Which sequence could be partially defined by the recursive formula.

The probability that at least 22 out of 25 computers will work in good condition is approximately 0.0250, or 2.5%.

To calculate the probability that at least 22 out of 25 computers will work in good condition, we can use the binomial distribution formula.

The binomial distribution formula is given by:

\(P(X = k) = C(n, k) \times p^k \times (1 - p)^{(n - k)\)

Where:

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

C(n, k) is the number of ways to choose k items from a set of n items (also known as the binomial coefficient),

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

n is the total number of trials.

In this case, n = 25 (the total number of computers selected), k ranges from 22 to 25 (at least 22 working computers), and p = 0.89 (probability of a computer working, which is 1 - 0.11).

Let's calculate the probability using these values:

P(X ≥ 22) = P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25)

\(P(X = k) = C(25, k) \times 0.89^k \times 0.11^{(25 - k)\)

\(P(X = 22) = C(25, 22) \times 0.89^{22} \times 0.11^3\)

\(P(X = 23) = C(25, 23) \times 0.89^{23} \times 0.11^2\)

\(P(X = 24) = C(25, 24) \times 0.89^{24} \times 0.11^1\)

\(P(X = 25) = C(25, 25) \times 0.89^{25} \times 0.11^0\)

Calculate the binomial coefficients, we can find:

P(X = 22) ≈ 0.0210

P(X = 23) ≈ 0.0038

P(X = 24) ≈ 0.0002

P(X = 25) ≈ 0.0000

Finally, summing up these probabilities:

P(X ≥ 22) ≈ 0.0210 + 0.0038 + 0.0002 + 0.0000

≈ 0.0250

Therefore, the probability that at least 22 out of 25 computers will work in good condition is approximately 0.0250, or 2.5%.

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The solution to the given differential equation is \(y(x) = -x^4/25 + x^2/15 - (3/25)e^(-3x) + (1/2)x^4cos(x) + (1/2)x^2sin(x) + C1e^(-3x) + C2\), where C1 and C2 are arbitrary constants.

To solve the given differential equation using the method of undetermined coefficients, we assume a particular solution of the form \(y_p = A(x^4 + Bx^2e^(-3x) + Csin(x))\), where A, B, and C are undetermined coefficients.

Step 1:

Differentiating y_p with respect to x, we obtain \(y_p' = 4Ax^3 + 2Bx(e^(-3x) - 3xe^(-3x)) + Ccos(x).\)

Taking the second derivative, we have \(y_p" = 12Ax^2 + 2B(e^(-3x) - 3xe^(-3x)) + 2Bx(-3e^(-3x) + 9xe^(-3x)) - Csin(x).\)

Step 2:

Substituting y_p, y_p', and y_p" into the given differential equation, we get:

\((12Ax^2 + 2B(e^(-3x) - 3xe^(-3x)) + 2Bx(-3e^(-3x) + 9xe^(-3x)) - Csin(x)) + 5(4Ax^3 + 2Bx(e^(-3x) - 3xe^(-3x)) + Ccos(x)) = 2x^4 + x^2e^(-3x) + sin(x).\)

Simplifying the equation and grouping the like terms, we have:

\((12A + 20Ax^3) + (-6B + 10Bx)e^(-3x) + (-15Bx^2 + 9Bx^3) + (12A + 10C)cos(x) + (-C + 2Bx)sin(x) = 2x^4 + x^2e^(-3x) + sin(x).\)

Comparing the coefficients of the terms on both sides, we can determine the values of A, B, and C. Equating the coefficients of each term, we obtain:

\(12A + 20Ax^3 = 2x^4,\)

\(-6B + 10Bx = x^2e^(-3x),\)

\(-15Bx^2 + 9Bx^3 = 0,\)

12A + 10C = 0,

-C + 2Bx = sin(x).

Solving these equations, we find A = -1/25, B = 1/15, and C = 0.

Therefore, the particular solution is \(y_p = (-1/25)x^4 + (1/15)x^2e^(-3x) + (1/2)x^2sin(x).\)

To obtain the general solution, we add the particular solution y_p to the complementary function y_c, where y_c is the solution of the homogeneous equation y" + 5y' = 0. The general solution is given by y(x) = y_c + y_p.

The complementary function can be found by solving the homogeneous equation:

y" + 5y' = 0.

