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2 years ago

Which expression is equivalent to 4^-5 * 4^8

Mathematics

1 answer:

Setler79 [48]2 years ago

8 0

Answer: C

Step-by-step explanation:

$a^{b} \times a^{c}=a^{b+c}$ , so $4^{-5} \times 4^{8}=4^{-5+8}=4^{3}$ .

The only option that is equal to this is C

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Check My Work According to the National Association of Realtors, it took an average of three weeks to sell a home in 2017. Data

Salsk061 [2.6K]

Complete question :

According to the National Association of Realtors, it took an average of three weeks to sell a home in 2017. Suppose data for the sale of 39 randomly selected homes sold in Greene County, Ohio, in 2017 showed a sample mean of 3.6 weeks with a sample standard deviation of 2 weeks. Conduct a hypothesis test to determine whether the number of weeks until a house sold in Greene County differed from the national average in 2017. Useα = 0.05for the level of significance, and state your conclusion

Answer:

H0 : μ = 3

H1 : μ ≠ 3

Test statistic = 1.897

Pvalue = 0.0653

fail to reject the Null ; Hence, we conclude that their is no significant to accept the claim that number I weeks taken to sell a house differs.

Step-by-step explanation:

Given :

Sample size, n = 40

Sample mean, x = 3.6

Population mean, μ = 3

Standard deviation, s = 2

The hypothesis :

H0 : μ = 3

H1 : μ ≠ 3

The test statistic :

(xbar - μ) ÷ (s/√n)

(3.6 - 3) / (2/√40)

0.6 / 0.3162277

Test statistic = 1.897

Using T test, we can obtain the Pvalue from the Test statistic value obtained :

df = n - 1; 40 - 1 = 39

Pvalue(1.897, 39) = 0.0653

Decison region :

If Pvalue ≤ α ; Reject the null, if otherwise fail to reject the Null.

α = 0.05

Pvalue > α ; We fail to reject the Null ; Hence, we conclude that their is no significant to accept the claim that number I weeks taken to sell a house differs.

7 0

3 years ago

Simplify 23x^5 + 26x^5

Margaret [11]

Answer:

49x^5

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Find the magnitude and direction of the vector <3,9>. Round angles to the nearest degree and other values to the nearest t

Katen [24]

Answer:

Magnitude: 3√10

Direction angle: 71.56°

Step-by-step explanation:

The magnitude ||v|| of a vector <a,b>, would be:

$||v||=\sqrt{a^{2}+b^{2}$

$||v||=\sqrt{3^{2}+9^{2}$

$||v||=\sqrt{9+81}$

$||v||=\sqrt{90}$

$||v||=3\sqrt{10}$

The vector's reference angle would be:

$tan\alpha =|\frac{b}{a}|$

$tan\alpha =|\frac{9}{3}|$

$tan\alpha =|3|$

$tan\alpha =3$

$\alpha = 71.56$

If $\alpha$ is your reference angle, then your direction angle ∅ depends on what quadrant the vector is located in. Since <3,9> is located in Quadrant I, then ∅= $\alpha$ , which means your direction angle is also 71.56°

8 0

3 years ago

In the state of Pennsylvania, each standard automobile license plate number consists of three letters followed by a four-digit n

Ann [662]

Answer:

17,576,000

Step-by-step explanation:

From A to Z, there are 26 possible letter characters (L).

From 0 to 9, there are 10 possible numeric characters (N)

If each standard automobile license plate number in Pennsylvania follows the pattern LLLNNNN, the number of license plates that can be formed is:

$n=26*26*26*10*10*10*10\\n=17,576,000$

17,576,000 distinct license plate numbers can be formed in Pennsylvania.

8 0

4 years ago

I am a number less than 100.When you divide me by 2, my remainder is 1. When you divide me by 25, my remainder is 2. What number

Rufina [12.5K]

Well, the number that is divided by 2 that = 1 is 2 and the number divided by 25 that = 2 is 50.
2 / 2 = 1
50/25 = 2.
But idk only one number that works for both situations

3 0

4 years ago