ALGEBRA
Choose the correct letter. Mrs. Decker walks for 30 minutes each day as often as possible. What is an equation that relates the number of days d that Mrs. Decker walks and the number of minutes m that she spends walking? A. m = 30d B. d = 30m C. d = m + 30 D. m = d + 30
PHYSICS
The largest living creature on Earth is the blue whale, which has an average length of 70 ft. The largest blue whale on record was $$ 1.10 \times 10 ^ { 2 } \mathrm { ft } $$ (a) Convert this length to meters. (b) If a double-decker London bus is 8.0 m long, how many double-decker-bus lengths is the record whale?
CALCULUS
Suppose that production of 1 unit of agriculture requires 1/3 unit of agriculture, 1/3 unit of manufacturing, and 1/3 unit of transportation. To produce 1 unit of manufacturing requires 1/2 unit of agriculture, 1/4 unit of manufacturing, and 1/4 unit of transportation. To produce 1 unit of transportation requires 0 units of agriculture, 1/4 unit of manufacturing, and 3/4 unit of transportation. Find the ratio of the three commodities in the closed model.
ALGEBRA2
Which translation takes y = |x| to y = |x + 3| - 1? A. 3 units right, 1 unit down B. 3 units right, 1 unit up C. 3 units left, 1 unit down D. 3 units left, 1 unit up
PRECALCULUS
For each function given below, find the initial value, specified factors and percent changes. a. $f(x)=2^{x / 3}$ i) Initial Value: ___ ii) 1-unit Growth Factor: ___ iii) 1-unit Percent Change: ___ iv) 4-unit Growth Factor: ___ v) 1/5-unit Growth Factor: ___. b. $f(x)=5 \cdot (0.98)^{x/4}$ i) Initial Value: ___ ii) 1-unit Decay Factor: ___ iii) 1-unit Percent Change: ___ iv) 3-unit Decay Factor: ___ v) 1/2-unit Decay Factor: ___. c. $f(x)=(0.25)^{2 x}$ i) Initial Value: ___ ii) 1-unit Decay Factor: ___ iii) 1-unit Percent Change: ___ iv) 5-unit Decay Factor: ___ v) 1/3-unit Decay Factor: ___. d. $f(x)=3 \cdot(1.6)^{3 x}$ i) Initial Value: ___ ii) 1-unit Growth Factor: ___ iii) 1-unit Percent Change: ___ iv) 3-unit Growth Factor: ___ v) 1/4-unil Growth Factor: ___.
HEALTH
Read the questions. Then, read the answer choices and choose the best possible answer for each. What type of sandwich classification is pizza? a. closed sandwich b. open-face sandwich c. triple-decker sandwich d. finger sandwich
CALCULUS
Suppose that production of unit of mining requires 1/5 unit of mining, 2/5 unit of manufacturing, and 2/5 unit of communication. To produce 1 unit of manufacturing requires 3/5 unit of mining, 1/5 unit of manufacturing, and 1/5 unit of communication. To produce 1 unit of communication requires 0 units of mining, 4/5 unit of manufacturing, and 1/5 unit of communication. Find the ratio of the three commodities in the closed model.
ALGEBRA2
Write an equation for each diagonal translation. y = 2x - 3, 1 unit down, 1 unit right
CALCULUS
An economy consists of three sectors: coal, steel, and railroads. To produce one unit of coal requires $\frac{1}{10}$ of a unit of coal, $\frac{1}{10}$ of a unit of steel, and $\frac{1}{10}$ of a unit of railroad services. To produce one unit of steel requires $\frac{1}{3}$ of a unit of coal, $\frac{1}{10}$ of a unit of steel, and $\frac{1}{10}$ of a unit of railroad services. To produce one unit of railroad services requires $\frac{1}{4}$ of a unit of coal, $\frac{1}{3}$ of a unit of steel, and $\frac{1}{10}$ of a unit of railroad services. Determine the production levels needed to satisfy an external demand for 300 units of coal, 200 units of steel, and 500 units of railroad services.
LINEAR ALGEBRA
Find the norm of v, a unit vector that has the same direction as v, and a unit vector that is oppositely directed to v. (a) v=(3, -5), (b) v=(3, 3, 1). (c) v=(0, 1, -1, 2, 6).
PRECALCULUS
Determine the growth or decay factor, percent change, and initial value for each of the following exponential functions. a. $f(x)=2^x$ Initial Value: ___ 1-unit Growth Factor: ___ 1-unit Percent Change: ___. b. $f(x) = (0.98)^x$ Initial Value: ___ 1-unit Decay Factor: ___ 1-unit Percent Change: ___. c. $f(x)=0.56 \cdot (0.25)^{x}$ Initial Value: ____ 1-unit Decay Factor:___ 1-unit Percent Change: ___. d. $f(x)=3 \cdot (1.6)^{x}$ Initial Value: ___ 1-unit Growth Factor: ___ 1-unit Percent Change: ___.
LINEAR ALGEBRA
Find the norm of v, a unit vector that has the same direction as v, and a unit vector that is oppositely directed to v. (a) v=(-5, 12). (b) v=(1, -1, 2). (c) v=(-2, 3, 3, -1).
PREALGEBRA
Graph a line that shows a 3-unit increase in y for every 1-unit increase in x. State the rate of change.
PREALGEBRA
Graph a line that shows a 3-unit increase in y for every 1-unit increase in x. State the rate of change.
CALCULUS
(a) find two unit vectors parallel to the given vector and (b) write the given vector as the product of its magnitude and a unit vector. From (1, 2, 3) to (3, 2, 1)
CALCULUS
Consider the following functions f, points P, and unit vectors u. Find the unit vector in the direction of maximum increase of f at P. $$ f ( x , y , z ) = \frac { x - z } { y - z } ; P ( 3,2 , - 1 ) ; \left\langle \frac { 1 } { 3 } , \frac { 2 } { 3 } , - \frac { 1 } { 3 } \right\rangle $$
CHEMISTRY
Circle the letter of each sentence that is true about units of volume. a. The SI unit for volume is derived from the meter, the SI unit for length. b. The liter (L) is a unit of volume. c. The liter is an SI unit. d. There are $$ 1000 \mathrm { cm } ^ { 3 } \text { in } 1 \mathrm { L } $$ , and there are also 1000 mL in 1 L, so $$ 1 \mathrm { cm } ^ { 3 } $$ is equal to 1 mL.
LINEAR ALGEBRA
Find the norm of v, and a unit vector that is oppositely directed to v. (b) v = (-2, 3, 3, -1)
ADVANCED MATH
A company assembles two products: A and B. Product A sells for $11 per unit, and product B sells for$23 per unit. A unit of product A requires 2 hours on assembly line 1 and 1 unit of raw material. A unit of product B requires 2 units of raw material, 1 unit of A, and 2 hours on line 2. For line 1, 1,300 hours of time are available and 500 hours of time are available on line 2. A unit of raw material may be bought (for $3 a unit) or produced (at no cost) by using 2 hours of time on line 1. Determine how to maximize profit.
CALCULUS
Consider points P(−1, 3), Q(1, 5), and R(−3, 7). Determine the requested vectors and express each of them a. in component form and b. by using the standard unit vectors. The unit vector in the direction of $\vec { P Q }$
CALCULUS
An economy depends on two commodities, goats and cheese. It takes 2/3 of a unit of goats to produce 1 unit of cheese and 1/2 unit of cheese to produce 1 unit of goats. (a) Write the input-output matrix for this economy. (b) Find the production required to satisfy a demand of 400 units of cheese and 800 units of goats.
CALCULUS
Find two unit vectors orthogonal to both (3 , 2, 1) and (- 1, 1, 0 ).
ALGEBRA2
Give the answer with the appropriate unit of measure. $-3 \frac{1}{3}$ miles $+1 \frac{2}{3}$ miles
QUESTION
Find a unit vector that is orthogonal to both u and v. u = ⟨4, -3, 1⟩ v = ⟨2, 5, 3⟩
ENGINEERING
Find a unit normal to the surface $x y^{2}-3 x z=-5$ at the point (1, −2, 3).