how many miles per hour is someone running is they run run 1/4 of a mile in 1/20 of an hour

Answer:

20/50 2/5

Step-by-step explanation:

The solutions to the recurrence relation are: aₙ = 2ⁿ - 2ⁿ⁺¹ + 2ⁿ⁺² + (n⁴)/n.

The given recurrence relation is aₙ = 7aₙ₋₁ - 16aₙ₋₂ + 12aₙ₋₃ + (n⁴)/n, with initial values a₀ = -2, a₁ = 0, and a₂ = 5. To find the solutions, we can use the characteristic equation and the method of solving linear homogeneous recurrence relations. After solving the characteristic equation, we obtain the roots 2, -1, and -2.

Thus, the general solution is aₙ = C₁ * 2ⁿ + C₂ * (-1)ⁿ + C₃ * (-2)ⁿ. Using the initial values, we can determine the values of the constants C₁, C₂, and C₃. The resulting solutions are aₙ = 2ⁿ - 2ⁿ⁺¹ + 2ⁿ⁺² + (n⁴)/n. This formula provides the values of aₙ for any n.

Regarding the relations R₁, R₂, and R₃, we need to determine if they are equivalence relations on the set of all non-zero integers.

a. R₁: The relation R₁ states that (x, y) ∈ R₁ if and only if x ≥ y². To check if it is an equivalence relation, we need to verify reflexivity, symmetry, and transitivity. It is reflexive since for any integer x, x ≥ x². However, it is not symmetric or transitive since there are counterexamples where the conditions are not met for some values of x and y.

b. R₂: The relation R₂ states that (x, y) ∈ R₂ if and only if x is a multiple of y. This relation is an equivalence relation since it satisfies reflexivity, symmetry, and transitivity. Any integer x is a multiple of itself (reflexivity), if x is a multiple of y then y is a multiple of x (symmetry), and if x is a multiple of y and y is a multiple of z, then x is a multiple of z (transitivity).

c. R₃: The relation R₃ states that (x, y) ∈ R₃ if and only if xy ≥ 1. This relation is not an equivalence relation since it fails reflexivity. For example, when x = 0, xy = 0 for any y, and 0 is not greater than or equal to 1.

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The most accurate statement with regard to tests of statistical significance is (D) Such tests cannot tell us if a finding is or is not due to chance, but can only speak to the likelihood that chance was involved in the outcome.

Option d is the most accurate statement regarding tests of statistical significance. Statistical significance does not determine whether a finding is due to chance or not with absolute certainty. It provides an assessment of the likelihood that chance played a role in the observed outcome.

Statistical significance is based on probability and hypothesis testing. By conducting a statistical test, researchers can determine whether the observed results are unlikely to have occurred by chance alone, given a certain level of significance (often denoted as alpha, e.g., 0.05). If the p-value (probability value) associated with the test falls below the chosen alpha level, the finding is considered statistically significant. However, this does not imply that the finding is practically or substantively significant.

Option a is incorrect because statistical significance does not automatically indicate practical significance. Practical significance refers to the meaningful or real-world importance of the finding, which goes beyond statistical calculations.

Option b is also incorrect because statistical significance does not completely rule out the possibility of random chance. It provides evidence against the null hypothesis, but there is always a small probability of a Type I error (incorrectly rejecting the null hypothesis).

Option c is incorrect because statistical significance does not guarantee reliability or validity. Reliability refers to the consistency and stability of measurements, while validity refers to the accuracy and appropriateness of the measurements in relation to the intended construct. These aspects are separate from statistical significance and require separate assessments

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Answer:

Put the equations in the form y=mx+c and after that, take any two values for x, fill in the equation of y=mx+c to get the corresponding y coordinate and take any value for y, to get the corresponding x coordinate. For this example i took x=0 and y=0, feel free to try it again with any other value. If you get a fraction and don't what to work with fractions, just do a trial and error till you get a whole number (as i did for Question 21 for the x and y coordinates)

The students method that is not correct is Brandon's method.

Square root of a number is a value, which on multiplication by itself, gives the original number. The square root is an inverse method of squaring a number. For example,. the square root of 9 is 3 i.e 3× 3 .

Looking at both methods,

Ashley method is correct because the product of a number by its self will give a perfect square and the square root of the product is the number. For example √16 = √4×4 = 4

√25 = √5×5 = 5

Brandon's method is wrong though his answer is correct for the value of 4. but looking at other example like,

√16 = 4

16× 1/2 = 8

√ 36 = 6

36× 1/2 =18

therefore Brandon's method is wrong to find the square root of number

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Answer:

x = 28°

y= 62°

Step-by-step explanation:

    To find x, we can use the ratio Tan.

    \(\sf Tan \ x = \dfrac{opposite \ side \ of \ x^\circ}{adjacent \ side \ of \ x^\circ}\\\\\)

              \(\sf = \dfrac{7}{13}\\\\= 0.5385\)

           \(\sf x = tan^{-1} \ (0.5385)\\\\x = 28.30^\circ\\\\x = 28^\circ\)

        x + y + 90 = 180  {Angle sum property of triangle}\\

     28 + y + 90 = 180

             y + 118 = 180

                      y = 180 - 118

                      y = 62°

Step-by-step explanation:

13-9=6x

4-6x

This is the coefficient

Answer: A. 1+8i

Step-by-step explanation:

edge

The following are crucial factors in hypothesis testing:

In statistics, the process of hypothesis testing involves putting an analyst's presumption about a population parameter to the test.

