Consider the following system of differential equations da V = 0, dt dy + 3x + 4y = 0. dt a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form ( )= a()+ (1) M C₂ where C₁ and C₂ are constants. Give the values of X1, 31, A2 and 32. Enter your values such that A₁ A2- A₁ 9/1 3/2 Input all numbers as integers or fractions, not as decimals. Find the particular solution, expressed as a (t) and y(t), which satisfies the initial conditions (0) = 3, y(0) = -7. y(t)

Answer: Here is what you need to solve your problem!

If A and B are independent events, it means that the occurrence of one event does not affect the probability of the occurrence of the other event. In other words, the probability of event A happening is the same whether or not event B happens and vice versa.

To illustrate this, let's consider an example. Say we have two events: flipping a coin and rolling a dice. The probability of getting heads on the coin is 1/2 and the probability of rolling a 3 on the dice is 1/6.

These events are independent because the outcome of one event does not affect the outcome of the other event. So, the probability of getting heads on the coin AND rolling a 3 on the dice is (1/2) x (1/6) = 1/12.

Another way to check if two events are independent is to use the formula P(A and B) = P(A) x P(B). If the result of this equation is true, then the events are independent. If not, they are dependent.

Overall, understanding the concept of independent events is important in probability theory because it helps us calculate the probability of multiple events happening simultaneously.

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Answer: 10 months

Step-by-step explanation:

432 + 40x >505 + 32x

40x >32x + 73

8x > 73

8x/8 > 73/8

x > 73/8 = 9.125

Round 9.125 to 10

The number of months that will take Lola to have more trading cards is obtained as 8.

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

The number of cards with Lola and Joel are 432 and 505 respectively.

Suppose the number of required month be x.

Then, the inequality expression can be written for the given case as,

432 + 40x > 505 + 32x

⇒ 40x - 32x > 505 - 432

⇒ 8x > 63

⇒ x > 63/8

The number of months should be an integer value.

And, the nearest integer value of the greater than 63/8 is 8.

Hence, the number of months required for the given case is 8.

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In the given word problem, the rate of change is the change in the cost of the ice cream concerning the change in the number of scoops.

That is, the rate of change is the ratio of the change in the cost of ice cream and the change in the number of scoops. Let's first calculate the initial rate of change or slope of the given deal: When we buy a waffle cone, the cost is $3, and we can buy one scoop of ice cream for $1.50.So, for one scoop of ice cream, the total cost would be 3 + 1.50 = $4.50.

We can represent the cost of one scoop of ice cream with the help of a linear equation: y = mx + b. Here, the slope or the rate of change, m = Change in cost of ice cream/ Change in the number of scoops= 1.5/1= 1.5Therefore, the rate of change of the ice cream with respect to the number of scoops is $1.50/scoop.

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Answer:

(7 x 3) + (7 x 1)

The average of the sample ranges for the weight of packages of Skittles is 0.11. So, the correct answer is (e) 0.11.

To find the average of the sample ranges for the weight of packages of Skittles, we first calculate the range for each sample. The range is the difference between the maximum and minimum values in each sample.

Sample 1: Range\(= 3.62 - 3.58 = 0.04\)

Sample 2: Range\(= 3.65 - 3.49 = 0.16\)

Sample 3: Range \(= 3.65 - 3.45 = 0.20\)

Sample 4: Range \(= 3.64 - 3.54 = 0.10\)

Sample 5: Range\(= 3.62 - 3.49 = 0.13\)

Next, we calculate the average of these sample ranges:

A\(verage = (0.04 + 0.16 + 0.20 + 0.10 + 0.13) / 5 = 0.11\)

Therefore, the average of the sample ranges for the weight of packages of Skittles is \(0.11\). So, the correct answer is (e) \(0.11.\)

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Answer:

660

Step-by-step explanation:

Here is the equation to get this answer-

A=2πrh+2πr2=2·π·7·8+2·π·72≈659.73446

then you round the 659.73446 to get 660

The number of patients received in the E.R. every 24 hours is D, 9.

Find the total number of patients in the E.R. at the end of the 24-hour period by integrating the net change or admission rate function over the 24-hour period.

