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3 years ago

What number is prime 465 822 600 743

Mathematics

2 answers:

pychu [463]3 years ago

3 0

743 u should do the divide by three trick

aliya0001 [1]3 years ago

3 0

I'm going to take your word for it ... that there IS a prime number
in the bunch.

-- 465 ? No. That's a multiple of 5 .

-- 822 ? No. That's an even number ... a multiple of 2.

-- 600 ? No. That's a multiple of 10 and 100, and also an even number.

So if there IS a prime number here, it must be 743 .

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An island is 1 mi due north of its closest point along a straight shoreline. A visitor is staying at a cabin on the shore that i

Elanso [62]

Answer:

The visitor should run approximately 14.96 mile to minimize the time it takes to reach the island

Step-by-step explanation:

From the question, we have;

The distance of the island from the shoreline = 1 mile

The distance the person is staying from the point on the shoreline = 15 mile

The rate at which the visitor runs = 6 mph

The rate at which the visitor swims = 2.5 mph

Let 'x' represent the distance the person runs, we have;

The distance to swim = $\sqrt{(15-x)^2+1^2}$

The total time, 't', is given as follows;

$t = \dfrac{x}{6} +\dfrac{\sqrt{(15-x)^2+1^2}}{2.5}$

The minimum value of 't' is found by differentiating with an online tool, as follows;

$\dfrac{dt}{dx} = \dfrac{d\left(\dfrac{x}{6} +\dfrac{\sqrt{(15-x)^2+1^2}}{2.5}\right)}{dx} = \dfrac{1}{6} -\dfrac{6 - 0.4\cdot x}{\sqrt{x^2-30\cdot x +226} }$

At the maximum/minimum point, we have;

$\dfrac{1}{6} -\dfrac{6 - 0.4\cdot x}{\sqrt{x^2-30\cdot x +226} } = 0$

Simplifying, with a graphing calculator, we get;

-4.72·x² + 142·x - 1,070 = 0

From which we also get x ≈ 15.04 and x ≈ 0.64956

x ≈ 15.04 mile

Therefore, given that 15.04 mi is 0.04 mi after the point, the distance he should run = 15 mi - 0.04 mi ≈ 14.96 mi

$t = \dfrac{14.96}{6} +\dfrac{\sqrt{(15-14.96)^2+1^2}}{2.5} \approx 2..89$

Therefore, the distance to run, x ≈ 14.96 mile

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Jean can pack 5 cartons in 15 minutes. Which expression can be used to show the number of cartons Jean can pack in x hours? Grou

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Step-by-step explanation:

First we should note that 60 minutes = 1 hour. Therefore, 15 minutes = 15/60 = 1/4 hour

Since Jean can pack 5 cartons in 1/4 hours, the number of carton that he can pack in one hour will be:

= 5 ÷ 1/4

= 5 × 4

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Therefore, to get the number of cartons that Jean can pack in x hours, we will multiply 20 by x. This will be:

= 20 × x

= 20x

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