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3 years ago

What is the product? (-2x- 9y2 )(-4x-3)

Mathematics

1 answer:

lara [203]3 years ago

4 0

Answer:

$36xy^2 + 8x^2 + 27y^2 + 6x$

Step-by-step explanation:

Use the FOIL method of multiplying binomials.

First term in each binomial: $-2x * -4x = 8x^2$

Outside terms: $-2x * -3 = 6x$

Inside terms: $-9y^2 * -4x = 36xy^2$

Last term in each binomial: $-9y^2 * -3 = 27y^2$

Now, rearrange the terms correctly. $36xy^2 + 8x^2 + 27y^2 + 6x$

This is our final answer, since it can not be simplified any more.

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3 years ago

According to the Vivino website, the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System i

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Answer:

The null hypothesis is $H_o : \mu = 32.48$

The alternative hypothesis is $H_a : \mu < 32.48$

$t = -1.504$

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Step-by-step explanation:

From the question we are told that

The mean price of is $\mu = \$ 32.48$

The sample size is n = 56

The sample mean is $\= x = \$30.15$

The standard deviation is $\sigma = \$12$

The null hypothesis is $H_o : \mu = 32.48$

The alternative hypothesis is $H_a : \mu < 32.48$

Generally the test statistic is mathematically represented as

$t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }$

=> $t = \frac{30.15 - 32.48 }{\frac{12 }{\sqrt{60} } }$

=> $t = -1.504$

Generally the p-value is mathematically represented as

$p-value = P (t < -1.504 )$

From the z-table

$P(t < -1.504) = 0.066291$

$p-value = 0.066291$

From the value we obtain we see that

$p -value > \alpha$

Then we fail to reject the null hypothesis

Hence there is no sufficient evidence to conclude that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48

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3 years ago