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Questions in mathematics

[Done] Assume you are working with a standard deck of 52 cards. There are 13 cards [tex]$(2,3,4,5,6,7,8,9,10$[/tex], jack, queen, king, and ace) in each of four suits (clubs, diamonds, hearts, and spades). What is [tex]$P$[/tex](Jack [tex]$\cap$[/tex] Heart) if you draw one card? A. 0 B. [tex]$\frac{17}{52}$[/tex] C. [tex]$\frac{4}{13}$[/tex] D. [tex]$\frac{1}{52}$[/tex]

[Done] Select the correct answer. Given the following formula, with $A=27$ and $t=3$, solve for $r$. $A=P(1+r t)$ A. $r=\frac{27-1}{3 P}$ B. $r=\frac{27-P}{3}$ C. $r=\frac{26}{3}$ D. $r=\frac{27-P}{3 P}$

[Done] By using the Pythagorean Theorem for right triangles, find the length in centimetres. Triangle: B | 5 | 13 | \ C---A Options: A. 8 B. 12 C. 18 D. 65

[Done] 18. Write the largest 5-digit number with all digits different and ending in 1. 19. Round off the following number to the nearest tens. b. 286875

[Done] 1. Dan has 20x pesos and his sister gave him 5x more. How much money does Dan have now? 2. A rectangular garden has a length of 7a meters, and another garden has a length of 2a meters. What is the total length of both gardens? 3. A vendor sold 6y mangoes in the morning and 4y in the afternoon. How many mangoes did he sell in all?

[Done] e) 33.50 + 5.66 + 66.14 + 33.66 f) 67.101 - 67

[Done] A parabola, with its vertex at the origin, has a directrix at $y=3$. Which statements about the parabola are true? Select two options. A. The focus is located at $(0,-3)$. B. The parabola opens to the left. C. The $p$ value can be determined by computing 4(3). D. The parabola can be represented by the equation $x^2=-12 y$. E. The parabola can be represented by the equation $y^2=12 x$.

[Done] {(16 \div 2)-6} \times 12

[Done] Simplify the expression below. $\left(x^6\right)\left(x^2\right)$ A. $x^4$ B. $x^6$ C. $x^8$ D. $x^{12}$

[Done] Solve the radical equation. Check for extraneous solutions. $a=\sqrt{7 a-6}$ $a=\sqrt{7 a-6}^2$ Step 1: Square to get rid of the square root. $-7 a-7 a$ Step 2: Subtract $7 a$ from both sides. $\begin{aligned} \frac{-6 a}{-6} & =\frac{-6}{-6} \\ a & =1 \end{aligned}$ Step 3: Divide by -6 . The above problem was solved INCORRECTLY. Describe the mistake that was made in this problem. A. Forgot to square the a in step 1. B. Should have added 7a instead of subtracting in step 2. C. Should have added 6 instead of dividing in step 3