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love history [14]
3 years ago
14

Specify the domain for the function !!! 10 points - Help needed !

Mathematics
1 answer:
leva [86]3 years ago
5 0
<h2>Hello!</h2>

The answer is:

The domain for the function is all the real numbers,

Domain:(-∞,∞)

<h2>Why?</h2>

Since we are working with fractions, the only restriction that we will have for the function is when the denominator of the function tends to 0.

We are given the function:

f(x)=\frac{1}{x^{2}-5x+25 }

Where, the denominator is given by the expression:

x^{2}-5x+25

For the given expression (quadratic equation), we have that:

a=1\\b=-5\\c=25

Calculating the discriminat of the quadratic function, in order to know if the denominator of the function has roots (zeroes) at the real numbers, we have:

Discriminant=b^{2} -4ac

Discriminant=-5^{2} -4(1)(25)

Discriminant=25 -100=-75

Now, as we know, if the discriminant of a quadratic function is less than 0, the quadratic function has no roots in the real numbers.

Therefore, since the denominator (quadratic function) has no roots in the real numbers, the domain for the function will be equal to all the real numbers.

Domain:(-∞,∞)

Hence, the answer is the third option, the domain for the function is all the real numbers,

Domain:(-∞,∞)

Have a nice day!

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Answer:

The random variable (number of toppings ordered on a large pizza) has a mean of 1.14 and a standard deviation of 1.04.

Step-by-step explanation:

<em>The question is incomplete:</em>

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<em> 0   0.30 </em>

<em>1    0.40 </em>

<em>2   0.20 </em>

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<em>4   0.04</em>

The mean can be calculated as:

M=\sum p_iX_i=0.3\cdot 0+0.4\cdot 1+0.2\cdot 2+0.06\cdot 3+0.04\cdot 4\\\\M=0+0.4+0.4+0.18+0.16\\\\M=1.14

(pi is the probability of each class, Xi is the number of topping in each class)

The standard deviation is calculated as:

s=\sqrt{\sum p_i(X_i-M)^2}\\\\s=\sqrt{0.3(0-1.14)^2+0.4(1-1.14)^2+0.2(2-1.14)^2+0.06(3-1.14)^2+0.04(4-1.14)^2}\\\\s=\sqrt{0.3(-1.14)^2+0.4(-0.14)^2+0.2(0.86)^2+0.06(1.86)^2+0.04(2.86)^2}\\\\ s=\sqrt{0.3(1.2996)+0.4(0.0196)+0.2(0.7396)+0.06(3.4596)+0.04(8.1796)}\\\\s=\sqrt{0.3899+0.0078+0.1479+0.2076+0.3272}\\\\ s=\sqrt{ 1.0804 }\\\\s\approx 1.04

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3 years ago
Segment EF is a mid segment of triangle ABC. If EF = 15 cm, what is the measure of segment BC?
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Answer:

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Step-by-step explanation:

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Isaac invested $77,000 in an account paying an interest rate of 4.6% compounded continuously. Assuming no deposits or withdrawal
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Answer:

132,090.30

Step-by-step explanation:

r = R/100

r = 4.6%/100

r = 0.046 per year,

A = P(1 + r/n)nt

A = 77,000.00(1 + 0.046/1)(1)(12)

A = $ 132,090.30

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An amusment park is insalling a new rollorr coaster. The park intends to charge $5 per adult and $4 per child fo each ride. It h
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so whats the question

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3 years ago
20 POINTS!!!
choli [55]

Hello from MrBillDoesMath!

Answer:

x = 0, 7

Discussion:

f(g(x)) =

f ( x^2-7x) =

1/ ( x^2 - 7x)


The points NOT in the domain are those where the denominator,  x^2 - 7x = 0.

x^2 - 7x   = 0       =>       factor x from each term

x(x-7) = 0            =>        one or both terms must each 0

x = 0 or x =7


Thank you,

MrB


6 0
3 years ago
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