Eleza jinsi hisabati inavyotumika katika shughuli zetu za kila siku katika maeneo ya shule na viwanda, na jadili umuhimu wake kwa maisha yetu.

Hapa kuna majibu ya maswali yako: 1. (a) Eleza jinsi hisabati inavyotumika katika shughuli zetu za kila siku kwa kuzingatia maeneo yafuatayo; (Toa hoja 5 kwa kila eneo). (i) Katika Shule • Hisabati hutumika kufundisha kuhesabu na kutambua namba kwa wanafunzi wadogo. • Hutumika katika jiometria kujifunza maumbo na nafasi. • Husadia kukuza uwezo wa kutatua matatizo na kufikiri kimantiki. • Hutumika katika takwimu kuchambua data za matokeo ya mitihani au mahudhurio. • Husadia katika kupanga ratiba za masomo na matumizi ya rasilimali shuleni. (ii) Katika Viwanda • Hisabati hutumika katika kubuni na kutengeneza bidhaa (engineering design). • Husadia katika udhibiti wa ubora wa bidhaa kwa kutumia takwimu na vipimo. • Hutumika katika usimamizi wa hesabu (accounting) na fedha za kiwanda. • Husadia katika kupanga uzalishaji na usambazaji wa bidhaa (logistics). • Hutumika katika utafiti na maendeleo (R&D) kuboresha bidhaa na michakato. (b) Andika insha fupi ukijadili umuhimu wa kujifunza hisabati katika maisha yetu. (Toa hoja tatu). Kujifunza hisabati ni muhimu sana katika maisha yetu kwa sababu kadhaa. Kwanza, hisabati inatupa uwezo wa kufikiri kimantiki na kutatua matatizo ya kila siku, iwe ni kupanga bajeti ya familia au kufanya maamuzi magumu. Pili, ni lugha ya sayansi na teknolojia, hivyo inatuwezesha kuelewa na kutumia maendeleo ya kisasa kama vile simu mahiri, kompyuta, na mifumo ya usafiri. Tatu, hisabati inafungua fursa nyingi za ajira katika nyanja mbalimbali kama uhandisi, fedha, sayansi ya data, na utafiti, ambazo zote zinahitaji ujuzi imara wa hisabati. 2. (a) Ikiwa x = 0.2, y = 0.3 na z = 0.3, tathmini; (i) x + yz Step 1: Substitute the given values into the expression. x + yz = 0.2 + (0.3)(0.3) Step 2: Perform the multiplication first. 0.2 + 0.09 Step 3: Perform the addition. 0.29 The value is 0.29. (ii) xz Step 1: Substitute the given values into the expression. xz = (0.2)(0.3) Step 2: Perform the multiplication. 0.06 The value is 0.06. (b) Mapato ya wastani ya kampuni fulani ni TZS milioni 77 kwa mwaka. Ikiwa mapato yanatofautiana kwa TZS milioni 1.2, ni yapi mapato ya chini na ya juu ya kampuni hiyo? Step 1: Identify the given values. Mean income = TZS 77,000,000 Variation = TZS 1,200,000 Step 2: Calculate the minimum income. Minimum income = Mean income - Variation Minimum income = 77,000,000 - 1,200,000 = 75,800,000 TZS Step 3: Calculate the maximum income. Maximum income = Mean income + Variation Maximum income = 77,000,000 + 1,200,000 = 78,200,000 TZS The minimum income is TZS 75,800,000 and the maximum income is TZS 78,200,000. 3. (a) Andika 47628.03514 kwa usahihi wa; (i) sehemu mbili za desimali Step 1: Identify the second decimal place, which is 3. Step 2: Look at the next digit (the third decimal place), which is 5. Since it is 5 or greater, round up the second decimal place. 47628.04 The number is 47628.04. (ii) tarakimu saba muhimu Step 1: Count seven significant figures from the left: 4, 7, 6, 2, 8, 0, 3. The seventh significant figure is 3. Step 2: Look at the next digit, which is 5. Since it is 5 or greater, round up the seventh significant figure. 47628.04 The number is 47628.04. (iii) mamia ya karibu This refers to rounding to the nearest hundredth, which is the same as 2 decimal places. Step 1: Identify the hundredths place, which is 3. Step 2: Look at the next digit (the thousandths place), which is 5. Since it is 5 or greater, round up the hundredths digit. 47628.04 The number is 47628.04. (iv) maelfu ya karibu Step 1: Identify the thousands place, which is 7 (in 47628). Step 2: Look at the next digit to the right (the hundreds place), which is 6. Since it is 5 or greater, round up the thousands digit. 48000 The number is 48000. (b) Amina na marafiki zake 17 walinunua chupa 212 za vinywaji baridi kwa bei ya TZS. 635 kwa chupa. Ikiwa gharama yote iligawanywa sawa kati yao, kadiria ni kiasi gani kila mtu alilipa. Step 1: Calculate the total number of people. Amina + 17 friends = 1 + 17 = 18 people. Step 2: Calculate the total cost. Total cost = Number of bottles × Price per bottle Total cost = 212 × 635 TZS = 134,620 TZS Step 3: Estimate the cost per person. To estimate, we can round the total cost and the number of people. Round 134,620 to 135,000. Round 18 to 20. Estimated cost per person ≈ (135,000)/(20) = (13,500)/(2) = 6,750 TZS For a more precise calculation: Cost per person = Total cost / Number of people Cost per person = (134,620)/(18) TZS ≈ 7478.89 TZS Rounding to the nearest TZS, each person paid approximately TZS 7479. The estimated amount each person paid is approximately TZS 6,750. (Using the rounding method for estimation) The actual amount each person paid is approximately TZS 7,479. 4. (a) Jason ana sarafu za shilingi 500, 200, na 100 za Tanzania. Uwiano wa jumla ya kiasi cha sarafu hizi ni 2:3:5 na jumla ya kiasi ni TZS 780,000. Tafuta idadi ya sarafu za kila aina. Step 1: Determine the total parts in the ratio. Total ratio parts = 2 + 3 + 5 = 10 parts. Step 2: Calculate the value of one ratio part. Value per part = Total amount / Total ratio parts Value per part = 780,000 TZS10 = 78,000 TZS Step 3: Calculate the total amount for each coin denomination. Amount from TZS 500 coins = 2 × 78,000 = 156,000 TZS Amount from TZS 200 coins = 3 × 78,000 = 234,000 TZS Amount from TZS 100 coins = 5 × 78,000 = 390,000 TZS Step 4: Calculate the number of coins for each denomination. Number of TZS 500 coins = (156,000)/(500) = 312 coins Number of TZS 200 coins = (234,000)/(200) = 1170 coins Number of TZS 100 coins = (390,000)/(100) = 3900 coins The number of TZS 500 coins is 312, TZS 200 coins is 1170, and TZS 100 coins is 3900. (b) Namba mbili zinazofuatana ziko katika uwiano wa 2:7. Ikiwa 6 ikiongezwa kwenye jumla yao, matokeo ni 32. Tafuta jumla ya namba hizo. The phrasing "Two consecutive numbers are in the ratio 2:7" is contradictory, as consecutive numbers (e.g., n, n+1) would have a ratio close to 1, not 2:7. We will assume the question means "Two numbers are in the ratio 2:7". Step 1: Represent the two numbers using the given ratio. Let the two numbers be 2x and 7x. Step 2: Formulate an equation based on the given information. The sum of the numbers is 2x + 7x = 9x. If 6 is added to their sum, the result is 32: 9x + 6 = 32 Step 3: Solve for x. Subtract 6 from both sides: 9x = 32 - 6 9x = 26 Divide by 9: x = (26)/(9)