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Questions in mathematics

[Done] Suppose that a chewing gum company claims that $92 \%$ of dentists recommend their chewing gum. Oliver wants to test if this is true. He surveys 132 randomly selected dentists. 1. Assuming the chewing gum company's claim is true, what is the probability that fewer than $86 \%$ of the dentists surveyed recommend the chewing gum? To answer this question, complete the following steps: * Let the random variable $\widehat{P}$ be the proportion of 132 randomly sampled dentists who recommend the chewing gum. How is $\widehat{P}$ distributed? $\widehat{P} \sim N(\square, \square)$ * List the $z$-scores needed to calculate the result. If there is more than one $z$-score, separate the values with a comma. $\square$ * Assuming the chewing gum company's claim is true, the probability that fewer than $86 \%$ of the dentists surveyed recommend the chewing gum is $\square$ . 2. If Oliver does find that fewer than $86 \%$ of the dentists surveyed recommend the chewing gum, would you doubt the chewing gum company's claim? Why or why not? (Consider this question on your own. You do not have to provide an answer here.)

[Done] Write a factor that you can use to rationalize the denominator of $\frac{4}{\sqrt{6}}$. A rationalizing factor is $\square$.

[Done] A transport company consumed 8749 litres of diesel during the first year. Its consumption of diesel in the second year was 8956 litres more than that of the first year. In the third year, the consumption was 4678 litres more than that of the second year. What was the total consumption of diesel in these three years? In an examination, 30378 students sat in the first year, 35410 sat in the second year, 36925 sat in the third year, and 27089 sat in the fourth year. How many students took the examination in four years? A school library has 35035 books printed in English, 58509 books printed in Hindi, and 4299 books printed in other languages. How many books are there in the library? There are 28539 bags of wheat, 25312 bags of rice, 43809 bags of sugar, and 19318 bags of barley in a godown. Find the total number of bags in that godown.

[Done] What is another way to call the probability of rejecting a null hypothesis that is false? (A) Type I error (B) Type II error (C) Type III error (D) Power of the test

[Done] Evaluate the function at the given values of the independent variables. Simplify the results. g(x, y) = ln(|x + y|) (a) g(1, 0) (b) g(0, −t²) (c) g(e, 0) (d) g(e, e)

[Done] Which skills are needed to copy a triangle? A. constructing perpendicular lines B. copying an angle C. copying an angle and copying a segment D. constructing parallel lines

[Done] The function [tex]$f(x)$[/tex] is to be graphed on a coordinate plane. [tex]$f(x)=\left\{\begin{array}{ll} -x, & x\ \textless \ 0 \\ 1, & x \geq 0 \end{array}\right.$[/tex] At what point should an open circle be drawn? A. (-1,0) B. (0,0) C. (0,1) D. (1,0)

[Done] a) $39 \times 0.04$ b) $74 \times 0.02$ c) $124 \times 0.003$

[Done] What is the discriminant of the polynomial below? [tex]2 x^2+5 x-8[/tex] A. 89 B. -39 C. 31 D. -59

[Done] What is the solution to this equation? [tex]\sqrt[3]{\left(\frac{1}{8}-x\right)}=-\frac{1}{2}[/tex] The solution is $\square$.