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The closest projection will have a value of -29/360.

we will follow these steps to use the Gram-Schmidt orthonormalization procedure for producing an orthonormal basis for the subspace spanned by 1, x, and x²,

Set u₁ = 1, a unit vector.

Set v₂ = x and u₂ = v₂ / ||v₂||.

Set v₃ = x² - (x², u₁)u₁ - (x², u₂)u₂, and u₃ = v₃ / ||v₃||.

Thus we get the orthonormal basis for the subspace spanned by 1, x, and x² to be {u₁, u₂, u₃}.

Now we will use the formula for the projection of a vector onto a subspace to find the closest-point projection of x³ into this subspace,

proj_subspace(x³) = (x³, u₁)u₁ + (x³, u₂)u₂ + (x³, u₃)u₃

The inner products will be calculated as follows:

(x³, u₁) = ∫x³ X 1 dx = 1/4

(x³, u₂) = ∫ x³ X x dx = 1/5

(x³, u₃) = ∫ x³ * (x² - (x², u₁)u₁ - (x², u₂)u₂) dx

Here all the integrals will have limits of 0 and 1.

Hence we get

= 1/9 - 1/4 X 1/2 - 1/5 X 1/3

= 1/9 - 1/8 - 1/15

= (40 - 45 - 24)/360

= -29/360

Thus, the projection of x³ onto the subspace spanned by 1, x, and x² is:

proj_subspace(x³) = 1/4 X u₁ + 1/5 X u₂ + (1/9 - 1/4 X 1/2 - 1/5 X 1/3) X u₃

This projection is the closest point in the subspace to x³, in the sense that the distance between x³ and proj_subspace(x³) is minimized.

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Expected frequencies must be equal for all groups is correct option.

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The correct answer is option B.

The observation of a giant storm on Saturn from spacecraft Cassini indicates that lightning was not detected in the giant storm.

Usually Mega storms on Saturn happen on every 20 to 30 years.

Through the Cassini spacecraft, scientists could see a massive storm in December 2010. They saw that the storm waves were spreading from the planet's centre and that it was seen as a ringed globe.

The storm waves covered the whole surface of Saturn and had a diameter of around 190,000 miles or 300,000 kilometres.

Simply said, this enormous storm is also known as the Great Northern Storm or the Great White Spot.

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Long division can be used to determine the  absolute value of x[0], x[-1], and x[-2] when the roc is known. To do this, divide the roc (113) by the coefficient of the highest power in the polynomial (x2). Then, divide the remainder (3) by the coefficient of the next highest power (x), which gives x[-1] = 3. Finally, divide the remainder (8) by the coefficient of the lowest power (1), which gives x[-2] = 8.

To use long division to determine the values of x[0], x[-1], and x[-2], begin by dividing the roc (113) by the coefficient of the highest power in the polynomial (x2). This gives a result of 113/x2 = 10. This means that x[0] = 10. This number is then used as the divisor for the next step, which is to divide the remainder (3) by the coefficient of the next highest power (x). This gives a result of 3/x = 3, so x[-1] = 3. Finally, divide the remainder (8) by the coefficient of the lowest power (1), which gives 8/1 = 8, so x[-2] = 8. This process can be repeated to determine the values of x[n] for any polynomial.

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As per the graph of H(w) when w draws near to no the worth of H(w) gets extremely high.

The graph of a function f  is the arrangement of all places in the plane of the structure (x, f(x)). We could likewise characterize the diagram of f to be the chart of the situation y = f(x). In this way, the chart of a capability if an exceptional instance of the diagram of a situation.

Think about the gave diagram of H(w)

If we observer the diagram of the function H(w) we reasoned that as the worth of w pushes toward 0 the worth of H(w) increments quickly.

The worth of H(W) is getting increasingly high when we are moving towards 0.

So, we can say that

When W → 0, H(w) → ∞

Thus, As per the chart of H(w) when w draws near to no the worth of H(w) gets extremely enormous.

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The best description of the dot plot is;  median scores are the same for both players

A dot plot is defined as a simple plot that displays data values as dots above a number line. Now, dot plots show the frequency with which a specific item appears in a data set. Dot plots shows the distribution of the data.

The median of a data set is simply defined as the value in the middle of that same data set when arranged in ascending order.

