19. Explain the difference
between (-12)2 and - 122.

Help!

In mathematical modeling, some values are considered fixed and cannot vary without consequence. These values are often referred to as constants or parameters, and they represent physical or environmental properties that are assumed to be constant throughout the problem.

For example, in a mathematical model of the motion of a pendulum, the length of the pendulum, the mass of the weight, and the force of gravity are typically considered constants that cannot vary without consequence. If any of these values were to change, the motion of the pendulum would be affected, and the solution to the problem would be different.

Similarly, in a mathematical model of heat transfer, the thermal conductivity of the material, the heat source or sink, and the boundary conditions are typically considered constants that cannot vary without consequence. If any of these values were to change, the temperature distribution and heat transfer rate within the system would be affected, and the solution to the problem would be different.

The choice of which values to consider as constants or parameters depends on the specific problem being modeled and the assumptions made.

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Answer: The product of two consecutive negative integers is 600. What is the value of the lesser integer?

Step-by-step explanation:

EDGE2021

a) If the test statistic is greater than 1.96, we reject the null hypothesis and is less than or equal to 1.96, we fail to reject the null hypothesis.  b) The p-value of the test is 0.025. c) The confidence interval is (16.72, 17.08). d) The power of the test is 0.945. e) The operating characteristic curve shows the probability of rejecting the null hypothesis for different values of δ/σ.

(a) The null hypothesis is that the mean fill volume is 16.9 ounces, and the alternative hypothesis is that the mean fill volume is not equal to 16.9 ounces.

The test statistic is:

z = (x - μ) / σ

where:

x is the sample mean

μ is the population mean

σ is the population standard deviation

The critical value for α = 0.05 is 1.96.

If the test statistic is greater than 1.96, we reject the null hypothesis.

If the test statistic is less than or equal to 1.96, we fail to reject the null hypothesis.

(b) The P-value for the test is:

P(z > 1.96) = 0.025

Since the P-value is less than α, we reject the null hypothesis.

This agrees with our answer to Part (a).

(c) The two-sided 95% confidence interval for μ is:

(16.72, 17.08)

This confidence interval does not include 16.9 ounces, so we can conclude that the mean fill volume is not equal to 16.9 ounces.

(d) The power of the test is the probability of rejecting the null hypothesis when the true mean is μ = 16.7 ounces.

The power of the test is:

1 - P(z < -1.645) = 0.945

(e) The operating characteristic curve for this test is shown below.

The operating characteristic curve shows the probability of rejecting the null hypothesis for different values of δ/σ.

As δ/σ increases, the probability of rejecting the null hypothesis increases.

Conclusion

The results of the hypothesis test, the confidence interval, and the operating characteristic curve all agree that the mean fill volume is not equal to 16.9 ounces.

The power of the test is 0.945, which means that there is a 94.5% chance of rejecting the null hypothesis when the true mean is μ = 16.7 ounces.

Therefore, we can conclude that the filling line is not achieving the advertised volume of 16.9 ounces.

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The Hypothesis test of probability of the type I error is True.

The Hypothesis test probability of the type II error is False.

The notion of the significance level of a hypothesis test is best described by the probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true. This is also known as the "p-value." A significance level is often set beforehand, such as alpha (α) = 0.05, and if the p-value is less than alpha, the null hypothesis is rejected.

The probability of a type I error is related to the significance level. A type I error occurs when the null hypothesis is rejected when it is actually true. The probability of a type I error is represented by alpha (α) and is the level of significance that was set for the test.

The probability of a type II error is the probability of failing to reject a false null hypothesis. It is represented by beta (β) and depends on the sample size, the true value of the parameter being tested, and the level of significance set for the test.

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Answer:

Step-by-step explanation:

285

Answer:

Company P's total cost is $285

Step-by-step explanation:

Graphed rates of changes and the lowest point was (2375, 285).

Given an observation that is two standard deviations above the expected value of the sum is 266.6667. The probability that the sum is larger than 256 is 0.0848 (approx).

The given observation is two standard deviations above the expected value of the sum. It means that the given observation is 2σ above the mean value. It implies the following relation:

(given value - expected value)/σ = 2

Putting the given values, we get

266.6667 - expected value)/σ = 2

⟹ (266.6667 - expected value)/σ = 2

⟹ 133.33335 - expected value = 2σσ

= (266.6667 - expected value)/2

Substitute σ in the above equation.

⟹ 133.33335 - expected value = (266.6667 - expected value)/2

⟹ 266.6667 - 2 × expected value = 266.6667/2 - 133.33335

⟹ 2 × expected value = 133.33335 - 266.6667/2

⟹ expected value = (133.33335 - 266.6667/2)/2

⟹ expected value = 59.99997

Now, we need to find the probability that the sum is larger than 256.Z = (X - μ) / σZ = (256 - 59.99997) / (266.6667/2)Z = 1.3745736

Probability, P(Z > 1.3745736) = 0.0848300

Therefore, the probability that the sum is larger than 256 is 0.0848 (approx).

Note: In the above solution, we have not used the standard deviation value given in the question. Rather we have found it using the given observation and expected value. This is because it is easy to find the expected value using the given data. Once we have expected value and observation, we can find the standard deviation using the relation (given value - expected value)/σ = 2.

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The store will break even after selling 35 books.

To find  what is the break-even point for this bookstore:

Given:

Let, n be the number of books.

Total costs = 12n + 105

The selling price of each book = $15

Total revenue = 15n

For breaking even, costs = revenue.

Therefore, the store will break even after selling 35 books.

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Answer:

C

Step-by-step explanation:

-Since dot or where the line originates is at 4 we know the answer will have the number 4.

-The dot is hollow, meaning it does not include the number it is on. So it cannot be "blank and equal to."

-Since the arrow points towards the right, we know it wants all values greater than 4, so we do: x>4.

-Back to my second point, we know it is not D because the dot is open and it does not include 4, so it cannot be equal to it.

Answer:

angle relationship is co-interior

x = 3.94

Step-by-step explanation:

(34x - 1 ) + 45 = 180 [co-interior angles add up to 180 degrees]

34x - 1 = 135

34x = 134

x= 134/34 =3.94

The sum of two Toeplitz matrices is a Toeplitz matrix, but the product of two Toeplitz matrices may not be a Toeplitz matrix.

The sum of two Toeplitz matrices is indeed a Toeplitz matrix. A Toeplitz matrix is a matrix in which each descending diagonal from left to right is constant. When you add two Toeplitz matrices, each corresponding element from the two matrices is added together. Since the constant values on the descending diagonals remain the same, the sum of the two Toeplitz matrices will also have constant values on the descending diagonals. Therefore, the sum of two Toeplitz matrices is still a Toeplitz matrix.

On the other hand, the product of two Toeplitz matrices may not necessarily be a Toeplitz matrix. The product of two matrices is obtained by multiplying each element from the first matrix with the corresponding element from the second matrix and summing the results. In general, this operation may change the structure of the matrix, including the constant values on the descending diagonals. Therefore, the product of two Toeplitz matrices may not exhibit the constant values on the descending diagonals, and hence, it may not be a Toeplitz matrix.

In summary, the sum of two Toeplitz matrices is a Toeplitz matrix, but the product of two Toeplitz matrices may not be a Toeplitz matrix.

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a. The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b. The probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c. Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

a) The three characteristics of this scenario that indicate we are working with Bernoulli trials are:

The experiment consists of a fixed number of trials (eight shots).

Each trial (shot) has two possible outcomes: hitting the target or missing the target.

The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b) To find the probability of hitting the 6th target (considered as a single trial), we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the binomial coefficient or number of ways to choose k successes out of n trials,

p is the probability of success in a single trial, and

n is the total number of trials.

In this case, k = 1 (hitting the target once), p = 0.88, and n = 1. Therefore, the probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c) To find the probability that the first time hitting the target is not until the 4th shot, we need to consider the complementary event. The complementary event is hitting the target before the 4th shot.

P(not hitting until the 4th shot) = P(hitting on the 4th shot or later) = 1 - P(hitting on or before the 3rd shot)

The probability of hitting on or before the 3rd shot is the sum of the probabilities of hitting on the 1st, 2nd, and 3rd shots:

P(hitting on or before the 3rd shot) = P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

Calculate these probabilities and sum them up to find P(hitting on or before the 3rd shot), and then subtract from 1 to find the desired probability.

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Answer:

D (-3, 5)

Step-by-step explanation:

270 counter clockwise is the same as 90 clockwise.

For a 90° clockwise or 270° counter clockwise, take the opposite of the x coordinate then switch the coordinates.

(-5, -3) -----> (5, -3) ------> (-3, 5)

You can also rotate your screen 90° clockwise to see the new coordinates for A.

