What is the slope of the line shown on the coordinate plane

Inverse of the given matrix A= \(\left[\begin{array}{ccc}-2&-3\\3&12\end{array}\right]\)  is \(A^{-1}\) = \(\left[\begin{array}{ccc}-0.8&-0.2\\0.2&0.13\end{array}\right]\)

for given matrix  A = \(\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]\)

                              \(A^{-1}\) = 1/IAI x\(\left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right]\)

              determinant of Matrix A is IAI = ad - bc

Here the given matrix A is  

                              A = \(\left[\begin{array}{ccc}-2&-3\\3&12\end{array}\right]\)

            determinant of A = I A I

                                        I A I = (-2 x 12) - (-3x3)

                                               = -24 + 9

                                              = -15

we know for a matrix  A = \(\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]\)

                              \(A^{-1}\) = 1/IAI x\(\left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right]\)

for   A = \(\left[\begin{array}{ccc}-2&-3\\3&12\end{array}\right]\)

                         \(A^{-1}\) = 1/-15 \(\left[\begin{array}{ccc}12&3\\-3&-2\end{array}\right]\)

                        \(A^{-1}\) = \(\left[\begin{array}{ccc}12/-15&3/-15\\-3/-15&-2/-15\end{array}\right]\)

                      \(A^{-1}\) = \(\left[\begin{array}{ccc}-0.8&-0.2\\0.2&0.13\end{array}\right]\)

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Answer:

If f=5 pounds of pressure, l=5.4 feet long

Step-by-step explanation:

Force needed to break a board varies inversely with the length of the board

Let

Force to break the board=f

Length of the board=l

f=k/l

Where k is a constant

If f=9 pounds of pressure and l=3 feet long

f=k/l

9=k/3

Cross product

9*3=k

27=k

If k=27, f=5 pounds of pressure. Find l?

f=k/l

5=27/l

Cross product

5l=27

l=27/5

=5.4

l=5.4 feet long

Using proportions, it is found that the board that requires 5 pounds of pressure to break is 1.67 inches long.

The rule of three is:

9 pounds - 3 feet

5 pounds - x feet

Applying cross multiplication:

\(9x = 3(5)\)

\(x = \frac{15}{9}\)

\(x = 1.67\)

The board that requires 5 pounds of pressure to break is 1.67 inches long.

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The statement 'The mode is the value of the observation that appears most frequently.' is True.

We know that, the mode is the most frequent number.

It is the number that occurs the highest number of times.

The observation occurring the most number of times or which has highest frequency is known as the mode.

For example,  in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6 as it occurs most often.

There is no mode when all observed values appear the same number of times in a data set.

Therefore, the statement 'The mode is the value of the observation that appears most frequently.' is True.

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The value of the hypotenuse y = 9, and the value of the opposite side of the right angle triangle x = 4.5

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the angle 30° in the right angle triangle, the hypotenuse is y, the opposite side is x and the adjacent side is 9√3

cos 30° = √3 = adjacent/hypotenuse

sin 30° = 1/2 = opposite/hypotenuse

√3 = 9√3/y {cross multiply}

y = 9√3/√3 {cancel out √3}

y = 9

1/2 = x/9 {cross multiply}

x = 9/2

x = 4.5

Therefore, by proper application of trigonometric ratios for the right angle triangle, the hypotenuse y is equal to 9 and the opposite side x is equal to 4.5.

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The probability of not getting a 6 or 10 total on either of two tosses of a pair of fair dice is 7/9.

To find the probability of not getting a 6 or 10 total on either of two tosses of a pair of fair dice, we first need to find the total number of possible outcomes when rolling two dice. There are 6 possible outcomes for the first die and 6 possible outcomes for the second die, giving us a total of 6 x 6 = 36 possible outcomes.

Next, we need to determine how many of these outcomes result in a total of 6 or 10. There are 5 ways to get a total of 6: (1,5), (2,4), (3,3), (4,2), and (5,1). There are also 3 ways to get a total of 10: (4,6), (5,5), and (6,4). So, there are 5 + 3 = 8 outcomes that result in a total of 6 or 10.

Therefore, the probability of not getting a 6 or 10 total on either of two tosses of a pair of fair dice is:

P(not 6 or 10) = 1 - P(6 or 10)

= 1 - 8/36

= 1 - 2/9

= 7/9

So the probability of not getting a 6 or 10 total on either of two tosses of a pair of fair dice is 7/9.

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Answer:

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Step-by-step explanation:

This was answered previously on here

Answer:

Square root of 61

Step-by-step explanation:

It was correct on my assignment

Answer:

\(x = \sqrt{36} = 6\)

Hope it helps

Have a good day Ahead

The distance traveled in the time interval 0 ≤ t ≤ 6 is 56/3 units.

