Find the measure of line segment TR

Mathematics

2 answers:

cestrela7 [59]2 years ago

7 0

Answer:

Step-by-step explanation:

trapecia [35]2 years ago

4 0

Answer:

TR = 24 units

Step-by-step explanation:

Given 2 secants from an external point to a circle, then

The product of the external part and the whole of one secant is equal to the product of the external part and whole of the other secant, that is

3x(3x + 5x) = 8(8 + 19)

3x × 8x = 8 × 27

24x² = 216 ( divide both sides by 24 )

x² = 9 ( take the square root of both sides )

x = ± $\sqrt{9}$ = ± 3

but x > 0, thus x = 3

Thus

TR = 8x = 8 × 3 = 24

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Komok [63]

Answer: Correct critical value = 2.2622

Step-by-step explanation:

Confidence interval for population mean when population standard deviation is unknown:

$\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}$ , where $\overline{x}$ = sample mean, n= sample size, s= sample standard deviation, $t_{\alpha/2}$ = two-tailed t value.

As per given: n= 10

degree of freedom : df = n-1=9

$\overline{x}=242.6\\\\s=73.33\\\\\alpha=5\%=0.05$

Critical t-value : $t_{\alpha/2,df}=t_{0.05/2,9}=t_{0.025,9}=2.2622$

So, the 95 percent confidence interval estimate for the mean :

$242.6\pm (2.2622)\dfrac{73.33}{\sqrt{10}}\\\\=242.6\pm (2.2622)(23.19)\\\\\approx242.6\pm52.46\\\\=(242.6-52.46,\ 242.6+52.46)\\\\=(190.14,\ 295.06)$