2. What is the tangent ratio of angle & within a right triangle?

It is unlikely that an algorithm for finding n-1 numbers such that their total equals x exists in polynomial time because the Subset Sum problem is NP-complete.

Finding a subset of n integers such that their total equals x from a given set of n-1 numbers are identical to the task at hand. Unfortunately, there is no known polynomial-time solution for solving this problem, which is also known as the Subset Sum problem and is a well-known NP-complete problem.

Consider the following reduction from the Subset Sum problem to understand why this is the case: Create a new set S' by adding a single element x to the original set S after receiving a Subset Sum problem instance consisting of a set S of n integers and a goal sum x.

Take into account the reduction from the Subset Sum problem to see why this is the case: Create a new set S' by adding a single element x to the existing set S in a case of the Subset Sum problem where the inputs are a set S of n integers and a goal sum x. Discover a subset of the n-1 items in S' that add up to x.

Therefore, It is unlikely that an algorithm for finding n-1 numbers such that their total equals x exists in polynomial time because the Subset Sum problem is NP-complete.

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Option c. 2

Among the given targets, two targets are correctly described:

Regarding chemical pesticide use, the target is to reduce it by 50% by 2050. This aligns with the vision presented in the Green Food System Strategy.

In terms of chemical fertilizers, the target is to reduce the use of chemical fertilizers produced in Japan from fossil fuels by 30% by 2050. This target is also consistent with the strategy's vision.

The remaining two targets are not correctly described:

The target of expanding the organic market and increasing the ratio of organic farming to arable land to 30% (1 million hectares) by 2050 is not mentioned in the given options.

The target of reducing household food loss by half from the FY2000 level by 2030 is also not mentioned in the given options.

Therefore, the correct answer is option c. 2, as two of the targets are accurately described in the provided options.

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To encode a message using matrix multiplication, an invertible matrix is chosen, and the original row matrices are multiplied by this chosen matrix on the right to obtain encoded row matrices.

Matrix multiplication is a common technique used in encoding and decoding messages. In this scenario, to encode a message, we select an invertible matrix, denoted as matrix A. The invertible property ensures that matrix A has an inverse, allowing us to undo the encoding process later.

To encode the message, we take the original row matrices, which represent the message or data, and multiply them by matrix A on the right. The resulting matrices obtained after multiplication are the encoded row matrices.

The process of multiplying the original row matrices by matrix A on the right is often referred to as matrix transformation or encoding. Each element in the original row matrices interacts with the corresponding elements in matrix A, resulting in a modified value in the encoded row matrices.

By performing the inverse operation, which involves multiplying the encoded row matrices by the inverse of matrix A, the original message can be decoded and recovered.

In conclusion, to encode a message using matrix multiplication, an invertible matrix is selected, and the original row matrices are multiplied by this chosen matrix on the right to obtain the encoded row matrices.

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Answer:

Step-by-step explanation:

Given the expression  (x-5) and (x-4)

The product of the two factors can be expressed as follows

\(= (x-5) (x-4)\\=x(x-4)-5(x-5)\\\)

Opening brackets we have

\(=x^2-4x-5x+25\)

Collecting like terms we have

\(=x^2-9x+25\)

2.375 number of standard deviation from mean outing with 74 assists.

Data dispersion in regard to the mean is quantified by a standard deviation, or "σ"

By figuring out how far off from the mean each data point is, the standard deviation may be determined as the square root of variance.

The deviation within the data set is bigger when the data points are more away from the mean.

According to the question,

Mean of the number of assists per match is 55

Standard deviation of the same is 8

Let x be the number of standard deviation from mean outing with 74 assists

=> 55 + 8x = 74

Solving for x

=> 8x = 74 - 55

=> 8x = 19

=> x = 19 / 8

=> x = 2.375

Hence, 2.375 number of standard deviation from mean outing with 74 assists.

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The solution to the system of linear inequalities (x, y) are (-1, 2)

A system of linear inequalities is just like a system of linear equations, except it is composed of inequalities instead of equations. Systems of linear inequalities are used to model scenarios with multiple constraints.

In the given problem, we can find the value of x and y as;

x + y > 1 ...eq(i)

-x + y ≤ 3 ...eq(ii)

Solving both inequalities;

The solution is;

1 - x < y ≤ 3 + x

We can easily plot this on a graph and the point of intersection will be our solution;

From the graph attached below, the solution to this inequality (x , y) are (-1, 2)

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the standard deviation is not less than 13 hours based on the given sample data.

