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PLEASE HELP QUICKIs X=[2 -1 6 -4] the inverse of A=[1/2 1/4 -2 -1/2]?Select answers from the drop-down menus to correctly complete the statements.The product of the matrices (a - is b - is not) the identity matrix. Therefore, X and A (a - are b - are not) inverses of each other. 6.Erin and Christa were working on cubingbinomials for math homework. Erin believed theycould save time with a shortcut. She wrote downthe rule below for Christa to follow.(a + b) = a + bDoes Erin's shortcut always work? Justify yourresult algebraically.PLEASE SHOW WORK find the vertex, y intercept, and x intercept to this quadratic function "y = x^2 + 2x - 3" pls show you work!I need help fast, PLS HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 15. Determine by inspection whether the given sets are linearly dependent. a) \( \left\{\left[\begin{array}{l}1 \\ 3\end{array}\right],\left[\begin{array}{l}2 \\ 6\end{array}\right]\right\} \) b) \( \ Hey is someone great at english if so can someone give me great ideas to mention in my introduction of my essay.So basically the essay is about how can Allegory of the Cave be analyzed with the formalist lensAnd my thesis is "The Allegory In The Cave" can be analyzed through the formalist lens because of the symbolism of light and darkness both literally and metaphorically throughout its text. "Right now I'm struggling on what to write in my intro before I add my thesis and I really want to write a good essay. And please explain well! ____ is the number of people living in a square mile. In the future, economically developed nations may not have enough money to take care of older citizens because of ____. In low-income nations, _____ is one reason for the low standard of living. Options for "___ is the number of people living in a square mile: a. Population densityb. Population controlc. Population growthOptions for "In the future, economically developed nations may not have enough money to take care of older citizens because of:a. Immigrationb. Underpopulationc. Urbanization Options for "In low-income nations, _____ is one reason for the low standards of living:a. Overpopulationb. Population limitsc. Underpopulation What do you need to do to get a perfect score in each category?Answer in a full paragraph. 44. A survey asked buyers whether color, size, or brand influenced their choice of cell phone. The results are below. How many people were influenced by brand? 5 only said color 8 only said size 16 only said brand 20 said only color and size42 said only color and brand 53 said only size and brand 102 said all three 20 said none of these A teacher gives out a variety of chocolate bars as a prize for students who correctly explain their answer.Cole randomly selects a candy from the bag what is the probability that the selected chocolate will be either cookies and cream or peanut butter cups There are three questions and 3 options.please reoly ASAPQ: location where chyme id neutralized so that rnzymes can digest nutrientsQ: produces enzymes that are used to digest nutrients in the intestinesQ: moisten food with slippery substanceoptions :PAROTID GLAND , DUODENUM ,PANCREAS If a cell was in an aqueous environment containing Na+ ions andoxygen, what would you predict would move across the membranefirst? Why? A firm is planning to issue two types of 20-year, noncallable bonds to raise a total of $10 million, $5 million from each type of bond. First, 5,000 bonds with a 10% semiannual coupon will be sold at their $1,000 par value to raise $5,000,000. These are called par bonds. Second, Original Issue Discount bonds, also with a 20-year maturity and a $1,000 par value, will be sold, but these bonds will have a semiannual coupon of only 6.25%. The original issue discount bonds must be offered at below par in order to provide investors with the same effective yield as the par bonds.How many Original issue discount bonds must the firm issue to raise $5,000,000 Given the supply and demand functions P = 2Q 2 S + 10Qs + 10 P = Q 2 D 5QD + 52 calculate the equilibrium price and quantity? 2. (a) State the fundamental theorem of_Group Hormomorphisms. Let (R, +) and (C, +) be the additive group of real numbers and the additive group of complex numbers respectively. The function : C -> R is defined by (x +iy) = y for all : x + iy C. (i) Show that o is a homomorphism. (ii) Find ker . (iii) Prove that c/r ~= R. (b) Let G = D6 = {1,r,r^2, s, sr, sr^2) and S = {1,r^2}. Find C_G(S). ryan invested 5000 in an account that grows continuously at an annual rate of 2.5%. What will ryans investment be worth after 7 years? Round to the nearest cent Around ____ BC, the first Asian civilizations arose along the_and_ River valleys.A. 5000; Yangtze; IndusB. 2000; Indus; YellowC. 6000; Yangtze; YellowD. 3000; Indus; Yellow determine the Least Common Multiple LCM of the factored polynomials x(x-2) and x(x+1) the LCM? What is |6.5|?........................................................ He set his face awayfrom the eclipse, his eyes seekingtheir way to a place where the sundoes not see. In the distance,the wheat waved and wilted under the windwhose breath blew beyond the bare field. The day found its bearings underthe chorus of cicadas chirping,their tempo keeping time like a moving train. He set his face away from all thisand beneath him, the rainwater from the storm drainedgroaning into a gorge with a slight gurgle and sigh. The fields fall fallow under the flood and freeze, and somehow he found herher hair dancinglike Medusa's split ends,his feet cementing himlike a scarecrow wearing fearless birds Given that velocity is 4, real GDP is 8, and the price level is 2. Suppose that the Central Bank decides to increase nominal money supply to 6 while velocity remains unchanged, calculate the percentage change in nominal GDP.