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2 years ago

F(x) = √3x

Mathematics

1 answer:

Nataly_w [17]2 years ago

4 0

The domain of the function is $(\frac{f}{g})(x) = \frac{\sqrt[3]{3x}}{5x + 2}$ . $x \ne -\frac 25$

<h3>How to determine the domain and the restrictions?</h3>

The attached image represents the complete form of the question

The functions are given as:

$f(x) = \sqrt[3]{3x}$

g(x) = 5x + 2

The function (f/g)(x) is calculated using:

$(\frac{f}{g})(x) = \frac{f(x)}{g(x)}$

This gives

$(\frac{f}{g})(x) = \frac{\sqrt[3]{3x}}{5x + 2}$

The denominator cannot be 0.

So, we have:

$5x + 2 \ne 0$

Solve for x

$x \ne -\frac 25$

Hence, the domain of the function is $(\frac{f}{g})(x) = \frac{\sqrt[3]{3x}}{5x + 2}$ . $x \ne -\frac 25$

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A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies. Random

Yuliya22 [10]

Answer:

b) independent samples t-test

$t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154$

$p_v =2*P(t_{8}>0.154) =0.881$

So with the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).

Step-by-step explanation:

The system of hypothesis on this case are:

Null hypothesis: $\mu_1 = \mu_2$

Alternative hypothesis: $\mu_1 \neq \mu_2$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 = 0$

Alternative hypothesis: $\mu_1 -\mu_2\neq 0$

Our notation on this case :

$n_1 =5$ represent the sample size for group 1

$n_2 =5$ represent the sample size for group 2

We can calculate the mean and deviation for eaach group with the following formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X_1 =5.92$ represent the sample mean for the group 1

$\bar X_2 =5.74$ represent the sample mean for the group 2

$s_1=1.88$ represent the sample standard deviation for group 1

$s_2=1.81$ represent the sample standard deviation for group 2

If we see the alternative hypothesis we see that we are conducting a bilateral test and with independnet samples t test.

b) independent samples t-test

The statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{\sqrt{\frac{s^2_1}{n_1}}+\frac{S^2_2}{n_2}}$

And now we can calculate the statistic:

$t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154$

The degrees of freedom are given by:

$df=5+5-2=8$

And now we can calculate the p value using the altenative hypothesis:

$p_v =2*P(t_{8}>0.154) =0.881$

7 0

3 years ago

Hi everyone! I have a question!

Tju [1.3M]

Answer:

7π

Step-by-step explanation:

SO first find the area of the whole circle

which has a radius of 3

a=πr^2

So 3^2=9

9π

Now the two circles which are the same in area due to having the same radius

so if you plug in the 1 for radius the answer would just be π or 1π

now multiply that by 2 becuase there are 2 identical circles

π*2=2π

Now subtract

9π-2π=7π

3 0

3 years ago

Read 2 more answers

I don’t understand someone help me <br> 4-16=2+5 (s+14)

mel-nik [20]

Answer: s= - 8/5

Step-by-step explanation:

Simplify 4-164−16 to -12−12.

-12=2+5(s+14)

−12=2+5(s+14)

2 Subtract 22 from both sides.

-12-2=5(s+14)

−12−2=5(s+14)

3 Simplify -12-2−12−2 to -14−14.

-14=5(s+14)

−14=5(s+14)

5 0

3 years ago

Read 2 more answers

Which of the following equations is a constant function?<br><br> x = 5<br> y = x<br> y = 5

GalinKa [24]

Answer:

Y=X

Step-by-step explanation:

5 0

3 years ago

What are transformation possible to change f(x) to g(x) on graph linear equation

Korolek [52]

Answer:

<h2>Vertical stretch or compression and vertical shift.</h2>

Step-by-step explanation:

When we talk about the transformation of functions, we can mention stretching, rotating, dilating, shifting. However, when we want to transform linear functions, there are only two transformations that are worthy in that case, those are vertical stretch or compression and vertical shift.

Now, you may ask, why only vertical transformation? the reason behind that is because horizontal transformation would give the exact same result because it's only a straight line which we are transforming.

Another common question would be, why only two transformations? it's because with these two you can get all the results because it's a straight line.

The image attached shows examples of this.

8 0

3 years ago