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MariettaO [177]
3 years ago
9

What is the area of this face? A.150in2 B.100in2 C.400in2 D.200in2

Mathematics
1 answer:
77julia77 [94]3 years ago
8 0

Answer:

it's

200 {in}^{2}

Step-by-step explanation:

10 \times 10 =  \:  \:  \:  \:  \: 100 \\ 10 \times 10 =  + 100 \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:= 200 {in}^{2}

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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

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4 years ago
SELECT ALL: The point (0, 10) is a solution to the following system of inequalities. Given that information, what could be the s
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A college football coach has decided to recruit only the heaviest 15% of high school football players. He knows that high school
Alla [95]

Answer:

The coach should start recruiting players with weight 269.55 pounds or more.                                                    

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 225 pounds

Standard Deviation, σ = 43 pounds

We are given that the distribution of weights is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

We have to find the value of x such that the probability is 0.15

P( X > x) = P( z > \displaystyle\frac{x - 225}{43})=0.15  

= 1 -P( z \leq \displaystyle\frac{x - 225}{43})=0.15  

=P( z \leq \displaystyle\frac{x - 225}{43})=0.85  

Calculation the value from standard normal z table, we have,  

P(z < 1.036) = 0.85

\displaystyle\frac{x - 225}{43} = 1.036\\\\x = 269.548 \approx 269.55

Thus, the coach should start recruiting players with weight 269.55 pounds or more.

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