Find the missing angle.
у
37
58°
y = [?]
Enter the number that belongs in the green box.

The given sample data has a mean of 17.00, a median of 15, a mode of 15, and a range of 21.

To find the mean, add up all the values in the sample and divide by the total number of values. For the given sample data (12, 11, 15, 16, 24, 15, 25, 21, 4), the mean is calculated as (12+11+15+16+24+15+25+21+4)/9 = 153/9 = 17.00 (rounded to two decimal places).

To find the median, arrange the values in ascending order and find the middle value. Since the sample has an odd number of values, the median is the middle value, which is 15.To find the mode(s), identify the value(s) that appear(s) most frequently. In this case, 15 appears twice, which is more frequent than any other value, so the mode is 15.

To find the range, subtract the minimum value from the maximum value. The minimum value in the sample is 4, and the maximum value is 25, so the range is 25 - 4 = 21.

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Answer:

The mistake that Andy made was on step 2 when he multiplied only the variables by 12.

Step-by-step explanation:

When you're solving an equation and are multiplying one side by a number, you need to multiply the other side by that number as well to keep the equation true. Since Andy multiplied only the variables and not the constants on each side of the equation, that means the equation would no longer be valid, and solving it would provide a wrong answer.

Answer:

person above me is right. that's is the answer.

whats the question

ill edit the answer in you put the question

Answer:

m∠3 = 78

Step-by-step explanation:

Okay, since a triangle has 3 sides, we only need to find the measure of m∠3.

A triangle is made up of 180 degrees, so we can make an equation with 180 as what the equation is equal to.

Since m∠1 = 70, and m∠2 = 32, we will add those together with a variable x,

70+32+x=180

70 plus 32 is 102.

102+x=180

To get 102 to the other side we need to do the opposite of addition, which is subtraction.

180-102=78

So the answer is 78.

Answer: Option 2

Step-by-step explanation:

Let f(y)=x.

\(x=2y+3\\\\x-3=2y\\\\y=\frac{1}{2}x-\frac{3}{2}\\\\f^{-1}(x)=\frac{1}{2}x-\frac{3}{2}\)

The inverse of the function is,

⇒ f ⁻¹(x) = 1/2 (x - 3)

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

⇒ f (x) = 2x + 3

Now,

We can find the inverse of function as;

⇒ f (x) = 2x + 3

Put y = f (x);

⇒ y = 2x + 3

Solve for x;

⇒ y - 3 = 2x

⇒ x = 1/2 (y - 3)

⇒ f ⁻¹(x) = 1/2 (x - 3)

Thus, The inverse of the function is,

⇒ f ⁻¹(x) = 1/2 (x - 3)

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The year it will take Mussman to reach a population of 27,000 resident is 10.7 years

Population growth is the increase in the number of people in a population or dispersed group.

We use exponential function when calculating increase in population per time

p(t) =p(o) e^kt

27000 = 13500 e^0.065t

e^0.065t = 27000/13500

0.065t = ln 2

0.065t = 0.693

t = 0.693/0.065

t = 10.7 years

therefore it will take 10.7years for the resident of Mussman to reach a population of 27000

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Answer:

4 or -4

Step-by-step explanation:

Y is directly proportional to x^2 means there is a constant, k, such that y=kx^2.

We are given y=8 when x=2. This information will allow us to find k in the equation y=kx^2.

8=k(2)^2

8=k(4)

This implies k=2 since 2(4)=8.

So the equation for any pair (x,y) is y=2x^2.

We want to find x when y=32.

32=2x^2

32/2=2x^2/2

16=x^2

This implies x=4 or -4.

The given limit can be expressed as the definite integral: lim (n→∞) n ∑(i=1 to n) i⁶/n⁷ = ∫[1/n, 1] x⁶ dx

To express the given limit as a definite integral, we need to determine the appropriate function f(x) and the integration limits b and 1.

Let's start by rewriting the given limit:

lim (n→∞) (1/n) ∑(i=1 to n) \(i^6/n^7\)

Notice that the term i⁶/n⁷ can be written as (i/n)⁶/n.