The net change in the number of patients over the 24-hour period is:

∫[0,24] [A(t) - R(t)] dt

= ∫[0,24] [(1/79)(768+23t - t²) - (1/65)(390 +41t-t²)] dt

Simplify expression by first expanding the terms inside the integrals and then combining like terms:

= ∫[0,24] [(192/395) + (18/395)t - (1/395)t²] dt

= [(192/395)t + (9/790)t² - (1/1185)t³] [0,24]

= [(192/395)(24) + (9/790)(24)² - (1/1185)(24)³] - [(192/395)(0) + (9/790)(0)² - (1/1185)(0)³]

= 6.32

Therefore, the approximate number of patients in the E.R. at the end of the 24-hour period is:

3 + 6.32 ≈ 9.32

Since a patient cannot be a fraction, the answer would be approximately 9 patients.

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Answer:

11° is the measure of the exterior angles

Step-by-step explanation:

Theorem:   Alternate exterior angles are congruent when two parallel lines cut by a transversal.

First we solve for x using the theorem

6x + 5 = 7x + 4

x = 1

Substitute x = 1 into 6x + 5

6(1) + 5 = 6 + 5 = 11°

(B) The p-esteem is more prominent than 0.05 yet under 0.10, in this manner there is no proof of a tremendous distinction in mean hunt times on the two sites.

The p-value that was derived from the data and the significance level (alpha) that was selected for the test must be compared in order to determine the correct response.

Since the importance level isn't given in the inquiry, we'll expect a typical worth of 0.05, which is much of the time utilized in speculation testing.

A two-sample t-test can be used to test the hypothesis that the two websites have significantly different mean search times. The test statistic and its corresponding p-value can be calculated using the sample means, standard deviations, and sample sizes.

The appropriate degrees of freedom are used to calculate the p-value using statistical software or a calculator.

In this instance, we reject the null hypothesis if the calculated p-value falls below the significance level (alpha) of 0.05, assuming that the conditions for inference are satisfied. In any case, if the p-esteem is more noteworthy than or equivalent to 0.05, we neglect to dismiss the invalid speculation.

Since the importance level isn't unequivocally referenced in the inquiry, we'll expect to be alpha = 0.05.

The correct response is, as a result of this:

B) The p-esteem is more prominent than 0.05 yet under 0.10, in this manner there is no proof of a tremendous distinction in mean hunt times on the two sites.

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Answer:

5

Step-by-step explanation:

Well, there are 4 "s" blocks that make up one "20" units block. So all you have to do is to divide 20/4 to get 5.

Answer:

7/11

Step-by-step explanation:

We are to write an equation describing the relationship between variables y and x, given that y varies inversely as the cube root of x, and when x = 216, y = 5.

An inverse variation relationship is expressed in the form:y = k/x

Where k is a constant of variation.

This means that if y varies inversely with the cube root of x,

then we can express this relationship as: y = k/x^(1/3)Taking x = 216 and y = 5,

we can find the value of k:k = xy^(1/3) = (216)(5^(1/3))

We can now substitute this value of k in the equation: y = k/x^(1/3)

= [(216)(5^(1/3))] / x^(1/3).

The relationship between the variables can be expressed as y = k/x^(1/3).

This equation is derived from the inverse variation relationship which states that y is inversely proportional to the cube root of x.

This equation can be used to find the value of y for any given value of x.

To find the value of k, we need to use the fact that when x = 216, y = 5.

Using these values, we can find the value of k to be k = xy^(1/3

) = (216)(5^(1/3)).

Substituting this value of k in the equation,

we get y = [(216)(5^(1/3))] / x^(1/3).

This equation can be used to find the value of y for any given value of x.

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The y intercept equation will be \(y=-2x+3\) .A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.

Finding the value of y at x=0 on a graph will reveal the y-intercept. The graph's intersection with the y-axis occurs at this location.

When a straight line is described by the equation "y = mx + b," the slope is the number "m" multiplied on the x, and the y-intercept is "b." (that is, the point where the line crosses the vertical y-axis).

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Answer:

D(-5,5), E(-3,4), F(-6,0), G(-8,1)

Step-by-step explanation:

You need to subtract 11 from x, (which is the first number in the parenthesis) because the rule is (x-11, y+4) and add 4 to y.

I really hope this helps!

