John has 36 sweets and he shares them in the ratio 2 : 7.

An executive for a large national restaurant chain with multiple locations in each of 513 counties wants to personally sample th

ohaa [14]

Answer:

D. Obtain a cluster sample by randomly selecting 20 counties and visiting every restaurant within those counties.

Step-by-step explanation:

Since this executive wants to minimize cost and expenses he should use a cluster sample of 20 counties and using the selected counties as a representative of the whole. Cluster sampling is a good and useful way of doing market research. It is more economical than other sampling methods and as the executive cannot get information on the whole population, he would be able to get information from the clusters.

4 0

2 years ago

Nikki used the calculations shown to determine whether a carton of 12 eggs or a carton of 18 eggs was the better buy. A carton o

Lemur [1.5K]

Given :

A carton of 12 eggs or a carton of 18 eggs was the better buy. A carton of 12 eggs cost $2.39, and a carton of 18 eggs cost $3.39. Unit price of the 12-egg carton = ($2.39)(12 eggs) = $28.68 per egg Unit price of the 18-egg carton = ($3.39)(18 eggs) = $61.02 per egg The 12-egg carton has the lower unit cost, so it is the better buy.

To Find :

What was her first error.

Solution :

Her first error is to find Unit price of egg in each carton.

To find, unit price we should divide total amount by number of units :

Unit price for carton of 12 eggs, $ (2.39)/12 = $0.199 .

Hence, this is the required solution.

4 0

2 years ago

Consider the following problem: A farmer with 950 ft of fencing wants to enclose a rectangular area and then divide it into four

Alina [70]

Answer:

Step-by-step explanation:

(a)

Suppose we came up with an ideology whereby we pick a value for the length including the length dividing the inside into 4 parts(5 parallel sides), then we can get the value for breath by using the following process.

Let assume the length of the rectangle is 50;

Then, the breath can be calculated as follows:

= 50 × 5 = 250 ( since the breath is divided into 5 parallel sides)

The fencing is said to be 950 ft

So, 950 - 250 = 700

Then divided by 2, we get:

= 700/2

= 350

So for the first diagram; the length = 50 and the breath = 350

The area = 50 × 350 = 17500 ft²

Now, let's go up a little bit.

If the length increase to 100;

Then 100 × 5 = 500

⇒ 950 - 500 = 450

⇒ 450/2 = 225

The area = 225 × 100 = 22500 ft²

Suppose the length increases to 150

Then 150 × 5 = 750

⇒ 950 - 750 = 200

⇒ 200/2 = 100

The area = 150 × 100 = 15000 ft²

The diagrams for each of the outline above can be seen in the image attached below.

(b) The diagram illustrating the general solution can be seen in the second image provided below.

(c) The expression for the total area A in terms of both x and y is:

Area A = x×y

(d) Recall that:

The fencing is said to be 950 ft.

And the length is divided inside into 5 parallel sides;

Then:

5x + 2y = 950 (from the illustration in the second image below)

2y = 950 - 5x

$y = \dfrac{950}{2} - \dfrac{5}{2}x$

$y = 475- \dfrac{5}{2}x$

(e)

From (c); replace the value of y in (d) into (c)

Then:

Area A = x×y

$f(x)= x\times ( 475 -\dfrac{5}{2}x)$

Open brackets

$f(x)= ( 475 x-\dfrac{5}{2}x^2)$

(f)

By differentiating what we have in (e)

$f(x)= ( 475 x-\dfrac{5}{2}x^2)$

$f'(x)= ( 475 (1)-\dfrac{5}{2}(2x))$

$f'(x)= 475 -5x$

$\implies 475 = 5x$

x = 475/5

x = 95

From (d):

$y = 475- \dfrac{5}{2}x$

$y = 475- \dfrac{5}{2}(95)$

$y =237.5$

∴

Area A = x × y

Area A = 95 × 237.5

Area A = 22562.5 ft²

5 0

2 years ago

The quality control team of a company checked 800 digital cameras for defects. The team found that 20 cameras had lens defects,

dmitriy555 [2]

Answer:

0.025

Step-by-step explanation:

-This is a conditional probability problem.

-Let L denote lens defect and C charging defect.

#We first calculate the probability of a camera having a lens defect;

$P(lens)=\frac{Lens}{Total}\\\\=\frac{20}{800}\\\\=0.025$

#Calculate the probability of a camera having a charging defect:

$P(Charging)=\frac{Charging}{Total}\\\\=\frac{25}{800}\\\\=0.03125$

The the probability that a camera has a lens defect given that it has a charging defect is calculated as:

$P(L|C)=\frac{P(C)P(L)}{P(C)}\\\\=\frac{0.025\times 0.03125}{0.03125}\\\\=0.025$

Hence, the probability that a camera has a lens defect given that it has a charging defect is 0.025

6 0

2 years ago

Oscar has received a $4,000 gift and is looking for a bank to start a savings account. Which option

kirza4 [7]

Answer:

The best option for him would be a real interest rate of 5%.

Step-by-step explanation:

The nominal interest rate is the one that represents the percentage of increase of the money that is in a certain investment, without discounting the depreciation due to inflation or the payment of taxes.

On the other hand, the real interest rate is the one that represents the real increase in the money invested, after discounting inflation and any taxes to be paid.

Therefore, the best option for Oscar would be to invest his $ 4,000 in a savings account with a real interest rate of 5% per year.

7 0

2 years ago