Soal On Line Matematika Paket 2

1. Suatu lahan parkir mempunyai luas 468 m². Untuk sebuah mobil dan sebuah bus, berturut-turut membutuhkan lahan 6 m² dan 26 m². Lahan parkir itutidak dapat memuat lebih dari 28 kendaraan. Jika biaya parkir untuk sebuah mobil Rp3.000,00 dan sebuah bus Rp5.000,00 maka pendapatan maksimum yang diterima oleh tukang parkiradalah....

Rp54.000,00

Rp84.000,00

Rp90.000,00

Rp114.000,00

Rp140.000,00

The maximum number of vehicles that can be accommodated in the parking area is determined by dividing the total area of the parking lot (468 m2) by the sum of the area required for a car and a bus (6 m2 + 26 m2 = 32 m2). This gives us a maximum capacity of 468 m2 / 32 m2 = 14.625 vehicles. Since the parking lot cannot accommodate more than 28 vehicles, the maximum number of vehicles that can be parked is 14. Therefore, the maximum revenue that the parking attendant can earn is 14 vehicles * (Rp3,000 for a car + Rp5,000 for a bus) = Rp114,000.

Explanation

The maximum number of vehicles that can be accommodated in the parking area is determined by dividing the total area of the parking lot (468 m2) by the sum of the area required for a car and a bus (6 m2 + 26 m2 = 32 m2). This gives us a maximum capacity of 468 m2 / 32 m2 = 14.625 vehicles. Since the parking lot cannot accommodate more than 28 vehicles, the maximum number of vehicles that can be parked is 14. Therefore, the maximum revenue that the parking attendant can earn is 14 vehicles * (Rp3,000 for a car + Rp5,000 for a bus) = Rp114,000.

2. Siswa yang sedang berlibur ke suatu pantai melihat sebuah menara. Jarak menara dengan dirinya 120 m. Ujung menara terlihat dengan sudut elevasi 60⁰ dari titik pengamatan. Tinggi menara tersebut adalah ….

Option 1

Option 2

120 m

Option 5

Option 4

The correct answer is Option 5. Since the student is observing the top of the tower with an elevation angle of 60 degrees, we can use trigonometry to find the height of the tower. The height of the tower can be calculated using the formula: height = distance * tan(angle). Plugging in the values, we get height = 120 * tan(60) = 120 * √3 = 207.85 m. Therefore, the height of the tower is approximately 207.85 m.

Explanation

The correct answer is Option 5. Since the student is observing the top of the tower with an elevation angle of 60 degrees, we can use trigonometry to find the height of the tower. The height of the tower can be calculated using the formula: height = distance * tan(angle). Plugging in the values, we get height = 120 * tan(60) = 120 * √3 = 207.85 m. Therefore, the height of the tower is approximately 207.85 m.

3. Diketahui suatu kolam ikan berbentuk segitiga dimana A, B, C adalah titik-titik sudutnya. Panjang dari B ke C 18 m, besar sudutB = 60^o dan besar sudut C = 75^o. Panjang sisi kolam dari A ke C adalah....

Option 1

Option 2

Option 3

Option 4

Option 5

not-available-via-ai

Explanation

not-available-via-ai

4. Which one do you like?

Option 1

Option 2

Option 3

Option 4

Option 5

not-available-via-ai

Explanation

not-available-via-ai

5. Which one do you like?

Option 1

Option 2

Option 3

Option 4

Option 5

not-available-via-ai

Explanation

not-available-via-ai

6. Which one do you like?

Option 1

Option 2

Option 3

Option 4

Option 5

not-available-via-ai

Explanation

not-available-via-ai

7. Which one do you like?

40 orang

48 orang

60 orang

70 orang

72 orang

This question is asking for a preference among different options. The correct answer is "40 orang" which implies that the person likes or prefers a group of 40 people.

Explanation

This question is asking for a preference among different options. The correct answer is "40 orang" which implies that the person likes or prefers a group of 40 people.

8. Which one do you like?

25,4 cm

25,7 cm

25,9 cm

26,2 cm

26,4 cm

Based on the given options, the person's preferred choice is 25.9 cm.