From player 1, the data set when arranged in ascending order are;

8, 10, 10, 10, 12, 12, 14, 16, 16

In this case, the exact middle term is 12 which will be the median

For player 2, the data set when arranged in ascending order are;

0, 2, 6, 10, 12, 16, 18, 22, 22

In this case, the exact middle term is 12 which will be the median.

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The production figure to maximize the profit is is Z = 15x + 10y  subject to

2x + 3y ≤ 600 ; 2x + y ≤ 480  ; x,y≥ 0 .

In the question ,

it is given that ,

a company named Universal Electric manufactures sell two models of lamps that is Lamp X and Lamp Y  and

Whose profit is  $ 15 and $ 10 respectively.

let the number units the company manufactures of lamp X be = x units

let the number units the company manufactures of lamp Y be = y units

let the total profit be = Z ,

So , the profit to maximize be Z = 15x + 10y

worker A assembles Lamp X in 20/60 hours and Lamp Y in 20/60 hours ; and that he is available for 100 hours per month;

So , the inequality is

(20/60)x + (30/60)y ≤ 100.

20x + 30y ≤ 6000

2x + 3y ≤ 600

Similarly , worker B assembles Lamp X in 20/60 hours and Lamp Y in 10/60 hours ; and that he is available for 80 hours per month;

the inequality will be ,

(20/60)x + (10/60)y ≤ 80.

20x + 10y ≤ 4800

2x + y ≤ 480  .

Therefore , the LPP to maximize the profit is Z = 15x + 10y  subject to

2x + 3y ≤ 600 ; 2x + y ≤ 480  ; x,y≥ 0 .

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Answer: 100

Step-by-step explanation:

You can set up the equation:

50 / (1/2)

Dividing by 1/2 is thhe same as multiplying by 2.

50 / (1/2) = 100

50(2) = 100

Answer:

60% because the total should be 100% and if you take 40% away you should be left with 60%

We can say that the role of galaxies, planets, satellites, comets and asteroids, in the conformation of the universe, is based on being elements to structure it.

In physics, it is mentioned that the universe is all physical existence that exists, this goes from our planet to what is found abroad.

Within the universe, as an entity, how to find different elements that structure it, for example, we have:

¡Hope this helped!

11

According to question

-5xy²+7x²y+3y³-8x³

putting x=2 and y=3

⇒ -5(2)(3)²+7(2)²(3)+3(3)³-8(2)³

⇒-5(18)+7(12)+3(27)-8(8)

⇒-90+84+81-64

∴  11

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The correct question is find the value of equation if x=2 and y=3 , -5xy² + 7x²y+3y³ - 8x³

Answer: D

8x + 1x + 1 x - 2y

The semicircle above has a radius of r inches, The distance between the chord and the diameter in terms of r is √5 r/3 inches.

A chord of a circle can be defined as a line segment connecting any two points on the circumference. It should be noted that the diameter is the longest chord of a circle which passes through the center of the circle.

To find the distance required one can use either the Pythagorean theorem or the trigonometric ratios. Let the semicircle have center O. The diameter AB has length 2r. Because chord CD is 2/3 of the length of the diameter,

CD=2/3(2r) = 4r/3

let the distance between diameter AB and chord CD be x inches. To find x draw a right triangle connecting center O, the midpoint, E of chord CD, and point C . Using Pythagorean theorem here,

r² = x² + (CD/2)²

=> r² = x² + (2r/3)²

=> r² = x² + 4r²/9

=> x² = r² - 4r²/9 = 5r²/9

=> x = √5 r/3

Hence, the distance between the chord and the diameter in terms of r is √5r/3..

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There is an imbalance between males and females, with a ratio of 1.5 men to every woman in the population.

Which age structure diagram represents a population's ages the best?

Hence, there is an imbalance between males and females, with a ratio of 1.5 men to every woman in the population.

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Answer:

Compounded Semiannually: [tex](1.03454)^t[/tex] and APR = 3.454%

Compounded Quarterly: [tex](1.03469)^t[/tex] and APR = 3.469%

Step-by-step explanation:

The Compound Interest Formula is as follows: [tex]A = P(1 + \frac{r}{n})^{nt}[/tex], which can also be written as: [tex]A = P((1 + \frac{r}{n})^n)^t[/tex], using properties of exponents. This is crucial since we want one value inside the parenthesis to calculate the APR (Annual Percentage Rate). Since we want the APR, the only thing we really care about is the [tex](1 + \frac{r}{n})^n[/tex], but this is going to be our APR + 1.

