Which expression is equivalent to (r^7)^6

Tell whether the two quantities vary directly. Explain your reasoning. The cafeteria provides three meals per day.

Dafna11 [192]

Answer:

The cafeteria provides three meals per day.

Reason 1

Yes, they vary directly

As number of days increases ,Total number of meals i.e

1st day ⇒ 3

2nd day⇒6

3 rd day⇒9

4th day⇒12

......................

.........................

increases.

Total number of Meals = k×Number of days

But there is another possibility also

Reason 2

1 st day ⇒ 3

2nd day ⇒3

3rd day⇒ 3

.....................

As you can see from the above expression On each day number of meals is

constant.

So we can say that ,

On each Day=Constant amount of meal=3

So, there is no Proportionality between Days and Meal.

3 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

A government agency was charged by the legislature with estimating the length of time it takes citizens to fill out various form

Lorico [155]

Answer:

The shorter range.

Step-by-step explanation:

When you think about the confidence interval you automatically think about how wide it is, in relation to its range. A typical confidence interval is generally 95%, however when it increases, it also increases the 'confidence' of the data and therefore its range.

Logically, a level of confidence of 85% will be much narrower than one of 90%, 95% or 99%, this implies that the wide range will be narrower than that of others. So things the 85% confidence interval in a multiple selection response, compared to the other three intervals, will always be the shortest.

6 0

2 years ago

Difference 7 7/8- 3 1/4

Nataly_w [17]

7 7/8 - 3 1//4 = 49/8 - 3/4 = 49/8 - 6/8 = 43/8 (or 5.375)

8 0

2 years ago

Y-r-1

AleksandrR [38]

Answer:

Step-by-step explanation:

SA = 4marks ?

im not sure to this one

5 0

2 years ago