Answer:

2/3

Step-by-step explanation:

Let's simplify the value,

→ 14/21

→ (14 ÷ 7)/(21 ÷ 7)

→ 2/3

Thus, the value is 2/3.

Answer:

Do you want it typed or handwritten

Answer:

188.7

Step-by-step explanation:

Answer:

1258/3

Step-by-step explanation:

find the value of n first

\( \frac{45}{100} n = 255 \\ n = \frac{1700}{3} \)

then let the new value that we wanna find is x

\(x = \frac{74}{100} n \\ = \frac{74}{100} \times \frac{1700}{3} \\ = \frac{1258}{3} \)

done

The random samples of 400 with true proportion in the range of the 27% to 32% correct option is ,

A. The result is not unusual as the probability which is p less than or equal to the sample proportion is 0.5, that is greater than 5%.

To determine whether it would be unusual for a random sample of 400 adults to result in 108 or fewer not owning a credit card,

Calculate the probability of obtaining such a result if the true proportion is within the expected range of 27% to 32%.

The sample proportion, denoted as p, can be calculated by dividing the number of adults who do not own a credit card by the total sample size.

Here, p = 108/400 = 0.27.

To determine the probability, use the normal approximation to the binomial distribution since the sample size is large (n = 400).

The mean of the binomial distribution is np, and the standard deviation is √(np(1-p)).

Here, np = 400 × 0.27

              = 108

and √(np(1-p)) = √(400 × 0.27 × 0.73)

                       ≈ 8.654.

To calculate the probability, standardize the value using the z-score formula,

z = (x - μ) / σ,

where x is the observed value, μ is the mean, and σ is the standard deviation.

For 108 or fewer adults not owning a credit card, the z-score is,

z = (108 - 108) / 8.654

  ≈ 0  

The probability that p is less than or equal to the sample proportion can be obtained by the z-score in the standard normal distribution calculator.

Since the z-score is 0, the corresponding probability is 0.5.

Therefore, for the given random samples the correct option is A. The result is not unusual because the probability that p is less than or equal to the sample proportion is 0.5, which is greater than 5%.

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A) The mean of the continuously compounded rate of return earned over a one-year period can be calculated using the formula: μ = ln(1 + R), where R is the annual rate of return.

Solving for R, we get: R = e^μ - 1
Substituting the given values, we get: R = e^0.17 - 1 = 0.1876 or 18.8% (rounded to the nearest tenth)
The standard deviation of the continuously compounded rate of return can be calculated using the formula:
σ_R = σ * sqrt(t), where t is the time period (in years).

Substituting the given values, we get: σ_R = 0.37 * sqrt(1) = 0.37 or 37% (rounded to the nearest tenth)

B) To construct a 95% confidence interval for the continuously compounded rate of return, we can use the formula:
CI = R ± z * (σ_R / sqrt(n)), where CI is the confidence interval, z is the critical value from the standard normal distribution for a 95% confidence level (which is 1.96), and n is the sample size (which is assumed to be large in the BSM model).
Substituting the given values, we get: CI = 0.188 ± 1.96 * (0.37 / sqrt(1)) = 0.188 ± 0.724
The 95% confidence interval is from 11.6% (0.188 - 0.724) to 24.0% (0.188 + 0.724), rounded to the nearest tenth.

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Answer:

i think is b

Step-by-step explanation:

because the equation 8x＜-48 means -48 greater than 8x so it if you choose a than i will become 8(6)＜-48 this is wrong because positif integer always is greater,zero also greater than negatif integer.So by comparing the another i think the answer is b.I hope it will help you and it is correct.

Answer:

Step-by-step explanation:

\(\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}\)

(A) The normal approximation to the binomial to approximate the probability that at least 99 99 respondents live at​ home is 84.21%

(B) The probability that 16 or more out of 19 community college male students live at home is 0.0037.

In algebra, a binomial is an expression in which two distinct terms are joined by an addition or subtraction operator. For example, 2xy + 7y is a binomial because there are two terms. Algebraic expressions can be classified into different types based on the number of terms that appear, such as monomial, binomial, trinomial, etc.

(a) Based on the sample of 19 students, the proportion of community college males live at home:

p = 16/19= 0.8421 or 84.21%.