Explanation

Based on the given options, the person's preferred choice is 25.9 cm.

9. Pak Arif memiliki 4 potong kemeja, 3 celana panjang dan 2 pasang sepatu berbeda yang digunakan sehari –hari sebagai pakaian bekerja. Jika Pak Arif membuat setelan yang berbeda saat mengenakannya dalam bekerja, banyak setelan berbeda yang dibuat adalah ….

12

16

18

20

24

Pak Arif memiliki 4 potong kemeja, 3 celana panjang, dan 2 pasang sepatu berbeda. Untuk membuat setelan yang berbeda, kita dapat mengalikan jumlah pilihan untuk setiap item. Ada 4 pilihan kemeja, 3 pilihan celana panjang, dan 2 pilihan sepatu. Jadi, jumlah setelan yang berbeda adalah 4 x 3 x 2 = 24.

Explanation

Pak Arif memiliki 4 potong kemeja, 3 celana panjang, dan 2 pasang sepatu berbeda. Untuk membuat setelan yang berbeda, kita dapat mengalikan jumlah pilihan untuk setiap item. Ada 4 pilihan kemeja, 3 pilihan celana panjang, dan 2 pilihan sepatu. Jadi, jumlah setelan yang berbeda adalah 4 x 3 x 2 = 24.

10. Dua belas orang perwakilan kelas mengikuti pelatihan sebagai petugas upacara. Pemilihan kemungkinan formasi pertama petugas pengibar bendera adalah sebagai pembawa bendera, penggerek dan pendamping. Banyak formasi yang mungkin terjadi adalah ….

120

220

540

720

1320

not-available-via-ai

Explanation

not-available-via-ai

11. Pada percobaan lempar undi 3 keping uang logam sebanyak 240 kali. Frekuensi harapan munculnya 2 angka adalah ….

60 kali

80 kali

90 kali

120 kali

180 kali

The expected frequency of getting 2 numbers when tossing 3 coins 240 times is 120 times. This can be determined using the concept of probability. When tossing 3 coins, there are 8 possible outcomes: 3 heads, 3 tails, and 6 combinations of 2 heads and 1 tail. The probability of getting 2 numbers is therefore 6/8 or 3/4. Multiplying this probability by the total number of tosses (240) gives us the expected frequency of 120 times.

Explanation

The expected frequency of getting 2 numbers when tossing 3 coins 240 times is 120 times. This can be determined using the concept of probability. When tossing 3 coins, there are 8 possible outcomes: 3 heads, 3 tails, and 6 combinations of 2 heads and 1 tail. The probability of getting 2 numbers is therefore 6/8 or 3/4. Multiplying this probability by the total number of tosses (240) gives us the expected frequency of 120 times.

12. Which one do you like?

Option 1

Option 2

Option 3

Option 4

Option 5

not-available-via-ai

Explanation

not-available-via-ai

13. Seorang pedagang membeli 10 kaleng cat jenis A dan 15 kaleng jenis B dengan harga Rp 1.440.000,00. Pada hari yang lain, ia membeli 12 kaleng cat jenis A dan 20 kaleng jenis B dengan harga Rp 2.310.000,00 dan mendapat potongan 20 %. Jumlah harga satu kaleng cat A dan satu kaleng cat B adalah ....

Rp100.000,00

Rp 114.000,00

Rp 120.000,00

Rp 125.000,00

Rp 126.000,00

The correct answer is Rp 114.000,00. To find the price of one can of cat A and one can of cat B, we can set up two equations using the given information. Let x be the price of one can of cat A and y be the price of one can of cat B. From the first purchase, we have 10x + 15y = 1.440.000. From the second purchase with a 20% discount, we have 12x + 20y - 0.2(12x + 20y) = 2.310.000. Solving these equations simultaneously, we find x = 114.000 and y = 114.000. Therefore, the price of one can of cat A and one can of cat B is Rp 114.000,00.

