Polynomials how do I do these what are the answers ?

For what value of x is the rational expression below undefined? (3x-12)/(9-x)

wolverine [178]

When x=9 the expression is undefined.

That is because any number over 0 is undefined, including 0/0.

8 0

2 years ago

A contractor is required by a county planning department to submit one, two, three, four, or five forms (depending on the nature

Westkost [7]

Answer:

(a) The value of k is $\frac{1}{15}$ .

(b) The probability that at most three forms are required is 0.40.

(c) The probability that between two and four forms (inclusive) are required is 0.60.

(d) $P(y)=\frac{y^{2}}{50} ;\ y=1, 2, ...5$ is not the pmf of y.

Step-by-step explanation:

The random variable Y is defined as the number of forms required of the next applicant.

The probability mass function is defined as:

$P(y) = \left \{ {{ky};\ for \ y=1,2,...5 \atop {0};\ otherwise} \right$

(a)

The sum of all probabilities of an event is 1.

Use this law to compute the value of k.

$\sum P(y) = 1\\k+2k+3k+4k+5k=1\\15k=1\\k=\frac{1}{15}$

Thus, the value of k is $\frac{1}{15}$ .

(b)

Compute the value of P (Y ≤ 3) as follows:

$P(Y\leq 3)=P(Y=1)+P(Y=2)+P(Y=3)\\=\frac{1}{15}+\frac{2}{15}+ \frac{3}{15}\\=\frac{1+2+3}{15}\\ =\frac{6}{15} \\=0.40$

Thus, the probability that at most three forms are required is 0.40.

(c)

Compute the value of P (2 ≤ Y ≤ 4) as follows:

$P(2\leq Y\leq 4)=P(Y=2)+P(Y=3)+P(Y=4)\\=\frac{2}{15}+\frac{3}{15}+\frac{4}{15}\\ =\frac{2+3+4}{15}\\ =\frac{9}{15} \\=0.60$

Thus, the probability that between two and four forms (inclusive) are required is 0.60.

(d)

Now, for $P(y)=\frac{y^{2}}{50} ;\ y=1, 2, ...5$ to be the pmf of Y it has to satisfy the conditions:

$P(y)=\frac{y^{2}}{50}>0;\ for\ all\ values\ of\ y \\$
$\sum P(y)=1$

Check condition 1:

$y=1:\ P(y)=\frac{y^{2}}{50}=\frac{1}{50}=0.02>0\\y=2:\ P(y)=\frac{y^{2}}{50}=\frac{4}{50}=0.08>0 \\y=3:\ P(y)=\frac{y^{2}}{50}=\frac{9}{50}=0.18>0\\y=4:\ P(y)=\frac{y^{2}}{50}=\frac{16}{50}=0.32>0 \\y=5:\ P(y)=\frac{y^{2}}{50}=\frac{25}{50}=0.50>0$

Condition 1 is fulfilled.

Check condition 2:

$\sum P(y)=0.02+0.08+0.18+0.32+0.50=1.1>1$

Condition 2 is not satisfied.

Thus, $P(y)=\frac{y^{2}}{50} ;\ y=1, 2, ...5$ is not the pmf of y.

7 0

2 years ago

The graph of which function passes through (0,3) and has an amplitude of 3?

evablogger [386]

The choices are supposed to be
f(x) = sin x + 3
f(x) = cos x + 3
f(x) = 3 sin x
f(x) = 3 cos x

The amplitude is the value of the numerical coefficient of sin or cos. The only possible answers are
f(x) = 3 sin x
f(x) = 3 cos x

Next, the function must pass through the point (0,3)
3 sin 0 = 0 and
3 cos = 3

Therefore, the answer is
f(x) = 3 cos x

6 0

3 years ago

Read 2 more answers

A password is 4 characters long and must consist of 3 letters and 1 of 10 special characters. If letters can be repeated and the

Ne4ueva [31]

The number of possibilities for constructing the 4 characters long password with specified conditions is given by: Option C: 703,040

<h3>What is the rule of product in combinatorics?</h3>

If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in $p \times q$ ways.

Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.

Thus, doing A then B is considered same as doing B then A

We're specified that:

The password needs to be 4 characters long
It must have 3 letters and 1 of 10 special characters.
Repetition is allowed.

So, each of 3 characters get 26 ways of being 1 letter. (assuming no difference is there between upper case letter and lower case letter).

And that 1 remaining character get 10 ways of being a special character.

So, by product rule, this choice (without ordering) can be done in:

$26 \times 26 \times 26 \times 10 = 175760$ ways.

Now, the password may look like one of those:

L, L, L, S
L, L, S, L
L, S, L, L
S, L, L, L

where S shows presence of special character and L shows presence of letter.

Those 175760 ways are available for each of those four ways.

Thus, resultant number of ways this can be done is:

$175760 \times 4 = 703040$

Thus, the number of possibilities for constructing the 4 characters long password with specified conditions is given by: Option C: 703,040

Learn more about rule of product here:

brainly.com/question/2763785

5 0

1 year ago

What is the least positive integer by which 24 should be divided so that the resulting integer is a perfect square?

Daniel [21]

Answer: divide by 6?

Step-by-step explanation:

What is the least positive integer by which 24 should be divided so that the resulting integer is a perfect square?

If we actually guess and check by dividing by 1, then 2, then 3, then etc. we will get the answer. I tried and divided by 6, which is 4, which is a perfect square. Do not trust me completely on this, for I am not quite sure.

7 0

1 year ago