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3 years ago

How to find the missing values ?! I never did this.

Mathematics

1 answer:

Semmy [17]3 years ago

8 0

Answer:

(a, b, c) = (2, -6, 2) or (2, 2, -6)

Step-by-step explanation:

Expand the expression on the right and match coefficients, or factor the expression on the left and match factors.

2x³ -8x² -24x = ax(x +b)(x +c)

2x(x² -4x -12) = ax(x +b)(x +c)

2x(x -6)(x +2) = ax(x +b)(x +c)

In this form, we can match the numbers to get ...

a = 2
b = -6
c = 2

You may recognize that b and c can be interchanged.

_____

Alternate solution

If you expand the expression on the right, you get ...

= ax³ +a(b+c)x² +abcx

This gives you 3 equations:

a = 2
2(b +c) = -8
2bc = -24

This is basically the same factoring problem in another form. You have ...

bc = -12

b+c = -4

The factors of -12 are ...

-12 = 1(-12) = 2(-6) = 3(-4) . . . . . . with sums -11, -4, -1

So, b and c are -6 and 2, in no particular order.

(a, b, c) = (2, -6, 2) or (2, 2, -6)

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Answer:

(a) H₀: μ ≥ 5.70 vs. Hₐ:μ < 5.70

(b) The rejection region is (t₀.₀₁,₉ ≤ -2.821).

(d) The true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

Step-by-step explanation:

A hypothesis test should be conducted to determine that the if the true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

(a)

The hypothesis is:

H₀: The true mean breaking strength of the new bonding adhesive is not less than 5.70 Mpa, i.e. μ ≥ 5.70.

Hₐ: The true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa, i.e. μ < 5.70.

(b)

The alternate hypothesis indicates that the hypothesis test is left-tailed.

The rejection region for the left tailed test will be towards the lower tail of the t-distribution curve.

The significance level of the test is: α = 0.01.

The critical value is:

$t_{\alpha ,(n-1)}=t_{0.01,(10-1)}=t_{0.01,9}$

Use the t-table for the critical value.

$t_{\alpha ,(n-1)}=t_{0.01,9}=-2.821$

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Thus, the rejection region is (t₀.₀₁,₉ ≤ -2.821).

(c)

The test statistic value is:

$t=\frac{\bar x-\mu}{s/\sqrt{n}}$

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The value of the test statistic is -4.33.

(d)

The value of the test is less than the critical value.

$t=-4.33$

This implies that the test statistic lies in the rejection region.

Hence the null hypothesis will be rejected at 1% significance level.

Conclusion:

As the null hypothesis is rejected it can be concluded that the true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

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The conditions required for the t-test for single mean to be valid is:

The data should be continuous.
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3 years ago

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x - 13 = 0
x = 13

x + 2 = 15

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