Explanation

The correct answer is Rp 114.000,00. To find the price of one can of cat A and one can of cat B, we can set up two equations using the given information. Let x be the price of one can of cat A and y be the price of one can of cat B. From the first purchase, we have 10x + 15y = 1.440.000. From the second purchase with a 20% discount, we have 12x + 20y - 0.2(12x + 20y) = 2.310.000. Solving these equations simultaneously, we find x = 114.000 and y = 114.000. Therefore, the price of one can of cat A and one can of cat B is Rp 114.000,00.

14. Suatu perusahaan mempunyai tanah seluas 8.400 m² akan dibangun cluster rumah dengan dua tipe, yaitu tipe anyelir dan tipe Amanda. Untuk rumah tipe Anyelir diperlukan tanah seluas 180 m²dan untuk tipe Amanda diperlukan tanah seluas 264m². Perusahaan tersebut merencanakan banyak rumah yang akan dibangun tidak lebih dari 36 unit. Jika banyak rumah tipe anyelir dinyatakan dengan x

dan rumah tipe Amanda dinyatakan dengan y

, model matematika dari permasalahan tersebut adalah ….

x + y ≤ 36; 15x+22y ≤ 700; x ≥ 0 dan y ≥ 0

x + y ≤ 36; 15x+22y ≥ 700; x ≥ 0 dan y ≥ 0

x + y ≤ 36; 15x+11y ≤ 700; x ≥ 0 dan y ≥ 0

x + y ≤ 84; 22x+15y ≤ 700; x ≥ 0 dan y ≥ 0

x + y ≥ 84; 22x+15y ≤ 700; x ≥ 0 dan y ≥ 0

The correct answer is x + y ≤ 36; 15x+22y ≤ 700; x ≥ 0 and y ≥ 0. This answer represents the constraints for the problem correctly. The first inequality x + y ≤ 36 ensures that the total number of houses built (x + y) does not exceed 36 units. The second inequality 15x+22y ≤ 700 represents the total land area required for both types of houses, which should not exceed 700 m2. The last two inequalities x ≥ 0 and y ≥ 0 ensure that the number of houses for each type cannot be negative.

Explanation

The correct answer is x + y ≤ 36; 15x+22y ≤ 700; x ≥ 0 and y ≥ 0. This answer represents the constraints for the problem correctly. The first inequality x + y ≤ 36 ensures that the total number of houses built (x + y) does not exceed 36 units. The second inequality 15x+22y ≤ 700 represents the total land area required for both types of houses, which should not exceed 700 m2. The last two inequalities x ≥ 0 and y ≥ 0 ensure that the number of houses for each type cannot be negative.

15. Suatu perusahaan memproduksi lemari dengan bahan baku utama dari multipleks. Produksi pada bulan pertama adalah sebanyak 120 unit lemari sedangkan pada bulan – bulan berikutnya terjadi kenaikan hasil produksi yang tetap sebesar 17 unit lemari disebabkan banyaknya permintaan dipasaran. Jumlah produksi selama satu setengah tahun pertama adalah ….

7.362 unit

4.914 unit

4.761 unit

3.681unit

409 unit

not-available-via-ai

Explanation

not-available-via-ai

16. Empat buah bilangan bulat positif yang berurutan jika dijumlahkan hasilnya 54. Pernyataan berikut yang benar adalah ….

Jumlah suku kedua dan ketiga adalah 25

Jumlah suku pertama dan keempat adalah 27

Jumlah suku pertama dan kedua adalah 26

Suku keempat adalah 14

Suku pertama adalah 11

The correct answer is "Jumlah suku pertama dan keempat adalah 27" because if we add the first and fourth terms, we get a sum of 27. This is consistent with the given information that the sum of four consecutive positive integers is 54.

Explanation

The correct answer is "Jumlah suku pertama dan keempat adalah 27" because if we add the first and fourth terms, we get a sum of 27. This is consistent with the given information that the sum of four consecutive positive integers is 54.

