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3 years ago

The sum of three consecutive numbers is 96. What are the smallest of these numbers? Write and Solve an Equation.

Mathematics

2 answers:

zlopas [31]3 years ago

5 0

Answer:

Step-by-step explanation:

Remark

The easy way to set this up is to make the smallest number x - 1. You will see why in a moment. It cuts down on one step)

Equation

(x - 1) + x + (x + 1) = 96 Remove the brackets

Solution

x - 1 + x + x + 1 = 96 Combine like terms

3x = 96 Divide by 3

x = 32

Note: that is not the smallest number. Remember, the smallest number is x - 1

So the smallest number is 31

vichka [17]3 years ago

4 0

Answer:

30+32+34

Step-by-step explanation:

so 30 would be the smallest number. Hope this helps, have a nice day!

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First ten nonzero multiples of 10

Ray Of Light [21]

10, 20, 30, 40, 50, 60, 70, 80, 90, 100

8 0

3 years ago

What is the value of z?

VashaNatasha [74]

Answer:

z = 61

Step-by-step explanation:

The exterior angle is congruent (equal to) the sum of the 2 farthest angles from it, so you can set the equation like this:

z + z - 11 = z + 50

Add like terms, which would be the 2 "z's" on the left side:

2z - 11 = z + 50

Then subtract the z on the right side from both sides:

2z - 11 = z + 50

-z -z

___________

z - 11 = 50

Add 11 to both sides:

z - 11 = 50

+ 11 +11

________

z = 61

6 0

3 years ago

A manufacturer knows that their items have a normally distributed length, with a mean of 15.4 inches, and standard deviation of

Masteriza [31]

Answer:

0.9452 = 94.52% probability that their mean length is less than 16.8 inches.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .