Consider the random variable X that follows an exponential distribution, with u - 20.The standard deviation of X is a =The parameter of the exponential distribution of X is Awhat is the probability that X is less than 10?A. P(X < 10) = 0.3935B P(X < 10) = 0.2212C. P(x < 10) = 0.7981D. p(x < 10) = 0.4908

The orthonormal basis B* = {v1, v2, v3}B* = {(2/7, 3/7, 6/7), (95/21, 343/147, 790/441), (-247664/20349, 224997/46683, 1463161/92313)}

Using Gram-Schmidt Algorithm : Make an orthogonal basis B* from the given basis B, using the appropriate inner product. Assume the standard inner product unless one is given.

2. B ∈ R3 ; B = {(2, 3, 6), (5 13, 10), (−80, 27, 5)}

The Gram-Schmidt algorithm constructs an orthogonal basis {v1, ..., vk} from a linearly independent basis {u1, ..., uk} of the subspace V of a real inner product space with inner product (,). This algorithm is used to construct an orthonormal basis from a basis {v1, ..., vk}.

The first vector in the sequence is defined as:v1 = u1

The second vector in the sequence is defined as:v2 = u2 - proj(v1, u2), where proj(v1, u2) = (v1, u2)v1/||v1||²where (v1, u2) is the inner product between v1 and u2.

The third vector in the sequence is defined as:v3 = u3 - proj(v1, u3) - proj(v2, u3), where proj(v1, u3) = (v1, u3)v1/||v1||², proj(v2, u3) = (v2, u3)v2/||v2||²

Using the Gram-Schmidt algorithm:

Let the given basis be B = {(2, 3, 6), (5, 13, 10), (-80, 27, 5)}

Firstly, Normalize u1 to get v1v1 = u1/||u1|| = (2, 3, 6)/7 = (2/7, 3/7, 6/7)

Next, we need to get v2v2 = u2 - proj(v1, u2)v2 = (5, 13, 10) - ((2/7)(2, 3, 6) + (3/7)(3, 6, 7))v2 = (5, 13, 10) - (4/7, 6/7, 12/7) - (9/7, 18/7, 54/7)v2 = (5, 13, 10) - (73/21, 108/49, 204/147)v2 = (95/21, 343/147, 790/441)

Lastly, we need to get v3v3 = u3 - proj(v1, u3) - proj(v2, u3)v3

= (-80, 27, 5) - ((2/7)(2, 3, 6) + (3/7)(3, 6, 7)) - ((95/21)(95/21, 343/147, 790/441) + (108/49)(5, 13, 10))v3

= (-80, 27, 5) - (4/7, 6/7, 12/7) - (9025/9261, 4115/2401, 23700/9261) - (540/49, 1404/49, 1080/49)v3

= (-247664/20349, 224997/46683, 1463161/92313)

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We square the residuals when using the least-squares line method to find the line of best fit because we believe that huge negative residuals (i.e., points well below the line) are just as harmful as large positive residuals (i.e., points that are high above the line).

We treat both positive and negative disparities equally by squaring the residual values.  We cannot discover a single straight line that concurrently minimizes all residuals. The average (squared) residual value is instead minimized.

We might also take the absolute values of the residuals rather than squaring them. Positive disparities are viewed as just as harmful as negative ones under both strategies.

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The two problems differ in their respective domains. Problem (a) is defined on the unit circle, while problem (b) is defined on the unit disk. The functions in each problem also have different forms, with problem (a) involving exponentiation and problem (b)

Problem (a) defines a function, (v) =\(x^2 + y + xy\), on the unit circle. The unit circle is a set of points (x, y) that satisfy the equation\(x^2 + y^2\)= 1. On the unit circle, x and y are restricted to values that satisfy this equation. The function (v) involves addition, multiplication, and exponentiation. To find the solutions to this problem, one needs to evaluate the function for all points on the unit circle.

On the other hand, problem (b) defines a function, f(y) =\(x + y^2 + xy,\)on the unit disk. The unit disk is a set of points (x, y) that satisfy the inequality\(x^2 + y^2\)≤ 1. Unlike the unit circle, the unit disk includes points within the circle as well. The function f(y) involves addition, multiplication, and squared terms. To solve this problem, one needs to evaluate the function for all points within or on the boundary of the unit disk.

The solutions to these problems may or may not be the same because the functions have different forms and are evaluated over different domains. The specific values of x and y that satisfy the equations in each problem will determine the solutions. It would require further analysis or computation to determine whether the solutions are equivalent or distinct in these two problems.

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The present ages of the man and his son are 60 years and 25 years, respectively.

Let's assume the present age of the son is x years. According to the given information, five years ago, the man was thrice as old as his son, so the man's age at that time was 3(x - 5) years.

