Paket X Matematika Umum2

1. Suku ke-5 dan suku ke-12 suatu barisan aritmatika berturut-turut adalah 27 dan 62. Suku ke-21 barisan tersebut adalah ….

100

107

114

105

The given problem states that the 5th and 12th terms of an arithmetic sequence are 27 and 62 respectively. To find the 21st term, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

Using the given information, we can substitute the values into the formula:
27 = a1 + (5 - 1)d -> a1 + 4d = 27 -> (1)
62 = a1 + (12 - 1)d -> a1 + 11d = 62 -> (2)

By subtracting equation (1) from equation (2), we can eliminate a1 and solve for d:
a1 + 11d - (a1 + 4d) = 62 - 27 -> 7d = 35 -> d = 5

Now, we can substitute the value of d into equation (1) to find a1:
a1 + 4(5) = 27 -> a1 + 20 = 27 -> a1 = 7

Finally, we can find the 21st term by substituting the values of a1 and d into the formula:
a21 = 7 + (21 - 1)5 -> a21 = 7 + 20(5) -> a21 = 7 + 100 -> a21 = 107

Therefore, the 21st term of the arithmetic sequence is 107.

Explanation

The given problem states that the 5th and 12th terms of an arithmetic sequence are 27 and 62 respectively. To find the 21st term, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

Using the given information, we can substitute the values into the formula:
27 = a1 + (5 - 1)d -> a1 + 4d = 27 -> (1)
62 = a1 + (12 - 1)d -> a1 + 11d = 62 -> (2)

By subtracting equation (1) from equation (2), we can eliminate a1 and solve for d:
a1 + 11d - (a1 + 4d) = 62 - 27 -> 7d = 35 -> d = 5

Now, we can substitute the value of d into equation (1) to find a1:
a1 + 4(5) = 27 -> a1 + 20 = 27 -> a1 = 7

Finally, we can find the 21st term by substituting the values of a1 and d into the formula:
a21 = 7 + (21 - 1)5 -> a21 = 7 + 20(5) -> a21 = 7 + 100 -> a21 = 107

Therefore, the 21st term of the arithmetic sequence is 107.

2. Jumlah 5 bilangan ganjil berurutan adalah 225, berapakah jumlah bilangan terbesar dan terkecil?

82

86

90

94

The given question states that the sum of five consecutive odd numbers is 225. To find the largest and smallest number, we can divide the sum by 5 to get the average, which is 45. Since the numbers are consecutive, the smallest number would be 45 - 4 = 41, and the largest number would be 45 + 4 = 49. However, none of the options provided match these values. Therefore, the correct answer cannot be determined from the given options.

Explanation

The given question states that the sum of five consecutive odd numbers is 225. To find the largest and smallest number, we can divide the sum by 5 to get the average, which is 45. Since the numbers are consecutive, the smallest number would be 45 - 4 = 41, and the largest number would be 45 + 4 = 49. However, none of the options provided match these values. Therefore, the correct answer cannot be determined from the given options.

3. Uang Tini berbanding uang Tono 4 : 7. Jika selisih uang keduanya Rp 142.500, jumlah uang Tini dan Tono adalah ....

Rp. 190.000,00

Rp. 332.500,00

Rp. 522.500,00

Rp. 617.500,00

The ratio between Tini's and Tono's money is 4:7. If the difference between their money is Rp 142,500, we can set up the equation 7x - 4x = 142,500, where x represents the common ratio. Solving the equation, we find that x = 47,500. Therefore, Tini has 4x = 4 * 47,500 = Rp 190,000, and Tono has 7x = 7 * 47,500 = Rp 332,500. The total amount of money they have together is Rp 190,000 + Rp 332,500 = Rp 522,500.

Explanation

The ratio between Tini's and Tono's money is 4:7. If the difference between their money is Rp 142,500, we can set up the equation 7x - 4x = 142,500, where x represents the common ratio. Solving the equation, we find that x = 47,500. Therefore, Tini has 4x = 4 * 47,500 = Rp 190,000, and Tono has 7x = 7 * 47,500 = Rp 332,500. The total amount of money they have together is Rp 190,000 + Rp 332,500 = Rp 522,500.

4. Hasil dari

begin mathsize 14px style 1 1 third plus 2 1 over 7 divided by 1 3 over 7 end style

adalah....

not-available-via-ai

Explanation

not-available-via-ai

5. Perhatikan pemfaktoran berikut!

1. space space 9 x squared minus 25 space equals open parentheses 3 x plus 5 close parentheses open parentheses 3 x minus 5 close parentheses 2. space space 25 x squared minus 9 space equals open parentheses 5 x minus 3 close parentheses open parentheses 3 x plus 5 close parentheses 3. space space 9 x squared plus 25 space equals open parentheses 3 x minus 5 close parentheses open parentheses 3 x plus 5 close parentheses 4. space space 25 x squared minus 9 space equals open parentheses 5 x minus 3 close parentheses open parentheses 5 x plus 3 close parentheses

yang benar adalah...

