All categories

3 years ago

The sum of three consecutive integers is -78. determine the smallest integer.

1 answer:

4 0

Lets x is the 1st consecutive even integers
x +2 :the 2nd consecutive even integers
x +4: the 3rd consecutive even integers

So sum of all 3 equals -78 then
x + (x+2) + (x+4) = -78
x + x + 2 + x + 4 = -78
Simplify
3x + 6 = -78
Subtract (-6) to both sides
3x +6 -6 = -78 - 6
Simplify
3x = -84
Divided both sides by 3
3x/3 = -84/3

x = -28
x + 2 = -28 + 2 = -26
x +4 = - 28 + 4 = -24

Double check: -28 + -26 + -24 = -78

So the three consecutive even integers are: -24, -26, -28

The smallest integer would be -28

You might be interested in

What kind of dimension does a point have?

Crazy boy [7]

Should be zero, I believe.

8 0

2 years ago

Read 2 more answers

frank and his family drove 6 hours every day during a road trip which graph best represents y the total of hours driven in x day

Marta_Voda [28]

Answer:Where is the graph?

Step-by-step explanation:

6 0

2 years ago

Write the equation in slope-intercept form of a line that has a slope of 1/3 and passes through the point (-6, 0).

Vesna [10]

Answer: y = 1/3x +2

Step-by-step explanation:

The equation of line in slope - point form is given as:

y - $y_{1}$ = m ( x - $x_{1}$ )

m = 1/3

$y_{1}$ = 0

$x_{1}$ = -6

substituting into the formula , we have

y - 0 = 1/3 ( x - {-6} )

y = 1/3 (x+6)

y = 1/3x +2

5 0

3 years ago

Read 2 more answers

A survey was taken of students in math classes to find out how many hours per day students spend

Hoochie [10]

Answer:

1. Mean, because there are no outliers that affect the center

Step-by-step explanation:

Second period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2

Sorted values : 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4

The mean = ΣX / n

n = sample size, n = 15

Mean = 34 / 15 = 2.666

The median = 1/2(n+1)th term.

1/2(16)th term = 8th term.

The 8th term = 2

The best measure of centre is the mean because the values for the second period has no outliers that might have affected the centre of the distribution.

Both interquartile range and standard deviation are measures of spread and not measures of centre.

6 0

2 years ago

At a new exhibit in the Museum of Science, people are asked to choose between 94 or 220 random draws from a machine. The machine

Tresset [83]

Answer:

0.0869 = 8.69% probability of getting more than 61% green balls.

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 estabilishes 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 $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$