The government increased teacher salary of sh. 480,000 by 25%. What is their new salary? 8. How many subsets…

Question

The government increased teacher salary of sh. 480,000 by 25%. What is their new salary? 8. How many subsets are in set B? 9. Write MMXXVI in words. 10. Find the sum of the next two numbers in the sequence. 4, 6, 8, 9, _, _. 11. Work out: −7 +9.

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7. The government increased teacher salary of sh. 480,000 by 25%. What is their new salary?

Tafuta kiasi cha ongezeko la mshahara.
$\text{Ongezeko} = 25\% \text{ ya sh. } 480,000$ $\text{Ongezeko} = \frac{25}{100} \times 480,000$ $\text{Ongezeko} = 0.25 \times 480,000 = \text{sh. } 120,000$
Ongeza ongezeko hilo kwenye mshahara wa awali ili kupata mshahara mpya.
$\text{Mshahara mpya} = \text{Mshahara wa awali} + \text{Ongezeko}$ $\text{Mshahara mpya} = \text{sh. } 480,000 + \text{sh. } 120,000 = \text{sh. } 600,000$
Mshahara wao mpya ni:
$\boxed{\text{sh. 600,000}}$
8. How many subsets are in set B?
Tambua vipengele vilivyopo katika seti B kutoka kwenye mchoro wa Venn.
Kutoka kwenye mchoro, seti B ina vipengele {a, e, b, 0}.
Hesabu idadi ya vipengele katika seti B.
Idadi ya vipengele katika seti B, $n(B) = 4$ .
Tumia fomula ya idadi ya vijisehemu (subsets), ambayo ni $2^n$ , ambapo $n$ ni idadi ya vipengele.
$\text{Idadi ya vijisehemu} = 2^{n(B)}$ $\text{Idadi ya vijisehemu} = 2^4 = 2 \times 2 \times 2 \times 2 = 16$
Idadi ya vijisehemu katika seti B ni:
$\boxed{16}$
9. Write MMXXVI in words.
Badilisha namba za Kirumi kuwa namba za Kiarabu.
M = 1000
M = 1000
X = 10
X = 10
V = 5
I = 1
Jumlisha thamani hizo.
$1000 + 1000 + 10 + 10 + 5 + 1 = 2026$
Namba MMXXVI kwa maneno ni:
$\boxed{\text{Elfu mbili na ishirini na sita}}$
10. Find the sum of the next two numbers in the sequence. 4, 6, 8, 9, ___, ___
Chunguza mpangilio wa namba ili kubaini kanuni.
Kuanzia 4, 6, 8, kuna ongezeko la 2.
$4 + 2 = 6$
$6 + 2 = 8$
Lakini kutoka 8 hadi 9, kuna ongezeko la 1.
$8 + 1 = 9$
Inaonekana kuna mabadiliko ya kanuni. Ikiwa tunachukulia kuwa mpangilio unaendelea kwa kuongeza 2 mara mbili, kisha 1, kisha 2 mara mbili, kisha 1, n.k.
Au, inaweza kuwa mpangilio wa namba shufwa (even numbers) na kisha namba witiri (odd numbers) au mchanganyiko mwingine.
Hata hivyo, kwa kuzingatia mpangilio wa kawaida wa maswali ya aina hii, mara nyingi kuna kanuni rahisi ya kuongeza au kutoa.
Hebu tuchunguze tofauti kati ya namba:
$6 - 4 = 2$
$8 - 6 = 2$
$9 - 8 = 1$
Inaonekana mpangilio ni kuongeza 2, kisha kuongeza 2, kisha kuongeza 1.
Ikiwa kanuni hii inajirudia, basi namba inayofuata baada ya 9 itafuata kanuni ya kuongeza 2.
$9 + 2 = 11$
Namba inayofuata baada ya 11 itafuata kanuni ya kuongeza 2.
$11 + 2 = 13$
Hivyo, namba mbili zinazofuata ni 11 na 13.
Tafuta jumla ya namba mbili zinazofuata.
$\text{Jumla} = 11 + 13 = 24$
Jumla ya namba mbili zinazofuata ni:
$\boxed{24}$
11. Work out: $-7 + 9$ .
Fanya hesabu ya kujumlisha namba chanya na hasi.
Unapojumlisha namba hasi na namba chanya, unatoa thamani ndogo kutoka kwa thamani kubwa na kuweka ishara ya namba yenye thamani kubwa.
$9 - 7 = 2$
Kwa kuwa 9 ni kubwa kuliko 7 na ina ishara chanya, jibu litakuwa chanya.

Jibu ni:
$\boxed{2}$

The government increased teacher salary of sh. 480,000 by 25%. What is their new salary? 8. How many subsets are in set B? 9. Write MMXXVI in words. 10. Find the sum of the next two numbers in the sequence. 4, 6, 8, 9, _, _. 11. Work out: -7 +9.

Step-by-step solution

Tafuta kiasi cha ongezeko la mshahara.

Ongeza ongezeko hilo kwenye mshahara wa awali ili kupata mshahara mpya.

Tambua vipengele vilivyopo katika seti B kutoka kwenye mchoro wa Venn.

Hesabu idadi ya vipengele katika seti B.

Tumia fomula ya idadi ya vijisehemu (subsets), ambayo ni $2^n$ , ambapo $n$ ni idadi ya vipengele.

Badilisha namba za Kirumi kuwa namba za Kiarabu.

Jumlisha thamani hizo.

Chunguza mpangilio wa namba ili kubaini kanuni.

Tafuta jumla ya namba mbili zinazofuata.

Fanya hesabu ya kujumlisha namba chanya na hasi.

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