The sum of two numbers is 21. the second number is six times the first number.

Math

notka56 [123]

Answer:

Step-by-step explanation:

4.5C

6 0

3 years ago

Read 2 more answers

Integral of ln times cube root x dx

zvonat [6]

If u = ln(x^(1/3))
then by the chain rule
du = [1/x^(1/3)] * (1/3)x^(-2/3) dx = (1/3)(1/x) dx.
You could get there faster by noting that
ln(x^(1/3)) = (1/3) ln(x), so du = (1/3) dx/x

3 0

2 years ago

Which one doesn’t belong? Why? Explain.

tino4ka555 [31]

Answer:

(x - 2)(x + 2)

Step-by-step explanation:

(x - 2)(x + 2) = x² - (2)² [Since (a - b)(a + b) = a² - b²]

= x² - 4

There are two terms in this expression. Therefore, the give term is a binomial.

(2x - 1)(x + 4) = 2x(x + 4) - 1(x + 4) [Distributive property]

= 2x² + 8x - x - 4

= 2x² + 7x - 4

There are three terms in this polynomial. Therefore, the given polynomial is a trinomial.

(x + 4)(x + 1) = x(x + 1) + 4(x + 1)

= x² + x + 4x + 4

= x² + 5x + 4

This polynomial is having 3 terms therefore, it's a trinomial.

(m - 4)(m + 1) = m(m + 1) - 4(m + 1)

= m² + m - 4m - 4

= m² - 3m - 4

Therefore, this polynomial is a trinomial.

Since (x - 2)(x + 2) is a binomial, so this expression doesn't belong to this group.

3 0

2 years ago

I don’t know the answer please help me out

Masteriza [31]

A. 1/3 x 45 < 45
Explanation:
1/3 x 45 is 15, so the comparison is correct because 15 is less than 45.

the rest of the choices are incorrect because:
B. 60 < 60 x 3/4 is wrong because 60 x 3/4 = 45 which is LESS than 60, not greater

C. 20 x 1/5 >20 is wrong because 20 x 1/5 = 4 which is LESS than 20, not greater

D. 25 < 2/3 x 25 is wrong because 2/3 x 25 = 16 2/3 which is LESS than 25, not greater

Have a nice day (brainliest pls tysm!)

5 0

2 years ago

To evaluate the effect of a treatment, a sample is obtained from a population, with a mean of u = 30, and the treatment is admin

Murrr4er [49]

Answer:

a) $t=\frac{31.3-30}{\frac{3}{\sqrt{16}}}=1.733$

$p_v =2*P(t_{15}>1.733)=0.104$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the we don't have a significant effect for the new treatment at 5% of significance.

b) $t=\frac{31.3-30}{\frac{3}{\sqrt{36}}}=2.6$

$p_v =2*P(t_{15}>2.6)=0.0201$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the we have a significant effect for the new treatment at 5% of significance.

c) When we increase the sample size we increse the probability of rejection of the null hypothesis since the z score tend to increase when the sample size increase.

Step-by-step explanation:

Data given and notation

Part a: If the sample consists of n=16 individuals, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with alpha = 0.05.

$\bar X=31.3$ represent the sample mean

$s=3$ represent the sample standard deviation

$n=16$ sample size

$\mu_o =30$ represent the value that we want to test

$\alpha=0.05$ 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 check if the mean is different from 30, the system of hypothesis are :

Null hypothesis: $\mu = 30$

Alternative hypothesis: $\mu \neq 30$

Since we don't know the population deviation, is better apply a z 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:

$t=\frac{31.3-30}{\frac{3}{\sqrt{16}}}=1.733$

P-value

First w eneed to find the degrees of freedom given by:

$df=n-1=16-1 =15$

Since is a two-sided test the p value would given by:

$p_v =2*P(t_{15}>1.733)=0.104$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the we don't have a significant effect for the new treatment at 5% of significance.

Part b: If the sample consists of n=36 individuals, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with alpha = 0.05.

Calculate the statistic

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

$t=\frac{31.3-30}{\frac{3}{\sqrt{36}}}=2.6$

P-value

First w eneed to find the degrees of freedom given by:

$df=n-1=16-1 =15$

Since is a two-sided test the p value would given by:

$p_v =2*P(t_{15}>2.6)=0.0201$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the we have a significant effect for the new treatment at 5% of significance.

Part c; Comparing your answer for parts a and b, how does the size of the sample influence the outcome of a hypothesis test

When we increase the sample size we increse the probability of rejection of the null hypothesis since the z score tend to increase when the sample size increase.

5 0

3 years ago