Write each number as a power of the given base. 1000; base 10

Determine the simple interest. Unless noted otherwise, assume the rate is an annual rate. Assume 360 days in a year. Round answers to the nearest cent. p=$550.31, r=8.9%, t=67 days

A survey indicated that chocolate is America's favorite ice cream flavor. Which of the following will lead to a decrease in the price of chocolate ice cream? A. A drought in the Midwest causes farmers to reduce the number of dairy cows they raise. B. A new report from the American Medical Association concludes that chocolate has significant health benefits. C. The price of vanilla ice cream increases. D. New freezer technology lowers the cost of producing ice cream. E. The price of ice cream toppings decreases.

In Yoshi’s garden,

$$\frac{3}{4}$$

of the flowers are tulips. Of the tulips,

$$\frac{2}{3}$$

are yellow. What fraction of the flowers in Yoshi’s garden are yellow tulips?

Find the solution of each system of equations. y = -4x² + x + 1, y = -7x + 1

Prove that for any $2\times2$ matrices A and B, $\text{det}AB=(\text{det}A)(\text{det}B)$.

Find the first four terms of the binomial series for the function.

$$( 1 + x ) ^ { 1 / 3 }$$

Graph the function. Label the axis of symmetry and the vertex. f(x) = 2x² + 2x + 1

Find all the real solutions of the equation.

$$x ^ { 3 } - 2 x ^ { 2 } - 5 x + 6 = 0$$

Solve the system using any elimination method. 6x-4y=14, 2x+8y=21

Find the function f(x) and all values of c such that

$$∫_c^x f(t) dt = x² + x -2$$

.

How long does it take a child on a swing to complete one swing if her center of gravity is 4.00 m below the pivot?

This problem may involve addition, subtraction, and multiplication of radical expressions, as well as rationalizing the denominator. Perform the operations and simplify, if possible. All variables represent positive real numbers.

$$\sqrt [ 5 ] { \frac { 2 } { 243 } }$$

State whether the given equation defines an elliptic paraboloid, a hyperbolic paraboloid, or an elliptic cone.

$$z = \left( \frac { x } { 4 } \right) ^ { 2 } + \left( \frac { y } { 3 } \right) ^ { 2 }$$