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2 years ago

Alfie buys two books, each at the same price. He pays with a £10 note and gets £2.30 change.

1 answer:

7 0

First subtract the amount he paid from the amount of change he got:

10 - 2.30 = 7.70

So the price for the two books was £7.70, now divide by 2.

7.70 / 2 = 3.85

So each book cost £3.85

You might be interested in

Given the two functions, which statement is true?

tia_tia [17]

Answer:

Option D

Step-by-step explanation:

f(x) = $\text{log}_{15}x$

Transformed form of the function 'f' is 'g'.

g(x) = $\frac{1}{2}\text{log}_{15}(x+4)$

Property of vertical stretch or compression of a function,

k(x) = x

Transformed function → m(x) = kx

Here, k = scale factor

1). If k > 1, function is vertically stretched.

2). If 0 < k < 1, function is vertically compressed.

From the given functions, k = $\frac{1}{2}$

Since, k is between 0 and $\frac{1}{2}$ , function f(x) is vertically compressed by a scale factor $\frac{1}{2}$ .

g(x) = f(x + 4) represents a shift of function 'f' by 4 units left.

g(x) = f(x - 4) represents a shift of function 'f' by 4 units right.

g(x) = $\frac{1}{2}\text{log}_{15}(x+4)$

Therefore, function f(x) has been shifted by 4 units left to form image function g(x).

Option D is the answer.

8 0

2 years ago

Find the number of ways of arranging the numbers

Doss [256]

First of all, note that all integers are either 0,1, or 2 modulo 3 (if you're not familiar with this terminology, it means that every integer is either a multiple of 3, or it is 1 or 2 away from a multiple of 3).

So, we can think of our numbers as

$\begin{array}{c|c}x&x\mod 3\\0&0\\1&1\\2&2\\3&0\\4&1\\5&2\\6&0\\7&1\\8&2\\9&0\end{array}$

In order to make sure that the sum of any three adjacent numbers is divisible by 3, we have to make sure that any group of 3 three adjacent numbers contains a 0, a 1 and a 2. This is possible only if we arrange our 9 numbers in 3 groups of 3 numbers containing 0,1 and 2 exactly once, repeating always the same pattern.

For example, we could arrange our numbers following the pattern

$0,1,2,0,1,2,0,1,2$

$2,0,1,2,0,1,2,0,1$

We have $3!=6$ possible patterns. Suppose for example that we choose the pattern

$0,1,2,0,1,2,0,1,2$

One possible way of following this pattern would be the arrangement

$3,1,2,6,4,5,9,7,8$

In fact, we substituted every '0' with a multiple of 3 (3, 6 or 9), every '1' with a number 1 away from a multiple of 3 (1, 4 or 7) and every '2' with a number 2 away from a multiple of 3 (2, 5 or 8).

This means that, once we fix a patter, we have 3 choices for the first 3 slots, 2 choices for the next 3 slots, and the final slot will be fixed. So, we have

$3\cdot 3\cdot 3\cdot 2 \cdot 2 \cdot 2 = 216$

possible ways of following a fixed pattern. Since the number of patterns was 6, we have

$216\cdot 6 = 1296$

possible arrangements.

7 0

2 years ago

Read 2 more answers

Which graph represents the solution set of the system of inequalities?

Novay_Z [31]

Answer:
(see image)
bottom right image

Explanation:
First try the origin (0,0) to rule out two of the graphs.
3y ≥ x - 9
3(0) ≥ (0) - 9
3 ≥ - 9 yes
3x + y > - 3
3(0) + (0) > - 3
3 > - 3 yes
so the origin should be in the shaded area of the graph, which rules out the top right and bottom left graphs.
Now try a coordinate that is in the shaded area of one of the remaining graphs, but not in the other one. If it works, the graph is the one that has that point in the shaded region, and vice versa.
Try point (4, 2)
3y ≥ x - 9
3(2) ≥ (4) - 9
6 ≥ - 5 yes
3x + y > - 3
3(4) + (2) > - 3
12 + 2 > - 3
14 > - 3 yes
So the graph is the bottom right one since (4, 2) is included in that shaded region.

4 0

2 years ago

Please help ASAP the answer are within the pic

DerKrebs [107]

Hey Ive taken this assesment. The answer is 55

6 0

2 years ago

The distance between (-5, 3) and B(5, 3) is

8090 [49]

In here, we will use the distance formula
$\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

Compute the distance between (-5, 3) and (5, 3)
 $=\sqrt{\left(5-\left(-5\right)\right)^2+\left(3-3\right)^2}$

= 10

The distance between (-5, 3) and (5, 3) is 10

8 0

2 years ago