Section A
[40 markah]
[40 marks]
Jawab semua soalan.
Answer all questions.
Harga bagi 1 kg buah manggis ialah RM(3x + 2). Sufri memperoleh RMx baki
bayaran setelah membayar 6 keping wang kertas RM10 untuk membeli x kg buah
manggis.
Hitung harga, dalam RM. bagi 1 kg buah manggis itu.
The price of 1 kg of mangosteen is RM(3x + 2). Sufri received the balance of purchase
of RMx after paying 6 pieces of RM10 notes for x kg of mangosteens.
Calculate the price, in RM, for 1 kg of mangosteen.
[4 markah]
[4 marks]
Jawapan/Answer:​

...It's A on Ap3x......

Answer:

7.50 + 14P < 60; 24 slices

Step-by-step explanation:

The probability that exactly one of the bridges will collapse in the next year in Dystopia county is 0.2988 (rounded to four decimal places).

To calculate the probability of exactly one bridge collapsing, we need to consider the probabilities of each bridge collapsing and not collapsing. Let E, Y, and A represent the events of the Elder, Younger, and Ancient bridges collapsing, respectively.

The probability of exactly one bridge collapsing can be found by considering three cases:

Only the Elder bridge collapses: P(E) * P(Y') * P(A') = 0.18 * (1 - 0.06) * (1 - 0.28) = 0.18 * 0.94 * 0.72.

Only the Younger bridge collapses: P(Y) * P(E') * P(A') = 0.06 * (1 - 0.18) * (1 - 0.28) = 0.06 * 0.82 * 0.72.

Only the Ancient bridge collapses: P(A) * P(E') * P(Y') = 0.28 * (1 - 0.18) * (1 - 0.06) = 0.28 * 0.82 * 0.94.

Summing up the probabilities from these three cases gives the total probability of exactly one bridge collapsing: 0.18 * 0.94 * 0.72 + 0.06 * 0.82 * 0.72 + 0.28 * 0.82 * 0.94 ≈ 0.2988.

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The reduced cost matrix for travelling salesperson problem in the given instance is shown below. The Travelling Salesperson Problem (TSP) is a classical combinatorial optimization issue that belongs to the category of NP-Hard problems.

This problem can be resolved using a branch and bound algorithm or by using dynamic programming.The reduced cost matrix for the given travelling salesperson problem instance The computation of the reduced cost matrix for travelling salesperson problem involves two steps: Identify the smallest element of each row and subtract the value from all the values in the row.

Identify the smallest element of each column and subtract the value from all the values in the column.In the given instance, the smallest element of each row is highlighted in bold. Therefore, after performing Step 1 the matrix becomes the matrix becomes Hence, the reduced cost matrix for the travelling salesperson problem is obtained.

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The 80% confidence interval estimate for the average browsing time is approximately 12.648572 minutes to 14.548572 minutes.

To construct an 80% confidence interval estimate of the average browsing time for the population of crownfashion.com visitors this week, we can use the following formula:

Confidence Interval = \(\bar{X}\) ± Z \(\times\)  (σ/√n)

Where:

\(\bar{X}\) is the sample mean (average browsing time) = 13.6 minutes,

Z is the Z-score corresponding to the desired confidence level (80% confidence level corresponds to a Z-score of 1.28),

σ is the population standard deviation = 5.2 minutes,

n is the sample size = 49.

Plugging in these values, we can calculate the confidence interval as follows:

Confidence Interval = 13.6 ± 1.28 \(\times\) (5.2/√49)

Simplifying the expression:

Confidence Interval = 13.6 ± 1.28 \(\times\) (5.2/7)

Confidence Interval = 13.6 ± 1.28 \(\times\) 0.742857

Confidence Interval = 13.6 ± 0.951428

The lower bound of the confidence interval is 13.6 - 0.951428 = 12.648572, and the upper bound is 13.6 + 0.951428 = 14.548572.

Therefore, the 80% confidence interval estimate for the average browsing time is approximately 12.648572 minutes to 14.548572 minutes.

The margin of error indicated by the interval is half of the width of the confidence interval, which is (14.548572 - 12.648572) / 2 = 0.95 minutes.

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In a net of a solid, the number of faces meeting at each vertex can be determined by examining the net and counting the number of lines that meet at each vertex. Each line corresponds to an edge of a face, so the number of lines meeting at a vertex is equal to the number of faces meeting at that vertex.

For example, if we consider a cube net, we can see that three faces meet at each vertex. Therefore, a cube has three faces meeting at each vertex.

Similarly, for other solids, we can count the number of faces meeting at each vertex by examining the net. For example, for a regular tetrahedron, four faces meet at each vertex; for a regular octahedron, four faces meet at each vertex; for a regular dodecahedron, three faces meet at each vertex; and for a regular icosahedron, five faces meet at each vertex.

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Answer:

x > 9

Step-by-step explanation:

for this inequality, we want to isolate x, so that we know the inequality of x

5x + 3 > 48

     - 3      -3        {subtract 3 from both sides to get x alone}

5x > 45

/5      /5                {divide both sides by 5 to find 1x}

x > 9

So , x > 9 is the inequality in terms of x {is the solution}

hope this helps! :)

Answer:

\(\huge\boxed{\sf x > 9}\)

Step-by-step explanation:

5x + 3 > 48

Subtract 3 to both sides

5x > 48 - 3

5x > 45

Divide 5 to both sides

x > 9

\(\rule[225]{225}{2}\)

Answer:

(a) \(x=\frac{19}{4}=4.75\)

(b) \(x=-\frac{1+\sqrt{193}}{6}\approx-2.4821, x=-\frac{1-\sqrt{193}}{6}\approx2.1487\)

Step-by-step explanation:

The detailed explanation is shown in the attached documents below.

90 students are taking both Math 245 and CS 108.

We can use the formula:

n(A or B) = n(A) + n(B) - n(A and B)

where n(A) is the number of students taking Math 245, n(B) is the number of students taking CS 108, and n(A and B) is the number of students taking both courses.

Plugging in the given values, we get:

n(A or B) = 150 + 200 - n(A and B)

n(A or B) = 350 - n(A and B)

We also know that the total number of students taking at least one of the courses is 260:

n(A or B) = 260

Substituting this value, we get:

260 = 350 - n(A and B)

n(A and B) = 90

Therefore, 90 students are taking both Math 245 and CS 108.

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Answer:

Step-by-step explanation:

a + b)^6 will have 7 terms so you want row 6 of the triangle 1 6 15 20 15 6 1

so (a + b)^6 = a^6 + 6a^(5)b + 15a^(4)b^2 + 20a^(3)b^3 + 15a^(2)b^4 + 6ab^5 + b^6

given a = d and b = -5y

∴ (d − 5y)^6 = d^6 + 6d^(5)(-5y) + 15d^(4)(-5y)^2 + 20d^(3)(-5y)^3 + 15d^(2)(-5y)^4 +

Given inequality: \($$3x^2+17x>-10$$\)We are required to solve the above inequality and write the answer using interval notation.Steps to solve the given inequality:Rearrange the inequality by taking all the terms to one side of the equation.\($$3x^2+17x+10>0$$\)Factorize the quadratic equation.

The factors of\($$3\times10 = 30$$\) which add up to 17 are 15 and 2.\($$3x^2+15x+2x+10>0$$\)Factorize the quadratic equation by grouping first two terms and last two terms separately.\($$3x(x+5)+2(x+5)>0$$(x+5)(3x+2)>0$$\)Now, let's solve this inequality for x separately for each interval. There are three intervals here, namely: \($$(-\infty,-\frac{2}{3})$$ $$(-5,-\frac{2}{3})$$ $$(-5,\infty)$$Put x = -6\), in the above inequality.(This is the point at which the function changes sign.)\($$(x+5)(3x+2)>0$$$$(-6+5)(3(-6)+2)>0$$$$(-1)(-16)>0$$$$16>0$$\)

The function is positive in \($$(-\infty,-\frac{2}{3})$$Put x = -3\), in the above inequality.(This is the point at which the function changes sign.)\($$(x+5)(3x+2)>0$$$$(-3+5)(3(-3)+2)>0$$$$(2)(-7)>0$$$$-14>0$$\)The function is negative in \($$(-\frac{2}{3},-5)$$Put x = 0\), in the above inequality.(This is the point at which the function changes sign.)\($$(x+5)(3x+2)>0$$$$(5)(2)>0$$$$10>0$$\)

The function is positive in \($$(-5,\infty)$$\)Hence, the solution of the given inequality in interval notation is\($$\boxed{(-\infty,-\frac{2}{3})\cup(-5,\infty)}$$\)

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For the 3×3 matrices having  det(A)=−3 det(A)=−3, det(B)=7 the det(AB) is -21 ,det(3A) is -81 ,det(Aᵀ) is -3 , det(B-¹) is 1/7 and

To find the det(B²) is 49. values of det(AB), det(3A), det(Aᵀ), det(B-¹),

and det(B²) given that A and B are 3x3 matrices, det(A) = -3, and det(B) = 7.

