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To show that the relation T defined on the set of integers Z is an equivalence relation, we need to prove three properties: reflexivity, symmetry, and transitivity.

1. Reflexivity: For any integer a, we need to show that aTa (mod). In modular arithmetic, a is congruent to itself modulo any integer, so this property holds.

2. Symmetry: For any integers a and b, if aTb (mod), then we need to show that bTa (mod). In modular arithmetic, if a is congruent to b modulo some integer, then b is also congruent to a modulo the same integer. Therefore, the symmetry property holds.

3. Transitivity: For any integers a, b, and c, if aTb (mod) and bTc (mod), then we need to show that aTc (mod). In modular arithmetic, if a is congruent to b modulo some integer and b is congruent to c modulo the same integer, then a is also congruent to c modulo that integer. Therefore, the transitivity property holds.

Since the relation T satisfies all three properties (reflexivity, symmetry, and transitivity), we can conclude that T is an equivalence relation.

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Answer:

1. 4 less than x

2. v = 15.00n

Answer:

4 minus x and v = 15.00n

Step-by-step explanation:

Answer:

The answer is 126 square inches.

Step-by-step expalation

Answer:

131.92ft²

Step-by-step explanation:

okay, so we have to find the area of both circles, and the circumference then multiply that with the height, it's confusing, so:

3² x 3.14 = 28.26 x 2 = 56.52 so that the area of the bases

3 x 2 x 3.14 = 18.85 x 4 = 75.4

75.4 + 56.52 = 131.92

So the surface area of the cylinder is 131.92ft²

The curvature of y = sin(–1x) at x = pi/4 is 2√2/3.

Curvature is the measure of how much a curve bends. It is the rate at which the unit tangent vector changes with respect to arc length. It is given by the formula,K = |dT/ds|Where K is curvature, T is the unit tangent vector, and s is arc length.So, the first step is to find the first derivative of y, which is given by,dy/dx = -1/√(1-x²)Now, we find the second derivative of y which is given by,d²y/dx² = x/(1-x²)^(3/2)At x = pi/4, we have,d²y/dx² = (π/4)/(1-(π/4)²)^(3/2) = 2√2/3Therefore, the curvature of y = sin(–1x) at x = pi/4 is 2√2/3.

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The population at time n=9 is approximately 11.95. The term "population" refers to the entire set of individuals, objects, or events that are of interest to a researcher or analyst.

Based on the given information, we have:

Initial population (P0) = 10

Growth rate (r) = 0.2

To find an explicit formula for Pn, we can use the formula for exponential growth:

Pn = P0 * (1 + r)^n

Substituting the given values:

Pn = 10 * (1 + 0.2)^n

Simplifying the formula, we have:

Pn = 10 * 1.2^n

Using this formula, we can find P9:

P9 = 10 * 1.2^9 ≈ 11.95

Therefore, the population at time n=9 is approximately 11.95.

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Answer:

the answer is 1-1, 1-2, 1-3, 1-4

Step-by-step explanation:

Answer:

Wait So...

Step-by-step explanation:

What Kind of Math is this?

Answer:

each friend ate 1/4 of pizza

Step-by-step explanation:

3/4 ÷ 3

= 1/4

Answer:

It would be 4 quarts.

Step-by-step explanation:

The answer is 2 quarts

Answer:

umm, i think the question is incomplete

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

How did it go from "rope" to "ribbon", therefore, the statement is incorrect. This is a man-made equation that clearly has a mistake. If it was to say, "Will Scott have enough rope?" then the answer will be "YES"

Answer:

the answer is NO

Step-by-step explanation:

0.89 x 889 = 8.01

Therefore, he is 1cm short

well, the triangle is an isosceles with twin sides, and so twin sides stemming from a common vertex will make twin angles on the other sides, the heck all that means?

well, it means that the twin sides of BC and BD make twin angles at C and D, so

[tex]6x-9~~ = ~~3x+24\implies 3x-9=24\implies 3x=33 \\\\\\ x=\cfrac{33}{3} \implies x=11 \\\\[-0.35em] ~\dotfill\\\\ \underset{ C }{\stackrel{ 6(11)-9 }{\text{\LARGE 57}^o}}\hspace{5em}\underset{ D }{\stackrel{ 3(11)+24 }{\text{\LARGE 57}^o}}\hspace{5em}\underset{ B }{\text{\LARGE 66}^o}[/tex]

Answer:

15 i don't think it is right

Answer:

C.

