Identify the vertex and the y -intercept of the graph of each function. $y=(x-125)^{2}+125$

Sketch the graph of a function whose derivative is always positive.

Miguel is answering an e-mail from his friend Jorge. Answer Jorge's questions, saying that the people will have already done these things by the time indicated. Use the future perfect.

1. ¿Encontrarás un trabajo cuando te gradúes?
2. ¿Le comprarás un regalo a Maru cuando te paguen?
3. ¿Escribirá el Sr. Díaz una novela cuando se jubile?
4. ¿Harás los preparativos para ir a España cuando termine el año escolar (school year)?
5. ¿Llenará David la solicitud cuando llegue a la entrevista?
6. ¿Olvidaré a mi ex novia cuando me vaya de vacaciones?

Draw the Lewis structure for a molecule of each of these compounds and ions. a. $\mathrm{H}_{\mathrm{2}} \mathrm{S}$ b. ${BF_4} ^ -$ c. $\mathrm{SO}_{2}$ d. $\mathrm{SeCl}_{2}$

Evaluate the determinant of each matrix.

$$\left[\begin{array}{lll}{1} & {4} & {0} \\ {2} & {3} & {5} \\ {0} & {1} & {0}\end{array}\right]$$

Two sinusoidal waves of the same period, with amplitudes of 5.0 and 7.0 mm, travel in the same direction along a stretched string; they produce a resultant wave with an amplitude of 9.0 mm. The phase constant of the 5.0 mm wave is 0. What is the phase constant of the 7.0 mm wave?

Select the best answer. A statistic is an unbiased estimator of a parameter when (a) the statistic is calculated from a random sample. (b) in a single sample, the value of the statistic is equal to the value of the parameter. (c) in many samples, the values of the statistic are very close to the value of the parameter. (d) in many samples, the values of the statistic are centered at the value of the parameter. (e) in many samples, the distribution of the statistic has a shape that is approximately Normal.

What are the two transition metals that are used in making jewelry and are the group 11 elements with the lowest atomic masses?

If the first two terms of a geometric sequence are negative, then so is the third. Justify your answer.

Consider the vector space

$$\mathbb { R } ^ { 2 }.$$

Define the mapping

$$\langle , \rangle \text { by } \langle \mathbf { v } , \mathbf { w } \rangle = 2 v _ { 1 } w _ { 1 } + v _ { 1 } w _ { 2 } + v _ { 2 } w _ { 1 } + 2 v _ { 2 } w _ { 2 } \quad \quad (5.1.14)$$

for all vectors

$$\mathbf { v } = \left( v _ { 1 } , v _ { 2 } \right) \text { and } \mathbf { w } = \left( w _ { 1 } , w _ { 2 } \right) \text { in } \mathbb { R } ^ { 2 }.$$

Verify that Equation (5.1.14) defines an inner product on

$$\mathbb { R } ^ { 2 }.$$

During heavy rain, a section of a mountainside measuring 2.5 km horizontally, 0.80 km up along the slope, and 2.0 m deep slips into a valley in a mud slide. Assume that the mud ends up uniformly distributed over a surface area of the valley measuring 0.40 km × 0.40 km and that mud has a density of 1900 kg/m³. What is the mass of the mud sitting above a 4.0 m² area of the valley floor?

Compute the atomic packing factor for cesium chloride using the ionic radii and assuming that the ions touch along the cube diagonals.

Male Rana catesbeiana bullfrogs are known for their loud mating call. The call is emitted not by the frog’s mouth but by its eardrums, which lie on the surface of the head. And, surprisingly, the sound has nothing to do with the frog’s inflated throat. If the emitted sound has a frequency of 260 Hz and a sound level of 85 dB (near the eardrum), what is the amplitude of the eardrum’s oscillation? The air density is 1.21 kg/m³.

The data below represent the age of the mother at the time of her first birth for a random sample of 30 mothers.

$$\begin{matrix} \text{21} & \text{35} & \text{33} & \text{25} & \text{22} & \text{26}\\ \text{21} & \text{24} & \text{16} & \text{23} & \text{25} & \text{20}\\ \text{30} & \text{20} & \text{20} & \text{29} & \text{21} & \text{19}\\ \text{18} & \text{24} & \text{33} & \text{22} & \text{23} & \text{25}\\ \text{17} & \text{23} & \text{25} & \text{29} & \text{25} & \text{19}\\ \end{matrix}$$

(a) Construct a boxplot of the data. (b) Use the boxplot and quartiles to describe the shape of the distribution.