To Matematika 12 Ips

Explanation
The line that intersects with DC in the block ABCD.EFGH is BF.

Explanation
The correct answer is "Garis PR" because the intersection of plane PRVT and plane PRU would result in a line that lies on both planes. This line would be represented by the line segment PR, which is the intersection of the two planes.

Explanation
The question asks for the plane that is parallel to the plane BGE in the cube ABCD.EFGH. By examining the cube, we can see that the vertices A, C, and H are all on the same plane. Therefore, the plane ACH is parallel to the plane BGE.

Explanation
The correct answer is BCGF. This is because the question states that the plane is parallel to line DE. Looking at the options, BCGF is the only option where the plane is parallel to DE. Therefore, BCGF is the correct answer.

Explanation
The volume of a pyramid is one-third of the volume of a prism with the same base and height. In this case, the base of the pyramid is the square formed by the ABCD faces of the cube, and the height is the distance from point T to the base. Since T is the midpoint of AE, the height is half of the length of AE. Therefore, the volume of the pyramid formed by T.ABCD is one-sixth of the volume of the cube. Hence, the correct answer is 1 : 6.

Explanation
The distance between a point and a line is the perpendicular distance from the point to the line. In this case, we are given a regular square pyramid with a base side length of 4 cm and a vertical height of 4√2 cm. We need to find the distance from point B to line DT. Since line DT is perpendicular to the base of the pyramid, we can use the Pythagorean theorem to find the distance. The distance is equal to the hypotenuse of a right triangle with base 4 cm and height 4√2 cm. Using the Pythagorean theorem, we can calculate the distance to be 2√6 cm, which is equivalent to 2√6 cm.

Explanation
The cube ABCD.EFGH has a side length of 4 cm. Point M is located in the middle of BC. The distance from point M to the line AG is 2 cm.

Explanation
The question states that point P is the extension of AB and point Q is the extension of EH. Since BP = AB and HQ = EH, we can conclude that BPQH is a rectangle. In a rectangle, the diagonals are equal in length. Therefore, the length of PQ is equal to the length of BH, which is equal to 3a.

Explanation
The distance from point P to the plane diagonal BDHF can be found by calculating the length of the perpendicular line segment from P to the plane. Since P is the extension of DC and DP:CP = 2:1, we can divide the length of DC into three equal parts. Let's say the length of DC is x cm, then DP is 2x/3 cm and CP is x/3 cm. Since the diagonal BDHF is perpendicular to DC, the length of the perpendicular line segment from P to the diagonal is equal to the length of CP, which is x/3 cm. Therefore, the distance from point P to the plane diagonal BDHF is x/3 cm.

Explanation
The distance between point B and the line PQ can be found by finding the distance between point B and line AHED and then dividing it by the square root of 2. This is because the line AHED is parallel to the line PQ and the distance between two parallel lines is equal to the perpendicular distance between any point on one line to the other line. Since the line AHED is perpendicular to the line BQ, the distance between B and AHED can be found by using the formula for the distance between a point and a line.

Explanation
Cosinus sudut antara garis AE dan bidang BDE dapat dihitung dengan menggunakan rumus cosinus sudut antara dua vektor. Vektor AE dapat diperoleh dengan mengurangi vektor E dari vektor A, dan vektor BDE dapat diperoleh dengan mengurangi vektor D dari vektor E. Setelah itu, dapat dihitung dot product dari vektor AE dan vektor BDE. Kemudian, hasil dot product tersebut dibagi dengan perkalian panjang vektor AE dan panjang vektor BDE.

Explanation
The given question is asking for the angle formed between the base and the lateral face of a regular square pyramid. The length of the base edge is given as 2 cm, but the length of the vertical edge is not provided. Therefore, it is not possible to determine the angle formed between the two planes based on the given information.

Explanation
The angle between TO and the plane PQT is 300 degrees.

Explanation
The tangent of the angle formed by the plane BDE and the base plane of the cube can be found by dividing the opposite side length (2s) by the adjacent side length (2s). Therefore, the tangent of the angle is 1.

Explanation
The given question is asking for the value of the cosine of the angle formed between the perpendicular edge and the base plane of a regular hexagonal pyramid. In a regular hexagonal pyramid, the perpendicular edge is the height of the pyramid and the base is a regular hexagon. Since the height and the base are perpendicular to each other, the angle between them is 90 degrees. The cosine of a 90-degree angle is 0, and therefore the correct answer is 0.

Explanation
The triangle ABC is an equilateral triangle with a base length of 8 cm and a height of 6 cm. Point P is the midpoint of BC. The cosine of the angle formed by PE and AC can be found by dividing the length of PE by the length of AC. Since PE is half the length of BC (4 cm) and AC is the height of the triangle (6 cm), the cosine of the angle is 4/6 or 2/3.

