Question 4: Matrices (15 marks) (a) Complete the following definition: the identity matrix is a square matrix which has Os in every entry except where it has 18 A. along the main diagonal B. the first and last columns C. the four comers D. along the off-diagonal (1 mark)

The answer is:

a. 100

Based on the given confusion matrix:

```

              Predicted Class

            |   0   |   1   |

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

Actual Class |       |       |

      0     |   30  |  3,000|

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

      1     |  100  |  221  |

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

```

To determine the number of class 1's that are incorrectly classified as class 0, we need to look at the value in the cell corresponding to predicted class 0 and actual class 1, which is 100.

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Answer:

Option (B)

Step-by-step explanation:

1). Given function is,

  \(f(x)=\frac{1}{x-1}+3\)

  It the given function 'f' is transformed by a translation of 2 units to the right, the new function will be,

h(x) = f(x - 2)

h(x) = \(\frac{1}{(x-2)-1}+3\)

      = \(\frac{1}{x-3}+3\)

Further the new function is translated by 6 units down,

g(x) = h(x) - 6

g(x) = \(\frac{1}{x-3}+3-6\)

      = \(\frac{1}{x-3}-3\)

Since, transformed function 'g' passes through a point (x, -2),

g(x) = \(\frac{1}{x-3}-3\)

-2 = \(\frac{1}{x-3}-3\)  

3 - 2 = \(\frac{1}{x-3}\)

x - 3 = 1

x = 4

Therefore, Option (B) will be the answer.

The perimeter of the rhombus is 34.40 units. The length of diagonal is 7.21 units. The perimeter of the rectangle is 44.98 units. The perimeter of the square is 42.44 units

1.  Given: a rhombus with diagonals 10 and 14

Half-length of the diagonals are 10/2 = 5 and 14/2 =7

Length of side = √(5²+7²) = √74 = 8.6 units

Perimeter, P = 4 × length of side

P = 4 × 8.60 = 34.40 units

2. Given: m<ADC = 60⁰

Missing...

3. Given: a rectangle with side length of 6 and 4. The length of one of its diagonal can be found using Pythagoras' theorem:

length of diagonal = √(4²+6²) = √52 = 7.21 units

4. Given: a rectangle with a diagonal length of 16 and side length of 10

other side length = √(16²-10²) = √156 = 12.49 units

Perimeter, P = 2(L+W)

P = 2(10+12.49) = 44.98 units

5. Given: a square with diagonal length of 15

Let represent the side length of the square

x² + x² = 15²

2x² = 15²

x² = 225/2

x² = 112.5

x = √112.5 = 10.61 units

Perimeter, P = 4 × side length

P = 4×10.61 = 42.44 units

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Answer:

87

Step-by-step explanation:

66 + 72 + 87 = 225

225 / 3 = 75

Answer:

1.25 km in 1 minute

125 km in 100 minutes

Step-by-step explanation:

Find its speed in km/min by dividing the km by number of minutes:

7.5/6

= 1.25

So, the train goes 1.25 km in 1 minute.

Using this speed, find how far it goes in 100 minutes, by multiplying the speed by 100:

1.25(100)

= 125

So, in 100 minutes, the train goes 125 km.

a. The distance travelled by the train in 1 minute, at a constant speed is 1.25 kilometers.

b. The distance travelled by the train in 100 minute, at a constant speed is 125 kilometers.

Given the following data:

To find how far (distance) the train go in 1 minute, we would use direct proportion:

7.5 kilometers = 6 minutes

X kilometers = 1 minute

Cross-multiplying, we have:

\(6 \times X = 7.5\\\\X = \frac{7.5}{6}\)

X = 1.25 kilometers.

b. To find how far (distance) the train go in 100 minute:

Since the train travels 1.25 kilometers in 1 minute, we would multiply that distance by 100.

\(D(100) = 1.25 \times 100\\D(100) = 125 \; kilometers\)

Distance = 125 kilometers.

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Answer:

6

Step-by-step explanation:

First order them from least to greatest:

1, 3, 6, 7, 9

The median is 6 because it is the middle value.

