Question 5 ( 30 marks) A card is drawn at random from a pack of 52 cards and is then replaced. Let \( A \) denote the event 'an ace is drawn,' and let \( R \) denote the event 'a red card is drawn.' Calculate the values of \( P(A), P(R), P(A \) \( n \mathrm{R}) \) and \( P(A \) u R). If this experiment is performed 4 times, find the probability i. That an ace will be drawn for the first time at the third attempt. ii. That a red card will be drawn exactly twice. iii. That a red card will be drawn at least once. Find also how many times the experiment must be performed to ensure that the probability of a red card being drawn at least once exceeds 0.99 .

A builder is building a new drive. She needs 710 bricks. On Monday she lays 150 bricks. On Tuesday she lays 300 more bricks than she laid on Monday. How many bricks are left to lay after Tuesday?

\( \frac{-5 k}{5}: \frac{35 k-7}{7 k}=\square \) первое окошко введи знак. Если число положительное, введи знак «+,

2. Escribir cada expresión en términos de coseno. \( \begin{array}{ll}\text { a. } \sec \theta+\tan \theta & \text { f. } 5 \cos \theta+3 \csc \theta+\tan \theta \\ \text { b. } \cot \theta+\frac{1}{\sec \theta} & \text { g. } \frac{2 \operatorname{sen} \theta \sec \theta}{\tan \theta} \\ \text { c. } \frac{\tan ^{2} \theta}{5 \sec \theta} & \text { h. } \frac{\operatorname{sen} \theta \cdot \cot \theta}{5} \\ \text { d. } 3 \csc ^{2} \theta+\frac{1}{5 \sec \theta} & \text { i. } 5 \operatorname{sen}^{2} \theta+\frac{\tan ^{2} \theta}{3} \\ \text { e. } \tan ^{2} \theta+\frac{3 \cot \theta}{\operatorname{sen} \theta} & \text { j. }(1+\operatorname{sen} \theta)^{2}-\frac{2 \operatorname{sen} \theta}{3}\end{array} \)

The art teacher would be 0.75 ti than their actua

Q. 5) Construct the following triangle. A) Construct \( \triangle \mathrm{AVP} \) in which base \( \mathrm{VP}=5.2 \mathrm{~cm} \), \( \mathrm{m} \angle \mathrm{V}=50^{\circ} \) and \( \mathrm{AV}+\mathrm{AP}=9 \mathrm{~cm} \). (3 Marks)