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3 years ago

Write the expression as a product of expressions.

Mathematics

1 answer:

scoray [572]3 years ago

8 0

Answer:

$a^2(ab^{3}-b^{2}-c^{2})$

Step-by-step explanation:

Given

$a^{3}b^{3}-a^{2}b^{2}-a^{2}c^{2}$

Required

Factor

$a^{3}b^{3}-a^{2}b^{2}-a^{2}c^{2}$

Factor out $a^2$

$a^2(ab^{3}-b^{2}-c^{2})$

The expression cannot be further factored

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A pole is used to support an observation platform. The top of the pole is secured by two guy wires, one 18 and the other 21 feet

Harman [31]

Let $A$ be the point on the ground to with the 18 foot guy is anchored and $D$ the point on the ground to with the 21 foot guy is anchored.

We can conclude that the the two wires at the points where they are anchored are 21 feet apart. Check the procedures in the picture attached.

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3 years ago

The nutrition label for Oriental Spice Sauce states that one package of sauce has 1100 milligrams of sodium. To determine if the

lora16 [44]

Answer:

We conclude that the sodium content is same as what the nutrition label states.

Step-by-step explanation:

We are given that the nutrition label for Oriental Spice Sauce states that one package of sauce has 1100 milligrams of sodium.

The FDA randomly selects 40 packages of Oriental Spice Sauce and determines the sodium content. The sample has an average of 1088.64 milligrams of sodium per package with a sample standard deviation of 234.12 milligrams.

Let $\mu$ = average sodium content.

So, Null Hypothesis, $H_0$ : $\mu$ = 1100 milligrams {means that the sodium content is same as what the nutrition label states}

Alternate Hypothesis, $H_A$ : $\mu$ $\neq$ 1100 milligrams {means that the sodium content is different from what the nutrition label states}

The test statistics that would be used here One-sample t test statistics as we don't know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}$ ~ $t_n_-_1$

where, $\bar X$ = sample average sodium content = 1088.64 milligrams

s = sample standard deviation = 234.12 milligrams

n = sample of packages of Oriental Spice Sauce = 40

So, test statistics = $\frac{1088.64-1100}{\frac{234.12}{\sqrt{40}}}$ ~ $t_3_9$

= -0.307

The value of z test statistics is -0.307.

Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 0.05 significance level the t table gives critical values of -2.0225 and 2.0225 at 39 degree of freedom for two-tailed test.

Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the sodium content is same as what the nutrition label states.

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4 years ago

Which is the slope of the line y=−3x+2?y=-3x+2?

Morgarella [4.7K]

The slope is -3.
Finding slope can be easy if you just remember that the formula is set up as y=mx+b.
The number in the 'm' place is always the slope.
Example: y=4x+1, the slope would be 4 because it's in the 'm' place.
If you have trouble remembering which place the slope is, trying thinking about skiing or sledding; you can only sled or ski down a Mountain slope. Mountain starts with M.
M=slope.
Hope this helps :)
If you have any questions, just let me know!

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3 years ago

How to calculate the rise and run of a slope (4,-1) and (-2,3)

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