Factorise fully the following: a) x² + 3x b) 2x? - 8x c) 6x + 9x d) 12x - 4x?

Mathematics

1 answer:

Talja [164]3 years ago

6 0

Answer:

a) $x(x+3)$

b) $2x(x-8)$

c) $3x(2+3x^{2})$

d) $4x^{2} (3x-1)$

Step-by-step explanation:

a) $x^{2} +3x=x(x+3)$

b) $2x^{2} -8x=2x(x-8)$

c) $6x+9x^{3} =3x(2+3x^{2})$

d) $12x^{3} -4x^{2} =4x^{2} (3x-1)$

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Consider the following hypothesis test:H0: 20Ha: < 20A sample of 60 provided a sample mean of 19.6. The population standard d

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Answer:

a: z = -1.936

b: 0.0265

d: z < -1.645

Reject H0 if z < -1.645

Step-by-step explanation:

We are given:

H0: µ = 20

HA: µ < 20

n = 60, sample mean: 19.6, σ = 1.6

Since the alternate hypothesis has a < sign in it, it is a left tailed test. The < or > sign in the alternate hypothesis points towards the rejection region.

For a: We need to calculate the test statistic for our situation. This is done with a z-score formula for samples.

For b: we need to use the z-score table to look up the p-value for the score we calculate in part a. The p-value is 0.0265. This means that there is only about a 2.65% chance that the sample values were a result of random chance.

For d: Since the significance level is 0.05, and this is a one tailed test, we have a critical value of z < - 1.645. This means that if the z-score we calculate in part a is less than -1.645, we will reject the null hypothesis

See attached photo for all the calculations!