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kirill115 [55]
3 years ago
15

5. Determine the sum of 2+4+6+8+...+250. (Hint: 2(1+2+3+4) = 2+4+6+8)

Mathematics
1 answer:
sergiy2304 [10]3 years ago
7 0

Answer:

The sum of 2+4+6+8+...+250 will be: 22650

Step-by-step explanation:

Given

2+4+6+8+...+250

2(1+2+3+4+...+150)....[A]

Considering the sequence

1+2+3+4+...+150

Lets calculate the sum of first 150 terms

\mathrm{Compute\:the\:differences\:of\:all\:the\:adjacent\:terms}:\quad \:d=a_{n+1}-a_n

2-1=1,\:\quad \:3-2=1

\mathrm{The\:difference\:between\:all\:of\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}

d=1

So the sequence is Arithmetic.

as

a_1=1

and

d=1

\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}

a_n=a_1+\left(n-1\right)d

a_n=\left(n-1\right)+1

a_n=n

\mathrm{Arithmetic\:sequence\:sum\:formula:}

n\left(a_1+\frac{d\left(n-1\right)}{2}\right)

\mathrm{Plug\:in\:the\:values:}

n=150,\:\spacea_1=1,\:\spaced=1

=150\left(1+\frac{1\cdot \left(150-1\right)}{2}\right)

=150\left(\frac{149}{2}+1\right)

=150\cdot \frac{151}{2}

\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}

=\frac{151\cdot \:150}{2}

=\frac{22650}{2}

=11325

So the sum of first 150 terms of the arithmetic

sequence 1+2+3+4+...+150 is: 11325

Now, according to expression [A], multiply 11325 by 2 to determine the sum of 2+4+6+8+...+250.

As

1+2+3+4+...+150 = 11325

Thus

2(1+2+3+4+...+150) = 2(11325) = 22650

Therefore, the sum of 2+4+6+8+...+250 will be: 22650

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Seventy-eigth hundred-thousandths​
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The decimal number for seventy eight hundred-thousandths is 5.

<h3>What is decimal number?</h3>

A decimal is a number that consists of a whole and a fractional part

The decimal numeral system is the standard system for denoting integer and non-integer numbers.

What is the decimal number for seventy eight hundred-thousandths?

= 78 x 10⁻⁵

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8 0
1 year ago
Determine if the expression -8c-9c^4d^2−8c−9c
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Answer:

-8c-9c^4d^2-8c-9c is a polynomial of type binomial and has a degree 6.

Step-by-step explanation:

Given the polynomial expression

-8c-9c^4d^2-8c-9c

Group like terms

=-9c^4d^2-8c-8c-9c

Add similar elements: -8c-8c-9c=-25c

=-9c^4d^2-25c

Thus, the polynomial is in two variables and contains two, unlike terms. Therefore, it is a 'binomial' with two, unlike terms.

Each term has a degree equal to the sum of the exponents on the variables.

The degree of the polynomial is the greatest of those.

25c has a degree 1

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Thus,

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4 0
3 years ago
A 2-pound bag of sugar contains 227 one-teaspoon servings and costs $2.49. A batch of muffins uses 1 2 cup of sugar. How many wh
ZanzabumX [31]

Answer:

a) 9 whole batches can be made

b) The cost of sugar for each batch = $0.26

Step-by-step explanation:

A 2-pound bag of sugar contains 227 one-teaspoon servings and costs $2.49.

This means:

2 pound bag of sugar = 227 teaspoon servings

2 pounds bag of sugar cost $2.49

We are told that:

A batch of muffins uses 1/2 cup of sugar.

a).How many whole batches can you make if you use as much of the sugar as possible?

(1 cup = 48 teaspoons)

Hence, A batch of muffins = 1/2 cups of sugar = 48 teaspoons of sugar ÷ 2

= 24 teaspoons of sugar

Hence:

24 teaspoons of sugar = 1 batch of muffins

227 teaspoons of sugar = x

Cross Multiply

24 × x = 1 × 227

x = 227/24

x = 9.4583333333 batches of muffins

We are asked to name the number of whole batches that can be made.

Therefore, 9 whole batches of muffins can be made

b) What is the cost of sugar for each batch? (do not consider leftover sugar in the cost calculation.) You can make a total of batches at $ per batch.

Since we are not to consider the leftover sugar in the cost calculation,

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The left over = 227 - 216 = 11 teaspoons of sugar is left

We know that:

227 teaspoons of sugar = $2.49

216 teaspoons of sugar = x

Cross Multiply

= 216 × $2.49/227

= $2.369339207

24 teaspoons of sugar = 1 batch of muffins

Therefore,

216 teaspoons of sugar =

$2.369339207

24 teaspoons of sugar =

24 × $2.369339207/ 216

= $0.2632599119

Approximately = $0.26

Therefore, the cost of sugar for each batch = $0.26

8 0
3 years ago
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irinina [24]
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