Find the change-of-coordinates matrix from B to the standard basis in R2 B = [ 4 ] [ 1 ]
[-2 ] [ 3 ]
The change of coordinates matrix is ____

Answer: 12

Step-by-step explanation:

6y - 3z

6(4) - 3(4)

24 - 12

12

Answer:

Step-by-step explanation:

All you need do is divide by m and you have the answer.

x*m/m = np/m

x = np/m

The vector z in the component form is z = < 21 , 24 , -27 >

Given data ,

A vector in component form is typically written as an ordered pair or triplet, where each component represents the magnitude of the vector along a specific coordinate axis.

Now , the vector u = < -1 , 3 , 1 >

v = < 4 , -3 , -1 >

w = < 10 , 5 , -10 >

Now , the value of vector z = < 3w - 2v + u >

z = 3w - 2v + u

z = 3w - 2 * < 4 , -3 , -1 > + < -1 , 3 , 1 >

Using scalar multiplication, we get:

z = < 30 , 15 , -30 > - < 8 , -6 , -2 > + < -1 , 3 , 1 >

Adding vectors, we get:

z = < 30 - 8 - 1 , 15 - (-6) + 3 , -30 + 2 + 1 >

z = < 21 , 24 , -27 >

Hence , the vector z in component form is z = < 21 , 24 , -27 >

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Answer:

Obi's age is 18 and Oba's age is 9

Step-by-step explanation:

Let Obi's age be x and Oba's age be y

Condition 1:

x = 2y -----------(1)

Condition 2:

(x-4) = 3(y-4)

=> x -4 = 3y-12

=> x - 3y = -9  -----(2)

Putting eq (1) in (2)

2y - 3y = -9

=> -y = -9

=> y = 9

Now,

x = 2y

=> x = 2(9)

=>  x= 18

Answer:

\(8\\4\)

Step-by-step explanation:

Obi's age is \(x\).

Oba's age is \(2x\).

4 years ago, Obi's age was \(x-4\).

4 years after, Obi's age is \(2x-4\)

3 times more than Oba's, so \(3(x-4)\)

\(2x - 4 = 3( x - 4)\)

\(2x - 4 = 3x-12\)

\(2x - 3x = -12+4\)

\(-1x=-8\)

\(x=8\)

\(x-4\\(8)-4=4\)

The polynomial 8x⁴ - (2/3)x² - (2/3)x correctly combines the like terms and puts the polynomial (1/3)x + 8x⁴ - (2/3)x² - x in the standard form option (C) is correct.

What is polynomial?

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

It is given that:

The polynomial:

(1/3)x + 8x⁴ - (2/3)x² - x

Adding combine like terms:

= 8x⁴ - (2/3)x² + (1/3)x - x

= 8x⁴ - (2/3)x² - (2/3)x

Thus, the polynomial 8x⁴ - (2/3)x² - (2/3)x correctly combines the like terms and puts the polynomial (1/3)x + 8x⁴ - (2/3)x² - x in the standard form option (C) is correct.

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The general solution to the given differential equation dy/dx = (cos y)/(a cos x) can be expressed as y = arcsin(e sin x) + C, where C is an arbitrary constant.

The general solution to the given differential equation dy/dx = (cos y)/(a cos x) is y = arcsin(e sin x) + C, where C is an arbitrary constant. This solution is obtained by integrating both sides of the differential equation with respect to x and solving for y.

To solve the differential equation dy/dx = (cos y)/(a cos x), we first observe that the equation involves the trigonometric function cosine (cos) of y and x. By rearranging the equation, we can separate the variables y and x on opposite sides of the equation. Then, we can integrate both sides with respect to x, treating y as a constant, to obtain the equation y = arcsin(e sin x) + C, where C represents the constant of integration. This equation represents the general solution to the given differential equation, as it satisfies the original equation for all values of x and corresponding values of y. The arbitrary constant C allows for different possible solutions within the family of curves defined by the equation.

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A 95% confidence interval about the mean age is (34.31, 40.69)

We know that, the confidence interval is:

\((\bar{x}-z\frac{\sigma}{\sqrt{n} },~ \bar{x}+z\frac{\sigma}{\sqrt{n} } )\)

where,

\(\bar{x}\) is the sample mean.

z is the critical value.

n is the sample size.

σ (OR s) is the standard deviation for the population.

For given question,

A sociologist randomly selects 32 death-row inmates and finds that their mean age is 37.5, with a standard deviation of 9.2

we need to calculate the 95% confidence interval about the mean age.

For 95%, the critical value is z = 1.96

We have been given x¯ = 37.5, σ = 9.2, and n = 32

So, the confidence interval would be,

\((37.5-1.96\frac{9.2}{\sqrt{32} },~ 37.5+1.96\frac{9.2}{\sqrt{32} } )\)

= (37.5 - 1.96(1.63), 37.5+ 1.96(1.63))

= (37.5 - 3.19, 37.5 + 3.19)

= (34.31, 40.69)

A 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value.

Therefore, a 95% confidence interval about the mean age is (34.31, 40.69)

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Answer:

∠ 1 = 109° , ∠ 2 = 29° , ∠ 3 = 71°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180° , then

∠ 1 + 35° + 36° = 180°

∠ 1 + 71° = 180° ( subtract 71° from both sides )

∠ 1 = 109°

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

∠ RVU and ∠ 1 are adjacent angles on a straight line and sum to 180° , then

∠ RVU + ∠ 1 = 180°

∠ RVU + 109° = 180° ( subtract 109° from both sides )

∠ RVU = 71°

In Δ RVU

∠ 2 + 80° + 71° = 180° ( sum of angles in triangle )

∠ 2 + 151° = 180° ( subtract 151° from both sides )

∠ 2 = 29°

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

∠ 3 and ∠ RVU are vertically opposite angles and are congruent , then

∠ 3 = 71°

Δ UVT has: ∠V₁ = 180⁰ - ∠TUV - ∠VTU = 180⁰ - 35⁰ - 36⁰ = 109⁰

We have: ∠RVU = ∠V₃ = 180⁰ - ∠V₁ = 180⁰ - 109⁰ = 71⁰

ΔRVU has: ∠U₂ = 180⁰ - ∠URV - ∠ RVU = 180⁰ - 80⁰ - 71⁰ = 29⁰

Answer:

Ok done. Thank to me :>

The perimeter of the triangle DEF is half the perimeter of triangle ABC.

We are given a triangle ABC with mid-points D,E, and F of AB, BC and CA respectively.

DEF forms a triangle.

We have to find the relationship between the perimeter of triangle ABC and triangle DEF.

Let us consider sides AB,BC, and CA as 2x, 2y and 2z.

We know that triangle ABC is divided into four equal triangles of sides which are half of the sides of triangle ABC.

Hence,

DE = x,

EF = y, and

DF = z

Hence,

Perimeter of triangle ABC = 2x + 2y + 2z = 2(x + y + z)

Perimeter of triangle DEF = x + y + z

Hence, we can say that the perimeter of triangle  DEF is half the perimeter of triangle ABC.

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Answer:

0.444

Step-by-step explanation:

The objective is to draw the tree diagram and find the probability that the roadrunner took the high road, given that he was caught.

The tree diagram is attached in the image below:

The required probability can be computed as:

\(P(high\ road \ | \ caught) = \dfrac{P(high \ road \ and \ caught)} {P(caught)} \\ \\ P(high \ road \ | \ caught) = \dfrac{P(high \ road \ and \ caught)}{P(high \ road \ and \ caught)+P(low \ road \ and \ caught)}\)

\(P(high \ road \ | \ caught) =\dfrac{ 0.8*0.01 }{ 0.80*0.01 + 0.20*0.05} \\ \\ P(high \ road \ | \ caught) = \dfrac{0.008 }{ 0.008 + 0.01} \\ \\\)

\(P(high \ road \ | \ caught) = \dfrac{0.008 }{ 0.018}\)

\(\mathbf{P(high \ road \ | \ caught) = 0.444}\)

The probability that he took the high road, given that he was caught is 0.444 and this can be determined by using the properties of probability.

Given :

The required probability is given by:

\(\rm P = \dfrac{P(High\;road\;and\;caught)}{P(Caught)}\)

\(\rm P = \dfrac{P(High\;road\;and\;caught)}{P(High \;road \;and \;caught)+P(Low\; road\; and \;caught)}\)

\(\rm P=\dfrac{0.8\times 0.01}{0.8\times 0.01 + 0.2\times 0.05}\)

\(\rm P=\dfrac{0.008}{0.018}\)

P = 0.444

The probability that he took the high road, given that he was caught is 0.444.

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Answer:

d po

Step-by-step explanation:

i hope its help

carry on learning

Given the equations

x + y = 5----------------------(1)

x - 3y = 3-----------------------(2)

Subtract equation (2) from (1)

x - x -3y - y = 3 - 5

-4y = -2

Divide both -4

Substitute y = 1/2 into equation (1)

x + y = 5

Hence, the solution to the equations is

The year-2 CPI is 102, and the rate of inflation from year 1 to year 2 is 2%.

To calculate the rate of inflation and the Consumer Price Index (CPI) change from year 1 to year 2, we need to follow these steps:

Step 1: Calculate the inflation rate:

Inflation Rate = (Year 2 CPI - Year 1 CPI) / Year 1 CPI

Step 2: Calculate the Year 2 CPI:

Year 2 CPI = (Year 2 Basket Price / Year 1 Basket Price) * 100

Let's calculate the values:

Year 1 Basket Price = $25.00

Year 2 Basket Price = $25.50

Step 1: Calculate the inflation rate:

Inflation Rate = ($25.50 - $25.00) / $25.00

Inflation Rate = $0.50 / $25.00

Inflation Rate = 0.02 or 2%

Step 2: Calculate the Year 2 CPI:

Year 2 CPI = ($25.50 / $25.00) * 100

Year 2 CPI = 1.02 * 100

Year 2 CPI = 102

Therefore, the year-2 CPI is 102, and the rate of inflation from year 1 to year 2 is 2%.

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Answer:

1 +6 x + 12 x 2 + 8x 3

Explanation:

We must use our knowledge of the binomial expansion:

Method 1:

We can use:

(

x

+

1

)

n

=

1

+

n

x

+

n

(

n

−

1

)

2

!

x

2

+

n

(

n

−

1

)

(

n

−

2

)

3

!

x

3

+

...

Substituting  

n

=

3

and  

x

for  

2

x

⇒

(

2

x

+

1

)

3

=

1

+

(

3

⋅

2

x

)

+

3

⋅

2

2

!

⋅

(

2

x

)

2

+

3

⋅

2

⋅

1

3

!

⋅

(

2

x

)

3

=

1

+

6

x

+

12

x

2

+

8

x

3

Method 2:

We can use:

(

A

+

B

)

n

=

A

n

+

(

n

1

)

A

n

−

1

B

1

+

(

n

2

)

A

n

−

2

B

2

+

...

Letting  

A

=

2

x

and

B

=

1

for this circumstance:

(

2

x

+

1

)

3

=

(

2

x

)

3

+

(

3

1

)

(

2

x

)

2

(

1

)

+

(

3

2

)

(

2

x

)

1

(

1

)

2

+

(

3

3

)

(

2

x

)

0

(

1

)

3

=

8

x

3

+

12

x

2

+

6

x

+

1

Step-by-step explanation:

Ali will receive £10, and Ben will receive £25 when they divide £35 in the ratio of 2:5.

To divide £35 in the ratio of 2:5, we first need to calculate the total parts of the ratio:

Total parts = 2 + 5 = 7

Next, we divide the total amount (£35) into 7 equal parts:

£35 / 7 = £5

Now, we can allocate the amounts to Ali and Ben based on the ratio:

Ali's share = 2 parts * £5 = £10

Ben's share = 5 parts * £5 = £25

Therefore, Ali will receive £10, and Ben will receive £25 when they divide £35 in the ratio of 2:5.

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Answer:

08.262=)))55668(4738dfrj

Answer:

Step-by-step explanation:

1

-

8 exponent 9

The algorithm ensures that g is a generator, satisfying the necessary conditions.

To show that the algorithm produces a generator, we need to verify two conditions:

The algorithm selects a number, g, that is coprime to p-1.

The algorithm checks if g raised to the power of (p-1)/q is not congruent to 1 modulo p for each prime factor, q, of p-1.

Let's go through the steps of the algorithm to demonstrate these conditions:

Start with the prime factorization of p-1: p-1 = q1^a1 * q2^a2 * ... * qn^an, where q1, q2, ..., qn are distinct prime factors.

For each prime factor, q, calculate g = h^((p-1)/q) modulo p, where h is a randomly selected number between 2 and p-1.

Check if g is congruent to 1 modulo p. If it is, go back to step 2 and select a different h.

Repeat steps 2 and 3 until g is not congruent to 1 modulo p for each prime factor, q.

Now let's analyze these conditions:

By raising h to the power of (p-1)/q for each prime factor, the resulting g is guaranteed to be coprime to p-1. This is because g is not divisible by any prime factor of p-1.

For each prime factor, q, g^(p-1)/q is not congruent to 1 modulo p. This is because g^(p-1)/q is congruent to h^((p-1)/q * (p-1)/q) modulo p, and since h^((p-1)/q) is coprime to p, raising it to the power of (p-1)/q * (p-1)/q will not result in 1 modulo p.

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The graph of the solution set for the inequality can be seen on the image at the end.

Here we have the following inequality:

x < 32*y^2

So x is smaller than the parabola.

First, because we have the symbol "<", we whill graph the parabola:

x = 32*y^2

With a dashed line, which means that the points on the parabola are not solutions.

Once we have that parabola graphed, we need to shade all the region to the left of the parabola, that shaded region is the solution set for the inequality.

The graph can be seen below.

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Answer:

Step-by-step explanation:

Let the solution to

2x^2 + x -1 =0

x^2+ (1/2)x -(1/2)

are a and b

Hence a + b = -(1/2) ( minus the coefficient of x )

ab = -1/2 (the constant)

A. We want to have an equation where the roots are a +5 and b+5.

Therefore the sum of the roots is (a+5) + (b+5) = a+ b +10 =(-1/2) + 10 =19/2.

The product is (a+5)(b+5) =ab + 5(a+b) + 25 = (-1/2) + 5(-1/2) + 25 = 22.

So the equation is

x^2-(19/2)x + 22 =0

2x^2-19x + 44 =0

B. We want the roots to be 3a and 3b.

Hence (3a) + (3b) = 3(a+b) = 3(-1/2) =-3/2 and

(3a)(3b) = 9(ab) =9(-1/2)=-9/2.

So the equation is

x^2 +(3/2) x -9/2 = 0

2x^2 + 3x -9 =0.

Answer:

Step-by-step explanation:

In a tent, there are nine boys.

There were five tents.

5 tents containing 9 boys can equal 45 boys.

(5 x 9 = 45)

In a cabin, there are seven boys.

There were four cabins.

4 cabins containing 7 boys can equal 28 boys.

(4 x 7 = 28)

Now, to find all the boys, add the numbers together.

28 boys with 45 boys will equal 73 boys.

Please check my answer for no one, not even me is right.

Good luck :)

The series ∑(n=3)∞ (ln(1+1/n))/(ln(n)ln(1+n)) is convergent, and its sum is 1/ln(3).

To determine the convergence of the series, we can use the limit comparison test. Let's consider the general term of the series, aₙ = (ln(1+1/n))/(ln(n)ln(1+n)). We can compare it to a known convergent series, bₙ = 1/(nln(n)).

Taking the limit as n approaches infinity of aₙ/bₙ, we have:

lim (n→∞) (ln(1+1/n))/(ln(n)ln(1+n))/(1/(nln(n))) = lim (n→∞) [(ln(1+1/n))(nln(n))]/[(ln(n)ln(1+n))]

Using limit properties and simplifying the expression, we find:

lim (n→∞) (ln(1+1/n))/(ln(n)ln(1+n)) = 1/ln(3)

Since the limit is a finite non-zero value, both series have the same convergence behavior. Thus, the series ∑(n=3)∞ (ln(1+1/n))/(ln(n)ln(1+n)) is convergent, and its sum is 1/ln(3).

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Answer:

Progressive

Step-by-step explanation:

Progressive tax rates increase as a person's income increases

Answer:

rational

Step-by-step explanation:

Answer:

The fraction 3/10 is a rational number. All fractions are rational numbers.

Answer:

Step-by-step explanation:

Original Cost Price (CP)= $921

Discount Rate (%)= 11 %

Discounted Money= Discount Rate* Cost Price=11%*$921=0.11*921= $ 101.31

Hence, Price after Discount= Original Cost Price- Discounted Money

                                              = $921 - $101.31

                                              = $ 819.69

Hence, The price of the mountain bike after the discount is $819.69.

The number 48,000,000,000 can be written in scientific notation as:

4.8 × 1010 or 48 × 109

Scientific notation is a way of expressing numbers in a concise form. It is typically used when dealing with very large or very small numbers. In scientific notation, a number is written as the product of two factors: a number between 1 and 10, and a power of 10.

For example, to express the number 48,000,000,000 in scientific notation we must first determine the two factors.

First factor: This is the number between 1 and 10. To determine this factor, we must count the number of places to the right of the decimal point (in this case, 0 places) and then move the decimal point that many places to the left.

48,000,000,000 → 4.8

Second factor: This is the power of 10. To determine this factor, we must count the number of places we moved the decimal point and then express this number as a power of 10.

In this example, we moved the decimal point 10 places to the left. Therefore, our power of 10 is 10.

Therefore, the number 48,000,000,000 can be written in scientific notation as:

4.8 × 1010 or 48 × 109

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Answer: A, A

Explanation:

48,000,000,000 g = 4.8 × 1010 g

0.000000655 mL = 6.55 × 10-7 mL

Answer:

$59.99

Step-by-step explanation:

11% of $59.99 is $6.60. $59.99+$6.60=66.59

Answer:

c

Step-by-step explanation: