This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Haya, nitasuluhisha maswali haya hatua kwa hatua. 15. Ikiwa modi ya seti ya data ni 12, ni ipi kati ya zifuatazo inaweza kuwa seti ya data? Hatua 1: Elewa maana ya modi. Modi ni nambari inayoonekana mara nyingi zaidi katika seti ya data. Hatua 2: Chunguza kila chaguo: A) 10, 12, 14, 16: Kila nambari inaonekana mara moja. Hakuna modi maalum ya 12. B) 5, 7, 12, 12, 12, 13: Nambari 12 inaonekana mara 3. Nambari zingine zinaonekana mara 1. Hivyo, 12 ndiyo modi. C) 5, 5, 8, 8, 12, 13: Nambari 5 inaonekana mara 2, na 8 inaonekana mara 2. Hivyo, modi ni 5 na 8, si 12 pekee. D) 6, 7, 8, 10, 12, 15: Kila nambari inaonekana mara moja. Hakuna modi maalum ya 12. Jibu sahihi ni B. 16. Ikiwa mlinganyo wa mstari ni y=2x+1, y-intercept ni ipi? Hatua 1: Tambua umbo la mlinganyo wa mstari. Mlinganyo wa mstari katika umbo la mteremko-kizuizi ni y = mx + c, ambapo m ni mteremko na c ni y-intercept. Hatua 2: Linganisha mlinganyo uliotolewa na umbo la jumla. y = 2x + 1 Hapa, c = 1. Y-intercept ni 1. Jibu sahihi ni B. 17. Mteremko wa mstari unaopita kwenye pointi (0, 2) na (3, 8) ni upi? Hatua 1: Tumia fomula ya mteremko. Mteremko m wa mstari unaopita kwenye pointi (x_1, y_1) na (x_2, y_2) hutolewa na: m = (y_2 - y_1)/(x_2 - x_1) Hatua 2: Badilisha maadili ya pointi (0, 2) na (3, 8) kwenye fomula. Hapa x_1 = 0, y_1 = 2, x_2 = 3, y_2 = 8. m = (8 - 2)/(3 - 0) Hatua 3: Fanya hesabu. m = (6)/(3) m = 2 Jibu sahihi ni C. 18. Pointi (2, 3) na (4, 7) ziko kwenye mstari ulionyooka. Mteremko wa mstari ni upi? Hatua 1: Tumia fomula ya mteremko. Mteremko m wa mstari unaopita kwenye pointi (x_1, y_1) na (x_2, y_2) hutolewa na: m = (y_2 - y_1)/(x_2 - x_1) Hatua 2: Badilisha maadili ya pointi (2, 3) na (4, 7) kwenye fomula. Hapa x_1 = 2, y_1 = 3, x_2 = 4, y_2 = 7. m = (7 - 3)/(4 - 2) Hatua 3: Fanya hesabu. m = (4)/(2) m = 2 Jibu sahihi ni 2. (Hakuna chaguo lililotolewa kwa swali hili, lakini jibu ni 2). Majibu ya mwisho: 15. B) 5, 7, 12, 12, 12, 13 16. B) 1 17. C) 2 18. 2 Drop the next question.