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3 years ago

A set contains three consecutive numbers. the sum of these three numbers is 54. what are the three numbers?

1 answer:

3 0

The three (3) consecutive numbers are: 17, 18, and 19.
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Explanation:
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x + (x+1) + (x+2) = 54 ;

in which the three consecutive number are: x, (x + 1), and (x + 2) ;
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Given:
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x + (x+1) + (x+2) = 54 ; Solve for: "x" ;

x + (x+1) + (x+2) = 54 ;

→ x + x + 1 + x + 2 = 54

3x + 3 = 54 ;

Subtract "3" from each side of the equation;

3x + 3 - 3 = 54 - 3 ;

to get:

3x = 51 ;

Divide each side of the equation by "3" ; to isolate "x" on one side of the equation; and to solve for "x" ;
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3x / 3 = 51 / 3 ;

x = 17 ;
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x + 1 = 18 ;

x + 2 = 19 ;
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The three (3) consecutive numbers are: 17, 18, and 19.
______________________________________________________
Let us check our work: 17 + 18 + 19 =? 54 ? ;

35 + 19 =? 54 ? Yes!
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Answer:

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Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

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In this problem, we have that:

$\mu = 60, \sigma = 5$

About what percent of students have scored less than 45 points?

This is the pvalue of Z when X = 45. So

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4 years ago

Find the sum of 14 + 8 + 2+ ... + ( 274) + (-280).

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The sum of the given sequence is -6384.

Step-by-step explanation:

The given Arithmetic sequence is 14 + 8 + 2+ ... + ( 274) + (-280).

The first term of the sequence = 14
The last term of the sequence = -280
The common difference ⇒ 14 - 8 = 6

To find the number of terms in the sequence :

The formula used is $n = (\frac{a_{n}-a_{1}} {d})+1$

where,

n is the number of terms.
$a_{n}$ is the late term which is -280.
$a_{1}$ is the first term which is 14.
d is the common difference which is 6.

Therefore, $n =(\frac{-280-14}{6}) +1$

⇒ $n =( \frac{-294}{6}) + 1$

⇒ $n = -49 + 1$

⇒ $n = -48$

⇒ n = 48, since n cannot be negative.

∴ The number of terms, n = 48.

To find the sum of the arithmetic progression :

The formula used is $S = \frac{n}{2}(a_{1} + a_{n} )$

where,

S is the sum of the sequence.
$a_{1}$ is the first term which is 14.
$a_{n}$ is the late term which is -280.

Therefore, $S = \frac{48}{2}(14+ (-280))$

⇒ $S = \frac{48}{2}(-266)$

⇒ $S = 48 \times -133$

⇒ $S = -6384$

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Answer:
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