Explanation:We are given two sets of observations, and we need to find the value of ( p – k ).
Set 1: Finding ( k )
The mean of the observations 29, 36, 21, 18, 7, 19, ( k ), ( k ) is given as 21.25.
The mean of the observations is calculated by the formula:

We have 8 observations in total (since ( k ) appears twice). So, the mean is:


Multiplying both sides by 8:
170 = 130 + 2k
Solving for ( k ):
170 – 130 = 2k
40 = 2k
k = 20
Set 2: Finding ( p )
The mode of the observations 29, 22, 15, 15, 22, 18, 21, ( p ), ( p ) is given as 29. The mode is the number that appears most frequently.
From the given data:
– The numbers 22 and 15 appear twice each.
– ( p ) also appears twice, so we must have ( p = 29 ), because the mode is 29, which must appear more times than any other number.
Thus, ( p = 29 ).
Finding ( p – k )
We know that:

So:
p – k = 29 – 20 = 9

Explanation:Let’s examine the given equation:
4 ÷ 8 + 5 – 6 × 2 = 34
We need to determine which two signs should be interchanged to make this equation correct.
Step 1: Evaluate the current equation
We’ll first evaluate the left-hand side as it is:
4 ÷ 8 + 5 – 6 × 2
Follow the order of operations (BIDMAS: Brackets, Indices, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)):
( 4 ÷ 8 = 0.5 )
( 6 × 2 = 12 )
Now, substitute these values back into the expression:
0.5 + 5 – 12
( 0.5 + 5 = 5.5 )
( 5.5 – 12 = -6.5 )
So, the left-hand side evaluates to -6.5, which is not equal to 34.
Step 2: Check possible sign interchanges
Now, let’s check the possible sign interchanges one by one.
»Option 1: Swap ( + ) and ( – )
The new equation will be:
4 ÷ 8 – 5 + 6 × 2
Now, let’s evaluate:
»1. ( 4 ÷ 8 = 0.5 )
»2. ( 6 × 2 = 12 )
So, we have:
0.5 – 5 + 12
»3. ( 0.5 – 5 = -4.5 )
»4. ( -4.5 + 12 = 7.5 )
This does not give 34, so Option 1 is not correct.
»Option 2: Swap ( ÷ ) and ( × )
The new equation will be:
4 × 8 + 5 – 6 ÷ 2
Now, let’s evaluate:
»1. ( 4 × 8 = 32 )
»2. ( 6 ÷ 2 = 3 )
So, we have:
32 + 5 – 3
»3. ( 32 + 5 = 37 )
»4. ( 37 – 3 = 34 )
This gives 34, which is correct!
Thus, the equation is satisfied when we swap ( ÷ ) and ( × ).
Final Answer:
The correct option is:
( ÷ ) and ( × ).

Explanation:We are given the equation:
0.17y = 10.2
Step 1: Solve for ( y ).
To isolate ( y ), divide both sides of the equation by 0.17:

Step 2: Perform the division.
y = 60

Explanation:To determine the day of the week for Shamita’s husband’s birthday (31 May 2020), we need to calculate the number of days between 15 March 2020 and 31 May 2020.
Steps:
»1. From 15 March to 31 March 2020:
– March has 31 days, so the number of days from 15 March to 31 March is:
31 – 15 = 16 {days}
»2. From 1 April to 30 April 2020:
– April has 30 days.
»3. From 1 May to 31 May 2020:
– May has 31 days.
Now, let’s sum up the total number of days from 15 March to 31 May:
16 \, (March) + 30 \, (April) + 31 \, (May) = 77days
»4. Determine the day of the week:
– Shamita’s birthday, 15 March 2020, was a Sunday.
– To find the day of the week for 31 May, we need to calculate the remainder when 77 is divided by 7 (since a week has 7 days):
77 ÷ 7 = 11 {remainder} \, 0
This means 77 days from Sunday is also a Sunday.

Explanation:Let’s analyze the given information step by step:
»1. Box M is placed above box N: This means M is above N.
»2. Box O is placed below box K: This means O is below K.
»3. Box N is placed above K: This means N is above K.
»4. Box L is placed below O: This means L is below O.
Now, let’s arrange the boxes based on these statements:
– Since M is above N and N is above K, we can place M > N > K.
– O is placed below K, so K > O.
– L is placed below O, so O > L.
Now the arrangement from top to bottom looks like this:
M > N > K > O > L
Thus, the bottom most box is L.