1. det(AB):
Using the property of determinants, det(AB) = det(A) * det(B).

So, det(AB) = (-3) * (7) = -21.

2. det(3A):
For a 3x3 matrix, det(kA) = k³ * det(A) where k is a scalar. In this case, k = 3.

So, det(3A) = 3³ * (-3) = 27 * (-3) = -81.

3. det(Aᵀ):
The determinant of the transpose of a matrix is equal to the determinant of the original matrix.

So, det(Aᵀ) = det(A) = -3.

4. det(B-¹):
For the inverse of a matrix, det(B-¹) = 1 / det(B).

So, det(B-¹) = 1 / 7.

5. det(B²):
Using the property of determinants for powers, det(B²) = det(B) * det(B) = 7 * 7 = 49.

So, det(AB) = -21, det(3A) = -81, det(Aᵀ) = -3, det(B-¹) = 1/7, and det(B²) = 49.

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Answer:

1) 48

2)44

Step-by-step explanation:

Answer:  48 44 Are The Correct Answers

Step-by-step explanation:Hope This Helps

Answer:

x=10, y=20

Step-by-step explanation:

3x+10=5x-10

2x=20

x=10

4y=5x-10+3x+10

4y=8x

y=2x

y=20

Hope it helps.

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False. The statement is incorrect. Unlike the z distribution, the t-distribution is not symmetric around 0, and its tails do not approach the horizontal axis and cross it.

The t-distribution is similar to the normal (z) distribution in the sense that it is bell-shaped. However, there are important differences. The t-distribution is not symmetric around 0 but is centered at 0. It has a shape that depends on its degrees of freedom (df). As the degrees of freedom increase, the t-distribution approaches the shape of the standard normal distribution (z-distribution).

The tails of the t-distribution are thicker than the tails of the z-distribution. The t-distribution has more probability in the tails, which means it has more extreme values compared to the z-distribution. As the degrees of freedom increase, the t-distribution approaches the normal distribution, and its tails become closer to the horizontal axis, but they do not cross it.

It's important to note that the shape and characteristics of the t-distribution are determined by the degrees of freedom. As the degrees of freedom increase, the t-distribution becomes more similar to the z-distribution. However, even with large degrees of freedom, the t-distribution will always have slightly thicker tails than the z-distribution.

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The fraction of KM that is required to obtain 20% Vmax is [S] = 0.2 KM.

The Michaelis-Menten equation is given by: V = Vmax[S] / (KM + [S])where, V is the velocity of the reaction, Vmax is the maximum velocity of the reaction,[S] is the substrate concentration, and KM is the Michaelis constant of the enzyme.

Substituting V = 0.2V

max and rearranging the equation,

0.2Vmax = Vmax[S] / (KM + [S])

Multiplying both sides by

(KM + [S]),0.2V

max(KM + [S]) = Vmax[S]

Expanding the equation,

0.2VmaxKM + 0.2Vmax[S]

= Vmax[S]0.2VmaxKM

= 0.8Vmax[S]

Dividing both sides by

Vmax,0.2KM = 0.8[S]

Simplifying the equation,

[S] = 0.2 KM / 0.8[S] = 0.25 KM

Therefore, the fraction of KM that is required to obtain 20% Vmax is [S] = 0.2 KM, which is option (a).

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Answer:

Step-by-step explanation:

The first questions are answered on the attachment.

The candle that will burn out first is the yellow candle rather than the blue candle.

Blue candle:

1/4 inch per hour or 0.25 inches per hour

8 / 0.25 = 32 hours to completely burn out

Yellow candle:

1/2 inch per hour or 0.5 inches per hour

12 / 0.5 = 24 hours

If the blue candle is lit 6 hours before the yellow candle then:

Blue candle: 32 - 6 = 26 hours left

Yellow candle: 24 hours left

This means the yellow candle will burn out first.

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Answer:

45in.

Step-by-step explanation:

The correct answer is A. The statement is false. R3 is not even a subset of R2. This can be answered by the concept of three-dimensional vector.

The statement is false because R3, which represents a three-dimensional vector space, cannot be a subspace of R2, which represents a two-dimensional vector space. In order for a set to be a subspace, it must satisfy three conditions: (1) it contains the zero vector, (2) it is closed under vector addition, and (3) it is closed under scalar multiplication.

R2 and R3 have different dimensions, and therefore, they do not have the same number of components in their vectors. Consequently, vector addition and scalar multiplication, which are defined component-wise, cannot be applied between vectors from R2 and R3. Therefore, R3 cannot be a subspace of R2.

Therefore, the correct answer is A. The statement is false. R3 is not even a subset of R2

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Answer:

an=87+(n-1)(-3.6)

Step-by-step explanation:

hope this helps

Answer:

an=87+(n-1)(-3.6)

Answer:

b = x - y

Step-by-step explanation:

Given the expression x - y = b

We are to rewrite the value of b;

We can simply do this by swapping both sides that are putting b at the Left hand side and x - y at the right as shown

b = x - y

Hence the correct expression will be b = x - y

The company fails to reject H0, making a Type II error. So the option B is correct.

In the given question,

Mars candy company is testing one of its machines in the factory to make sure it is producing more than 98% high-quality candy (H0: p = 0.98; Ha: p > 0.98; α = 0.05).

The test results in a p-value of 0.15.

However, the company is unaware that it is actually producing 99% high-quality candy.

We have to find MOST likely happens as a result of the testing.

The given options are:

A. The company rejects H0, making a Type I error.

B. The company fails to reject H0, making a Type II error.

C. The company rejects H0, making a Type II error.

D. The company fails to reject H0, making a Type I error.

E. The company rejects H0 correctly.

The company will not be rejecting the null hypothesis when it should have been, given the P-value is approaching 0.05.

Hence, the business commits a Type II error by failing to reject H0.

So the option B is correct.

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Jeff's golf score was 1 stroke under par.

Let's first find out what was Mike's golf score.

We know that Mike's score was 2 strokes more than Sam's score, so if Sam's score was 2 over par, then Mike's score must have been:

2 + 2 = 4 over par

We also know that Jeff's score was 5 strokes less than Mike's score. Therefore, Jeff's score relative to par would be:

4 + (-5) = -1 over par

So Jeff's golf score was 1 stroke under par.

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To solve this problem, we can set up a proportion based on the given information. Let's assume that the number of machines is directly proportional to the number of devices produced .

The time taken is inversely proportional to the number of devices produced. From the given information: 24 machines can make 5 devices in 30 minutes. let's assign variables:  Let m1 be the number of machines.

Let d1 be the number of devices. Let t1 be the time taken. We have the following ratios: m1:d1 = 24:5 (number of machines to number of devices)

t1:d1 = 30:5 (time taken to number of devices).  Now we need to find the time it would take for 4 machines to make 15 devices. Let m2 be the number of machines (4 in this case). Let d2 be the number of devices (15 in this case). Let t2 be the time taken (to be determined). We can set up the following proportion:  m1:d1 = m2:d2.  Substituting the values we have: 24:5 = 4:15.  To find t2, we can set up the following proportion:

t1:d1 = t2:d2.  Substituting the values we have: 30:5 = t2:15.   Now we can solve for t2: 24/5 = 4/d2 (Cross-multiply).  24d2 = 4 * 5.  24d2 = 20.  d2 = 20/24. d2 = 5/6. So, 4 machines will make 15 devices in 5/6 of the time it took 24 machines to make 5 devices. To find the time, we can set up a proportion: 30/5 = t2/(5/6) (Cross-multiply). 30 * (5/6) = t2. 25 = t2. Therefore, 4 machines will take 25 minutes to make 15 devices. To convert this to hours, divide the time by 60: 25 minutes = 25/60 hours

25/60 = 5/12(Answer) .

Therefore , if 24 machines can make 5 devices in 30 minutes,  4 machines will take 5/12 of an hour to make 15 devices.

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Answer:

B and D are both correct

Step-by-step explanation:

Answer:

5/9 or 55.5%

Step-by-step explanation:

there are 5 numbers divisible by 4, 12-20 inclusive:  4, 8, 12, 16, 20

there are 9 numbers from 12-20, inclusive

answer would be 5/9

Answer: please provide more information

Step-by-step explanation: