Which sets of measurements could be the interior angle measures of a triangle?

How do you find the parameterization of a helix?

Marina CMI [18]

Answer:

$\left\{\begin{array}{l}x=r\cos t\\ \\ y=r\sin t\\ \\z=at\end{array}\right.$

Step-by-step explanation:

A <u>helix</u> is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not directly above the other) is a fractional turn of a helix, as can be seen by cutting the cylinder along one of its sides, flattening it out, and noting that a straight line connecting the points becomes helical upon re-wrapping (see attached diagram for helix).

The parametrization for the helix is

$\left\{\begin{array}{l}x=r\cos t\\ \\ y=r\sin t\\ \\z=at\end{array}\right.,$

where $r$ is the radius of the helix, $a$ is the constant, and $t\in [0,2\pi )$ is the parameter

7 0

3 years ago

Which modified box plot represents the data set? 10, 12, 2, 4, 24, 2, 7, 7, 9

Ratling [72]

The fourth option is the answer. When graphed, Min is 2, Q1 is 3, Median is 7, Q3 is 11, and Max is 24. The fourth option is the one that follow all of those!

7 0

2 years ago

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The amount of time all students in a very large undergraduate statistics course take to complete an examination is distributed c

Anestetic [448]

Answer:

a) The mean is $\mu = 60$

b) The standard deviation is $\sigma = 9$

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The probability a student selected at random takes at least 55.50 minutes to complete the examination equals 0.6915.

This means that when X = 55.5, Z has a pvalue of 1 - 0.6915 = 0.3085. This means that when $X = 55.5, Z = -0.5$

So

$Z = \frac{X - \mu}{\sigma}$

$-0.5 = \frac{55.5 - \mu}{\sigma}$

$-0.5\sigma = 55.5 - \mu$

$\mu = 55.5 + 0.5\sigma$

The probability a student selected at random takes no more than 71.52 minutes to complete the examination equals 0.8997.

This means that when X = 71.52, Z has a pvalue of 0.8997. This means that when $X = 71.52, Z = 1.28$

So

$Z = \frac{X - \mu}{\sigma}$

$1.28 = \frac{71.52 - \mu}{\sigma}$

$1.28\sigma = 71.52 - \mu$

$\mu = 71.52 - 1.28\sigma$

Since we also have that $\mu = 55.5 + 0.5\sigma$

$55.5 + 0.5\sigma = 71.52 - 1.28\sigma$

$1.78\sigma = 71.52 - 55.5$

$\sigma = \frac{(71.52 - 55.5)}{1.78}$

$\sigma = 9$

$\mu = 55.5 + 0.5\sigma = 55.5 + 0.5*9 = 55.5 + 4.5 = 60$

Question

The mean is $\mu = 60$

The standard deviation is $\sigma = 9$

6 0

2 years ago

Need help ASAP !!!!!!!

Anestetic [448]

First we distribute $\frac{1}{5}$ into $n$ and $-\frac{1}{7}$ .

$\frac{1}{5} * n = \frac{1}{5} n$
$\frac{1}{5} * -\frac{1}{7} = - \frac{1}{35}$

That makes the left side of the equation

$\frac{1}{5} n - \frac{1}{35} = \frac{1}{6} n$

Now we subtract $\frac{1}{5}n$ from $\frac{1}{6} n$ , which makes $\frac{1}{30}$

Now the equation is

$-\frac{1}{35} = -\frac{1}{30n}$

Our goal is to isolate $n$ , so we both sides by 30

$30* -\frac{1}{35} = - \frac{1}{30}n * 30$

That will make the equation

$- \frac{30}{35} = -n$

We multiply -1 on both sides of the equation:

$\frac{30}{35} = n$

Finally we simplify $\frac{30}{35}$ , which makes $\frac{6}{7}$

So the answer is $n = \frac{6}{7}$

5 0

2 years ago

A pet store has 15 birds and 75 fish.

Ludmilka [50]

Answer:

1/5

Step-by-step explanation:

6 0

2 years ago

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