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2 years ago

Select the solutions to the following inequality:

Mathematics

1 answer:

Elena L [17]2 years ago

8 0

X+2> _ 5, x >_5-2, x>_3

-x-2>_5, x<_ -2-5, x<_-7

the last is the answer

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Find the sum of the convergent series 7 0.7 0.007

mafiozo [28]

$7+0.7+0.007+\cdots=7\left(1+\dfrac1{10}+\dfrac1{100}+\cdots\right)$

Let $S_n$ denote the $n$ th partial sum of the series, i.e.

$S_n=1+\dfrac1{10}+\dfrac1{100}+\cdots+\dfrac1{100^n}$

Then

$\dfrac1{10}S_n=\dfrac1{10}+\dfrac1{100}+\dfrac1{1000}+\dfrac1{10^{n+1}}$

and subtracting from $S_n$ we get

$S_n-\dfrac1{10}S_n=\dfrac9{10}S_n=1-\dfrac1{10^{n+1}}$
$\implies S_n=\dfrac{10}9\left(1-\dfrac1{10^{n+1}}\right)$

As $n\to\infty$ , the exponential term vanishes, leaving us with

$\displaystyle\lim_{n\to\infty}S_n=\dfrac{10}9$

and so

$7+0.7+0.007+\cdots=7.777\ldots=\dfrac{70}9$

3 0

2 years ago

A) Write 91 as the product of prime factors. Write the prime factors in ascending order.

amid [387]

Answer:

1 7 13 91 prime factors in ascending order

3 0

2 years ago

Read 2 more answers

Plsss helppp its worth 20 points

Mazyrski [523]

Answer:

a. sides BC & EF

b. <A & <D

2a. A / B, not that sure

8 0

1 year ago

A drama class has a total of

Alecsey [184]

42-14= 28
28÷2=14
answer: there are 14 females in the class and 28 males in the class

Check:14+28=42

5 0

3 years ago

Read 2 more answers

Una parte de 25 000 dólares se invierte al 10% de interés, otra parte al 12 % y el resto al 16%. El ingreso anual total de las t

Drupady [299]

Answer:

$5000 at 10%, $10000 at 12% and 10000 at 16%

Step-by-step explanation:

One part of $ 25,000 is invested at 10% interest, another part at 12%, and the rest at 16%. The total annual income from the three investments is $ 3,200. Also, the income from the investment at 16% is equal to the income from the other two investments combined. How much was invested at each interest rate?

==================

Let the parts be x, y and z

As per given we get below system of equations:

x + y + z = 25000
0.1x + 0.12y + 0.16z = 3200
0.1x + 0.2y = 0.16z

Substitute 0.1x + 0.2y in the second equation:

0.16z + 0.16z = 3200
0.32z = 3200
z = 3200/0.32
z = 10000

Now we have:

x + y + 10000 = 25000 ⇒ x + y = 15000

and

0.1x + 0.12y + 0.16*10000 = 3200 ⇒ 0.1x + 0.12y = 1600

Multiply the second equation and then subtract the first one:

10(0.1x + 0.12y) = 10(1600) ⇒ x + 1.2y = 16000
x + 1.2y - (x + y) = 16000 - 15000
0.2y = 1000
y = 10000

Then

x = 15000 - 10000 = 5000

So the parts are:

$5000 at 10%, $10000 at 12% and 10000 at 16%

4 0

2 years ago