Hope this helps! Brainliest would be really appreciated

Correct option is 1 experiment with 500 trials.

The possibility or chance of an event occurring is measured by probability. It is a number between 0 and 1, where 0 denotes the impossibility of the occurrence and 1 denotes its certainty.

In this case, conducting one experiment with 500 trials would provide a large sample size that would help to reduce the effects of random variation, producing a more accurate estimate of the experimental probability.

Conversely, the other methods described (combined data with 3 experiments with 1 trial each, combined data with 10 experiments with 5 trials each, and 1 experiment with 1 trial) would not provide as much data as the 1 experiment with 500 trials. As a result, they would not produce as reliable or accurate of an estimate of the experimental probability.

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The procedure for revising probabilities based on additional information is referred to as Bayesian updating

The procedure for revising probabilities based on additional information is referred to as Bayesian updating. Bayesian updating is a fundamental concept in Bayesian statistics, which allows for the incorporation of new evidence or data to update and refine prior beliefs or probabilities.

In Bayesian updating, the process begins with an initial prior probability, which represents the initial belief or knowledge about an event or hypothesis before any evidence is observed. As new evidence or data becomes available, it is used to update the prior probability and generate a posterior probability. The posterior probability represents the revised belief or probability after incorporating the new information.

Bayesian updating follows the principles of Bayes' theorem, which mathematically describes the relationship between prior probabilities, likelihoods, and posterior probabilities. It involves combining the prior probability with the likelihood of observing the data given the hypothesis and then normalizing the result to obtain the posterior probability.

The beauty of Bayesian updating is that it allows for a flexible and iterative process of continuously updating beliefs and probabilities as new information emerges. It provides a framework for incorporating both subjective prior beliefs and objective data to make more informed decisions and predictions. Bayesian updating has applications in various fields, including machine learning, decision-making, and scientific research.

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Answer:

a,khoảng cách từ thị trấn P đến thị trấn Q là

Step-by-step explanat  io  n:

36*5=180(km)

b,Muthu đi xe đạp từ thị trấn P đến thị trấn Q hết số phút là:

180/40=4,5(h)=270(phút)

If you look at the graph, you will realize that it is highest to the left and lowest to the right and that as x increases, the y decreases, and when x decreases, y increases. Thus it has a NEGATIVE slope.

Answer:

The answer is A.

Step-by-step explanation:

First, you have to add 2 to both sides, to get rid of the -2 on the left side :

\(9x - 2 = 2x + 12\)

\(9x - 2 + 2 = 2x + 12 + 2\)

\(9x = 2x + 14\)

Next, you have to subtract 2x to both sides, to make all the x terms to one side and then, solve it :

\(9x - 2x = 2x + 14 - 2x\)

\(7x = 14\)

\(x = 14 \div 7\)

\(x = 2\)

Answer:

400

Step-by-step explanation:

The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.

Answer:

400

Step-by-step explanation:

I used the cake/ladder method. The screen shot below shows the cake/ladder method for this problem.

The last part not shown in the photo, is that you have to multiply the highlighted part: 2 × 2 × 5 × 4 × 1 × 5 = 400

I hope this helps!

When dealing with the simultaneous occurrence of two events A and B, the probability can be determined by using the probability of one event and the conditional probability of the other event given that the first event has occurred. Both P(A) * P(B|A) and P(B) * P(A|B) are valid ways to calculate this probability.

The concept of probability is fundamental in various fields such as mathematics, statistics, and even in everyday life. The probability of the simultaneous occurrence of two events A and B is a critical concept in probability theory. According to the definition, the probability of A and B occurring at the same time is equal to the probability of A multiplied by the conditional probability of B given that A has occurred. This equation is also valid in the reverse case, where the probability of B and A occurring simultaneously is equal to the probability of B multiplied by the conditional probability of A given that B has occurred.

Understanding the relationship between the probability of two events and their conditional probabilities is essential in predicting the likelihood of these events happening together. In real-life situations, this concept can be used to determine the probability of two events such as the success of a product launch and the corresponding increase in sales. The probability of these two events occurring simultaneously can be predicted by analyzing the probability of the product launch's success and the conditional probability of sales increasing given that the product launch is successful.

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The correlation coefficients and security returns provided suggest a relationship between security 1 and security 2.

The given information includes security returns and correlation coefficients between different securities. Based on the data, it is evident that there is a relationship between security 1 and security 2. The correlation coefficient P12 is -1, indicating a perfect negative correlation between the two securities. This means that when security 1's returns increase, security 2's returns decrease, and vice versa.

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Answer:

Step-by-step explanation:

1 Simplify 19-7 to 12.

12^2−8×3+4×3−5

2 Simplify 12^2 to 144

144−8×3+4×3−5

3 Simplify 8×3 to 24.

144−24+4×3−5

4 Simplify 4×3 to 12.

144−24+12−5

5 Simplify 144-24 to 120.

120+12-5

6 Simplify 120+12 to 132.

132-5

7 Simplify.

127

A. We should use the binomial distribution since we are interested in the number of successes (customers who purchase a national brand) out of a fixed number of trials (10 customers).

b. To find the probability exactly 4 of the 10 customers will purchase a national brand, we can use the dbinom function in R:

dbinom(4, 10, 0.75)

The answer is 0.2503 (to 4 decimal places).

c. To find the probability that at most 7 customers will purchase a national brand, we can use the pbinom function in R:

pbinom(7, 10, 0.75)

The answer is 0.9831 (to 4 decimal places).

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The coordinates of the vertices of \(\triangle Q'R'S'\) are \(Q'(x,y) = (0, -4)\), \(R'(x,y) = (7,-6)\) and \(S'(x,y) = (8, -3)\), respectively.

Vectorially speaking, a point is translated to another location on Cartesian plane by means of this expression:

\(A'(x,y) = A(x,y) + T(x,y)\) (1)

Where:

If we know that \(Q(x,y) = (-4,2)\), \(R(x,y) = (3,0)\), \(S(x,y) = (4, 3)\) and \(R'(x,y) = (7, -6)\)\(T(x,y) = (4, -6)\), then the coordinates of the vertices of the triangle \(Q'R'S'\) are:

\(Q'(x,y) = Q(x,y) + T(x,y)\)

\(Q'(x,y) = (-4,2) + (4,-6)\)

\(Q'(x,y) = (0, -4)\)

\(R'(x,y) = R(x,y) + T(x,y)\)

\(R'(x,y) = (3,0) +(4,-6)\)

\(R'(x,y) = (7,-6)\)

\(S'(x,y) = S(x,y) + T(x,y)\)

\(S'(x,y) = (4, 3) + (4, -6)\)

\(S'(x,y) = (8, -3)\)

The coordinates of the vertices of \(\triangle Q'R'S'\) are \(Q'(x,y) = (0, -4)\), \(R'(x,y) = (7,-6)\) and \(S'(x,y) = (8, -3)\), respectively.

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The value of x IS 5/2.

The value of y is 9/16.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

x = 8y - 2 _____(1)

x + 8y = 7 ______(2)

Substitute (1) in (2).

8y - 2 + 8y = 7

16y - 2 = 7

16y = 7 + 2

16y = 9

y = 9/16

Now,

Substitute y = 9/16 in (1).

x = 8 x 9/16 - 2

x = 9/2 - 2

x = (9 - 4) / 2

x = 5/2

Thus,

The value of x and y are 5/2 and 9/16.

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Grace would need to use her cell phone for 58 minutes this month to have an average usage of 55 minutes over the four months.

To find out how many minutes Grace would need to use her cell phone this month to have an average usage of 55 minutes over the four months, we can follow these steps:

Step 1: Calculate the total usage for the first three months.

Total usage = 43 minutes + 62 minutes + 57 minutes = 162 minutes

Step 2: Calculate the total usage for the four months.

Total usage for four months = Total usage + X (usage for this month)

Step 3: Set up an equation for the average usage.

Average usage = Total usage for four months / 4

Step 4: Solve for X (usage for this month).

