Solve the given system of differential equations by systematic elimination.
(D − 1)x+ (D² + 1)y = 1
(D² − 1)x+ (D + 1)y = 2

(x(t), y(t)) = (e^-t/2 [-5/3cos(√47/2)t - 125/3 sin(√47/2)t]+ 20/3 cos (3t) + 20/3 sin (3t)

Answer:

What do you mean lucky?

Answer:

Yes

Step-by-step explanation:

Answer:

I think 60 s.sq m

Answer:

a) x= -5

b) x= 3

c) x= -5

Answer:

about 11.5 cm.

Step-by-step explanation:

I know the measurement of the other leg is about 11.5 cm. I know because I used the Pythagorean theorem.

a^2+b^2=c^2.

"a" and "b" are the values of the legs of the triangle, while "c" is the measure of the hypotenuse. We know that 8cm is the measure of one of the legs, and 14 cm is a measure of the hypotenuse.

8^2+b^2=14^2 simplified: 64+b^2=196

Then, I subtracted 64 on both sides, so I would have "b" by itself.

b^2=132

Next, I found the square root of both b^2 and 132, so I would find the true value of "b."

b=11.4891252931

So, the measure of the other leg rounded to the nearest tenth is about 11.5.

The approximate probability of obtaining at least 37 ones is -0.000005.

Given that, a fair die is tossed 180 times. A one refers to the face with one dot.

Thus, P(one) = 1/6.The probability of obtaining at least 37 ones can be approximated using the normal distribution.

Using the central limit theorem, we have,μ = n * P = 180 * (1/6) = 30 andσ² = n * P * (1 - P) = 180 * (1/6) * (1 - 1/6) = 25/6

Since we cannot use a normal distribution directly since we need to find the probability of at least 37 ones, we use a continuity correction by considering the range from 36.5 to 37.5 ones.

Now, using the standard normal distribution, we have, z = (37.5 - 30) / √(25/6) = 5.40 and z = (36.5 - 30) / √(25/6) = 4.87

Using a table of standard normal distribution, the probability corresponding to z = 5.40 and z = 4.87 are 0.0000034 and 0.0000084, respectively.Using continuity correction, the approximate probability of obtaining at least 37 ones is given by,P(X ≥ 37) ≈ P(36.5 ≤ X ≤ 37.5) = P( z ≤ 5.40) - P(z ≤ 4.87)= 0.0000034 - 0.0000084= -0.000005

Therefore, the approximate probability of obtaining at least 37 ones is -0.000005.

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The approximate probability of obtaining at least 37 ones is 0.8051.

Given that a fair die is tossed 180 times where the probability of getting a one is 1/6.

We need to find the approximate probability of obtaining at least 37 ones.

Using the binomial probability distribution, the probability of getting r successes in n independent trials can be given by:

[tex]P(r) = nCr x (p^r) x (1-p)^(n-r)[/tex]

Where n = 180, p = 1/6, q = 1- p = 5/6

We want to find the probability of getting at least 37 ones.

Therefore, we can subtract the probability of getting less than 37 ones from 1.

[tex]P(X≥37) = 1 - P(X<37) = 1 - P(X≤36)So, P(X≤36) = P(X=0) + P(X=1) + P(X=2) + .....+ P(X=36)P(X= r) = nCr x (p^r) x (q)^(n-r)[/tex]

On substituting the given values, we get:

P(X≤36) = ∑P(X = r)

n = 180

r = 0 to 36

p = 1/6, q = 5/6

[tex]P(X≤36) = ∑(nCr) × (p^r) × (q)^(n-r)[/tex]

n = 180, p = 1/6, q = 5/6= 0.1949

On subtracting it from 1, we get:

[tex]P(X≥37) = 1 - P(X<37) = 1 - P(X≤36)≈ 1 - 0.1949≈ 0.8051[/tex]

Therefore, the approximate probability of obtaining at least 37 ones is 0.8051.

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Given:

The formula for nth term of a sequence is:

[tex]\dfrac{5}{6}+\dfrac{1}{2}n[/tex]

To find:

The 12th term in the given sequence.

Solution:

Consider the formula for nth term of a sequence:

[tex]a_n=\dfrac{5}{6}+\dfrac{1}{2}n[/tex]

Putting [tex]n=12[/tex], we get

[tex]a_{12}=\dfrac{5}{6}+\dfrac{1}{2}{12}[/tex]

[tex]a_{12}=\dfrac{5}{6}+6[/tex]

[tex]a_{12}=\dfrac{5+36}{6}[/tex]

[tex]a_{12}=\dfrac{41}{6}[/tex]

Therefore, the 12th in the given sequence is [tex]\dfrac{41}{6}[/tex].

Answer:

the answers are 12.5, 5, 2, 0.8 and 0.32

Step-by-step explanation:

2(0.4)^-2

=2(6.25)

= 12.5

2(0.4)^-1

= 2(2.5)

=5

2(0.4)^0

=2(1)

=2

2(0.4)^1

=2(0.4)

=0.8

2(0.4)^2

=2(0.16)

=0.32

Answer:

B: 60mm

Step-by-step explanation:

Answer:

B. 60 mm

Step-by-step explanation:

1 cm = 10 mm

6 cm = 6 * 1 cm = 6 * 10 mm = 60 mm

Answer: B. 60 mm

Answer: Greater than or equal to 2.

Step-by-step explanation:

Given

Function is  [tex]f(x)=2x^2+5\sqrt{x-2}[/tex]

The entity inside a square root is always positive i.e. greater than equal to zero

[tex]\therefore \ x-2\geq 0\\\Rightarrow x\geq2[/tex]

So, the domain of the function is all real numbers greater than or equal to 2.

Answer:

2,000(1 + 1)⁵ = 64000, or in alternate form, 40³

Answer:

73% = parameter

68% = statistic

Step-by-step explanation:

Parameter and statistic differs from one another in statistical parlance in that, parameter refers to nemwrical characteristic derived from the population data. In the scenario described above, 73% describes the percentage of all registered Voters (population of interest). On the other hand, statistic refers to numerical characteristic derived from the sample data. 68% represents the percentage of democrats from the sample surveyed from the the larger population.

Hence,

68% is a sample statistic and 73% is a population parameter.

The permutations value of ₅P₂/₁₀P₄ is 1/252.

To perform the indicated calculation of ₅P₂/₁₀P₄, we need to evaluate the permutations.

The formula for permutations is given by nPr = n! / (n - r)!, where n is the total number of items and r is the number of items selected.

Let's calculate each permutation separately:

₅P₂ = 5! / (5 - 2)!

= 5! / 3!

= (5 * 4 * 3!) / 3!

= (5 * 4)

= 20

₁₀P₄ = 10! / (10 - 4)!

= 10! / 6!

= (10 * 9 * 8 * 7 * 6!) / 6!

= (10 * 9 * 8 * 7)

= 5,040

Now we can substitute the values into the expression:

₅P₂ / ₁₀P₄ = 20 / 5,040

Simplifying the division:

₅P₂ / ₁₀P₄ = 1 / 252

Therefore, the value of ₅P₂/₁₀P₄ is 1/252.

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Complete question:

Perform the indicated calculation: ₅P₂/₁₀P₄

9514 1404 393

Answer:

  down: $436.50

  payment total: $2,908.08

  total paid: $3,344.58

  finance charge: $434.58

Step-by-step explanation:

A) The down payment is 15% of the cost, so is ...

  0.15 × $2910 = $436.50

__

B) The total of the 18 monthly payments of $161.56 each is ...

  18 × $161.56 = $2908.08

__

C) The total amount paid for the car is the sum of the down payment and the  monthly payments:

  $436.50 +2,908.08 = $3,344.58

__

D) The finance charge is the difference between the amount paid and the original cost of the car:

  $3,344.58 -2,910 = $434.58

Answer:

2020

Step-by-step explanation:

Answer:

2020  i think i hope it is the right answer for you

Answer:

Coordinates of R = (1,2)

Step-by-step explanation:

Let the coordinate of R be (x, y)

Since coordinates of S and T are S(-9,-4) and T(6,5). Then we can use the Formula for length of line from coordinates to find coordinates of R since SR/RT = 2/1

Thus; 1(S) = 2(T)

Coordinates of R = [(1(-9) + 2(6))/(1 + 2)], [(1(-4) + 2(5))/(1 + 2)

Coordinates of R = (3/3), (6/3)

>> (1, 2)

Given function is `f(x) = √√√x³ + x² + x + 1`. Now, we are going to find out the first derivative of f(x).f(x) = √√√x³ + x² + x + 1

Therefore, `(f¹)' (2) = 693 / 16√√√21`This is how the value of `(f¹)' (2)` for the function `f(x) = √√√x³ + x² + x + 1` is evaluated.

