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coldgirl [10]
3 years ago
11

Choose the correct simplification of the expression (8x − 5)(2x2 − 5x − 6). (1 point)

Mathematics
1 answer:
OleMash [197]3 years ago
6 0
The easiest terms to check are the first (8x)(2x²) = 16x³ and the last (-5)(-6) = 30. This check eliminates the first choice. The remaining choices differ only in the sign and coefficient of the squared term, so that is the one we need to find.

The squared term will be the sum of the products of factors whose degrees total 2:
  (8x)(-5x) + (-5)(2x²) = -40x² -10x² = -50x²

The appropriate choice is
  16x³ -50x² -23x +30
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A proportion is an equation that states two _____ are equal.
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The U.S. population in 1910 was 92 million people. In 1990, the population was 280 million. This could either be a linear or exp
HACTEHA [7]

Answer:

The linear model means that there is a uniform increase and in this case of US population from  92  million people in  1910  to  250  million people in  1990 .  

This means an increase of  250 − 92 = 158  million in  1990 -1910 = 80  years or   158 80 = 1.975  million per year and in  x  years it will become   92 + 1.975 x  million people. This can be graphed using the linear function  1.975 ( x − 1910 ) + 92 ,

graph{1.975(x-1910)+92 [1890, 2000, 85, 260]}

The exponential model means that there is a uniform proportional increase i.e. say  p %  every year and in this case of US population from  92  million people in  1910  to  250  million people in  1990 .  

This means an increase of  250 − 92 = 158  million in  1990 − 1910 = 80  years or  

p %  given by  92 ( 1 + p ) 80 = 250  which gives us  ( 1 +p ) 80 = 250 92  which simplifies to  p = ( 250 92 ) 0.0125 − 1 = 0.0125743  or  1.25743 % .  

This can be graphed as an exponential function  92 × 1.0125743 ( x − 1910 ) , which gives population in a year  y  and this appears as graph{92(1.0125743^(x-1910)) [1900, 2000, 85, 260]}

Step-by-step explanation:

Hope this helps

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Step-by-step explanation:

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A boiler has five identical relief valves. The probability that any particular valve will open on demand is 0.95. Assuming indep
Gre4nikov [31]

Answer:

a) There is a 99.99997% probability that at least one valve opens.

b) There is a 22.62% probability that at least one valve fails to open.

Step-by-step explanation:

For each valve, there are only two possible outcomes. Either it open, or it does not. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem we have that:

p = 0.95, n = 5

(a) What is the probability that at least one valve opens?

Either no valves open, or at least one opens. The sum of the probabilities of these events is decimal 1. So

P(X = 0) + P(X \geq 1) = 1

We want P(X \geq 1)

So

P(X \geq 1) = 1 - P(X = 0)

P(X = 0) = C_{5,0}.(0.95)^{0}.(0.05)^{5} = 0.0000003

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0000003 = 0.9999997

There is a 99.99997% probability that at least one valve opens.

(b) What is the probability that at least one valve fails to open?

Either all valves open, or at least one does not open. The sum of the probabilities of these events is decimal 1. So

P(X = 5) + P(X \leq 4) = 1

We want P(X \leq 4)

So

P(X \leq 4) = 1 - P(X = 5)

P(X = 5) = C_{5,5}.(0.95)^{5}.(0.05)^{0} = 0.7738

P(X \leq 4) = 1 - P(X = 5) = 1 - 0.7738 = 0.2262

There is a 22.62% probability that at least one valve fails to open.

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