The value represents the is D(-5,5), E(-3,4), F(-6,0), G(-8,1) (-8,1) . A rectangle is a quadrilateral with four right angles in the Euclidean plane.

A rectangle is a quadrilateral with four right angles in the Euclidean plane. A parallelogram with a right angle or an equiangular quadrilateral, where equiangular means that all of its angles are equal, are other ways to describe it. A rectangle with four equally length sides is a square.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form.

Given,

vertices D(61), E(8,0),

F(5.-6), and G(3-5); (x, y)(x-11, y + 4)

Because the rule is (x-11, y+4), you must subtract 11 from x, which is the first number in the parenthesis, and then add 4 to y.

D(-5,5), E(-3,4), F(-6,0), G(-8,1) (-8,1)

Therefore D(-5,5), E(-3,4), F(-6,0), G(-8,1) (-8,1)  is the value represents the rectangle.

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Step-by-step explanation:

a drop in temperature means the temperature will decrease.

That decrease is represented with a negative integer which should be added to the previous temperature.

Given:

given solution is (0,3)

check for sol. put the value in equation then:

for another equation :

so the solution of x and y is right.

Answer:

Step-by-step explanation:

We need to multiply 0.98 by 2 which is 1.96 now we need to divide 0.98 by two which is 0.49, so add those together and you have 2.45. Hope this helps :)

9514 1404 393

Answer:

  126°

Step-by-step explanation:

To find the exterior angle, we need to know one of the acute angles. Those are found using the fact that they are complementary.

  (5x -6) +(3x) = 90

  8x = 96 . . . . . . . . . . . add 6, collect terms

  x = 12 . . . . . . . . . . . . . divide by 8

  3x° = 3·12° = 36° . . . . . . find the "remote" acute angle

  exterior angle = 90° +36°

  exterior angle = 126°

__

The exterior angle is the supplement of the one marked (5x-6)°. It is also the sum of the two remote interior angles, 90° and 3x°. Being lazy, we figure that 90 +3·12 is easier to compute than 180 - (5·12 -6). Either way, the exterior angle is 126°.

Answer:

g=-13.8

d=-16

Step-by-step explanation:

hope this helps :)

Answer:

To create this table, first, you must find the values of x that you want to use, in this case, i will use the set:

{1, 2, 3, 4, 5, 6}

Now, first make a table as:

\(\left[\begin{array}{ccc}x&y\\1&\\2&\\3&\\4&\\5&\\6&\end{array}\right]\)

Now we need to complete the values of y.

we know that y(x) = x^2

then when we have x = 1, y(1) = 1^2 = 1.

when x = 2, y(2) = 2^2 = 4.

and so on, you input the values of x in the function y = f(x) = x^2

and the values of y are recorded in the table.

f(1) = 1^2 = 1

f(2) = 2^2 = 4

f(3) = 3^2 = 9

f(4) = 4^2 = 16

f(5) = 5^2 = 25

f(6) = 6^= 36

Then the completed table is:

Answer:

7mm

Step-by-step explanation:

Area=l*b

35cm²=l*50mm

350mm²/50mm=l

7mm=l

Answer:

Part A

The two figures, ΔABC and ΔPQR are congruent by the SSS rule of congruency

Part B

The rigid motion that maps ΔABC to ΔPQR are a 180° clockwise rotation about the origin, followed by a horizontal shift of 1 unit to the right

Step-by-step explanation:

Part A

The given coordinates of the vertices of triangle ABC are;

A(-8, -2), B(-3, -6), C(-2, -2)

The length of side AB = √((-6 - (-2))² + (-3 - (-8))²) = √41

The length of side AC = √((-2 - (-2))² + (-2 - (-8))²) = 6

The length of side BC = √((-6 - (-2))² + (-3 - (-2))²) = √17

The given coordinates of the vertices of triangle PQR are;

P(9, 2), Q(4, 6), R(3, 2)

The length of side PQ = √((6 - 2)² + (4 - 9)²) = √41

The length of side PR = √((2 - 2)² + (3 - 9)²) = 6

The length of side RQ = √((6 - 2)² + (4 - 3)²) = √17

Given that the length of the three sides of triangle ABC are equal to the lengths of the three sides of triangle PQR, we have;

ΔABC ≅ ΔPQR by Side Side Side rule of congruency

Part B

Whereby AB and PQ, and BC and RQ are pair of corresponding sides, the rigid motion that maps ΔABC to ΔPQR are;

1) A 180° clockwise (or counterclockwise) rotation about the origin followed by

2) A shift of 1 unit to the right.