To calculate the standard deviation of the sample mean, we can use the formula:

Standard deviation of the sample mean = Standard deviation of the population / √(sample size)

Given that the population standard deviation is 180 and the sample size is 345, we can plug in these values:

Standard deviation of the sample mean = 180 / √345 ≈ 9.693

The standard deviation of the sample mean represents the average variability or spread of sample means that could be obtained from repeated sampling. In this case, it indicates how much the sample means would typically vary from the true population mean. A smaller standard deviation of the sample mean suggests that the sample means are closer to the population mean, leading to greater precision and accuracy in estimating the population mean.

Regarding the assumptions for the confidence interval at 95%, they typically include:

1. Random Sample: The sample should be selected randomly from the population to ensure its representativeness.

2. Independence: The observations within the sample should be independent of each other. Each data point should not be influenced by others.

3. Normality or Large Sample Size: The population distribution should be approximately normal, or the sample size should be large enough to satisfy the Central Limit Theorem. The CLT states that for a large sample size, the distribution of the sample mean becomes approximately normal, regardless of the population distribution.

4. Unbiasedness: The sample should be unbiased and free from selection or measurement bias.

As for testing the claim that the standard deviation is at least 13 hours, we can use a one-sample t-test with the null and alternative hypotheses:

Null hypothesis (H0): The standard deviation is less than 13 hours.

Alternative hypothesis (Ha): The standard deviation is at least 13 hours.

Using the sample data, we can calculate the test statistic:

t = (sample standard deviation - claimed standard deviation) / (standard deviation of the sample mean / √sample size)

t = (10.4 - 13) / (10.4 / √32) ≈ -2.035

Next, we determine the critical value at a significance level (α) of 0.05 for a one-tailed test with degrees of freedom (df) = sample size - 1 = 32 - 1 = 31. Checking a t-distribution table or using a statistical calculator, we find the critical value to be approximately -1.697.

Since the calculated t-value (-2.035) is less than the critical value (-1.697), we have evidence to reject the null hypothesis. Therefore, we can conclude that the standard deviation is not less than 13 hours based on the given sample data.

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Answer:

shown in drawing attached

y=x-2

Step-by-step explanation:

Shift each point down by two. First plot y=x, then shift down by 2 for each point.

please give thanks :)

You have to subtract 2 from the y-coordinate to shift the graph of y = x down to 2 units.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

To shift the graph of y = x down 2 units, you can subtract 2 from the y-coordinate of each point on the graph.

This will be done by replacing y with y-2 in the equation, so the new equation would be y = x + (-2) which is y = x - 2

So the new equation for the graph will be y = x - 2

This will cause the graph to move down 2 units along the y-axis.

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Given:

novel: 3/4

dictionary: 4 1/2

Let's first convert the two given height into similar fractions (with the sa

Answer:

Step-by-step explanation:

The initial height of the rocket before it is launched can be found by evaluating the function h(t) at t=0. To do this, you can substitute 0 for t in the function:

h(0) = -5(0)² + 42(0) + 54

h(0) = 0 + 0 + 54

h(0) = 54

Therefore, the initial height of the rocket before it is launched is 54 meters.

Answer: 54 meters.

Step-by-step explanation: The initial height of the rocket before it is launched is represented by the constant term in the quadratic function, which is 54. This means that the rocket's height at time t = 0 (before it is launched) is 54 meters.

To confirm this, you can plug in t = 0 into the quadratic function to get:

h(0) = -5(0)² + 42(0) + 54 = 54 meters

This means that the initial height of the rocket before it is launched is 54 meters.

Answer:

Slope = \(\frac{11\\}{10}\)

Unit Rate = \(\frac{11}{10}\)

Step-by-step explanation:

(0, 0) (10, 11)

The probability that a randomly selected 9-year-old has a BMI greater than 26.8 is 0.031. Hence, the answer is 0.031.

What is the formula to calculate standard deviation?

The formula to calculate standard deviation is:

SD = sqrt [(Σ(xi - μ)²) / N]

Where, SD = standard deviation

x = individual data points

μ = mean of the sample

N = sample size

What is the formula for z-score?

The formula for z-score is:

z = (x - μ) / σ

Where,

z = z-score

x = raw score

μ = mean of the population

σ = standard deviation of the population

Given that, The average BMI (body mass index) value of children 9 years old is 18.4 with a standard deviation of 4.5.

To find the probability that a randomly selected 9-year-old has a BMI greater than 26.8, we have to find the z-score.

z = (x - μ) / σz = (26.8 - 18.4) / 4.5z = 1.86

Now, we have to find the probability from the z-table, which is 0.9686. But we have to find the probability greater than 26.8, so we have to subtract it from 1.1 - 0.9686 = 0.0314 ≈ 0.031

Therefore, the probability that a randomly selected 9-year-old has a BMI greater than 26.8 is 0.031. Hence, the answer is 0.031.

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Answer:

A ≈ 22.2 ft²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × \(\frac{50}{360}\)

   = π × 7.13² × \(\frac{5}{36}\)

    = 50.8369π × \(\frac{5}{36}\)

    ≈ 22.2 ft² ( to the nearest tenth )

The table of values corresponding to the linear function that goes through (0, -2) and (2,0) is has points (x,y) in the following format:

(x, x - 2).

A linear function is modeled by:

y = mx + b

In which:

The line goes through (0,-2), hence the y-intercept is b = -2. The slope is given by:

m = (0 - (-2))/(2 - 0) = 2/2 = 1.

Hence the equation is:

y = x - 2.

Thus the points on the table are related as follows:

(x, x - 2).

For example

x  f(x)

0  -2

1   -1

2   0

3   1

4   2

5   3

And so on...

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Answer:

i think its 22400

Step-by-step explanation:

i times it by

The greatest number of identical packages that Shaquira can make is 2.

Given data:

Shaquira has made 86 chocolate chip cookies and 42 sugar cookies.

Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies.

To find:

The greatest number of identical packages that Shaquira can make

In order to find the greatest number of packages, we find the HCF of 86 and 42.

Write down this part from the attached image.

Here, 86 = 1 × 2 × 43, 42 = 1 × 2 × 21

Thus HCF = 1 × 2 = 2

So, Shaquira can make 2 identical packages the most.

Each package will have

(86 ÷ 2) = 43 chocolate chips and

(42 ÷ 2) = 21 sugar cookies.

For questions like these you would need to find out the Least Common Multiple, or L.C.M

If Camryn plays the trumpet and the flute today, and they both are in intervals of 11 and 3 days, you would need to find the LCM for 11 and 3.

LCM:

11 = 11, 1

3 = 3, 1

As they both have no common factors, and are prime numbers, multiply 11 x 3 = 33.

So, the least amount of days required for the trumpet and the flute to be played together is 33 days. And the interval between practising them both on the same day is 33 days.

Hence, the number of days until Camryn practices the trumpet and the flute on the same day is 33 days.

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Answer:

thanks for your points and the time

The sum of the given two vectors A and B is found to be R = 3i + 3j. The magnitude of vector R is found to be 3√2 and its direction is 45°.

The sum of the two vectors A and B is given by: R = A + B

Here, vector A = i + 4j And, vector B = 2i - j

Now, to find R, we will add the respective components of the two vectors, i.e,

R = (i + 4j) + (2i - j)

= 3i + 3j

The magnitude of vector R is given by the formula:

|R| = \(\sqrt{(R_x^2 + R_y^2)}\)

Substituting the values,

|R| = √(3² + 3²) = √18 = 3√2

The direction of vector R is given by the formula:

θ = tan⁻¹(\(R_y/R_x\))

θ = tan⁻¹(3/3)

θ = 45°

Therefore, the magnitude of vector R is 3√2 and its direction is 45°.

The sum of the given two vectors A and B is found to be R = 3i + 3j. The magnitude of vector R is found to be 3√2 and its direction is 45°.

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Answer:

it is 12

Step-by-step explanation:

for n= 36 divided by 3.

Answer:

y = x

Step-by-step explanation:

y = mx + b

m = slope, b = y - intercept

y = 1x + 0

y = x

Answer:

Step-by-step explanation:

i hope it helps :)

Answer:

\(218.18\)

Step-by-step explanation:

To find what number 96 is 44% of is we can use the formula:

\(\frac{part}{whole} =\frac{percent}{100}\)

Just substitute 94 and 44 into the equation:

\(\frac{96}{x} =\frac{44}{100}\)

\(9600=44x\\218.1818...\)

Or rounded,

\(218.18\)

Answer: $47,000 at 10% annually is ≈ $77,297.70 and $47,000 at 5% monthly is ≈ $569,611.01

Step-by-step explanation:

Use the compound interest formula. A=P(1+r/n)^nt

The threshold price F * for insurance is F * = c1c2. If F >F *, it would not be rational for Nick to purchase insurance. If F < F *, it would be rational for Nick to purchase insurance as it provides a net benefit.

To find the threshold price F *  for insurance where Nick is indifferent over buying insurance, we need to determine the point at which Nick's expected utility is the same whether he purchases insurance or not.

Let's consider the two scenarios:

1. No insurance purchased (F' = 0):
In this case, if Nick consumes c1 chocolate bars in period 1 and c2 chocolate bars in period 2, his utility function becomes U(c1;c2;0) = c1c2.

2. Insurance purchased (F' = F):
If Nick purchases insurance by paying F upfront, his utility function becomes U(c1;c2;F) = c1c2 - F.

Now, let's find the threshold price F * by comparing the expected utilities for both scenarios:

1. No insurance:
The expected utility without insurance is the utility multiplied by the probability of not having his chocolate stolen (1 - 0.25 = 0.75):
E(U(c1;c2;0)) = 0.75 * (c1c2)

2. Insurance:
The expected utility with insurance is the utility multiplied by the probability of not having his chocolate stolen, minus the cost of insurance (F), multiplied by the probability of having his chocolate stolen (0.25):
E(U(c1;c2;F)) = 0.75 * (c1c2) + 0.25 * (c1c2 - F)

To find the threshold price F *, we set the expected utilities equal to each other and solve for F:
0.75 * (c1c2) = 0.75 * (c1c2) + 0.25 * (c1c2 - F)

By simplifying the equation, we get:
0 = 0.25 * (c1c2 - F)

Solving for F gives us:
F = c1c2

Therefore, the threshold price F * for insurance is F * = c1c2.

Now let's consider the scenarios when F > F * and F < F *:

- F > F *:
If the price of insurance (F) is greater than the threshold price (F *), it means that the cost of insurance is higher than the expected loss from chocolate being stolen. In this case, it would not be rational for Nick to purchase insurance because he would be paying more than the potential loss.

- F < F *:
If the price of insurance (F) is less than the threshold price (F *), it means that the cost of insurance is lower than the expected loss from chocolate being stolen. In this case, it would be rational for Nick to purchase insurance as it provides a net benefit by reducing the potential loss.

In summary, the threshold price F * for insurance is F * = c1c2. If F > F *, it would not be rational for Nick to purchase insurance. If F < F *, it would be rational for Nick to purchase insurance as it provides a net benefit.

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A company pays $5,000 for equipment. The book value of the equipment at the end of Year 2 will be $4,000.

The book value of an asset can be calculated by subtracting the accumulated depreciation from the initial cost of the asset.

Given:

Initial cost of the equipment = $5,000

Annual depreciation = $500

After Year 1, the accumulated depreciation would be $500.

So, the book value at the end of Year 1 would be:

Book value at the end of Year 1 = Initial cost - Accumulated depreciation

Book value at the end of Year 1 = $5,000 - $500 = $4,500

After Year 2, the accumulated depreciation would be $500 + $500 = $1,000 (since depreciation is $500 per year).

So, the book value at the end of Year 2 would be:

Book value at the end of Year 2 = Initial cost - Accumulated depreciation

Book value at the end of Year 2 = $5,000 - $1,000 = $4,000

Therefore, the book value of the equipment at the end of Year 2 is $4,000. Hence, the correct answer is option a. $4,000.

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The component form of vector a⃗, rounded to the nearest hundredth, is:

a⃗ = 〈-12.99, 19.97〉

To find the component form of vector a⃗, which is expressed in magnitude and direction form as a⃗ =〈26√,140°〉, we can use the formulas for converting polar coordinates to rectangular coordinates:

x = r * cos(θ)
y = r * sin(θ)

In this case, r (magnitude) is equal to 26√ and θ (direction) is equal to 140°. Let's calculate the x and y components:

x = 26√ * cos(140°)
y = 26√ * sin(140°)

Note that we need to convert the angle from degrees to radians before performing the calculations:

140° * (π / 180) ≈ 2.4435 radians

Now, let's plug in the values:

x ≈ 26√ * cos(2.4435) ≈ -12.99
y ≈ 26√ * sin(2.4435) ≈ 19.97

Therefore, the component form of vector a⃗ is:

a⃗ = 〈-12.99, 19.97〉

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TRUE .The domain of the function is all real numbers.

FALSE , The range of the function is (0, [infinity]).

FALSE, The y-intercept is (0, 0).

FALSE , The center of symmetry is (0, 8).

True. The function f(x) = 2x^3 + 8 can take any real number as input and produce a real number as output.

False. The range of the function is all real numbers greater than or equal to 8, i.e., [8, [infinity]).

False. The y-intercept of the function is (0, 8), meaning that when x = 0, the output of the function is 8.

False. The function f(x) = 2x^3 + 8 does not have a center of symmetry, as it is an odd degree polynomial.

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Answer:

B) 2.5

Step-by-step explanation:

12x+5=8x+15

12x-8x=15-5

4x=10

x=10/4

x=2.5