סו ל 3) Determine the luck! maxima, minima, & saddle point of the function f(x, y) = x² - 4xy + y² +12y +4

The percentage of IQ scores greater than 64 is 100% - 1.06% = 98.94%.

We need to use the standard normal distribution and the standard score (z-score) formula to convert IQ scores to standard normal values in order to find the percentage of IQ scores greater than 64.

The standard scoring formula is as follows:

z = (x - μ) / σ

where x is the IQ score, is the IQ distribution's mean (98), and is the IQ distribution's standard deviation (17).

So, for an IQ of 64, the standard score is:

z = (64 - 98) / 17 = -2.35

With the standard score in hand, we can use a standard normal table or a z-score calculator to calculate the percentage of IQ scores greater than 64. A z-score of -2.35 indicates a probability of 0.0106. This means that 1.06% of IQ scores less than or equal to 64.

Therefore, the percentage of IQ scores greater than 64 is 100% - 1.06% = 98.94%.

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An equation is formed of two equal expressions. The value of x is -28/9.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given expression can be simplified as,

\(2 \frac17+\dfrac37(3x-5)=-4\\\\\dfrac{15}{7} + \dfrac{9x-15}{7} = -4\\\\ \dfrac{15+9x-15}{7} = -4\\\\9x = -28\\\\x = \dfrac{-28}{9}\)

Hence, the value of x is -28/9.

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Answer:

The variable c=9 is the answer the varibles

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

c = −15.8571428571

Step-by-step explanation:

-42 = 5(2c + 9) - 3(c + 8)

-42 = 10c + 45 - 3c + 24

-42 = 10c - 3c + 45 + 24

-42 = 7c + 69

-7c -7c

-------------------

-7c - 42 = 69

+42. +42

___________

-7c/-7 = 111/-7

c = −15.8571428571

The maximum interest rate that can be charged during the fifth year is 6.75%. The correct option is the third option c. 6.75%

From the question, we are to determine the maximum interest rate that can be charged during the fifth year

A 2/1 ARM means that the interest rate is fixed for the first two years and then adjusts annually based on a specified index plus a margin. The "2/10 cap" means that the interest rate can only increase or decrease by a maximum of 2 percentage points each year, and can never be more than 10 percentage points higher than the initial rate.

Since the initial rate is 2.75%, the maximum rate that can be charged during the fifth year is:

2.75% + (2 x 2%) = 6.75%

Hence, the maximum interest rate that can be charged during the fifth year is 6.75%.

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The net profit margin for this shirt is 55%.

What is net profit?

Net profit is the amount of money your business earns after deducting all operating, interest and tax expenses over a period of time. To arrive at this value, you need to know the company's gross profit. If the value of net profit is negative, it is called net loss.

Net profit is another important parameter that determines the financial health of your business. It shows whether the company can earn more than it spends. Net profit helps you decide when and how to expand your business and when to cut costs.

It is important for a business owner to know the difference between profit and profitability. Profit is an absolute number equal to revenues minus expenses. Profitability, on the other hand, is a relative number (percentage) that equals the ratio of profit to revenue.

Profitability is a measure of efficiency and is useful in determining the success or failure of a business.

Given,

Revenue = $12

Cost of goods sold = $3

Operating expenses = 20% of revenue = 20/100 x $12 = $2.4

We know,

Net Profit = Revenue - Cost of goods sold - Operating expenses

\(Net \: Profit = 12 - 3 - 2.4\)

Hence, Net Profit = $6.6

Again,

Net Profit Margin = (Net Profit / Revenue) x 100%

Net Profit Margin \(= ( \frac{6.6}{ 12}) \times 100\%\)

SO, Net Profit Margin = 55%

Therefore, the net profit margin for this shirt is 55%.

So, it is clear that choice A is correct.

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Answer:

40

Step-by-step explanation:

we can ask as

How many groups of 360 hundredth are there in 9 hundredth.

Mark me as brainliest.

