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Ireland
(Sugt Questions (a) Expiress in its simplest form: 6x−23+2x+75 ◻ b) Divide 2x3−9x2−10x+25 by (x−5). 2x3−9x2−10x+25(x−5)
Algebra Mar 30, 2025
Derive a formula for the number of right angles in an n-sided polygon. pel
Geometry Mar 30, 2025
9. Write down the centre and radius length of the circle x2+y2−6x−2y−15=0. If the line 3x+4y+c=0 is a tangent to this circle, find the two values of c. 10. For what values of k is the line 2x−ky−3=0 a tangent to the circle
Geometry Mar 30, 2025
10. Use simultaneous equations to verify that the lines 2x+3y=12 and 3x−4y=1 intersect at the point (3,2). 11. In the diagram, the lines AB and CD are perpendicular to each other and intersect at the point (1,4). The line AB crosses the x-axis at (3,0). Calculate the coordinates of the points P and Q.
Algebra Mar 28, 2025
Use simultaneous equations to find the point of intersection of the following pairs of lines: 4. x+y=52x−y=1 5. x−y=22x+y=7 6. 2x+5y=1x−3y=−5 7. 2x−3y=4 8. 3x−2y=17 9. 2x+3y=−8 4x+3y=0 x+3y=132x+5y=21
Algebra Mar 28, 2025
10. Use simultaneous equations to verify that the lines 2x+3y=12 and 3x−4y=1 intersect at the point (3;2)
Algebra Mar 27, 2025
6. The line x−2y−1=0 intersects the circle x2+y2+2x−8y−8=0 at the points L and M. (i) Find the coordinates of L and M . (ii) Find the midpoint of [LM]. (iii) Find the equation of the circle with [LM] as diameter.
Geometry Mar 27, 2025
\begin{tabular}{l} A study was set up to examine the association between brain volume and \\ schizophrenia. Investigators measured the grey matter volume \( \left(\mathrm{cm}^{3}\right) \) in 40 \\ healthy and 40 schizophrenic subjects. A two-sided, two-sample t-test for \\ equality of means yielded a p-value of 0.024 , and the \( 95 \% \) confidence \\ interval of the difference in population mean grey matter volumes was \\ found to be \( \left(4.413 \mathrm{~cm}^{3}, 58.859 \mathrm{~cm}^{3}\right) \). \\ It is known that a difference of at least \( 70 \mathrm{~cm}^{3} \) in grey matter volume is \\ clinically important; the difference between the two means: \\ \hline is not clinically important \\ \hline is clinical importance cannot be determined based on the information available. \\ \hline may be clinically important \end{tabular}
Statistics Mar 27, 2025
\begin{tabular}{l} A study was set up to examine the association between brain volume and \\ schizophrenia. Investigators measured the grey matter volume \( \left(\mathrm{cm}^{3}\right) \) in 40 \\ healthy and 40 schizophrenic subjects. The results of an analysis are \\ summarised as follows: \\ - a mean grey matter volume of \( 715.7040 \mathrm{~cm}^{3} \) was measured for the \\ sample of healthy subjects; \\ - a mean grey matter volume of \( 684.0680 \mathrm{~cm}^{3} \) was measured for the \\ sample of schizophrenic subjects; \\ - testing for equality of variances yielded a p-value \( <0.001 \); \\ - applying two-sample t-test for equality of means under the hypothesis \\ of equal population variances yielded a p-value of 0.022 ; \\ - applying two-sample \( t \)-test for equality of means under the hypothesis \\ of unequal population variances yielded a p-value of 0.024 . \\ Based on this analysis, the difference in population variances is: \\ O Not statistically significant \\ O Statistically significant \\ Unknown \\ \hline Cannot be determined \end{tabular}
Statistics Mar 27, 2025
\begin{tabular}{l} A study was set up to examine the association between brain volume and \\ schizophrenia. Investigators measured the grey matter volume \( \left(\mathrm{cm}^{3}\right) \) in 40 \\ healthy and 40 schizophrenic subjects. The results of an analysis are \\ summarised as follows: \\ - a mean grey matter volume of \( 715.7040 \mathrm{~cm}^{3} \) was measured for the \\ sample of healthy subjects; \\ - a mean grey matter volume of \( 684.0680 \mathrm{~cm}^{3} \) was measured for the \\ sample of schizophrenic subjects; \\ - testing for equality of variances yielded a p-value <0.001; \\ - applying the appropriate two-sample \( t \)-test for equality of means \\ yielded a p-value of 0.022 ; \\ - applying two-sample \( t \)-test for equality of means under the hypothesis \\ of unequal population variances yielded a p-value of 0.024 . \\ Based on this analysis, the p-value for the appropriate test of population \\ means is: \\ \hline \( 0<0.001 \) \\ \hline 0.022 \\ \hline 0.046 \\ 0.024\end{tabular}
Statistics Mar 27, 2025
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