find the variable y=[y1 y2] of the form y=Mx, where M is a matrix so that the differential equation x′=Ax, A=[4414] is diagonal for the variable y. use that this coefficient matrix A has eigenpairs λ1 = 6, v1 = [1 2], and λ2 = 2, v2 = [1 -2]

Answer:

12

Step-by-step explanation:

Hello. Y/x = a constant k because y and x are by definition always in the same ratio. (y varies directly as x so if x is doubled y is also doubled etc.)

Answer:

I believe the answer is 7

Answer:

12

Step-by-step explanation:

9 * 12 - 2 = 61

7 * 12 + 12 = 61

Answer:

fx=19 and fx-4= -1

Step-by-step explanation:

Add and divide those 2 problems and subtract.

Answer:

$60

Step-by-step explanation:

20 + 40 = 60

The ratio of boy to girl who play kickball at race is 6 to 2. There are 18 girl on the team. the number of boys who play kickball at race is 12 boys.

The ratio of boy to girl who play kickball at race is 6 to 2

6 boys: 2 girls

Multiply the number of girls by the ratio:

18 girls x (6 boys / 2 girls) = 18 x 3 = 54

Subtract the number of girls from the total to get the number of boys:

54 - 18 = 36

Therefore, there are 12 boys who play kickball at race.

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For Pearson correlation the most common purpose to examine is given by option a. The relationship between 2 variables.

The Pearson correlation is a statistical measure that indicates the extent to which two continuous variables are linearly related.

It measures the strength and direction of the relationship between two variables.

Ranging from -1 perfect negative correlation to 1 perfect positive correlation.

And with 0 indicating no correlation.

It is commonly used in research to examine the association between two variables.

Such as the relationship between height and weight, or between income and education level.

Therefore, the most common purpose of a Pearson correlation is to examine the relationship between 2 variables.

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The above question is incomplete, the complete question is:

The most common purpose for a Pearson correlation is to examine,

a. The relationship between 2 variables

b. Relationships among groups

c. Differences between variables

d. Differences between two or more groups

Answer:

C

Step-by-step explanation:

Answer:

found the x

it is sideways

it is 10x2

Step-by-step explanation:

2x + 1

89°

and 10x2

The average score of Adrian’s favorite team relative to its opponent using the observations Adrian made during the game is -0.3333.

What is data set?

A data set is a group of related data. In the case of tabular data, a data set relates to one or more database tables, where each row refers to a specific record in the corresponding data set and each column to a specific variable.

Here, we have

Given: Adrian kept an eye on the basketball game score by looking online every 10 minutes. Over 2 hours, 4 times Adrian’s favorite team was ahead by 3 points, and 4 times Adrian’s favorite team was behind by 4 points. All the other times, the two teams were tied.

The mean of a data set is given by the sum of all observations divided by the number of observations.

Adrian looked at the scores every 10 minutes in 2 hours, thus 12 times, as

= (2×60)/10 = 12

4 times ahead by 3 points, thus 4×3 = 12

4 times behind by 4 points, thus -4×4 = -16

At the other moments, the game was tied, thus the observation is 0.

Thus, the mean is of:

M = (12 - 16 = 0)/12 = -4/12 = -0.333

Hence, The average score of Adrian’s favorite team relative to its opponent using the observations Adrian made during the game is -0.3333.

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The actual distance from Indianapolis to South Bend is 4.185 miles, which is closest to the answer of 4 miles.

To determine the actual distance from Indianapolis to South Bend given the map scale, we need to use the formula:

Actual distance = Map distance x Scale

In this case, the map distance is 15 centimeters, and the scale is 1 cm : 6 miles. To use the formula, we need to convert the map distance to miles:

Map distance = 15 cm

Scale = 1 cm : 6 miles

15 cm x 1 inch/2.54 cm x 1 foot/12 inches x 1 mile/5280 feet = 0.279 miles

Now we can calculate the actual distance using the formula:

Actual distance = Map distance x Scale

Actual distance = 0.279 miles/cm x 15 cm

Actual distance = 4.185 miles

Therefore, the actual distance from Indianapolis to South Bend is 4.185 miles, which is closest to the answer of 4 miles.

