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Given the 3 Vertices A(3,-1) B(7,-4) C(1,-7) of a triangle, calculate the vector equation and the explicit equation of the height corresponding to side BC

Find two non-negative numbers whose sum is 30 that make the maximum product of the square of one and the cube of the other.

A $1,000,000 lottery prize pays $50,000 per year for the next 20 years. If the current rate of return is 3.75%, what is the present value of this prize. (Assume the lottery pays out as an ordinary annuity. Round your answer to the nearest cent.)

Crm systems are built around a database is accessed by employees and customers using a website the technology is often referred to as e-CRM. Explain the common applications that uber ,McDonald's and coca cola use. Which could be integrated in a CRM system and what CRM programs include

How do you identify the Noel and alternative hypothesis?

There are 42 students in a certain class 1/3 of them are not good in Science. How many students that are good in science

Dilute the IgG protein standard (200 µg/mL) to create a 6-point standard curve ranging from 0 – 75 µg/mL (in duplicate). Determine the valid concentrations for each tube. The final volume is 1.0 mL. Table 1. Preparation of IgG standard curve including volumes, concentrations, and absorbance values determined by undertaking a Bradford assay (2 mark). Tube 1 2 3 4 5 6 7 8 9 10 11 12 IgG (200 µg/mL), mL H2O, mL Final [IgG] (µg/mL) 0 0 75 75

Determine the type of reaction, predict the products, and balance the compounds and reaction.  Aluminum sulfate + magnesium bromide →

A given polymer, whose mean square radius of gyration is 7.54·10^3 Å^2, has at its ends two reactive groups capable of emitting light when they are less than 5 Å away (regardless of which one it is in particular). this distance). The emission is proportional to the number of molecules that at each moment meet the aforementioned condition and we consider ideal dilute solutions, or “theta” in which the probability of the two terminal groups of different molecules approaching is small. Obtain the ratio between the amount emitted by a solution of a practically monodisperse sample of said polymer and another similar one, and of the same concentration by weight, but in which the mean square radius of gyration of the molecules is 1.32·10^ 4 Å^2.

The questions are independent. 1. Let F = {(a+2b+c, a+c, a+c, a+2b), a,b,c ∈ R}. Justify that F is a vector subspace of R4, give a base and specify its dimension. 2. Is the family (1, 2, 2), (2, 3, 0), (−1, 3, 1) a basis of R3? Justify.