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3 years ago

Is 60,714,298 divisible by 6? YES OR NO HELP ME PLZ!!!!!!

Mathematics

2 answers:

Mariana [72]3 years ago

8 0

The divisibility rule of 6 is that when the given number is divisible by both 2 & 3 then it is also divisible by 6.

$\rule{300pt}{3pt}$

<h3>Let's check with 2 first of all</h3>

$60714298$

It is divisible by 2, Because the last of digit of number is even i.e. 8

<h3>Let's check for 3 now</h3>

$60714298 \\ 6 + 0 + 7 + 1 + 4 + 2 + 9 + 8 = 27 \\ 27 \div 3 = 9$

Yes, It is divisible by 3, Because the sum of digits in the given number is divisible by 3.

The number is divisible by both 2 & 3. Thus, making it divisible by 6 also.

MakcuM [25]3 years ago

3 0

Answer:

Yes it is.

Step-by-step explanation:

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USA Today reported that about 47% of the general consumer population in the United States is loyal to the automobile manufacture

anygoal [31]

Answer: No, It does not indicates that the population proportion of consumers loyal to Chevrolet is more than 47%.

Step-by-step explanation:

Let p denotes the proportion of consumers loyal to Chevrolet.

As per given , we have

$H_0: p=0.47\\\\ H_a: p>0.47$

Since the alternative hypothesis $(H_a)$ is right-tailed so the test would be a right-tailed test.

Also , it is given that ,Chevrolet did a study of a random sample of 1006 Chevrolet owners and found that 490 said they would buy another Chevrolet.

i.e. n = 1006

x= 490

$\hat{p}=\dfrac{490}{1006}=0.487$

Test statistic :

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

, where p=population proportion.

$\hat{p}$ = sample proportion

n= sample size.

i.e. $z=\dfrac{0.487-0.47}{\sqrt{\dfrac{0.47(1-0.47)}{1006}}}=1.08$

P-value (for right-tailed test)= P(z>1.08)=1-P(z≤1.08) [∵P(Z>z)=1-P(Z≤z)]

=1- 0.8599=0.1401 [By z-value table.]

Decision : Since p-value (0.14) is greater than the significance level ( $\alpha=0.01$ ) , it means we are failed to reject the null hypothesis.

Conclusion : We have sufficient evidence to support the claim that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice.

Hence, it does not indicates that the population proportion of consumers loyal to Chevrolet is more than 47%.

7 0

4 years ago

5 (Picture) CONVERGENT AND DIVERGENT SERIES PLEASE HELP!!

ella [17]

Yes, this series converges. We can check using the integral test; we have

$\displaystyle\frac1{25}+\frac1{36}+\frac1{49}+\cdots=\sum_{n=5}^\infty\frac1{n^2}$

and

$\displaystyle\sum_{n=5}^\infty\frac1{n^2}\le\int_5^\infty\frac{\mathrm dx}{x^2}=\frac15$

6 0

3 years ago

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Which of the following statements must be true about the diagram

Dovator [93]

Answer:

D ) x+y=w

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

4 0

3 years ago

Which shows the dilation with a possible scale factor of One-half?

Anvisha [2.4K]

Answer:

Option B

Step-by-step explanation:

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3 years ago

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Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. (Enter your answers using inte

Mashcka [7]

Answer:

f'(x) > 0 on $(-\infty ,\frac{1}{e})$ and f'(x)<0 on $(\frac{1}{e},\infty)$

Step-by-step explanation:

1) To find and interval where any given function is increasing, the first derivative of its function must be greater than zero:

$f'(x)>0$

To find its decreasing interval :

$f'(x)$

2) Then let's find the critical point of this function:

$f'(x)=\frac{\mathrm{d} }{\mathrm{d} x}[6-2^{2x}]=\frac{\mathrm{d} }{\mathrm{d}x}[6]-\frac{\mathrm{d}}{\mathrm{d}x}[2^{2x}]=0-[ln(2)*2^{2x}*\frac{\mathrm{d}}{\mathrm{d}x}[2x]=-ln(2)*2^{2x}*2=-ln2*2^{2x+1\Rightarrow }f'(x)=-ln(2)*2^{2x}*2\\-ln(2)*2^{2x+1}=-2x^{2x}(ln(x)+1)=0$

2.2 Solving for x this equation, this will lead us to one critical point since x' is not defined for Real set, and x'' $=\frac{1}{e}$ ≈0.37 for e≈2.72

$x^{2x}=0 \ni \mathbb{R}\\(ln(x)+1)=0\Rightarrow ln(x)=-1\Rightarrow x=e^{-1}\Rightarrow x\approx 2.72^{-1}x\approx 0.37$

3) Finally, check it out the critical point, i.e. f'(x) >0 and below f'(x)<0.

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3 years ago