Find the solution of the initial-value problem y'" – 84" + 16Y' – 128y = sec 4t, y(0) = 2, y'(0) = 2, y"0) = 88. A fundamental set of solutions of the homogeneous equation is given by the functions: yı(t) = eat, where a = yz(t) = yz(t) = A particular solution is given by: Y(t) = ds-yi(t) to + ]) •yz(t) + • Y3(t) t) Therefore the solution of the initial-value problem is: y(t)=___ +Y(t).

Using the normalized power iteration method, two iterations : were performed for a given matrix and initial vector. The dominant eigenvalue and corresponding eigenvector were roughly predicted.

The normalized power iteration method is an iterative algorithm used to approximate the dominant eigenvalue and eigenvector of a matrix. The algorithm involves repeatedly multiplying the matrix by a vector and normalizing the result to converge towards the dominant eigenvector.

To perform two iterations, the initial vector is multiplied by the matrix twice, and normalization is applied after each iteration. The resulting vector after the second iteration provides an approximation of the dominant eigenvector. The corresponding eigenvalue can be estimated by taking the dot product of the resulting vector and the product of the matrix and the vector from the previous iteration.

The predicted dominant eigenvalue and eigenvector may not be exact due to the limited number of iterations performed. However, they can provide a rough approximation. Further iterations can be performed to refine the estimation.

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Answer:

15.71m

Step-by-step explanation:

One revolution is equal to the circumference of the wheel

Circumference = πD

22/7 X 5 = 15.71m

The velocity of seawater flowing through a horizontal tube with a variable cross-sectional area, having dimensions of 21cm and 7cm, and manometric pressures of 2.5 N/cm and 3.9 N/cm at the narrow and wide sections respectively, can be calculated using Bernoulli's equation.

According to Bernoulli's equation, the total pressure at any point in a fluid is equal to the sum of its static pressure, dynamic pressure, and potential energy per unit volume. In this case, we can assume that the height difference between the narrow and wide sections is negligible, so the potential energy term can be ignored. Thus, we can write:

where P1 and P2 are the manometric pressures at the narrow and wide sections respectively, ρ is the density of seawater (1.07 g/cm³), V1 and V2 are the velocities at the narrow and wide sections respectively.

Solving for V2, we get:

Substituting the given values, we get:

Therefore, the velocity of seawater flowing through the tube can be calculated using this equation.

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Complete Question:

In a horizontal tube of variable section, the cross sections are 21cm and 7em respectively. If seawater (1.07 g/cm*) flows through the tube and the gauge pressures in the narrowing and wide part are 2.5 N/cm and 3.9N/cm

When a single card is randomly drawn from a standard deck of 52 playing cards, the odds in favor of the card being a 3, 4, 5, 6, or 7 can be calculated by considering the total number of these cards and the total number of cards in the deck.

In a standard deck, there are four suits (hearts, diamonds, clubs, and spades), each containing one card of each rank (from Ace to King). Therefore, there is one 3, 4, 5, 6, and 7 in each suit, which results in a total of 4 cards for each rank (3s, 4s, 5s, 6s, and 7s). As there are five ranks in question, there are 4 x 5 = 20 cards that are either a 3, 4, 5, 6, or 7.

To find the odds in favor of drawing one of these cards, we'll divide the number of favorable outcomes (20) by the total number of possible outcomes (52). So, the odds in favor are:

20 (favorable outcomes) / 52 (total outcomes) = 5/13

Therefore, the odds in favor of drawing a 3, 4, 5, 6, or 7 from a standard deck of cards are 5/13.

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Answer:

21x^2 + 33x + 16

Step-by-step explanation:

(14x^2 + 13x + 12) + (7x^2 + 20x + 4)

Combine like terms:

14x^2 + 7x^2 = 21x^2

13x + 20x = 33x

12 + 4 = 16

Thus:

21x^2 + 33x + 16

Answer:

21x^2 + 33x + 16.

Step-by-step explanation:

(14x2 + 13x + 12) + (7x2 + 20x + 4)   Remove the parentheses:

= 14x2 + 13x + 12 + 7x2 + 20x + 4    Bring like terms togethher:

= 14x^2 + 7x^2 + 13x + 20x + 12 + 4

= 21x^2 + 33x + 16.

Answer:

7 ÷ 1 = 7

Step-by-step explanation:

Answer:

I think

Step-by-step explanation:

I think you are subtracting

The negative correlation coefficient of -0.73 between consumption of vitamin A and the cancer rate of a particular type of cancer suggests that as vitamin A consumption increases, the cancer rate tends to decrease.

A correlation coefficient measures the strength and direction of the linear relationship between two variables.

In this case, a correlation coefficient of -0.73 indicates a negative correlation between consumption of vitamin A and the cancer rate.

Interpreting this correlation, it can be inferred that there is an inverse relationship between the two variables. As consumption of vitamin A increases, the cancer rate tends to decrease.

However, it is important to note that correlation does not imply causation.

It would be incorrect to conclude that consuming more vitamin A causes this type of cancer. Correlation does not provide information about the direction of causality.

Other factors and confounding variables may be involved in the relationship between vitamin A consumption and cancer rate.

To establish a causal relationship, further research, such as experimental studies or controlled trials, would be necessary. These types of studies can help determine whether there is a causal link between vitamin A consumption and the occurrence of this particular cancer.

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As per the combination method, the number of ways to form a committee with six members if it must have more women than men is 91,350.

The total number of ways to form a committee with six members from the 27 people in the department is:

²⁷C₆ = 27! / (6! * (27 - 6)!) = 134,490

Now, we need to find the number of ways to form a committee with more women than men. We can use the concept of unitary method to do this. Let x be the number of women in the committee, then the number of men in the committee will be (6 - x), since the total number of members in the committee is 6.

Since we need to have more women than men, we have the following inequality:

x > (6 - x)

Simplifying this inequality, we get:

2x > 6

x > 3

Therefore, the number of women in the committee must be greater than 3.

Now, we can use another formula for combinations to find the number of ways to form a committee with more women than men. Let's call this number W, then we have:

W = (¹⁵C₄ x ¹²C₂) + (¹⁵C₅ x ¹²C₁) + (¹⁵C₆ x ¹²C₀)

The first term in this equation represents the number of ways to choose 4 women and 2 men from the department, the second term represents the number of ways to choose 5 women and 1 man, and the third term represents the number of ways to choose 6 women and 0 men.

Using the formula for combinations, we get:

¹⁵C₄ = 15! / (4! * (15 - 4)!) = 1,386

¹²C₂ = 12! / (2! * (12 - 2)!) = 66

¹⁵C₅ = 15! / (5! * (15 - 5)!) = 3,003

¹²C₁ = 12! / (1! * (12 - 1)!) = 12

¹⁵C₆ = 15! / (6! * (15 - 6)!) = 5005

¹²C₀ = 1

Therefore, we have:

= (1,386 x 66) + (3,003 x 12) + (5005 x 1)

= 91,350

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Answer: 135, 21, 30, 63, 90

Step-by-step explanation:

Answer:

C:  \(\frac{2}{9}\)

Step-by-step explanation:

Given the function,  \(f(x) = 2*3^{x}\), for f(–2):

Substitute the given input value into the function:

\(f(-2) = 2(3)^{-2} = 2(\frac{1}{3^{2} }) = 2(\frac{1}{9}) = \frac{2}{9}\)

Therefore, f(–2) = \(\frac{2}{9}\), making C the correct answer.

Please mark my answers as the Brainliest if my explanations were helpful :)

Answer:

Step-by-step explanation:

The expression 83 - 7.5 t represents the amount of water that is left in the tank after t hours as 7.5 l of water drains every hour from the large water tank.

We are given that:

7,5 l of water drains from the large water tank every hour.

Also, the water level in the large water tank initially was 83 l

We need to tell what does the expression 83 - 7.5 t represent.

It represents the amount of water that is left in the tank after t hours as 7.5 l of water drains every hour from the large water tank.

Therefore, the expression 83 - 7.5 t represents the amount of water that is left in the tank after t hours as 7.5 l of water drains every hour from the large water tank.

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Answer:

A.  \(p(x)=7x-2\)

Step-by-step explanation:

Given function:

\(y=\dfrac{x+2}{7}\)

Rearrange to make x the subject:

\(\implies 7y=x+2\)

\(\implies x=7y-2\)

Swap x and y:

\(\implies y=7x-2\)

This is the inverse of the original function.