Answer:

4.5 Cubic Feet

Step-by-step explanation:

1. You want to find the volume of the box. (Length x width x height)

2.5 x 2 x 1.5 = 7.5

2. The present has a volume of 3 cubic feet, so you would subtract that from the volume of the box.

7.5 - 3 = 4.5

3. The volume of the empty space in the box is 4.5 cubic feet.

Hope this helped! :)

Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Answer:not true

Step-by-step explanation:

To say not true we need only one example so we can take x as -5

[-5]= [-5+1]

5 not equal with 4

7 % of 100 %

Formula :

\( \frac{x \%}{y \%} × 100 \)

Lets , solve it :

\( \frac{7\%}{100\%}× 100 \)

\(7\)

The function g(x) is the result of a reflection across the y-axis, a vertical compression by a factor of 4, a horizontal translation to the left by 5 units, and a vertical translation up 6 units of the parent function f(x) = eˣ.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The parent function of the exponential functions is indeed f(x) = eˣ.

The function g(x) = -4eˣ⁻⁵ + 6 is similar to the parent function, but it has undergone several transformations.

The transformation that the classmate has correctly identified are:

The reflection across the y-axis, which is done by multiplying the function by -1.

The vertical compression by a factor of 4, which is done by multiplying the function by 4.

The translation to the left 5 units, which is done by subtracting 5 from the argument of the exponential function.

The translation up 6 units, which is done by adding 6 to the function.

Hence, the function g(x) is the result of a reflection across the y-axis, a vertical compression by a factor of 4, a horizontal translation to the left by 5 units, and a vertical translation up 6 units of the parent function f(x) = eˣ.

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Answer:

8%, 1/8, 18%, 8/18, 0.8

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question isn't clear...

Given that v0 = (2, 1, -2), v1 = (-2, 1, 1), and v2 = (1, 2, 2), we can find the orthonormal basis that should be parallel to v0, and w0 and w1 should span the same subspace as v0 and v1.To find the orthonormal basis that should be parallel to v0.

we need to follow these steps:

Let v0 be a vector in Rn with nonzero norm ||v0||, and let V be the subspace of Rn that is perpendicular to v0 (so if y is in V, then y·v0 = 0).

Then, we can construct an orthonormal basis {v1, . . . , vp} for V, and {v0/v0, v1, . . . , vp} will be an orthonormal basis for Rn.

To find {v1, . . . , vp}, we apply Gram-Schmidt to the basis {v0, v1, . . . , vp}.

Specifically, we compute vi' = vi - projv0vi for i = 1, . . . , p.

This ensures that {v1, . . . , vp} are all in V and that {v0/v0, v1, . . . , vp} is an orthonormal basis for Rn that is parallel to v0.

So, in this case, we can take v0 = (2, 1, -2), which has norm ||v0|| = sqrt(2^2 + 1^2 + (-2)^2) = sqrt(9) = 3.

Now, we need to find w0 and w1 that span the same subspace as v0 and v1. Since {v0, v1} is a basis for this subspace, any two linearly independent vectors in this subspace will span the same subspace. So, we can just pick any two such vectors. Let w0 = (2, 1, -2) and w1 = (-2, 5, 1).

We claim that {w0, w1} is linearly independent and spans the same subspace as {v0, v1}.To show that {w0, w1} is linearly independent, suppose that aw0 + bw1 = 0 for some scalars a and b. Then, we have(2a - 2b, a + 5b, -2a + b) = (0, 0, 0).This gives us two equations:2a - 2b = 0a + 5b = 0

Solving for a and b, we geta = 5/7 and b = -2/7.

Since a and b are not both zero, this shows that {w0, w1} is linearly independent.

To show that {w0, w1} spans the same subspace as {v0, v1}, we need to show that every vector in this subspace can be written as a linear combination of w0 and w1. Let (x, y, z) be any vector in this subspace.

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Answer:

(x-8) (x+3)

Step-by-step explanation:

The function computes the total phone bill by adding these two components together.

