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4 years ago

I don’t know where to start on my elementary math class homework!! This needs to be shown full work also!!

Mathematics

1 answer:

leva [86]4 years ago

3 0

Answer:

See explanation

Step-by-step explanation:

1. Number is divisible by 5 if it ends with 0 or 5. Since number 360,142,731 ends with 1, this number is not divisible by 5. Number 360,142,730 is divisible by 5, then the remainder when number 360,142,731 is divided by 5 is 1.

2. Number is divisible by 3 when the sum of its digits is divisible by 3. The sum of digits of number 672,183,012 is

$6+7+2+1+8+3+0+1+2=30,$

then number 672,183,012 is divisible by 3 (thus the remainder is 0).

3. Number is divisible by 6, when it is even and divisible by 3. Number 239,857,293 is not even number because it is not even number. Number 239,857,290 is divisible by 6 (it is even and the sum of its digits is 45 that is divisible by 3), so the remainder when number 239,857,293 is divided by 6 is 1.

4. Number is divisible by 4, when two last digits form number divisible by 4. In number 684,313,540 two last digits form number 40 that is divisible by 4, so number 684,313,540 is divisible by 4 (thus the remainder is 0).

5. Number is divisible by 9 when the sum of its digits is divisible by 9. The sum of digits of number 873,512,436 is

$8+7+3+5+1+2+4+3+6=39,$

then number 873,512,436 is not divisible by 9. Number number 873,512,433 is divisible by 9 (the sum of its digits is 36), then the remainder when number 873,512,436 is divided by 9 is 3.

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A random sample of 384 people in a mid-sized city (city one) revealed 112 individuals who worked at more than one job. A second

Svetlanka [38]

Answer:

99% confidence interval is:

(0.00278 < P1 - P2< 0.15921)

Step-by-step explanation:

For calculating a confidence intervale for the difference between the proportions of workers in the two cities, we calculate the following:

$[(p_{1} - p_{2}) \pm z_{\alpha/2} \sqrt{\frac{p_{1}(1-p_{1})}{n_{1}} + \frac{p_{2}(1-p_{2})}{n_{2}} }$

Where $p_{1}$ : proportion sample of individuals who worked

at more than one job in the city one

$n_{1}$ : Number of respondents in the city one

$p_{1}$ : proportion sample of individuals who worked

at more than one job in the city two

$n_{1}$ : Number of respondents in the city two

Then

α = 0.01 and α/2 = 0.005

and $z_{\alpha/2} = 2.575$

$p_{1} = \frac{112}{384} = 0.2916$

$p_{2} = \frac{91}{432} = 0.2106$

$n_{1}= 384$ and $n_{2}= 432$

The confidence interval is:

$[(0.2916 - 0.2106) \pm 2.575 \sqrt{\frac{0.2916(1-0.2916)}{384} + \frac{0.2106(1-0.2106)}{432} }$

(0.00278 < P1 - P2< 0.15921)

5 0

3 years ago

Find the root of the quadratic equation y=3x^2-30x+45

LuckyWell [14K]

$y=3x^2-30x+45\\\\a=3;\ b=-30;\ c=45\\\Delta=b^2-4ac\\\\\Delta=(-30)^2-4\cdot3\cdot45=900-540=360 \ \textgreater \ 0\\\\therefore\\x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{360}=\sqrt{36\cdot10}=\sqrt{36}\cdot\sqrt{10}=6\sqrt{10}\\\\x_1=\dfrac{30-6\sqrt{10}}{2\cdot3}=\dfrac{30-6\sqrt{10}}{6}=\boxed{5-\sqrt{10}}\\\\x_2=\dfrac{30+6\sqrt{10}}{2\cdot3}=\dfrac{30+6\sqrt{10}}{6}=\boxed{5+\sqrt{10}}$