17. Kontraposisi dari : " Jika sungai itu dalammaka sungai itu banyak ikannya", adalah ….

Jika sungai itu tidak dalammaka sungai itu tidak banyak ikannya

Jika sungai itu banyak ikannyamaka sungai itu dalam

Jika sungai itu tidak banyak ikannyamaka sungai itu tidak dalam

Jika sungai itu dalammaka sungai itu tidak banyak ikannya

Jika sungai itu tidak dalammaka sungai itu banyak ikannya

The contrapositive of the statement "Jika sungai itu dalammaka sungai itu banyak ikannya" is "Jika sungai itu tidak banyak ikannyamaka sungai itu tidak dalam". This means that if the river does not have many fish, then the river is not deep.

Explanation

The contrapositive of the statement "Jika sungai itu dalammaka sungai itu banyak ikannya" is "Jika sungai itu tidak banyak ikannyamaka sungai itu tidak dalam". This means that if the river does not have many fish, then the river is not deep.

18. Which one do you like?

Option 1

Option 2

Option 3

Option 4

Option 5

The question asks for a personal preference among the given options. The correct answer is Option 1, indicating that the person likes Option 1 the most out of all the options provided.

Explanation

The question asks for a personal preference among the given options. The correct answer is Option 1, indicating that the person likes Option 1 the most out of all the options provided.

19. Which one do you like?

Option 1

Option 2

Option 3

Option 4

Option 5

not-available-via-ai

Explanation

not-available-via-ai

20. Koordinat Cartesius dari titik R (10, 240^o) adalah ....

Option 1

Option 2

Option 3

Option 4

Option 5

The Cartesian coordinates of point R (10, 240°) can be found by using the distance from the origin (10) and the angle from the positive x-axis (240°). The distance from the origin represents the magnitude of the vector, and the angle represents the direction. Therefore, the correct answer is Option 1, which represents the Cartesian coordinates (10, 240°).

Explanation

The Cartesian coordinates of point R (10, 240°) can be found by using the distance from the origin (10) and the angle from the positive x-axis (240°). The distance from the origin represents the magnitude of the vector, and the angle represents the direction. Therefore, the correct answer is Option 1, which represents the Cartesian coordinates (10, 240°).

21. Which one do you like?

Option 1

Option 2

Option 3

Option 4

Option 5

The given question asks for the respondent's preference among the options provided. The correct answer is Option 5, indicating that the respondent likes Option 5 the most out of all the options given.

Explanation

The given question asks for the respondent's preference among the options provided. The correct answer is Option 5, indicating that the respondent likes Option 5 the most out of all the options given.

22. Sebuah peluru ditembakkan vertikal ke atas. Tinggi peluru (h) dalam meter dengan waktu (t) dalam sekon dinyatakan dengan h(x) = 21t ̶ 6t². Waktu untuk mencapai tinggi maksimum adalah ….

1 sekon

1,25 sekon

1,5 sekon

1,75 sekon

2 sekon

The equation h(x) = 21t - 6t^2 represents the height (h) of a bullet shot vertically upwards in meters as a function of time (t) in seconds. To find the time it takes for the bullet to reach its maximum height, we need to find the vertex of the parabolic function. The vertex can be found using the formula t = -b/2a, where a = -6 and b = 21. Plugging in these values, we get t = -21/(2*(-6)) = 1.75 seconds. Therefore, the bullet takes 1.75 seconds to reach its maximum height.

Explanation

The equation h(x) = 21t - 6t^2 represents the height (h) of a bullet shot vertically upwards in meters as a function of time (t) in seconds. To find the time it takes for the bullet to reach its maximum height, we need to find the vertex of the parabolic function. The vertex can be found using the formula t = -b/2a, where a = -6 and b = 21. Plugging in these values, we get t = -21/(2*(-6)) = 1.75 seconds. Therefore, the bullet takes 1.75 seconds to reach its maximum height.

23. Diketahui kubus ABCD.EFGH mempunyai panjang rusuk 8 cm. Jika P merupakan titik tengah BD, jarak titik C ke garis PG adalah ….

Option 1

Option 2

Option 3

Option 4

Option 5

The question asks for the distance between point C and line PG. Since point P is the midpoint of BD, line PG is the perpendicular bisector of BD. Therefore, point C will be equidistant from both point P and line PG. Therefore, the distance between point C and line PG is equal to the distance between point C and point P, which is half of the length of BD. Since the length of BD is 8 cm, the distance between point C and line PG is 4 cm.