Now, let's consider the future scenario. In 10 years, the man's age will be (3(x - 5) + 10) years, and the son's age will be (x + 10) years.

According to the second given information, the man will be twice as old as his son in 10 years, so we can write the equation:

3(x - 5) + 10 = 2(x + 10)

Simplifying the equation:

3x - 15 + 10 = 2x + 20

3x - 5 = 2x + 20

3x - 2x = 20 + 5

x = 25

Therefore, the present age of the son is 25 years. Substituting this value into the equation for the man's age five years ago:

Man's present age = 3(x - 5) = 3(25 - 5) = 3(20) = 60 years

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The amount of Protein intake is 900 kilocalorie.

We have - 2000 Kilocalories of diet and 45 Percent of calories come from Proteins.

Wе have to find out the amount of protein intake.

Percentage of students affected are -  \(\frac{x}{n} \times 100\)

In the question given -

Let the amount of Protein intake be y.

Then -

45 = y % of 2000

45 = \(\frac{y}{2000} \times100\)

y = \(\frac{45\times2000}{100}\)

y = 900 Kilocalorie

Hence, the amount of Protein intake is 900 kilocalorie.

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Answer:

\(\displaystyle \int^x_0\sin(3t^2)\,dt\approx x^3-\frac{27}{42}x^7\)

Step-by-step explanation:

Recall the MacLaurin series for sin(x)

\(\displaystyle \sin(x)=x-\frac{x^3}{3!}+\frac{x^5}{5!}-...\)

Substitute 3t²

\(\displaystyle \displaystyle \sin(3t^2)=3t^2-\frac{(3t^2)^3}{3!}+\frac{(3t^2)^5}{5!}-...=3t^2-\frac{3^3t^6}{3!}+\frac{3^5t^{10}}{5!}-...\)

Use FTC Part 1 to find degree 7 for F(x)

\(\displaystyle \int^x_0\sin(3t^2)\,dt\approx\frac{3x^3}{3}-\frac{3^3x^7}{7\cdot3!}\\\\\int^x_0\sin(3t^2)\,dt\approx x^3-\frac{27}{42}x^7\)

Hopefully you remember to integrate each term and see how you get the solution!

Answer:

probably 4 times since it is not 100% accurate I guess

Answer:

292 acres.

Step-by-step explanation:

OK so if there are 73,000 acres of trees in total and 0.4% are old we would simply calculate what 0.4% of 73,000 which is 292. So of those 73,000 acres of trees 292 acres of them would be "old-growth trees".

Answer:

EVALUATE

false

Step-by-step explanation:

Complex number

(39+5=5a=9)

Answer:

[0.45(many 0's)1] through [0.459] repeating 9

Step-by-step explanation:

All these numbers fall in between 0.45 and 0.46. So if you were to draw out a number line you can find all the answers in between, example being: 0.456, 0.45897, etc.

The decimal numbers are given as 0.451, 0.452, 0.453, and 0.454 respectively.

A decimal number is the representation of a number in whole and a part. The whole is represented by an integer while the part is equivalent to a number divided by the order of 10.

The given decimal numbers are 0.45 and 0.46.

In order to write the numbers between them, write the given decimals up to 3 places as follows,

The numbers are 0.450 and 0.460.

The four decimals between them are as follows,

0.451, 0.452, 0.453, and 0.454.

Hence, the four decimals that lies between 0.45 and 0.46 are given as 0.451, 0.452, 0.453, and 0.454 respectively.

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Answer:

πr^2h

Step-by-step explanation:

please mark me as brainlest

Step-by-step explanation:

HOPE IT'S HELPFUL TO YOU

PLS MARK ABOVE GUY ANSWER AS BRAINLIEST

The subtended arc will be theta times the radius

Therefore, the radian measure of Angle A is:

Answer:

The second smoothie recipe has more strawberries compared to other ingredients

Step-by-step explanation:

Recipe 1:

2 cups of strawberries : 7 cups of other ingredients

= 2/7

= 0.29

Recipe 2:

3 cups of strawberries : 9 cups of other ingredients.

= 3/9

= 1/3

= 0.33

The second smoothie recipe has more strawberries compared to other ingredients

Answer:

5x-15+90+2x=7x+75

Step-by-step explanation:

you just want to add together the like terms which gives you 7x+75 like terms are just numbers that are similar such as 5x and 2x, or -15 and 90.

Maria must cut an additional $70 from her expenses each month in order to save enough money to buy a new TV that costs $420 in 6 months. By allocating this additional amount towards her savings goal, she will be able to reach her target within the desired timeframe. It's important for Maria to review her budget and identify areas where she can reduce expenses in order to make room for the additional savings. This could involve cutting back on discretionary spending, finding ways to save on daily expenses, or exploring opportunities to increase her income.

Maria must cut an additional $70 from her expenses each month.

To determine how much additional money Maria must cut from her expenses each month to afford a new TV that costs $420 in 6 months, we divide the total cost by the number of months.

Additional money per month = Total cost / Number of months

Additional money per month = $420 / 6

Additional money per month = $70

With careful planning and commitment to her budget, Maria can achieve her goal of purchasing a new TV without compromising her financial stability.

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The final conclusion is limit of the sequence as n approaches infinity is 2.

In Mathematics, a limit is defined as a value that a function approaches the output for the given input values. Limits are important in calculus and mathematical analysis and used to define integrals, derivatives, and continuity.

To determine the limit of the sequence defined by an = 2 − (0.2)n as n approaches infinity, we can substitute infinity for n in the expression. Doing so gives us:

lim n→[infinity] an = lim n→[infinity] (2 − (0.2)n) = 2 − lim n→[infinity] (0.2)n

Since 0.2 is between -1 and 1, we know that as n approaches infinity, (0.2)n approaches 0. Therefore, we have:

lim n→[infinity] an = 2 − lim n→[infinity] (0.2)n = 2 - 0 = 2

So the limit of the sequence as n approaches infinity is 2.

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The equation for the tangent plane to the ellipsoid is bcp⁶x - acp⁶y - abp⁶z + acp⁶ - abcp³ = 0

Let's start by considering the ellipsoid with the equation:

(x²/a²) + (y²/b²) + (z²/c²) = 1

This equation represents a three-dimensional surface in space. Our goal is to find the equation of the tangent plane to this surface at the point P = (a/p³, b/p³, c/p³), where p is a positive constant.

The gradient of a function is a vector that points in the direction of the steepest ascent of the function at a given point. For a function of three variables, the gradient is given by:

∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)

In our case, the function f(x, y, z) is the equation of the ellipsoid: (x²/a²) + (y²/b²) + (z²/c²) = 1.

Let's compute the partial derivatives of f(x, y, z) with respect to x, y, and z:

∂f/∂x = (2x/a²) ∂f/∂y = (2y/b²) ∂f/∂z = (2z/c²)

Now, let's evaluate these partial derivatives at the point P = (a/p³, b/p³, c/p³):

∂f/∂x = (2(a/p³)/a²) = 2/(ap³) ∂f/∂y = (2(b/p³)/b²) = 2/(bp³) ∂f/∂z = (2(c/p³)/c²) = 2/(cp³)

So, the gradient of the ellipsoid function at the point P is:

∇f = (2/(ap³), 2/(bp³), 2/(cp³))

This vector is normal to the tangent plane at the point P.

Now, we need to find a point on the tangent plane. The given point P = (a/p³, b/p³, c/p³) lies on the ellipsoid surface, which means it also lies on the tangent plane. Therefore, P can serve as a point on the tangent plane.

Using the normal vector and the point on the plane, we can write the equation of the tangent plane in the point-normal form:

N · (P - Q) = 0

where N is the normal vector, P is the given point on the plane (a/p³, b/p³, c/p³), and Q is a general point on the plane (x, y, z).

Expanding the equation further, we have:

(2/(ap³))(x - (a/p³)) + (2/(bp³))(y - (b/p³)) + (2/(cp³))(z - (c/p³)) = 0

Now, let's simplify the equation:

(2/(ap³))(x - (a/p³)) + (2/(bp³))(y - (b/p³)) + (2/(cp³))(z - (c/p³)) = 0

(2(x - (a/p³)))/(ap³) + (2(y - (b/p³)))/(bp³) + (2(z - (c/p³)))/(cp³) = 0

Multiplying through by ap³ * bp³ * cp³ to clear the denominators, we obtain:

2(x - (a/p³))(bp³)(cp³) + 2(y - (b/p³))(ap³)(cp³) + 2(z - (c/p³))(ap³)(bp³) = 0

Simplifying further:

2(x - (a/p³))(bcp⁶) + 2(y - (b/p³))(acp⁶) + 2(z - (c/p³))(abp⁶) = 0

Expanding and rearranging the terms:

2bcp⁶x - 2abcp³ - 2acp⁶y + 2abcp³ - 2abp⁶z + 2acp⁶ = 0

Simplifying:

bcp⁶x - acp⁶y - abp⁶z + acp⁶ - abcp³ = 0

Finally, we can write the equation of the tangent plane to the ellipsoid at the point P = (a/p³, b/p³, c/p³) as:

bcp⁶x - acp⁶y - abp⁶z + acp⁶ - abcp³ = 0

This equation represents the tangent plane to the ellipsoid at the given point.

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Using Mathematica, we can find the roots of the function y = x^3 Exp[-x] Sin[2x] by substituting x = 3t and evaluating the expression for t in the range [0,1]. The roots correspond to the values of t where the function crosses the x-axis.

To find the roots of the given function, we substitute x = 3t into the expression y = x^3 Exp[-x] Sin[2x]. This gives us y = (3t)^3 Exp[-3t] Sin[2(3t)]. Simplifying further, we have y = 27t^3 Exp[-3t] Sin[6t].

Using Mathematica, we can evaluate this expression for t values ranging from 0 to 1. The roots of the function correspond to the values of t where y equals zero, indicating that the function crosses the x-axis. By plotting the function or using numerical methods such as FindRoot or NSolve in Mathematica, we can determine the values of t where y = 0, thus finding the roots of the function.

In summary, by substituting x = 3t and evaluating the expression y = x^3 Exp[-x] Sin[2x] for t in the range [0,1] using Mathematica, we can find the roots of the function, which represent the values of t where the function crosses the x-axis.

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(i) For the point (-1, -3-√): r=2, θ=4π/3 | (ii) For the point (-1, -3-√): r=-2, θ=π/3 | For the point (-2, 3): (i) r=√(13), θ=  | (ii) r=-√(13), θ=

(i) For the point (-1, -3-√) with r > 0 and 0 ≤ θ < 2π:

r = 2

θ = 4π/3

(ii) For the point (-1, -3-√) with r < 0 and 0 ≤ θ < 2π:

r = -2

θ = π/3

For the point (-2, 3):

(i) With r > 0 and 0 ≤ θ < 2π:

r = √(13)

θ =

(ii) With r < 0 and 0 ≤ θ < 2π:

r = -√(13)

θ =

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Answer:

B=28

Step-by-step explanation:

Answer:

region 2 for the first one ad I think 3 for the second one!

Step-by-step explanation

Answer:

x = 122°

Step-by-step explanation:

There is remote angle( non- adjecent angle) and their sum equal to the exterior angle .

Exterior angle is an angle formed from one side of the polygone and the extended side so

<A and <B are remot angle and <BCD is exterior angle .

And we write the equetion as

<A + <B = <BCD

58° + 64° = x°

122° = X°

so the exterior angle ( x ) measures 122° .

The term that suggests that the threat of loss has a greater impact on a decision than the possibility of an equivalent gain is prospect theory.

Prospect theory is a theory that describes how individuals make decisions under uncertainty. The theory suggests that people think about gains and losses differently and that the value they assign to a particular change in their situation depends on their current situation. The theory is based on the observation that people often violate the principle of expected utility. They make decisions that do not maximize their expected utility. The theory suggests that people evaluate outcomes based on changes from a reference point, rather than in absolute terms. This means that people are more sensitive to changes in their situation than to the situation itself.

For example, a loss of $100 is more painful than the pleasure of gaining $100, and the pleasure of gaining $100 is less than the pain of losing $100.

In summary, Prospect theory suggests that the threat of a loss has a greater impact on a decision than the possibility of an equivalent gain.

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The store's markup on the tablet is equal to $350. Hence, option D is correct.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the information in the question,

Don bought a new tablet.

The cost of buying a tablet for Don = $550

The cost at which the store is buying the tablet = $200

Then, the markup on the tablet will be,

= 550 - 200

= $350

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Answer:

35+52+3(x+2)=180(sum of interior angle of triangle)

3(x+2)=180-87

x+2=93/3

x=31-2=29 is your answer.

Answer:

60 miles per hour

Step-by-step explanation:

We need to simply divide the total distance he traveled by the total time it took him.

At 10:00 AM, he is 200 miles from New York.

At 12:00 PM, he is 80 miles from New York.

This means that 2 hours has elapsed and the distance he has traveled is:

200 - 80 = 120 miles

Therefore, his average speed is:

120 / 2 = 60 miles per hour

Angle a is labeled as left parenthesis 2y plus 20 right parenthesis degrees, angle b is labeled as left parenthesis 5 x right parenthesis degrees, and angle c is labeled as 40 degrees. So the value of y is 40.

In the given question, we have to find the value of y.

Given that;

Y = an isosceles triangle abc.

Sides a, b and a, c are equal.

Sides a, b and a, c are labeled with single tick marks.

Angle a is labeled as left parenthesis 2y+20 right parenthesis degrees, angle b is labeled as left parenthesis 5xright parenthesis degrees, and angle c is labeled as 40 degrees.

If using A,B,C as variables for the measure of the corresponding interior angles and A is the vertex point Band C are the base angles, triangle isosceles, then:

A=2y+20

B=5x

C=40

Angle B and C are equal

B=C

5x=40

X=8

Both B and C are each is 40 degrees

A+B+C=180

A+40+40=180

A+80=180

A=100

After putting the value of A:

A=2y+20

100=2y+20

2y=80

Y=40

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Answer:

The bicycle will be worth less than 1000 after 4 years.

Step-by-step explanation: