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2 years ago

Which values of m and b will create a system of equations with no solution? Select two options.

Mathematics

1 answer:

Roman55 [17]2 years ago

6 0

Answer:

2nd and 5th options

Step-by-step explanation:

the solution to a system of equations is at the point of intersection of the 2 lines.

If the lines are parallel then they never intersect and will have no solution.

The slopes m of parallel lines are equal.

The options with equal slopes , both - 2 are the

2nd and 5th options

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Negative 5 1 half plus 7 3 over 4

erastovalidia [21]

Answer:

$2 \dfrac{1}{4}$

Step-by-step explanation:

$-5 \dfrac{1}{2} + 7 \dfrac{3}{4} =$

$= -5 \dfrac{2}{4} + 7 \dfrac{3}{4}$

$= 7 \dfrac{3}{4} - 5 \dfrac{2}{4}$

$= 2 \dfrac{1}{4}$

8 0

2 years ago

Researchers are interested if a school breakfast program leads to taller children. Assume that the population of all 5 year-old

DedPeter [7]

Answer:

$39-1.96\frac{1}{\sqrt{25}}=38.608$

$39+1.96\frac{1}{\sqrt{25}}=39.392$

So on this case the 95% confidence interval would be given by (38.608;39.392)

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".

$\bar X=39$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=1$ represent the population standard deviation

n=25 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The margin of error is given by:

$ME= z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$