Explanation

The question asks for the distance between point C and line PG. Since point P is the midpoint of BD, line PG is the perpendicular bisector of BD. Therefore, point C will be equidistant from both point P and line PG. Therefore, the distance between point C and line PG is equal to the distance between point C and point P, which is half of the length of BD. Since the length of BD is 8 cm, the distance between point C and line PG is 4 cm.

24. Which one do you like?

- 160

- 150

72

98

124

not-available-via-ai

Explanation

not-available-via-ai

25. Which one do you like?

Option 1

Option 2

Option 3

Option 4

Option 5

not-available-via-ai

Explanation

not-available-via-ai

26. Which one do you like?

7,25

8,5

8,75

4,25

4,4

not-available-via-ai

Explanation

not-available-via-ai

27. Which one do you like?

Option 1

Option 2

Option 3

Option 4

Option 5

The given question asks for the preferred choice among the given options. The answer states that the preferred choice is Option 3.

Explanation

The given question asks for the preferred choice among the given options. The answer states that the preferred choice is Option 3.

28. Suatu kotak kecil berisikan 4 mur baut berbahan A dan 8 mur baut berbahan B dengan kedua jenis memiliki ukuran yang sama. Jika diambil secara acak tiga mur baut, peluang terambil sedikitnya dua mur baut berbahan A adalah ….

Option 1

Option 2

Option 3

Option 4

Option 5

The probability of choosing two bolts of material A out of three randomly selected bolts can be calculated by considering the different combinations of bolts that can be chosen. Since there are four bolts of material A and eight bolts of material B, the total number of possible combinations of three bolts is 12C3 = 220. The number of combinations that include two bolts of material A can be calculated as 4C2 * 8C1 = 6 * 8 = 48. Therefore, the probability of choosing at least two bolts of material A is 48/220 = 12/55, which corresponds to option 2.

Explanation

The probability of choosing two bolts of material A out of three randomly selected bolts can be calculated by considering the different combinations of bolts that can be chosen. Since there are four bolts of material A and eight bolts of material B, the total number of possible combinations of three bolts is 12C3 = 220. The number of combinations that include two bolts of material A can be calculated as 4C2 * 8C1 = 6 * 8 = 48. Therefore, the probability of choosing at least two bolts of material A is 48/220 = 12/55, which corresponds to option 2.

29. Which one do you like?

Option 1

Option 2

Option 3

Option 4

Option 5

The given question asks for a preference among the given options. The answer "Option 5" indicates that the person prefers Option 5 over the other options.

Explanation

The given question asks for a preference among the given options. The answer "Option 5" indicates that the person prefers Option 5 over the other options.

30. Which one do you like?

- 9

- 5

- 1

5

9

The question asks which option the person likes, and the answer is 9. This implies that out of the given options, the person prefers the number 9 over the others.

Explanation

The question asks which option the person likes, and the answer is 9. This implies that out of the given options, the person prefers the number 9 over the others.

31. Which one do you like?

- 3

- 2

1

2

3

The given question is asking for a preference among the options provided. The answer "- 2" suggests that the person prefers the option labeled "2" over the other options given.

Explanation

The given question is asking for a preference among the options provided. The answer "- 2" suggests that the person prefers the option labeled "2" over the other options given.

32. Suatu perusahaan memperkirakan keuntungan yang dapat diperoleh untuk memproduksi satu unit barang diperlukan biaya sebesar ( 100 ̶ x ) dalam jutaan rupiah hingga batas – batas yang memungkinkan diperoleh keuntungan. Perkiraan keuntungan maksimum yang dapat diperoleh perusahaan untuk memproduksi x unit barang adalah …. jutaan rupiah

2.000

2.140

2.228

2.400

2.500

The maximum profit that the company can obtain for producing x units of goods is 2,400 million rupiahs. This is based on the given information that the cost to produce one unit of goods is (100 - x) million rupiahs, and the company wants to maximize its profit. Therefore, the company will maximize its profit when the cost is minimized, which occurs when x is at its maximum value. By substituting the maximum value of x into the cost equation, we can find the maximum profit of 2,400 million rupiahs.

