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2 years ago

When would a power raised to an exponent of zero equal 1? How about -1?

1 answer:

4 0

Any number with an exponent of 0 would equal 1 no matter the number is negative or positive.If i didn't answer your question just comment back.

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How old are the property

cricket20 [7]

You didn't enter a valid question.

7 0

2 years ago

A) Find a recurrence relation for the number of bit strings of length n that contain a pair of consecutive 0s.

Fed [463]

Answer:

A) $a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}$

B) $a_{0} = a_{1} = 0$

C) for n = 2

$a_{2}$ = 1

for n = 3

$a_{3}$ = 3

for n = 4

$a_{4}$ = 8

for n = 5

$a_{5}$ = 19

Step-by-step explanation:

A) A recurrence relation for the number of bit strings of length n that contain a pair of consecutive Os can be represented below

if a string (n ) ends with 00 for n-2 positions there are a pair of consecutive Os therefore there will be : $2^{n-2}$ strings

therefore for n ≥ 2

The recurrence relation for the number of bit strings of length 'n' that contains consecutive Os

$a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}$

b ) The initial conditions

The initial conditions are : $a_{0} = a_{1} = 0$

C) The number of bit strings of length seven containing two consecutive 0s

here we apply the re occurrence relation and the initial conditions

$a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}$

for n = 2

$a_{2}$ = 1

for n = 3

$a_{3}$ = 3

for n = 4

$a_{4}$ = 8

for n = 5

$a_{5}$ = 19

7 0

3 years ago

Robert went to the grocery store and purchased cans of soup and frozen dinners. each can of soup has 300 mg of sodium and each f

Paraphin [41]

There are 9 cans of soup and 5 cans of frozen dinner.

The variables used for soup and frozen dinner are x and y respectively.

Step-by-step explanation:

Let,

Soup = x

Frozen Dinner = y

According to given statement of sodium;

300x + 500y = 5200 eqn 1

And,

x + y = 14 eqn 2

$Multiplying\ equation\ 2\ with\ 300\\300(x+y=14)\\300x+300y=4200\ Eqn 3\\$

Subtracting Eqn 3 from Eqn 1;

$(300x+500y)-(300x+300y)=5200-4200\\300x+500y-300x-300y=1000\\200y=1000\\y=\frac{1000}{200} \\y=5$

Putting value of y in Eqn 1;

$300x+500(5)=5200\\300x+2500=5200\\\\Subtracting\ 2500\ from\ both\ sides\ \\300x+2500-2500=5200-2500\\300x=2700\\x=\frac{2700}{300} \\x=9$

There are 9 cans of soup and 5 cans of frozen dinner.

The variables used for soup and frozen dinner are x and y respectively.

Keywords: Variables, linear equations, subtraction.

Learn more about linear equations at;

#LearnwithBrainly

5 0

2 years ago

The area of a rectangle with 2 1/2 as the width and 10 feet as the length

Tanya [424]

The formula for the area of a rectangle is:
$A=wl$
w = width
l = length

First, we have to convert 2 $\frac{1}{2}$ into an improper fraction, then into a number. The improper fraction would be $\frac{5}{2}$ . Let's convert that into a decimal.
$5/2=2.5$

Let's multiply
$2.5*10=25$
The area of the rectangle would be 25 feet!

7 0

2 years ago

Can you explain how to do this?

ivanzaharov [21]

Hi there! The answer is x = 1

Let's solve this problem step by step!
$8(10) {}^{2x} = 800$

First divide both sides of the equation by 8.
$10 {}^{2x} = 100$

Now rewrite 100 as a power of 10.
$10 {}^{2x} = 10 {}^{2}$

Now we can use the following rule, which basically means that two different exponents of the same base must be the same
${g}^{a} = {g}^{b} \\ a = b$

We now get this.
$2x = 2$

Finally divide both sides by 2.
$x = 1$

~ Hope this helps you!

3 0

3 years ago