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3 years ago

Theoretical probability of drawing an 'N' tile?

Mathematics

1 answer:

Hitman42 [59]3 years ago

7 0

Answer:

238/1250.

Step-by-step explanation:

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8. What is the domain of <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7Bx%5E%7B2%7D%20%2B20x%2B75%7D" id="TexFormula1" title

antiseptic1488 [7]

Answer:

8. Domain: (-∞, -15) ∪ (-15, -5) ∪ (-5, ∞)

9. Domain: [7/13, ∞)

Range: [1, ∞)

Step-by-step explanation:

Question 8

Given rational function:

$f(x)=\dfrac{x}{x^2+20x+75}$

Factor the denominator of the given rational function:

$\implies x^2+20x+75$

$\implies x^2+5x+15x+75$

$\implies x(x+5)+15(x+5)$

$\implies (x+15)(x+5)$

Therefore:

$f(x)=\dfrac{x}{(x+15)(x+5)}$

Asymptote: a line that the curve gets infinitely close to, but never touches.

The function is undefined when the denominator equals zero:

$x+15=0 \implies x=-15$

$x+5=0 \implies x=-5$

Therefore, there are vertical asymptotes at x = -15 and x = -5.

Domain: set of all possible input values (x-values)

Therefore, the domain of the given rational function is:

(-∞, -15) ∪ (-15, -5) ∪ (-5, ∞)

---------------------------------------------------------------------------------

Question 9

Given function:

$f(x)=\sqrt{13x-7}+1$

Domain: set of all possible input values (x-values)

As the square root of a negative number is undefined:

$\implies 13x-7\geq 0$

$\implies 13x\geq 7$

$\implies x\geq \dfrac{7}{13}$

Therefore, the domain of the given function is:

$\left[\dfrac{7}{13},\infty\right)$

Range: set of all possible output values (y-values)

$\textsf{As }\:\sqrt{13x-7}\geq 0$

$\implies \sqrt{13x-7}+1\geq 1$

Therefore, the range of the given function is:

[1, ∞)

8 0

1 year ago

If there are 3 cats and 2 run away how many are left

Len [333]

1 cat is remaining :D

3 0

3 years ago

Nancy's percentile rank on a science test was 78. this means that

lys-0071 [83]

The percentile rank of a certain score is the score percentages in its frequency distribution that are equal to it or lower that it.

This means that:
Nancy's percentile rank on a science test was 78. this means that Nancy equaled or surpassed 78% of all those who took the test.

4 0

3 years ago

Which number can be added to a rational number to explain that the sum of two rational numbers is rational? A) π B) 3 7/8 C) 8 D

Vikki [24]

I believe the answer would be C

6 0

3 years ago

Read 2 more answers

In ∆RST, which side is included between ∠R and ∠S?

Lera25 [3.4K]

Hi there!

Since triangle RST is stated with the sides in order (R is connected to S, which is connected to T, which is then connected to R), the side between R and S is T.

Hope this helps!

3 0

3 years ago

Read 2 more answers