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2 years ago

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What is the simplified form of the following expression? Assume x not-equals 0. RootIndex 5 StartRoot StartFraction 10 x Over 3

x cubed EndFraction EndRoot

1 answer:

SVEN [57.7K]2 years ago

5 0

Answer:

$\dfrac{\sqrt[5]{810x^3}}{3x}$

Step-by-step explanation:

As a rule, the "simplified form" means there are no fractions under a radical.

$\sqrt[5]{\dfrac{10x}{3x^3}}=\sqrt[5]{\dfrac{10x(3^4x^2)}{3x^3(3^4x^2)}}=\sqrt[5]{\dfrac{810x^3}{(3x)^5}}=\boxed{\dfrac{\sqrt[5]{810x^3}}{3x}}$

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Gunnar’s car gets 22.4 miles per gallon, and his gas tank can hold 17.82 gallons of gas. PART B: Gunnar’s car is close to empty

dedylja [7]

Answer:

399.17 miles

Step-by-step explanation:

Gunnar's car gets 22.4 miles per gallon. His gas tank can hold 17.82 gallons of gas.

Gunnar's car travels with one gallon of gas = 22.4 miles

He can travel with 17.82 gallon of gas = 17.82 × 22.4

= 399.168 ≈ 399.17 miles

Gunnar can travel 399.17 miles if he uses all of the gas in the gas tank.

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2 years ago

Livia’s bill for lunch came to $8 before tax and tip. The restaurant included a 7 percent sales tax, and she left a 15 percent t

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Take 8 times 7% and then take 8 time 15% add those numbers too $8 and you will find your answer. 7% = 7/100 and 15% = 15/100

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2 years ago

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From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that ag

Jlenok [28]

Answer:

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we to reject the null hypothesis, and the the actual mean starting age of smokers is significantly lower than 19.

Step-by-step explanation:

1) Data given and notation

$\bar X=18.1$ represent the mean age when smokers first start to smoke varies

$s=1.3$ represent the standard deviation for the sample

$\sigma=2.1$ represent the population standard deviation

$n=37$ sample size

$\mu_o =5.7$ 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)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the mean starting age is at least 19, the system of hypothesis would be:

Null hypothesis: $\mu\geq 19$

Alternative hypothesis: $\mu < 19$

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-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:

$z=\frac{18.1-19}{\frac{2.1}{\sqrt{37}}}=-2.607$

Calculate the P-value

Since is a one-side lower test the p value would be:

$p_v =P(z$

Conclusion

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we to reject the null hypothesis, and the the actual mean starting age of smokers is significantly lower than 19.

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2 years ago

In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achi

lubasha [3.4K]

Answer:

Shift 2 unit left

Flip the graph about y-axis

Stretch horizontally by factor 2

Shift vertically up by 2 units

Step-by-step explanation:

Given:

Parent function: $f(x)=\log x$

Transformation function: $f(x)=\log(-2x-4)+2$

Take -2 common from transform function f(x)

$f(x)=\log[-2(x+2)]+2$

Now we see the step-by-step translation

$f(x)=\log x$

Shift 2 unit left ( x → x+2 )

$f(x)=\log(x+2)$

Flip the graph about y-axis ( (x+2) → - (x+2) )

$f(x)=\log[-(x+2)]$

Stretch horizontally by factor 2 [ -x(x+2) → -2(x+2) ]

$f(x)=\log[-2(x+2)]$

Shift vertically up by 2 units [ f(x) → f(x) + 2 ]

$f(x)=\log[-2(x+2)]+2$

Simplify the function:

$f(x)=\log(-2x-4)+2$

Hence, Using four step of transformation to get new function $f(x)=\log(-2x-4)+2$

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