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2 years ago

Factor completely 14g^5 - 21g^7

Mathematics

1 answer:

Dennis_Churaev [7]2 years ago

3 0

Answer:

7g^2 (2 - 3g^2

Step-by-step explanation:

First, you have to factor out the GCF

in this case, factor out 7g^5 to get

7g^2 (2 - 3g^2)

At this point you can't factor anymore, so you get

7g^2 (2 - 3g^2)

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Give an example of a 2x2 matrix whose determinant is 13.

elixir [45]

If all your entries are integers, the determinant is also an integer.
For this problem, 1 0
0 13

For this question, you should just fix 3 values and make the 4th value an unknown and solve it.
I hope my answer helped you somehow.

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2 years ago

Read 2 more answers

The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean μ, the act

stealth61 [152]

Answer: 0.2551

Step-by-step explanation:

Given : The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean μ, the actual temperature of the medium, and standard deviation σ.

Significance level : $\alpha=1-0.95=0.05$

The critical z-value for 95% confidence : $z_{\alpha/2}=1.960$ (1)

Since , $z=\dfrac{x-\mu}{\sigma}$ (where x be any random variable that represents the temperature reading from a thermocouple.)

Then, from (1)

$\dfrac{x-\mu}{\sigma}=1.96\\\\ x-\mu=1.96\sigma$ (2)

Also, all readings are within 0.5° of μ,

i.e. $x-\mu$

i.e. $1.96\sigma$ [From (2)]

i.e. $\sigma$

i.e. $\sigma\approx0.2551$

The required standard deviation : $\sigma=0.2551$

3 0

2 years ago

To make lemonade, you used one quart of water, one pint of lemon juice, and 9 ounces of your secret ingredient: honey. How much

WITCHER [35]

To solve this problem you must follow the proccedure shown below:

1. Amount of lemonade in pints:

1 quart of water=2 pints
1 pint of lemon
(9 ounces of honey)(0.0625 pints/1 ounce)=0.56 pints

Total in pints=2 pints+1 pint+0.56 pints
Total in pints=3.56 pints

2. Amount of lemonade in cups:

Total in cups=(3.56 pints)(2 cups/1 pint)
Total in cups=7.12 cups

3. Amount of lemonade in ounces:

Total in ounces=(7.12 cups)(8 ounces/1 cup)
Total in ounces=56.96 ounces

4 0

2 years ago

The ratio of the radii of two similar cylinders is 3:5. The volume of the smaller cylinder is 54pi cubic centimeters. Find the v

8090 [49]

5/3 = 1.66667

1.666666^3=4.6296 (Volume is measured in cubic units)
54x4.6396=250
250 x pi = 250Pi.

8 0

2 years ago

Weight of a rock: In a geology course, students are learning to use a balance scale to accurately weigh rocks. One student plans

statuscvo [17]

Answer:

The student who weighted the rock 5 times has a 95% confidence interval of (25.2, 29.1) which is guaranteed to be more wider (less precise) than the other student who weighted the rock 20 times.

Step-by-step explanation:

What is Confidence Interval?

The confidence interval represents an interval that we can guarantee that the target variable will be within this interval for a given confidence level.

The confidence interval is given by

$CI = \bar{x} + t_{\alpha/2}(\frac{\sigma}{\sqrt{n} } ) \\$

Where $\bar{x}$ is the mean weight $\sigma$ is the standard deviation $t_{\alpha/2}$ is the critical value from t-table and n is the sample size.

The term $t_{\alpha/2}(\frac{\sigma}{\sqrt{n} } )$ is known as margin of error.

As the sample size is decreased the corresponding margin of error increases which results in wider confidence interval which means smaller precision.

The student who weighted the rock 5 times has a 95% confidence interval of (25.2, 29.1) which is guaranteed to be more wider (less precise) than the other student who weighted the rock 20 times.

We can say with 95% confidence that the true mean weight of the rock is within the interval of (25.2, 29.1).

7 0

2 years ago