In 1970 the United States produced 63.5 quadrillion BTU (British Thermal Units) of energy and consumed 67.86 quadrillion BTU. From 1970 through 2001, the total U.S. energy production increased by about 0.2813 quadrillion BTU per year, and the total U.S. energy consumption increased by about 0.912 quadrillion BTU per year. a. Write two equations that model the total U.S. energy production and consumption (in quadrillion BTU) as functions of the number of years since 1970. b. How much more energy was consumed than produced in the U.S. in 1970 and in 2001? What was the change in the amount of energy consumed from 1970 to 2001?

Find the indefinite integral (a) using integration tables and (b) using the given method. Integral: ∫ x²e^3x dx Method: Integration by parts

Write a possible explicit rule for the nth term of the sequence.

$$5,0.5,0.05,0.005 , \dots$$

Find the x- and y-intercepts. -3y+x=15

A thin-walled metal spherical shell of radius a has a charge $q_a$. Concentric with it is a thin-walled metal spherical shell of radius b$\uparrow$ a and charge $q_b$. Find the electric field at points a distance r from the common center, where $r < a$.

Each pair of points lies on a line with the given slope. Find x or y. (3, 5), (x, 2); undefined slope

Calculate. $\int{x(1+x)^{1/3}}dx$

Subtract. 35. 33 - (-28)

Sara has $36 in$1, $5, and$10 bills. She has the same number of $5 bills as$10 bills, and she has 10 bills in all. How many bills of each denominator does she have? a. 8 $1 bills, 1$5 bill, 1 $10 bill, b. 6$1 bills, 2 $5 bills, 2$10 bills, c. 4 $1 bills, 3$5 bills, 3 $10 bills, d. 2$1 bills, 4 $5 bills, 4$10 bills

Find the product.

$$5 x ^ { 2 } ( 3 x - 2 )$$

(a) Perform the indicated calculation by first converting each number to scientific notation. Write your answer in decimal notation. (b) Confirm the result found in part (a) by performing the calculation on a scientific calculator. 8,400,000/70,000

(a) identify the claim and state

$$H _ { 0 }$$

and

$$H _ { a }$$

, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic

$$\chi ^ { 2 }$$

, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the population is normally distributed. A school administrator claims that the standard deviation for eighth-grade students on a U.S. history assessment test is greater than 30 points. A random sample of 18 eighth-grade students has a standard deviation of 30.6 points. At

$$\alpha = 0.01$$

, is there enough evidence to support the administrator's claim?

Write a recursive rule for the exponential function $y = 25(0.2)^x$ .

Translate each sentence into an equation. Then solve the equation. A number decreased by 7 and then divided by 5 is 13.