A symbolic representation for the linear function that computes the long distance phone bill in dollars for calling t minutes at 20 cents per minute and a fixed fee of $3.95 can be written as:

L(t) = 0.20t + 3.95

In this representation, L(t) represents the phone bill in dollars and t represents the number of minutes of the call. The term 0.20t represents the cost of the call based on the number of minutes at 20 cents per minute, and the constant term 3.95 represents the fixed fee. The function computes the total phone bill by adding these two components together.

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a. Segment AC is a radius of the circle = 7.5 cm

b. Segment CD is a diameter of the circle = 15 cm.

The radius of a circle is the line segment that is drawn from the center of the circle to any point on the circumference of the circle. The length of a radius is half the length of the diameter of a circle.

The diameter of a circle is the line segment that divides the circle at its center into two halves. The length of the diameter of any circle is twice the length of the radius of the circle.

a. In the image given below, a radius of the circle is segment AC.

AC = 1/2(15)

Length of segment AC = 7.5 cm.

b A diameter in the circle is CD.

The length of segment CD = 15 cm.

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All the terms are variable name and the level of measurment are            A. Age- Ratio, B. Military dictatorship - Nominal, C. Strongly oppose - Ordinal, D. Election year - Interval, E. 62 percent - Ratio, F. Asian - Nominal, G. Class rank - Ordinal, H. Commute distance - Ratio.

A. Age - (i) Variable name (ii) Ratio
B. Military dictatorship - (i) Variable name (ii) Nominal
C. Strongly oppose - (i) Variable value (ii) Ordinal
D. Election year - (i) Variable name (ii) Interval
E. 62 percent - (i) Variable value (ii) Ratio
F. Asian - (i) Variable value (ii) Nominal
G. Class rank - (i) Variable name (ii) Ordinal
H. Commute distance - (i) Variable name (ii) Ratio

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Answer:

0.35

Step-by-step explanation:

In the basis step of the mathematical induction proof for P(n), we show that the equation is true for n = 1. The equation of the inductive hypothesis (IH) is P(k), where k is an arbitrary natural number. In the inductive step, we need to show that if P(k) is true, then P(k+1) is also true.

In the basis step, we substitute n = 1 into the equation 11⋅2+12⋅3+⋅⋅⋅+1n⋅(n+1)=nn+1. This gives us the equation 1⋅2 = 1+1, which is true.

The inductive hypothesis (IH) is denoted as P(k), where k is an arbitrary natural number. We assume that P(k) is true, meaning that 11⋅2+12⋅3+⋅⋅⋅+1k⋅(k+1)=kk+1 holds.

In the inductive step, we need to show that if P(k) is true, then P(k+1) is also true. This involves substituting n = k+1 into the equation 11⋅2+12⋅3+⋅⋅⋅+1n⋅(n+1)=nn+1 and demonstrating that the equation holds for this value. The specific equation we need to show in the inductive step is 11⋅2+12⋅3+⋅⋅⋅+1(k+1)⋅((k+1)+1)=(k+1)(k+1+1).

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In the basis step, we need to show that the equation P(1) is true. The equation of the inductive hypothesis (IH) is P(k), where k is any natural number greater than or equal to 1. In the inductive step, we need to show that if P(k) is true, then P(k+1) is also true.

To prove the equation P(n): 11⋅2 + 12⋅3 + ... + 1n⋅(n+1) = n(n+1) using mathematical induction, we follow the two-step process.

1. Basis Step:

We start by showing that the equation is true for the base case, which is n = 1:

P(1): 11⋅2 = 1(1+1)

Simplifying, we get: 2 = 2, which is true.

2. Inductive Step:

Assuming that the equation is true for some arbitrary value k, the inductive hypothesis (IH) is:

P(k): 11⋅2 + 12⋅3 + ... + 1k⋅(k+1) = k(k+1)

In the inductive step, we need to show that if P(k) is true, then P(k+1) is also true:

P(k+1): 11⋅2 + 12⋅3 + ... + 1k⋅(k+1) + 1(k+1)⋅((k+1)+1) = (k+1)((k+1)+1)

By adding the (k+1)th term to the sum on the left side and simplifying the right side, we can demonstrate that P(k+1) is true.

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Answer:

x = 4√7

Step-by-step explanation:

You can use the pythagorean theorem which is a² + b² = c²

if you plug it in, it would be...

x² + 12² = 16²

x² + 144 = 256, subtract 144 to both sides

x² = 112, square root both sides to make x by itself.

x = 4√7  

Answer:

Step-by-step explanation:  Hello!

I don't remember all of the postulates to these, but I hope this will help you! Vertical angles are congruent, so both angles SRT and PRQ are congruent.  This also means that line segments PQ and ST are congruent.  You also know that angles Q and S are congruent which is given.  By the ASA Theorem, when two angles and a side are congruent, then the triangles are congruent.

Answer:

When y = 5; x = 2

Step-by-step explanation:

What we have to do here is to first go to the point y = 5 on the y-axis

Now, the next thing is to trace this to the plot

The tracing will meet the plot at a point

At this point, we can now drop a line to the x-axis

By this, we can get that at y = 5; then x = 2

Now, we want to check the validity from the linear equation given

That would be;

y = -x + 7

y = -2 + 7

y = 5

This holds according to the linear equation given

Answer:

Start with equation,

         y''(x) = f(x) = 6y/(10x-x²)               about point x₀ = 5

Then,

       y(x) = a₀ + a₁(x-5) + a₂(x-5)²+ a₃(x-5)³ + a₄(x-5)⁴...….

by inspection,

           y(5) = a₀      and       y'(5) = a₁

then,

y''(5) = 6a₀/(50-25) = 6a₀/25              

y'''(x) = 6y'/(10x-x2) - 6y(10-2x)/(10x-x2)2

then,                      

                              y'''(5) = 6a₁/25 - 0 = 6a₁/25                

y''''(x) = 6y''/(10x-x2) -12y'(10-2x)/(10x-x2)² + 12y/(10x-x2)² + 12y(10-2x)2/(10x-x2)³

then,

    y''''(5) = (6/25)(6a₀/25) + 0 + 12a₀/625 + 0

              = 48a₀/625

So,

y(x) = f(x) = f(5) + f'(5)(x-5) + f''(5)(x-5)2/2! + f'''(5)(x-5)3/3! + f''''(5)(x-5)4/4! …

                                                       or

y(x) = f(x) = a₀ + a₁(x-5) + (6ao/25)(x-5)2/2! + (6a1/25)(x-5)3/3! + (48a₀/625)(x-5)4/4!...

                                                         or

y(x) = f(x) = a₀ + a₁(x-5) + (3a₀/25)(x-5)²+ (a₁/25)(x-5)³+ (2a₀/625)(x-5)⁴.....

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The height of the wind turbine where the distance from it's base to buoy is 150 meters and angle of elevation is 28°, is equals to the 281.95 meters.

See the above figure carefully. Let there present right angled triangle be ∆ABC. We have length of buoy away from the base of a wind turbine(AB), BC = 150 meters

Angle of elevation from the buoy to the top of the wind turbine, BAC = 28°

We have to determine height of the wind turbine that is length of AB. As we see this is a right angled triangle so we will use trigonometric functions. Now, tangent function of angle

= height/base length. Here, consider the function for angle 28°, so tan (28°) = BC/AB

=> tan (28°) = 150/AB

=> AB = 150/tan (28°)

=> AB = 150/0.532

=> AB = 281.954887218 ~ 281.95

Hence, required value is 281.95 meters.

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Complete question:

The above figure comples the question. A buoy is 150 meters away from the base of a wind turbine the angle of elevation from the buoy to the top of the wind turbine is 28 degrees

what is the height of the wind turbine?

give your answer in 2 d. P