Correct Answer: B. 41.5

Correct Answer: B. 41

Explanation

Arranging the scores in ascending order, we have: 2, 5, 12, 17, 21, 29, 33, 41, 43, 45.

The upper quartile = 41.

Correct Answer: D. \(\frac{y^2}{x}\)

Explanation

\(\frac{x}{x+y}=\frac{y}{x+CE}\\

xy + xCE = xy + y^2\\

?xCE = y^2\\

CE=\frac{y^2}{x}\)

Correct Answer: ?D. ?120\(\sqrt{2}\)

Explanation

\(60^2 + x^2 + x^2\)

\(360^2 = 2x^2\)

\(x^2\) = 1800

x = \(\sqrt{1800}\)

x = 42.4264

x = 42.4264

perimeter = 4x

= 4 x 42.4264

= 169.7056

= 120\(\sqrt{2}\)

= 120\(\sqrt{2}\)

Correct Answer: C. p ⇒ q

Explanation

The symbolic form for the statement "If Siah is from Foya, then Foya is in Lofa" is:

p ⇒ q

This is read as "p implies q". It means that if p is true, then q must also be true.

In other words, if Siah is from Foya, then Foya must be in Lofa.

Correct Answer: B. \(8\sqrt{3}\)

Explanation

\((1 + 2\sqrt{3})^{2} = 1 + 4\sqrt{3} + 12 = 13 + 4\sqrt{3}\)

\((1 - 2\sqrt{3})^{2} = 1 - 4\sqrt{3} + 12 = 13 - 4\sqrt{3}\)

\(13 + 4\sqrt{3} - (13 - 4\sqrt{3}) = 13 + 4\sqrt{3} - 13 + 4\sqrt{3}\)

= \(8\sqrt{3}\)

Correct Answer: D. 31

Explanation

When finding the median, you are looking for the middle number. Always arrange the numbers in ascending order. Since, the numbers are not in order, lets arrange them. The new set is 4,15,26,36,79,100. Then, we count the numbers in the set. There are six. Then divide six by two. We do this because we will split the number set in half. Because six does divide evenly into two, this means we can't easily determine the median. Since six divided by two is three, we are going to eliminate three numbers from leftmost in number set toward the right direction and three numbers from rightmost in number set toward the left direction. The last number crossed out in both direction are 26 and 36. To find the middle number, just add both numbers and divide by two. 26+36/2=62/2=31 That's the final answer.

Explanation

(a) From the pyramid, construct \(\Delta BFG\) by drawing a line from B to F.

\(|BF|^{2} = 4^{2} + 3^{2}\)

\(|BF| = 25 \implies |BF| = 5m\)

In calculating the height,

\(h^{2} = 5^{2} - (\frac{5}{2})^{2}\)

\(h^{2} = \frac{75}{4}\)

\(h = \sqrt{75}{4}\)

= \(4.33 m\)

Volume of a pyramid = \(\frac{1}{3} \times 4 \times 3 \times 4.33\)

= \(17.32 m^{3}\)

Volume of a cuboid = \(l \times b \times h\)

= \(3 \times 4 \times 2\)

= \(24 m^{3}\)

Total volume of the shape = \(17.32 + 24\)

= \(41.32 m^{3}\)

(b) \(5 - (x - 2) = d\)

\((x + 2) - 5 = d\)

\(\therefore (x + 2) - 5 = 5 - (x - 2)\)

\(x - 3 = 7 - x\)

\(2x = 10\)

\(x = 5\)

Correct Answer: C. 7

Explanation

2x + y = 7 = i

3x - 2y = 3 = ii

i x 2 + ii = 4x + 2y = 14

\(\frac {3x - 2y = 3}{7x = 17}\)

x = \(\frac {17}{7}\) = 7x = 17 x 1/7 x 7

17 - 10 = 7

Correct Answer: B. 1/2