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2 years ago

Simplify the following expression:

Mathematics

2 answers:

Katyanochek1 [597]2 years ago

4 0

Answer:

$\boxed{-3\left(\sqrt{2}-1\right)}$

Step-by-step explanation:

$\left(3\sqrt{3-2\sqrt{2}}\right)\left(\sqrt{3}-2\right)\left(\sqrt{3}+2\right)$

$-3\sqrt{3-2\sqrt{2}}\left(-1\right)$

$-3\sqrt{3-2\sqrt{2}}$

$-3\left(\sqrt{2}-1\right)$

d1i1m1o1n [39]2 years ago

3 0

Answer:

Step-by-step explanation:

$(a + b)(a -b) = a^{2}-b^{2}\\\\\\a = \sqrt{3} \ & \ b = 2\\\\(\sqrt{3}-2)(\sqrt{3}+2)=(\sqrt{3})^{2}-2^{2} \\\\ = 3 - 4\\\\= -1$

$(3\sqrt{3-2\sqrt{2}})(\sqrt{3}-2)(\sqrt{3}+2)=(3\sqrt{3-2\sqrt{2}})*(-1)\\ \ = (-3)\sqrt{3-2\sqrt{2}}$

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3 years ago

Hayden is a manager at a landscaping company. He has two workers to landscape an entire park, Cody and Kaitlyn. Cody can complet

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4 years ago

A random sample of 150 men found that 88 of the men excercise regularly, while a random sample 200 women found that 130 of the w

melamori03 [73]

Answer:

The hypothesis is:

H₀: $p_{X}-p_{Y}=0$ .

Hₐ: $p_{X}-p_{Y}$ .

Step-by-step explanation:

Let X = number of men who exercise regularly and Y = number of women who exercise regularly.

The information provided is:

$n_{X}=150\\X=88\\n_{Y}=200\\Y=130$

Compute the sample proportion of men and women who exercise regularly as follows:

$\hat p_{X}=\frac{X}{n_{X}}=\frac{88}{150}=0.587$

$\hat p_{Y}=\frac{Y}{n_{Y}}=\frac{130}{200}=0.65$

The random variable X follows a Binomial distribution with parameters n = 150 and $\hat p_{X}=0.587$ .

The random variable Y also follows a Binomial distribution with parameters n = 200 and $\hat p_{Y}=0.65$ .

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

$\hat p=p$

The standard deviation of this sampling distribution of sample proportion is:

$\sigma_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}}$

So, the sampling distribution of the proportion of men and women who exercise regularly follows a Normal distribution.

A two proportion z-test cab be performed to determine whether the proportion of women is more than men who exercise regularly.

The hypothesis for this test cab be defined as:

H₀: The proportion of women is same as men who exercise regularly, i.e. $p_{X}-p_{Y}=0$ .

Hₐ: The proportion of women is more than men who exercise regularly, i.e. $p_{X}-p_{Y}$ .

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3 years ago

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Vesnalui [34]

Answer:

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Step-by-step explanation:

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3 years ago

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Rosa has $117 in her savings account and $95 in her checking account. Each week she will put $21 into her savings account and $2

mr_godi [17]

Answer:

It will take Rosa 5 and a half (5.5) weeks to have the same amount of money in both accounts.

Step-by-step explanation:

For this problem, we will have to set two expressions equal to each other. The first expression will represent Rosa's saving account, which already has $117 in it. Every week ( $x$ ), she adds $21 to her savings account:

$21x+117$

The second expression will represent Rosa's checking account. Rosa's checking account already has $95 in it. Every week ( $x$ ), she adds $25 to her checking account:

$25x+95$

Now that we have our two expressions, set them equal to each other. This is our equation that will be used to find the number of weeks ( $x$ ) it takes until Rosha has the same amount of money in both accounts:

$21x+117=25x+95$