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Questions in mathematics

📝 Answered - What is the quotient? $6 \longdiv { 5 3 8 . 0 0 }$ $\frac{-480}{58}$ -54 $\begin{array}{r}40 \\ -36 \\ \hline 40\end{array}$ $-36$ A. $89 . \overline{5}$ B. 89.6 C. $89 . \overline{6}$ D. 89.7

📝 Answered - If $y=12x-7$ were changed to $y=12x+1$, how would the graph of the new function compare with the original? A. It would be shifted down. B. It would be less steep. C. It would be shifted up. D. It would be steeper.

📝 Answered - Find the focus and directrix of the following parabola: $(y-6)^2=12(x-2)$ Focus: ([ ? ], $\square$ ) Directrix: $x=$ $\square$

📝 Answered - Find the value of each of the following. Leave each answer as a mixed number in its simplest form where applicable. (a) [tex]$10 \frac{3}{5}-3 \frac{1}{5}$[/tex] (b) [tex]$2 \frac{3}{7}-\frac{4}{7}$[/tex] (c) [tex]$\frac{37}{18}-1 \frac{7}{18}$[/tex] (d) [tex]$2 \frac{8}{11}-2 \frac{9}{22}$[/tex] (e) [tex]$10 \frac{3}{8}-6 \frac{13}{24}$[/tex] (f) [tex]$\frac{15}{4}-2 \frac{1}{6}$[/tex] (g) [tex]$3 \frac{5}{8}-1 \frac{5}{6}$[/tex] (h) [tex]$3 \frac{5}{7}-\frac{7}{5}$[/tex]

📝 Answered - The equation of a circle centered at the origin is $x^2+y^2=64$. What is the radius of the circle? A. 32 B. 8 C. 4 D. 64

📝 Answered - If the area of a square is 64 square centimeters, what's the length of one side? A. 4 cm B. 8 cm C. 16 cm D. 32 cm

📝 Answered - Evaluate the integral $\int_0^3 \frac{3(x+2)}{\sqrt{x+1}} d x$. A. 32 B. 24 C. 16 D. 18 E. 20

📝 Answered - Given two dependent random samples with the following results: | Population 1 | 30 | 47 | 19 | 49 | 42 | 31 | 24 | |---|---|---|---|---|---|---|---| | Population 2 | 45 | 37 | 29 | 44 | 46 | 46 | 34 | Use this data to find the $90 \%$ confidence interval for the true difference between the population means. Assume that both populations are normally distributed. Step 3 of 4: Calculate the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

📝 Answered - Determine whether the normal distribution can be used to compare the following population proportions. [tex]$n_1=45, \quad n_2=29, \quad \hat{p}_1=0.689, \quad \hat{p}_2=0.897$[/tex] Are the conditions for using the normal distribution met?

📝 Answered - Use synthetic division to solve $(3 x^4+6 x^3+2 x^2+9 x+10) \div (x+2)$. What is the quotient?