The answer is: [C]: -0.7, ⅕, 0.35, ⅔ .
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Explanation:
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<span>
Note that in this correct Answer choice "C" given, we have the following arrangement of numbers:
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</span>→ -0.7, ⅕, 0.35, ⅔ ;
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We are asked to find the "Answer choice" (or, perhaps, "Answer choices?") given that show a set of numbers arranged in order from "least to greatest"; that is, starting with a value that is the smallest number in the arrangement, and sequentially progressing, in order from least to greatest, with the largest (greatest) number in the arrangement appearing as the last number in the arrangement.
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Note the EACH of the 4 (four) answer choices given consists of an arrangement with ONLY one negative number, "- 0.7". Only TWO of the answer choices—Choices "B" and "C"—have an arrangement beginning with the number, "-0.7 "; So we can "rule out" the "Answer choices: [A] and [D]".
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Let us examine: Answer choice: [B]: <span>-0.7, 0.35, ⅕, ⅔ ;
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Note: The fraction, "⅕" = "2/10"; or, write as: 0.2 .
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The fraction, "⅔" = 0.6666667 (that is 0.6666... repeating; so we often see a "final decimal point" rounded to "7" at some point.
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Through experience, one will be able to automatically look at these 2 (two) fractions and immediately know their "decimal equivalents".
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Otherwise, one can determine the "decimal form" of these values on a calculator by division:
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→ ⅕ = 1/5 = 1 ÷ 5 = 0.2
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→ ⅔ = 2/3 = 2 ÷ 3 = 0.6666666666666667
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For Answer choice: [B], we have:
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→ -0.7, 0.35, ⅕, ⅔ ;
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→ So, we can "rewrite" the arrangement of "Answer choice [B]" as:
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→ -0.7, 0.35, 0.2, 0.666666667 ;
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→ And we can see that "Answer choice: [B]" is INCORRECT; because
"0.2" (that is, "⅕"), is LESS THAN "0.35". So, "0.35" should not come BEFORE "⅕" in the arrangement that applies correctly to the problem.
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Let us examine: Answer choice: [C]: -0.7, ⅕, 0.35, 0.666666667 .
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→ Remember from our previous— and aforementioned—examination of "Answer Choice: [B]" ; that:
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→ ⅕ = 0.2 ; and:
→ ⅔ = 0.666666667
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So, given:
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→ Answer choice: [C]: -0.7, ⅕, 0.35, ⅔ ;
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→ We can "rewrite" this given "arrangement", substituting our known "decimal values for the fractions:
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→ Answer choice: [C]: -0.7, 0.2, 0.35, 0.666666667 ;
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→ As mentioned above, this sequence starts with "-0.7", which is the ONLY negative number in the sequence; as such, the next positive number is correct. Nonetheless, "0.2" (or, "(⅕") is the next number in the sequence, and is greater than "-0.7". The next number is "0.35. "0.35" is greater than "⅕" (or, "0.2"). Then next number is "(⅔)" (or, "0.666666667").
"(⅔)"; (or, "0.666666667") is greater than 0.35.
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This set of numbers: "-0.7, ⅕, 0.35, ⅔" ; is arranged in order from least to greatest; which is "Answer choice: [C]: -0.7, ⅕, 0.35, ⅔" ; the correct answer.
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Answer:
1. 625,000 J
2. 100 J
4. 5 kg
5. √5 ≈ 2.236 m/s
Step-by-step explanation:
You should be aware that the SI derived units of Joules are equivalent to kg·m²/s².
To reduce confusion between <em>m</em> for mass and m for meters, we'll use an <em>italic m</em> for mass.
In each case, the "find" variable is what's left after we put the numbers into the formula. It is what the question is asking for. The "given" values are the ones in the problem statement and are the values we put into the formula. The formula is the same in every case.
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1. KE = (1/2)<em>m</em>v² = (1/2)(2000 kg)(25 m/s)² = 625,000 kg·m²/s² = 625,000 J
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2. KE = (1/2)<em>m</em>v² = (1/2)(0.5 kg)(20 m/s)² = 100 kg·m²/s² = 100 J
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4. KE = (1/2)<em>m</em>v²
250 J = (1/2)<em>m</em>(10 m/s)² = 50 m²/s²
(250 kg·m²/s²)/(50 m²/s²) = <em>m</em> = 5 kg
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5. KE = (1/2)<em>m</em>v²
2000 kg·m²/s² = (1/2)(800 kg)v²
(2000 kg·m²/s²)/(400 kg) = v² = 5 m²/s²
v = √5 m/s ≈ 2.236 m/s
Answer:
In this question, Adrian initially has $52,000 and his salary is 1.2 times the previous year's salary. This means the income should look like this:52000*1.2^n
30% of his income is budgeted for rent, then the equation should look like this: 30% * income= 30%*(52000*1.2^n)
Adrian's income increases by $2,300 each year as a result of gifts will make this equation:2300n
if you put the 3 equation together you will get
f(n)= 52000*1.2^n - 0.3(52000*1.2^n) +2300n
f(n)= 36400*1.2^n +2300n