Step-by-step explanation:

Since the slope is 1 meaning it goes up and over by 1 the GPA would increase by 1 every hour

Answer:

c

Step-by-step explanation:

Step-by-step explanation:

2 would be the answer .

hope it helps u .

2 cubed = 8

equasion; 2 Cubed = [tex]2^{3}[/tex] = 2 × 2 x 2 = 8

i hope this helps <3

Answer:

A,C and D

Step-by-step explanation:

A: 3x2=6

    3x4X=12X

     6+12X

C: 5x1=5

    5x2X=10X

    5+10X+1+2X

   6+12X

D: 7x1=7

    7x2X=14X

     7+14X-2X-1

     6+14X-2X

     6+12X

Answer:

95 < 75 + 0.80m 20 < m Company A will charge less than Company B for mileages less than 20.

The probability of event E is 0.20, the probability of event F is 0.45, and the probability of both E and F occurring is 0.10. Therefore, the probability of either event E or event F occurring, denoted as P(E or F), is 0.65.

Given that P(E) = 0.20 and P(F) = 0.45, we also know that P(E and F) = 0.10. Using the formula P(E or F) = P(E) + P(F) - P(E and F), we can substitute the values and calculate the probability of either event E or event F occurring.

P(E or F) = P(E) + P(F) - P(E and F)

P(E or F) = 0.20 + 0.45 - 0.10

P(E or F) = 0.65

Therefore, the probability of either event E or event F occurring, denoted as P(E or F), is 0.65.

The concept behind this formula is that when we add the individual probabilities of E and F, we count their intersection (P(E and F)) twice. Since we want to avoid double-counting the intersection, we subtract P(E and F) from the sum of P(E) and P(F). This gives us the probability of either event E or event F occurring.

In this case, the probability of either event E or event F occurring is 0.65, indicating a relatively high likelihood of one of the events happening.

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The equation for the line of reflection is x = 6

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15.

Given that, a graph, we need to find the equation of the reflection of the polygon graphed,

We can see, all the vertices on the polygon are being mirrored across the line x = 6.

So, we can say the line of reflection is x = 6.

Hence, the equation for the line of reflection is x = 6

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Answer:

The train is more reliable.

Step-by-step explanation:

The train is more reliable. The bus is on-time 87.5% of the time, while the train is on-time 90% of the time.

There is a significance at the level 0.01.

We can use a two-sample t-test for this purpose.

A two-sample t-test is used to examine whether two data samples have a mean difference that is statistically significant.The null hypothesis for this test is that there is no significant difference between the mean systolic blood pressure of those adolescents classified as having low sleep efficiency and that of other adolescents.

Hence, H0: μ1 = μ2

where μ1 is the mean systolic blood pressure of those adolescents classified as having low sleep efficiency and μ2 is the mean systolic blood pressure of other adolescents.

The alternative hypothesis is that there is a significant difference between the two means:

H1: μ1 ≠ μ2

The level of significance (α) is 0.01, so the critical value of t can be found using a t-distribution table with 254 degrees of freedom (n1+n2-2=254).

The critical value at a 0.01 level of significance is ±2.576.

From the question, we know that the mean difference between the two groups is 5.6 mm Hg and the standard deviation of this difference is 1.8 mm Hg.

Therefore, the t-statistic can be calculated as:

t = (5.6 - 0) / (1.8 / sqrt(256))

= 56 / 1.8 = 31.11

Since the calculated t-statistic (31.11) is greater than the critical value (±2.576), we reject the null hypothesis.

Thus, we can conclude that there is a significant difference in systolic blood pressure between the two groups at the 0.01 level of significance.

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Answer:

Step-by-step explanation:

"quaratic" should be "quadratic."

The coefficients of this quadratic are 4, 2 and -1.  Thus, the discriminant is

b^2 - 4ac, or here, 4 - 4(4)(-1) = 20

Since the discriminant is positive, our quadratic has two real, different roots.

