MATH

A ________ is a procedure that answers the question “Did these data come from a particular type of distribution?”

_____ are determinants of submatrices associated with particular entries in the original square matrix.

A resistor in a certain circuit is specified to have a resistance in the range of 99 ohms to 101 ohms. An engineer obtains two resistors. The probability that both of them meet the specification is 0.30, the probability that exactly one of them meets the specification is 0.60, and the probability that neither of them meets the specifications is 0.10. Let X represent the number of resistors that meet specifications. Find the mathematical expectation of X.

An industrial engineer has found that when she takes a sample of size 5 of a product, 90% of the time there are no defectives in the sample, 3% of the time there is 1 defective, 2% of the time there are 2 defectives, 2% of the time there are 3 defectives, 2% of the time there are 4 defectives, and 1% of the time there are 5 defectives. What is the probability of taking a sample that has at least 3 defectives in the 5?

When f′′(x) > 0, the curve is “concave up”; when f′′(x) < 0, the curve is “concave down”; and when f′′(x) = 0, the curve is _______.

The first 115 Kentucky Derby winners by color of horse were as follows: roan, 1; gray, 4, chestnut, 36; bay, 53; dark bay, 17, and black 4. (You should “bet on the bay”) Which of the following visual displays is most appropriate?

Which of the ff. Are true statements? I. If the sample has variance zero, the variance of the population is zero. II. If the population has variance zero, the variance of the same is also zero. III. If the sample has variance zero, the sample mean and the sample median are equal.

If the poles or zeros are repeated, then the function is said to be having __________ poles or ________ zeros.

What is the ROC of z-transform of finite duration anti-causal sequence?

Three machines A, B and C produce respectively 60%, 30% and 10% of the total number of items of a factory. The percentages of defective output of these machines are respectively2%, 3% and 4%. An item is selected at random and is found defective. Find the probability that the item was produced by machine C.

The unit of ▽ x H is ______.

What gives the cumulative probability that a numerical event will be less than or equal to event X?

A discontinuity that occurs when the curve “breaks” at a particular place and starts somewhere else is called ______.

The partial differential equation ∂u/∂t - k∂²u/∂x² = 0 is a ______.

What is defined as correlation of a signal with itself and is a measure of similarity between a signal and its time delayed version?

A sampling distribution is the probability distribution for which one of the following:

In hypothesis testing, a Type 2 error occurs when:

What are the two types of correlation?

If f(x) = ax❴ + bx² and ab > 0, then:

The expected value of a random variable is the:

The confidence level for a confidence interval for a mean is:

What refers to the process of finding the numerical value of a derivative of a given function at a given point?

(x + y – z)(∂z/∂x) + (3x + 2y)(∂z/∂y) + 2z = x + y is ______.

The equation (2x + 3y)p + 4xq – 8pq = x + y is _______.

The mean square is the sum of squares divided by:

When f′(x) > 0, the curve is rising; when f′(x) < 0, the curve is falling; when f′(x) = 0, the curve is _____.

The ______ of a differential equation is the solution of the differential equation when the input u(t) is identically zero.

What occurs when the curve has a “hole” in it from a missing point because the function has a value at that point that is “off the curve”?

The _____ of a system is the output y(t) of the system when the input u(t) = δ(t) and all initial conditions are zero.

The partial differential equation ∂²u/∂t² - c²(∂²u/∂x² + ∂²u/∂y²) = 0, where c ≠ 0 is known as:

What is used to evaluate a definite integral when there is no closed-form expression for the integral or when the explicit function is not known and the data is available in tabular form only?

The ANOVA procedure is a statistical approach for determining whether or not the:

If two events (both with probability greater than 0) are mutually exclusive, then:

Which of the following is true about the inequality between mean and variance of the Binomial distribution?

In calculus, what is used when you’re given composite functions, that is, a function inside of another function?

A _______ X on a sample space S is a function from S into the set R of real numbers such that the preimage of every interval of R is an event of S.

€�If y = f(x) is continuous on the interval [a, b], and is differentiable everywhere on the interval (a, b) and if f(a) = f(b) = 0, then there is at least one number c between a and b such that f’(c) = 0.” This is known as _____.

What is a branch of mathematics that is concerned with the selection of objects, called elements from a given set of elements?

What refers to the procedure for determining how much of the total variability among scores to attribute to a range of sources of variation and for testing hypotheses concerning some of the sources?

What type of error rejects a true null hypothesis?

What is the method of drawing samples from a population such that every possible sample of a particular size has an equal chance of being selected?

A range of values computed from data so that a specified percentage (often 95%) of all possible random samples from the same population will give intervals that contain the true population value is called ________.

What type of experiment is tossing a coin or rolling a fair die?

What type of skew distribution has its longer tail extends to the left?

_______ probability is one that uses sample spaces

The product of two even signals or two odd signals is a/an _______.

