10 POINTS!

Atoms contain charged particles called protons and electrons. Each proton has a charge of +1, and each electron has a charge of

pav-90 [236]

-2
16 positive protons + 18 negative electrons

7 0

3 years ago

Read 2 more answers

The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports it

brilliants [131]

Answer:

(a) 11.25 and 1.68

(b) 0.1651

(c) 0.3903

(d) 0.6865

Step-by-step explanation:

We are given that GTC, the Georgetown Telephone Company, reports it can resolve customer problems the same day they are reported in 75% of the cases and suppose the 15 cases reported today are representative of all complaints.

This situation can be represented through Binomial distribution as;

$P(X=r)= \binom{n}{r}p^{r}(1-p)^{n-r} ; x = 0,1,2,3,....$

where, n = number of trials (samples) taken = 15

r = number of success

p = probability of success which in our question is % of cases in

which customer problems are resolved on the same day, i.e.;75%

So, here X ~ $Binom(n=15,p=0.75)$

(a) Expected number of problems to be resolved today = E(X)

E(X) = $\mu$ = n * p = 15 * 0.75 = 11.25

Standard deviation = $\sigma$ = $\sqrt{n*p*(1-p)}$ = $\sqrt{15*0.75*(1-0.75)}$ = 1.68

(b) Probability that 10 of the problems can be resolved today = P(X = 10)

P(X = 10) = $\binom{15}{10}0.75^{10}(1-0.75)^{15-10}$

= $3003*0.75^{10} *0.25^{5}$ = 0.1651

(c) Probability that 10 or 11 of the problems can be resolved today is given by = P(X = 10) + P(X = 11)

= $\binom{15}{10}0.75^{10}(1-0.75)^{15-10}+\binom{15}{11}0.75^{11}(1-0.75)^{15-11}$

= $3003*0.75^{10} *0.25^{5} + 1365*0.75^{11} *0.25^{4}$ = 0.3903

(d) Probability that more than 10 of the problems can be resolved today is

given by = P(X > 10)

P(X > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)

= $\binom{15}{11}0.75^{11}(1-0.75)^{15-11}+\binom{15}{12}0.75^{12}(1-0.75)^{15-12} + \binom{15}{13}0.75^{13}(1-0.75)^{15-13}+\binom{15}{14}0.75^{14}(1-0.75)^{15-14} + \binom{15}{15}0.75^{15}(1-0.75)^{15-15}$

= $1365*0.75^{11} *0.25^{4} + 455*0.75^{12} *0.25^{3}+105*0.75^{13} *0.25^{2} + 15*0.75^{14} *0.25^{1}+1*0.75^{15} *0.25^{0}$

= 0.6865

3 0

3 years ago

Explain how you would distribute 4 ones into 5 groups.m

jenyasd209 [6]

Answer:

Step-by-step explanation:

bvfghhgf

7 0

3 years ago

if one gallon of paint covers 825 square feet, how much paint is needed to cover 2640 square feet? Make a prediction

Nitella [24]

Answer:

3.2 gallons

Step-by-step explanation:

Write a proportion:

1 gallon / 825 square feet = x / 2640 square feet

Solve:

x = 3.2 gallons

7 0

3 years ago

Rewrite in the form . Then find q(x) and r(x).

gizmo_the_mogwai [7]

Answer:

q(x)= 2x+5

r(x)=6

b(x)=x+4

Step-by-step explanation:

I have found what is missing in your question: Rewrite 2x^2+13x+26/x+4 in the form q(x)+r(x)/b(x).

First, we have to divide the polynomial by x+4 and remember that is x times 2x.

By multiplying this we are going to get $2x^{2} + 8x$ and now we are doing separation of it and getting $2x^{2} + 13x + 26$ and getting $2x^{2} + 13x + 26/ x + 4 = 2x^{2} +8x/x+4=5x+26/x+4=2x + 5x+26/x+4$

Because 5 is showing x times 5 we are going to multiply (x + 4) with 5 and that is 5x + 20.

$5x+26/x+4 = 5x + 20/x+4 = 6/ x+4=5 + 6/x+4$

Now when we can get more simplified we are having:

$2x^{2} +13+26/x+4=2x + 5= 6/x+4$

3 0

3 years ago