The tower below is made up of a square pyramid on top of a rectangular prism. What is the

Which equation represents a linear function? Equation 1: y = 2x + 1 Equation 2: y2 = 3x + 1 Equation 3: y = 5x5 − 1 Equation 4:

Andreyy89

Equation 1 represents a linear function.

6 0

3 years ago

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What is the exact volume of a cylinder whose radius is 21 centimeters and whose height is 30 centimeters?

olga nikolaevna [1]

Volume of cylinder
v = πr²
v = 22/7 x 21²
v = 1385.441 cm³

4 0

3 years ago

Prove algebraically that r = 10/2+2sinTheta is a parabola

Xelga [282]

Answer:

$y = - \frac{ 1 }{10} {x}^{2} + \frac{5}{2}$

Step-by-step explanation:

We want to prove algebraically that:

$r = \frac{10}{2 + 2 \sin \theta}$

is a parabola.

We use the relations

${r}^{2} = {x}^{2} + {y}^{2}$

and

$y = r \sin \theta$

Before we substitute, let us rewrite the equation to get:

$r(2 + 2 \sin \theta) = 10$

Or

$r(1+ \sin \theta) = 5$

Expand :

$r+ r\sin \theta= 5$

We now substitute to get:

$\sqrt{ {x}^{2} + {y}^{2} } + y = 5$

This means that:

$\sqrt{ {x}^{2} + {y}^{2} }=5 - y$

Square:

${x}^{2} + {y}^{2} =(5 - y)^{2}$

Expand:

${x}^{2} + {y}^{2} =25 - 10y + {y}^{2}$

${x}^{2} =25 - 10y$

${x}^{2} - 25 = - 10y$

$y = - \frac{ {x}^{2} }{10} + \frac{5}{2}$

This is a parabola (0,2.5) and turns upside down.

4 0

3 years ago

Find the slope of the line that passes through (9,-3) and (9,-8)

miskamm [114]

Answer:

The line has no slope. I hope this helps

7 0

2 years ago

Manufacture of a certain component requires three different machining operations. Machining time for each operation has a normal

tigry1 [53]

Answer:

0.0314 = 3.14% probability that it takes at most 1 hour of machining time to produce a randomly selected component

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Sum of normal variables:

When normal variables are added, the mean is the sum of the means while the standard deviation is the square root of the sum of the variances.

The mean values are 20, 15, and 30 min, respectively:

This means that $\mu = 20 + 15 + 30 = 65$

The standard deviations are 1, 2, and 1.5 min, respectively.

This means that $\sigma = \sqrt{1^2 + 2^2 + 1.5^2} = 2.6926$

What is the probability that it takes at most 1 hour of machining time to produce a randomly selected component?

Mean and standard deviation are in minutes, so this is the pvalue of Z when X = 60.

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

$Z = \frac{60 - 65}{2.6926}$

$Z = -1.86$

$Z = -1.86$ has a pvalue of 0.0314

0.0314 = 3.14% probability that it takes at most 1 hour of machining time to produce a randomly selected component

7 0

2 years ago