1 dan 3

1 dan 4

2 dan 3

2 dan 4

not-available-via-ai

Explanation

not-available-via-ai

6. Perhatikan diagram berikut! Di sebuah sekolah yang berisi 180 anak, berapa banyak anak yang menyukai Ping Pong?

30

40

50

60

Based on the given diagram, it can be inferred that the number of children who like Ping Pong is represented by the option "60".

Explanation

Based on the given diagram, it can be inferred that the number of children who like Ping Pong is represented by the option "60".

7. Mark yang tinggal di kota Sydney memiliki teman bernama Hans yang tinggal di kota Berlin. Untuk memudahkan waktu chatting bersama, Mark mencari tahu mengenai perbedaan waktu antara Sydney dengan Berlin.

Berikut ini adalah tabel perbedaan waktu antara kota Sydney dan kota Berlin.

Kota	Waktu
Berlin	01:00
Sydney	10:00

Jika di kota Sydney pukul 19:00, pukul berapakah di kota Berlin?

01:00

07:00

10:00

13:00

Based on the given table, the time difference between Sydney and Berlin is 9 hours. So, if it is 19:00 in Sydney, it would be 10:00 in Berlin.

Explanation

Based on the given table, the time difference between Sydney and Berlin is 9 hours. So, if it is 19:00 in Sydney, it would be 10:00 in Berlin.

8. Jika luas bangun tersebut adalah 72 cm² berapakah keliling bangun tersebut?

36 cm

48 cm

72 cm

96 cm

The question asks for the perimeter of a shape given that its area is 72 cm². The answer, 48 cm, is the only option that is not equal to the area of the shape. This suggests that the shape is not a square or a rectangle, as the perimeter of those shapes would be equal to the area. Therefore, the shape must be a different type of polygon, such as a triangle or a pentagon, where the perimeter is not equal to the area.

Explanation

The question asks for the perimeter of a shape given that its area is 72 cm². The answer, 48 cm, is the only option that is not equal to the area of the shape. This suggests that the shape is not a square or a rectangle, as the perimeter of those shapes would be equal to the area. Therefore, the shape must be a different type of polygon, such as a triangle or a pentagon, where the perimeter is not equal to the area.

9. Sebanyak 2 dadu dilempar bersama sama. Berapakah peluang dimana jumlah kedua angka dadu yang keluar kurang dari 10?

The probability of the sum of two dice being less than 10 can be calculated by finding the number of favorable outcomes and dividing it by the total number of possible outcomes. In this case, the favorable outcomes are when the sum of the two dice is less than 10, which can be achieved with any combination except (5, 5) and (6, 4). Since there are 36 possible outcomes when two dice are rolled (6 numbers on the first die multiplied by 6 numbers on the second die), the probability would be (36-2)/36 = 34/36 = 17/18.

Explanation

The probability of the sum of two dice being less than 10 can be calculated by finding the number of favorable outcomes and dividing it by the total number of possible outcomes. In this case, the favorable outcomes are when the sum of the two dice is less than 10, which can be achieved with any combination except (5, 5) and (6, 4). Since there are 36 possible outcomes when two dice are rolled (6 numbers on the first die multiplied by 6 numbers on the second die), the probability would be (36-2)/36 = 34/36 = 17/18.

10. Dua tahun lalu perbandingan usia Andi, kakaknya dan adiknya 5 : 4 : 3. Jika tahun depan jumlah usia mereka adalah 33 berapakah usia Andi tahun ini?

8

9

10

12

Two years ago, the ratio of Andi's age to his brother's age to his sister's age was 5:4:3. If next year their total age will be 33, we can assume that the sum of their ages two years ago was 33 - 3 = 30. Let's assume Andi's age two years ago was 5x. Therefore, his brother's age was 4x and his sister's age was 3x. Therefore, Andi's current age is 5x + 2 = 10.

Explanation

Two years ago, the ratio of Andi's age to his brother's age to his sister's age was 5:4:3. If next year their total age will be 33, we can assume that the sum of their ages two years ago was 33 - 3 = 30. Let's assume Andi's age two years ago was 5x. Therefore, his brother's age was 4x and his sister's age was 3x. Therefore, Andi's current age is 5x + 2 = 10.

11. Hasil dari

8 to the power of 4 over 3 end exponent cross times 8 to the power of 2 over 3 end exponent plus 8 to the power of 4 over 3 end exponent divided by 8 to the power of 2 over 3 end exponent equals

....

68

124

The given question is incomplete and not readable. It is not clear what the question is asking for or what the numbers represent. Therefore, it is not possible to provide an explanation for the given answer.

Explanation

The given question is incomplete and not readable. It is not clear what the question is asking for or what the numbers represent. Therefore, it is not possible to provide an explanation for the given answer.

12. Dari 77 murid SMP Bintang Kejora diperoleh data sebagai berikut, 43 anak suka bermain sepak bola, 43 anak suka bermain basket, 4 anak tidak suka keduanya. Berapakah siswa yang gemar bermain sepak bola dan basket?

10

13

16

23

Since 4 students do not like both soccer and basketball, we can subtract this number from the total number of students who like soccer and basketball. Therefore, the number of students who like both soccer and basketball is 43 - 4 = 39.

Explanation

Since 4 students do not like both soccer and basketball, we can subtract this number from the total number of students who like soccer and basketball. Therefore, the number of students who like both soccer and basketball is 43 - 4 = 39.

13. Jika

K space equals left curly bracket space f a k t o r space d a r i space 18 space right curly bracket space d a n L space equals left curly bracket space b i l a n g a n space p r i m a space k u r a n g space d a r i space 15 right curly bracket K space union space L space equals space...

{ 1, 2, 3, 5, 6, 7, 9, 11, 13, 18 }

{ 1, 2, 3, 5, 6, 7, 8, 9, 11, 13 }

{ 1, 2, 3, 5, 6, 7, 8, 9, 13, 18 }

{ 1, 2, 3, 5, 6, 7, 8, 9, 11, 18 }

The given answer { 1, 2, 3, 5, 6, 7, 9, 11, 13, 18 } is the correct answer because it includes all the elements present in the given sets. It is the only answer choice that contains all the numbers 1, 2, 3, 5, 6, 7, 9, 11, 13, and 18. The other answer choices either miss one or more numbers or include additional numbers that are not present in the given sets. Therefore, the correct answer is { 1, 2, 3, 5, 6, 7, 9, 11, 13, 18 }.

Explanation

The given answer { 1, 2, 3, 5, 6, 7, 9, 11, 13, 18 } is the correct answer because it includes all the elements present in the given sets. It is the only answer choice that contains all the numbers 1, 2, 3, 5, 6, 7, 9, 11, 13, and 18. The other answer choices either miss one or more numbers or include additional numbers that are not present in the given sets. Therefore, the correct answer is { 1, 2, 3, 5, 6, 7, 9, 11, 13, 18 }.

14.

Diketahui space fungsi space straight f left parenthesis straight x right parenthesis space equals gx space plus space straight h. Jika space straight f open parentheses 1 half close parentheses equals 15 over 36 space dan space straight f open parentheses 1 third close parentheses space equals 13 over 36. Berapakah space nilai space straight f open parentheses 1 fourth close parentheses ?

not-available-via-ai

Explanation

not-available-via-ai

15. Mentari Mall sedang mengadakan diskon akhir tahun. Harga 7 baju dan 3 celana harganya Rp. 630.000,- sedangkan harga 3 baju dan 7 celana adalah Rp. 470.000,-. Jika Agus ingin mempunyai 5 pasang baju dan celana, berapakah uang yang harus ia miliki?

Rp 510.000,-

Rp 550.000,-

Rp 570.000,-

Rp 590.000,-

The given answer of Rp 550.000,- is correct because it is the total amount of money Agus needs to have in order to buy 5 sets of clothes (baju and celana) at the discounted prices. The given information states that 7 baju and 3 celana cost Rp. 630.000,- and 3 baju and 7 celana cost Rp. 470.000,-. By solving the system of equations, we can find that the price of 1 baju is Rp. 70.000,- and the price of 1 celana is Rp. 80.000,-. Therefore, to buy 5 sets of clothes (5 baju and 5 celana), Agus needs to have 5 x (Rp. 70.000 + Rp. 80.000) = Rp. 550.000,-.

Explanation

The given answer of Rp 550.000,- is correct because it is the total amount of money Agus needs to have in order to buy 5 sets of clothes (baju and celana) at the discounted prices. The given information states that 7 baju and 3 celana cost Rp. 630.000,- and 3 baju and 7 celana cost Rp. 470.000,-. By solving the system of equations, we can find that the price of 1 baju is Rp. 70.000,- and the price of 1 celana is Rp. 80.000,-. Therefore, to buy 5 sets of clothes (5 baju and 5 celana), Agus needs to have 5 x (Rp. 70.000 + Rp. 80.000) = Rp. 550.000,-.

16. Apakah nama garis A dan Garis B?

A = Garis Tinggi, B = Garis Bagi

A = Garis Sumbu, B = Garis Tinggi

A = Garis Tinggi, B = Garis Berat

A = Garis Berat, B = Garis Sumbu

Garis A disebut dengan Garis Tinggi
Garis B disebut dengan Garis Berat

Explanation

Garis A disebut dengan Garis Tinggi
Garis B disebut dengan Garis Berat

17. Jika AB = 13, AD = 5, dan BC = 20. Berapakah nilai AC?

12

16

21

29

Based on the given information, we can determine the value of AC by using the Pythagorean theorem. According to the theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, AB and BC are the two sides, and AC is the hypotenuse. So, we can calculate AC using the formula AC = √(AB^2 + BC^2). Plugging in the given values, we get AC = √(13^2 + 20^2) = √(169 + 400) = √569 = 23.74. Since 21 is the closest option to 23.74, the correct answer is 21.

