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Karo-lina-s [1.5K]
3 years ago
10

Factor the expression 4b4 − 144 using the polynomial identity (x2 − y2) = (x − y)(x + y).

Mathematics
2 answers:
sladkih [1.3K]3 years ago
6 0
4b^4=(2b^2)^2
144=(12)^2

(2b^2)^2-(12)^2=(2b^2-12)(2b^2+12)
Masteriza [31]3 years ago
3 0
So we need a perfect square. The "O" and "I" values in the FOIL method will cancel leaving you with an exponent and a negative integer. Look for the square root of both expressions.

4b^4 - 144 =
(2b^2 - 12)(2b^2 + 12)
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The objective is to study whether there is a greater force after impacting on one- handed backhand drive in advanced tennis players than in intermediate tennis players.

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Assuming that both variables have a normal distribution and both population variances are equal, to compare these two populations is best to do so trough their population means using a t-test for independent samples.

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t= \frac{(X_[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}

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t_{H_0}= \frac{(40.29-21.40)-0}{9.66\sqrt{\frac{1}{6} +\frac{1}{8} } } = 3.62

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The p-value for this test is 0.00024, it is less than the level of significance, so the decision is to reject the null hypothesis.

This means that at a 5% significance level you can conclude that the average force experienced on the hand after a one-handed backhand drive for advanced players is greater than the average force experienced on the hand after a one-handed backhand drive for intermediate players.

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