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3 years ago

Which of the following expressions is equivalent to the one shown below (3/2)^8

Mathematics

1 answer:

vichka [17]3 years ago

8 0

Option B is the right answer

Step-by-step explanation:

Given expression is:

$(\frac{3}{2})^8$

The exponent properties are used to solve these type of questions,

One of the property states that if an exponent is applied to a fraction, it can be applied to the numerator and denominator separately.

so,

for the given expression, the exponent 8 will be applied to 2 and 3 separately

$(\frac{3}{2})^8 = \frac{3^8}{2^8}$

Hence,

Option B is the right answer

Keywords: Exponents, fractions

Learn more about exponents at:

#LearnwithBrainly

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A new centrifugal pump is being considered for an application involving the pumping of ammonia. The specification is that the fl

cricket20 [7]

Answer:

1) We need to conduct a hypothesis in order to check if the true mean is higher than 5 gpm, the system of hypothesis would be:

Null hypothesis: $\mu \leq 5$

Alternative hypothesis: $\mu > 5$

2) $df=n-1=8-1=7$

Since is a one sided test the p value would be:

$p_v =P(t_{(7)}>2.233)=0.0304$

3) For this case is we use a significance level of 1% or 99% of confidencewe see that $p_v >\alpha$ and we don't have enough evidence to conclude that the specification is satified. But if we use a value of significance $\alpha=0.05$ or 95% of confidence we see that $p_v$ and we have enough evidence to conclude that the specification is satisfied.

Step-by-step explanation:

Data given and notation

$\bar X=6.5$ represent the sample mean

$s=1.9$ represent the sample standard deviation

$n=8$ sample size

$\mu_o =5$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

Part 1: State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is higher than 5 gpm, the system of hypothesis would be:

Null hypothesis: $\mu \leq 5$

Alternative hypothesis: $\mu > 5$

If we analyze the size for the sample is <30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{6.5-5}{\frac{1.9}{\sqrt{8}}}=2.233$

Part 2: P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=8-1=7$

Since is a one sided test the p value would be:

$p_v =P(t_{(7)}>2.233)=0.0304$

Part d: Conclusion

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant higher compared to the height of men in 1960 at 1% of signficance.

Part 3

For this case is we use a significance level of 1% or 99% of confidencewe see that $p_v >\alpha$ and we don't have enough evidence to conclude that the specification is satified. But if we use a value of significance $\alpha=0.05$ or 95% of confidence we see that $p_v$ and we have enough evidence to conclude that the specification is satisfied.

4 0

3 years ago

What's the Estimate of 615-342

Alekssandra [29.7K]

The estimate is 273
615-342=273

4 0

3 years ago

Glamour runs 2/3 mile each day she wants to know how many days she has to run before she has run a whole number of miles

Gelneren [198K]

Hello!

2/3 × 1 = 2/3

2/3 × 2 = 4/3 (or 1 1/3)

2/3 × 3 = 2

You can also convert 2/3 to a decimal by dividing the numerator by the denominator and then multiply that to get a whole number.

ANSWER:

Glamour will have to run for 3 days to run a whole number of miles. The whole number is 2.

7 0

3 years ago

Complete the problem <br> 5/10 + 8/100 =

12345 [234]

29/50 or 0.58 is the answer

4 0

3 years ago

One of the wagers in roulette is to bet that the ball will stop on a number that is a multiple of 3. (Both 0 and 00 are not incl

Arlecino [84]

Answer:

The players expectation is -0.1052

Step-by-step explanation:

Consider the Roulette numbers to from 1-36, also the two green zeroes 0 and 00,

Thus, there are 38 places on which the ball can land.

On first 36 numbers, 12 of them are divisible by 3. Also there are 26 numbers which are not divisible by 3.

The probability of a wager winning is: 12/38 or 6/19

Now the probability of a wager to loss is: 26/38 or 13/19

So for a 6/19 chance of winning $4 and a 13/19 chance of losing $2.

Therefore, the expected outcome is:

4 × 6/19 + -2 × 13/19 = 1.2632 - 1.3684 = -0.1052

The expected value comes up with a negative sign. Hence, he will lose money.

The players expectation is -0.1052

8 0

3 years ago