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1 year ago

8.06

Mathematics

1 answer:

Lera25 [3.4K]1 year ago

6 0

Answer:

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Probability Problems.

Based on the study that Shane conducted we can assume a couple of things. Firstly, we can see that a vast majority of shoppers are buying products they saw advertised, so we can assume that advertising a product directly affects and contributes to the sales of that particular product.

Secondly, we can tell from the study that the number 1 method for advertising products is the Internet. Since 70% of all the interviewed shoppers are buying a product they saw on the internet.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

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A pond forms as water collects in a conical depression of radius a and depth h. Suppose that water flows in at a constant rate k

Scrat [10]

Answer:

a. dV/dt = K - ∝π(3a/πh)^⅔V^⅔

b. V = (hk^3/2)/[(∝^3/2.π^½.(3a))]

The small deviations from the equilibrium gives approximately the same solution, so the equilibrium is stable.

c. πa² ≥ k/∝

Step-by-step explanation:

The rate of volume of water in the pond is calculated by

The rate of water entering - The rate of water leaving the pond.

Given

k = Rate of Water flows in

The surface of the pond and that's where evaporation occurs.

The area of a circle is πr² with ∝ as the coefficient of evaporation.

Rate of volume of water in pond with time = k - ∝πr²

dV/dt = k - ∝πr² ----- equation 1

The volume of the conical pond is calculated by πr²L/3

Where L = height of the cone

L = hr/a where h is the height of water in the pond

So, V = πr²(hr/a)/3

V = πr³h/3a ------ Make r the subject of formula

3aV = πr³h

r³ = 3aV/πh

r = ∛(3aV/πh)

Substitute ∛(3aV/πh) for r in equation 1

dV/dt = k - ∝π(∛(3aV/πh))²

dV/dt = k - ∝π((3aV/πh)^⅓)²

dV/dt = K - ∝π(3aV/πh)^⅔

dV/dt = K - ∝π(3a/πh)^⅔V^⅔

b. Equilibrium depth of water

The equilibrium depth of water is when the differential equation is 0

i.e. dV/dt = K - ∝π(3a/πh)^⅔V^⅔ = 0

k - ∝π(3a/πh)^⅔V^⅔ = 0

∝π(3a/πh)^⅔V^⅔ = k ------ make V the subject of formula

V^⅔ = k/∝π(3a/πh)^⅔ -------- find the 3/2th root of both sides

V^(⅔ * 3/2) = k^3/2 / [∝π(3a/πh)^⅔]^3/2

V = (k^3/2)/[(∝π.π^-⅔(3a/h)^⅔)]^3/2

V = (k^3/2)/[(∝π^⅓(3a/h)^⅔)]^3/2

V = (k^3/2)/[(∝^3/2.π^½.(3a/h))]

V = (hk^3/2)/[(∝^3/2.π^½.(3a))]

The small deviations from the equilibrium gives approximately the same solution, so the equilibrium is stable.

c. Condition that must be satisfied

If we continue adding water to the pond after the rate of water flow becomes 0, the pond will overflow.

i.e. dV/dt = k - ∝πr² but r = a and the rate is now ≤ 0.

So, we have

k - ∝πa² ≤ 0 ---- subtract k from both w

- ∝πa² ≤ -k divide both sides by - ∝

πa² ≥ k/∝

5 0

2 years ago

The sum of 23.8 and a number is 28.17, as shown below. What number should go in the box to complete the addition problem?

gregori [183]

Since there is no picture to show the box, all I can say is that 28.17- 23.8 = 4.37 and 23.8 + 4.37 = 28.17

5 0

2 years ago

Read 2 more answers

Write the multiple regression equation for miles per gallon as the response variable. Use weight and horsepower as predictor var

Naily [24]

Answer:

Step-by-step explanation:

Response Variable: Miles per gallon

Predictor Variables: Weight, Horsepower

The multiple regression equation would be: M = aW + bH + c

where M = miles per gallon

a = slope of the graph of W on M OR rate of change in M due to change in W

W = weight

b = slope of the graph of H on M OR rate of change in M due to change in H

H = horsepower

c = intercept of M on the y-axis OR constant variable

How might the car rental company use this model?

The car rental company might use the regression model to determine the following:

- Effect of weight (of car) on miles run per gallon (of premium motor spirit)

- Effect of horsepower on miles per gallon; etc.

8 0

2 years ago

If h(x) = 6 - X, what is the value of (h*n (10)?

faltersainse [42]

Answer:

<u>(h * h)(10) = 16</u>

Step-by-step explanation:

We should know that: (f*g)(x) = f(x)*g(x)

Given: h(x) = 6 - x

∴(h * h)(x) = (6-x) (6-x) = (6-x)²

To find (h * h)(10), substitute with x = 10 at (h * h)(x)

∴ (h * h)(10) = (6-10)² = (-4)² = 16

==============================================

Note: if we want to find (hoh)(10)

(hoh)(x) = h[h(x)] = 6 - (6 - x) = 6 - 6 + x = x

∴ (hoh)(10) = 10

8 0

1 year ago

Management is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 5 perc

Olegator [25]

Answer:

The bonus will be paid on at least 4099 units.

Step-by-step explanation:

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

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

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 percentile of this measure.

In this problem, we have that:

The highest 5 percent is the 95th percentile.

Past records indicate that, on the average, 4,000 units of a small assembly are produced during a week. The distribution of the weekly production is approximately normally distributed with a standard deviation of 60 units. This means that $\mu = 4000, \sigma = 60$ .