The characteristic equation associated with the homogeneous equation is r^2 + 5r = 0. Solving this quadratic equation

, we find two distinct roots: r = 0 and r = -5.

Therefore, the complementary function is \(y_c = C1e^(-5x) + C2\), where C1 and C2 are arbitrary constants.

Finally, the general solution to the given differential equation is:

\(y(x) = C1e^(-5x) + C2 - (1/25)x^4 + (1/15)x^2e^(-3x) + (1/2)x^2sin(x).\)

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The radius of curvature of the lens is = 8cm

The radius of curvature is defined as the radius of the circle that is made by a spherical mirror or lens.

The focal length is defined as the distance between the point of convergence of your lens and the sensor

The refractive index is the measure of bending of a light ray when passing from one medium to another.

The relationship between focal length and radius of curvature is that R=2f

Where R = radius of curvature

f= Focal length

Therefore, radius of curvature = 2×4 =8cm

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Answer:

d. $6

Step-by-step explanation:

Answer:

I would go with A.) 4

Step-by-step explanation:

It might be wrong, I got these because on the y side you can see that  4 is being subtracted. tell me if am I right or wrong.

Don't fully trust me on this

Answer:

I am not 100% sure but I believe it is 45

Answer:

4 fl oz =12 cup

9 qt =214 gal and 6 gal = 24 qt

Step-by-step explanation:

Answer:

not enough info .

Step-by-step explanation:

sorry it needs more info

The probability the mean age at heart attack after using cocaine is greater than 42 is 0.9192. Hence, the correct option is D. 0.9192.

The standard deviation of the age of people who suffered heart attacks soon after using cocaine was 10 years. In a random sample of size 49, what is the probability the mean age at heart attack after using cocaine is greater than 42?We are given the following details:

The mean age of people in the study who suffered heart attacks soon after using cocaine was only 44.

Standard deviation = 10

Sample size = 49

Now we need to find the z-score using the formula:

z = (x - μ) / (σ / √n)

wherez is the z-score

x is the value to be standardized

μ is the mean

σ is the standard deviation

n is the sample size.

Substitute the values in the formula as given,

z = (42 - 44) / (10 / √49)z = -2 / (10/7)

z = -1.4

Probability of z > -1.4 can be found using the standard normal distribution table or calculator.

P(z > -1.4) = 0.9192

Therefore, the probability the mean age at heart attack after using cocaine is greater than 42 is 0.9192. Hence, the correct option is D. 0.9192.

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Answer:

-29?

Step-by-step explanation:

The lead time for the first row in the data frame Onlineta City Hotels v2 is 65.

The lead time for the first row in the data frame Onlineta City Hotels v2 is calculated as follows: Take the difference of the checkout date (88) and the booking date (23) to get 65.

Lead Time = Checkout Date - Booking Date

Lead Time = 88 - 23

Lead Time = 65

Lead time is the time difference between when a customer books a hotel room and when they check out of the hotel. This lead time is important for a hotel, as it allows them to plan ahead and anticipate the demand for their rooms. Knowing the lead time helps a hotel manager to manage the availability of their rooms, ensure that they have enough staff on hand to accommodate guests, and plan for any other services that may be needed. It is also important for marketing purposes, as it allows a hotel to target customers who may be more likely to book a room in advance.

The lead time for the first row in the data frame Onlineta City Hotels v2 is 65.

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Answer:

The lead time in the first row of the onlineta_city_hotels_v2 data frame is 88. By using a filter with ggplot2, you are able to select specific segments of your data and plot them using R. Going forward, you can use filters and facets to compare visualizations of different aspects of the same data to gain even deeper insights from your analyses.

Step-by-step explanation:

To optimize his long-term predicted profit percentage, he should select 20.567%.

Both decimal and fractional forms of the expression are acceptable.

Given, The boat's daily running expense is $2,250.

$1.50 is the minimal amount.

a maximum of $5.50

Most likely value is $3.50. Now, each day's conclusion.

More lobsters mean a lower price per pound which the grocery shop will accept ($3.85 - $0.0005). × y,

Amir's daily haul of lobster has a normally distributed with a mean of 1,500 pounds and a standard deviation of 12,500 pounds.

He should therefore select 20.567% to increase his anticipated profit in the long run.

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To find the values of sin 75° and cos 15°, we'll use the given trigonometric identities.

