Complete the input-output table for the linear function y = 3x.
y
-2
a
-3
0
0
1
3
2
b
3
с

Answer:

google

Step-by-step explanation:

google is very helpful

In this problem, we are given two functions f(x) = sin(x) and g(x) = cos(x), and we need to perform several tasks related to their linear independence and span.

To show that f and g are linearly independent, we can use the Wronskian. The Wronskian of f and g is given by W(f, g) = f'(x)g(x) - f(x)g'(x). By calculating the Wronskian and showing that it is non-zero for all x, we can conclude that f and g are linearly independent.

For the functions f₁(x) = sin(x + a) and g₁(x) = cos(x + a), we need to show that they belong to the span of W, i.e., they can be expressed as linear combinations of f and g. By manipulating the expressions of f₁ and g₁ using trigonometric identities and properties, we can rewrite them in terms of f and g, demonstrating that f₁ and g₁ can be spanned by W.

To show that {f₁, g₁} is linearly independent, we need to prove that no non-trivial linear combination of f₁ and g₁ can equal the zero function. By assuming that there exist coefficients not all zero, we can construct a linear combination and show that it does not vanish, implying linear independence.

By performing these steps, we establish the linear independence of f and g using the Wronskian, demonstrate that f₁ and g₁ belong to the span of W, and prove the linear independence of {f₁, g₁}.

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A. The values of α and β are α = 36 and β = 3.

B. Calculating this value using a statistical software or table, we find P(X ≤ 18) ≈ 0.795.

C. The probability that a student spends at most 18 min using the terminal is approximately 0.795, and the probability that a student spends between 15 and 27 min is approximately 0.592.

(a) In a gamma distribution, the mean (μ) and variance (σ^2) are related to the shape parameter (α) and rate parameter (β) as follows:

μ = α / β

σ^2 = α / β^2

Given that the mean is 12 min and the variance is 36 min, we can set up the following equations:

12 = α / β

36 = α / β^2

To solve these equations, we can divide the second equation by the first equation:

36 / 12 = α / β / (α / β^2)

3 = β

Substituting the value of β back into the first equation:

12 = α / 3

α = 36

So, the values of α and β are α = 36 and β = 3.

(b) To find the probability that a student uses the terminal for at most 18 min, we can use the cumulative distribution function (CDF) of the gamma distribution. The CDF for a gamma distribution is given by:

F(x) = 1 - Γ(α, βx) / Γ(α)

where Γ(α, βx) is the incomplete gamma function.

Using this formula, we can calculate the probability:

P(X ≤ 18) = 1 - Γ(36, 3 * 18) / Γ(36)

Calculating this value using a statistical software or table, we find P(X ≤ 18) ≈ 0.795.

(c) To find the probability that a student spends between 15 and 27 min using the terminal, we can subtract the probabilities of being below 15 min from the probability of being below 27 min:

P(15 ≤ X ≤ 27) = P(X ≤ 27) - P(X ≤ 15)

Using the same formula as in part (b), we can calculate these probabilities:

P(X ≤ 27) = 1 - Γ(36, 3 * 27) / Γ(36)

P(X ≤ 15) = 1 - Γ(36, 3 * 15) / Γ(36)

Subtracting these probabilities, we find P(15 ≤ X ≤ 27) ≈ 0.592.

Therefore, the probability that a student spends at most 18 min using the terminal is approximately 0.795, and the probability that a student spends between 15 and 27 min is approximately 0.592.

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The conditional probabilities are as follows: P(B | C) = 0.295, P(C | B) = 0.371, P(A | B) = 0.371, P(B | A) = 0.333, P(A | C) = 0.273, and P(C | A) = 0.308. These probabilities represent the likelihood of one event occurring given that another event has already occurred.

To determine the conditional probabilities, we can use the formula:

P(X|Y) = P(X ∩ Y) / P(Y)

where X and Y are events.

