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3 years ago

(3m2 + 8 - 3) + (n + 3) Simplified

Mathematics

1 answer:

RUDIKE [14]3 years ago

3 0

Answer:

$\boxed {3m^{2} + n + 8}$

Step-by-step explanation:

Simplify the following expression:

$(3m^{2} + 8 - 3) + (n + 3)$

-Subtract $3$ from $8$ :

$(3m^{2} + 8 - 3) + (n + 3)$

$3m^{2} + 5 + n + 3$

-Add $5$ and $3$ :

$3m^{2} + 5 + n + 3$

$\boxed {3m^{2} + n + 8}$

Therefore, the final answer is $3m^{2} + n + 8$ .

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3 years ago

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Answer:

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

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

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Step-by-step explanation:

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

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

(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:

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

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Condition 1 is fulfilled.

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Condition 2 is not satisfied.

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