What exactly is a rate? how do I write it? how is it different from a unit rate

What is a number line for 5a + 18 < -27?

Colt1911 [192]

Step-by-step explanation:

$5a + 18 < - 27 \\ \\ \therefore \: 5a < - 27 - 18 \\ \\ \therefore \: 5a < - 45 \\ \\ \therefore \: a < \frac{ - 45}{5} \\ \\ \therefore \: a < - 9$

8 0

3 years ago

When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let

sergiy2304 [10]

Answer:

(a) P(X=3) = 0.093

(b) P(X≤3) = 0.966

(c) P(X≥4) = 0.034

(d) P(1≤X≤3) = 0.688

(e) The probability that none of the 25 boards is defective is 0.277.

(f) The expected value and standard deviation of X is 1.25 and 1.089 respectively.

Step-by-step explanation:

We are given that when circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%.

Let X = the number of defective boards in a random sample of size, n = 25

So, X ∼ Bin(25,0.05)

The probability distribution for the binomial distribution is given by;

$P(X=r)= \binom{n}{r} \times p^{r}\times (1-p)^{n-r} ; x = 0,1,2,......$

where, n = number of trials (samples) taken = 25

r = number of success

p = probability of success which in our question is percentage

of defectivs, i.e. 5%

(a) P(X = 3) = $\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$

= $2300 \times 0.05^{3}\times 0.95^{22}$

= 0.093

(b) P(X $\leq$ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= $\binom{25}{0} \times 0.05^{0}\times (1-0.05)^{25-0}+\binom{25}{1} \times 0.05^{1}\times (1-0.05)^{25-1}+\binom{25}{2} \times 0.05^{2}\times (1-0.05)^{25-2}+\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$

= $1 \times 1 \times 0.95^{25}+25 \times 0.05^{1}\times 0.95^{24}+300 \times 0.05^{2}\times 0.95^{23}+2300 \times 0.05^{3}\times 0.95^{22}$

= 0.966

(c) P(X $\geq$ 4) = 1 - P(X < 4) = 1 - P(X $\leq$ 3)

= 1 - 0.966

= 0.034

(d) P(1 ≤ X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

= $\binom{25}{1} \times 0.05^{1}\times (1-0.05)^{25-1}+\binom{25}{2} \times 0.05^{2}\times (1-0.05)^{25-2}+\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$

= $25 \times 0.05^{1}\times 0.95^{24}+300 \times 0.05^{2}\times 0.95^{23}+2300 \times 0.05^{3}\times 0.95^{22}$

= 0.688

(e) The probability that none of the 25 boards is defective is given by = P(X = 0)

P(X = 0) = $\binom{25}{0} \times 0.05^{0}\times (1-0.05)^{25-0}$

= $1 \times 1\times 0.95^{25}$

= 0.277

(f) The expected value of X is given by;

E(X) = $n \times p$

= $25 \times 0.05$ = 1.25

The standard deviation of X is given by;

S.D.(X) = $\sqrt{n \times p \times (1-p)}$

= $\sqrt{25 \times 0.05 \times (1-0.05)}$

= 1.089

8 0

3 years ago

What is the value of 0.1561 rounded to the nearest tenth?

Ainat [17]

We have to round the value of 0.1561 to the nearest tenth.

The number after decimal is the number at tenth place. Consider the number to the right of the tenths place and use the number to determine if you will round up or stay the same. Notice that the number to the right of tenth place is more than or equal to 5 or less than 5. If that number is greater than or equal to 5, then the number will round up but if that number is less than 5, then the number will not round up. It will remain same.

Let us consider the given number 0.1561

The number at tenths place is 1

The number after the tenths place is 5 (which is either greater than or equal to 5)

So, the number will round up to 0.2

8 0

3 years ago

Read 2 more answers

Which of the following best describes the expression 3x + 2y + 8z?

Evgesh-ka [11]

The sum of 3 products...there r 3 terms

6 0

3 years ago

Read 2 more answers

Can someone please help me. I need help on the 5 one

soldi70 [24.7K]

Answer:

The second option

Step-by-step explanation:

On the right hand side you have all the multiples of 4, on the left hand side you have 5

The multiples of four are ...,-8,-4,0,4,8,....

so the simbol that means that 5 is not an element of the multiples of four is the second option.

4 0

3 years ago