One year a surf board maker had $3.5 million in sales. In later year,
sales y (in millions) increased by about 15% each year. Which function
models the amount of money the maker will have after t years?

Answer:

a) 0.3191 = 31.91% probability that at least one individual with a reservation cannot be accommodated on the trip.

b) The expected number of available places when the limousine departs is 0.1.

c) [tex]P(X = 3) = 0.09[/tex]

[tex]P(X = 4) = 0.25[/tex]

[tex]P(X = 5) = 0.32[/tex]

[tex]P(X = 6) = 0.34[/tex]

Step-by-step explanation:

For each reservation, there are only two possible outcomes. Either the person appears for the trip, or the person does not. The probability of a person appearing for the trip is independent of any other person. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The expected value of the binomial distribution is given by:

[tex]E(X) = np[/tex]

The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation.

This means that [tex]n = 6[/tex]

35% of all those making reservations do not appear for the trip.

This means that 100 - 35 = 65% appear, so [tex]p = 0.65[/tex]

A) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip?

This will happen if more than four appear, as the limousine can accommodate up to four passengers on any one trip. So

[tex]P(X > 4) = P(X = 5) + P(X = 6)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{6,5}.(0.65)^{5}.(0.35)^{1} = 0.2437[/tex]

[tex]P(X = 6) = C_{6,6}.(0.65)^{6}.(0.35)^{0} = 0.0754[/tex]

[tex]P(X > 4) = P(X = 5) + P(X = 6) = 0.2437 + 0.0754 = 0.3191[/tex]

0.3191 = 31.91% probability that at least one individual with a reservation cannot be accommodated on the trip.

B) If six reservations are made, what is the expected number of available places when the limousine departs?

The expected number of arrivals is given by:

[tex]E(X) = np = 6*0.65 = 3.9[/tex]

Since the are four places:

4 - 3.9 = 0.1

The expected number of available places when the limousine departs is 0.1.

C) Suppose the probability distribution of the number of reservations made is given in the accompanying table.Number of reservations 3 4 5 6Probability 0.09 0.25 0.32 0.34Let X denote the number of passengers on a randomly selected trip. Obtain the probability mass function of X.

This is the probability of each outcome. So

[tex]P(X = 3) = 0.09[/tex]

[tex]P(X = 4) = 0.25[/tex]

[tex]P(X = 5) = 0.32[/tex]

[tex]P(X = 6) = 0.34[/tex]

Answer:

W = 882 N

Step-by-step explanation:

Given that,

The weight of a person, W = 90 kg

The value of acceleration due to gravity, g = 9.8 m/s²

We need to find the weight of the person on Earth. The formula for the weight of an object is given by :

W = mg

Substitute all the values,

W = 90 kg × 9.8 m/s²

W = 882 N

So, the weight of the person is equal to 882 N.

Answer:

A perpendicular bisector of a line segment is a line segment perpendicular to and passing through the midpoint of (left figure). The perpendicular bisector of a line segment can be constructed using a compass by drawing circles centered at and with radius and connecting their two intersections.

Answer:

2 + 3 = 5

Step-by-step explanation:

ones Place Value

2 + 3 = 5

Put the 5 in Ones place

carry  

 2

+  3

= 5

Answer:

w = 1/4

Step-by-step explanation:

Distribute:

-3w + 9 - 9w -9 = 4w + 8 -12

Combine like terms:

-16w = -4

w = 1/4

Answer:

w=1/4

Step-by-step explanation:

-3w+9-9w-9=4w+8-12

-12w=4w+8-12

-12w=4w-4

-12w-4w=-4

-16w=-4

w=-4/-16

w=1/4

First off, remember that finding the x-intercepts means setting y equal to zero and solving for the x-values, so this question is really asking you to "Solve 4x2 – 2x – 5 = 0".

Now, let's start the completing-the-square process. To begin, we have the original equation (or, if we had to solve first for "= 0", the "equals zero" form of the equation). In this case, we were asked for the x-intercepts of a quadratic function, which meant that we set the function equal to zero

Answer:

Step-by-step explanation:

Correct choice is D

Answer:

volume = 502.4 cm³

Step-by-step explanation:

volume = 4²π(10) = 160π = 502.4 cm³

Answer:

40

Step-by-step explanation:

solve for two squares. Square 1: 32. Square 2: 8. answer: 32 + 8

Answer:

[tex] y = 1 [/tex]

Step-by-step explanation:

Given:

[tex] a^{3y - 5} = \frac{1}{a^2} [/tex]

Apply the negative exponent rule

[tex] a^{3y - 5} = a^{-2} [/tex]

The bases will cancel each other

[tex] 3y - 5 = -2 [/tex]

[tex] 3y - 5 + 5 = -2 + 5 [/tex]

[tex] 3y = 3 [/tex]

[tex] \frac{3y}{3} = \frac{3}{3} [/tex]

[tex] y = 1 [/tex]

Answer:

5km

35 divided by 7 is 5

Answer:

24÷8=3

Step-by-step explanation:

because 24÷8=3

Answer:

The area of this shape can not be solved using the information given

Step-by-step explanation:

There is no given side length of any of the shapes.

If one side is given then the whole shape could be solved.

Answer: varibles coffeeefishents exponets study then eat

Step-by-step explanation:

Answer:

3s+7.99= 71.83 .

Step-by-step explanation:

since there are 3 shirts you would multiply s by 3 so 3s. To me it looks like 7.99 is the constant and 71.83 is the total including this constant. so putting all of these together in  y=mx+b format you get the equation 71.83= 3s+7.99

hope this helps

Answer:

what?????????????????????????

Answer:

What do you need help with?

Step-by-step explanation:

Answer:

x=-1

Step-by-step explanation:

1/4x+1/2=2/4x+3/4

1/4x+2/4=2/4x+3/4

2/4=(2/4x-1/4x)+3/4

2/4=1/4x+3/4

2/4-3/4=1/4x

-1/4=1/4x

-1=x

x=-1

Step-by-step explanation:

rectangle

= 15.3 × (8.2 - 5.7 )

= 15.3 × 2.5

= 38.25

triangle

= 1/2 × (15.3 - 5.1+6.7) × 5.7

= 1/2 × 3.5 × 5.7

= 1/2 × 19.95

= 9, 97

total = 38.25+9.97 = 48.22 ft

Answer:

3+78=81

Step-by-step explanation:

2+2

Answer:

x-32

Step-by-step explanation:

Answer:

X-32 :)

Explanation:

Put together an expression.

Answer:

m∠3 = 119°

Step-by-step explanation:

All the angles must equal 360° when added together. You have two known angles that are right next to each other. If you add m∠1 and m∠2, 119 + 61, it is equal to 180°. This means that m∠3 and m∠4 must be equal to 180° as well and since there are only two lines, it is safe to assume that opposing angles are the same so m∠1 = m∠3 and m∠2 = m∠4.

Answer:

K12 answer

Step-by-step explanation:

Answer: 40 beads

Step-by-step explanation: Its said that Ben have 13 fewer beads than Jori. That mean 27+13=40

Answer:

40

Step-by-step explanation:

27 + 13 = 40

Answer:

~114.56

Step-by-step explanation:

Because you're asked to find the number so that x% is y, we will have to find that number. The equation in that case would be NUM * 0.934 = 107. Divide both sides by .934 to get an answer of approximately 114.56.

Answer:

Your answer is C.

exponential is to the power of a value and hence c meets the requirements

Answer:

K=7

Step-by-step explanation:

hope it helps you

have a wonderful day!!!