Questions in mathematics

Questions in mathematics

[Done] Find the exact value using reference angles: \(\cot \left(-\frac{53\pi}{6}\right)\)

[Done] A container is shaped like a rectangular solid with sides of 3 inches, 3 inches, and 11 inches. What is its approximate capacity, if 1 gallon equals 231 cubic inches?

[Done] The cost of a certain brand of camera has been increasing at 8% per year. If a camera now costs $150, what will be the cost next year?

[Done] Use Newton's method to approximate a root of the equation \[ \cos(x^2 + 3) = x^3 \] as follows. Let \( x_1 = 1 \) be the initial approximation. What is the second approximation \( x_2 \)?

[Done] The ratio of boys to girls in the ninth grade is 6:5. If there are 185 girls in the class, how many boys are there?

[Done] What two numbers multiply to 120 and add to get -22?

[Done] If you are only given the slope-intercept form of a line, how would you sketch the line?

[Done] Which quadrilateral does NOT always have congruent diagonals? Explain why. A. Rhombus Note: A rhombus does not always have congruent diagonals because while its diagonals bisect each other at right angles, they are not necessarily equal in length.

[Done] A man walks 15 blocks to work every morning at a rate of 2 miles per hour. If there are 20 blocks in a mile, how long does it take him to walk to work?

[Done] There are 240 students in a marching band. If the director wants the band to march in 40 equal rows, which equation could be used to find the number of students, [tex]s[/tex], in each row? A. [tex]s = \frac{240}{40}[/tex] B. [tex]s = 240 \times 40[/tex] C. [tex]s = 240 + 40[/tex] D. [tex]s = 240 - 40[/tex]