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Makovka662 [10]

3 years ago

6

The mathematical fact: a(b+c) = ab + ac ______________________________

1 answer:

Greeley [361]3 years ago

3 0

Answer:

Distributive law, in mathematics, the law relating the operations of multiplication and addition, stated symbolically, a(b + c) = ab + ac; that is, the monomial factor a is distributed, or separately applied, to each term of the binomial factor b + c, resulting in the product ab + ac.

Step-by-step explanation:

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Suppose that a box contains one fair coin (Heads and Tails are equally likely) and one coin with Heads on each side. Suppose fur

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Using conditional probability, it is found that there is a 0.1 = 10% probability that the chosen coin was the fair coin.

Conditional Probability

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.
$P(A \cap B)$ is the probability of both A and B happening.
P(A) is the probability of A happening.

In this problem:

Event A: Three heads.
Event B: Fair coin.

The probability associated with 3 heads are:

$0.5^3 = 0.125$ out of 0.5(fair coin).
1 out of 0.5(biased).

Hence:

$P(A) = 0.125 + 0.5 = 0.625$

The probability of 3 heads and the fair coin is:

$P(A \cap B) = 0.5(0.125) = 0.0625$

Then, the conditional probability is:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0625}{0.625} = 0.1$

0.1 = 10% probability that the chosen coin was the fair coin.

A similar problem is given at brainly.com/question/14398287

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2 years ago

A researcher compares the effectiveness of two different instructional methods for teaching physiology. A sample of 178 students

xxTIMURxx [149]

Answer:

critical value = 1.645

The 90% confidence interval = ( -22.62, -17.58)

Step-by-step explanation:

Given that:

the sample size $n_1$ = 178

the sample size $n_2$ = 226

the sample mean $\overline x_1$ = 54.4

the sample mean $\overline x_2$ = 74.5

population standard deviation $\sigma_1$ = 18.58

population standard deviation $\sigma_2$ = 9.52

level of significance ∝ = 1 - 0.90 = 0.10

The critical value for $Z_{\alpha/2} = Z _{0.10/2} = Z_{0.005}$ is 1.645

For the construction of our confidence interval, we use 90% since that is used to find the critical value.

∴

The margin of error = $Z \times\sqrt{\dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma_2^2}{n_2}}$

$1.645 \times\sqrt{\dfrac{18.58^2}{178} + \dfrac{9.52^2}{226}}$

$1.645 \times\sqrt{\dfrac{345.2164}{178} + \dfrac{90.6304}{226}}$

$1.645 \times\sqrt{2.34042}$

$\simeq$ 2.52

The lower limit = $( \overline x_1 - \overline x_2) - (M.O.E)$

= ( 54.4-74.5) - (2.52)

= -20.1 - 2.52

= -22.62

The upper limit = $( \overline x_1 - \overline x_2) + (M.O.E)$

= ( 54.4-74.5) + (2.52)

= -20.1 + 2.52

= -17.58

The 90% confidence interval = ( -22.62, -17.58)

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2 years ago

What is 2.5 x 200(what does it equal)

Nastasia [14]

Answer:

500

Step-by-step explanation:

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