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4 years ago

Find the product. a^3b^2 • 4ab^3

Mathematics

1 answer:

attashe74 [19]4 years ago

8 0

Answer:

4a^4·b^5

Step-by-step explanation:

The applicable rule of exponents is ...

(x^a)(x^b) = x^(a+b)

The commutative and associative properties of multiplication apply, so we can write the expression as ...

4·(a^3·a)·(b^2·b^3) = 4·a^(3+1)·b^(2+3) = 4·a^4·b^5

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A consumer wanted to compare two types of battery storage. One type is refrigerated and the other is room temperature. It is a c

bearhunter [10]

Answer:

A) Matched pairs design

Step-by-step explanation:

In experimental design, the match pairs experimental design is one that often involves only two treatment conditions; which in this case are the 'refrigerated and the room temperature battery storage types'.

Thus, these two treatment conditions form a matched pair because we are told that 10 fully charged batteries are placed into each type of storage.

5 0

3 years ago

Freida earns $5.25 per hour and time-and-a-half for overtime for all hours over 40 hours. How much did she earn the week she wor

nikdorinn [45]

Answer:

Total earned= $273

Step-by-step explanation:

Giving the following information:

Regular labor hours= $5.25

Overtime labor hours= $5.25*1.5= $7.875

To calculate the total earned, we need to use the following formula:

Regular labor hours= 40*5.25= 210

Overtime labor hours= 8*7.875= 63

Total earned= 210 + 63

Total earned= $273

8 0

3 years ago

Various studies indicate that approximately 11% of the world's population is left handed. You think this number is actually high

Irina-Kira [14]

Answer:

a. H0 : p ≤ 0.11 Ha : p >0.11 ( one tailed test )

d. z= 1.3322

Step-by-step explanation:

We formulate our hypothesis as

a. H0 : p ≤ 0.11 Ha : p >0.11 ( one tailed test )

According to the given conditions

p`= 31/225= 0.1378

np`= 225 > 5

n q` = n (1-p`) = 225 ( 1- 31/225)= 193.995> 5

p = 0.4 x= 31 and n 225

c. Using the test statistic

z= p`- p / √pq/n

d. Putting the values

z= 0.1378- 0.11/ √0.11*0.89/225

z= 0.1378- 0.11/ √0.0979/225

z= 0.1378- 0.11/ 0.02085

z= 1.3322

at 5% significance level the z- value is ± 1.645 for one tailed test

The calculated value falls in the critical region so we reject our null hypothesis H0 : p ≤ 0.11 and accept Ha : p >0.11 and conclude that the data indicates that the 11% of the world's population is left-handed.

The rejection region is attached.

The P- value is calculated by finding the corresponding value of the probability of z from the z - table and subtracting it from 1.

which appears to be 0.95 and subtracting from 1 gives 0.04998

8 0

4 years ago

Plz help with 6,7,8 and 9

Reil [10]

Grayson's mistake was that he multiplied 4 and 3 and then used the exponent he had to square 3 and then multiply it by 4.

Emily's mistake was that she added 2 to 36 instead of multiplying it by -2

Pat's mistake was that he forget to make y into -2 instead of 2

The right way to do this is 4(3^2)+2(-2)
(3^2)=9 9×4=36 2(-2)=-4 -4+9=5

3 0

3 years ago

Make r the subject of the formula <img src="https://tex.z-dn.net/?f=v%20%3D%20%5Cpi%20%5C%3A%20h%20%7B%7D%5E%7B2%7D%28r%20-%

Vaselesa [24]

Answer:

$\boxed{r = \frac{h}{3} + \frac{v}{\pi {h}^{2} } }$

Step-by-step explanation:

$Solve \: for \: r: \\ = > v= \pi {h}^{2}(r - \frac{h}{3} ) \\ \\ v=\pi {h}^{2}(r - \frac{h}{3} )is \: equivalent \: to \: {h}^{2}\pi(r - \frac{h}{3} ) = v: \\ = > {h}^{2}\pi(r - \frac{h}{3} ) = v \\ \\ Divide \: both \: sides \: by \: \pi {h}^{2} : \\ = > r - \frac{h}{3} = \frac{v}{\pi {h}^{2} } \\ \\ Add \: \frac{h}{3} \: to \: both \: sides: \\ = > r = \frac{h}{3} + \frac{v}{\pi {h}^{2} }$

8 0

3 years ago