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3 years ago

4 nail polishes for $8.50 as a rate

Mathematics

2 answers:

Taya2010 [7]3 years ago

8 0

Answer:

Come one! Who actually knows this l bozo

Step-by-step explanation:

erik [133]3 years ago

7 0

8.50/4=2.13 per unit

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The Alvin Secretarial Service procures temporary office personnel for major corporations. They have found that 60% of their invo

Hoochie [10]

Answer:

0.9942 = 99.42% probability that at least 6 of the invoices will be paid within ten working days

Step-by-step explanation:

For each invoice, there are only two possible outcomes. Either they are paid within 10 working days, or they are not. The probability of an invoice being paid within 10 working days is independent of other invoices. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

60% of their invoices are paid within ten working days.

This means that $p = 0.6$

A random sample of 18 invoices is checked.

This means that $n = 18$

What is the probability that at least 6 of the invoices will be paid within ten working days?

Either less than 6 are paid within 10 working days, or at least 6 are paid. The sum of the probabilities of these events is 1. So

$P(X < 6) + P(X \geq 6) = 1$

We want $P(X \geq 6)$ . So

$P(X \geq 6) = 1 - P(X < 6)$

In which

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$

Then

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{18,0}.(0.6)^{0}.(0.4)^{18} \approx 0$

$P(X = 1) = C_{18,1}.(0.6)^{1}.(0.4)^{17} \approx 0$

$P(X = 2) = C_{18,2}.(0.6)^{2}.(0.4)^{16} \approx 0$

$P(X = 3) = C_{18,3}.(0.6)^{3}.(0.4)^{15} = 0.0002$

$P(X = 4) = C_{18,4}.(0.6)^{4}.(0.4)^{14} = 0.0011$

$P(X = 5) = C_{18,5}.(0.6)^{5}.(0.4)^{13} = 0.0045$

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0 + 0 + 0 + 0.0002 + 0.0011 + 0.0045 = 0.0058$

Finally

$P(X \geq 6) = 1 - P(X < 6) = 1 - 0.0058 = 0.9942$

0.9942 = 99.42% probability that at least 6 of the invoices will be paid within ten working days

6 0

3 years ago

Neela is making rectangular place mats that are 12 inches wide and 15 inches long. What is the least amount of ribbon that she w

schepotkina [342]

Believe it or not, :), the width of the ribbon needs to be known to get the right answer. If the ribbon had an infinitely small width the ribbon needed would just be the perimeter.

P=2(L+W)

P=2(12+15)

P=54 in

However an infinitely small width is not something that has any practical application. For example, if the width of the ribbon were 1/2 in.

P=2((L+1)+W)

P=2(16+12)

P=56 in So the perimeter increased by 2 in when the ribbon was only 1/2 in wide.

The "infinitely small" width and the perimeter of 54 in is only a decent approximation if the ribbon were a very thin string.

8 0

4 years ago

Given the expression: 3x10 − 48x2

BartSMP [9]

Factorization involves representing an expression with smaller terms.

When the greatest common factor is factored out, the equivalent expression is: $3x^2(x^8 - 16)$ .
The complete factored expression is: $3x^2(x^4 - 4)(x^4 + 4)$