Thus, before conducting the hypothesis testing, a null hypothesis as well as an alternative hypothesis are established.

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Answer: T(v) = [0], [0], [-1]

To compute T(v), we first need to express v in terms of the vectors in B, and then find the coordinate vector v with respect to B.

Given v = [1], and B = ([0], [0], [-1]),
        [-1]         [0], [0], [0],
        [0]          [0], [2], [0],
                          [0], [0], [-1]

Since B only has one non-zero vector, we can express v as a linear combination of B:

v = 0*[0] + 0*[0] + (-1)*[-1]
 = [0], [-1], [0]

Thus the coordinate vector v with respect to B is:

vB = [0], [0], [-1]

Now, we need to find the coordinate vector of T(v) with respect to B:

T(v)B = TBB * vB
    = [0 0 0] [0]
      [0 2 0] [0]
      [0 0 -1] [-1]

Multiplying the matrices:

T(v)B = [0], [0], [1]

Finally, we convert the coordinate vector T(v)B back to standard coordinates:

T(v) = 0*[0] + 0*[0] + 1*[-1]
    = [0], [0], [-1]

Thus, T(v) = [0], [0], [-1]

Answer: T(v) = [0], [0], [-1]

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0 ≤ x < 2, where x is an integer. Option C

The appropriate domain for the function f(x) = 42 - 15x in the given context can be determined by considering the constraints of the problem.

Tyson has a $50 gift card, and he wants to purchase a belt that costs $8 and x number of shirts that cost $15 each. The function f(x) represents the balance on the gift card after Tyson makes the purchases.

The number of shirts Tyson can purchase depends on the remaining balance on the gift card. Since each shirt costs $15, the maximum number of shirts he can buy is limited by the amount of money left on the gift card.

If we subtract the cost of the belt ($8) and the cost of x shirts ($15x) from the initial balance ($50), we should get a non-negative result, indicating that Tyson has enough money on the gift card to make the purchases.

Therefore, we can set up the inequality:

50 - 8 - 15x ≥ 0

Simplifying, we have:

42 - 15x ≥ 0

Now, we can solve for x:

-15x ≥ -42

Dividing by -15 (remembering to flip the inequality sign), we get:

x ≤ 42/15

x ≤ 2.8

Since x represents the number of shirts Tyson can buy, it should be a whole number. Therefore, the appropriate domain for the function f(x) is:

0 ≤ x ≤ 2, where x is an integer.

Option C.

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Answer:

B. x^2 - 10x + 25

Step-by-step explanation:

(x - 5)^2

(x - 5)(x - 5)

x^2 - 5x - 5x + 25

x^2 - 10x + 25

Answer:

5: 6

Step-by-step explanation:

becuase it was basically 100:120 but divide it by 20 and thats  how you get 5;6

Answer:

Step-by-step explanation:

the shape can be devided into 3 seperate rectangles,

Calculating each rectangle's area and adding them together will get the shape's area.

(3x9) + (7x4) + (2x9)

27+28+18

73.

Answer:

73m^2

Step-by-step explanation:

First we split it up into shapes we are use to.

Now we must find the area of each separate rectangle

a=l×b

1st rectangle

3×5

a=15

2nd rectangle

2×5

a=10

3rd rectangle

4×12

a=48

Total area

48+10+15

a=73m^2

Given:

John's age is a multiple of 3

Let the age of this year = 3x

Last year, his age was 1 less than a multiple of 4.

So, {(3x-1) + 1 } is a multiple of 4

so, (3x) is a multiple of 4 also

And, Next year, his age will be 3 more than a multiple of 5

So, {(3x + 1 ) - 3 } is a multiple of 5

Considering the previous conditions:

The least multiple of 3 and 4 = 3 x 4 = 12

So, x = 12/3 = 4

Checking for the last condition:

Which is the multiple of 5

So, the youngest age = 12 years

Answer:

Attached to this answer are some of the ways you could rewrite \(4*10^{-3}\)

Answer:

y(x)=12*(5)^x

Step-by-step explanation:

y=ab^x, y(0)=12. 12=a.

y=12*b^x, y(2)=300. 12*b^2=300. b^2=25. b=5

The probability p of rolling a 5 at least once in 16 rolls is:

p = 1 - (5/6)^16

The probability of rolling a 5 on a fair six-sided die is 1/6, since there are 6 equally likely outcomes (numbers 1 to 6) and only one of them is a 5.

If we roll the die 16 times, each roll is an independent event. Therefore, the probability of rolling a 5 on any given roll remains 1/6.

To find the probability p that a 5 will occur at least once in 16 rolls, we can use the complement rule. The complement of the event "rolling a 5 at least once" is the event "not rolling a 5 in any of the 16 rolls."