The solution to the given quadratic expression is x = -1 and x = 5

Given the quadratic equation below

f(x) = x^2 - 4x - 5

Factorize

f(x) = x^2 - 5x + x - 5 = 0
f(x) = x(x - 5) + 1(x - 5) = 0
(x+1)(x-5) = 0
x = -1 and x = 5

Hence the solution to the given quadratic expression is x = -1 and x = 5

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Answer:

x = -1; x = 5

Step-by-step explanation:

Standard Form of a Quadratic Function: f(x) = ax² + bx + c, where a ≠ 0

Given function: f(x) = x² - 4x - 5

⇒ a = 1, b = -4, c = -5

We are asked to solve the following function by factoring. In order to do so, let's rewrite the middle term by finding the factors that give a product of the first and last terms (a • c = -5) and give us the sum of the middle term (b = -4).

Factors that give a product of a • c: 1 • -5 = -5

Factors that give a sum of b: 1 + (-5) = -4

Step 1: Substitute f(x) = 0.

⇒ 0 = x² - 4x - 5

Step 2: Rewrite the equation with the factors.

⇒ 0 = x² + x - 5x - 5

Step 3: Factor out x and -5.

⇒ 0 = (x² + x) + (-5x - 5)

⇒ 0 x(x + 1) - 5(x + 1) [ Factor out the common factor. ]

⇒ 0 = (x - 5)(x + 1)

Step 4: Apply the Zero-Product Property (if m•n = 0, then m = 0 or n = 0)

a) 0 = x - 5 ⇒ 0 + 5 = x - 5 + 5 ⇒ 5 = x

b) 0 = x + 1 ⇒ 0 - 1 = x + 1 - 1 ⇒ -1 = x

Therefore, the missing solution for this quadratic function is x = 5.

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a) Yes, It does. The scatterplot support the newspaper report about number of semesters and starting salary.

b) The value is relatively low, indicating that there are other factors that also contribute to starting salary.

c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables.

a) The scatterplot appears to show a positive association between the number of semesters needed to complete an academic program and the starting salary in the first year of a job. As the number of semesters increases, the starting salary generally increases as well. Therefore, the scatterplot supports the newspaper report.

b) The coefficient of determination, or R-squared value, represents the proportion of the variation in the dependent variable (starting salary) that is explained by the independent variable (number of semesters). A value of 0.335 means that 33.5% of the variation in starting salary is explained by the number of semesters. This value is relatively low, indicating that there are other factors that also contribute to starting salary.

c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables. A value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no correlation. The correlation coefficient for this data is not provided in the problem, so it is not possible to determine it. Without the correlation coefficient, it is not possible to interpret the strength and direction of the association between number of semesters and starting salary.

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Answer:

Step-by-step explanation:

70+85+150+x=360 degree(sum of 4 angles is always 360 degree)

305+x=360

x=360-305

x=55 degree

Answer:

85+1 50+70+x=360{ sum of interior angels of of quadrilateral}

305+x=360

x=360-305

x=55degree

Answer:

6 boys and 11 girls

Step-by-step explanation:

hello,

let 's note x the number of boys and y the number of girls, we can write two equations

"there are a total of 17 kids"

(1)  x + y  = 17

"There are 5 more girls than boys"

(2) y = x + 5

We can replace (2) in (1) it comes

x + x + 5 = 17

<=> 2x = 17-5 = 12

<=> x = 6

and then y = 11

So, there are 6 boys and 11 girls

graphs below

hope this helps

The number of girls in the club is 6

An equation is a mathematical statement formed from two algebraic expression when equated by an equal sign.

It is given that

Total Kids = 17

Let the number of boys be x

There are 5 more girls than boys

Let number of girls be y

y = x+5

The number of girls = x +5

x +y = 17

The graph is plotted  and is attached with the answer.

The intersection of the graph gives us the total number of girls and boys

(6,11) is the point of intersection and therefore

Number of boys = 6

No. of girls = 11

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