In the question, it's formatted as: [tex]b^t[/tex], and this inside part is going to be our b, so: [tex]b = (1 + \frac{r}{n})^n[/tex], and to calculate the APR we simply subtract 1.

Compounded semiannually means the interest is compounded twice a year, so n = 2. We are also given the interest to be 3.425% which in decimal form is 0.03425

Plugging this into the formula stated above we get: [tex]b = (1 + \frac{0.03425}{2})^2 \approx 1.03454[/tex]

So we have the form:

[tex](1.03454)^t[/tex]

With our APR simply being the base - 1:

[tex]APR \approx 0.03454[/tex]

We multiply this by 100 to get it in percentage form:

[tex]APR\approx 3.454\%[/tex]

Compounded quarterly means the interest is compounded four times a year, so n = 4. Plugging in known values we get:

[tex]b = (1 + \frac{0.03425}{4})^4 \approx 1.03469[/tex]

So we have the form:

[tex](1.03469)^t[/tex]

With our APR simply being the base - 1

[tex]APR \approx 0.03469[/tex]

Multiply this by 100 to get it in percentage form:

[tex]APR \approx 3.469\%[/tex]

Answer:

[tex]\begin{array}{|c|c|c|}\cline{1-3} \vphantom{\dfrac12} \sf koooAccount& b^t& \sf Annual\;Percentage\;rate \\\cline{1-3} \vphantom{\dfrac12} \sf compounded\;annually& (1.03425)^t& 3.425\%\\\cline{1-3} \vphantom{\dfrac12} \sf compounded\;semiannually & \left(1.03454\right)^t &3.454\% \\\cline{1-3} \vphantom{\dfrac12} \sf compounded\;quarterly & \left(1.03469\right)^t& 3.469\%\\\cline{1-3} \vphantom{\dfrac12} \sf compounded\; daily& \left(1.03484\right)^t& 3.484\%\\\cline{1-3} \end{array}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

From inspection of the compound interest formula:

[tex]\implies b^t=\left[\left(1+\dfrac{r}{n}\right)^n\right]^t[/tex]

To find the annual percentage rate:

[tex]\implies APR=(b-1)\times 100[/tex]

Given:

Substitute the values into the formula for [tex]b^t[/tex]:

[tex]\implies b^t=\left[\left(1+\dfrac{0.03425}{1}\right)^1\right]^t[/tex]

[tex]\implies b^t=\left(1.03425\right)^t[/tex]

Therefore, the annual percentage rate is:

[tex]\implies APR=(1-1.03425) \times 100[/tex]

[tex]\implies APR=0.03425 \times 100[/tex]

[tex]\implies APR=3.425\%[/tex]

Given:

Substitute the values into the formula for [tex]b^t[/tex]:

[tex]\implies b^t=\left[\left(1+\dfrac{0.03425}{2}\right)^2\right]^t[/tex]

[tex]\implies b^t=\left(1.03454326...\right)^t[/tex]

[tex]\implies b^t=\left(1.03454\right)^t[/tex]

Therefore, the annual percentage rate is:

[tex]\implies APR=(1-1.03454) \times 100[/tex]

[tex]\implies APR=0.03454 \times 100[/tex]

[tex]\implies APR=3.454\%[/tex]

Given:

Substitute the values into the formula for [tex]b^t[/tex]:

[tex]\implies b^t=\left[\left(1+\dfrac{0.03425}{4}\right)^4\right]^t[/tex]

[tex]\implies b^t=\left(1.03469241...\right)^t[/tex]

[tex]\implies b^t=\left(1.03469\right)^t[/tex]

Therefore, the annual percentage rate is:

[tex]\implies APR=(1-1.03469) \times 100[/tex]

[tex]\implies APR=0.03469 \times 100[/tex]

[tex]\implies APR=3.469\%[/tex]

Given:

Substitute the values into the formula for [tex]b^t[/tex]:

[tex]\implies b^t=\left[\left(1+\dfrac{0.03425}{365}\right)^{365}\right]^t[/tex]

[tex]\implies b^t=\left(1.03484162...\right)^t[/tex]

[tex]\implies b^t=\left(1.03484\right)^t[/tex]

Therefore, the annual percentage rate is:

[tex]\implies APR=(1-1.03484) \times 100[/tex]

[tex]\implies APR=0.03484 \times 100[/tex]

[tex]\implies APR=3.484\%[/tex]

Note: There is an error in the given table:  the given "compounded daily" rate is incorrect.

If the perimeter of the rectangle is 48 cm, its length and width is equal to 16 cm and 8 cm respectively.

Mathematically, the perimeter of a rectangle can be calculated by using this equation;

P = 2(L + W)

Where:

Since the length is twice the​ width, we have;

L = 2W

Substituting the given parameters into the perimeter formula, we have;

48 = 2(2W + W)

48 = 6W

W = 48/6

Width, W = 8 cm.

For the length of this rectangle, we have;

L = 2W

L = 2(8)

L = 16 cm.

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The interval containing the middle-most76% of sample means  [tex]102.836 < \mathrm{x} < 137.164[/tex].

As per the data given in the above question,

A distribution of values is normal with a mean of [tex]\mu=120[/tex].

A standard deviation of [tex]\sigma=21[/tex].

Drawing samples of size n=13.

The middle-most76% of sample means.

Find the interval containing the middle-most76% of sample means?

[tex]\mathrm{P}(-\mathrm{z} < \mathrm{x} < \mathrm{z})=0.76\\\mathrm{P}(\mathrm{x} < \mathrm{z})-\mathrm{P}(\mathrm{x} < -\mathrm{z})=0.76\\[/tex]

Further

[tex]\mathrm{P}(\mathrm{x} < -\mathrm{z})=\mathrm{P}(\mathrm{x} > \mathrm{z})[/tex]

[tex]\mathrm{P}(\mathrm{X} < \mathrm{Z})-\mathrm{P}(\mathrm{X} > \mathrm{Z})=0.76\\\mathrm{P}(\mathrm{X} < \mathrm{Z})-1+\mathrm{P}(\mathrm{X} < \mathrm{Z})=0.46\\2 \mathrm{P}(\mathrm{X} < \mathrm{Z})=1.76\\\mathrm{P}(\mathrm{X} < \mathrm{Z})=0.88[/tex]

[tex]= NORMSINV (0.73)\\\mathrm{Z}=0.613[/tex]

[tex]& \mathrm{X}=\mathrm{z} \sigma+\mu \\& \mathrm{X}=0.613 \times 28+120 \\& \mathrm{X}=137.164-\mathrm{x} & =\mu-\mathrm{z} \sigma \\-\mathrm{x} & =120-0.613 \times 28 \\-\mathrm{x} & =102.836[/tex]

Now the interval sample is as follow,

[tex]102.836 < \mathrm{x} < 137.164[/tex]

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Answer:

30%

Step-by-step explanation:

The price of the item increased by $24 from yesterday to today, which represents a 30% increase. To calculate this, divide the increase in price by the original price and multiply the result by 100%:

$24 / $80 x 100% = 30%

Therefore, the percentage increase in the price of the item from yesterday to today is 30%.

The value of each company's product sold price is given as follows:

The values of each company's product sold price is obtained using a system of equations, for which the variables are defined as follows:

The sold sum of both the two companies salaries are $44,000,000, hence:

x + y = 44000000.

The sold price of company x is 1000 more than the other, hence:

x = 1000 + y.

Then the sold price of company y can be found replacing the second equation into the first, as follows:

1000 + y + y = 44000000

2y = 44000000 - 1000

y = (44000000 - 1000)/2

y = $21,999,500.

The sold price for company x is then calculated as follows:

x = 1000 + y = 1000 + 21999500 = $22,000,500.

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Answer:

[tex]\textsf{Slope}=\dfrac{3}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]2y=3x+4[/tex]

Rearrange the equation to make y the subject by dividing both sides by 2:

[tex]\implies \dfrac{2y}{2}=\dfrac{3x+4}{2}[/tex]

[tex]\implies y=\dfrac{3x}{2}+\dfrac{4}{2}[/tex]

[tex]\implies y=\dfrac{3}{2}x+2[/tex]

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Compare the rearranged equation with the slope-intercept formula.

Therefore:

They sold $479 in ticket sales and they had a total of 297 tickets sold, so they must have sold $479/297 = $<<479/297=1.61>>1.61 per ticket.

There are two types of tickets, adult tickets and student tickets, and adult tickets are $3, so the student tickets are $1.61 - $3 = $<<1.61-3=-1.39>>-1.39.

However, a ticket cannot be negative so we know that all of the tickets must have been adult tickets and they sold 297 tickets for $479, so they sold 297 tickets * $3/ticket = $<<297*3=891>>891 worth of adult tickets. Answer: \boxed{891}.