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Answer:

Rational

125

7,548,123

Irrational

-0.75 v2

Any number (or part of a number) that contains a square root is irrational because NO square root can be expressed as a fraction.  (Or a "ratio", hence the term "irRATIOnal" - meaning no ratio or no fraction)

Step-by-step explanation:

Answer:

D. y= x^2 - 5x + 2

Step-by-step explanation:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:  

(

5

2

,

−

33

4

)

Focus:  

(

5

2

,

−

8

)

Axis of Symmetry:  

x

=

5

2

Directrix:  

y

=

−

17

2

x

y

0

−

2

1

−

6

5

2

−

33

4

3

−

8

4

−

6

_______________

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:  

(

5

4

,

−

9

8

)

Focus:  

(

5

4

,

−

1

)

Axis of Symmetry:  

x

=

5

4

Directrix:  

y

=

−

5

4

x

y

−

1

9

0

2

5

4

−

9

8

2

0

3

5

_____________

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:  

(

1

,

0

)

Focus:  

(

1

,

1

8

)

Axis of Symmetry:  

x

=

1

Directrix:  

y

=

−

1

8

x

y

−

1

8

0

2

1

0

2

2

3

8

____________

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:  

(

5

2

,

−

17

4

)

Focus:  

(

5

2

,

−

4

)

Axis of Symmetry:  

x

=

5

2

Directrix:  

y

=

−

9

2

x

y

0

2

1

−

2

5

2

−

17

4

3

−

4

4

−

2

The probability that both people own a dog is 0.1225, written as a decimal using the appropriate rounding rule. To solve this problem, we can use the multiplication rule of probability which states that the probability of two independent events occurring together is the product of their individual probabilities.

So, the probability of the first person owning a dog is 0.35, and the probability of the second person owning a dog (assuming independence) is also 0.35.  Therefore, the probability that both people own a dog is 0.35 x 0.35 = 0.1225.
To write this as a decimal using appropriate rounding rule, we can round to two decimal places, giving us 0.12 as our final answer. The probability that both people own a dog, we will use the concept of random, probability, and decimal.
1. Convert the percentage of people owning dogs to a decimal: 35% = 0.35
2. Since the two people are picked at random and we assume independence, we can multiply the probabilities: 0.35 * 0.35
3. Calculate the result: 0.35 * 0.35 = 0.1225

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The equation "ax2 = y," which has one solution unless a = 4, and none unless a = 4, has a solution. x = √(-4ay) / (2a) restricted by the condition that y be negative.

We may use the quadratic formula to determine the solutions to an equation for various values of an to construct a solution to the equation "ax² = y," which has no solution when a = 4 & just one solution in all other cases.

According to the quadratic formula, the answers to the problem "ax2 + bx + c = 0" are provided by

x = (-b +/- √(b² - 4ac)) / (2a)

In this formula, if we add "ax² = y," we obtain

x = (-0 +/- √(0² - 4ay)) / (2a)

which simplifies to

x = √(-4ay) / (2a)

If a = 4, the equation becomes

x = √(-16y) / 8

The equation has no solutions if y is positive because the value of (-16y) is fictitious. The value of (-16y) is real if y is negative, but the equation is still unsolvable since x cannot have a negative value. As a result, when a = 4, the problem has no solutions.

The equation has a single solution provided by any other value of a.

x = √(-4ay) / (2a)

For example, if a = 3, the equation becomes

x = √(-12y) / 6

Since √(-12y) is imaginary if y is positive, the problem has no solutions. If y is negative, √(-12y) has a real value, and there is only one solution to the problem.

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Answer:

she wills substitute r with 7%.

Step-by-step explanation:

Just did it.

Answer:

R = 7%

Principal (P)

Rate (R)

Time (t)

Step-by-step explanation:

The full intrest rate formula is i=prt

You are looking for r

R is the interest rate 7%

So i = 12,876*7%*3years will be the full equation.

Answer: 7/8?

Step-by-step explanation:

The greatest possible mass of the rock to two decimal places is 86.34 g

Since the mass of the piece of rock is 86.3 g, correct to the nearest 0.1 g. Thus, the actual mass of the rock  in 2 decimal places could be between 86.25 g and 86.34 g.

To find the greatest possible mass of the rock, we need to round up to the higher end of the range of the mass of the rock.

