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2 years ago

There are 4 circles and 6 triangles. What is the simplest ratio of circles to triangles?

Mathematics

1 answer:

KIM [24]2 years ago

6 0

Answer:

2/3

Step-by-step explanation:

Since there are 4 circles and 6 triangles, and they are asking for the ratio of circles to triangles, the fraction would be 4/6

4/6 when divided by two = 2/3 which is the simplest form of the fraction 4/6

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In order for the data in the table to represent a linear function with a rate of change of –8, what must be the value of m? m =

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3 years ago

What is the probability that a randomly selected permutation of the letters A, A, C, C, L, L, O, R, T, U would spell "calculator

kirill [66]

Answer:

See explanation

Step-by-step explanation:

Total number of letters = n! = 10

Permutation for 10 letters = n!

= 10!

= 10*9*8*7*6*5*4*3*2*1

= 3628800

From n letters:

Number of A = 2

Number of C = 2

Number of L = 2

A₁, A₂, C₁, C₂, L₁, L₂, O, R, T, U

Out of 3628800 permutations the word calculator can be spelled as:

C₁ A₁ L₁ C₂ U L₂ A₂ T O R

C₂ A₂ L₂ C₁ U L₁ A₁ T O R

and so on

So total number of different permutations are

(permutation of number of letters) / permutation of (number of As * number of Cs * number of Ls)

= 10! / (2! 2! 2 !)

= 10*9*8*7*6*5*4*3*2*1 / (2*1) (2*1) (2*1)

= 3628800 / 2 * 2 * 2

= 3628800 / 8

= 453600

Hence probability that a randomly selected permutation of the letters A, A, C, C, L, L, O, R, T, U would spell "calculator" is:

1 / total number of different permutations

= 1 / 10! / (2! 2! 2 !)

= 1/453600

= 0.000002

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3 years ago

Make a rational equations with the following requirements

Rufina [12.5K]

Answer:

$f(x)=\dfrac{-50(x-1)(x-2)}{(x-5)(x+5)}$

Step-by-step explanation:

Since f(x) has asymptotes at x = 5 and x = -5, then the denominator of the rational function contains the terms (x - 5) and (x + 5):

$f(x)=\dfrac{?}{(x-5)(x+5)}$

Since f(x) has x-intercepts at x = 2 and x = 1, then the numerator of the rational function contains the terms (x - 2) and (x - 1):

$f(x)=\dfrac{A(x-1)(x-2)}{(x-5)(x+5)}$

Now substitute the point (0, 4) and solve for A:

$f(0)=4\\\\\implies \dfrac{A(0-1)(0-2)}{(0-5)(0+5)}=4\\\\\\\implies -\dfrac{2}{25}A=4\\\\\\\implies A=-50$

So final rational function:

$f(x)=\dfrac{-50(x-1)(x-2)}{(x-5)(x+5)}$

4 0

2 years ago