Write the vector formulation for the given system of differential equations.

$$x _ { 1 } ^ { \prime } = e ^ { 2 t } x _ { 2 } , x _ { 2 } ^ { \prime } + ( \sin t ) x _ { 1 } = 1.$$

Use any strategy to solve the problem. A certain number is multiplied by 3, and then 5 is added to the result. The final answer is 41. What is the number?

Find the distance between the points algebraically and confirm graphically by using centimeter graph paper and a centimeter ruler. $(−4.2, 3.1), (−12.5, 4.8)$

Convert each temperature as indicated. When appropriate, give your answer to the nearest tenth of a degree. -10°F=_°C

Evaluate the definite integral.

$$\int _ { - 2 } ^ { - 2 / \sqrt { 3 } } \frac { d x } { | x | \sqrt { x ^ { 2 } - 1 } }$$

Write a function g whose graph represents the indicated transformation of the graph of f. Use a graphing calculator to check your answer. f(x) = -x + 1; reflection in the y-axis.

3x-9 is greater than or equal to -3

Round to the nearest hundredth.

$$\frac { 16 } { d } = \frac { 25 } { 40 }$$

Suppose that the time to failure T of a certain hinge is an exponential random variable with probability density $f(t)=\theta e^{-\theta t}, \quad t>0$ From prior experience we are led to believe that $\theta$ is a value of an exponential random variable with probability density $\pi(\theta)=2 e^{-2 \theta}, \quad \theta>0$ If we have a sample of n observations on T, show that the posterior distribution of $\Theta$ is a gamma distribution with parameters $\alpha=n+1 \quad \text { and } \quad \beta=\left(\sum_{i=1}^{n} t_{i}+2\right)^{-1}.$

Solve. Check your answer.

$$\frac { 6 } { n } = \frac { 7 } { n ^ { 2 } } - 1$$

Find the probability. Write your answer in simplest form. Picking a diamond from a standard deck of playing cards which has 13 cards in each of four suits: spades, hearts, diamonds and clubs.

Responde a las siguientes preguntas con oraciones completas.

1. ¿Cuál es el origne del nombre Colombia?
2. ¿Cuál es el clima en Venezuela y Colombia?
3. ¿En qué año fue la primera producción comercial de café en Colombia?

Explain the difference between an experiment that utilizes a completely randomized design and one that utilizes a randomized block design.

Find the value of each expression.

$$5 ^ { 2 } + 8 \div 2 =$$