math

The value of a tractor decreases over time and is given by V(t) = 75,000 − 7,500t, where V(t) is the value in dollars of the tractor after t years. Find the value (in dollars) of the tractor after 6 years.

$30,000

The value in dollars of a $3,000 investment after n years is given by f(n) = 3,000(1.05)n. Find the value of the investment (in dollars) after 6 years. (Round your answer to the nearest cent.)

$4020.29

Give a counterexample to the given statement. The product of two positive numbers is greater than either of the two numbers. Enter two numbers that serve as a counterexample to the statement. (Enter your answers as a comma-separated list.)

3,1

The area of a square is a function of the measure, s, of a side of the square and given by f(s) = s2. Find the area (in square centimeters) of a square whose sides measure 11 centimeters.

121 sq cm

Use inductive reasoning to predict the next number in the given sequence. 4, 9, −1, 4, −6, −1, −11, −6, −16, ?

-11

Time (seconds) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Distance (inches) 10.0 17.9 20.0 17.9 10.0 2.1 0.0 2.1 10.0 17.9 20.0 17.9 10.0 2.1 Using inductive reasoning, what distance (in in.) will the block be from the wall after 14 seconds?

0 in.

Evaluate the function to answer the question. The height h, in feet, of a ball that is released 6 ft above the ground with an initial upward velocity of 70 ft/s is a function of the time t, in seconds, the ball is in the air and is given by the following. h(t) = −16t2 + 70t + 6, 0 ≤ t ≤ 4.45 Find the height of the ball (in feet) above the ground 4 s after it is released.

30

Evaluate the function to answer the question. The height h, in feet, of a ball that is released 6 ft above the ground with an initial upward velocity of 70 ft/s is a function of the time t, in seconds, the ball is in the air and is given by the following. h(t) = −16t2 + 70t + 6, 0 ≤ t ≤ 4.45 Find the height of the ball (in feet) above the ground 2 s after it is released.

82

Give a counterexample to the given statement. A figure with four equal sides is a square. A diamond shape can have four equal sides and is not a square. A pentagon can have four equal sides and is not a square. A triangle can have four equal sides and is not a square. A circle can have four equal sides and is not a square. A trapezoid can have four equal sides and is not a square.

A diamond shape can have four equal sides and is not a square

Depth (meters) 0 5 10 15 20 25 30 35 40 Temperature (°C) 25 23 20 18 17 15 14 13 10 Which of the following general premises can be assumed to be true? As the ocean gets deeper the water gets colder. The water is the same temperature at all ocean depths. As the ocean gets deeper the water gets warmer. Use deductive reasoning to determine whether the temperature will be more than or less than 10°C when the depth is 45 meters. less than 10°C more than 10°C

As the ocean gets deeper the water gets colder. less than 10°C

Consider the following sequence. 4/7, 7/10, 10/13, 13/16, 16/19, ? Inspect the sequence and complete the following statement.

The denominator of the first number is 3 more than the numerator of the first number. The numerator of the second number is equal to the denominator of the first number . The denominator of the second number is 3 more than the numerator of the second number. Use inductive reasoning to predict the missing number in the sequence. 19/22

Consider the following sequence. 1, 4, 9, 16, 25, 36, 49, ? Inspect the sequence and complete the following statement.

The first two numbers differ by 3 . The second and third numbers differ by 5 . The third and fourth numbers differ by 7 . The difference between any two successive numbers always seems to be 2 more than the preceding difference. Use inductive reasoning to predict the missing number in the sequence. 64

Give a counterexample to the given statement. All mammals have legs. Whales are mammals and do not have legs. Snakes are mammals and do not have legs. Sharks are mammals and do not have legs. Chickens are mammals and do not have legs. Bears are mammals and do not have legs.

Whales are mammals and do not have legs.

The speed, s, of sound is a function of temperature, T, of the air. Name the independent and dependent variables.

independent variable-T dependent variables-s

The speed, s, of an object released from a point above ground when it impacts the ground is a function of the height, h, from which it falls. Name the independent and dependent variables.

independent variable-h dependent variable-s

The speed, s, of an object released from a point above ground when it impacts the ground is a function of the height, h, from which it falls. The name of this function is Sp; write an equation for the function. h = s(Sp) Sp = h(s) h = Sp(s) s = h(Sp) s = Sp(h)

s = Sp(h)

The speed, s, of sound is a function of temperature, T, of the air. The name of this function is v; write an equation for the function. T = s(v) s = v(T) T = v(s) s = T(v) v = T(s)

s = v(T)

The Changs, Steinbergs, Ontkeans, and Gonzaleses were winners in the All-State Cooking Contest. There was a winner in each of four categories: soup, entrée, salad, and dessert. From the following clues, determine which category each family won. The soups were judged before the Ontkeans' winning entry. This year's contest was the first for the Steinbergs and for the winner in the dessert category. The Changs and the winner of the soup category entered last year's contest. The winning entrée took 2 hours to cook, whereas the Steinbergs' entrée required no cooking at all.

soup-Gonzales's entrée=Chang's salad=Steinberg's dessert=Ontkean''s

Each of four siblings (Anita, Tony, Maria, and Jose) is given $5,000 to invest in the stock market. Each chooses a different stock. One chooses a utility stock, another an automotive stock, another a technology stock, and the other an oil stock. From the following clues, determine which sibling bought which stock. Anita and the owner of the utility stock purchased their shares through an online brokerage, whereas Tony and the owner of the automotive stock did not. The gain in value of Maria's stock is twice the gain in value of the automotive stock. The technology stock is traded on NASDAQ, whereas the stock that Tony bought is traded on the New York Stock Exchange.

utility stock-Maria automotive stock-Jose technology stock-Anita oil stock-Tony