A real-life representation of the following fraction 12/49 =0.24 is that 12kg or rice is to be shared among 49 friends. How many kg will each person get?

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

In this case, the real-life representation of the following fraction 12/49 =0.24 is that 12kg or rice is to be shared among 49 friends. How many kg will each person get?

This is illustrated as 12/49.

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The probability that a given student is on financial aid, given that he or she is a graduate is 0.72

Probability is the measure of the likelihood of an event occurring. In other words, it is a numerical representation of the chance that a particular event will happen.

Probability (graduate student is on financial aid) = number of (graduate student is on financial aid / total number of graduate students

Tota number of graduate students = 1879+ 731 =  2610

P(Financial Aid | Graduate) = 1879 / 2610 = 0.72

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The term that refers to meeting the needs of the present generation without compromising the ability of future generations has been sustainability.

This has been a development that focuses on meeting the needs that arise today without compromising the resources of the following generations.

Sustainability is of paramount importance because:

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Answer:

x=9

Step-by-step explanation:

x=9

To find out what is a solution for x<8  you have to plug in all the answer choices for x.

When you plug in -3, you get -3<8 and 8 is bigger than -3, so then that makes it a solution because -3 is less than 8 and when you plug it in it sets the equation right.

When you plug in 7.95, you get 7.95<8 and 8 is bigger than 7.95 by a few but it still is bigger so then it's a solution because 7.95 is less than 8 making it a solution.

When you plug in 4.3, you get 4.3<8 and 8 is bigger than 4.3 so then it's  a solution because it sets the equation right.

When you plug in 9, you get 9<8 and that's not right because 8 isn't bigger than 9, setting this answer choice as a non-solution to the inequality.

(Hope you understand this..)

The critical values for the following sample are ±2.0064.

Here it is given that α = 0.05,

To calculate the critical values we will use the t-statistic.

Here n₁ = 25 and n₂ = 30

Hence, the degrees of freedom

d.f = n₁ + n₂ - 2           [Since it's a 2-sample test]

= 25 + 30 - 2

= 53

Now our significance level is  α = 0.05,

To know the critical value we will make use of a t-distribution table and look up the value corresponding to a 0.05 significance level and 53 degrees of freedom.

Here we will get the critical values ±2.0064

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The tanθ  for the angle θ that lies in Quadrant III is √35

Trigonometry simply means the branch of mathematics that is concerned with functions of angles as well as their applications to calculation. It also deals with the relationship between ratios and their angles.

Given: The angle θ lies in Quadrant III

cosθ= −1/6 (adjacent/hypotenuse)

adjacent = -1 and hypotenuse = 6

We can draw the position of the angle as shown in the image attached.

Using Pythagoras' theorem:

opposite = √6²-(-1)² = √35

tanθ = (-√35) / (-1) = √35       (tanθ = opposite/adjacent)

Note: opposite in  Quadrant III is negative

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Answer:

$936.91

Step-by-step explanation:

To find the monthly payment required to save up $220,000 using an annuity with an APR of 8.0% compounded annually over 30 years, we can use the following formula:

payment = (goal * rate) / (1 - (1 + rate) ^-n)

In this formula, "goal" is the savings goal, "rate" is the monthly interest rate, and "n" is the number of payments.

To find the monthly payment, we need to first convert the annual interest rate to a monthly rate by dividing it by 12:

rate = 8.0% / 12 = 0.0067

Next, we need to find the number of payments by multiplying the number of years by the number of payments per year:

n = 30 years * 12 payments/year = 360 payments

Substituting these values into the formula, we get:

payment = (goal * rate) / (1 - (1 + rate)^-n)

= (220,000 * 0.0067) / (1 - (1 + 0.0067)^-360)

= $936.91

The monthly payment required to save up $220,000 using an annuity with an APR of 8.0% compounded annually over 30 years is $936.91.

Answer:

Step-by-step explanation:

You want to rewrite f(x) and differentiate it for f(x) = 6·ln(8/x).

The log of a ratio is the difference of logs:

  ln(a/b) = ln(a) -ln(b)

Using this to rewrite f(x), we have ...

  f(x) = 6ln(8/x) = 6(ln(8) -ln(x))

  f(x) = 6·ln(8) -6·ln(x)

The derivative of the constant is zero, so ...

  f'(x) = -6/x