Therefore, we can rewrite the above limit as:

lim (n→∞) (1/n) ∑(i=1 to n) (i/n)⁶/n

This can be further rearranged as:

lim (n→∞) (1/n^7) ∑(i=1 to n) (i/n)⁶

Now, let's define the function f(x) = x⁶, and rewrite the limit using the integral notation:

lim (n→∞) (1/n^7) ∑(i=1 to n) (i/n)⁶ = ∫[a,b] f(x) dx

To determine the integration limits a and b, we need to consider the range of values that x can take. In this case, x = i/n, and as i varies from 1 to n, x varies from 1/n to 1. Therefore, we have a = 1/n and b = 1.

Hence, the given limit can be expressed as the definite integral:

lim (n→∞) n ∑(i=1 to n) i⁶/n⁷ = ∫[1/n, 1] x⁶ dx

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Given:

Amount needed = $12,300

Time = 4 years

Interest = 6% ==> 0.06

Compounded annually.

Let's find the present value.

To find the present value, apply the compounded interest formula:

Where:

A is the amount needed = $12,300

r is the interest rate = 0.06

t is the time = 4 years

P is the principa or the present value.

Ipput values into the formula and solve for P.

We have:

Divide both sides by 1.26245:

Therefore, the present value is $9742.75

ANSWER:

$9742.75

Answer:

x = 5.200

Step-by-step explanation:

Given equation is,

x³ - 4.6x² - 7.03x = -20.332

x³ - 4.6x² - 7.3x + 20.332 = 0

By graphing this equation with the help of a graphing calculator,

Solutions of the equation are the points where y = 0.

In other words, x intercepts are the solutions.

Solutions for the given equation are,

x = -2.3, 1.7 and 5.2

Therefore, solution for the given equation in the interval [4, 7] is x = 5.200

The rate of change is found using the slope formula

m = ( y2-y1)/(x2-x1)

We have two points

( 1995, 2.54) ( 2010, 3.18)

m = (3.18-2.54) / (2010-1995)

=.64/15

$.042666666 per year

Rounding to the nearest cent

$.04 per year

We know that the price went up from 1995 to 2010 so the price increased

It increased an average of $.04 each year

A. The price of a gallon of gasoline increased by an average of $_.04__ per year from 1995 to 2010

Before adding equations, one must first understand the problem and identify what you are trying to solve.

we must also make sure that both equations are written in the same form, and that all variables are written in the same order. we should also check to make sure that each equation contains the same number of terms and that all terms have the same variables.

Finally, we should check to make sure that the equations have the same number of unknown, so that the equations can be added together. If any of these conditions are not met, we should simplify the equations or manipulate them until all conditions are met.

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Using the Counting the faces of two dice,

the atleast 17 number of faces are possible on the combination of two dice.

First, we have to count the favorable cases,

We know both dice have atleast 6 faces.

It gives 6 favorable cases for a sum of 7.

If we can count them if mean even if dice had more than 6 faces, will matter of for sum of 7.

Now, the mean, we need 6× 4/3=8 (favorable cases for the sum of 10)

If we count 3 favorable cases for each having 6 faces.

For more than 9 faces on a dice matter give the denominator (sample space) are the same for both sum of 7 and the sum of 10, and the probability of one is in proportion to the other.

It mean, additional 5 cases must be ( 7,2), (2,7), (8,2), (2,8) ,(9,1)

So , one of the dice has 8 faces and the other has atleast 9 faces.

Now, we must have atleast 17 combined faces of two dice for probability . So, we get if 12 with configration of 8 faces on one dice.

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The circumference of the circle is 6.28 yards.

"It  is the length of the boundary of the circle."

C = 2 × π × r, where 'r' is the radius of the circle.

For given example,

r = 1 yd.

π = 3.14

Using the formula for the circumference of circle,

⇒ C = 2 × π × r

⇒ C = 2 × 3.14 × 1

⇒ C = 6.28 yd.

Therefore, the circumference of the circle is 6.28 yards.

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Given :

a) total amount of money she earns for assembling

b) total no. of toys assembled by Fiona by earning:

convert $459 into cents

divide the sum by the cost of a single toy

hence, she assembled 540 toys and earned $459 out of them.

c) no. of toys she must assemble to earn

convert the sum into cents

divide the sum by the cost of a single toy

hence, she must assemble 235 toys in order to earn $200

convert the sum into cents

divide the sum by the cost of a single toy

hence,she must assemble 729 toys in order to earn $620

A statement which would be the best measures of center and variation to use to compare the data include the following: B. Both distributions are nearly symmetric, so the mean and the standard deviation are the best measures for comparison.

In Mathematics and Statistics, skewness can be defined as a measure of the asymmetry of a box plot (box-and-whisker plot) and as such, a box plot (box-and-whisker plot) has a normal distribution when it is symmetrical.

By critically observing the table which represent the test scores of students who studied for a test as a group (Group A) and students who studied individually (Group B), we can reasonably infer and logically deduce that the mean and the standard deviation are the best measures for comparison because both data distributions are nearly symmetric.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

2/3

Step-by-step explanation:

There's two different ideas that might be making this problem a challenge for you. Real quick, let's look at what a log is. Then we can solve it, but maybe exponents are giving you a hard time as well.

A logarithm is just a different way to write exponents. The base (subscript) in a log is the base in an exponent expression (the regular-sized number that the exponent is sitting on). All by itself on the OTHER side of the equal sign from the "log" expression is the number that is the exponent in the exponent expression. Then the other number (regular-sized) that is WITH the log is the answer in the exponent expression. See image.

log_27 (9) = ?

can be rewritten as:

27^? = 9

see image.

To solve without a calculator, you can use a common base.

27 is 3^3 and 9 is 3^2. So they are both powers of 3. An exponent rule that can help is that if you have a power to a power, you multiply the exponents.

Sorry, I got solving using a box instead of an x in the image. But if you need to show work just write an x instead of the box. See image.

Answer: C. 2/3

Step-by-step explanation:

x + yi = (1 + i)⁴

then -4 + 4 = x

The inequality is (3,∞) < x < 4.

A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a b indicates that an is smaller than b.

When a > b is used, it indicates that an is bigger than b.

Given Data

x is a number less than 4

x<4

Numbers which are less than 4 are 3 to infinity

So,

The inequality is:

(3,∞) < x < 4

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The steps to connect the components for an internet connection are as follows:

Step 1: Add the cable modem to the workspace. Modems are small boxes that are responsible for converting digital signals to analog signals and vice versa. Modems are necessary for accessing the internet. Therefore, it is important to add the cable modem to the workspace first.

Step 2: Use an RG-6 coaxial cable to connect the modem to the WAN connection on the wall plate.A WAN (Wide Area Network) connection is a type of internet connection that is typically used for larger networks. In order to connect a cable modem to the internet using a WAN connection, an RG-6 coaxial cable is needed.

Step 3: Connect the computer to the cable modem.In order to access the internet, the computer must be connected to the cable modem. This can be done using an Ethernet cable.

Step 4: Connect the modem to the power outlet.Modems require power in order to function. Therefore, it is necessary to connect the modem to a power outlet.

Step 5: Verify the internet connection using the network. After completing the above steps, the internet connection can be verified by opening a web browser and attempting to access a webpage. If the webpage loads successfully, the internet connection has been successfully established.Important: It is important to not click Score Lab until after all tasks have been attempted. Once Score Lab is clicked, the user will advance to the next lab question and will not be able to restart this lab. This applies to all subsequent labs in this exam.

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We need to find the probability of exactly three successes in six trials of a binomial experiment. Probability of success 50% (no success is 50%).

To find this probability, we need to use the following formula for Bernoulli Trials (or Binomial Experiment):

The combinations are given by:

Then, we have:

Thus, the probability of exactly three successes in six trials of a binomial experiment (which the probability of success is 50%) is 0.0625.

Rounding to the nearest tenth is about p = 0.1 (1/10) or 10%.

The square root of the quantity x plus 7 end quantity minus 1 equals x=2.

To find the square root:

Check for extraneous solutions:

Therefore, the square root of the quantity x plus 7 end quantity minus 1 equals x = 2.

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The correct question is given below:
The square root of the quantity x plus 7 end quantity minus 1 equals x

(A) Total number of points served by Samson and multiply by 100  (B) Null hypothesis(H0) and Alternative hypothesis (Ha) (C)  there would be a 24% chance of observing a difference in performance as extreme as the one observed in the data.

