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2 years ago

Find the first three terms of the arithmetic series described. a_1=1,a_n=19,S_n=100

Mathematics

1 answer:

Rudik [331]2 years ago

3 0

Answer:

1, 3, 5

Step-by-step explanation:

The sum of an arithmetic series is:

S_n = n (a_1 + a_n) / 2

100 = n (1 + 19) / 2

n = 10

The nth term of an arithmetic sequence is:

a_n = a_1 + d (n − 1)

19 = 1 + d (10 − 1)

d = 2

The common difference is 2. So the first three terms are 1, 3, and 5.

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Write the equation of the line that is parallel to the line y=-7/4x-2 through the point (4,2)! Help please

Sladkaya [172]

as you already know, the equation y=-7/4x-2, is already in slope-intercept form and thus its slope is the coefficient of the "x", namely -7/4.

parallel lines have the same exact slope, so a parallel line to this one will also have a slope of -7/4, and it passes through 4,2,

$\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad \qquad \qquad slope = m\implies -\cfrac{7}{4} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-2=-\cfrac{7}{4}(x-4) \\\\\\ y-2=-\cfrac{7}{4}x+7\implies y=-\cfrac{7}{4}x+9$

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2 years ago

The minimum distance from Earth to the Sun is 91.4 million miles. The maximum distance is 94.5 million miles write a absolute va

d1i1m1o1n [39]

Solution :

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The maximum distance is 94.5 million miles

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$d=\frac{d_{min} + d_{max}}{2}$

$d=\frac{91.4 + 94.5}{2}$

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$d_{sol}=\frac{94.5 - 91.4}{2}$

$d_{sol} =1.55$

Absolute Value Equation:

|x - d| = $d_{sol}$

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2 years ago

70434 ÷ 78 how do this with long division

rosijanka [135]

The answer is 903!!!!!!

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2 years ago

Read 2 more answers

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SVETLANKA909090 [29]

Answer: The two answers are 1.08T and (1 + $\frac{8}{100}$ )T.

Step-by-step explanation:

Try multiplying 1.08 times any random number. If you use 5, 1.08 times 5 gives you 5.4. This makes sense. Solve the other other expression as well and substitute T with the SAME number that you used before (5). Hope that helps!

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2 years ago

An observational study found that the amount of sleep an employee gets each night is associated with job performance. The correl

Elina [12.6K]

Answer:

The correct option is D.) Causation cannot be determined from an observational study.

Step-by-step explanation:

The conclusion is not correct because

D.) Causation cannot be determined from an observational study.

Causation determined from an observational study is speculative and cannot be confirmed without data from a real experiment.

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2 years ago