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5

---- is the answer to the question

-6

Answer:

y= 4/6x + 4

Step-by-step explanation:

The "rise" of the slope is 4 and the "run" of the slope is 6.

Answer:

I love algebra anyways  

the ans is in the picture with the steps  

(hope it helps can i plz have brainlist :D hehe)

Step-by-step explanation:

The  f(x) = [tex]e^x[/tex] and g(x) = x form a linearly independent set of functions.

To show that the functions f(x) = [tex]e^x[/tex] and g(x) = x are linearly independent, we can calculate their Wronskian and verify that it is nonzero for all values of x.

The Wronskian of two functions f(x) and g(x) is defined as the determinant of the matrix:

| f(x) g(x) |

| f'(x) g'(x) |

Let's calculate the Wronskian of f(x) = [tex]e^x[/tex] and g(x) = x:

f(x) = [tex]e^x[/tex]

f'(x) = [tex]e^x[/tex]

g(x) = x

g'(x) = 1

Now we can form the Wronskian matrix:

| [tex]e^x[/tex] x |

| [tex]e^x[/tex] 1 |

The determinant of this matrix is:

Det = ([tex]e^x[/tex] * 1) - ([tex]e^x[/tex] * x)

      = [tex]e^x[/tex] - x[tex]e^x[/tex]

      = [tex]e^x[/tex](1 - x)

We can see that the determinant of the Wronskian matrix is not zero for all values of x. Since the Wronskian is nonzero for all x, it implies that the functions f(x) = [tex]e^x[/tex]and g(x) = x are linearly independent.

Therefore, f(x) = [tex]e^x[/tex] and g(x) = x form a linearly independent set of functions.

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Answer:

48in^2

Step-by-step explanation:

The area of a triangle is calculated by the formula A= b*h1/2. Substitute b for 24, h for 4, and solve.

The probability that a randomly selected student obtained a score between 150 and 162 on the verbal part of the GRE exam is approximately 0.383, or 38.3%.

To find the probability that a student obtained a score between 150 and 162, we need to calculate the area under the normal distribution curve between these two scores. Since the distribution is normal with a mean of 160 and a standard deviation of 8, we can use the Z-score formula to standardize the scores.

First, we calculate the Z-score for a score of 150:

Z1 = (150 - 160) / 8 = -1.25

Next, we calculate the Z-score for a score of 162:

Z2 = (162 - 160) / 8 = 0.25

Using a standard normal distribution table or a statistical calculator, we can find the area under the curve between these two Z-scores. The probability of obtaining a score between 150 and 162 is equal to the area to the right of Z1 minus the area to the right of Z2.

P(150 ≤ X ≤ 162) = P(Z1 ≤ Z ≤ Z2) ≈ P(Z ≤ 0.25) - P(Z ≤ -1.25)

Looking up these values in the standard normal distribution table, we find that P(Z ≤ 0.25) is approximately 0.5987 and P(Z ≤ -1.25) is approximately 0.1056. Subtracting the second probability from the first, we get:

P(150 ≤ X ≤ 162) ≈ 0.5987 - 0.1056 ≈ 0.4931

Therefore, the probability that a randomly selected student obtained a score between 150 and 162 is approximately 0.4931, or 49.3%.

To find the score of a student who scored in the 82nd percentile, we need to find the Z-score that corresponds to the 82nd percentile. The Z-score can be found using the inverse standard normal distribution (also known as the Z-score table or a statistical calculator).

The Z-score corresponding to the 82nd percentile is approximately 0.905. We can use this Z-score to find the corresponding score on the distribution using the formula:

X = Z * σ + μ

Substituting the values, we get:

X = 0.905 * 8 + 160 ≈ 167

Therefore, the score of a student who scored in the 82nd percentile on the verbal part of the GRE is approximately 167.

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There are no possible positions for Ismael's house.

In this case, we need the following geometrical constructions:

1) Given that Ismael's house has the same distance from towns A and B, we must create a line segment between A and B and perpendicular line passing through the midpoint of line segment AB.

2) Since Ismael's house is 20 miles away from town C, we must create a circle centered at C.

All possible positions of Ismael's house are the set of points where both the perpendicular line and the circle intercepts each other. After making all operations defined above, we conclude that there are no possible positions for Ismael's house.

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Answer:

320 m2

Step-by-step explanation:

I think the answer would be B) 340 m2

Answer:

A. 6.25x + 7.50 = 26.25

Step-by-step explanation:

Clara paid 7.50 for an admission ticket, each round was 6.25 and she did it for x rounds. 6.25x is the same thing as 6.25 times x rounds.

Answer:

whered all the time go? :(

Step-by-step explanation:

Answer:

The removed numbers are 13 and 19, and the product is:

13*19 = 247

Step-by-step explanation:

We have the set:

{9, 13, 15, 17, 19, 23, 31, 49}

The original median is the number that is just in the middle of the set (in a set of 8 numbers, we take the average between the fourth and fifth numbers)

then the median is:

(17 + 19)/2 = 18

and the mean is:

(9 + 13 + 15 + 17 + 19 + 23 + 31 + 49)/8 = 22

We want to remove two numbers such that the mean and the median increase by two.

Is immediate to notice that if we want the median to increase by two, we need to remove the number 19 and one number smaller than 17.

Then the median will be equal to:

(17 + 23)/2 = 20

which is 2 more than the previous median.

because 19 assume that we remove the 19 and number N.

To find the value of N, we can solve for the new mean:

((9 + 13 + 15 + 17  + 23 + 31 + 49 - N)/6 = 22 + 2

(this means that if we remove the number 19 and the number N, the mean increases by 2.

(9 + 13 + 15 + 17  + 23 + 31 + 49 - N)/6 = 22 + 2

(9 + 13 + 15 + 17  + 23 + 31 + 49 - N) = 24*6 = 144

157 - N = 144

157 - 144 = N = 13

This means that the other number we need to remove is 13

Then we remove the numbers 13 and 19

The product of the two removed numbers is:

13*19  =247

Answer:

247

Step-by-step explanation:

The average of the original numbers is 176/8 = 22. The median of the original numbers is the average of the middle two numbers: 17 + 19/2 = 18.

Thus, after removing two numbers, we should obtain a list of six numbers whose average is 24 and whose median is 20.

For the median of six numbers to be 20, the middle two numbers in that list must add up to 40. Searching our original list for pairs of numbers that add up to 40, we find two such pairs: 9, 31 and 17, 23. But 9 and 32 can't be the middle numbers after we remove two numbers, so 17 and 23 must be the middle numbers. This tells us that one of the removed numbers must be 19.

For the average of six numbers to be 24, the sum of the six numbers must be 6 ∙ 24 = 144. This is 32 less than the original sum of 176, so if one of the removed numbers is 19, the other must be 32 - 19 = 13.

Therefore, the product of the two removed numbers is 13 ∙ 19 = 247.

Answer:

See Below.

Step-by-step explanation:

We are given that PQRS is a parallelogram, where X and Y are points on the diagonal QS such that SX = QY.

And we want to prove that quadrilateral PXRY is a parallelogram.

Since PQRS is a parallelogram, its diagonals bisect each other. Let the center point be K. In other words:

[tex]SK=QK\text{ and } PK = RK[/tex]

SK is the sum of SX and XK. Likewise, QK is the sum of QY and YK:

[tex]SK=SX+XK\text{ and } QK=QY+YK[/tex]

Since SK = QK:

[tex]SX+XK=QY+YK[/tex]

And since we are given that SX = QY:

[tex]XK=YK[/tex]

So we now have:

[tex]XK=YK\text{ and } PK=RK[/tex]

Since XY bisects RP and RP bisects XY, PXRY is a parallelogram.

Answer:

1 /3

Step-by-step explanation:

Total Number of routes = 6

Probability = required outcome / Total possible outcomes

Probability of any one of the routes :

Required outcome / Total possible outcomes

Probability of choosing any one of the routes = 1/6

Hence,

Probability of choosing either Hilltop. Drive or medical avenue =

1/6 + 1/6 = (1 + 1) / 6 = 2 /6 = 1/3