Determine the size and location of an image produced by a convex lens with a focal length of $14.5 \mathrm{~cm}$ of an object $10.5 \mathrm{~cm}$ from the lens and $2.35 \mathrm{~cm}$ high?

Use Euler's Formula for Polyhedra to answer the following questions.

a. If a convex polyhedron has 10 vertices and 8 faces, how many edges does it have?

b. Can a convex polyhedron that has 8 faces, 12 edges, and 7 vertices be constructed? Give reasons for your answer.

Mark the statement True or False (T/F). Justify each answer.

If y = C1 V1 + C2 V2 + C3 V3 and Ct + C2 + C3 = 1, then y is a convex combination of v1, v2, and v3.

Write the quadratic function in vertex form, if not already in that form. Then identify the vertex, axis of symmetry, and direction of opening.

$$y=\frac{1}{3}(x-1)^2+2$$

Find an equation of the plane tangent to the sphere $(x-1)^{2}+(y+2)^{2}+(z-2)^{2}=6$ at the point (2,-1,0).

A boy is standing near a convex mirror in a fun house at a fair. He notices that his image appears to be 0.60 m tall. If the magnification of the mirror is $\frac{1}{3}$, what is the boy’s height?

Write each series using sigma notation. Find the sum. - 7 - 42 - 252 - ... - 54.432

Find the maximum and minimum values of the function $f(x, y)=3 x-y+4$ for the polygonal convex set determined by the system of inequalities.

$$\begin{array}{l} x+y \leq 8 \\ y \geq 3 \\ x \geq 2 \end{array}$$

Circulez dans la classe pour demander à vos camarades s'ils prennent rarement, une fois (once) par semaine ou tous les jours la boisson ou le plat (dish) indiqués. Écrivez (Write) les noms sur la feuille, puis présentez vos réponses à la classe.

Boissons ou plats$\hspace{1cm}$ uncement$\hspace{1cm}$ une fois par semaine$\hspace{1cm}$ tous les jours

cabé

Convex pentagon PQRST has vertices P(0, 0), Q(-2, 2), R(-1, 4), S(x, y), and T(2, 2). QR = ST and RS = 2. Find (x, y).

Find the appropriate values of

$$n _ { 1 } \text { and } n _ { 2 }$$

(assume that

$$n _ { 1 } = n _ { 2 }$$

) needed to estimate

$$\left( \mu _ { 1 } - \mu _ { 2 } \right)$$

with A 90% confidence interval of width 1.0. Assume that

$$\sigma _ { 1 } ^ { 2 } \approx 5.8 \text { and } \sigma _ { 2 } ^ { 2 } \approx 7.5$$

The graph above shows the number of suburban dwellers in the United States as a percentage of the total population. Study the data displayed in the graph and answer the questions below.
a.What trend in the percentage of suburban dwellers does this graph show?
b.How might the trend of suburban dwellers shown on this graph have affected life in suburbs and cities?

(I) A properly exposed photograph is taken at $f / 16$ and $\frac{1}{120} \mathrm{~s}$. What lens opening is required if the shutter speed is $\frac{1}{1000} \mathrm{~s}$ ?

Write each equation in standard form. Identify the vertex, axis of symmetry, and direction of opening of the parabola.

$$y=2x^2-24x+40$$