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3 years ago

12

A bag contains 5 blue, 3 red, 6 green, 9 orange, and 20 black marbles. What is the ratio of the number of blue marbles to the nu

mber of marbles that are orange or green?

2 answers:

Zigmanuir [339]3 years ago

5 0

Answer:the answer is C

Step-by-step explanation:there are 5 blue marbles then you add 6 green and 9 orange, that makes 15 so your answer is 5 to 15

barxatty [35]3 years ago

4 0

Answer:

C

Step-by-step explanation:

blue+green=15

blue is 5

5 to 15

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The guide on a tour bus is giving a lecture to the 72 passengers about the historical sites they are passing. The passengers con

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There are 72 passengers in total and 35 are men and women as one category.

The number of children are 72 - 35 = 37

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So the success is 37 (number of children. And the total number of people is 72.

The probability of a child being asked is 37/72.

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3 years ago

The volume of a cone is 196π ft ^3 . It's radius is 7 ft. Find the height.

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Step-by-step explanation:

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3 years ago

Find the equation of a line in slope-intercept form, containing the points (9,2.6) and (8,2.2).

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3 years ago

Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .

kogti [31]

Answer:

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if $(x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}$ . From statement, we must fulfill the following identity:

$a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}$

By Associative and Commutative properties, we can reorganize the expression as follows:

$a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}$ (1)

Then, we have the following system of equations:

$x = a$ (2)

$(b^{2}-1) = 2\cdot x\cdot y$ (3)

$y = c$ (4)

By (2) and (4) in (3), we have the following expression:

$(b^{2} - 1) = 2\cdot a \cdot c$

$b^{2} = 1 + 2\cdot a \cdot c$

$b = \sqrt{1 + 2\cdot a\cdot c}$

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, $a, b, c > 1$ . If $a$ , $b$ and $c$ are prime numbers, then $2\cdot a\cdot c$ must be an even composite number, which means that $a$ and $c$ can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.

In addition, $b$ must be a natural number, which means that:

$1 + 2\cdot a\cdot c \ge 4$

$2\cdot a \cdot c \ge 3$

$a\cdot c \ge \frac{3}{2}$

But the lowest possible product made by two prime numbers is $2^{2} = 4$ . Hence, $a\cdot c \ge 4$ .

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Example: $a = 2$ , $c = 2$

$b = \sqrt{1 + 2\cdot (2)\cdot (2)}$

$b = 3$

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3 years ago

How do I graph y=0.17x?

Tomtit [17]

Answer: you can use desmos and type it in just like that a graph will pop up. Go to google and type in desmos

Step-by-step explanation:

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3 years ago