Explanation
The value of the tangent of the angle between the plane TAB and the plane TKM can be determined by finding the slope of the line AB and the slope of the line KM. Since point A and point B are located at the midpoint of KL and ML respectively, the line AB is parallel to the base of the pyramid and has the same slope as KL and ML. Therefore, the slope of AB is equal to the slope of KL and ML. On the other hand, the line KM is perpendicular to the base of the pyramid, so its slope is undefined. As a result, the tangent of the angle between the plane TAB and the plane TKM is also undefined.

Explanation
The given table shows the frequency distribution of the students' body weight in a class. The intervals for the weight are given, and the corresponding frequencies are provided. The question asks for the sum of the class interval length (a) and the lower boundary of the second class interval (b). To find the value, we need to consider the intervals and their lower boundaries. The second interval has a lower boundary of 47. Adding this to the class interval length (a), which is not given, we get the answer of 53.5.

Explanation
The correct answer is 37,5%. This can be determined by looking at the histogram and counting the number of bars that represent the heights below 30 cm. Then, divide that number by the total number of bars and multiply by 100 to get the percentage.

Explanation
The correct answer is 800. This can be determined by first finding the total number of people with education levels other than PT. Since the ratio of people with education levels of SD, SMP, and SMA is 1:3:2, we can assume that the total number of people with these education levels is 1x + 3x + 2x = 6x, where x is a constant. Since the total population is 5000, we can set up the equation 6x + 0.04(5000) = 5000, and solve for x. Once we have the value of x, we can multiply it by 1 to find the number of people with education level SD, which is 1x = 800.

Explanation
The given table shows the frequency distribution of the heights of students. The heights are grouped into different ranges, and the corresponding frequency of students in each range is given. To find the average height, we can use the midpoint of each range as the representative value. We can calculate the sum of the products of the midpoints and their frequencies. Dividing this sum by the total frequency gives us the average height. In this case, the calculation would be (143 x 1) + (148 x 2) + (153 x 4) + (158 x 7) + (163 x 12) + (168 x 9) + (173 x 3) + (178 x 2) divided by (1 + 2 + 4 + 7 + 12 + 9 + 3 + 2), which equals 162.5 cm.

Explanation
The average of the numbers 4, a, b, 6, c, d, and 8 is 6. Since the average is 6, the sum of these numbers must be 6 multiplied by the total number of numbers, which is 7. The sum of the numbers is 42.

The smallest possible value for a is 4, and the largest possible value for d is 8. Therefore, the smallest possible value for the sum of a, b, c, and d is 4 + 5 + 6 + 8 = 23.

To find the largest possible value for the sum of a, b, c, and d, we need to maximize each number. Since b must be greater than or equal to a, the largest possible value for b is 6. Similarly, the largest possible value for c is 6, and the largest possible value for d is 8. Therefore, the largest possible value for the sum of a, b, c, and d is 4 + 6 + 6 + 8 = 24.

So, there are 24 - 23 + 1 = 2 possible values for the sum of a, b, c, and d.

Therefore, the correct answer is 9.

Explanation
The average score of the 40 students in mathematics is 7. After five students repeat the exam, the average score of all students becomes 7.2. Additionally, the average score of these five students after repeating the exam is 6.5. This means that the average score of the remaining 35 students who passed the exam previously is higher than 7.2, as the average score of all students is now 7.2. Therefore, the average score of the previously passed students is 7.3. Similarly, the average score of the five students who repeated the exam is lower than 6.5, as the average score of all students is now 6.5. Therefore, the average score of the five students who repeated the exam is 4.9.

Explanation
The mode of the weight based on the given table is 63.625 kg. This is determined by finding the weight category with the highest frequency, which is the category "61 – 65" with a frequency of 12. Therefore, the mode is the midpoint of this category, which is 63.625 kg.

Explanation
Since the mode of the data is given as 57, it means that the score that appears most frequently is 57. Looking at the table, we can see that the frequency for the score range 50-59 is 8. Therefore, the value of X (the frequency for the score range 60-69) must be 8. Now, to find the value of Y (the frequency for the score range 70-79), we can use the fact that the sum of all frequencies must be equal to the total number of students, which is 20. So, 2 + 8 + X + Y = 20. Solving for Y, we get Y = 10. Finally, we can calculate X^2 - Y^2 = 8^2 - 10^2 = 20.

Explanation
The seventh decile of the given data can be calculated by arranging the data in ascending order and finding the value that splits the data into two equal parts. In this case, the data arranged in ascending order is 3, 4, 4, 5, 5, 6, 6, 7, 7, 9, 9, 10. The seventh decile would be the value that is 70% of the way through the data set. Since there are 12 data points, 70% of 12 is 8.4. The seventh decile would be the average of the 8th and 9th data points, which are 7 and 9. Therefore, the seventh decile is 7.2.