A system is called anticipative if its output at the present time depends on future values of the input. What is another term for this system?

If rise time is also taken into consideration, it should be _____ to the settling time.

The overall transfer function from block diagram reduction for cascaded blocks is:

If the highest power of x in a rational expression is in the numerator, then the limit as x approaches infinity is ______.

What type of discontinuity that occurs when you have a rational expression with common factors in the numerator and denominator?

The integral of dx/cube root (x – 3)² from limits – 24 to 4:

The general solution of the differential equation xdy = ydx is a family of ______.

The general solution of the differential equation dy/dx = (1 – 2x)/y is a family of ______.

The orthogonal trajectories of the family of curves y = cx² are the general equation for a family of ______.

The equation y’ + P(x)y = R(x)y^∞ is ______.

Determine the curl of the vector F(x, y, z) = 3x²i + 7eˣyj.

What is the domain of f(x) = (x – 1)/(x² + 1)?

Let A and B be events with P(A) = 1/2, P(B) = 1/3 and P(A ∝ B) = 1/4. Find P(Aᶜ|Bᶜ).

Given P(A) = 1/4, P(B) = 1/5, P(AUB) = 1/3. Find P(A ∝ B).

Ten samples from a dataset are 92, 78, 82, 93, 95, 99, 93, 91, 90, and 89. Determine the standard deviation.

Let S be the collection of all sets with at most 5 elements. Then:

What is the t-tests (based on Student’s distribution) useful for?

If A and B are both uncountably infinite sets, then A U B could be ______.

What theorem shows that the vector field is uniquely determined by its divergence and curl?

A vector field is solenoidal if its _______ is zero.

The curl of a conservative vector function is ________.

An official of the Environmental Protection Agency estimates that t years from now the level of a particular pollutant in the air will be increasing at the rate of (0.3 + 0.4t) parts per million per year (ppm/yr). According to this estimate, what will be the change in the pollutant level during the second year?

A tank initially contains 50 gal of pure water. A solution containing 2 lb/gal of salt is pumped into the tank at 3 gal/min. The mixture is stirred constantly and flows out at the same rate of 3 gal/min. How much salt is in the tank after a long time?

Suppose a flu-like virus is spreading through a population of 50,000 at a rate proportional both to the number of people already infected and to number of still uninfected. If 100 people were infected yesterday and 130 are infected today, how many people will be infected for the virus to spread the fastest?

If the half-life of a radioactive substance is 8 years, how long will it take, in years, for two thirds of the substance to decay?

Find the integrating factor of (y² - x)dx + 2ydy = 0.

A ladder 3.9 m long is placed in a vertical plane which is at right angle to the vertical wall, the foot of the ladder being on horizontal ground, If the foot of the ladder is pushed towards the wall at 1.8 m/s, at what rate is the top of the ladder ascending the wall when the foot is 1.5 m from the wall?

In a lottery, 10,000 tickets are sold at $1 each with a prize of $7500 for one winner. What is the average result for each bettor?

The differential equation in the form of y’ = P(x)y² + Q(x)y + R(x) is called a/an _____.

Find the volume of the solid generated when the region bounded by the y–axis, y = eˣ, and y = 2 is rotated around the y–axis.

A cylinder with a closed top and bottom is to have a volume of 101in³. If the cost of the material for the circular top and bottom costs three times as much as that for the curved surface, the diameter of the cylinder to minimize cost should be?

The radius r of a sphere is increasing at the uniform rate of 0.3 inches per second. At the instant when the surface area S becomes 100π square inches, what is the rate of increase, in cubic inches per second, in the volume V?

There are 25 calculators in a box. Two of them are defective. Suppose five calculators are randomly picked for inspection (i.e., each has the same chance of being selected). What is the probability that only one of the defective calculators will be included in the inspection?

The volume of a cone of radius r and height h is given by V = (1/3)πr²h. If the radius and the height both increases at a constant rate of ½ cm per second, at what rate, in cu cm per second, is the volume increasing when the height is 9 cm and the radius is 6 cm?

An _______maximum or minimum occurs either at an artificial point or an end point.

A box contains 5 green balls and 4 red balls. The probability of selecting 2 green balls and 1 red ball with a random sample of 3 balls without replacement is:

At a certain instant, car A is 60 miles north of car B. A is travelling south at a rate of 20 mi/h while B is travelling east at 30 mi/h. How fast is the distance between them changing 1 hour later?

An area in Quadrant 1 is bounded by y = x³, x = 2, and the x-axis. What is the volume generated by revolving the area about the y-axis?

A certain metal has a temperature of 75°C and is placed in a room with a temperature of 18°C. After 20 minutes, the temperature of the metal is now 50°C. How long will it take the metal to reach a temperature of 40°C?

The radius of convergence of the power series Σ((-1)❿ (x❿)/(4❿ ln(n)), 2, ∞) is

Solve for the Fourier Transform of the given function f(t) =e^(-a|t|).