A normally distributed random variable X has a mean of 90. Given that the probability $\mathrm{P}(X<85) \approx 0.16 :$ a. find the proportion of scores between 90 and 95, i.e., find P(90 < X < 95) b. find an estimate of the standard deviation for the random variable X.

Why might the Supreme Court have declared some New Deal measures unconstitutional?

A music theorist associates the fundamental frequency of a pitch $f$ with a real number defined by

$$p=69+12 \log _{2}(f / 440)$$

Source: Science. a. Standard concert pitch for an A is $440$ cycles per second. Find the associated value of p. b. An A one octave higher than standard concert pitch is $880$ cycles per second. Find the associated value of $p$.

Use the Ratio or Root Test to determine the radius of convergence of the following power series. Test the endpoints to determine the interval of convergence, when appropriate.

$$\Sigma \left( \frac { x } { 9 } \right) ^ { 3 k }$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Eccentricity and polar coordinates enable me to see that ellipses, hyperbolas, and parabolas are a unified group of interrelated curves.

Three, and only three, bright fringes can be seen on either side of the central maximum when a grating is illuminated with light

$$( \lambda = 510 \mathrm { nm } )$$

What is the maximum number of lines/cm for the grating?

A magnetic field of 37.2 T has been achieved at the MIT Francis Bitter National Magnetic Laboratory. Find the current needed to achieve such a field (a) 2.00 cm from a long, straight wire; (b) at the center of a circular coil of radius 42.0 cm that has 100 turns; (c) near the center of a solenoid with radius 2.40 cm, length 32.0 cm, and 40,000 turns.

Graph the solution set of each inequality and write it in interval notation. $1 \leq x < 7$

Give examples of the types of taxes that wage earners pay to federal, state, or local governments.

Use the Vertical Line Test to determine whether y is a function of x. To print an enlarged copy of the graph.

$$x^{2}-y=0$$

What is an intermediate of a reaction?

Atmospheric scientists often use mixing ratios to express the concentrations of trace compounds in air. Mixing ratios are often expressed as ppmv (parts per million volume): ppm of $X = \frac { \text { vol of } X \text { at } S T P } { \text { total vol of air at } S T P } \times 10 ^ { 6 }$ On a certain November day, the concentration of carbon monoxide in the air in downtown Denver, Colorado, that time was 628 torr and the temperature was $0 ^ { \circ } \mathrm { C }.$ What was the concentration of CO in molecules per cubic centimeter?

How are the formulas for the surface area of a prism and the surface area of a pyramid alike? How are they different?

What is the square root of 24?