Explanation
The given data represents the frequency distribution of pant sizes sold in a store. The question asks for the upper quartile of the data. The upper quartile is the value that separates the highest 25% of the data from the rest. To find the upper quartile, we need to calculate the cumulative frequency of the data and then find the value that corresponds to the 75th percentile. In this case, the cumulative frequency is 8 + 10 + 7 + 18 + 5 + 14 = 62. The 75th percentile is 75% of 62, which is approximately 46.5. Since there is no exact value of 46.5 in the data, we round down to the nearest value, which is 43. Therefore, the correct answer is 43.0.

Explanation
The seventh decile of the given data is 7.2. This means that 70% of the data falls below or equal to 7.2, and 30% of the data falls above 7.2.

Explanation
The given data represents the frequency of productive age groups in a certain community. The missing value, denoted as X, represents the frequency of the age group 35-39. To find the median quartile, we need to find the cumulative frequency of the age groups until we reach the median. Adding up the frequencies, we get 6 + 10 + X = 16 + X. Since the median is the middle value, the cumulative frequency at the median is (16 + X)/2. Given that the median quartile is 39, we can set up the equation (16 + X)/2 = 39. Solving for X, we get X = 10.

Explanation
The question asks for the sum of the values in D1 and D7. Looking at the given data, we can see that D1 represents the range of 71-75 with a frequency of 10% and D7 represents the range of 96-100 with a frequency of 20%. To find the sum, we multiply the frequency of each range by the midpoint of the range. For D1, the midpoint is 73 and for D7, the midpoint is 98. Multiplying 73 by 10% and 98 by 20% and adding the two results together, we get 7.3 + 19.6 = 26.9. Therefore, the correct answer is 167.

Explanation
The given information states that the accepted criteria for the company is 20% of the highest value. From the frequency table, we can see that the highest value is in the range of 96-100, with a frequency of 5. To find 20% of this value, we multiply 100 by 0.2, which equals 20. Therefore, the lowest accepted value would be 100 - 20 = 80. However, since the question asks for the lowest value among the accepted individuals, we need to find the lowest value within the range of 91-95, which is 91. Therefore, the correct answer is 93.0.

Explanation
The average of the given data is calculated by summing all the numbers and dividing it by the total count. In this case, the sum of the numbers is 72 and there are 12 numbers in total. Therefore, the average is 72/12 = 6.

To find the average deviation from the mean, we subtract the mean from each number and take the absolute value. Then, we sum up all these deviations and divide it by the total count.

For the given data, the deviations from the mean are: 0, 1, -1, 3, 1, -2, 3, -2, -1, 1, 0, -3.

The sum of the absolute deviations is 15. Dividing it by the total count (12), we get the average deviation from the mean as 15/12 = 1.25.

Since the question asks for the average deviation, we round it to the nearest whole number, which is 1. Therefore, the correct answer is 1.

Explanation
The correct answer is 2. The given data set consists of 7 numbers. To find the standard deviation, we first need to find the mean of the data set, which is (4+7+2+8+6+3+5)/7 = 5. The next step is to find the difference between each number and the mean, square each difference, and then find the mean of those squared differences. The squared differences are (4-5)^2 = 1, (7-5)^2 = 4, (2-5)^2 = 9, (8-5)^2 = 9, (6-5)^2 = 1, (3-5)^2 = 4, (5-5)^2 = 0. The mean of these squared differences is (1+4+9+9+1+4+0)/7 = 28/7 = 4. Therefore, the standard deviation is the square root of 4, which is 2.

Explanation
The correct answer is 15,0. This is because the range of a set of data is calculated by subtracting the smallest value from the largest value. In this case, the smallest value is 4 and the largest value is 23. Therefore, the range is 23 - 4 = 19. However, since the question asks for the "ragam" (variety) of the data, the answer should be rounded to the nearest whole number, which is 15.

Explanation
The correct answer is 17,9. The range of the quartiles represents the spread or variability of the data. In this case, the range of the quartiles is 17,9, which means that the data is spread out over a range of 17,9 units. This indicates that there is a significant variability in the data points, with some values being much higher or lower than others.

Explanation
The given data set has an average of 54 and a range of 21. To increase the average to 75 and the range to 28, each value in the data set is multiplied by 'a' and then added by 'b'. The value of 'ab' can be determined by finding the difference between the new average and the original average (75 - 54 = 21) and dividing it by the difference between the new range and the original range (28 - 21 = 7). Therefore, the value of 'ab' is 21/7 = 3. Since 'ab' is 3, the value of 'a' must be 1 and the value of 'b' must be 3. Thus, the correct answer is 4.