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2 years ago

How many three-digit positive integers have at least one prime digit?

Mathematics

1 answer:

ivann1987 [24]2 years ago

7 0

Answer:

210

Step-by-step explanation:

$512=2^9 \\$ has 9 prime factors

Now, if you want to maximize the number of different prime factor, apply the following method: let $p(n)$ be the nth prime number, in increasing order. Let $v$ define as follow : $v(0)=1,v(n+1)=v(n)p(n+1)$ , and find n such that $v(n) < 1000,v(n+1) > 1000$ . n will be the number of factors and v(n) your integer.

$v(1)=2v(0)=2v(2)=3v(1)=6v(3)=5v(2)=30v(4)=7v(3)=210v(5)=11v(4)=2310$

There you are, 210 , with only 4 different prime factors.

→Credits: Xavier Dectot←

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The quotient of 7/8 / 3/8

aleksandr82 [10.1K]

Answer:

7/3

Step-by-step explanation:

Keep Change Flip -KCF (not to be confused with kfc )

7/8 x 8/3

Keep Change Flip in other words, keep the first fraction change from division to multiplication (since multiplication is the opposite of division) and flip the second fraction

8 0

3 years ago

Cylinders A and B are similar solids. The base of cylinder A has a circumference of 4π units. The base of cylinder B has an area

Alex

The formula for the circumference of a circle is
C = 2π·r
or
r = C/(2π)
The radius r of cylinder A is
r = (4π)/(2π) = 2

The formula for the area of a circle is
A = π·r²
or
r = √(A/π)
The radius of cylinder B is
r = √(9π/π) = 3

The dimensions of cylinder A must be multiplied by 3/2 to produce the corresponding dimensions of cylinder B.

4 0

3 years ago

Read 2 more answers

A zookeeper is buying fencing to enclose a pen at the zoo. The pen is an isosceles right triangle. There is already a fence alon

pav-90 [236]

Answer:

He should buy 189.47 feets.

Step-by-step explanation:

Since there's a hypotenuse this triangle is rectangular and since it's an isosceles triangle we know that both cathetus are equal. We were given the area of this triangle, wich is 4500 square feet, the equation to compute this area is A = b*h/2, since the cathetus are equal b = h and we can solve for either of this variables. So we have:

A = b*b/2

4500 = b*b/2

b*b= 9000

b = sqrt(9000) = 94.87 feet

Since the hypotenuse of this triangle already has a fence we only need to buy the fencing for the cathetus, wich should be two times b, since there are two cathetus. So the amount of fence is 2*b = 2*94.87 = 189.74 feets.

5 0

4 years ago

Calculator question.

alexgriva [62]

Answer:

D. [0,pi/2]

Step-by-step explanation:

when Ф = 0 in radian

r²= 4cos (2(0))

r² = 4 * 1

r² = 4

∴ r = √4 = 2

r = 2.

when Ф = π/2 in radian

r²= 4cos (2(π/2))

r² = 4 * -1

r² = -4

∴ r = 0

3 0

3 years ago

Find the midpoint of PQ with endpoints P (-4, 3) and Q (4,-1) . Then write an equation of the line that passes through the midpo

Marianna [84]

Answer:

Equation of the line that passes through the midpoint and is perpendicular to PQ is 2 x - y +1 = 0

Step-by-step explanation:

Step(i):-

Given points are P( -4 ,3 ) and Q ( 4,-1)

Mid -point of PQ

= $(\frac{x_{1} + x_{2} }{2} , \frac{y_{1} + y_{2} }{2} )$

= $(\frac{-4+4}{2} , \frac{3-1}{2} ) = ( 0 , 1 )$

Step(ii):-

Slope of PQ

$m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } = \frac{-1-3}{4+4} = \frac{-4}{8} = \frac{-1}{2}$

The slope of the line is Perpendicular to PQ

$m_{2} = \frac{-1}{m_{1} } = \frac{-1}{\frac{-1}{2} } = 2$

Equation of the line that passes through the midpoint and is perpendicular to PQ

$y - y_{1} = m ( x - x_{1} )$

$y - 1 = 2 ( x - 0 )$

2 x - y +1 = 0

Final answer:-

Equation of the line that passes through the midpoint and is perpendicular to PQ

2 x - y +1 = 0

3 0

3 years ago