Last Question of the day!

1 answer:

7 0

$GEOMETRIC \: \: PROGRESSIONS \\ \\ \\\\Taking \: \: L.H.S. \: \\ \\ 0.999... \: = \: 0 \: + \: \frac{9}{10} \: + \: \frac{9}{100} \: + \: \frac{9}{1000} + \: ... \: \: \infty \\ \\ \\ 0.999... \: = \: \frac{9}{10} \: ( \: 1 \: + \frac{1}{10} \: + \: \frac{1}{100} \: + \: \frac{1}{1000} + \: ... \: \: \infty \: \: ) \\ \\ \\ 0.999... \: = \: \frac{9}{10} \: ( \: 1 + \: \: \frac{1}{ {10}^{1} } \: + \: \frac{1}{ {10}^{2} } \:+ \: \frac{1}{ {10}^{3} } \: + \: ... \: \: \infty \: ) \\ \\ \\ As \: we \: can \: see \: \: , \: \\ \\ Above \: expression \: in \: bracket \: forms \: a \: \\ Infinite \: Geometric \: Progression \\ \\ Where \: \: ,\: \: \: \: \\ a = 1 \: \: \: \: \: and \: \: \: \: \: r = \frac{1}{10} \\ \\ Sum \: of \: Infinite \: Geometric \: \\ Progression \: \: = \: \: \frac{a}{1 - r} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{1 - \frac{1}{10} } \: \: = \: \: \frac{1}{ \frac{9}{10} } \: \: = \: \: \frac{10}{9} \\ \\ \\ Putting \: in \: above \: , \: we \: get \: - \: \\ \\ 0.999... \: \: = \: \: \frac{9}{10} \times \frac{10}{9} \: \: \\ \\ \\ 0.999... \: \: = \: \: 1 \: \: = \: R.H.S. \\ \\ Hence , \: above \: expression \: is \: TRUE \: \: :)$

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A recipe calls for 1 ½ cups of flour, 2/3 cup of white sugar, and 1/3 cup of brown sugar. The recipe makes 6 servings. A) How ma

Goryan [66]

A) How many cups of flour are there per serving?

1 ½ cups of flour --------6 servings
? cups of flour ------- 1 serving

1 ½
------------
6

= 3/2 x 1/6
= 1/4

answer: 1/4 cups of flour per serving

B) how many total cups of sugar(white and brown) are there per serving?
total white and brown: 2/3 + 1/3 = 3/3 = 1 cups (combine)

1 cup of sugar (white and brown) --------6 servings
? cups of sugar (white and brown) ------ 1 serving

1
----- = 1/6
6
answer: 1/6 cups of sugar (white and brown) per serving

 (c) Suppose you modify the recipe so that it makes 9 servings. How much more flour do you need for the modified recipe than you need for the original recipe?

3/2 cups of flour --------6 servings
? cups of flour -----------9 servings

9 * 3/2
-----------
6

= (13 1/2) / 6
= 2 1/4

2 1/4 ( 9 servings) - 1 1/2(6 servings) = 3/4 cups

answer: you need 3/4 more cups of flour

6 0

3 years ago

Read 2 more answers

I need help ASAP! Raymonds grandfather is 50 years older than him. His grandfathers age was six times pf Raymond six years ago.

morpeh [17]

Answer:

he is fifty years old

Step-by-step explanation:

six years ago he would have been 44 yearsold

8 0

3 years ago

Which rules of exponents will be used to evaluate the expression. Check all that apply

julia-pushkina [17]

Hello!

The answer are:

- Product of powers.

- Power of a power.

- Negative exponents.

Let's solve it!

It's a math rule that we must solve first what's into a brake or parenthesis, so,

First: Product of powers $[(7)^{5}*(7)^{3}]$

According to the exponent's law, we have a product of powers case, so, we need to sum the exponents and keep the base

Exponents: 5 and 3

Base: 7

Applying it we have:

$(7)^{5+3}$

$(7)^{8}$

Then,

We have a power of a power case, which involves multiplying the exponents:

$[(7)^{5}*(7)^{3}]^{-4}$

Exponents: 3 and -4

Then,

$(7)^{8*-4}$

Finally, we can apply the negative exponents, the negative exponent's rules state that negative exponents are the reciprocal of the positive exponents,

So, we will have that:

$(7)^{-32}=\frac{1}{7^{32} }$