\(10+4-5\times2=19\)
Signs \(\times\) and \(+\), Numbers 2 and 4
Equation Correction by Interchanging Signs and Numbers
The problem asks us to identify which pair of sign changes and number changes correctly solves the given mathematical equation. We need to find the specific interchanges that make the equation true.
The initial equation provided is:
$10 + 4 - 5 \times 2 = 19$
Our task is to test the given options to see which one satisfies this equation after performing the specified interchanges.
Analyzing Option 2: Signs '+' and '$\times$', Numbers '4' and '2'
Option 2 suggests the following interchanges:
- Signs to interchange: The plus sign ($+$) and the multiplication sign ($\times$).
- Numbers to interchange: The number 4 and the number 2.
Let's apply these changes step-by-step to the original equation:
Original equation: $10 + 4 - 5 \times 2 = 19$
Step 1: Interchange the signs '+' and '$\times$'.
- The '+' sign located between 10 and 4 is replaced with '$\times$'.
- The '$\times$' sign located between 5 and 2 is replaced with '+'.
- The '-' sign remains unchanged.
- After this sign interchange, the equation becomes: $10 \times 4 - 5 + 2 = 19$
Step 2: Interchange the numbers '4' and '2'.
- The number '4' (which is now after the first operator) is replaced with '2'.
- The number '2' (which is now at the end of the expression) is replaced with '4'.
- After this number interchange, the equation becomes: $10 \times 2 - 5 + 4 = 19$
Verification of the Corrected Equation
To confirm if this corrected equation is true, we evaluate the left-hand side (LHS) using the standard order of operations (PEMDAS/BODMAS):
The corrected equation is $10 \times 2 - 5 + 4 = 19$.
- Perform multiplication first: $10 \times 2 = 20$.
- The expression simplifies to: $20 - 5 + 4$.
- Perform subtraction next (from left to right): $20 - 5 = 15$.
- The expression simplifies to: $15 + 4$.
- Perform addition last: $15 + 4 = 19$.
The calculated value of the LHS is $19$. This matches the right-hand side (RHS) of the original equation ($19$). Therefore, interchanging the signs '+' and '$\times$', along with the numbers '4' and '2', correctly solves the equation.
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Important Questions from Probability
Two dice are thrown simultaneously and the sum of the numbers appearing on them is noted. What is the probability that the sum is 12?
If a box contains 3 white cushions, 4 red cushions and 5 blue cushions, what is the probability of selecting a white or blue cushion?
A. 2/3
B. 3/4
C. 1/4
D. 1/9Statements followed by some conclusions are given below.
Statements:
1. A bag has 2 white, 3 black, 4 red and 6 green balls.
2. 1 ball selected at random from the bag.
Conclusions:
I. The probability that a black ball is selected is 1/5
II. The probability that a red ball is selected is 6/15
Find which of the conclusions logically follows from the given statement
A. Only conclusion I follows.
B. Only conclusion II follows.
C. Both I and II follow.
D. Neither I nor II follows.
In a shooting test, the probabilities of hitting the target are 1/2 for A, 2/3 for B and 3/4 for C. If they fire at the same target, what is the probability that only one of them hits the target?
A bag contains balls numbered from 1 to 42. One ball is drawn at random from these balls. The probability that its number is a multiple of 7 or 8 is:
