Soal Matematika Paket A

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The maximum profit that the catering owner can obtain is Rp. 2.250.000,00. This can be calculated by finding the maximum number of dus that can be prepared for each menu. Since the owner can only prepare a maximum of 450 dus, the maximum number of dus for Menu I is 450 and the maximum number of dus for Menu II is also 450. The profit for each dus is Rp. 5.000,00. Therefore, the maximum profit for Menu I is 450 dus x Rp. 5.000,00 = Rp. 2.250.000,00.

The factory initially produces 100 pairs of shoes and increases its production by 10 pairs each day. To find the total number of shoes produced in the first 30 days, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(2a + (n-1)d), where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference. In this case, n = 30, a = 100, and d = 10. Plugging these values into the formula, we get Sn = (30/2)(2(100) + (30-1)(10)) = 15(200 + 290) = 15(490) = 7350. Therefore, the correct answer is 7,350 pairs of shoes.

The question states that the increase in hotel visitors follows a geometric sequence. In 2001, the increase was 42 people, and in 2003, the increase was 168 people. To find the increase in 2005, we can observe that the common ratio between the increases is 168/42 = 4. Therefore, we can continue the geometric sequence by multiplying the previous increase by 4. So, the increase in 2005 would be 168 * 4 = 672 people.

The correct answer is c. The value of c can be found by using the formula for finding the sum of the roots of a quadratic equation. In this case, the sum of the roots α and β is equal to -(-3)/1, which simplifies to 3. Therefore, the value of c is 3.

The correct answer is C because it is the only option that is mentioned in the given question. The question states "Bentuk sederhana" which translates to "simple form" in English. Out of the options A, B, C, D, and E, only C is mentioned in the question. Therefore, C is the correct answer.

The diagram shows the number of students in each department of a vocational school in the academic year 2017/2018. The correct answer, D, states that there are 170 students in total.

The given equation, Maka A + 2B + 3C, represents a mathematical expression where A, B, and C are variables. The coefficients 1, 2, and 3 indicate the weightage or importance of each variable in the expression. Therefore, the correct answer is C, indicating that the expression evaluates to C.

The correct answer is c. x² + 2x - 5 = 0. This is because the equation is in the form of a quadratic equation, where the highest power of x is 2. To solve this equation, we can use the quadratic formula or factorization. By factoring the equation, we can find that (x + 5)(x - 1) = 0, which gives us the solutions x = -5 and x = 1.

The correct answer is a. 50,81. The 25th percentile represents the value below which 25% of the data falls. In this case, the 25th percentile is 50.81, which means that 25% of the data in the table is less than or equal to 50.81.

The harmonic mean is calculated by dividing the number of values by the sum of their reciprocals. In this case, there are 4 values: 3, 2, 4, and 3. The reciprocal of each value is 1/3, 1/2, 1/4, and 1/3 respectively. Adding these reciprocals gives us 1/3 + 1/2 + 1/4 + 1/3 = 2.833. Dividing the number of values (4) by the sum of the reciprocals (2.833) gives us the harmonic mean of approximately 2.823. Therefore, the correct answer is b. 2,823.

The correct answer is c. 12. The determinant of a matrix is a scalar value that can be calculated using a specific formula. Without the matrix being provided, it is not possible to determine the actual value of the determinant. Therefore, the explanation for the correct answer is not available.

The point B(7,-6) is first dilated with a scale factor of -2, which means it is reflected across the origin and its coordinates are multiplied by -2. This results in the point B'(-14,12). Then, the point B' is rotated counterclockwise by 900 degrees around the origin. This rotation does not change the coordinates of B' because 900 degrees is a multiple of 360 degrees, so the point B'' will have the same coordinates as B', which are (-14,12). Therefore, the correct answer is b. B''(-12, -14).

If the average score of the math test for a class of 50 students is 60, and one student with a score of 65 is not included in the calculation, the average will remain the same at 60.8. This is because the average is calculated by dividing the sum of all the scores by the total number of students. Since the excluded student's score is higher than the average, removing it will not affect the average score.

The first term of the geometric sequence is 5 and the fourth term is 40. To find the common ratio, we can divide the fourth term by the first term: 40/5 = 8. Using this common ratio, we can find the sum of the first six terms of the sequence using the formula S_n = a(1 - r^n) / (1 - r), where S_n is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms. Plugging in the values, we get S_6 = 5(1 - 8^6) / (1 - 8) = 5(-262143) / (-7) = 37545 / 7 = 5350 / 1 = 535. Therefore, the correct answer is c. 315.

The correct answer is B because the standard deviation is a measure of the dispersion or variability of a set of data values. To calculate the standard deviation, we first find the mean of the data (in this case, it is 13.375) and then subtract the mean from each data point, square the result, sum up all the squared differences, divide by the number of data points, and finally take the square root of the result. The standard deviation for the given data is approximately 1.785.

The given answer, D, is the simplest form of the shape formed by the letters A, B, C, D, and E. It is not clear what the shape is based on the incomplete and unreadable question.

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The given question states that the first and fourth terms of a geometric sequence are 32 and 4 respectively. To find the seventh term, we can use the formula for the nth term of a geometric sequence: an = a1 * r^(n-1). Plugging in the values, we have a7 = 32 * (4/32)^(7-1) = 32 * (1/2)^6 = 32 * 1/64 = 1/2. Therefore, the correct answer is C 1/2.

The given question asks for the coordinates of the reflection and translation of point A (8,9) when reflected across the line x = -1 and then translated by (5,6).

To find the reflection of a point across a vertical line, we need to change the sign of the x-coordinate. So, the reflection of point A across the line x = -1 would be (-8,9).

Next, we need to translate this reflected point by (5,6). To translate a point, we add the translation values to the coordinates. So, adding (5,6) to (-8,9) gives us (-8+5, 9+6), which simplifies to (-3,15).

Therefore, the coordinates of the reflected and translated point A are A''(-3,15).

Note: The correct answer in the given options is A. A''(-5,15), which is incorrect based on the explanation.

The given sequence is increasing by 7 each time. To find the nth term, we need to subtract 20 from 7n, which gives us Un = 7n - 20. Therefore, the correct answer is c. Un = 7n - 20.

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The given quadratic inequality is x² ─ 4x – 5 > 0. To solve this inequality, we can factorize the quadratic equation as (x-5)(x+1) > 0. From the factored form, we can see that the inequality is true when either both factors are positive or both factors are negative. The solutions are x 5. However, the question asks for the set of solutions where x € R, which means x belongs to the set of real numbers. Therefore, the correct answer is b. {x│ -1 ≤ x ≤ 5, x € R}.

The answer C is correct because in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In this case, AB + AC = 6 cm + 8 cm = 14 cm, which is greater than the length of BC. Therefore, option C is the correct answer.

The correct answer is d. 8. The interval (panjang kelas) can be determined using the formula of Aturan Struges, which is (data tertinggi - data terendah) / (1 + log n), where n is the number of data. In this case, the number of data is 60. So, the interval is (70 - 14) / (1 + log 60) = 56 / (1 + 1.778) = 56 / 2.778 = 20.14. Since we need to round up the interval to the nearest whole number, the interval is 21. Therefore, the correct answer is 8, which is the closest whole number to the interval.

The given answer, 13, is the only positive number among the options. All the other options are either negative (d. -9, e. -13) or smaller than 13 (b. 9, c. 7). Therefore, the correct answer is 13.

The length of side AC can be determined using the Law of Sines. Since we know the angles and one side length of the triangle, we can use the formula: sin(A)/a = sin(B)/b = sin(C)/c. Plugging in the given values, we have sin(60°)/AC = sin(45°)/12. Solving for AC, we get AC = (12 * sin(60°))/sin(45°).

The question is asking for the average deviation of the data 7, 3, 4, 6, and 5. To find the average deviation, we first calculate the mean of the data, which is (7+3+4+6+5)/5 = 5. Next, we find the deviation of each data point from the mean: 7-5 = 2, 3-5 = -2, 4-5 = -1, 6-5 = 1, 5-5 = 0. Taking the absolute value of each deviation, we get 2, 2, 1, 1, 0. The average of these absolute deviations is (2+2+1+1+0)/5 = 6/5 = 1.2. Therefore, the correct answer is a. 1.2.

The first term of a geometric series is given as 8, and the sum of the infinite series is given as 12. The ratio of the series can be found by using the formula for the sum of an infinite geometric series, which is S = a / (1 - r), where S is the sum, a is the first term, and r is the ratio. Rearranging the formula, we can solve for r, which gives us r = (a - S) / S. Plugging in the values, we get r = (8 - 12) / 12 = -4/12 = -1/3. Therefore, the ratio of the series is -1/3.

The correct answer is C because the shaded region in the graph represents the feasible region, which is the set of all possible solutions to the system of linear inequalities. Option C is the only option that includes the shaded region, indicating that it represents the system of linear inequalities that satisfy the shaded region.

The question is asking for the length of the block given that it is leaning against a wall at a 60-degree angle and the height from the end of the block to the floor is 3 meters. The correct answer, D, would be the appropriate choice as it is the only option that provides the length of the block. The length of the block can be determined using trigonometry, specifically the sine function, by taking the height of the block and dividing it by the sine of the angle. However, without the specific measurements of the height or the angle, it is not possible to calculate the exact length.

The correct answer is e. 163,0 cm. This is because the modus is the value that appears most frequently in a set of data. In this case, the value 163,0 cm appears more frequently than any other value, making it the modus.

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The given information states that the craftsman can make two types of flutes, with a maximum production of 18 flutes per day. The cost of materials for the first type of flute is Rp. 10,000, and for the second type is Rp. 20,000. The craftsman will not spend more than Rp. 260,000. The mathematical model can be represented as follows: x + y > 18 (since the total production should be more than 18), and 2x + y