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babunello [35]
3 years ago
12

What is the greatest common factor of 42a5b3, 35a3b4, and 42ab4?

Mathematics
1 answer:
tiny-mole [99]3 years ago
4 0

For this case we have that by definition, the Greatest Common Factor (GCF) is the largest factor that 2 numbers have in common.

So, we have the following expressions:

42a ^ 5b ^ 3\\35a ^ 3b ^ 4\\42ab ^ 4

We look for the positive integers that divide to 35 and 42 without leaving residue:

42: 1,2,3,6,7,14,21

35: 1,5,7

Thus, the GCF of 42 and 35 is 7

Then, the GCF of the three expressions is:

7ab ^ 3

Answer:

7ab ^ 3

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Write the expression 12 x 4^2 in words
lawyer [7]

Answer and Step-by-step explanation:

Twelve times four squared.

This is how you would write the expression in word format.

<em><u>#teamtrees #PAW (Plant And Water)</u></em>

7 0
3 years ago
A coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that
mafiozo [28]

Answer:

(a) The significance level of the test is 0.002.

(b) The power of the test is 0.3487.

Step-by-step explanation:

We are given that a coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5.

The test rejects the null hypothesis if either 0 or 10 heads are observed.

Let p = <u><em>probability of obtaining head.</em></u>

So, Null Hypothesis, H_0 : p = 0.5

Alternate Hypothesis, H_A : p \neq 0.5

(a) The significance level of the test which is represented by \alpha is the probability of Type I error.

Type I error states the probability of rejecting the null hypothesis given the fact that the null hypothesis is true.

Here, the probability of rejecting the null hypothesis means we obtain the probability of observing either 0 or 10 heads, that is;

            P(Type I error) = \alpha

         P(X = 0/H_0 is true) + P(X = 10/H_0 is true) = \alpha

Also, the event of obtaining heads when a coin is thrown 10 times can be considered as a binomial experiment.

So, X ~ Binom(n = 10, p = 0.5)

P(X = 0/H_0 is true) + P(X = 10/H_0 is true) = \alpha

\binom{10}{0}\times 0.5^{0} \times (1-0.5)^{10-0}  +\binom{10}{10}\times 0.5^{10} \times (1-0.5)^{10-10}  = \alpha

(1\times 1\times 0.5^{10})  +(1 \times 0.5^{10} \times 0.5^{0}) = \alpha

\alpha = 0.0019

So, the significance level of the test is 0.002.

(b) It is stated that the probability of heads is 0.1, and we have to find the power of the test.

Here the Type II error is used which states the probability of accepting the null hypothesis given the fact that the null hypothesis is false.

Also, the power of the test is represented by (1 - \beta).

So, here, X ~ Binom(n = 10, p = 0.1)

1-\beta = P(X = 0/H_0 is true) + P(X = 10/H_0 is true)

1-\beta = \binom{10}{0}\times 0.1^{0} \times (1-0.1)^{10-0}  +\binom{10}{10}\times 0.1^{10} \times (1-0.1)^{10-10}  

1-\beta = (1\times 1\times 0.9^{10})  +(1 \times 0.1^{10} \times 0.9^{0})

1-\beta = 0.3487

Hence, the power of the test is 0.3487.

3 0
3 years ago
A cone has a radius of 5 inches and a height of 10 inches. What is the volume of the cone? Use 3.14 for pi. Round to the nearest
RideAnS [48]

Answer:

261.8 in^3

Step-by-step explanation:

The formula for the volume of a cone is V = (1/3)(base)(height), where "base" is the area of the base.

In this case, with the radius being 5 in and the height 10 in, we get:

V = (1/3)*π*(5 in)^2*(10 in), which simplifies to 261.8 in^3.

8 0
3 years ago
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yanalaym [24]

Answer:

64 for number 1.  Not sure on number 2 sorry.

Step-by-step explanation:

3 0
3 years ago
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What is t²=81. thanks!!
seraphim [82]

Answer:

t= 9, t= -9

Step-by-step explanation:

6 0
3 years ago
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