What is the purpose of a control in an experiment? to eliminate variability to devermine whether the active treatment works to measure response bias

Question 7 (a) Write 65489 correct to 1 significant figure.

The total cost (in dollars) of manufacturing \( x \) auto body frames is \( C(x)=90,000+700 x \). (A) Find the average cost per unit if 250 frames are produced. (B) Find the marginal average cost at a production level of 250 units. (C) Use the results from parts (A) and (B) to estimate the average cost per frame if 251 frames are produced. (A) If 250 frames are produced, the average cost is \( \$ \) \( \square \) per frame.

\( \frac{1}{3}+\frac{5}{6}-\frac{3}{5}.\frac{3}{2} \)

Sabendo que, para \( a>0 \) e \( b>0 \), tem-se \( \sqrt{a \times b}=\sqrt{a} \times \sqrt{b} \) e \( \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}} \) Simplifica as seguintes expressóes: \( \begin{array}{ll}\text { 1. } \sqrt{4 \times 3} \times(1-\sqrt{3}) & \text { 3. }(\sqrt{3})^{2}+\sqrt{3}-4 \\ \text { 2. } 2 \sqrt{5}-3 \sqrt{5}+4 \sqrt{5} & \text { 6. }(1-\sqrt{3})(1+\sqrt{3}) \\ \text { 3. }(3-\sqrt{2})^{2} & \text { 7. }(1-\sqrt{2})(3+\sqrt{2}) \\ \text { 4. } \frac{1}{\sqrt{5}} \times \frac{\sqrt{20}}{3} & \text { 8. } \frac{2 \sqrt{3}-8 \sqrt{3}}{\sqrt{3}}\end{array} \)

3. A contractor is helping a client narrow some choices on a home remodel. The contractor wants to present 3 layout options out of 5 possibilities, 2 roof materials out of 6 possibilities, and 4 front door options out of 8 possibilities. How many different layout+roof + front door choices will the contractor present to the client?