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3 years ago

If the length, width, and height of a cube all change by a factor of 9, what happens to the volume of the cube?

Mathematics

2 answers:

luda_lava [24]3 years ago

7 0

Answer:

The volume will increase 729 fold.

Step-by-step explanation:

If the length, width, and height of a cube all change by a factor of 9.

The answer is 729 fold, or 9 cubed.

As if original length is l

The original width is w

And original height is h

Volume = l x w x h

But when all change by a factor of 9, we get

9l x 9w x 9h

= 729 fold

Therefore, the volume will increase 729 fold.

solong [7]3 years ago

4 0

the volume will also increase by the factor of 9

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The matrix

$A=\begin{bmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{bmatrix}$

has eigenvalues $\lambda$ such that

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3 years ago

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3 years ago

Create a circle with center A and a radius of your choice. Create a point B on the circle, and find the coordinates of B. Draw t

ser-zykov [4K]

<u>Corrected Question</u>

Create a circle with center A and a radius of your choice. Create a point B on the circle, and find the coordinates of B. Draw the radius AB. What is the slope-intercept form (y = mx + b) of the equation of AB? Show your work.

Answer:

y=0.62x+2

Step-by-step explanation:

In the attached circle drawn using Geogebra

Center is at point A(0,2)
Point B on the circumference has coordinates (1.7,3.05)
Radius of the circle=2 Units

Gradient of AB, $m=\dfrac{y_2-y_1}{x_2-x_1}$ where $(x_1,y_1)=A(0,2)$ and (x_2,y_2)=B(1.7,3.05)$

$m=\dfrac{3.05-2}{1.7-0} \\=\dfrac{1.05}{1.7}\\\\\approx 0.62$

Line AB intercepts the y-axis at y=2, therefore: b=2

The slope-intercept form of the line AB (in this case) is therefore:

y=0.62x+2

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3 years ago

The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3903

polet [3.4K]

Answer:

0.9861 = 98.61% probability that the weight will be less than 4884 grams.

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.

Mean weight of 3903 grams and a standard deviation of 446 grams.

This means that $\mu = 3903, \sigma = 446$

If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 4884 grams.

P-value of z when X = 4884. So

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

$Z = \frac{4884 - 3903}{446}$

$Z = 2.2$

$Z = 2.2$ has a p-value of 0.9861

0.9861 = 98.61% probability that the weight will be less than 4884 grams.

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3 years ago