Gary got on the Ferris wheel at the amusement park at 2:40 P.M. It went around many times and finally let him off at 3:16 P.M. How long was Gary on the ride?

Answer:

A point travels East 3 spaces and South 8 spaces.

Algebraic equation

Step-by-step explanation:

From the viewpoint of Linear Algebra, the description can be described by means of translation, which is defined as:

(1)

Where:

- Initial position of the traveller, dimensionless.

- Translation vector, dimensionless.

- Final position of the traveller, dimensionless.

Let suppose that represents the number of steps to the north, and , the number of steps to the east.

If we know that and , then the resulting equation is:

Answer:

The error bound is 3.125%.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence interval , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

For this problem, we have that:

A sample of 506 California adults.. This means that .

76% of California adults (385 out of 506 surveyed) feel that education is one of the top issues facing California. This means that

We wish to construct a 90% confidence interval

So , z is the value of Z that has a pvalue of , so .

The lower limit of this interval is:

The upper limit of this interval is:

The error bound of the confidence interval is the division by 2 of the subtraction of the upper limit by the lower limit. So:

The error bound is 3.125%.

Answer:

We can therefore conclude that the geographical distribution of hotline callers could be the same as the U.S population distribution.

Step-by-step explanation:

The null Hypothesis: Geographical distribution of hotline callers could be the same as the U.S. population distribution

Alternative hypothesis: Geographical distribution of hotline callers could not be the same as the U.S. population distribution

The populations considered are the Midwest, South, Northeast, and west.

The number of categories, k = 4

Number of recent calls = 200

Let the number of estimated parameters that must be estimated, m = 0

The degree of freedom is given by the formula:

df = k - 1-m

df = 4 -1 - 0 = 3

Let the significance level be, α = 5% = 0.05

For  α = 0.05, and df = 3,

from the chi square distribution table, the critical value = 7.815

Observed and expected frequencies of calls for each of the region:

Northeast

Observed frequency = 39

It contains 18.1% of the US Population

The probability = 0.181

Expected frequency of call = 0.181 * 200 = 36.2

Midwest

Observed frequency = 55

It contains 21.9% of the US Population

The probability = 0.219

Expected frequency of call = 0.219 * 200 =43.8

South

Observed frequency = 60

It contains 36.7% of the US Population

The probability = 0.367

Expected frequency of call = 0.367 * 200 = 73.4

West

Observed frequency = 46

It contains 23.3% of the US Population

The probability = 0.233

Expected frequency of call = 0.233 * 200 = 46

Where observed frequency

Expected frequency

Calculate the test statistic value, x²

Since the test statistic value, x²= 5.535 is less than the critical value = 7.815, the null hypothesis will not be rejected, i.e. it will be accepted. We can therefore conclude that the geographical distribution of hotline callers could be the same as the U.S population distribution.  

Answer:

Ascend

Step-by-step explanation:

In order to solve this problem, we are going to use some principles of vector calculation. The concepts we are going to use are Partial derivatives, gradient vector, velocity vector, direction vector, and directional derivative.

The gradient vector is a vector that describes how is the 'slope' in the space of a multivariable function at a specified point; it is built as a vector of partial derivatives. The vector velocity is a vector that describes the direction and speed of the movement of a body, if we make the velocity a unitary vector (a vector whose norm is 1), we obtain the direction vector (because we are not considering the real norm of the vector, just direction). Finally, the directional derivative is a quantity (a scalar) that describes the slope that we get on a function if we make a displacement from a particular point in a specific direction.  

The problem we have here is a problem where we want to know how will be the slope of the hill if we stand in the point (120, 80, 764) and walk due south if the hill has a shape given by z=f(x,y). As you see, we have to find the directional derivative of z=f(x,y) at a specific point (120, 80, 764) in a given displacement direction; this directional derivative will give us the slope we need. The displacement direction 'u' is (0,-1): That is because 'y' axis points north and our displacement won't be to the east either west (zero for x component), just to south, which is the opposite direction of that which the y-axis is pointing (-1 for y component). Remember that the direction vector must be a unitary vector as u=(0,-1) is.

Let's find the gradient vector:

Evaluate the gradient vector at (120,80) (764 is z=f(120,80); you may confirm)

Finally, find the directional derivative; if you don't remember, it can be found as a dot product of the gradient vector and the direction vector):

As you see, the slope we find is positive, which means that we are ascending at that displacement direction.