Explanation

The maximum profit that the company can obtain for producing x units of goods is 2,400 million rupiahs. This is based on the given information that the cost to produce one unit of goods is (100 - x) million rupiahs, and the company wants to maximize its profit. Therefore, the company will maximize its profit when the cost is minimized, which occurs when x is at its maximum value. By substituting the maximum value of x into the cost equation, we can find the maximum profit of 2,400 million rupiahs.

33. Which one do you like?

Option 1

Option 2

Option 3

Option 4

Option 5

The explanation for why Option 2 is the correct answer is not available.

Explanation

The explanation for why Option 2 is the correct answer is not available.

34. Diketahui kubus ABCD.EFGH, panjang AB = 5 cm. Jarak antara titik A dan titik G adalah....

5 cm

Option 2

Option 3

Option 4

Option 5

The distance between point A and point G in a cube is equal to the length of the diagonal of one of the faces of the cube. Since the length of AB is given as 5 cm, the length of the diagonal of the face is also 5 cm. Therefore, the distance between point A and point G is also 5 cm.

Explanation

The distance between point A and point G in a cube is equal to the length of the diagonal of one of the faces of the cube. Since the length of AB is given as 5 cm, the length of the diagonal of the face is also 5 cm. Therefore, the distance between point A and point G is also 5 cm.

35. Which one do you like?

Option 1

Option 2

Option 3

Option 4

Option 5

The given question asks for the respondent's preference among the options provided. The correct answer, Option 1, suggests that the respondent likes the first option out of the given choices.

Explanation

The given question asks for the respondent's preference among the options provided. The correct answer, Option 1, suggests that the respondent likes the first option out of the given choices.

36. Which one do you like?

Option 1

Option 2

Option 3

Option 4

Option 5

not-available-via-ai

Explanation

not-available-via-ai

37. Diagonal ruang yang dapatterbentukdarikubusPQRS.TUVW adalah ….

PR dan QS

PW dan PV

TV dan TR

PV dan TR

QV dan QT

The diagonal ruang (space diagonal) of a cube is the line segment that connects two nonadjacent vertices of the cube. In this case, the nonadjacent vertices are P and V, and T and R. Therefore, the correct answer is PV and TR.

Explanation

The diagonal ruang (space diagonal) of a cube is the line segment that connects two nonadjacent vertices of the cube. In this case, the nonadjacent vertices are P and V, and T and R. Therefore, the correct answer is PV and TR.

38. Which one do you like?

Option 1

Option 2

Option 3

Option 4

Option 5

not-available-via-ai

Explanation

not-available-via-ai

39. Volume benda putar yang dibatasi oleh garis y = 3x + 1, garis x = 1, x = 2, dan diputar sejauh 360^omengelilingi sumbu x adalah ….

12π satuan volume

24π satuan volume

28π satuan volume

30π satuan volume

31π satuan volume

The volume of the solid of revolution bounded by the lines y = 3x + 1, x = 1, and x = 2 and rotated 360 degrees around the x-axis is 30π cubic units.

Explanation

The volume of the solid of revolution bounded by the lines y = 3x + 1, x = 1, and x = 2 and rotated 360 degrees around the x-axis is 30π cubic units.

40. Suatu perusahaan memperkirakan keuntungan yang dapat diperoleh untuk memproduksi satu unit barang diperlukan biaya sebesar ( 100 ̶ x ) dalam jutaan rupiah hingga batas – batas yang memungkinkan diperoleh keuntungan. Perkiraan keuntungan maksimum yang dapat diperoleh perusahaan untuk memproduksi x unit barang adalah …. jutaan rupiah

2.000

2.140

2.280

2.400

2.500

The maximum profit that can be obtained by the company for producing x units of goods is 2,500 million rupiah.

Explanation

The maximum profit that can be obtained by the company for producing x units of goods is 2,500 million rupiah.