Pencils A hexagonal pencil is a regular hexagonal prism, as shown

An airplane has 100 seats for passengers. Assume that the probability that a person holding a ticket appears for the flight is 0

zmey [24]

Answer:

96.33% probability that everyone who appears for the flight will get a seat

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 105, p = 0.9$

So

$\mu = E(X) = np = 105*0.9 = 94.5$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{105*0.9*0.1} = 3.07$

What is the probability that everyone who appears for the flight will get a seat

100 or less people appearing to the flight, which is the pvalue of Z when X = 100. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{100 - 94.5}{3.07}$

$Z = 1.79$

$Z = 1.79$ has a pvalue of 0.9633

96.33% probability that everyone who appears for the flight will get a seat

7 0

3 years ago

10 pts

RoseWind [281]

263.25 is the volume of the box in inches cubes you have to multiply 4.5 by 9 by 6.5

6 0

3 years ago

Read 2 more answers

Find the x intercepts of the parabola with vertex (-1,-16) and y intercept (0,-15)

Arlecino [84]

first, write the equation of the parabola in the required form: 
(y - k) = a·(x - h)² 

Here, (h, k) is given as (-1, -16). 
So you have: 
(y + 16) = a · (x + 1)² 

Unfortunately, a is not given. However, you do know one additional point on the parabola: (0, -15): 

-15 + 16 = a· (0 + 1)² 
.·. a = 1 

.·. the equation of the parabola in vertex form is 
y + 16 = (x + 1)² 

The x-intercepts are the values of x that make y = 0. So, let y = 0: 

0 + 16 = (x + 1)² 
16 = (x + 1)² 

We are trying to solve for x, so take the square root of both sides - but be CAREFUL! 

± 4 = x + 1 ...... remember both the positive and negative roots of 16...... 

Solving for x: 
x = -1 + 4, x = -1 - 4 
x = 3, x = -5. 

Or, if you prefer, (3, 0), (-5, 0).

8 0

3 years ago

To create a giant gemstone, sara first made two identical square pyramids that each had a base area of 100 square inches. Then s

inysia [295]

Answer:

8 inches.

Step-by-step explanation:

From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.

Ab = s ^ 2 = 100

Therefore each side would be:

s = (100) ^ (1/2)

s = 10

So, side of the square base = 10 inches

Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:

Ap = 520/2 = 260

For an area of the square pyramid we have the following equation:

Ap = 2 * x * s + s ^ 2

Where x is the height of each triangular surface and s is the side of the square base

Replacing we have:

260 = 2 * x * 10 + 10 ^ 2

20 * x + 100 = 260

20 * x = 160

x = 160/20

x = 8

Therefore, the value of x is 8 inches.

5 0

3 years ago

Solve the following system of equations.

krek1111 [17]

The answer is B.

The attached file is how I got the answer.

Hope this helped :)

5 0

3 years ago