Questions in mathematics

Questions in mathematics

📝 Answered - A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting a heart or club. (b) Compute the probability of randomly selecting a heart or club or spade. (c) Compute the probability of randomly selecting a four or spade.

📝 Answered - The number of days required to make shirts is proportional, as shown in the table below: | Factory | Number of Days | Number of Shirts | |---|---|---| | A | 2 | 600 | | B | 3 | 900 | | C | 4 | 1200 | | D | 5 | 1500 | Factory E can make shirts at the same rate as the first four factories. Which table(s) could represent the production rate of factory E? | Factory | Number of Days | Number of Shirts | |---|---|---| | E | 1 | 400 | | Factory | Number of Days | Number of Shirts | |---|---|---| | E | 1 | 300 | | Factory | Number of Days | Number of Shirts | |---|---|---| | E | 6 | 1,800 |

📝 Answered - Given any triangle [tex]$A B C$[/tex] with corresponding side lengths [tex]$a, b$[/tex], and [tex]$c$[/tex], the law of cosines states: A. [tex]$c^2=a^2+b^2-2 a b \cos (C)$[/tex] B. [tex]$c^2=a^2+b^2-2 b c \cos (B)$[/tex] C. [tex]$c^2=a^2-b^2-2 b c \cos (C)$[/tex] D. [tex]$c^2=a^2+b^2-2 b c \cos (A)$[/tex]

📝 Answered - The standard diameter of a golf ball is 42.67 mm. A golf ball factory does quality control on the golf balls it manufactures. Golf balls are randomly measured to ensure the correct size. If the discrepancy in diameter is more than 0.004 mm, the production is stopped. Which function could represent this situation? [tex]\checkmark f(x)=|42.67-x|^2[/tex] What are the acceptable diameters for the golf balls? 42.675 mm 42.6668 mm 42.664 mm 42.673 mm 72.676 mm

📝 Answered - Polynomial fitting involves finding a polynomial of degree n that best fits a set of data points. What is n in this context? A. Order of the polynomial B. Number of data points C. Slope of the polynomial D. Intercept of the polynomial

📝 Answered - Art and his friends spent $62 at the movies. Admission tickets cost $12 apiece, and a bucket of popcorn costs $7. Which equation written in standard form represents the number of tickets bought, $t$, and the number of buckets of popcorn bought, $p$? A. $12p+7t=62$ B. $7p+12t=62$ C. $12p=62-7t$ D. $7p=62-12t

📝 Answered - Consider the graph of the line [tex]y=\frac{1}{2} x-4[/tex] and the point $(-4,2)$. The slope of a line parallel to the given line is $\square$. A point on the line parallel to the given line, passing through ( $-4,2$ ), is $\square$. The slope of a line perpendicular to the given line is $\square$ A point on the line perpendicular to the given line, passing through $(-4,2)$, is $\square$

📝 Answered - What is the value of [tex]$i^{20+1}$[/tex]? A. 1 B. -1 C. -1 D. [tex]$i$[/tex]

📝 Answered - Which are the solutions of $x^2=-5 x+8 ?$ $ \frac{-5-\sqrt{57}}{2}, \frac{-5+\sqrt{57}}{2}$ $ $ \frac{-5-\sqrt{7}}{2}, \frac{-5+\sqrt{7}}{2}$ $ $ \frac{5-\sqrt{57}}{2}, \frac{5+\sqrt{57}}{2}$ $ $ \frac{5-\sqrt{7}}{2}, \frac{5+\sqrt{7}}{2}$

📝 Answered - In which triangle is the measure of the unknown angle, [tex]$x$[/tex], equal to the value of [tex]$\sin ^{-1}\left(\frac{5}{8.3}\right)$[/tex]?