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GuDViN [60]
3 years ago
11

Which of the equations are true identities? \begin{aligned} \text{A. }&(y+6)(y-7)+42=y^2-y \\\\ \text{B. }&(x+3)(x-8)=x^

2-5x \end{aligned} A. B. ​ (y+6)(y−7)+42=y 2 −y (x+3)(x−8)=x 2 −5x ​
Mathematics
2 answers:
BaLLatris [955]3 years ago
8 0

Answer:

its only A

Step-by-step explanation:

got it from khan academy

musickatia [10]3 years ago
5 0

Answer:

Only A, the first equation is true.

Step-by-step explanation:

A. (y + 6)(y – 7) + 42 = y² + 6y –7y – 42 + 42 = y² – y. This means A is true

B. (x + 3)(X – 8) = x² + 3x – 8x – 24 = x² – 5x – 24. This means B is false.

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How can one variable equations have more than one solution in some cases and no solutions in others?
yawa3891 [41]

Answer:A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).

Step-by-step explanation:

7 0
3 years ago
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3. What is wrong with the following statement? If d/e = f, then d multiplied by f = e.f should be divided by e.F and e should be
Molodets [167]

the initial statement is:

\frac{d}{e}=f

and then:

d\cdot f=e

So the second statement is false because f should be multiply by e, not by d so is option C)

4 0
1 year ago
An automobile manufacturer finds that 1 in every 2500 automobiles produced has a particular manufacturing defect. ​(a) Use a bin
Advocard [28]

Answer:

a) 0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.

b) 0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.

Step-by-step explanation:

Binomial 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.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given interval.

To use the Poisson approximation for the binomial, we have that:

\mu = np

1 in every 2500 automobiles produced has a particular manufacturing defect.

This means that p = \frac{1}{2500} = 0.0004

a) Use a binomial distribution to find the probability of finding 4 cars with the defect in a random sample of 7000 cars.

This is P(X = 4) when n = 7000. So

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

P(X = 4) = C_{7000,4}.(0.0004)^{4}.(0.9996)^{6996} = 0.1558

0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.

(b) The Poisson distribution can be used to approximate the binomial distribution for large values of n and small values of p.

Using the approximation:

\mu = np = 7000*0.0004 = 2.8. So

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 4) = \frac{e^{-2.8}*(2.8)^{4}}{(4)!} = 0.1557

0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.

6 0
3 years ago
How many degrees in a full rotation?
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Answer:

Step-by-step explanation:

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