(i) To find sin 75°, we can rewrite it as sin (45° + 30°). Using the angle sum identity, sin (A + B) = sin A cos B + cos A sin B, we have:

sin (45° + 30°) = sin 45° cos 30° + cos 45° sin 30°. We know that sin 45° = cos 45° = 1/√2 and sin 30° = 1/2, cos 30° = √3/2.

Substituting these values, we get: sin (45° + 30°) = (1/√2)(√3/2) + (1/√2)(1/2)

= √3/2√2 + 1/2√2

= (√3 + 1)/(2√2).

(ii) To find cos 15°, we can rewrite it as cos (45° - 30°). Using the angle difference identity, cos (A - B) = cos A cos B + sin A sin B, we have:

cos (45° - 30°) = cos 45° cos 30° + sin 45° sin 30°.

Substituting the known values, we get: cos (45° - 30°) = (1/√2)(√3/2) + (1/√2)(1/2)

= √3/2√2 + 1/2√2

= (√3 + 1)/(2√2).

Therefore, the values of sin 75° and cos 15° are both (√3 + 1)/(2√2).

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The final answers are as follows: Function f(x) is even.

Function g(x) is odd.

Function h(x) is neither even nor odd

To determine if a function is even, we check if f(x) = f(-x) for all x in the domain. Let's evaluate f(x) and f(-x) for the given function:

f(x) = \(x^{2}\) + 2\(x^{4}\)

f(-x) = \(-x^{2}\) + 2\(-x^{4}\)

Since f(x) = f(-x), the function is even.

Function: g(x) = \(x^{3}\) - x

To determine if a function is odd, we check if f(x) = -f(-x) for all x in the domain. Let's evaluate g(x) and -g(-x) for the given function:

g(x) = \(x^{3}\) - x

-g(-x) = -\(x^{3}\) - (-x) = -\(x^{3}\) + x

Since g(x) = -g(-x), the function is odd.

Function: h(x) = 2x + \(x^{2}\)

To determine if a function is even or odd, we need to satisfy the conditions mentioned above. Let's evaluate h(x) and h(-x) for the given function:

h(x) = 2x + \(x^{2}\)

h(-x) = 2(-x) + -\(x^{2}\) = -2x + \(x^{2}\)

Since h(x) is not equal to h(-x) or -h(-x), the function is neither even nor odd.

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Assuming the cost of each check is the same for both banks, Bank A will charge less in fees than Bank B if the number of monthly checks is less than 33.

Let's assume the number of monthly checks is "x".

For Bank A, the monthly fee is $5.00, and the per-check fee is $0.15. So the total cost for x checks is:

Total cost = $5.00 + ($0.15 * x)

For Bank B, the monthly fee is $2.50, and the per-check fee is $0.35. So the total cost for x checks is:

Total cost = $2.50 + ($0.35 * x)

To find the number of checks that will cause Bank A to charge less in fees than Bank B, we need to set the two equations equal to each other and solve for x:

$5.00 + ($0.15 * x) = $2.50 + ($0.35 * x)

$2.50 = ($0.20 * x)

x = 12.5

So if the number of monthly checks is less than 33 (since you can't have half a check), Bank A will charge less in fees than Bank B. If the number of monthly checks is greater than 33, Bank B will charge less in fees than Bank A.

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To obtain the basis for the set of all vectors of the form [a – 2b + 5c 2a + 5b – 8c -a– 4b + 7c 3a +b+c], follow the following steps

:Step 1: Vectorize the given system, which is: { x1 = a - 2b + 5c x2 = 2a + 5b - 8c x3 = -a - 4b + 7c x4 = 3a + b + c }Then we form a vector X = (x1,x2,x3,x4). We want to determine the basis for the set of all possible X.

Step 2: Then, rewrite the given system in vector form as follows: X = a(1,2,-1,3) + b(-2,5,-4,1) + c(5,-8,7,1)This follows from X = a(1,0,-1,3) + b(0,5,-4,1) + c(0,-8,7,1) which is obtained from reducing the original augmented matrix to reduced row echelon form.

We can easily deduce from the above expression that the columns of the coefficient matrix [1 2 -1 3; -2 5 -4 1; 5 -8 7 1] are linearly independent and hence form a basis for the set of all possible vectors X.

Step 3: Hence, a possible basis for the set of all vectors of the form [a – 2b + 5c 2a + 5b – 8c -a– 4b + 7c 3a +b+c] is the set of vectors corresponding to the columns of the coefficient matrix, which are: [1 -2 5; 2 5 -8; -1 -4 7; 3 1 1]

Therefore, a basis for the set of all vectors of the form [a – 2b + 5c 2a + 5b – 8c -a– 4b + 7c 3a +b+c] is { [1 -2 5], [2 5 -8], [-1 -4 7], [3 1 1] }

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Number of clients who do not play either the piano or the guitar is 22

To find the number of clients who do not play either instrument, we need to subtract the number of clients who play either the piano or the guitar or both from the total number of clients.

Let A be the set of clients who play the piano, and B be the set of clients who play the guitar. Then, we can use the formula A union B

|A ∪ B| = |A| + |B| - |A ∩ B|

where |A ∪ B| is the number of clients who play either the piano or the guitar or both, |A| is the number of clients who play the piano, |B| is the number of clients who play the guitar, and |A ∩ B| is the number of clients who play both instruments

Substituting the given values, we get

|A ∪ B| = 46 + 58 - 17

|A ∪ B| = 87

Therefore, the number of clients who do not play either instrument is:

109 - 87 = 22

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Jamaal using whole interval type of data recording to collect the data on Freddie’s on-task behavior.

One form of interval recording technique is whole interval recording. An interval recording approach involves watching to see if a behavior happens or not within predetermined intervals of time. After determining the duration of an observation session, the time is divided into shorter segments that are all of the same length. To record the incidence of behavior, ten boxes may be utilized to divide a 10-minute observational session into 1-minute intervals. A whole interval recorder uses a X for occurrence and a O for no non-occurrence to indicate if a behavior occurred during the entire interval.

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The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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Answer:

Length = 4 times width

Area = length * width

=(4w)w

=4w²

So 4w²=1024 cm² (given)

w²=1024/4=256

w=√(256 cm²)

=16 cm (reject negative value of square-root)

Step-by-step explanation:

Hope this helps you

Crown me as brainliest:)

The graph of the piecewise function is given by the image presented at the end of the answer.

A piece-wise function is a function that has different definitions, depending on the input of the function.

The definitions of the function in this problem are given as follows:

Hence the graph with these two definitions is given by the image presented at the end of the answer.

The closed part of the interval is at point (-1, -1), while the interval is open at (-1,1).

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The proportion of a normal distribution between z-scores of -0.25 and +0.25 is 0.1974, between -0.67 and +0.67 is 0.4994, and between -1.20 and +1.20 is 0.7699.

The normal distribution is a bell-shaped curve that is symmetrical about the mean. The area under the curve is equal to 1 and the z-score represents the standard deviations from the mean

a) The proportion of a normal distribution between z = -0.25 and z = +0.25 is 0.1974.
b) The proportion of a normal distribution between z = -0.67 and z = +0.67 is 0.4994.
c) The proportion of a normal distribution between z = -1.20 and z = +1.20 is 0.7699.

These proportions can be found by using a calculator with normal distribution functions.

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Answer:

y = 2x there is not y-intercept and the slope is 2

Michael’s child is going to college in 13 years. If he saves $ 7,000 a year at 9% compounded annually. Therefore,  the amount available for Peter's child education will be $147,330.55.

Given that Michael is saving $7,000 per year for his child's education which will occur in 13 years. If the interest rate is 9% compounded annually,

The problem of finding the amount of money Michael will have saved in 13 years is a compound interest problem.

In this case, the formula for calculating the future value of the annuity is: $FV = A[(1 + r)n - 1] / r

where: FV is the future value of the annuity, A is the annual payment,r is the annual interest rate, and n is the number of payments.

Using the above formula; the future value of Michael's savings is:

FV = 7000[(1 + 0.09)^13 - 1] / 0.09= 7000(1.09^13 - 1) / 0.09= 147,330.55

Therefore, the amount available for Peter's child education will be $147,330.55.

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Answer: yes

Step-by-step explanation:

Answer:

It's D

Step-by-step explanation:

Answer:

p^4

Step-by-step explanation:

when multiplying exponents, you just add them. Since this is just 1 on each, it will turn out to be 4.

Answer

p^4

Step-by-step explanation:

because it is

Answer:

Step-by-step explanation:

D. the corresponding sides of triangle ABC and triangle A'B'C' are congruent

because the sides do not change their length when we rotate the triangle