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Questions in mathematics

[Done] Study the following pattern: [tex]$\begin{array}{l} 84 \times 99=8,316 \\ 84 \times 999=83,916 \\ 84 \times 9,999=8,39,916 \end{array}$[/tex] Write the next seven steps in the pattern.

[Done] Divide using long division. $(4 x^3-2 x^2+2 x+2) \div(x+3)$

[Done] Which one of the following angles in standard position has the same reference angle as an angle of 215°? A. 335° B. 155° C. 35° D. 315°

[Done] What is the center of a circle whose equation is $x^2+y^2+4 x-8 y+11=0$? A. $(-2,4)$ B. $(-4,8)$ C. $(2,-4)$ D. $(4,-8)$

[Done] A company tracks the number of products sold daily. The sales data follows a normal distribution with a mean of 200 and a standard deviation of 20. Approximately what percentage of daily sales falls between 180 and 220?

[Done] Read the following carefully: Frank, Charlie, Johnny, and George decide to visit their friend. The surnames of the 4 boys, in no particular order, are Little, Grant, Tailor, and Miller. Miller arrived first, followed by Johnny, then Little. George arrived last. Each boy came with a present for their friend. Miller gave a DVD, Frank gave a pen, George gave a bar of chocolate, and Tailor gave a book. Using this information, work out the full name of each boy (first name and surname). Answer: Frank Charlie Johnny George

[Done] Which is the solution of the quadratic equation $(4 y-3)^2=72$? A. $y=\frac{3+5 \sqrt{2}}{4}$ and $y=\frac{3-5 \sqrt{2}}{4}$ B. $y=\frac{3+6 \sqrt{2}}{4}$ and $y=\frac{-3-6 \sqrt{2}}{4}$ C. $y=\frac{9 \sqrt{2}}{4}$ and $y=\frac{-3 \sqrt{2}}{4}$ D. $y=\frac{9 \sqrt{2}}{4}$ and $y=\frac{3 \sqrt{2}}{4}$

[Done] The perimeter of a scalene triangle is 14.5 cm. The longest side is twice that of the shortest side. Which equation can be used to find the side lengths if the longest side measures 6.2 cm? A. $6.2+b=14.5$ B. $9.3+b=14.5$ C. $12.4+b=14.5$ D. $18.6+b=14.5

[Done] A child is hopping along a sidewalk. The ratio table below shows the comparison between the number of hops and the distance traveled. | Number of hops | Distance traveled (ft) | |------------------|------------------------| | 20 | 30 | | 50 | 75 | | 80 | 120 | | 150 | ? | Which statement correctly explains how to find the distance traveled after 150 hops? A. Subtract [tex]$120-75$[/tex] to get 45, then add that number to 120. B. Add [tex]$30+75+120$[/tex]. C. Find a number that when multiplied by 50 (number of hops in the 2nd row) will give a product of 150 (number of hops in the 4th row), then multiply 75 by that number. D. Find a number that when multiplied by 50 (number of hops in the 2nd row) will give a product of 150 (number of hops

[Done] Shanti wrote the predicted values for a data set using the line of best fit [tex]y=2.55 x-3.15[/tex]. She computed two of the residual values. | x | Given | Predicted | Residual | |---|---|---|---| | 1 | -0.7 | -0.6 | -0.1 | | 2 | 2.3 | 1.95 | 0.35 | | 3 | 4.1 | 4.5 | a | | 4 | 7.2 | 7.05 | b | What are the values of [tex]a[/tex] and [tex]b[/tex]? A. [tex]a=0.4[/tex] and [tex]b=-0.15[/tex] B. [tex]a=-0.4[/tex] and [tex]b=0.15[/tex] C. [tex]a=8.6[/tex] and [tex]b=14.25[/tex] D. [tex]a=-8.6[/tex] and [tex]b=-14.25[/tex]