The mean of a set of 6 integers is 30. When one of the numbers is removed, the new mean is

34. What was the number that was removed?

A

Four

B.

Five

С

Eight

D

Ten

The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A.

The above statement is True.

Eigenvalue:

An eigenvalue is a special set of scalar values ​​associated with the most probable system of linear equations in a matrix equation. Eigenvectors are also called eigenvalues. It is a non-zero vector which can be modified by at most its scalar factor after applying a linear transformation.

According to the Question:

If the geometric multiple of the eigenvalues ​​is greater than or equal to 2, the linearly independent set of eigenvectors is no longer unique to the multiple as before. For example, for the diagonal matrix A=[3003], one could also choose the eigenvectors [11] and [1−1], or any pair of two linearly independent vectors.

Sometimes vectors are simply expanded to vector times matrix. If this happens, this vector is called the eigenvector of the matrix and the "stretch factor" is called the eigenvalue. Example: Given a square matrix A, λ is the eigenvalue of A, and the corresponding eigenvector x is

Ax = λx.

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Answer:

Describe how anthropology challenges more commonly held notions of progress

Step-by-step explanation:

Answer:

1.  You can prove that a line parallel to one side of a triangle divides the other 2 sides proportionally by using the Triangle Proportionality Theorem.  

2. You prove the base angles are congruent by constructing the angle bisector through the vertex angle of an isosceles triangle. By constructing the angle bisector, we designed two congruent triangles and then used CPCTC to show that the base angles are congruent.

Step-by-step explanation:

Answer:

60 miles

Step-by-step explanation:

Ashok and Brian are both walking east along the same path; Ashok walks at a faster constant speed than does Brian. If Brian starts 30 miles east of Ashok and both begin walking at the same time, how many miles will Brian walk before Ashok catches up with him?

Statement 1. Brian’s walking speed is twice the difference between Ashok’s walking speed and his own

Statement 2. If Ashok’s walking speed were five times as great, it would be three times the sum of his and Brian’s actual walking speeds

Solution

A. Brian’s walking speed is twice the difference between Ashok’s walking speed and his own.

Let Brian speed=b

Ashok speed=a

Brian's walking speed=2(a-b)

b=2(a-b)

Divide both sides by 2

b/2=a-b

Ashok catches up in (time)= distance /( relative rate

=30/(a-b)

=30/(b/2)

=30÷b/2

=30*2/b

=60/b.

By that time Brian will cover a distance of

distance=rate*time

=b*60/b

=2(a-b)*60/2(a-b)

=60 miles

(2) If Ashok’s walking speed were five times as great, it would be three times the sum of his and Brian’s actual walking speeds.

5a=3(a+b)

5a=3a+3b

5a-3a=3b

2a=3b

Answer:

237500000000

Step-by-step explanation:

1.14 × \(10^{6}\) = 1140000

4.8 × \(10^{-6}\) = 0.000005

1140000 ÷ 0.000005 = 237500000000

The probability of a student completing the final examination in less than 65 minutes is 13.45%.

The time it takes to complete a final examination in a particular college course is normally distributed with a mean of 77 minutes and a standard deviation of 12 minutes. This can be expressed mathematically as X~N(77, 12).

The probability of a student completing the final examination in less than 65 minutes can be calculated by using the Z-score formula:

Z = (x - μ) / σ

Where x = 65 minutes, μ = 77 minutes, and σ = 12 minutes.

Plugging these values into the formula, we get:

Z = (65 - 77) / 12 = -1.17

Using a Z-score table, we can find the probability of a student completing the final examination in less than 65 minutes, which is equal to 0.1345, or 13.45%. Therefore, the probability of a student completing the final examination in less than 65 minutes is 13.45%.

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Answer:

Is this what you meant?

(2x + 3x) × (3 + 15) = 12x + 36

(5x) × (18) = 12x + 36

90x = 12x + 36

78x = 36

x = 36 / 78

x = 18 / 39

_____________________

or

3(2x+3x) + 15 = 12x + 36

10x + 15 = 12x + 36

-21 = 2x

2x = -21

x = -21/2

Answer:

Find the area of the triangle, then multiply by the length of the prism.

