Which expressions are equivalent to 1/5 x 1/5 x 1/5 x 1/5 Choose 2 answers:

Which set of numbers is arranged in order from least to greatest?

charle [14.2K]

The answer is: [C]: -0.7, ⅕, 0.35, ⅔ .
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Explanation:
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Note that in this correct Answer choice "C" given, we have the following arrangement of numbers:
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→ -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]: -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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6 0

3 years ago

What is the formula for a confidence interval?

ikadub [295]

Answer:

a) The formula is given by mean $\pm$ the margin of error. Where the margin of error is the product between the critical value from the normal standard distribution at the confidence level selected and the standard deviation for the sample mean.

b) $\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

If the distribution for X is normal or if the sample size is large enough we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

Part a

The formula is given by mean $\pm$ the margin of error. Where the margin of error is the product between the critical value from the normal standard distribution at the confidence level selected and the standard deviation for the sample mean.

Part b

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

5 0

3 years ago

Eric bought 21 pounds of sugar for $12 . how many dollars did he pay per pound of sugar?

Stels [109]

$1.75 per pound of sugar

8 0

3 years ago

Hi guys can u pls help me with this problem thanx

salantis [7]

Answer:

$\frac{1}{4}$ left

Step-by-step explanation:

The question says she used $\frac{1}{2}$ of it, so she probably used $\frac{1}{2}$ of it. I'm assuming this is an error in the question, and it should be asking how much is left. To solve for that: