Numerade

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70 percent of the students passed the math exam, and 60 percent of the students passed the science exam. What’s the minimum percentage of students that passed both math cans?

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2) Complete the total synthesis below by writing the correct sequence of reactions and products that it takes to get to the target molecule. You do not have to show electron pushing. multiple steps OH OH SH

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6) Let $K_4 = \{1, (1,2)(3,4), (1,3)(2,4), (1,4)(2,3)\} \subset A_4$. Show that $K_4 \triangleleft A_4$. Write elements of $A_4/K_4$. This $K_4$ is called the Klein 4 group and remember $A_4$ is the alternating group (subgroup of even permutations in $S_4$).

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We now have to find the equilibrium price, $p^*$, by substituting $q^* = 8$ back into one of the equations. Let's use $p = 7 + q^2$. So $p^* = $

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is the percentage of an additional dollar of income that is paid in tax. marginal tax rate average tax rate fairness tax rate regressive tax rate

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21. The cross-price elasticity of demand between gasoline and car tires is estimated to equal -4. Suppose the price of gas decreased by 10% this year. What is the resulting percentage change in the quantity demanded of tires? a. 40% decrease b.40% increase c. 2.5% increase d. 2.5% decrease e. None of the above

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What term describes the phenomenon where individuals with substance use disorders continue to use a substance despite negative consequences? a. Tolerance b. Dependence c. Addiction d. Sensitization

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3. Subspaces Consider the subspaces $U$, $V$ of $\mathbb{R}^3$: $U = \left\{ \begin{pmatrix} x \\ y \\ z \end{pmatrix} \in \mathbb{R}^3 \mid x + 3y - 2z = 0 \right\}$, $V = \text{Span}\left\{ \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix}, \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}, \begin{pmatrix} 2 \\ 1 \\ 1 \end{pmatrix} \right\}$ (a) Give bases for $U$ and $V$. (b) Give a basis for the subspace sum $U + V$. (c) Give a basis for the intersection $U \cap V$.

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In a football match, the tickets for children and adults were sold at D 3.00 and D 5.00 respectively. If 400 people attended the football match and D 1,700 was collected in ticket sales, the following questions arise: (a) How many tickets were sold for adults? (b) Mr. Sonko sold D 250 tickets. If 175 of the tickets were sold for adults, how much sale did he make altogether?

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Given that $f(x) = \begin{cases} 4x + 11, & \text{if } x < -2\\ 3, & \text{if } -2 \le x \le 1\\ -\frac{1}{2}x + \frac{7}{2}, & \text{if } x > 1 \end{cases}$ \\ Calculate $f(3)$ and $f(-3)$?\\ $f(-3) = -1$ and $f(3) = 2$\\ $f(-3) = 2$, and $f(3) = -1$\\ $f(-3) = -2$ and $f(3) = 1$\\ $f(-3) = 1$, and $f(3) = -2$

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cathy a.