Math Questions

Uma uses 5 gallons of red paint for every 2 pints of green paint. What is the rate of gallons of red paint to 1 gallon of green paint? 20 gallons of red paint/1 gallon of green paint 10 gallons of red paint/1 gallon of green paint 8 gallons of red paint/1 gallon of green paint 5 gallons of red paint/1 gallon of green paint

Consider the line y=-4/3x-8. Find the equation of the line that is parallel to this line and passes through the point (8, 6). Find the equation of the line that is perpendicular to this line and passes through the point (8, 6). Note that the ALEKS graphing calculator may be helpful in checking your answer, Equation of parallel line: Equation of perpendicular line:

Given this function: f(x)=35+arcsin(x/11) an equation for the line tangent to the graph of y = f(x) at the point where x=11/2 is:

A vector w has initial point (5,-2) and terminal point (-1, -3). Write w in component form. W =

The volume of a cylinder is 20 cubic inches. If the radius of the bases of the cylinders is tripled, what will the new volume be? (How is the radius of a cylinder related to the volume of a cylinder?)

Solve the quadratic equation by completing the square x² +6x+4=0. To complete the square, what number should be added to both sides of the equation?

Solve the quadratic equation by completing the square. x² - 10x+12=0 First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas. Form: Solution:

The cost, y, of a frult drink is proportional to x, the number of fruit drinks. The constant of proportionality Is 3.25. Which will check that y is proportional to x? Graph y = 3.25 x and check that the graph is a straight line that goes through (1, 3.25). Graph y = 3.25 x and check that the graph is a straight line that goes through (0, 0). Graph x = 3.25 y and check that the graph is a straight line that goes through (0,0). Graph y = 3.25 x and check that the graph is a straight line that goes through (0, 1).

Deshaun wants to buy a bond that will mature to $4500 in eight years. How much should he pay for the bond now if it earns interest at a rate of 2.5% per year, compounded continuously?

Find the exact value of cos(u + v) given that sin u =4/5 with u in quadrant II, and sin v=12/13 with v in the quadrant II. (Simplify your answer. Type an integer or a simplified fraction.) cos (u + v) =

The vertex form of the equation of a horizontal parabola is given by z= 1/4p(y-k)2+h, where (h, k) is the vertex of the parabola and the absolute value of p is the distance from the vertex to the focus, which is also the distance from the vertex to the directrix. You will use GeoGebr to create a horizontal parabola and write the vertex form of its equation. Open GeoGebra , and complete each step below. Part A Mark the focus of the parabola you are going to create at R(-5, 2). Draw a vertical line that is 8 units to the right of the focus. This line will be the directrix of your parabola. What is the equation of the line?

Fill in the blank. To solve x² +6x=5 by completing the square, add___to both sides of the equation. To solve x² + 6x = 5 by completing the square, add to both sides of the equation.

There are 6 grams of fat per serving in granola. Each serving provides 180 calories. There are 9 calories of fat in each gram. The percentage of calories from fat in granola is a. 20% b. 30% c. 54% d. 67%

Joanne owns a brick home with a full value of $97,000. The coverage rate for her homeowners insurance is 0.325%. The cost of Joanne's homeowners insurance is a. $298.46 b. $315.25 c. $325.00 d. $3,152.50

The population of California is approximately 38,040,000. The population of Texas is about 2.606 x 107. What is the approximate total population of these two states? 40.646 * 107 40.646 × 106 6.410 × 107 6.410 × 1014

A guy wire to the top of a tower makes an angle of 66° with the level ground. At a point 30 feet farther from the base of the tower and in line with the base of the wire, the angle of elevation to the top of the tower is 29°. What is the length of the guy wire? 24.17 ft 15.92 ft 56.53 ft 45.54 ft

Find the probability that when a couple has 2 children, they will have exactly 1 boy. Assume that boys and girls are equally likely and that the gender of any child is not influenced by the gender of another child.

Substitute the given values into the given formula and solve for the unknown variable. If necessary, round to one decimal place. S = 4LW + 2WH; S = 170, L= 7, W=5. (Surface area of a special rectangular box)

A vector w has initial point (0, 0) and terminal point (-3,-2). Write w in the form w=ai+bj.

Find the direction angle of the vector u = -7i+4j. That is, find the angle between 0° and 360° that u makes with the positive x-axis (measured counterclockwise), when u is in standard position.

The velocity of an object is the distance it travels per unit time. Suppose the cm velocity of a gliding bird is measured to be 197cm/s Calculate the time it will take S the bird to travel 3.7 m.

A box has twelve balls in it, seven white and five red. We select one ball, do not put it back in the box, and select a second ball, etc. We are not returning any balls to the box. So we are selecting multiple balls from the box. Find the probability of the following events (each scenario below is separate and is not dependent upon another): a. The probability of selecting a white ball on the first draw and selecting a white ball on the second draw. b. The probability of selecting a white ball on the first draw and selecting a red ball on the second draw. c. The probability of selecting a red ball on the first draw, selecting a white ball on the second draw and selecting a white ball on the third draw. 30 916 tedt ginays to sing sediazab bna 91691) 81 d. The probability of selecting a red ball on the first draw, selecting a red ball on the second draw, selecting a white ball on the third draw and selecting a white ball on the fourth draw.

Graph the solution of the following system. y ≥ 4x-3 y<5/6x

Which equation has the same solution as x² 13x + 3 = -7? (x+6.5)² = −52.25 (x − 6.5)² = 32.25 (x+6.5)² = 32.25 (x − 6.5)² = -52.25

A chemistry student needs 20.0 g of tetrahydrofuran for an experiment. By consulting the CRC Handbook of Chemistry and Physics, the student discovers that the density of tetrahydrofuran is 0.889 g cm-3 Calculate the volume of tetrahydrofuran the student should pour out. Be sure your answer has the correct number of significant digits.

