Expand each expression. In (2x)4 4 In 2 + 4 In 4 In 2 + In x 8 In x

The polynomial P(x)=3x^3-5x^2-4x+4 has a factor of (x-2) rewrite P(x) as a product of linear factors

Ivenika [448]

Answer: P(x)=(x+1)(3x−2)(x−2)

4 0

3 years ago

Jada surveyed some students to see which tool they most favored for communicating with grit. The results of her survey are shown

nikklg [1K]

Answer:

120 students did Jada survey

Step-by-step explanation:

* Lets explain how to solve the problem

- The results of Jada survey are shown in this circle graph

# Communication tools Text messages 5/12

# Phone 1/5

# Emails 1/20

# Other messaging apps 1/3

- A total of 50 students said they favored text messages to

communicate with friends

- We need to find the total number of the students in Jada survey

- Assume that the total number of the students in the survey is x

∵ The Communication tools Text messages expressed by a

fraction 5/12 of the circle graph

∵ The total of 50 students said they favored text messages to

communicate with friends

- That means The fraction $\frac{5}{12}$ of x equivalent to 50

∴ $\frac{5}{12}*x=50$

- Multiply both sides by 12

∴ 5x = 600

- Divide both sides by 5

∴ x = 120

∵ x represents the number of the students in Jada survey

∴ 120 students did Jada survey

6 0

3 years ago

You are making a banner. You have a sheet of paper that is 2 m wide and want to leave a 35-cm blank margin on either side. How m

Dennis_Churaev [7]

100 cm = 1 meter.
Ok you have 200 cm of paper. Each side needs 35 cm for a margin so:
35 + 35 = 70.
Then subtract 70 from 200 and you are left with 130 cm of space left for text.

7 0

3 years ago

What is 2/3 divided by 4/5?

m_a_m_a [10]

Answer:

5/6

Step-by-step explanation:

Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.

8 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