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Tju [1.3M]
2 years ago
5

Expand (2x-5y)⁷ and find fourth form​

Mathematics
1 answer:
elena55 [62]2 years ago
3 0

Step-by-step explanation:

By binomial theorem,

T(r+1) = nCr * a^(r+1) * b^r

Term 4 = 7C3 * (2x)^4 * (-5y)^3 = 35 * (16x^4) * (-125y^3) = -70000x^4y^3.

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The answer should be 7/10!
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Salvador’s class has collected 88 cans in a food drive. They plan to sort the cans into x bags, with an equal number of cans in
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I believe it’s C, I’m not every sure
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2 years ago
HELP ME PLEASE!
hammer [34]

the answer is B

because 54x 3= 162 x3 = 486x3= 1458x3=4,374x3=13,122x3=39,366x3=118,098x3=354,294

7 0
3 years ago
Consider the question of whether the home team wins more than half of its games in the National Basketball Association. Suppose
spayn [35]

Answer:

0.0037 = 0.37% probability that the home team would win 65% or more of its games in a simple random sample of 80 games

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

The home team therefore wins 50% of its games

This means that p = 0.5

Determine the probability that the home team would win 65% or more of its games in a simple random sample of 80 games

Sample of 80 means that n = 80 and, by the Central Limit Theorem:

\mu = p = 0.65

s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.5*0.5}{80}} = 0.0559

This probability is 1 subtracted by the pvalue of Z when X = 0.65. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.65 - 0.5}{0.0559}

Z = 2.68

Z = 2.68 has a pvalue of 0.9963

1 - 0.9963 = 0.0037

0.0037 = 0.37% probability that the home team would win 65% or more of its games in a simple random sample of 80 games

7 0
2 years ago
Find the value for x. Round your answer to the nearest hundredth. Area of the triangle = 8 ft^2​
zmey [24]

Answer:

x = 3.51

Step-by-step explanation:

Since, formula to determine the area f a triangle is,

Area = \frac{1}{2}(\text{Base})(\text{Height})

     8 = \frac{1}{2}(x + 1)(3x - 7)

16 = x(3x - 7) + 1(3x - 7)

16 = 3x² - 7x + 3x - 7

16 = 3x² - 4x - 7

0 = 3x² - 4x - 23

3x²- 4x - 23 = 0

By quadratic formula,

x = \frac{-b\pm \sqrt{b^{2}-4ac}}{2a}

x = \frac{4\pm \sqrt{(-4)^{2}-4(3)(-23)}}{2(3)}

x = \frac{4\pm \sqrt{292}}{6}

x = \frac{4\pm 17.09}{6}

x = 3.51, -2.18

But the length of sides can't be negative.

Therefore, x = 3.51 will be the answer.

8 0
2 years ago
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