Solve for n in the follow equation 4n

At a high school, students can choose between three art electives, four history electives, and five computer electives. Each stu

dangina [55]

If one is to choose among given choices and the order is not important, we use the concept of combination. First, we calculate for the sample space or number available since there is a total number of 12 electives and a student may choose 2 out of them.
S = 12C2
That is "the sample space is equal to combination of 12 taken 2". The answer to this is equal to 66.

Next, we determine the number of outcomes. The equation will be,
O = (5C1) x (3C1)
That is "outcome is equal to combination of 5 taken 1 times combination of 3 taken 1". This is equal to 15. The probability is equal to,
P = O/S

Substituting,
P = (15/66) = 0.227270
The answer to this item is the third choice.

6 0

2 years ago

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The function g(x) = 5x2 – 10x written in vertex form is g(x) = 5(x – 1)2 – 5. The function g(x) is shown on the graph along with

natka813 [3]

The general vertex form of the a quadratic function is y = (x - h)^2 + k. In this form, the vertex is (h,k) and the axis of symmetry is x = h. Then, you only need to compare the vertex form of g(x) with the general vertex form of the parabole to conclude the vertex point and the axis of symmetry. g(x) = 5(x-1)^2 - 5 => h = 1 and k = - 5 => theis vertex = (1, -5), and the axis of symmetry is the straight line x = 1. <span>Answer: the vertex is (1,-5) and the symmetry axis is x = 1.</span>

8 0

2 years ago

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During the 2015-16 NBA season, J.J. Redick of the Los Angeles Clippers had a free throw shooting percentage of 0.901 . Assume th

ser-zykov [4K]

Answer: 0.5898

Step-by-step explanation:

Given : J.J. Redick of the Los Angeles Clippers had a free throw shooting percentage of 0.901 .

We assume that,

The probability that .J. Redick makes any given free throw =0.901 (1)

Free throws are independent.

So it is a binomial distribution .

Using binomial probability formula, the probability of getting success in x trials :

$P(X=x)^nC_xp^x(1-p)^{n-x}$

, where n= total trials

p= probability of getting in each trial.

Let x be binomial variable that represents the number of a=makes.

n= 14

p= 0.901 (from (1))

The probability that he makes at least 13 of them will be :-

$P(x\geq13)=P(x=13)+P(x=14)$

$=^{14}C_{13}(0.901)^{13}(1-0.901)^1+^{14}C_{14}(0.901)^{14}(1-0.901)^0\\\\=(14)(0.901)^{13}(0.099)+(1)(0.901)^{14}\ \ [\because\ ^nC_n=1\ \&\ ^nC_{n-1}=n ]\\\\\approx0.3574+0.2324=0.5898$

∴ The required probability = 0.5898

5 0

2 years ago

Simplify 14.2 + 6.5(p + 3q) – 4.05q

anzhelika [568]

Answer is C
14.2+6.5(p+3q)-4.05q
14.2+6.5p+19.5q-4.05q
14.2+6.5p+15.45q→6.5p+15.45q+14.2
so the answer is C

7 0

2 years ago

g In a survey of 500 residents, 300 were opposed to the use of the photo-cop for issuing traffic tickets.The standard error of t

Evgesh-ka [11]

Answer:

Z-score 1.96

Margin of error d= 0.04323

Step-by-step explanation:

Hello!

The study variable in this case is

X: Number of people that oppose the use of photo-cop for issuing traffic tickets in a sample of 500.

n= 500

The parameter of interest is the proportion of people that opposes it.

The estimated proportion is p'= 300/500= 0.6

To estimate the population proportion per Confidence interval you have to approximate the distribution of the sample proportion p' to normal:

p'≈N(p;p(1-p)1/n)

The mean of this distribution is p and the variance is p*(1-p)*1/n

To construct the Confidence interval, since the value of the population proportion is unknown, an estimated variance is used:

p'(1-p')*1/n ⇒ then the estimated standard error is √(p'(1-p')*1/n)

The formula for the confidence interval is:

p' ± $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'(1-p')}{n} }$

Where " $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'(1-p')}{n} }$ " represents the margin of error of the interval.

Now for a confidence level of 0.95 the value of Z is $Z_{0.975}= 1.965$

The estimated standard error is already calculated: $\sqrt{\frac{p'(1-p')}{n} } = 0.022$

The margin of error (d) is then:

d= $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'(1-p')}{n} }$ = 1.965 * 0.022

d= 0.04323

I hope it helps!

7 0

2 years ago

Solve for n in the follow equation 4n - p = 3r