If P(x 3), Q(7, -1) and PQ= 5 units, find the possible value of x.

Mathematics

1 answer:

Neporo4naja [7]2 years ago

5 0

Given :

P(x 3), Q(7, -1) and PQ= 5 .

To Find :

The possible value of x.

Solution :

We know, distance between two points in coordinate plane is given by :

$PQ = \sqrt{(x-7)^2 + ( 3-(-1))^2}\\\\PQ^2 = (x-7)^2 + ( 3-(-1))^2\\\\(x-7)^2 + 4^2 = 5^2\\\\( x- 7)^2 = 3^2 \\\\x - 7 = \pm 3\\\\x = 10 \ and \ x = 4$

Therefore, the possible value of x are 10 and 4.

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How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winner

Liula [17]

Answer:

The 95% confidence interval would be given by (14444.04;33657.30)

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".

Data: $26,650 $6,060 $52,820 $8,490 $13,660$25,840 $49,840 $23,790 $51,480 $18,960$990 $11,450 $41,810 $21,060 $7,860

We can calculate the mean and the deviation from these data with the following formulas:

$\bar X= \frac{\sum_{i=1}^n x_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}$

$\bar X=24050.67$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=17386.13 represent the sample standard deviation

n=15 represent the sample size

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

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

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=15-1=14$

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: "=-T.INV(0.025,14)".And we see that $t_{\alpha/2}=2.14$