(D) Based on the p-value of 0.24, we do not have strong evidence to reject the null hypothesis. (E) it would be a Type II error. (F) Type II error would mean that we concluded there is no difference in Samson's performance when serving and when his opponent is serving, but in reality, there is a difference. (G) To reduce the likelihood of a Type II error occurring, we can increase the sample size (H)  No, we cannot conclude that Samson's serving is the cause of the difference in his ability to win points when serving compared to when his opponent is serving

a) The difference in the percentage of points won when serving and when the opponent is serving can be calculated by subtracting the percentage of points won when the opponent is serving from the percentage of points won when serving.  To find the percentage of points won when serving, we divide the number of points won when serving by the total number of points served by Samson and multiply by 100. Similarly, to find the percentage of points won when the opponent is serving, we divide the number of points won when the opponent is serving by the total number of points served by the opponent and multiply by 100.

b) The hypotheses we are interested in testing are:
- Null hypothesis (H0): There is no difference in Samson's performance when serving and when his opponent is serving.
- Alternative hypothesis (Ha): Samson performs better when serving compared to when his opponent is serving.

c) A p-value of 0.24 indicates that if the null hypothesis were true, there would be a 24% chance of observing a difference in performance as extreme as the one observed in the data. In other words, the p-value represents the probability of obtaining the observed difference in performance or a more extreme difference, assuming that there is no actual difference in Samson's performance when serving.

d) Based on the p-value of 0.24, we do not have strong evidence to reject the null hypothesis. This means that the data does not provide convincing evidence that Samson plays better when serving compared to when his opponent is serving.

e) If our conclusion from part d was in error, it would be a Type II error. This occurs when we fail to reject the null hypothesis even though it is false. In this case, it would mean that there is a difference in Samson's performance when serving, but we failed to detect it.

f) In the context of this question, a Type II error would mean that we concluded there is no difference in Samson's performance when serving and when his opponent is serving, but in reality, there is a difference. This could potentially lead to underestimating Samson's ability to perform better when serving.

g) To reduce the likelihood of a Type II error occurring, we can increase the sample size. By collecting more data, we can increase the power of our test and improve our ability to detect a difference in performance if it truly exists. Additionally, we can also adjust the significance level of our test (e.g., from 0.05 to 0.01) to make it more likely to detect smaller differences.

h) No, we cannot conclude that Samson's serving is the cause of the difference in his ability to win points when serving compared to when his opponent is serving. The data provided only shows an association between serving and winning points, but it does not establish a causal relationship. Other factors, such as skill, strategy, or the opponent's performance, could also contribute to the difference observed. To establish causality, further investigation and controlled experiments would be needed.

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Answer:

Here,

initial price (p)=$6500

Time from 2007 to 2020 (t)= 13yrs.

rate (r)=14.3%

now,

\(present \: price \: (pt) = p(1 - \frac{r}{100} )\)

or, pt = $6500(1-14.3/100)

by simplifying it we get,

The, present price is $5570.5.

now, if you are searching for depreciated amount only then,

depreciated amount =$6500-$5570.5

=$929.5.

Hope it helps...

Answer:

1) 9

2) -3

3) -14

4) -27

5) 40

6) -30

7) -1

8) -81

Each Sum Or Difference:- (1). 9   (2). -3    (3). -14   (4). -27    (5). 40   (6). -30    (7). -1    (8). -81

As we know,

Suppose a and b be two numbers then to find the sum or difference of these two, we can follow some conditions that are given below:

+ or - becomes - and the answer has a sign of greater one from them

+ or + becomes + and answer has +ve sign

- or + becomes - and the answer has a sign of greater one from them

- or - becomes + but the answer has a -ve sign

Then, according to the above conditions the solutions are given below:

1). 12 + (-3) = 9

2). -7 + 4 = -3

3). -8 + (-6) = -14

4). -42 + 15 = -27

5). 32 - (-8) = 32 + 8 = 40

6). -18 - 12 = -30

7). -15 - (-14) = -15 + 14 = -1

8). -76 - 5 = -81

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Answer: 16.7%

I took the k12 unit test

The inflation rate is given by the percentage error and is given by the equation A = 16.71 %

What is Percentage Error?

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage error is the difference between the measured value and the true value , as a percentage of the true value

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Given data ,

Let the inflation rate of percentage error be represented as A

Let the cost of the Jolly Peanut butter be = $ 3.59

So , the original cost = $ 3.59

Let the increased rate of Jolly Peanut butter be = $ 4.19

So , the increased rate = $ 4.19

Now , the inflation rate is given by the equation

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Substituting the values in the equation , we get

Inflation rate A = ( ( 4.19 - 3.59 ) / 3.59 ) x 100

On simplifying the equation , we get

Inflation rate A = ( 0.6 / 3.59 ) x 100

Inflation rate A = 0.16713 x 100

Inflation rate A = 16.71 %

Therefore , the value of A is 16.71 %

Hence , the inflation rate is 16.71 %

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Answer:

Link to the Answer:

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Step-by-step explanation:

Hope it Helps!!!!

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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9514 1404 393

Answer:

  11 cartons

Step-by-step explanation:

By shipping all 96 boxes as large boxes, the merchant will have shipped

  (96 boxes)/(8 boxes/large carton) = 12 large cartons*

He can ship as many boxes in 4 cartons of small boxes as in 5 cartons of large boxes. So trading 5 cartons of large boxes for 4 cartons of small boxes, he can reduce the number of cartons shipped by 1.

The merchant shipped 11 cartons:

  7 cartons of large boxes (56 large boxes)

  4 cartons of small boxes (40 small boxes)

__

Any further such trade would reduce the number of large boxes to fewer than small boxes, violating the problem constraint.

_____

* In this expression, we use the term "large carton" to mean "carton of large boxes".

Since both sides are equal, we have shown that ∑(i=1 to 6) (dx_i + e) = d(∑\((i=1 to 6) x_i\)) + 6e. This represents the summation of the terms \((5x_3 + i)\) for i = 1 to 6.

To show that ∑(i=1 to 6) \((dx_i + e)\)= d(∑(i=1  \(x_i\)) + 6e, we can expand both sides and compare.

Left-hand side:

∑\((i=1 to 6) (dx_i + e) = (dx_1 + e) + (dx_2 + e) + (dx_3 + e) + (dx_4 + e) +\)(dx_5 + \(e) + (dx_6 + e)\)

                        = \(dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6 + e + e + e + e\)+ e + e

                        = \((dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6) + 6e\)

Right-hand side:

d(∑\((i=1 to 6) x_i)\)+ 6e = d\((x_1 + x_2 + x_3 + x_4 + x_5 + x_6)\)+ 6e

Now, let's compare the two sides:

Left-hand side: \((dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6)\) + 6e

Right-hand side: d\((x_1 + x_2 + x_3 + x_4 + x_5 + x_6)\) + 6e

Since both sides are equal, we have shown that ∑\((i=1 to 6) (dx_i + e)\) = d(∑(i=1 to 6)\(x_i)\) + 6e.

To represent the equation\((5x_3 + 4) + (5x_3 + 5) + (5x_3 + 6) + (5x_3 +\)7) + \((5x_3 + 8) + (5x_3 + 9)\) using a Sigma operator notation, we can write it as:

∑\((i=1 to 6) (5x_3 + i)\)

This represents the summation of the terms \((5x_3 + i)\)for i = 1 to 6.

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The orthogonal basis for the subspace W is { -1, (0, sqrt(2y^2) + sqrt(6y^6))/(3sqrt(2y^2 + 6y^6)), (sqrt(2)y^2 + (sqrt(2)sqrt(6)y^6)/(3sqrt(2y^2 + 6y^6)), sqrt(2)sqrt(6)y^6 - (sqrt(2)sqrt(6)y^6)/(3sqrt(2y^2 + 6y^6)), sqrt(2/6))/sqrt(2y^4 + 12y^12 + 1/3) }.

To apply the Gram-Schmidt Process to the given vectors, we will first normalize each vector to obtain a unit vector. Then, we will subtract the projection of each subsequent vector onto the previous vectors to obtain orthogonal vectors. Finally, we will normalize the orthogonal vectors to obtain an orthogonal basis for the subspace W.

Let's begin:

1. Normalize the first vector -3:

\(v1 = (-3)/sqrt((-3)^2) = (-3)/3 = -1\)

2. Normalize the second vector (0, sqrt(2y^2), sqrt(6y^6)):

\(v2 = (0, sqrt(2y^2), sqrt(6y^6))/sqrt(0^2 + (sqrt(2y^2))^2 + (sqrt(6y^6))^2)\)

\(v2 = (0, sqrt(2y^2), sqrt(6y^6))/sqrt(2y^2 + 6y^6)\)

3. Subtract the projection of v2 onto v1:

proj_v2_v1 = ((v2 . v1)/(v1 . v1)) * v1

where . represents the dot product

v2_orth = v2 - proj_v2_v1

v2_orth = (0, sqrt(2y^2), sqrt(6y^6))/sqrt(2y^2 + 6y^6) - ((0 + sqrt(2y^2) + sqrt(6y^6))(-1/3))(-1)

v2_orth = (0, sqrt(2y^2), sqrt(6y^6))/sqrt(2y^2 + 6y^6) + (sqrt(2y^2) + sqrt(6y^6))/3

4. Normalize the orthogonal vector v2_orth:

u2 = v2_orth/|v2_orth| = (0, sqrt(2y^2) + sqrt(6y^6))/(3sqrt(2y^2 + 6y^6))

5. Normalize the third vector (sqrt(2)y^2, sqrt(2)sqrt(6)y^6, sqrt(2/6)):

v3 = (sqrt(2)y^2, sqrt(2)sqrt(6)y^6, sqrt(2/6))/sqrt((sqrt(2)y^2)^2 + (sqrt(2)sqrt(6)y^6)^2 + (sqrt(2/6))^2)

v3 = (sqrt(2)y^2, sqrt(2)sqrt(6)y^6, sqrt(2/6))/sqrt(2y^4 + 12y^12 + 1/3)

6. Subtract the projection of v3 onto v1 and v2:

proj_v3_v1 = ((v3 . v1)/(v1 . v1)) * v1

proj_v3_v2 = ((v3 . u2)/(u2 . u2)) * u2

v3_orth = v3 - proj_v3_v1 - proj_v3_v2

v3_orth = (sqrt(2)y^2, sqrt(2)sqrt(6)y^6, sqrt(2/6))/sqrt(2y^4 + 12y^12 + 1/3) - (sqrt(2)y^2)(-1) - ((sqrt(2)sqrt(6)y^6)/(3sqrt(2y^2 + 6y^6)))(sqrt(2) + sqrt(6))

v3_orth = (sqrt(2)y^2 + (sqrt(2)sqrt(6)y^6)/(3sqrt(2y^2 + 6y^6)), sqrt(2)sqrt(6)y^6 - (sqrt(2)sqrt(6)y^6)/(3sqrt(2y^2 + 6y^6)), sqrt(2/6))/sqrt(2y^4 + 12y^12 + 1/3)

7. Normalize the orthogonal vector v3_orth:

u3 = v3_orth/|v3_orth| = (sqrt(2)y^2 + (sqrt(2)sqrt(6)y^6)/(3sqrt(2y^2 + 6y^6)), sqrt(2)sqrt(6)y^6 - (sqrt(2)sqrt(6)y^6)/(3sqrt(2y^2 + 6y^6)), sqrt(2/6))/sqrt(2y^4 + 12y^12 + 1/3)

Therefore, the orthogonal basis for the subspace W is { -1, (0, sqrt(2y^2) + sqrt(6y^6))/(3sqrt(2y^2 + 6y^6)), (sqrt(2)y^2 + (sqrt(2)sqrt(6)y^6)/(3sqrt(2y^2 + 6y^6)), sqrt(2)sqrt(6)y^6 - (sqrt(2)sqrt(6)y^6)/(3sqrt(2y^2 + 6y^6)), sqrt(2/6))/sqrt(2y^4 + 12y^12 + 1/3) }.

To know more about Gram-Schmidt Process refer here:

https://brainly.com/question/30761089

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