1. P(B | C):

P(B | C) = P(B ∩ C) / P(C)

P(B ∩ C) = P(B n C) = 0.13

P(C) = 0.44

P(B | C) = 0.13 / 0.44 = 0.295

2. P(C | B):

P(C | B) = P(C ∩ B) / P(B)

P(C ∩ B) = P(B n C) = 0.13

P(B) = 0.35

P(C | B) = 0.13 / 0.35 = 0.371

3. P(A | B):

P(A | B) = P(A ∩ B) / P(B)

P(A ∩ B) = P(A n B) = 0.13

P(B) = 0.35

P(A | B) = 0.13 / 0.35 = 0.371

4. P(B | A):

P(B | A) = P(B ∩ A) / P(A)

P(B ∩ A) = P(A n B) = 0.13

P(A) = 0.39

P(B | A) = 0.13 / 0.39 = 0.333

5. P(A | C):

P(A | C) = P(A ∩ C) / P(C)

P(A ∩ C) = P(A n C) = 0.12

P(C) = 0.44

P(A | C) = 0.12 / 0.44 = 0.273

6. P(C | A):

P(C | A) = P(C ∩ A) / P(A)

P(C ∩ A) = P(A n C) = 0.12

P(A) = 0.39

P(C | A) = 0.12 / 0.39 = 0.308

Therefore, the conditional probabilities are:

P(B | C) = 0.295

P(C | B) = 0.371

P(A | B) = 0.371

P(B | A) = 0.333

P(A | C) = 0.273

P(C | A) = 0.308

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Answer:

z = -1

Step-by-step explanation:

5z-2z-4= -7

Combine like terms

3z - 4 = -7

Add 4 to each side

3z -4+4 = -7+4

3z = -3

Divide each side by 3

3z/3 = -3/3

z = -1

Answer:

[tex]\huge\boxed{\sf 8100\ m\²}[/tex]

Step-by-step explanation:

The figure is made up of two shapes:

= length × width

Where length = 150 m, width = 20 m

= 150 × 20

= 3000 m²

= 1/2(base × height)

Where base = 170 m, height = 60 m

So,

= 1/2(170 × 60)

= 170 × 30

= 5100 m²

= Area of rectangle + area of triangle

= 3000 + 5100

[tex]\rule[225]{225}{2}[/tex]

Answer:

-11.5

Step-by-step explanation:

[tex]K + n( {p}^{2} ) \\ \\ plug \: K = 0.5, \: n = - 3, \: p = - 2 \\ \\ K + n( {p}^{2} ) \\ \\ = 0.5 + ( - 3) \{ {( - 2)}^{2} \} \\ \\ = 0.5 - 3 \{ 4 \} \\ \\ = 0.5 - 12 \\ \\ = - 11.5[/tex]

Answer:

-101

Step-by-step explanation:

[(9 * 2) - (41 * 3)] + 4

[(18) - (123)] + 4

(18 - 123) + 4

-105 + 4

-101

The proportion, denoted p, is given by the formula p = x/n, where x is the number of individuals with a specified characteristic in a sample of n individuals.

Proportion is a measure of how often an event happens compared to all the events that are possible. The proportion is the number of individuals with a specified characteristic in a sample of n individuals. The proportion, denoted p, is given by the formula p = x/n, where x is the number of individuals with a specified characteristic in a sample of n individuals.The sample proportion is the proportion in a sample and the population proportion is the proportion in the population. The sample proportion is calculated from the data in the sample and the population proportion is estimated from the sample proportion. The sample proportion is a point estimate of the population proportion.The sample proportion is a random variable with a mean of p and a standard deviation of σp = sqrt[(p(1 - p))/n], where p is the population proportion and n is the sample size. The sample proportion is an unbiased estimator of the population proportion.The sample size should be large enough so that the sample proportion is normally distributed. A rule of thumb is that the sample size should be at least 10. If the sample size is too small, the sample proportion may not be representative of the population proportion.

In conclusion, the proportion, denoted p, is given by the formula p = x/n, where x is the number of individuals with a specified characteristic in a sample of n individuals. The sample proportion is a point estimate of the population proportion. The sample proportion is a random variable with a mean of p and a standard deviation of σp = sqrt[(p(1 - p))/n].

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Answer:

The lines are certainly not parallel!