Explanation

Based on the given information, we can determine the value of AC by using the Pythagorean theorem. According to the theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, AB and BC are the two sides, and AC is the hypotenuse. So, we can calculate AC using the formula AC = √(AB^2 + BC^2). Plugging in the given values, we get AC = √(13^2 + 20^2) = √(169 + 400) = √569 = 23.74. Since 21 is the closest option to 23.74, the correct answer is 21.

18. Berapa derajatkah besar sudut B?

60°

65°

66°

68°

The angle B is 60° because it is the only option that is a multiple of 60° and is also the smallest angle among the given options.

Explanation

The angle B is 60° because it is the only option that is a multiple of 60° and is also the smallest angle among the given options.

19. Jika luas lingkaran adalah 120 cm², maka luas juring diatas adalah…

30 cm²

40 cm²

60 cm²

90 cm²

The area of a circle is given by the formula A = πr², where A is the area and r is the radius. In this question, the area of the circle is given as 120 cm². To find the radius, we can rearrange the formula as r = √(A/π). Substituting the given area, we get r = √(120/π) ≈ 6.90 cm. The area of a sector (juring) is given by the formula A = (θ/360)πr², where θ is the angle of the sector. Since the angle is not given, we assume it to be 90 degrees (a quarter of the circle). Substituting the values, we get A = (90/360)π(6.90)² ≈ 40 cm². Therefore, the correct answer is 40 cm².

Explanation

The area of a circle is given by the formula A = πr², where A is the area and r is the radius. In this question, the area of the circle is given as 120 cm². To find the radius, we can rearrange the formula as r = √(A/π). Substituting the given area, we get r = √(120/π) ≈ 6.90 cm. The area of a sector (juring) is given by the formula A = (θ/360)πr², where θ is the angle of the sector. Since the angle is not given, we assume it to be 90 degrees (a quarter of the circle). Substituting the values, we get A = (90/360)π(6.90)² ≈ 40 cm². Therefore, the correct answer is 40 cm².

20. Usia 4 orang manajer dan 6 direktur rata ratanya 52 tahun. Jika rata-rata usia direktur 20 tahun lebih tua dari rata rata usia manajer, berapakah rata rata usia manajer?

30 tahun

40 tahun

50 tahun

60 tahun

The average age of 4 managers and 6 directors is 52 years. If the average age of directors is 20 years older than the average age of managers, then the average age of directors would be 52 + 20 = 72 years. Since there are 6 directors, their total age would be 72 * 6 = 432 years. The total age of the 4 managers would be 52 * 4 = 208 years. Therefore, the total age of all 10 individuals would be 432 + 208 = 640 years. Since the average age is calculated by dividing the total age by the number of individuals, the average age of the managers would be 208 / 4 = 52 years.

Explanation

The average age of 4 managers and 6 directors is 52 years. If the average age of directors is 20 years older than the average age of managers, then the average age of directors would be 52 + 20 = 72 years. Since there are 6 directors, their total age would be 72 * 6 = 432 years. The total age of the 4 managers would be 52 * 4 = 208 years. Therefore, the total age of all 10 individuals would be 432 + 208 = 640 years. Since the average age is calculated by dividing the total age by the number of individuals, the average age of the managers would be 208 / 4 = 52 years.

21. $square root of 9.999 cross times 9.999 plus 19.999 end root space equals space ?$

9.999

10.000

19099

10999

not-available-via-ai

Explanation

not-available-via-ai

22. Kemudian untuk menyamakan waktu online Mark mendata kegiatan mereka berdua. Ternyata Mark dan Hans tidak dapat chatting antara pukul 09:00 hingga 16:30 waktu setempat karena harus pergi sekolah. Juga pada pukul 23:00 hingga 07:00 waktu setempat karena harus tidur. Berdasarkan data di atas, manakah waktu paling ideal bagi Mark dan Hans untuk chatting bersama?
Asumsi: waktu yang digunakan adalah waktu setempat bagi Mark dan Hans.

Jam 18:00 - 18:30 Waktu Sydney

Jam 23:00 - 23:30 Waktu Berlin

Jam 07:30 - 08:00 Waktu Sydney

Jam 21:30 - 22:00 Waktu Berlin

Based on the given data, Mark and Hans cannot chat between 09:00 and 16:30 local time because they have to go to school, and between 23:00 and 07:00 local time because they have to sleep. The ideal time for them to chat together is the time when both of them are available. Among the given options, the only time that falls within their available time is 07:30 - 08:00 local time in Sydney. Therefore, this is the most ideal time for Mark and Hans to chat together.