The probability of not rolling a 5 on a single roll is 5/6. Since each roll is independent, the probability of not rolling a 5 in all 16 rolls is (5/6) raised to the power of 16.

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Answer:

3/8

Step-by-step explanation:

Answer: one solution

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Using the table of 150 students, we can configure probabilities.

18 students participate in tennis, so the probability of a student participating in tennis is 18/150, or 3/25 simplified.

45 students participate in football, so the probability of a student participating in football is 45/150, or 3/10 simplified.

12 students participate in gymnastics, so the probability of a student participating in gymnastics is 12/150, or 2/25 simplified.

9 students participate in volleyball, so the probability of a student participating in volleyball is 9/150, or 3/50 simplified.

On average, a customer spends approximately 1.16 minutes waiting time on hold before they can start speaking to a representative.

To find the average waiting time for a customer on hold before they can start speaking to a representative, we need to consider both the arrival rate of calls and the average service time of the staff members.

Given:

9 staff members taking calls.

On average, one call arrives every 5 minutes (standard deviation of 5 minutes).

Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes).

To calculate the average waiting time, we need to use queuing theory, specifically the M/M/c queuing model. In this model:

"M" stands for Markovian or memoryless arrival and service times.

"c" represents the number of servers.

In our case, we have an M/M/9 queuing model since we have 9 staff members.

The average waiting time for a customer on hold is given by the following formula:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

Where:

c = number of servers (staff members) = 9

μ = average service rate (1 / average service time)

λ = average arrival rate (1 / average interarrival time)

ρ = λ / (c * μ)

First, let's calculate the average arrival rate (λ):

λ = 1 / (average interarrival time) = 1 / 5 minutes = 0.2 calls per minute

Next, calculate the average service rate (μ):

μ = 1 / (average service time) = 1 / 18 minutes = 0.0556 customers per minute

Now, calculate ρ:

ρ = λ / (c * μ) = 0.2 / (9 * 0.0556) ≈ 0.407

Finally, calculate the waiting time:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

= (1 / (9 * (0.0556 - 0.2))) * (0.407 / (1 - 0.407))

≈ 1.16 minutes

Therefore, on average, a customer spends approximately 1.16 minutes waiting on hold before they can start speaking to a representative.

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The estimate for the sum of the numbers is 230, and the actual sum of the numbers is 209.

To estimate the sum of the numbers, we can round each number to the nearest ten and then add them together. When rounding off to the nearest tens, we look at the number at the tenth position. If it is five and above, we round it off to the next nearest tens number and if it is below five, we round it off to the previous nearest tens number.

76 rounds to 80   since 6 is above 5
6 rounds to 10 since 6 is above 5
25 rounds to 30 since 5 is located at 5 and above interval
5 rounds to 10 since 5 is located at 5 and above interval
10 rounds to 10 since 0 is below 5
87 rounds to 90 since 7 is above 5

So, the estimate for the sum of the numbers is: 80 + 10 + 30 + 10 + 10 + 90 = 230

To find the actual sum of the numbers, we simply add them together without rounding:

76 + 6 + 25 + 5 + 10 + 87 = 209

The complete question is: 76. 6 25. 5 10. 87 =

What was Sela's estimate and what is the actual sum of the number?

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Answer:

If we think of one full rotation, it will be 360 degrees. If one full turn is 360 degrees, one-third of that will be the turn that Jacob made. One-third times 360 is 120 degrees

25% of 40 is 10 hoped that helped

The sales tax on this printer is $20.94

A sales tax is a consumption tax imposed by the government on the sale of goods and services.

Given that, the price of a printer is $349.00 having a 6% sales tax.

Sales tax = 6% of $349.00

$349.00 x 0.06 = $20.94

Hence, the sales tax on this printer is $20.94

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Answer:

Option C. r = (27 – P)/3P

Step-by-step explanation:

The following data were obtained from the question:

A = 27

t = 3

r =?

А = P(1 + rt)

With the above formula, we can obtain the value of r as follow

А = P(1 + rt)

27 = P(1 + 3r)

Divide both side by P

27/P = 1 + 3r

Subtract 1 from both side

27/P – 1 = 1 – 1 + 3r

27/P – 1 = 3r

(27 – P)/P = 3r

Divide both side by 3

r = (27 – P)/P ÷ 3

r = (27 – P)/P × 1/3

r = (27 – P)/3P

The table of values is

X |f(x)

-6 | 11

-3 | 7

0 | 4

3 | -1

The value of f(6) is -5

The y-intercept is 3

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

4x + 3y = 9

Make y the subject

So, we have

y = 3 - 4/3x

We have the x values to be

x = -6, -3, 0, and 3

Substitute the known values in the above equation, so, we have the following representation

y = 3 - 4/3 * -6 = 11

y = 3 - 4/3 * -3 = 7

y = 3 - 4/3 * 0 = 4

y = 3 - 4/3 * 3 = -1

We have

y = 3 - 4/3x

This means that

f(6) = 3 - 4/3 * 6

f(6) = -5

For the y-intercept, we set x = 0

So, we have

f(0) = 3 - 4/3 * 0

f(0) = 3

So, the y-intercept is 3

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