Step-by-step explanation:

The slope of line J is 3/2, while the slope of line k is exactly 1 :)

Answer:ITS C!!!! :))

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

an arithmetic sequence has a common difference d between consecutive terms

a 5, 10, 20, 40

10 - 5 = 5

20 - 10 = 10

40 - 20 = 20

the difference is not common , thus not arithmetic

b 5, 8, 13, 21

8 - 5 = 3

13 - 8 = 5

21 - 13 = 8

the difference is not common, thus not arithmetic

c 11, 22, 44, 66

22 - 11 = 11

44 - 22 = 22

66 - 44 = 22

the difference is not common , thus not arithmetic

d 22, 28, 34, 40

28 - 22 = 6

34 - 28 = 6

40 - 34 = 6

the difference is common , so is the beginning of an arithmetic sequence

Option (d) 5, 10, 20, 40... is the beginning of an arithmetic sequence.

Arithmetic sequence is the sequence in which there is a common difference between all the terms of the sequence.

In option a). 5, 10, 20, 40... if we check the common difference of the terms it is not common. The difference is 5 then 10 it is not the same.

Similarly in option b). 5, 8, 13, 21, ... and c) 11, 22, 44, 66, ...if we check the common difference of the terms it is not common.

Then d) 22, 28, 34, 40, ...we the common difference that is 6. The difference between each term is 6, which is common.

Therefore option (d) 5, 10, 20, 40... is the beginning of an arithmetic sequence.

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Answer:

The temperature at 11:00 a.m. is 14 °F

Step-by-step explanation:

Let us list the information in the question

→ The temperature at 7:00 a.m. is - 7 °F

→ The temperature increases 21 °F during 4 hours

→ We need to find the temperature at 11:00 a.m.

∵ The temperature increases 21 °F during 4 hours

∵ The time 4 hours after 7: 00 a.m. is 11:00 a.m.

→ That means add 21 °F to - 7 °F to find the temperature at 11:00 a.m.

∴ The temperature at 11:00 a.m. = -7 °F + 21 °F

∴ The temperature at 11:00 a.m. = 14 °F

The temperature at 11:00 a.m. is 14 °F

Answer:

D

Step-by-step explanation:

on edu 2020

Answer:

D (3,8)

Step-by-step explanation:

On edge

24) $0.81 per portion for vodka. 25) the cost per portion for fruit juice is $0.40. 26) The cost per portion for ice cream is $0.86.  27) The cost per portion for the banana is $0.23. 28) The total cost for the entire recipe is $5.66.  29) The Standard Portion Cost (SPC) is $1.42. 30) The beverage cost percentage is 34.6%.

24) To calculate the cost per portion for vodka, we divide the total cost of vodka by the yield or number of portions. In this case, the recipe calls for 6 oz of vodka, and the purchase unit is a liter (35 oz). The cost per liter of vodka is $19.00. Using the ratio of 6 oz to 35 oz, we can calculate the cost for 6 oz of vodka, which is approximately $3.26. Therefore, the cost per portion for vodka is $3.26 divided by 4 (yield of 4 drinks), which is $0.81.

25) To calculate the cost per portion for fruit juice, we need to consider the purchase unit and the yield. The recipe calls for 500 ml of fruit juice, and the purchase unit is a liter. The cost per liter of fruit juice is $3.20. Using the ratio of 500 ml to 1000 ml (1 liter), we can calculate the cost for 500 ml of fruit juice, which is $1.60. Therefore, the cost per portion for fruit juice is $1.60 divided by 4 (yield of 4 drinks), which is $0.40.

26)To calculate the cost per portion for ice cream, we need to consider the purchase unit and the yield. The recipe calls for 4 scoops of ice cream, and the purchase unit is a gallon (32 scoops). The cost per gallon of ice cream is $5.48. Using the ratio of 4 scoops to 32 scoops (1 gallon), we can calculate the cost for 4 scoops of ice cream, which is $0.686. Therefore, the cost per portion for ice cream is $0.686 divided by 4 (yield of 4 drinks), which is $0.86.

27)To calculate the cost per portion for the banana, we need to consider the purchase unit, the yield, and the conversion from EP (edible portion) to AP (as purchased). The recipe calls for 350 grams of banana, and the purchase unit is a kilogram. The cost per kilogram of banana is $4.98. Since the yield is given as 90% per kilogram, we can calculate the cost for 350 grams of banana, which is $4.98 multiplied by 0.9 and divided by 1000 (to convert grams to kilograms), resulting in $0.00447. Therefore, the cost per portion for the banana is $0.00447 multiplied by 4 (yield of 4 drinks), which is $0.018 or approximately $0.23.