                                -2 ± (√4)(√5)

The roots are:  x = ---------------------

                                       2(4)

                                    -1 ± √5

This reduces to   x = ---------------

                                           8

a. Null hypothesis (H0): The average caloric intake among female Canadian athletes is equal to or greater than the recommended amount (µ ≥ 2811.5 kcal/day).

Alternative hypothesis (H1): The average caloric intake among female Canadian athletes is less than the recommended amount (µ < 2811.5 kcal/day).

b. The value of n that should be used is 201

c. SEM = 880 / √201

d. To sketch the normal curve and label the test statistic, we need the test statistic value and the critical region corresponding to the significance level α = 0.05

e. Without the test statistic or critical region, we cannot calculate the p-value.

f. Since we don't have the test statistic, critical region, or p-value, we cannot make a decision to reject or fail to reject the null hypothesis at this point.

g. Without the test statistic, critical region, or p-value, we cannot draw a conclusion regarding the evidence for or against the deficiency in caloric intake among female Canadian athletes.

a. The appropriate null and alternative hypotheses to test whether female Canadian athletes are deficient in caloric intake can be stated as follows:

Null hypothesis (H0): The average caloric intake among female Canadian athletes is equal to or greater than the recommended amount (µ ≥ 2811.5 kcal/day).

Alternative hypothesis (H1): The average caloric intake among female Canadian athletes is less than the recommended amount (µ < 2811.5 kcal/day).

b. The value of n that should be used is 201, which represents the number of female athletes in the study. The key word in the last sentence of the paragraph ("n=201 women") indicates that the information provided specifically pertains to the female athletes, not the entire sample of 324 athletes.

c. To calculate the test statistic, we need to determine the standard error of the mean (SEM) using the formula:

SEM = σ / √n

where σ is the population standard deviation and n is the sample size. In this case, the population standard deviation is given as 880 kcal/day, and the sample size is 201.

SEM = 880 / √201

d. To sketch the normal curve and label the test statistic, we need the test statistic value and the critical region corresponding to the significance level α = 0.05. However, the critical region is not provided in the given information.

e. The p-value represents the probability of obtaining a test statistic as extreme as or more extreme than the observed value, assuming the null hypothesis is true. Without the test statistic or critical region, we cannot calculate the p-value.

f. Since we don't have the test statistic, critical region, or p-value, we cannot make a decision to reject or fail to reject the null hypothesis at this point.

g. Without the test statistic, critical region, or p-value, we cannot draw a conclusion regarding the evidence for or against the deficiency in caloric intake among female Canadian athletes. Further analysis is required to obtain the missing information and make a conclusive statement.

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Answer:

B is the answer

because if you observe very well the angles look similar in a way when you turn it the other way round ...

The solution to the differential equation y' + 3y = f(t), y(0) = α using Laplace transforms is y(t) = αe⁻³ᵗ + F(s)/(s+3), where F(s) is the Laplace transform of f(t).

We use the Laplace transform on both sides of the problem in order to solve the given differential equation. Let Y(s) and F(s) represent the Laplace transforms of y(t) and f(t), respectively. Taking the Laplace transform of both sides of the equation, we have:

sY(s) - y(0) + 3Y(s) = F(s)

Substituting y(0) = α, we get,

sY(s) - α + 3Y(s) = F(s)

Rearranging the equation and solving for Y(s), we have,

Y(s) = (F(s) + α)/(s + 3)

Now, we need to find the inverse Laplace transform of Y(s) to obtain y(t). Using the properties of Laplace transforms, we know that the inverse Laplace transform of Y(s) is y(t) = L⁻¹{Y(s)}. Applying the inverse Laplace transform, we find,

y(t) = αe⁻³ᵗ + L⁻¹{F(s)/(s+3)}

The term αe⁻³ᵗ corresponds to the initial condition y(0) = α. The remaining term L⁻¹{F(s)/(s+3)} represents the inverse Laplace transform of F(s)/(s+3), which depends on the specific function f(t) and its Laplace transform.

Therefore, the solution to the differential equation is y(t) = αe⁻³ᵗ + F(s)/(s+3), where F(s) is the Laplace transform of f(t).

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