1/2(6)(5)(11)

3(5)(11)

15(11)

165

Let me know if this helps!

Answer:165

Step-by-step explanation:

The optimal consumption bundle with initial prices is (X,Y) = ($5,$5). The optimal consumption bundle changes when the price of good X increases.

The new optimal consumption bundle with the increased price of X is (X,Y) = ($3.33,$6.67).

The total effect is a decrease in the consumption of good X by approximately $1.67.

The income effect is zero, and the substitution effect is a decrease in the consumption of good X by approximately $1.67.

To find the optimal consumption bundle, we maximize the utility function subject to the budget constraint. The budget constraint is given by the equation Px*X + Py*Y = Income.

1. Initial prices:

Here, Px = $1, Py = $1, and the consumer has $10 as income. To find the optimal consumption bundle, we substitute the utility function into the budget constraint and differentiate it with respect to X. By setting the derivative equal to zero, we find the optimal consumption bundle:

Px = Py

1 = 1

X = Y

Substituting X = Y into the budget constraint:

1*X + 1*X = 10

2*X = 10

X = 5

Thus, the optimal consumption bundle with initial prices is (X,Y) = ($5,$5).

2. Increased price of X:

When the price of X increases to $3, we need to find the new optimal consumption bundle. By following the same steps as above, we differentiate the utility function with respect to X, taking into account the new price of X:

Px = Py

3 = 1

X = Y

Substituting X = Y into the budget constraint:

3*X + 1*X = 10

4*X = 10

X = 2.5

The new optimal consumption bundle is (X,Y) = ($2.5,$2.5).

To calculate the total effect, we compare the change in the consumption of good X between the initial and new optimal bundles. The total effect is the decrease in the consumption of good X, which is approximately $1.67.

To decompose the total effect into income and substitution effects, we need to hold the consumer's utility constant at the initial level. By adjusting the consumer's income, we find that the income effect is zero. Thus, the total effect can be attributed entirely to the substitution effect.

The optimal consumption bundle changes when the price of good X increases. The consumer reduces their consumption of good X and increases their consumption of good Y. The total effect is a decrease in the consumption of good X by approximately $1.67, which is solely attributed to the substitution effect.

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Answer:

40

Step-by-step explanation:

4(sqrt(147/3)+3)

=4(sqrt(49)+3)

=4(7+3)

=4(10)

=40

Answer:

They are all equal sides so divide 180 by 3

Step-by-step explanation:

Answer:

$60

Step-by-step explanation:

Let's say we need t $2 bills and v $5 bills.

We need 9 more $2 bills than $5 bills, so:

t = 9 + v

We also know that the amount of money in t $2 bills is 2 * t = 2t. The amount of money in v + 9 $5 bills is 5 * (v + 9) = 5v + 45. These amounts are equal:

5v + 45 = 2t

Plug v + 9 in for t in 5v = 2t + 18:

5v = 2t + 18

5v = 2 * (9 + v) + 18

5v = 18 + 2v + 18

3v = 36

v = 12

We have 12 $5 bills, so that total cost is 12 * 5 = $60.

~ an aesthetics lover

Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

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The equivalent of 0.85 hectogram (hg) is 850 decigram (dg)

The measure is given as:

0.85 hg

As a general rule:

1 hectogram (hg) = 1000 decigram (dg)

So, multiply both sides of the above equation by 0.85

So, we have:

0.85 * 1 hectogram (hg) = 0.85 * 1000 decigram (dg)

Evaluate the product

0.85 hectogram (hg) = 850 decigram (dg)

Hence, the equivalent of 0.85 hectogram (hg) is 850 decigram (dg)

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These are the polynomial equations:

A = x^ (1/4) - ∛x + 4√x - 8x + 16

B = 3x² - 5x⁴ + 2x - 12

C = x³ - 7x² + 9x - 5x⁴ - 20

D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1

These are the non-polynomial equations:

E = 4/x⁴ + 3/x³ - 2/x² - 1

F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1

Polynomials are mathematical expressions that only use addition, subtraction, multiplication, and non-negative exponentiation of the variables, along with coefficients (constants that multiply with the variables), coefficients, and constants.

Some of the elements of an equation are coefficients, variables, operators, constants, terms, expressions, and the equal to sign. An equation must always begin with the "=" sign and have terms on both sides.

Let the polynomial equations be represented by the following letters: A, B, C, D, E, and F.

In the equation, we can solve for other values to obtain:

Moreover, a polynomial equation is not an algebraic equation that has a negative exponent or an exponent that is fractional. Thus, negative exponent expressions are not polynomials.

A = x^ (1/4) - ∛x + 4√x - 8x + 16

This polynomial exists.

B = 3x² - 5x⁴ + 2x - 12

This polynomial exists.

C = x³ - 7x² + 9x - 5x⁴ - 20

This polynomial exists.

D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1

It is a polynomial.

E = 4/x⁴ + 3/x³ - 2/x² - 1

It is not a polynomial.

F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1

A polynomial is not what it is.

The polynomials are thus resolved.

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The number of oranges that are expected to weigh more than 4 oz is:

1400 - (1400 × 0.0228)≈ 1368.

The mean weight of the oranges growing in an orchard is 8 oz and standard deviation is 2 oz, the distribution of the weight of oranges can be represented as normal distribution.

From the batch of 1400 oranges, the number of oranges is expected to weigh more than 4 oz can be found using the formula for the Z-score of a given data point.

\(z = (x - μ) / σ\)

Wherez is the Z-score of the given data point x is the data point

μ is the mean weight of the oranges

σ is the standard deviation

Now, let's plug in the given values.

\(z = (4 - 8) / 2= -2\)

The area under the standard normal distribution curve to the left of a Z-score of -2 can be found using the standard normal distribution table. It is 0.0228. This means that 0.0228 of the oranges in the batch are expected to weigh less than 4 oz.

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Product is the multiplication of numbers. The product of the (5x-11)² is (25x²-110x+121).

A product is the multiplication of a number or expression to another expression.

We know in order to find the product of (5x-11)², we need to multiply each of the terms inside the bracket to each term in the second bracket. therefore, the solution of the problem can be given as,

\((5x-11)^2\\\\= (5x-11) \times (5x-11)\\\\= (5x \times 5x)-(5x \times 11)-(5x \times 11)(11 \times 11)\\\\= 25x^2 - 55x - 55x + 121\\\\= 25x -110x +121\)

Hence, the product of the (5x-11)² is (25x²-110x+121).

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Answer:

y=x+1  mayby

Step-by-step explanation:

The equation of the given line is y = 2x

The standard equation of a line is y = mx + b

From the graph, we can use the coordinate point (1, 2) and (2, 4)

Get the slope

m = 4-2/2-1

m = 2/1

m = 2

Since the line pass through the origin, hence b = 0

Get the required equation:

y = 2x + 0

y = 2x

Hence the equation of the given line is y = 2x

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The value of y in the right triangle is 9.3 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the value of y in the right angle triangle.

Using trigonometric ratios,

sin 51 = opposite / hypotenuse

sin 51 = y / 12

cross multiply

12 sin 51  =y

y = 12 × 0.77714596145

y = 9.32575153748

y = 9.3 units

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Answer:

\(14.1\)

Step-by-step explanation:

Since we have two sides of a triangle and the angle between them, we can use the Law of Cosines.

For any triangle, the Law of Cosines states:

\(b^2=a^2+c^2-2ac\cos B\), where \(a\), \(b\), and \(c\) are all interchangeable.

Substituting given values, we have:

\(b^2=9^2+19^2-2(9)(19)\cos 45^{\circ},\\b^2=200.169480834,\\b\approx \boxed{14.1}\)

Answer:

answer is 28

Step-by-step explanation:

3x=84

x=84/3= 28