Therefore, the greatest possible mass of the rock to two decimal places is 86.34 g

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By the binomial theorem,

\(\displaystyle (2x+y)^7 = \sum_{k=0}^7 \binom7k (2x)^{7-k} y^k=\sum_{k=0}^7 \binom7k 2^{7-k} x^{7-k} y^k\)

where

\(\dbinom nk=\dfrac{n!}{k!(n-k)!}\)

is the binomial coefficient.

We get the x⁴y³ terms with k = 3, for which the coefficient would be

\(\dbinom73 2^{7-3}=\dfrac{7!}{3! 4!} 2^4=\boxed{560}\)

2 ( 3y + 10)

Use 2 to multiply both 3y and 10

Therefore, you have

2 x 3y + 2 x 10

6y + 20

It sounds like you want to find how many diagonals a nonagon has.

A nonagon has n = 9 sides.

The number of diagonals would be...

\(d = \text{number of diagonals}\\\\d = \frac{n(n-3)}{2}\\\\d = \frac{9(9-3)}{2}\\\\d = \frac{9(6)}{2}\\\\d = \frac{54}{2}\\\\d = 27\\\\\)

A nonagon has 27 different diagonals.

Answer:8/15

Step-by-step explanation:

Tanθ in a right angle triangle is the ratio of its perpendicular to its base. The ratio that represents the Tan(∠H) is \(\dfrac{8}{15}\).

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,

\(\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}\)

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

Base is the adjacent smaller side of the angle θ.

As it is given that the two of the given triangles are similar triangles, therefore, their corresponding sides will be in the same ratio.

\(\dfrac{QR}{HJ} = \dfrac{RP}{JG} = \dfrac{PQ}{GH}\)

Further, the sides can be written as,

\(\dfrac{QR}{HJ} = \dfrac{RP}{JG}\\\\\dfrac{QR}{RP} = \dfrac{HJ}{JG}=\dfrac{15}{8}\)

Now, the Tan(∠H) can be written as,

\(\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}\)

Substituting the value for the ∠H in ΔHJG,

\(\rm Tangent(\angle H) = \dfrac{JG}{HJ}\)

As the ratio is already known, therefore,

\(\rm Tangent(\angle H) = \dfrac{8}{15} = 0.5\bar3\)

Hence, the ratio that represents the Tan(∠H) is \(\dfrac{8}{15}\).

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Answer:

2/3 = 0.666666667

hopefully i helped :)

Answer:

I hope this is what you were looking for.

Step-by-step explanation:

There was a party 30 people were supposed to show up, but only 1/2 of those people did. There was a pie with 4 pieces, until someone ate a quarter of the pie they were left with 3/4. Only 3 more people will get a piece of pie.

(a) To find the probability that Dan wins two checker games in a row, we multiply the probability of winning a single game by itself since the events are independent.

The probability of winning a single game is 25%, or 0.25. Therefore, the probability that Dan wins two checker games in a row is:

0.25 * 0.25 = 0.0625

(b) Similarly, to find the probability that Dan wins four checker games in a row, we multiply the probability of winning a single game by itself four times:

0.25 * 0.25 * 0.25 * 0.25 = 0.00390625

(c) The probability that Dan wins four checker games in a row but does not win five in a row can be found by subtracting the probability of winning five games in a row from the probability of winning four games in a row. Since the events are independent, their complements are also independent. The complement of winning four games in a row is losing the fifth game. The probability of winning four games in a row is 0.00390625, and the probability of losing the fifth game is 0.75 (since Dan's chance of losing is 1 - 0.25). Therefore, the probability that Dan wins four games in a row but does not win five in a row is:

0.00390625 * 0.75 = 0.0029296875

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Answer:

Step-by-step explanation:

i

Answer:

B.12

Step-by-step explanation:

I Hope This Helps :)

Answer:

B. 12

Step-by-step explanation:

Apply Pythagoras theorem in triangleCED where CD = 10 units!!

Answer:

The answer is B. 50

Step-by-step explanation:

180-105=75

75+55=130

180-130=50

Answer:

PV= $925

Step-by-step explanation:

Giving the following information:

Money is borrowed at ​8% simple interest. After one​ year, ​$999 pays off the loan.

To calculate the original value of the loan, we need to use the following formula:

PV= FV/(1+i*n)

PV= 999/(1+0.08*1)

PV= $925

Answer:

0.4 x 10^-1

Step-by-step explanation:

4 x 10^0

=> 4

=> 0.4 x 10^-1