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3 years ago

I need help evaluating

Mathematics

1 answer:

Alika [10]3 years ago

7 0

I’m guessing 27 4? I’m not sure

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Can somebody prove this mathmatical induction?

Flauer [41]

Answer:

See explanation

Step-by-step explanation:

1 step:

n=1, then

$\sum \limits_{j=1}^1 2^j=2^1=2\\ \\2(2^1-1)=2(2-1)=2\cdot 1=2$

So, for j=1 this statement is true

2 step:

Assume that for n=k the following statement is true

$\sum \limits_{j=1}^k2^j=2(2^k-1)$

3 step:

Check for n=k+1 whether the statement

$\sum \limits_{j=1}^{k+1}2^j=2(2^{k+1}-1)$

is true.

Start with the left side:

$\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}\ \ (\ast)$

According to the 2nd step,

$\sum \limits_{j=1}^k2^j=2(2^k-1)$

Substitute it into the $\ast$

$\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}=2(2^k-1)+2^{k+1}=2^{k+1}-2+2^{k+1}=2\cdot 2^{k+1}-2=2^{k+2}-2=2(2^{k+1}-1)$

So, you have proved the initial statement

4 0

3 years ago

the area of a rectangle city park is 25/54 sqaure miles. the length of the park is 5/9 mile. what is the width in miles of the p

andreyandreev [35.5K]

A = lw

Plug in what we know:

25/54 = (5/9)w

Divide 5/9 to both sides or multiply by its reciprocal, 9/5:

25/54 * 9/5 = w

Multiply the numerators and denominators together:

225/270 = w

Simplify:

<span>w = 5/6</span>

6 0

3 years ago

Gene ran 90 meters in 16.3 seconds. alma ran 90 meters in 17.2 seconds. who had the fastest time

maria [59]

Answer:

Gene ran faster

Step-by-step explanation:

The fastest time is the smallest time since they ran the same distance

gene ran 90 meters in 16.3 seconds.

alma ran 90 meters in 17.2 seconds

16.3 < 17.2

Gene ran faster

7 0

1 year ago

Question is in picture.

Norma-Jean [14]

Answer:

Step-by-step explanation:

Having the system of equations in its simplest form

$\left\{\begin{array}{ccc}ax+by=c\\dx+ey=f\end{array}\right$

$a=d,\ b=e,\ c=f$

then the system of equations has infinitely many solutions.

$a=d,\ b=e,\ c\neq f$

then the system of equations has no solution.

$a\neq d\ or\ b\neq e$

then the system of equations has one solution.

We have the equation

$y=-2x+4$

Convert to the standard form Ax + By = C<em>:</em>

<em /> $y=-2x+4$ <em> add 2x to both sides</em>

$y+2x=-2x+2x+4\\\\2x+y=4$

3 0

3 years ago

A contractor finds that 3 gallons of paint will cover 375 sq ft of wall area. How much wall area could be covered with 18 gallon

ss7ja [257]

It will cover 2050 square feet

8 0

3 years ago