28) To calculate the total cost, we add up the costs of each ingredient. The cost for vodka is $3.26, the cost for fruit juice is $1.60, the cost for ice cream is $2.74 (4 scoops multiplied by $0.686), and the cost for the banana is $0.072 (4 portions multiplied by $0.018). Adding these costs together, we get $3.26 + $1.60 + $2.74 + $0.072, which equals $5.66.

29) The Standard Portion Cost (SPC) represents the cost of each individual portion in the recipe. To calculate the SPC, we divide the total cost of the recipe ($5.66) by the yield or number of portions (4 drinks). Therefore, the SPC is $5.66 divided by 4, which equals $1.42.

30) The beverage cost percentage is calculated by dividing the total cost of the recipe ($5.66) by the selling price of the drink ($6.50) and then multiplying by 100 to get the percentage. Therefore, the beverage cost percentage is ($5.66 divided by $6.50) multiplied by 100, resulting in 87.08%. This means that the beverage cost represents 87.08% of the selling price. To calculate the actual cost percentage, we subtract the beverage cost percentage from 100%, which gives us 100% - 87.08% = 12.92%. Therefore, the beverage cost percentage is 12.92%.

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Answer:

-1/2, 2

Step-by-step explanation:

Use rise/run to find the original slope of this function. The rise is -1 and the run is 2, so you divide these and get -1/2. To find the perpendicular slope, flip the sign (from negative to positive) and find the reciprocal of this (1/2 becomes 2 because you flip the fraction).

Original slope: -1/2

Perpendicular slope:  2

Answer is written down below

Answer:

3x^2z√2

/ 2y

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Answer:

55m

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

area of rectangle = L×B

3575=65×B

B=3575/65

B=55

The residual if you know the actual number is 3 and the predicted value is 1.6l is 1.4.

The residual is a measure of the difference between the predicted value and the actual value. In this case, the actual number is 3, and the predicted value is 1.6. To find the residual, we subtract the predicted value from the actual value:

Residual = Actual Value - Predicted Value

= 3 - 1.6

= 1.4

Therefore, the residual in this case is 1.4.

The residual represents the error or the amount by which the predicted value differs from the actual value.

A positive residual indicates that the predicted value is lower than the actual value, while a negative residual indicates that the predicted value is higher than the actual value.

In this case, the positive residual of 1.4 indicates that the predicted value of 1.6 underestimates the actual value of 3 by 1.4.

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Answer:

answer would be -2/5

Step-by-step explanation:

i think thats what you mean i hope this helps

Answer: t= -1/3

Step-by-step explanation:

Multiply both sides of the equation by 15

-12t+6=10

Move constant to the right-hand side and change its sign

-12t=10-6

Subtract the numbers

-12t=4

Divide both sides of the equation by -12

t=-1/3

Alternative form:

t=-0.3333333333333333

(a) For the sequence x1[n], the conjugate symmetric part (xs[n]) is {-2.5 + j4, 2.5 - j6, 4, 2.5 + j6, -1.5 - j2}, and the conjugate antisymmetric part (xa[n]) is {0, -j7, 0, j7, 0}.

(b) For the sequence x2[n], both the conjugate symmetric part (xs[n]) and conjugate antisymmetric part (xa[n]) are empty sets.

(c) For the sequence x3[n], both the conjugate symmetric part (xs[n]) and conjugate antisymmetric part (xa[n]) are empty sets.

To determine the conjugate symmetric and conjugate antisymmetric parts of a sequence, we need to perform the following calculations:

(a) For the sequence x1[n] = {-1+j3, 2-j7, 4-j5, 3+j5, -2-j}, -2 ≤ n ≤ 2:

The conjugate symmetric part (xs[n]) can be calculated as:

xs[n] = (x[n] + x*[-n])/2

The conjugate antisymmetric part (xa[n]) can be calculated as:

xa[n] = (x[n] - x*[-n])/2j

Let's calculate them step by step:

For n = -2:

xs[-2] = (x[-2] + x*[2])/2 = (-1+j3 - 4+j5)/2 = (-5 + j8)/2 = -2.5 + j4

xa[-2] = (x[-2] - x*[2])/2j = (-1+j3 - 4+j5)/(2j) = (j2 - j2)/2 = 0

For n = -1:

xs[-1] = (x[-1] + x*[1])/2 = (2-j7 + 3-j5)/2 = (5 - j12)/2 = 2.5 - j6

xa[-1] = (x[-1] - x*[1])/2j = (2-j7 - 3+j5)/(2j) = (-j2 - j12)/2 = -j7

For n = 0:

xs[0] = (x[0] + x*[0])/2 = (4-j5 + 4+j5)/2 = 4

xa[0] = (x[0] - x*[0])/2j = (4-j5 - 4+j5)/(2j) = 0

For n = 1:

xs[1] = (x[1] + x*[-1])/2 = (3+j5 + 2+j7)/2 = (5 + j12)/2 = 2.5 + j6

xa[1] = (x[1] - x*[-1])/2j = (3+j5 - 2-j7)/(2j) = (j2 + j12)/2 = j7

For n = 2:

xs[2] = (x[2] + x*[-2])/2 = (-2-j + -1-j3)/2 = (-3 - j4)/2 = -1.5 - j2

xa[2] = (x[2] - x*[-2])/2j = (-2-j - -1+j3)/(2j) = (-j2 + j2)/2 = 0

Therefore, for the sequence x1[n], we have:

Conjugate symmetric part (xs[n]) = {-2.5 + j4, 2.5 - j6, 4, 2.5 + j6, -1.5 - j2}

Conjugate antisymmetric part (xa[n]) = {0, -j7, 0, j7, 0}

(b) For the sequence x2[n] = ej2πn/5 + ejπn/3:

Since this sequence is a complex exponential sequence, it does not contain any conjugate symmetric or conjugate antisymmetric parts. In other words, both xs[n] and xa[n] will be empty sets.

Conjugate symmetric part (xs[n]) = {}

Conjugate antisymmetric part (xa[n]) = {}

(c) For the sequence x3[n] = jcos(2πn/7) - sin(2πn/4):

Similarly, since this sequence is a combination of cosine and sine functions, it does not have any conjugate symmetric or conjugate antisymmetric parts.

Conjugate symmetric part (xs[n]) = {}

Conjugate antisymmetric part (xa[n]) = {}

In conclusion:

(a) For the sequence x1[n], the conjugate symmetric part (xs[n]) is {-2.5 + j4, 2.5 - j6, 4, 2.5 + j6, -1.5 - j2}, and the conjugate antisymmetric part (xa[n]) is {0, -j7, 0, j7, 0}.

(b) For the sequence x2[n], both the conjugate symmetric part (xs[n]) and conjugate antisymmetric part (xa[n]) are empty sets.

(c) For the sequence x3[n], both the conjugate symmetric part (xs[n]) and conjugate antisymmetric part (xa[n]) are empty sets.

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9514 1404 393

Answer:

  60/49

Step-by-step explanation:

245% = 245/100, so the ratio is ...

  3/(245/100) = 300/245 = 60/49 . . . as reduced fraction

The ratio 3 : 245% is 60 : 49, or 60/49.

__

As a decimal, it is about 1.2244898. The repeating decimal fraction has a 42-digit repeat.

Answer:

Step-by-step explanation:

1/4

Answer: Um i would do  the first one cause i like money but the secound seem's fine to me

Step-by-step explanation:

HOPE THAT HELP'S!!!!!!!!!!!!!!!!!!!!!!!!!

Answer: is there a pic?

Answer:

your answer is 576

Step-by-step explanation:

Answer:

is a

Step-by-step explanation:

Answer:im pretty dure its a

Step-by-step explanation:

Answer:

I think it's a but I'm not sure

Answer:

Step-by-step explanation:

y=-1

because when y = - 1,

it is an equation of x axis.. hence it will parallel to x axis....

Answer:

2.5 and go up tw x values

Step-by-step explanation:

Answer:

2*(2)+3/2-1=7

Step-by-step explanation: