (18 / 3)

= (118 / 3) square units.

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The Poisson distribution with a parameter λ = 1 accurately models the production stoppages, where on average, the company experiences one stoppage per month with a relatively small amount of variability.

The  scenario describes a company's production stoppages, which can be modeled using a Poisson distribution with a parameter (mean) of λ = 1. In a Poisson distribution, the mean, variance, and standard deviation are all equal.

The mean (μ) represents the average number of stoppages per month, which in this case is 1. This means that, on average, the company experiences one production stoppage per month.

The variance (σ^2) also has a value of 1 in a Poisson distribution. It measures the spread or variability of the data around the mean. In this case, the variance of 1 indicates that there is some fluctuation in the number of stoppages, but it is relatively small.

The standard deviation (σ) is equal to the square root of the variance, which is also 1 in this scenario. It represents the average amount of deviation from the mean. A standard deviation of 1 suggests that most of the observations will be within one unit of the mean.

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Answer:

54 students

Step-by-step explanation:

if 7 of 331 students did not go on buses then 331 - 7 = 324 went on buses.

324 divided by 6 = 54 students

Answer:

829.2 miles

Step-by-step explanation:

To find how far they traveled in total, add together all of the distances:

417 + 45.3 + 366.9

= 829.2

So, all together, they traveled 829.2 miles

Answer:

no

Step-by-step explanation:

Answer:

The answer is 21 units²

Step-by-step explanation:

To find the area of a right triangle you use the formula A=ab/2

So

A=6×7/2 = 21

The method that begins with a matrix or table describing the characteristics of a target population is quota sampling.

Quota sampling is a non-probability sampling method in which the researcher first creates a matrix or table describing the characteristics of the target population. Once the matrix is created, the researcher then selects a certain number of people from each category in the matrix until the desired sample size is reached.

For example, if the researcher is interested in studying the political views of college students, they might create a matrix with the following categories:

Gender: Male, Female

Age: 18-21, 22-25, 26-30

Political affiliation: Democrat, Republican, Independent

Once the matrix is created, the researcher might then select 100 students from each category, for a total sample size of 300.

Quota sampling is a quick and easy way to obtain a sample of a population. However, it is not a probability sampling method, which means that the sample may not be representative of the population. This is because the researcher is not randomly selecting participants from the population. Instead, they are selecting participants based on their characteristics.

As a result, quota sampling can lead to bias in the results of a study. For example, if the researcher selects more students from one political affiliation than another, the results of the study may be biased in favor of that political affiliation.

Overall, quota sampling is a useful tool for researchers who need to obtain a sample of a population quickly and easily. However, it is important to be aware of the limitations of this method and to take steps to minimize bias in the results of the study.

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Answer:

56 oz or 3 1/2 lbs

Step-by-step explanation:

1 1/4 + 1 1/2 = 2 3/4lbs = 44 oz

44 oz + 12 oz = 56 oz

Answer:

81/4

Step-by-step explanation:

the answer is not sure

Answer: javier is taller

Step-by-step explanation:

68inches=5' 8"

The main difference between Hexagon and Quadrilateral is that the Hexagon is a polygon with six sides and Quadrilateral is a polygon with four sides. In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six sided polygon or 6-gon.

Answer:

171

Step-by-step explanation:

6x6x4.75 is 171

The P-value of a one-tailed test is generally smaller than that of a two-tailed test when testing the same null hypothesis and using the same level of significance.

The P-value of a one-tailed test is generally smaller than that of a two-tailed test when testing the same null hypothesis and using the same level of significance. This is because a one-tailed test focuses on a specific direction of the hypothesis, while a two-tailed test considers both directions.

In a one-tailed test, the null hypothesis is rejected only if the test statistic falls in the critical region in one direction. For example, if the null hypothesis is that a mean is less than or equal to a certain value, the critical region will be in the lower tail of the distribution. Therefore, the probability of obtaining a test statistic in the critical region is smaller compared to a two-tailed test, where the critical region is split between both tails of the distribution.

As a result, the P-value of a one-tailed test is smaller than that of a two-tailed test, given the same null hypothesis and level of significance. However, it's important to note that the choice between a one-tailed or two-tailed test should be based on the specific research question, rather than the desire for a smaller P-value.

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Answer:

2d) d = 60°

3a) x = 50°

Step-by-step explanation:

2d) both of the diagonals pass through the centre of the circle and divide the rectangle into 4 triangles,then it means that;

30 + d = 90°

d = 90 - 30

d = 60°

3a) since O is the centre of the circle, and we can see that the 2 chords directly above and below the centre are parallel to each other, it means that angle x = 50° since the two sides projecting from the centre to form x° and 50° are equal and in essence used to form isosceles triangle.

Answer:

20%

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

19.99 - 3.998(20%) = 15.992 which when rounded is 15.99

Answer:

4 is a percent of 15 is 0.6

Step-by-step explanation:

if you out 15/0.6 as a fraction you will get 4

Answer:

4%

Step-by-step explanation:

STEP 1: Put the numbers into a fraction

0.6/15

STEP 2: Divide

0.6/15 = 0.04

STEP 3: Move decimal point two places to the right

0.04 -> 4

Answer: 4%

Answer:

I'm pretty sure no because a square always has 4 right angles and all sides are the same length

the parallelogram could possibly be a rectangle tho

I could be completely wrong but I hope this helps

Answer:

24 IN.

Sorry for all caps

Step-by-step explanation:

Ill-conditioned means that the problem or system being considered is sensitive to small changes in the input or data, leading to unstable or inaccurate results.

When solving a least squares problem using the normal equations, ill-conditioning refers to situations where the matrix involved is nearly singular or has a high condition number.

This means that small perturbations or errors in the data can result in large changes in the computed solution.

In the context of QR factorization, if the normal equations for a least squares problem are ill-conditioned, it implies that the matrix being decomposed using QR factorization is close to being singular or has a high condition number. QR factorization can help in such cases by providing a more stable and accurate solution compared to directly solving the normal equations.

QR factorization decomposes a matrix into the product of an orthogonal matrix Q and an upper triangular matrix R. This factorization can help mitigate the effects of ill-conditioning by providing a numerically stable way to solve the least squares problem.

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