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3 years ago

Please factor and find the zeros of each relation (18 marks)

Mathematics

1 answer:

AlekseyPX3 years ago

3 0

Answer:

$C. \ \frac{-2}{3} , \ \frac{-4}{5}\\\\D. \ -2, \ -4$

Step-by-step explanation:

$30x^2 + 44x +16 = 0\\\\2(15x^2 + 22 + 8) = 0\\\\2(15x^2 + 12x + 10x + 8) = 0\\\\2(3x(5x + 4)+2(5x + 4))=0\\\\2((3x + 2)(5x + 4)) = 0\\\\Zeroes : 3x + 2 = 0 => x = \frac{-2}{3}\\$

$5x+ 4 = 0 => x = \frac{-4}{5}$

$10x^2 + 60x +80 = 0\\\\10(x^2 + 6x + 8)= 0\\\\10(x^2 + 4x + 2x + 8)=0\\\\10(x(x+4)+2(x+4))=0\\\\10((x+2)(x+4))=0\\\\Zeroes : x + 2 = 0 =>x = -2$

$x + 4 = 0 => x= -4$

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A random sample of size n1= 25, taken from a normal population with a standard deviation σ1= 5, has a mean X1= 80. A second rand

sesenic [268]

Answer:

The 94% confidence interval would be given by $2.898 \leq \mu_1 -\mu_2 \leq 7.102$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X_1 =80$ represent the sample mean 1

$\bar X_2 =75$ represent the sample mean 2

n1=25 represent the sample 1 size

n2=36 represent the sample 2 size

$\sigma_1 =5$ sample standard deviation for sample 1

$\sigma_2 =3$ sample standard deviation for sample 2

$\mu_1 -\mu_2$ parameter of interest.

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2}\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =80-75=5$

Since the Confidence is 0.94 or 94%, the value of $\alpha=0.06$ and $\alpha/2 =0.03$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.03,0,1)".And we see that $z_{\alpha/2}=1.88$