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Questions in mathematics

[Done] [tex]\frac{2}{9}+\frac{2}{6}=[/tex]

[Done] $\frac{5 x^7 y^5}{10 x y^3}$

[Done] Write three ratios that are equivalent to $14: 21$.

[Done] What is the approximate value of $x$ in the equation below? [tex]\log _5 15=x+3[/tex]

[Done] What is the exact value of $\cos \left(195^{\circ}\right) ?$ A. $\frac{\sqrt{6}-\sqrt{2}}{4}$ B. $\frac{\sqrt{6}+\sqrt{2}}{4}$ C. $\frac{-\sqrt{6}-\sqrt{2}}{4}$ D. $\frac{-\sqrt{6}+\sqrt{2}}{4}$

[Done] Consider the table showing the given, predicted, and residual values for a data set. \begin{tabular}{|c|c|c|c|} \hline$x$ & Given & Predicted & Residual \\ \hline 1 & -1.6 & -1.2 & -0.4 \\ \hline 2 & 2.2 & 1.5 & 0.7 \\ \hline 3 & 4.5 & 4.7 & -0.2 \\ \hline 4 & 6.1 & 6.7 & -0.6 \\ \hline \end{tabular} Which point would be on the residual plot of the data? A. $(1,-1.6)$ B. $(2,1.5)$ C. $(3,4.5)$ D. $(4,-0.6)

[Done] As shown above, a classic deck of cards is made up of 52 cards, 26 are black, 26 are red. Each color is split into two suits of 13 cards each (clubs and spades are black and hearts and diamonds are red). Each suit is split into 13 individual cards (Ace, 2-10, Jack, Queen, and King). If you select a card at random, what is the probability of getting: (Round to 4 decimal places where possible) a) A 9 of Hearts? [tex]\square[/tex] 0.0192 b) A Heart or Club? [tex]\square[/tex] 0.5000 c) A number smaller than 4 (counting the ace as a 1 )? [tex]\square[/tex] 0.02308

[Done] Example: A recovering heart attack patient is told to walk a certain distance each week. The patient walks 5 km the first week, 8 km the second week, 11 km the third week, and so on for 10 weeks. How many km did the patient walk on the 10th week?

[Done] 4. 3h² - 147 = 0 p√t = √x t = x

[Done] $g(x)=\frac{1}{5} x^2-2 x-1$