Consider the following hypotheses about a population proportion \( p \) : \[ H_{0}: p=0.45 \text { against } H_{1}: p \neq 0.45 \] An analyst wants to test the hypotheses. He conducted 320 trials that resulted in 128 successes. The \( p \)-value for the test is

The perimeter of a circle is called the CIRCUMFERENCE. Circumference of a circle is given by the formula \( \mathrm{C}=2 \pi \mathrm{r} \) Where \( \pi=22 / 7 \) or 3.14 \( \mathrm{r}= \) The length from the midpoint(center) of the circle to the edge (side) Solve the formula for r and use it to answer the following question: If the Circumference of a circle is 31.4 centimeters (cm.) and you know that \( \pi=3.14 \), find the length of the radius of the circle ( r )?

06) "Sendo o número \( \mathbf{n}=\mathbf{6 8 4}^{\mathbf{2}}-\mathbf{6 8 3}^{\mathbf{2}} \), a soma dos algarismos de n é:"

Evaluate the expression \( \sin ^{-1}\left(\cos \left(\frac{7 \pi}{6}\right)\right) \) . Give your answer as an exact value

a) \( 3(x-6)=2(5-2 x) \)

05) Simplifique as frações algébricas: (a) \( \left(16 x^{2}\right):\left(-4 x^{2}\right) \) (b) \( \left(36 x y^{2}\right):(-6 x y) \) (c) \( (-35 a):(+7 a) \) (d) \( \left(+3 a b^{2}\right):\left(-\frac{10}{5}\right) \) (e) \( \left(-\frac{4}{5} x^{2} y\right):\left(+\frac{4}{3} x^{2} y\right) \)