Find the indicated partial sum of the series. $\sum_{i=1}^{\infty} \frac{2}{3^{i}}$ Fifth partial sum

Solve the equation. Check your solution. 12x - 19 = 3x + 8

Explain imprinting in relation to Lorenz's geese. What would most likely have happened If the first thing the goslings saw was a dog?

Suppose $\tan \theta=\frac{4}{3}$ and $-\frac{\pi}{2} \leq \theta<\frac{\pi}{2}.$ Enter each answer as a decimal. Round your answer to the nearest tenth, if necessary. What is $\cot \theta+\cos \theta ?$

Find the sale price of the item. Round to two decimal places when necessary. Original price: $45.00; Markdown: 22%

A triangle has sides that measure $\sqrt{37}$, $\sqrt{44}$, and 9. Is the triangle a right triangle? A. Yes, B. No, C. Not enough information to tell.

How long must a pendulum be on the Moon, where g = 1.6 m/s², to have a period of 2.0 s?

A student simplifies the expression $\left( \frac { 6^4 } { 3 ^ { 2 } } \right) ^ { 3 }$ as follows: $\left[ ( 6 \div 3 ) ^ { 4 - 2 } \right] ^ { 3 } = \left( 2 ^ { 2 } \right) ^ { 3 } = 64.$ What mistake did the student make in simplifying the expression? What is the correct simplification?

The discharge of suspended solids from a phosphate mine is normally distributed with mean daily discharge 27 milligrams per liter (mg/L) and standard deviation 14 mg/L. In what proportion of the days will the daily discharge be less than 13 mg/L?

Using the formula for $\varphi(n)$ in terms of the factorization of $n$, as given in Eq. $\varphi(n)=2^{\nu-1} p_1^{s_1-1} \cdots p_t^{s_t-1}\left(p_1-1\right) \cdots\left(p_t-1\right)$, compute the value of $\varphi(60)$.

In an isosceles trapezoid ABCD, $\overline{B H}$ and $\overline{C G}$ are the heights from one base to another. Make a sketch. If AH=2 cm, what is the length of $\overline{G D}$?

What is the hybridization of the underlined nitrogen atom in each of the following molecules or ions? a. $\underline { N } O ^ { + },$ b. ${ N } _ { 2 } { O } _ { 3 } \left( O _ { 2 } {N} \underline {N} O \right),$ c. $\underline { N } { O } _ { 2 } ^ { - },$ d. $\underline { N } _ { 2 }.$

Test the sets of polynomials for linear independence. For those that are linearly dependent, express one of the polynomials as a linear combination of the others.

$$\left\{ 1 + x , 1 + x ^ { 2 } , 1 - x + x ^ { 2 } \right\} \text { in } \mathscr { P } _ { 2 }$$

In a recent poll, the Gallup Organjzation found that 45% of adult Americans believe that the overall state of moral values in the United States is poor. Suppose a survey of a random sample of 25 adult Americans is conducted in which they are asked to disclose their feelings on the overall state of moral values in the United States. (a) Find and interpret the probability that exactly 15 of those surveyed feel the state of morals is poor. (b) Find and interpret the probability that no more than 10 of those surveyed feel the state of morals is poor. (c) Find and interpret the probability that more than 16 of those surveyed feel the state of morals is poor. (d) Find and interpret the probability that 13 or 14 believe the state of morals is poor. (e) Would it be unusual to find 20 or more adult Americans who believe the overall state of moral values is poor in the United States? Why?