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Questions in mathematics

📝 Answered - a) The area of a rectangular field is [tex]$\left(x^2+8 x+15\right)$[/tex] sq. m. (i) Find the length and breadth of the field. (ii) Find the perimeter of the field.

📝 Answered - Suppose an object is thrown upward with an initial velocity of 63 feet per second from a height of 105 feet. The height of the object [tex]$t$[/tex] seconds after it is thrown is given by [tex]$h(t)=-16 t^2+63 t+105$[/tex]. Find the average rate of change of the position of the object for the time period [tex]$t=0$[/tex] to [tex]$t=3$[/tex]. The average rate of change of the object is $\square$ $\square$.

📝 Answered - $\frac{3}{4} x+3-2 x=-\frac{1}{4}+\frac{1}{2} x+5$

📝 Answered - Approximate: [tex]$\log _5 \frac{4}{7}$[/tex]

📝 Answered - To determine if his teaching method increases students' learning, a professor administers a pretest to his class at the beginning of the semester and then a posttest at the end of the semester. The results from 10 randomly chosen students are given below. Let Population 1 be the Pretest scores and Population 2 be the Posttest scores. Test Scores Pretest Posttest 50 71 73 82 64 80 50 62 86 92 76 71 60 74 71 80 76 81 70 68 Step 1 of 2: Construct a $90 \%$ confidence interval for the true mean difference between the scores to determine if the teaching method increases students' knowledge of the course material. Round the endpoints of the interval to one decimal place, if necessary.

📝 Answered - Graph the following inequality. $y \geq x^2+5$

📝 Answered - What is 18% of 222 rounded to the nearest whole number?

📝 Answered - The high temperature on Friday was 8 degrees above zero. The low temperature was 3 degrees below zero. Which expression gives the average of the low and high temperatures? A. $-(3+8)+2$ B. $(-3+8)-2$ C. $(-3+8)-(-2)$ D. $[(-3+(-8)]-(2)$

📝 Answered - The table shows the shoe size of 23 students. A student is picked at random. | Shoe Size | Frequency | | --------- | --------- | | 5 | 2 | | 6 | 11 | | 7 | 5 | | 8 | 4 | | 9 | 1 | (a) Work out the probability that the student has a shoe size of 8. (b) Work out the probability that the student has a shoe size of 7 or smaller.

📝 Answered - The vertex of this parabola is at $(5,-4)$. Which of the following could be its equation? A. $y=2(x-5)^2-4$ B. $y=2(x-5)^2+4$ C. $y=2(x+5)^2+4$ D. $y=2(x+5)^2-4$