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2 years ago

A movie theater sells popcorn in bags of different sizes. The table shows the volume of popcorn and the price of the bag.

Mathematics

1 answer:

scoundrel [369]2 years ago

6 0

Answer:

<em>The price for a 60-ounce bag of popcorn would be $16</em>

Step-by-step explanation:

<u>Function Modeling</u>

The behavior of some parameters that depend on a set of variables can be modeled in several ways, like linear, quadratic, exponential, logarithmic, among many others.

The selection of the model is often a complex decision that involves statistics and data analysis.

The question provides us with four points where the volume of popcorn bags and the price in dollars. The easiest function that can be used is the line.

The equation of a line of the volume V and the price p can be found with the expression

$\displaystyle p-p_1=\frac{p_2-p_1}{V_2-V_1}(V-V_1)$

We'll use the first two values (6,10) (8,20)

$\displaystyle p-6=\frac{8-6}{20-10}(V-10)$

Simplifying and rearranging, we get the model

$\displaystyle p(V)=\frac{1}{5}V+4$

To test the accuracy of the model, we compute the values of p for V=35 and for V=48

$\displaystyle p(35)=\frac{1}{5}(35)+4=11$

$\displaystyle p(48)=\frac{1}{5}(48)+4=13.6$

Since the computed values are equal to those of the table, the model is accurate. We can now predict the price for V=60

$\displaystyle p(60)=\frac{1}{5}(60)+4=16$

The price for a 60-ounce bag of popcorn would be $16

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A toddler is allowed to dress himself on Mondays, Wednesdays, and Fridays. For each of his shirt, pants, and shoes, he is equall

avanturin [10]

Answer:

0.0286 = 2.86% probability that today is Monday.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Dressed correctly

Event B: Monday

Probability of being dressed correctly:

100% = 1 out of 4/7(mom dresses).

(0.5)^3 = 0.125 out of 3/7(toddler dresses himself). So

$P(A) = 0.125\frac{3}{7} + \frac{4}{7} = \frac{0.125*3 + 4}{7} = \frac{4.375}{7} = 0.625$

Probability of being dressed correctly and being Monday:

The toddler dresses himself on Monday, so (0.5)^3 = 0.125 probability of him being dressed correctly, 1/7 probability of being Monday, so:

$P(A \cap B) = 0.125\frac{1}{7} = 0.0179$

What is the probability that today is Monday?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0179}{0.625} = 0.0286$

0.0286 = 2.86% probability that today is Monday.

4 0

2 years ago

The top of a ladder is 4m up a vertical wall.The bottom is 2m from the wall.The coordinate axes are the wall and the horizontal

mash [69]

Answer:

Part a) $y=-2x+4$

Part b) The coordinates of the point are $(\frac{4}{3},\frac{4}{3})$

Step-by-step explanation:

Part a) Find the equation representing the ladder

we have the ordered pairs

(0,4) and (2,0)

Find the slope

$m=(0-4)/(2-0)=-2$

Find the equation of the line in slope intercept form

$y=mx+b$

we have

$m=-2\\b=4$

substitute

$y=-2x+4$

Part b) A square box just fits under the ladder.Find the coordinates of the point where the box touches the ladder.

If the box is a square

the x-coordinate of the point where the box touches the ladder must be equal to the y-coordinate

x=y

$y=-2x+4$

substitute

$x=-2x+4\\3x=4\\x=\frac{4}{3}$

$y=x=\frac{4}{3}$

therefore

The coordinates of the point are $(\frac{4}{3},\frac{4}{3})$

6 0

1 year ago

World wind energy generating1 capacity, W , was 371 gigawatts by the end of 2014 and has been increasing at a continuous rate of

Sunny_sXe [5.5K]

Answer:

a) $W(t) = 371(1.168)^{t}$

b) Wind capacity will pass 600 gigawatts during the year 2018

Step-by-step explanation:

The world wind energy generating capacity can be modeled by the following function

$W(t) = W(0)(1+r)^{t}$

In which W(t) is the wind energy generating capacity in t years after 2014, W(0) is the capacity in 2014 and r is the growth rate, as a decimal.

371 gigawatts by the end of 2014 and has been increasing at a continuous rate of approximately 16.8%.

This means that

$W(0) = 371, r = 0.168$

(a) Give a formula for W , in gigawatts, as a function of time, t , in years since the end of 2014 . W= gigawatts

$W(t) = W(0)(1+r)^{t}$

$W(t) = 371(1+0.168)^{t}$

$W(t) = 371(1.168)^{t}$

(b) When is wind capacity predicted to pass 600 gigawatts? Wind capacity will pass 600 gigawatts during the year?

This is t years after the end of 2014, in which t found when W(t) = 600. So

$W(t) = 371(1.168)^{t}$

$600 = 371(1.168)^{t}$

$(1.168)^{t} = \frac{600}{371}$

$(1.168)^{t} = 1.61725$

We have that:

$\log{a^{t}} = t\log{a}$

So we apply log to both sides of the equality

$\log{(1.168)^{t}} = \log{1.61725}$

$t\log{1.168} = 0.2088$

$0.0674t = 0.2088$

$t = \frac{0.2088}{0.0674}$

$t = 3.1$

It will happen 3.1 years after the end of 2014, so during the year of 2018.

7 0

2 years ago

Suppose two individuals (smith and jones) each have 10 hours of labor to devote to producting either ice cream (x) or chicken so

sattari [20]

It has to be either 10x or 10y

5 0

2 years ago

What is the horizontal asymptote for y(t) for the differential equation dy dt equals the product of 2 times y and the quantity 1

marta [7]

First, we need to solve the differential equation.
$\frac{d}{dt}\left(y\right)=2y\left(1-\frac{y}{8}\right)$
This a separable ODE. We can rewrite it like this:
$-\frac{4}{y^2-8y}{dy}=dt$
Now we integrate both sides.
$\int \:-\frac{4}{y^2-8y}dy=\int \:dt$
We get:
$\frac{1}{2}\ln \left|\frac{y-4}{4}+1\right|-\frac{1}{2}\ln \left|\frac{y-4}{4}-1\right|=t+c_1$
When we solve for y we get our solution:
$y=\frac{8e^{c_1+2t}}{e^{c_1+2t}-1}$
To find out if we have any horizontal asymptotes we must find the limits as x goes to infinity and minus infinity.
It is easy to see that when x goes to minus infinity our function goes to zero.
When x goes to plus infinity we have the following:
$$$\lim_{x\to\infty} f(x)$$=y=\frac{8e^{c_1+\infty}}{e^{c_1+\infty}-1} = 8$
When you are calculating limits like this you always look at the fastest growing function in denominator and numerator and then act like they are constants.
So our asymptote is at y=8.

3 0

2 years ago