To determine where v(t) = t²+ 4t -32 is positive or negative, we can use the quadratic formula to find the roots of the equation:

t = (-4 ± √(4² - 4(1)(-32)))/2(1)

Simplifying, we get:

t = (-4 ± 12)/2

t = -8 or t = 4

Therefore, v(t) is negative for t < -8 and for -8 < t < 4, and positive for t > 4.

Now, to find the distance traveled in the time interval 0 ≤ t ≤ 6, we need to integrate the absolute value of v(t) over this interval:

distance = ∫|t²+4t-32| dt from 0 to 6

Since v(t) is negative for 0 ≤ t < 4, we can write:

distance = ∫(-(t²+4t-32)) dt from 0 to 4 + ∫(t²+4t-32) dt from 4 to 6

Simplifying, we get:

distance = (-1/3)t³ - 2t² + 32t from 0 to 4 + (1/3)t³ + 2t² - 32t from 4 to 6

distance = 128/3 - (512/3 - 64) + (216/3 - 32 - 64)

distance = 128/3 - 184/3

distance = -56/3

However, we know that distance must be positive, so we take the absolute value:

distance = 56/3 units

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Total bit strings of length are 512.

What is bit ?

In each computing and digital communications, the bit is that the most elementary unit of information. The word could be a combination of 2 binary digits. A logical state with one amongst 2 potential values is portrayed by the bit.

Main body:

1 bit: 2 strings: 0, 1

2bit: 4 strings: 00, 01, 10, 11

3bit: 8 strings: 000, 001, 010, 011, 100, 101, 110, 111

4bit: 16 strings: 0000,0001,0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001. 1010, 1011, 1100, 1101, 1110, 1111

5bit: 32 strings

6bit: 64 strings

7bit: 128 strings

8bit: 256 strings

9 bits: 512 strings

OR this can be done by

Each bit has 2 possible values, so a string of length 9 has 2⁹ = 512 possible values.

Hence total bit sting are 512.

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Answer:

x=0.18 repeating

Step-by-step explanation:

Solve the rational equation by combining expressions and isolating the variable x

Answer:

3x+5y+22

Step-by-step explanation:

Answer:

3x + 5y + 22

Step-by-step explanation:

Given expression:- x + 3y + 2x + 10 + 2y + 12

Here, you can add all the 'x' terms together and 'y' terms together.

There is an 'x' and '2x'.

On adding them, you get 2x + x equals 3x.

Then add the 'y' terms

There is a '3y' and a '2y'. On adding them, you get 3y + 2y equals 5y.

Then add the numbers that are left. 12 and 10.

12 + 10 equals 22.

Then take all the values we got after addition:- 3x, 5y and 22.

2x, 5y and 22 cannot be added together. So, the expression in the simplified form would be:-

Answer:

Step-by-step explanation:

20+20+7.5+7.5= 55

this is for the bottom have

20+20+6.5+6.5= 53

thats for the upper half

than you just add them and get 108

Answer:

All false.

Step-by-step explanation:

The ratio is 3:4.

For every 3 girls, there are 4 boys.

If a class has 7 people, 3 are girls and 4 are boys.

Hence the fraction of boys is 4/7 and girls are 3/7.

Therefore, a and b are False.

The number of boys in the class cannot be 6. If the number of boys is 6, then the number of girls must be 4.5 to maintain the 3:4 ratio, but there cannot be half a girl. So, c is also false. d) the number of pupils in the class is 12. To maintain a 3:4 ratio, the number of pupils in the class must be in multiples of 7. Hence, d is also false.

3:7 are the odds in favor of choosing a book of poetry

given that

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. [note 1] [1] [2] The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin. The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half

the probability of randomly picking out a book of poetry from a bookshelf is 3/10

now, we need to find what are the odds in favor of choosing a book of poetry

P(poerty) = 3/10

P(non-poerty) = 1 - 3/10 = 7/10

number of odds = P(poerty) /P(non-poerty)

                          = 3/10/7/10

                          = 3/7

                          = 3:7

3:7 are the odds in favor of choosing a book of poetry

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Answer:

Step-by-step explanation:

40 : 30 = x : 63 ⇒ x = (40*63)/30 = 84

y = 59°

The value of w in terms of a is follows:

The subject of a formula is the variable which is expressed in terms of the other variables.

The formula is given as follows:

\(a = \frac{4+w}{30}\)

Variables are numbers represented with letters in an equation. The variables are a and w.

Therefore, let's find w in terms of a.

Hence,

\(a = \frac{4+w}{30}\)

cross multiply

30a = 4 + w

subtract 4 from both sides of the equation

30a = 4 + w

30a - 4 = 4 - 4 + w

Therefore,

w = 30a - 4

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Answer:

Height is 0.5

Step-by-step explanation:

height of parallelogram = area ÷ base

= 2.5 ÷ 5 = 0.5

False. An intrinsic reward is enjoying what one does for its own sake, while an extrinsic reward is an inducement such as money, grades, or recognition.

Intrinsic and extrinsic rewards are two different types of motivational factors that can influence behavior.

Intrinsic rewards are those that come from within oneself, such as the enjoyment of doing a task or the sense of accomplishment that comes from completing it. These rewards are inherently satisfying and enjoyable, and they motivate people to continue doing the task or activity because of the pleasure they derive from it. For example, a person may engage in a hobby like playing music, painting, or playing a sport simply because they find it enjoyable and rewarding in itself.

On the other hand, extrinsic rewards are external motivators that are used to induce or encourage behavior. These rewards are typically tangible, such as money, grades, or recognition, and are given as a result of completing a task or activity. They are designed to incentivize individuals to perform specific actions, often with the aim of achieving a specific goal or outcome. For example, a person may work hard at their job in order to earn a promotion or raise, or may study hard in school to earn good grades.

Intrinsic and extrinsic rewards can both be effective motivators, but they operate in different ways. Intrinsic rewards are powerful because they come from within the individual and are based on personal enjoyment and satisfaction. Extrinsic rewards, on the other hand, are often seen as less powerful and may only work in the short term, because they are not inherently satisfying and may not motivate people to continue performing the task or activity once the reward is removed. However, when used effectively, extrinsic rewards can be a useful tool for motivating people and achieving specific outcomes.

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The evaluation approach described in the given scenario is B.) forced distribution.

Forced distribution is an evaluation approach where performance ratings are distributed among employees according to predetermined percentages. In this case, the professor has predetermined that 10% of the class will receive an "A", 20% will receive a "B", 40% will receive a "C", 20% will receive a "D", and 10% will receive an "F".

This approach imposes a forced ranking system that restricts the distribution of grades based on predetermined proportions. Forced distribution can be useful in certain contexts as it helps differentiate performance levels and prevent grade inflation or deflation.

However, it also has limitations, as it may not accurately reflect individual performance and can create a competitive environment among students. It is important for educators to carefully consider the implications and potential drawbacks of using forced distribution in educational settings.

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The law of diminishing marginal utility is national income = 325, C = 225, and for an economic system without government interference, Savings from income reach their overall balance when they equal zero.

                   C = 0. 6Y + 30                       \(y =\)National income.

                       \(I =\) ⊥00                             \(C=\) consumption expenditure.

                      \(Y = C+ I\)                           \(I=\) investment expenditure.

                  \(Y ='6Y+30+100\)

                         \(Y =\frac{1300}{14}\)

                        \(Y =325\)

So (a) national income =325

  (b) 0.6 × 325 +30

            C = 225

    (c) At equilibrium level of income

          saving = income

          saving = ⊥00

GDP plus National Production Abroad minus Domestic Production Abroad is the formula for National Income.

The entire monetary worth of all the goods and services that a country produces during a certain period of time is known to as national income. It really is, in these other respects, the total of all factor revenue produced within a production year. An indication of a country's economic activity is its national income.

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Great question! A midpoint is exactly what it sounds like; the point in the middle of two objects (in this case it's the middle of these two coordinates). Another way to think of the middle of something in math is by using the average. To find the midpoint of two points, we just find the average of the x-values and the average of the y-values:

((x1 + x2)/2 , (y1 + y2)/2)

((5 + -13) / 2 , (-4 + 12) / 2)

( -8 / 2 , 8 / 2)

(-4 , 4)

a. To calculate a 95% confidence interval for b0, you need the necessary statistical information and data from Exercise 11.7.

b. The interpretation of H0: b0 = 0 for the problem in Exercise 11.7 needs to be explained.

c. You need to test the hypotheses H0: b0 = 0 versus Ha: b0 ≠ 0.

d. The p-value of the test of H0: b0 = 0 needs to be determined.

a. To calculate a 95% confidence interval for b0, you would need to refer to the Minitab output for the data provided in Exercise 11.7. The confidence interval would give you a range of values within which the true value of b0 is likely to fall with 95% confidence.

b. The interpretation of the null hypothesis H0: b0 = 0 in the context of Exercise 11.7 would suggest that there is no significant relationship between the presence of pectin and the firmness of canned sweet potatoes. It implies that the coefficient b0, representing the effect of the pectin concentration, is not significantly different from zero.

c. To test the hypotheses H0: b0 = 0 versus Ha: b0 ≠ 0, you would typically perform a hypothesis test using the estimated coefficient b0, the standard error, and the appropriate test statistic (e.g., t-test or z-test). The test would assess whether the coefficient b0 is significantly different from zero, indicating a significant effect of pectin concentration on firmness.

d. The p-value of the test of H0: b0 = 0 would quantify the strength of evidence against the null hypothesis. A small p-value (typically less than the significance level, such as 0.05) would indicate strong evidence to reject the null hypothesis and conclude that there is a significant relationship between pectin concentration and firmness.

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Answer: 3/7

Step-by-step explanation:

The answer would be 89 after 534 divided by 6 and applying the concept of arithmetic operation.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.

It is given that:

534 divided by 6

\(\begin{matrix}\:\:\:\:\:\:\emptyspace8\emptyspace9\:\:\:\:\:\:\:\:\:\:\:\:\\ 6\overline{|\smallspace534}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace4\emptyspace8}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\emptyspace5\emptyspace4\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace5\emptyspace4}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

The A = 48

B = 54

C = 54

After applying the concept of arithmetic operation.

Thus, the answer would be 89 after 534 divided by 6 and applying the concept of arithmetic operation.

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In this scenario, we are given a string that is 2.3 meters long and under a tension of 26 N. Additionally, a pulse travels the length of the string in 54 ms.

When a pulse travels through a string, it causes the string to vibrate and move. The tension of the string determines how quickly the pulse can travel and how far it can go. In this case, the tension of 26 N is relatively high, which means that the pulse can travel quickly and over a significant distance.
The fact that the pulse travels the length of the string in 54 ms tells us something about the speed of the pulse. We can use the formula speed = distance / time to calculate the speed of the pulse. In this case, the distance is the length of the string, which is 2.3 m. The time is 54 ms, or 0.054 s.
So, speed = distance / time = 2.3 m / 0.054 s = 42.59 m/s.
We now know the speed of the pulse, but what about the tension and length of the string? We can use the formula v = sqrt(T/μ) to calculate the speed of a pulse in a string, where v is the speed of the pulse, T is the tension of the string, and μ is the mass per unit length of the string.
Rearranging this formula, we get T = μv^2. We can use this formula to find the tension of the string. Plugging in the values we know, we get:
T = μv^2 = (mass per unit length of string) * (speed of pulse)^2
We don't know the mass per unit length of the string, but we can find it using the formula μ = m / L, where m is the mass of the string and L is its length.
Assuming the string has a uniform density, we can calculate its mass using the formula m = ρAL, where ρ is the density of the string, A is its cross-sectional area, and L is its length.
We don't know the cross-sectional area, but we can make a rough estimate based on the thickness of the string. Assuming the string has a circular cross-section, we can use the formula A = πr^2, where r is the radius of the string.
Again, we don't know the radius of the string, but we can make a rough estimate based on its diameter. Assuming the string has a diameter of 2 mm, its radius is 1 mm, or 0.001 m.
Plugging in these values, we get:
A = π(0.001 m)^2 = 7.85 x 10^-7 m^2
m = ρAL = (density of string) * (cross-sectional area) * (length of string)
  = (density of string) * (7.85 x 10^-7 m^2) * (2.3 m)
We don't know the density of the string, but assuming it is made of nylon or a similar material, its density is around 1100 kg/m^3. Plugging in this value, we get:
m = 2.039 x 10^-3 kg
μ = m / L = 2.039 x 10^-3 kg / 2.3 m = 8.86 x 10^-4 kg/m
Now we can use the formula T = μv^2 to find the tension of the string. Plugging in the values we know, we get:
T = μv^2 = (8.86 x 10^-4 kg/m) * (42.59 m/s)^2 = 159.3 N
So the tension of the string is 159.3 N, which is much higher than the original tension of 26 N. This makes sense, since the pulse travels quickly and over a significant distance, indicating that the tension must be high.

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Answer:

an order of squares

Step-by-step explanation:

7^2 = 49

8^2 = 64

9^2 = 81

etc

The statement "System analysts define an object's attributes during the systems design process" is true because  defining object attributes is an essential part of the systems design process to ensure that the system meets the desired functional requirements.

In systems design, objects are used to represent real-world entities that are relevant to the system being developed. These objects have attributes that describe their characteristics or properties, which are used to identify and manipulate them within the system. System analysts define these attributes during the systems design process to ensure that the system meets the desired functional requirements.

For example, in a library system, a book object may have attributes such as title, author, publisher, and ISBN. Defining these attributes helps ensure that the system can properly manage and retrieve books as needed. Object-oriented design is a popular approach to systems design that relies heavily on defining objects and their attributes.

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