Therefore, the answer is A  \(p(x)=7x-2\)

The probability that a student who had a dog also had a cat would be = 7/25.

To calculate the possible outcome of the given event, the formula for probability should be used and it's given below as follows. That is;

Probability = possible outcome/sample space

possible outcome = 7

sample space = 7+2+3+13 = 25

Probability = 7/25

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Answer:

50 miles per hour

Step-by-step explanation:

Divide 100 by 2

50

Hope this helped :)

Answer:

6,912....

Step-by-step explanation:

6 times 12 times 6 time 4 times 4 = 6,912

Answer:

= 360 ft³

Step-by-step explanation:

Rectangular prism

Volume = length x width x height

V = l x w x h

V = 12 x 6 x 4

V = 288 ft³

Triangular prism

Volume = 1/2 x base x height x length

V = 1/2 x 6 x 4 x 6 ( the width of the rectangular prism is the base of the triangular prism)

V = 1/2 x 144

V = 72 ft³

ADD BOTH VOLUMES

= 288 + 72

= 360 ft³

Let us first understand what is meant by the term probability of happening of an event. The term probability of an event happening tells us about the extent or how many times it is likely to happen in a given number of tries. For example, if we throw a die of six faces, then the probability of a number to come on the top of the dice tells us about the extent to which that is likely to occur.

The probability of an event to occur in an experiment is equal to the ratio of the outcomes in which this event happens to the total number of outcomes of the experiment. A pack of cards contains 52 total cards. Therefore, when we pick a card from the set there can be 52 different outcomes.

(i) A pack of cards contains 13 red cards. Therefore, out of those 52 outcomes, 13 outcomes are required. Hence, the probability of getting a red card is 1352=14.

(ii) A pack of cards contains 13 black cards. Therefore, out of those 52 outcomes, 13 outcomes are required. Hence, the probability of getting a black card is 1352=14

(iii) A pack of cards contains 4 black cards. Therefore, out of those 52 outcomes, 4 outcomes are required. Hence, the probability of getting an ace is 452=113.

Note: Note that probability is not always sure or it doesn’t guarantee that the specific event will surely happen in those number of trials. This means that the probability of getting an ace card does not mean that in four tries we will surely get an ace. Probability just tells us how likely the event may happen.

It is critical to open a compass with over half the way in order for the arcs formed to meet for perpendicular bisector.

A perpendicular bisector would be a line that cuts a line segment in half and forms a 90-degree angle at the intersection point. In other words, a perpendicular bisector separates a line segment now at midpoint, forming a 90-degree angle.

Now, consider an example;

When you wish to build a perpendicular line on a line segment, like line AB, you do the following;

A line AB appears to be bisected perpendicularly as a result. The arcs would not have met if the compass is opened less than half way down line AB.

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Since angle y and angle x form vertical angles, the measure of angle x is equal to 50°.

In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

Furthermore, the sum of the angles on a straight line is equal to 180. Therefore, we would sum up all of the angles as follows;

60° + 70° + y = 180°

130° + y = 180°

y = 180° - 130°

y = 50°

Since both angle x and angle y are vertical angles, we can logically deduce that they are congruent and as such the magnitude of angle x is equal to 50°.

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The length of the altitude to line segment $\overline{em}$ in triangle $gem$ is 16 units.

Let's denote the length of the altitude to line segment $\overline{em}$ in triangle $gem$ as $h$.

The area of a triangle is given by the formula:

Area = (base * height) / 2

The area common to triangle $gem$ and square $aime$ is 80 square units. Since the base of triangle $gem$ is $\overline{em}$, we have:

80 = (10 * h) / 2

160 = 10h

Solving for $h$, we have:

h = 160 / 10

h = 16

Therefore, the length of the altitude to line segment $\overline{em}$ in triangle $gem$ is 16 units.

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Answer:

B

Step-by-step explanation:

Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1.

Answer:

Luis’s, because he flipped the inequality sign when he subtracted

Step-by-step explanation:

Luis’s, because he flipped the inequality sign when he subtracted

The probability that Juan loses his next tennis match is 48%

From the question, we have the following parameters

The proportion of tennis matches won

p = 52%

This proportion implies that the probability that the player will win his next tennis match

So, we have the following representations

Probability of winning, p = 52%

Express the percentage as decimal

So, we have the following representations

Probability of winning, p = 0.52

The probability of losing the next match is the complement of the probability of winning

This is represented as

Probability of losing = 1 - Probability of winning,

Substitute the known values in the above equation

So, we have the following equation

Probability of losing = 1 - 0.52

Evaluate

Probability of losing = 0.48

Hence, the probability is 0.48 or 48%

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A solution to this system of linear equations is (1, -2).

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

4x - 2y = 8     ......equation 1.

y = -2     ......equation 2.

Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant IV and it is given by the ordered pair (1, -2).

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Answer:

-3, -2.5, -3/4, 0.8, 2.5, 6 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/2 = 0.5

6 = 6

6 + 0.5 = 6.5

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

1/4 = 0.25

-1/4 = -0.25

-3/4 = -0.75

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

Hope this helps! <3

The expressions that are True are 8 < 10, 10 != 8,  8 <= 10 and 10 >= 8 Thus correct options are b, c, d and e

Let's go through each expression and determine if it evaluates to True or False:

a. 10=8: This expression checks if 10 is equal to 8. Since 10 is not equal to 8, this expression evaluates to False.

b. 8 < 10: This expression checks if 8 is less than 10. Since 8 is indeed less than 10, this expression evaluates to True.

c. 10 != 8: This expression checks if 10 is not equal to 8. Since 10 is not equal to 8, this expression evaluates to True.

d. 8 <= 10: This expression checks if 8 is less than or equal to 10. Since 8 is less than 10, this expression evaluates to True.

e. 10 >= 8: This expression checks if 10 is greater than or equal to 8. Since 10 is indeed greater than 8, this expression evaluates to True.

In summary, the expressions that evaluate to True are:

b. 8 < 10

c. 10 != 8

d. 8 <= 10

e. 10 >= 8

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Answer: 149.12

Step-by-step explanation:

to find out the extended warranty we do,

466*(32/100)=149.12

The extended warranty cost is $149.12.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, a set of floor speakers costs $466.

If the extended warranty on the speakers costs 32% of the price of the speakers.

Now, extended price =32% of 466

32/100 ×466

= 0.32×466

= $149.12

Therefore, the extended warranty cost is $149.12.

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This bad is because It can lead to adding variables with little or no predicative power.

Given,

In the question:

As more independent variables are added to a regression model, the coefficient of determination tends to increase.

How is this bad?

Now, According to the question:

Let's know:

What is meant by a regression model?

A regression model is a statistical model that estimates the relationship between one dependent variable and one or more independent variables using a line (or a plane in the case of two or more independent variables).

Hence, This bad is because It can lead to adding variables with little or no predicative power.

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Answer:

3u+12

Step-by-step explanation:

Answer:

x ≈ 44.4°

Step-by-step explanation:

Using the sine ratio in the right triangle

sin x = \(\frac{opposite}{hypotenuse}\) = \(\frac{7}{10}\) , then

x = \(sin^{-1}\) (\(\frac{7}{10}\) ) ≈ 44.4° ( to the nearest tenth )

The missing term in the equation (x + 9)² = x² + 18x + is 81. The simplified form of the (x + 9 )² = x² + 18x + 81. The correct option is C.

Given

(x + 9)² =  x² + 18x +----

Required to find the missing term =?

It is given the form of ( a + b)² = a² + 2ab + b²

Putting the given values in the above form we get the value of the missing term from the equation

(x + 9 )² = x² + 2 × x ×9 + 9 × 9

              = x² + 18x + 81  

A quadratic equation is a second-order polynomial equation in one variable that goes like this: x ax2 + bx + c=0, where a 0. Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.

Thus, we get the value of the missing term as 81.

Thus, the ideal selection is option C.

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Answer:

x=15

Step-by-step explanation:

5x+25=100

Subtract 25 from both sides.

5x+25−25=100−25

5x=75

Divide both sides by 5.

5x÷5=75÷5

x=15

\(5x+25=100\\x=\)

Subtract 25 from both sides:

\(5x+25-25=100-25\\5x=75\)

Divide both sides by 5:

\(\frac{5x}{5} =\frac{75}{5}\)

\(\fbox{x=15}\)