"The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N obj

We have to calculate the result of the division problem.

To determine the result, long division will be employed.

)

Initially, we quotient with x since fits into , x times.

Thus, we have:

)(x

After subtraction, we obtain:

We can see that fits into , -2 times; therefore, the next addition to the quotient will be -2. This results in a final quotient of (x-2).

Answer:

The mass of the water removed is 66.67 kg

Step-by-step explanation:

Given data

The solids blended with sugar make up 10%.

Final product achieved = 15% product.

Final product contains = 15% sugar solids.

The initial product weighs = 200 kg

Solution

Here, we find the needed sugar amount as follows:

The amount of sugar required = 200 ×

Thus, the needed sugar = 20 kg

We recognize that total solids = product solids + sugar solids...............1

Also, the initial product equals the final product.

So,

0.20 × 200kg= 0.30 × total mass of the final product

The mass of the final product = 133.33 kg

However,

the final product contains 15% product solids and 15% sugar solids, which means that the amount of product solids equals the sugar solids.

Thus, the mass of water removed = 200 kg - 133.33 kg.

The mass of the water removed is 66.67 kg.

Based on a table of values, the outputs of f(x) for whole numbers are 0, 1, 4, 9, 16, 25, 36, and further. Meanwhile, for the same inputs, g(x) generates outputs of 1, 2, 4, 8, 16, 32, and 64. It is evident that g(x) consistently doubles its outputs, leading to numbers that surpass those produced by f(x). The exponential function, g(x), experiences a constant multiplicative change rate, allowing it to accelerate more quickly compared to the quadratic function.

(ed. just click all of them)

Answer:

(1, 3)

Step-by-step explanation:

Provided:

A circle containing these specified points-

(4, 2), (-2, 2), (-1, 4), (1, 1), (1, 3), (2, -3).

A function resembles a mechanism that produces an output for each unique input. Each input must yield a distinct output.

The function's input is characterized as the domain, and the output corresponds to its range.

The domain is indicated by the 'x' coordinate while the range is represented by the 'y' coordinate.

This means the domain serves as the independent variable, and the range is contingent upon the domain’s values.

In this case, a relation or set of points constitutes a function only if every 'x' in the ordered pairs is unique.

Within the described relation, the pairs (1, 1) and (1, 3) share the same input. Thus, removing either one will convert the relation into a function.

Therefore, choosing (1, 3) is the right answer.

Response:

The loop's length is roughly 49.58 km.

Step-by-step details:

Given:

Duration to cycle the loop = 2 hours and 30 minutes

It is known that;

60 minutes = 1 hour

30 minutes = 0.5 hour

therefore, 2 hours and 30 minutes =

∴ Time to cycle the loop = 2.5 hours

Let 's' denote the cycling speed.

Denote the total loop distance as 'd'

From our understanding;

Distance equals speed times time.

Representing this as an equation we have;

Given:

If her speed increased by 1 km/hr, the time taken around the loop would decrease by 7 minutes.

As a result, we can say;

Speed =

The time then will be shortened by 7 minutes.

7 minutes = 0.12 hours

Consequently, time = 2.5 - 0.12 = 2.38

Again, Distance is calculated as speed times time.

This can be expressed with equations;

The distances are equivalent in both scenarios, thus we will determine speed by equating the equations.

So, Speed = 19.83 km/hr

Loop length (d) =

Therefore, the loop length is approximately 49.58 km.