Super fine 40-gauge copper wire has a diameter of only 0.080 mm and weighs only 44.5 g/km. Suppose a spool of 40-gauge wire weighs 245. g less after some wire is pulled off to wind a magnet. How could you calculate how much wire was used? Set the math up. But don't do any of it. Just leave your answer as a math expression. Also, be sure your answer includes all the correct unit symbols. length of wire =

Suppose that f(x) is a continuous function with f(1) = -6 and f(5)= 6. Determine which choice best describes the following statement. "f(3) = 0 Always true Sometimes true and sometimes false Always false

Find the average rate of change of g (x)=2x² +8 from x=2 to x = 4.

Consider the line y=-8x+7. Find the equation of the line that is parallel to this line and passes through the point (-6, -2). Find the equation of the line that is perpendicular to this line and passes through the point (-6, -2). Note that the ALEKS graphing calculator may be helpful in checking your answer.

A biologist has a 691-gram sample of a radioactive substance. Find the mass of the sample after two hours if it decreases according to a continuous exponential decay model, at a relative rate of 14% per hour.

Fill in the blank. To complete the square of x²-8x, add To complete the square of x²-8x, add (Type an integer or a simplified fraction.)

P (n), given below, is the price P in dollars for n grams of vitamins. P(n)=0.8n+5.2 Complete the following statements. Let P-¹ be the inverse function of P. Take x to be an output of the function P. That is, x= P (n) and n = P-¹(x). (a) Which statement best describes P-¹(x)? The amount of vitamins (in grams) for a price of x dollars. The price (in dollars) for x grams of vitamins. The ratio of the price (in dollars) to the number of grams, x. The reciprocal of the price (in dollars) for x grams of vitamins. (b) p-¹(x) = (c) P-¹(10.4) =

If using the method of completing the square to solve the quadratic equation x² + 8x + 37 = 0, which number would have to be added to "complete the square"?

Suppose that the functions & and t are defined for all real numbers x as follows. s(x)=4x-3 t(x)=x-2

Use the Factor Theorem to determine whether x-3 is a factor of P(x) = -x4+x3+5x²-4. Specifically, evaluate P at the proper value, and then determine whether x-3 is a factor.

Use the ALEKS graphing calculator to find the vertex and x-intercept(s) for the quadratic function. f(x)=-3.38x²-5.2x-2

A vector u has initial point (5, 4) and terminal point (4, -2). Write u in the form u = ai + bj.

Find the unit vector in the direction of (15, 8).

Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits. minimum = 8, maximum = 78, 6 classes The class width is. Choose the correct lower class limits below. A. 8, 19, 32, 43, 55, 68 B. 8, 20, 32, 44, 56, 68 C. 19, 31, 44, 55, 67, 79 D. 20, 31, 44, 56, 68, 79 Choose the correct upper class limits below. A. 20, 32, 44, 56, 68, 79 B. 19, 31, 44, 56, 67, 79 C. 19, 31, 43, 55, 67, 79 D. 20, 32, 43, 55, 68, 79

How long will it take for a $4000 investment to grow to $7148 at an annual rate of 9.4%, compounded quarterly? Assume that no withdrawals are made.

13. Diego wants to purchase a used car that sells for $6,399. The dealer has offered him $299 on his trade-in car. The total cost of the car Diego wants to buy will be a. $4,543 b. $6,100 c. $6,399 d. $6,698

Given vectors a = (4, -5) and b=(3, 6), find 5a-3b.

Identify and graph the polar equation. r=7-7 sin θ What shape does the polar equation form when graphed? A. Limacon without an inner loop. C. Limacon with an inner loop. B.Cardioid that is symmetric to line θ =π/2 D. Cardioid that is symmetric to the polar axis.

A building 160 feet tall casts a 90 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle between the end of the shadow and the vertical side of the building (to the nearest degree)? (Assume the person's eyes are level with the top of the building.) 61° 56° 29° 34°

12. Harrison loaned his friend Mattson $100 for one year at a simple interest rate of 5%. The total amount of money that Mattson will pay back at the end of the year is a. $5.00 b. $100.00 c. $105.00 d. $120.00

A chemistry student needs 20.0 g of diethylamine for an experiment. By consulting the CRC Handbook of Chemistry and Physics, the student discovers that the density of diethylamine is 0.706 g/cm^3 . Calculate the volume of diethylamine the student should pour out.

The functions f and g are defined as follows. f(x)=x²+9x+5 and g(x)= 3/ x²-2 Find f(x-3) and g(-/x)

Andrea simplified a polynomial expression. The solution was 4x²-7x + 5. Which of the following could have been the original expressions? SELECT ALL THAT APPLY. (3x²-9x+8)+(x²+2x-3) (2x² - 4x-5)-(-2x² + 3x - 10) (5x²-2)-(x²+7x+3) (4x² + 3x) -(10x + 5)

If θ=210°, find the exact value of each expression below. (a) 2 sin θ = (b) sin (-θ) = (c) sin 2θ =

Which situation is an example of exponential decay? The amount of a radioactive element is decreasing at a rate of 35% per year. The weekly earnings of a part-time job that pays $8 per hour is increased by a weekly bonus of $25. The amount deducted for taxes decreases an annual salary by about 22%. The number of ants in an ant farm is increasing at a rate of 108% per week.