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satela [25.4K]
3 years ago
13

What is "the sum of twice a number and six is the same as three subtracted from the number itself"?

Mathematics
1 answer:
inysia [295]3 years ago
4 0

Answer:

x=-1

Step-by-step explanation:

2x+6=3-x

Step 1: Simplify both sides of the equation.

2x+6=3−x

2x+6=3+(−x)

2x+6=−x+3

Step 2: Add x to both sides.

2x+6+x=−x+3+x

3x+6=3

Step 3: Subtract 6 from both sides.

3x+6−6=3−6

3x=−3

Step 4: Divide both sides by 3.

3x/3=−3/3

x=−1

Answer:

x=−1

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A community college has a math placement exam that has a mean of 65 and a standard deviation of 8.2. If a student takes the exam
Marat540 [252]

Answer:

The score that cuts off the bottom 2.5% is 48.93.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 65, \sigma = 8.2

What is the score that cuts off the bottom 2.5%

This is X when Z has a pvalue of 0.025, so X when Z = -1.96.

Z = \frac{X - \mu}{\sigma}

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X - 65 = -1.96*8.2

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The score that cuts off the bottom 2.5% is 48.93.

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