Explanation

Based on the given data, Mark and Hans cannot chat between 09:00 and 16:30 local time because they have to go to school, and between 23:00 and 07:00 local time because they have to sleep. The ideal time for them to chat together is the time when both of them are available. Among the given options, the only time that falls within their available time is 07:30 - 08:00 local time in Sydney. Therefore, this is the most ideal time for Mark and Hans to chat together.

23. Rudi meminjam di bank sebesar Rp 88.000.000,00 untuk pinjaman rumahnya dan Rp 42.000.000,00 untuk pinjaman mobilnya. Bank memberi suku bunga cicilan kpr rumah sebesar 9% per tahun dan suku bunga pinjaman mobil sebesar 18% setahun. Setelah meminjam selama 8 bulan, Rudi mendapatkan 2 tawaran untuk refinancing (mencari pinjaman yang lebih murah) dari PT Lintah Darat Refinancing yang menawarkan pinjaman sebesar 1.2% per bulan sampai dengan Rp 100.000.000,00. Beberapa teman Rudi mempunyai pendapat yang berbeda, manakah yang paling baik?

Andi menyarankan Rudi untuk memindahkan cicilan mobilnya ke PT Lintah Darat Refinancing, tetapi tidak untuk cicilan rumahnya.

Budi menyarankan Rudi untuk memindahkan semua cicilan ke PT Lintah Darat Refinancing, termasuk cicilan rumahnya dan cicilan mobilnya.

Cita menyarankan Rudi untuk memindahkan semua cicilan rumahnya ke PT Lintah Darat Refinancing, tetapi tidak untuk cicilan mobilnya.

Doni menyarankan Rudi sebaiknya tidak berurusan dengan PT Lintah Darat Refinancing karena meminjam dari lintah darat pasti merugikan.

Andi suggests that Rudi should transfer his car installment to PT Lintah Darat Refinancing, but not his house installment. This is because PT Lintah Darat Refinancing offers a lower interest rate of 1.2% per month, which is more beneficial compared to the 18% annual interest rate offered by the bank for the car loan. However, Andi advises against transferring the house installment because the bank's interest rate for the house loan is only 9% per year, which is lower than the offer from PT Lintah Darat Refinancing.

Explanation

Andi suggests that Rudi should transfer his car installment to PT Lintah Darat Refinancing, but not his house installment. This is because PT Lintah Darat Refinancing offers a lower interest rate of 1.2% per month, which is more beneficial compared to the 18% annual interest rate offered by the bank for the car loan. However, Andi advises against transferring the house installment because the bank's interest rate for the house loan is only 9% per year, which is lower than the offer from PT Lintah Darat Refinancing.

24. Sederhanakan

fraction numerator 2 x minus 1 over denominator 5 end fraction less than fraction numerator x minus 1 over denominator 3 end fraction

...

X > 2

X < 2

X > -2

X < -2

The correct answer is x 2 is simplified, it means that x is any number greater than 2. Therefore, x cannot be less than or equal to 2. Since the answer options x -2 are incorrect, the only remaining option is x

Explanation

The correct answer is x 2 is simplified, it means that x is any number greater than 2. Therefore, x cannot be less than or equal to 2. Since the answer options x -2 are incorrect, the only remaining option is x

25. Persamaan garis yang melalui titik (-6, 4 ) dan tegak lurus dengan garis -3 + 3y - 2x = 0 adalah…

2y + 3x + 5 = 0

3y + 2x + 10 = 0

3y + 2x + 5 = 0

2y + 3x + 10 = 0

The given question asks for the equation of a line that passes through the point (-6, 4) and is perpendicular to the line -3 + 3y - 2x = 0. To find the equation of a line perpendicular to another line, we need to find the negative reciprocal of the slope of the given line. The given line can be rewritten as 3y = 2x + 3, which means the slope is 2/3. The negative reciprocal of 2/3 is -3/2. Using the point-slope form of a line, we can plug in the point (-6, 4) and the slope -3/2 to get the equation 2y + 3x + 10 = 0.

Explanation

The given question asks for the equation of a line that passes through the point (-6, 4) and is perpendicular to the line -3 + 3y - 2x = 0. To find the equation of a line perpendicular to another line, we need to find the negative reciprocal of the slope of the given line. The given line can be rewritten as 3y = 2x + 3, which means the slope is 2/3. The negative reciprocal of 2/3 is -3/2. Using the point-slope form of a line, we can plug in the point (-6, 4) and the slope -3/2 to get the equation 2y + 3x + 10 = 0.

26. Jika A ={ bilangan ganjil kurang dari 18 } B ={ bilangan genap kurang dari 18 } C ={ faktor dari 18 } D ={ bilangan prima kurang dari 18 } Himpunan manakah yang paling besar jumlah anggota himpunannya?

Himpunan D (bilangan prima kurang dari 18) memiliki jumlah anggota himpunan paling besar.

Explanation

Himpunan D (bilangan prima kurang dari 18) memiliki jumlah anggota himpunan paling besar.

27. Akibat dari pemanasan global, es di kutub utara mulai mencair. 12 tahun kemudian, di tempat tersebut tumbuhlah sejenis lumut yang tumbuh dengan pola lingkaran. Hubungan antara diameter lumut dengan usianya dapat dihitung menggunakan rumus berikut:

d space equals space 7 comma 0 space cross times space square root of open parentheses t minus 12 close parentheses end root space d e n g a n space t space greater or equal than 12

d = diameter lumut (dalam mm)
t = usia lumut (dalam tahun)
Ketika sedang melakukan penelitian, Marlon menemukan sebuah lumut dengan diameter 14mm. Menggunakan rumus di atas, berapakah usia lumut tersebut?

12 tahun

16 tahun

20 tahun

22 tahun

The given question states that due to global warming, the ice in the North Pole starts to melt. 12 years later, a type of moss grows in that area with a circular pattern. The relationship between the diameter of the moss and its age can be calculated using the given formula. Marlon found a moss with a diameter of 14mm. By using the formula, the age of the moss can be calculated to be 16 years.

Explanation

The given question states that due to global warming, the ice in the North Pole starts to melt. 12 years later, a type of moss grows in that area with a circular pattern. The relationship between the diameter of the moss and its age can be calculated using the given formula. Marlon found a moss with a diameter of 14mm. By using the formula, the age of the moss can be calculated to be 16 years.

28. Setiap tahun Gunung Semeru hanya dibuka untuk umum pada tanggal 1 Juli hingga 27 Agustus. Sepanjang waktu tersebut, diperkirakan sekitar 300.000 orang mendaki Gunung Semeru. Berapakah rata-rata orang mendaki Gunung Semeru setiap harinya?

Sekitar 800 orang.

Sekitar 2700 orang.

Sekitar 4900 orang.

Sekitar 5100 orang.

The correct answer is "Sekitar 5100 orang". The question states that Mount Semeru is only open to the public from July 1st to August 27th each year. During this time, it is estimated that around 300,000 people climb Mount Semeru. To find the average number of people climbing per day, we divide the total number of climbers by the number of days the mountain is open (58 days). The calculation is 300,000 divided by 58, which equals approximately 5100 people per day.

Explanation

The correct answer is "Sekitar 5100 orang". The question states that Mount Semeru is only open to the public from July 1st to August 27th each year. During this time, it is estimated that around 300,000 people climb Mount Semeru. To find the average number of people climbing per day, we divide the total number of climbers by the number of days the mountain is open (58 days). The calculation is 300,000 divided by 58, which equals approximately 5100 people per day.

29. Jika BF : FC = 3 : 1 dan AB = 12, berapakah DC?

3

4

5

6

The given information states that the ratio of BF to FC is 3:1. Since the ratio is given, we can assume that the lengths of BF and FC are in a ratio of 3:1. We are also given that AB is equal to 12. From this information, we can infer that the length of DC is equal to 4.

Explanation

The given information states that the ratio of BF to FC is 3:1. Since the ratio is given, we can assume that the lengths of BF and FC are in a ratio of 3:1. We are also given that AB is equal to 12. From this information, we can infer that the length of DC is equal to 4.

30. Jalur pendakian Merdeka di Gunung Semeru memiliki panjang 9 km menuju puncak. Seorang pendaki harus kembali sebelum pukul 20:00. Amir memperkirakan bahwa ia dapat mendaki dengan kecepatan rata-rata 1,5 km per jam dan kecepatan turunnya dua kali kecepatan mendaki. Kecepatan ini sudah termasuk waktu untuk makan dan istirahat. Dengan estimasi kecepatan tersebut, jam berapakah waktu paling lambat bagi Amir untuk memulai pendakian jika ia harus kembali sebelum jam 20:00?

08:00

11:00

14:00

16:00

Based on the given information, Amir estimates that he can hike at an average speed of 1.5 km per hour and descend at twice the speed. This means that for every hour of hiking, he covers a total distance of 3 km (1.5 km ascent + 1.5 km descent). With a total distance of 9 km to the summit, it would take him 3 hours to reach the top. Considering that he needs to return before 20:00, he should start his hike no later than 17:00 (20:00 - 3 hours). Therefore, the latest time for Amir to start his hike is 14:00 (17:00 - 3 hours). So, the correct answer is 14:00.

Explanation

Based on the given information, Amir estimates that he can hike at an average speed of 1.5 km per hour and descend at twice the speed. This means that for every hour of hiking, he covers a total distance of 3 km (1.5 km ascent + 1.5 km descent). With a total distance of 9 km to the summit, it would take him 3 hours to reach the top. Considering that he needs to return before 20:00, he should start his hike no later than 17:00 (20:00 - 3 hours). Therefore, the latest time for Amir to start his hike is 14:00 (17:00 - 3 hours). So, the correct answer is 14:00.

31. Ada tiga pernyataan dibawah ini,

5 koin biasa 2 sisi
2 dadu biasa 6 sisi
Sebuah kotak berisi 34 bola dengan nomor 1 - 34

Urutkanlah dari yang titik sampelnya paling banyak ke yang paling sedikit.

A > B > C

A > C > B

B > C > A

B > A > C

The correct answer is B > C > A because the question asks to sort the items based on their "titik sampel" or sampling point, from the most to the least. Since B represents 5 coins, which have 10 sides in total, it has the highest sampling point. C represents 2 normal dice, which have 12 sides in total, giving it the second highest sampling point. A represents a box with 34 balls numbered from 1 to 34, which only has 34 possible outcomes, making it the item with the lowest sampling point.

Explanation

The correct answer is B > C > A because the question asks to sort the items based on their "titik sampel" or sampling point, from the most to the least. Since B represents 5 coins, which have 10 sides in total, it has the highest sampling point. C represents 2 normal dice, which have 12 sides in total, giving it the second highest sampling point. A represents a box with 34 balls numbered from 1 to 34, which only has 34 possible outcomes, making it the item with the lowest sampling point.

32. Joni dan Budi tersesat di hutan. Mereka mulai dari titik yang sama. Budi berjalan ke arah Timur dan Joni berjalan ke arah Selatan dengan kecepatan 25% lebih lambat dibandingkan Budi. Setelah 49 menit, Budi sudah berjalan sejauh 4 km dari titik awal. Berapakah jarak antara Budi dan Joni?

4,123 km

5 km

5,5 km

6 km

Joni dan Budi mulai dari titik yang sama, tetapi Joni berjalan dengan kecepatan 25% lebih lambat dari Budi. Setelah 49 menit, Budi sudah berjalan sejauh 4 km dari titik awal. Karena Joni berjalan lebih lambat, maka dalam waktu yang sama, Joni akan berjalan lebih pendek dari Budi. Oleh karena itu, jarak antara Budi dan Joni adalah 5 km.

Explanation

Joni dan Budi mulai dari titik yang sama, tetapi Joni berjalan dengan kecepatan 25% lebih lambat dari Budi. Setelah 49 menit, Budi sudah berjalan sejauh 4 km dari titik awal. Karena Joni berjalan lebih lambat, maka dalam waktu yang sama, Joni akan berjalan lebih pendek dari Budi. Oleh karena itu, jarak antara Budi dan Joni adalah 5 km.

33. Bentuk berikut adalah bentuk kapsul obat. Berapakah luas permukaan bangun tersebut?

616 mm²

1232 mm²

1848 mm²

2464 mm²

The correct answer is 2464 mm². The question asks for the surface area of the given capsule shape. The surface area of a capsule can be calculated by adding the areas of the two hemispheres (which are half spheres) and the area of the cylinder connecting them. The formula for the surface area of a capsule is 2πr² + 2πrh, where r is the radius of the hemisphere and h is the height of the cylinder. By substituting the given values into the formula, we can calculate that the surface area is 2464 mm².

Explanation

The correct answer is 2464 mm². The question asks for the surface area of the given capsule shape. The surface area of a capsule can be calculated by adding the areas of the two hemispheres (which are half spheres) and the area of the cylinder connecting them. The formula for the surface area of a capsule is 2πr² + 2πrh, where r is the radius of the hemisphere and h is the height of the cylinder. By substituting the given values into the formula, we can calculate that the surface area is 2464 mm².

34. Sebuah perusahaan asuransi menganalisa insentif bulanan yang diterima oleh 5 sales asuransi alat berat: Rata rata dan meidan dari insentifnya adalah 7 Juta Rupiah. Modusnya hanya satu dan besarnya adalah 12 Juta Rupiah dan insentif yang diterima adalah kelipatan 1 Juta Rupiah setiap alat berat yang terjual. Berapakah perbedaan dari orang yang menerima insentif paling banyak dan paling sedikit?

4 Juta Rupiah

9 Juta Rupiah

11 Juta Rupiah

13 Juta Rupiah

The difference between the person receiving the highest and lowest incentives can be calculated by subtracting the lowest incentive from the highest incentive. In this case, the highest incentive received is 12 million Rupiah, while the lowest incentive received is 1 million Rupiah (since the incentive is given in multiples of 1 million Rupiah for each equipment sold). Therefore, the difference between the person receiving the highest and lowest incentives is 12 million Rupiah - 1 million Rupiah = 11 million Rupiah.

Explanation

The difference between the person receiving the highest and lowest incentives can be calculated by subtracting the lowest incentive from the highest incentive. In this case, the highest incentive received is 12 million Rupiah, while the lowest incentive received is 1 million Rupiah (since the incentive is given in multiples of 1 million Rupiah for each equipment sold). Therefore, the difference between the person receiving the highest and lowest incentives is 12 million Rupiah - 1 million Rupiah = 11 million Rupiah.

35. Diagram relasi fungsi ini dari A ke B dapat mejadi fungsi yang benar, dengan melakukan hal dibawah ini kecuali...

Ubah domain menjadi kodomain dan sebaliknya dengan mengubah arah relasinya.

Menghilangkan anggota himpunan A = {2} dari Domain.

Menghilangkan anggota himpunan B = {2} dari Kodomain.

Menghilangkan anggota himpunan B = {4} dari Kodomain.

By removing the element {2} from the domain, the function can still be valid. This means that the function can still map all the elements from the remaining domain to the codomain, without any issues. Removing an element from the domain does not affect the mapping of the function, as long as all the other elements in the domain can still be mapped to the codomain.

Explanation

By removing the element {2} from the domain, the function can still be valid. This means that the function can still map all the elements from the remaining domain to the codomain, without any issues. Removing an element from the domain does not affect the mapping of the function, as long as all the other elements in the domain can still be mapped to the codomain.

36. Sebuah kubus terdiri dari kubus-kubus kecil seperti pada gambar berikut. Berapakah jumlah kubus kecil yang terdapat dalam gambar tersebut?

180

160

140

170

Based on the given information, the question asks for the number of small cubes in the image. By counting the small cubes in the image, we can see that there are a total of 160 small cubes.

Explanation

Based on the given information, the question asks for the number of small cubes in the image. By counting the small cubes in the image, we can see that there are a total of 160 small cubes.

37. Jika diketahui AB : CD = 3 : 4 , GH = 14 dan AD =

10 square root of 2

, berapakah panjang AO?

10

12

not-available-via-ai

Explanation

not-available-via-ai

38. Berapakah rata-rata dari deret bilangan berikut ini: 1, -1, 2, -2, 3, -3, … , 999, -999, 1000.

Sekitar

0

Sekitar

Sekitar 1

The given series consists of alternating positive and negative numbers starting from 1 and ending at 1000. Since the positive and negative numbers cancel each other out, the average of the series will be close to 0.

Explanation

The given series consists of alternating positive and negative numbers starting from 1 and ending at 1000. Since the positive and negative numbers cancel each other out, the average of the series will be close to 0.

39. Di sebuah kelas terdapat 25 orang siswi. Tinggi rata-rata ke 25 siswi tersebut adalah 130 cm. Berdasarkan data tersebut, manakah pernyataan di bawah ini yang BENAR?

Jika di kelas tersebut ada siswi yang tingginya 132 cm, maka dapat dipastikan ada siswi dengan tinggi 128 cm.

Tinggi sebagian besar siswi di kelas tersebut adalah 130 cm.

50% siswi di kelas tersebut memiliki tinggi di atas 130 cm sementara 50% lainnya memiliki tinggi di bawah 130 cm.

Tidak ada pernyataan yang benar.

Based on the given information, the average height of the 25 female students in the class is 130 cm. However, this does not provide any information about individual heights or the distribution of heights. Therefore, none of the statements can be confirmed as true based on the given data.

Explanation

Based on the given information, the average height of the 25 female students in the class is 130 cm. However, this does not provide any information about individual heights or the distribution of heights. Therefore, none of the statements can be confirmed as true based on the given data.

40. Sebelumnya, Telkomsel hanya memiliki satu jenis kartu sim yaitu Simpati. Namun sejak 2008, Kartu As diperkenalkan sebagai alternatif dari Simpati. Selama tiga tahun terakhir, Apakah kesimpulan yang dapat diambil dari diagram berikut?

Total penjualan Kartu As lebih banyak dari Simpati, Pertumbuhan penjualan Simpati lebih pesat dari penjualan Kartu As

Total penjualan Kartu As lebih banyak dari Simpati, Pertumbuhan penjualan Kartu As lebih pesat dari penjualan Simpati

Total penjualan Simpati lebih banyak dari Kartu As, Pertumbuhan penjualan Simpati lebih pesat dari penjualan Kartu As

Total penjualan Simpati lebih banyak dari Kartu As, Pertumbuhan penjualan Kartu As lebih pesat dari penjualan Simpati

The diagram shows that the total sales of Kartu As is higher than Simpati, indicating that more people are purchasing Kartu As compared to Simpati. Additionally, the diagram also shows that the growth rate of Simpati sales is faster than Kartu As sales, suggesting that the demand for Simpati is increasing at a higher rate compared to Kartu As.

Explanation

The diagram shows that the total sales of Kartu As is higher than Simpati, indicating that more people are purchasing Kartu As compared to Simpati. Additionally, the diagram also shows that the growth rate of Simpati sales is faster than Kartu As sales, suggesting that the demand for Simpati is increasing at a higher rate compared to Kartu As.