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user100 [1]
3 years ago
7

Which of the following is a factor of 7x2 - 12x - 4? (6 points)

Mathematics
1 answer:
grin007 [14]3 years ago
4 0

Answer:

We conclude that 'None of the above' is the correct answer.                    

Step-by-step explanation:

Given the expression

7x^2\:-\:12x\:-\:4

Breaking the expression into groups

7x^2\:-\:12x\:-\:4=\left(7x^2+2x\right)+\left(-14x-4\right)

Factor out x from 7x^2\:+\:2x

=x\left(7x+2\right)

Factor out -2 from \left(-14x-4\right)

=-2\left(7x+2\right)

so the expression becomes

7x^2\:-\:12x\:-\:4=\left(7x^2+2x\right)+\left(-14x-4\right)

                         =x\left(7x+2\right)-2\left(7x+2\right)

Factor out the common term 7x+2

                         =\left(7x+2\right)\left(x-2\right)

Therefore, from the given options, we conclude that 'None of the above' is the correct answer.                    

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a) 37.31 b) 42.70 c) 0.57 d) 0.09

Step-by-step explaanation:

We are regarding a normal distribution with a mean of 35 and a standard deviation of 6, i.e., \mu = 35 and \sigma = 6. We know that the probability density function for a normal distribution with a mean of \mu and a standard deviation of \sigma is given by

f(x) = \frac{1}{\sqrt{2\pi}\sigma}\exp[-\frac{(x-\mu)^{2}}{2\sigma^{2}}]

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f(x) = \frac{1}{\sqrt{2\pi}6}\exp[-\frac{(x-35)^{2}}{2(6^{2})}]

Let X be the random variable that represents a row score, we find the values we are seeking in the following way

a)  we are looking for a number x_{0} such that

P(X\leq x_{0}) = \int\limits^{x_{0}}_{-\infty} {f(x)} \, dx = 0.65, this number is x_{0}=37.31

you can find this answer using the R statistical programming languange and the instruction qnorm(0.65, mean = 35, sd = 6)

b) we are looking for a number  x_{1} such that

P(X\leq x_{1}) = \int\limits^{x_{1}}_{-\infty} {f(x)} \, dx = 0.9, this number is x_{1}=42.70

you can find this answer using the R statistical programming languange and the instruction qnorm(0.9, mean = 35, sd = 6)

c) we find this probability as

P(28\leq X\leq 38)=\int\limits^{38}_{28} {f(x)} \, dx = 0.57

you can find this answer using the R statistical programming languange and the instruction pnorm(38, mean = 35, sd = 6) -pnorm(28, mean = 35, sd = 6)

d) we find this probability as

P(41\leq X\leq 44)=\int\limits^{44}_{41} {f(x)} \, dx = 0.09

you can find this answer using the R statistical programming languange and the instruction pnorm(44, mean = 35, sd = 6) -pnorm(41, mean = 35, sd = 6)

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