(b) the probability that 16 or more out of 19 community college male

students live at home, assuming that the proportion who live at home is 52%. Using binomial distribution with parameters

n = 19, p = 0.52, q = 1-p = 0.48,

The probability that 16 or more out of 19 community college male students live at home is

P (16 or more) = P19 (16)+ P19 (17)+ P19 (18)+ P19 (16)=

= C₁₉ ¹⁶P Q³ + C₁₉ ¹⁷P Q² + C₁₉ ¹⁸P Q¹ + C₁₉ ¹⁸P Q⁰= 0.0037.

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Answer:

Step-by-step explanation:

19) 340-76=               264 ft

20) -320+23 =         -297 F

21) 50-85-12+93 =    46 points

22) 26-5-2+1-6 =       14$

23) -3 + 18 =             15 F

Answer: 2.19 pounds

Step-by-step explanation:

35 / 16 is 2.1875, if you round that you get 2.19

Answer:

3

Step-by-step explanation:

When finding their H.C.F, we can list out their prime factors first.

12: 2² × 3

15: 3 × 5

60: 2² × 3 × 5

3 is the only common prime factor between 12, 15 and 60, so it is the H.C.F.

Answer:

the brackets

Step-by-step explanation:

Answer:

Side EH is congruent to side FG. Reason: given by tic marks

Angle FEG is congruent to Angle HGE. Reason: given

Side EG is congruent to side GE. Reason: identity

Triangle EFG is congruent to triangle GHE. Reason: Side Angle Side.

Step-by-step explanation:

This is the simplest proof. There may be another way using the given FG is parallel to HE.

the first 6 terms of the sequence defined by an = (−1)n 13nn2 4n 5 are: a1 = -1/2, a2 = 21, a3 = -50/3, a4 = 285, a5 = -335/3, and a6 = 433.

Given a sequence defined by the formula, an = (−1)n 13nn2 4n 5

To find the first 6 terms of the sequence, we need to substitute n=1, 2, 3, 4, 5, and 6 in the above formula and evaluate the expression.

When we substitute n=1, we get:a1 = (−1)1 (13)1(12) 4(1) 5= -1(13)(12) + 4 + 5= -1/2

When we substitute n=2, we get:a2 = (−1)2 (13)2(22) 4(2) 5= 1(13)(4) + 8 + 5= 21

When we substitute n=3, we get:a3 = (−1)3 (13)3(32) 4(3) 5= -1(13)(9) + 12 + 5= -50/3

When we substitute n=4, we get:a4 = (−1)4 (13)4(42) 4(4) 5= 1(13)(16) + 16 + 5= 285

When we substitute n=5, we get:a5 = (−1)5 (13)5(52) 4(5) 5= -1(13)(25) + 20 + 5= -335/3

When we substitute n=6, we get:a6 = (−1)6 (13)6(62) 4(6) 5= 1(13)(36) + 24 + 5= 433

Thus, the first 6 terms of the sequence defined by an = (−1)n 13nn2 4n 5 are: a1 = -1/2, a2 = 21, a3 = -50/3, a4 = 285, a5 = -335/3, and a6 = 433.

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Given a sequence, `a\(n = (-1)^(n-1) * 13n^2 / (4n + 5)`.To find the first 6 terms of the sequence, we can substitute n=1,2,3,4,5, and 6 in the above equation.\)

\(Using the formula,`an = (-1)^(n-1) * 13n^2 / (4n + 5)`.

Put `n = 1`.Then, `a1 = (-1)^(1-1) * 13(1)^2 / (4(1) + 5)=13/9`.Put `n = 2`.

Then, `a2 = (-1)^(2-1) * 13(2)^2 / (4(2) + 5)=-52/18=-26/9`.Put `n = 3`.Then, `a3 = (-1)^(3-1) * 13(3)^2 / (4(3) + 5)=39/14`.

Put `n = 4`.Then, `a4 = (-1)^(4-1) * 13(4)^2 / (4(4) + 5)=-52/21`.Put `n = 5`.

Then, `a5 = (-1)^(5-1) * 13(5)^2 / (4(5) + 5)=65/18`.Put `n = 6`.Then, `a6 = (-1)^(6-1) * 13(6)^2 / (4(6) + 5)=-78/25`.\)

Therefore, the first 6 terms of the sequence are \(`{13/9, -26/9, 39/14, -52/21, 65/18, -78/25}\)`.

Hence, the required terms of the given sequence are given as follows\(;a1 = 13/9a2 = -26/9a3 = 39/14a4 = -52/21a5 = 65/18a6 = -78/25\)

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The 95% confidence interval for the difference between the two population proportions is (0.1, 0.16).

The parameter being estimated is the difference between two population proportions.

To find the 95% confidence interval for this parameter, we can use the margin of error formula:

where z is the z-score for the desired level of confidence (95% in this case), p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.

We know that the difference between the sample proportions (phat1 - phat2) is 0.13, and the margin of error is 3%. Since the sampling distribution is assumed to be symmetric and bell-shaped, we can assume that the standard deviation of the difference between the sample proportions is equal to the standard error, which can be estimated by the margin of error.

Setting up an equation using the margin of error formula, we get:

We don't know the sample sizes or the sample proportions, so we can't solve for the confidence interval directly. However, we can use a conservative estimate for the standard deviation of the difference between the sample proportions:

Using this formula, we get:

This is approximately equal to the margin of error, so we can assume that z ≈ 1.96 (the z-score for 95% confidence) and use the formula:

Therefore, the 95% confidence interval for the difference between the two population proportions is (0.1, 0.16).

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(a) To find AB, perform matrix multiplication of matrices A and B.

(b)  It is not possible to find BA because the number of columns in matrix A does not match the number of rows in matrix B.

(e)  To find the determinant of matrix A, evaluate the determinant using the provided matrix.

4. To find 3A + 2B, perform scalar multiplication and matrix addition using matrices A and B.

(a)Matrix A:

A = |1 -13|

      |0   6|

      |9   2|

Matrix B:

B = |6 -5|

      |10  1|

Performing matrix multiplication:

AB = |(1 * 6) + (-13 * 10)  (1 * -5) + (-13 * 1)|

       |(0 * 6) + (6 * 10)     (0 * -5) + (6 * 1)|

       |(9 * 6) + (2 * 10)     (9 * -5) + (2 * -7)|

Simplifying the multiplication:

AB = |-124 -18|

       | 60   -5|

       | 76  -53|

Therefore, AB = |-124 -18|

                       | 60   -5|

                       | 76  -53|

(b)Matrix A has 2 columns and matrix B has 3 rows. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. Since the dimensions do not match (2 columns vs. 3 rows), we cannot find the product BA.

(e)Matrix A:

A = |0 -1|

      |6  2|

      |5 -1|

Using the formula for a 2x2 matrix determinant:

det(A) = (0 * 2) - (-1 * 6)

            = 0 + 6

            = 6

Therefore, the determinant of matrix A, det(A), is 6.

4.Matrix A:

A = |0 -1|

      |6  2|

      |5 -1|

Matrix B:

B = |0 -3|

      |0 -7|

      |5 -1|

Performing scalar multiplication and matrix addition:

3A = |3 * 0  3 * -1| = |0  -3|

        |3 * 6  3 * 2|     |18   6|

        |3 * 5  3 * -1|     |15  -3|

2B = |2 * 0  2 * -3| = |0  -6|

        |2 * 0  2 * -7|     |0 -14|

        |2 * 5  2 * -1|     |10  -2|

Adding 3A and 2B:

3A + 2B = |0  -3| + |0  -6| = |0  -9|

              |18   6|     |0 -14|     |18 -8|

              |15  -3|     |10  -2|     |25  -5|

Therefore, 3A + 2B = |0  -9|

                            |18 -8|

                            |25  -5|

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Answer:

Tank A and Tank D

Step-by-step explanation:

Got it right

The tanks that have the capacity more than 90 cu.ft is Tank A and C.

Volume is the amount of space occupied by a three dimensional object, it is represented in cubic units.

The volume of a Cylinder is given by

V = πr²h

The Volume of a Cone is given by

V= πr²h/3

The volume of the composite figure in Tank A and D,

Volume =  Volume of cylinder + Volume of Cone

Tank A :

Volume =  πr²h + πr²h/3

Volume = ( π * 2.5² * 4 ) + ( π *2.5² *2 )/3

Volume = 91.58 cu.ft

Tank B :

Volume =  πr²h/3

Volume =  π * 4² *5 /3

Volume = 83.7 cu.ft

Tank C

Volume = πr²h

Volume = π * 2² * 6

Volume = 75.36 cu.ft

Tank D:

Volume =  πr²h + πr²h/3

Volume = π * 3²*3 + π *3²* 3 /3

Volume = 113.04 cu.ft

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The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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