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wariber [46]
3 years ago
9

Erin says the first step is to set Latex: 2x+7

Mathematics
1 answer:
garik1379 [7]3 years ago
6 0

Answer:

3=47x86= and 4838x7694

Step-by-step explanation:

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Find the sum of the positive integers less than 200 which are not multiples of 4 and 7​
taurus [48]

Answer:

12942 is the sum of positive integers between 1 (inclusive) and 199 (inclusive) that are not multiples of 4 and not multiples 7.

Step-by-step explanation:

For an arithmetic series with:

  • a_1 as the first term,
  • a_n as the last term, and
  • d as the common difference,

there would be \displaystyle \left(\frac{a_n - a_1}{d} + 1\right) terms, where as the sum would be \displaystyle \frac{1}{2}\, \displaystyle \underbrace{\left(\frac{a_n - a_1}{d} + 1\right)}_\text{number of terms}\, (a_1 + a_n).

Positive integers between 1 (inclusive) and 199 (inclusive) include:

1,\, 2,\, \dots,\, 199.

The common difference of this arithmetic series is 1. There would be (199 - 1) + 1 = 199 terms. The sum of these integers would thus be:

\begin{aligned}\frac{1}{2}\times ((199 - 1) + 1) \times (1 + 199) = 19900 \end{aligned}.

Similarly, positive integers between 1 (inclusive) and 199 (inclusive) that are multiples of 4 include:

4,\, 8,\, \dots,\, 196.

The common difference of this arithmetic series is 4. There would be (196 - 4) / 4 + 1 = 49 terms. The sum of these integers would thus be:

\begin{aligned}\frac{1}{2}\times 49 \times (4 + 196) = 4900 \end{aligned}

Positive integers between 1 (inclusive) and 199 (inclusive) that are multiples of 7 include:

7,\, 14,\, \dots,\, 196.

The common difference of this arithmetic series is 7. There would be (196 - 7) / 7 + 1 = 28 terms. The sum of these integers would thus be:

\begin{aligned}\frac{1}{2}\times 28 \times (7 + 196) = 2842 \end{aligned}

Positive integers between 1 (inclusive) and 199 (inclusive) that are multiples of 28 (integers that are both multiples of 4 and multiples of 7) include:

28,\, 56,\, \dots,\, 196.

The common difference of this arithmetic series is 28. There would be (196 - 28) / 28 + 1 = 7 terms. The sum of these integers would thus be:

\begin{aligned}\frac{1}{2}\times 7 \times (28 + 196) = 784 \end{aligned}.

The requested sum will be equal to:

  • the sum of all integers from 1 to 199,
  • minus the sum of all integer multiples of 4 between 1\! and 199\!, and the sum integer multiples of 7 between 1 and 199,
  • plus the sum of all integer multiples of 28 between 1 and 199- these numbers were subtracted twice in the previous step and should be added back to the sum once.

That is:

19900 - 4900 - 2842 + 784 = 12942.

8 0
3 years ago
At a rental car company, a customers daily rental charge D (in dollars) for m miles driven is determined by the function D = 35
lianna [129]

Answer:

See below

Step-by-step explanation:

<u>Given function:</u>

  • D = 35 + 0.4m

m represents the domain and D represents the range of the function, therefore m = x, D = y

<u>Filling in the table:</u>

  • for x = 10, y = 35 + 0.4*10 = 35 + 4 = 39 and so on for the rest of the values
  • x = 10, 30, 50, 75, 100
  • y = 39, 47, 55, 65, 75
3 0
3 years ago
Please help<br><br>p/5 = 3.1; p=​
aalyn [17]
P=15.5 would be the answer
3 0
3 years ago
Read 2 more answers
Which of these describes an angle?
stealth61 [152]
A part of a line that connects two endpoints I believe
7 0
3 years ago
Tim needs 3 pounds of vegetables for a vegetable soup recipe.
klio [65]

Answer:

25/12 - pounds more vegetables

Step-by-step explanation:

first we need to put these variables into like terms

36/12 - 3

8/12 - 2/3

3/12 - 1/4

add the last two up and subtract from the first and you get how much you need left over

8 0
3 years ago
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