55 minutes = (Total usage + X) / 4

Step 5: Multiply both sides of the equation by 4 to eliminate the fraction.

220 minutes = Total usage + X

Step 6: Substitute the value of the total usage.

220 minutes = 162 minutes + X

Step 7: Solve for X.

X = 220 minutes - 162 minutes

X = 58 minutes

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[(-2-5 )x (-6) ]  is greater than (-2 ) +(-5)x(-6) ]  and the absolute value of greatest integer is 42.

A number system is defined as a system of writing to express numbers.

{(−2)−5}×(−6) and (−2)+(−5×(−6)

Let us solve the expression

{(−2)−5}×(−6)

=-7×(−6)

=42

similarly let us solve for expression [ (-2 ) +(-5)x(-6) ]

=(-2 ) +30

=28

As 42>28

{(−2)−5}×(−6) > (−2)+(−5×(−6)

Therefore [(-2-5 )x (-6) ]  is greater than  (−2)+(−5×(−6).

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The distance between two opposite corners of the floor is 9.4 meters. The result is obtained by using Pythagorean theorem.

A diagonal is a straight line that connects the opposite corners of a polygon.

The floor of a storage unit is 8.5 meters long and 4.1 meters wide.

Find the distance between two opposite corners of the floor!

We have

It means that the shape of the floor is a rectangle. See the illustration picture in the attachment! The distance between two opposite corners is called diagonal.

We can determine the diagonal length by using Pythagorean theorem.

a² + b² = c²

c is the longest side of a triangle.

In this case, c is the diagonal of the rectangle. So,

8.5² + 4.1² = c²

72.25 + 16.81 = c²

c² = 89.06

c = 9.437

c ≈ 9.4 m

Hence, the diagonal length of the rectangle floor is 9.4 meters.

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Answer: No!

Step-by-step explanation: This is a parabola. The graph for this function is not straight. We can also tell this is not a linear function because the degree of the function is 2.

Hope this helps :)

No.

y = 3x² + 2 has a degree of 2. So, it'll not make a graph which is a straight line. It's NOT a linear function. Linear functions have a degree of 1 or 0.

This is a quadratic polynomial (degree = 2) & when drawn on a graph, it'll make a parabola.

_____

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The smallest measurement used in the apothecary system for volume is the minim.

The apothecary system is an outdated system of measurements primarily used in pharmacy and medicine. It includes various units for measuring volume, weight, and other quantities.

In the apothecary system, the minim is the smallest unit of measurement for volume. It is equivalent to approximately 0.0616 milliliters.

The minim is a small unit of measurement and is typically used for precise dosing of liquids in the apothecary system. It is commonly used in pharmaceutical compounding and in the preparation of medications.

However, it's important to note that the apothecary system is no longer widely used in modern healthcare practices. The metric system, with units such as milliliters and liters, has become the standard for measuring volume in most countries.

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Answer:

The coordinates of the center of this circle is (-1, -3).

Step-by-step explanation:

As we know that \(A = (-4,2)\) and \(B = (2,-8)\) are points lying on circle T, the center is the midpoint of the segment AB, whose location can be obtained from Midpoint formula:

\(C = \frac{1}{2}\cdot A + \frac{1}{2}\cdot B\)

\(C = \frac{1}{2}\cdot (-4,2)+\frac{1}{2}\cdot (2,-8)\)

\(C = (-2, 1)+(1,-4)\)

\(C=(-2+1,1-4)\)

\(C=(-1,-3)\)

The coordinates of the center of this circle is (-1, -3).

Answer:

The average weight change is a loss of 8.75 pounds per person.

Step-by-step explanation:

This one was fairly simple, the 7 weeks have nothing to do with it. All you have to do is take the total amount of weight lost, 35 pounds, and divide it by the 4 people in the class. After the calculation, it equals an average loss of 8.75 pounds per person.

Answer:

95 6 11

Step-by-step explanation:

im really smart lol    jp   :/

Answer:

m∠C'B'D' = 95

CQ = 6

B'D' = 11

Step-by-step explanation:

Edge2020

Have a great day! :)