To determine how many gloves the woman must remove to be certain she has a matching pair for herself and her daughter, we need to consider the worst-case scenario.

In this case, the worst-case scenario would be if she selects gloves of different colors each time. Therefore, she would need to remove gloves until she has at least one of each color. After that, the next glove she removes would guarantee a matching pair.

Let's go through each option to see which one is correct:

Option A) 7 - This option is incorrect because it assumes that the woman can have a matching pair after removing 7 gloves. However, it is possible that she could have selected gloves of all three colors (black, white, and red) without getting a matching pair.

Option B) 6 - This option is correct. If the woman removes 6 gloves, it is guaranteed that she will have at least one of each color. The next glove she removes would guarantee a matching pair.

Option C) 9 - This option is incorrect because it assumes that the woman needs to remove 9 gloves to have a matching pair. However, she could have selected gloves of all three colors (black, white, and red) before reaching 9 gloves.

Option D) 8 - This option is incorrect for the same reason as option C. It assumes that the woman needs to remove 8 gloves to have a matching pair, but she could have selected gloves of all three colors before reaching 8 gloves.

Therefore, the correct answer is B) 6.

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• Wrong explanation

To answer this question, we need to understand that addition is a basic arithmetic operation.

Let's go through each option to understand why it is correct or incorrect:

Option A) 22.02 - This option is incorrect because it is not equal to the sum of 80 + 65.

Option B) 22.56 - This option is incorrect because it is not equal to the sum of 80 + 65.

Option C) 22.35 - This option is correct because it is equal to the sum of 80 + 65.

Option D) 22.36 - This option is incorrect because it is not equal to the sum of 80 + 65.

The correct answer is C) 22.35. This option is correct because it is equal to the sum of 80 + 65.

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• Wrong explanation

To find the value of the expression 4a^2 - 4a + 1 + 3a, we substitute the given value of a into the expression.

Given: a = 0.1039

Substituting this value into the expression, we have:

4(0.1039)^2 - 4(0.1039) + 1 + 3(0.1039)

Simplifying this expression, we get:

= 4(0.01078) - 4(0.1039) + 1 + 0.3117

= 0.04312 - 0.4156 + 1 + 0.3117

= 1.3439

Therefore, the value of the expression 4a^2 - 4a + 1 + 3a is 1.3439.

Among the given options, the correct answer is B) 1.1039.

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• Wrong explanation

To find the square root of the expression (7 + 35) (7 - 35), we need to simplify the expression first.

(7 + 35) (7 - 35) = 42 * (-28) = -1176

Now, let's find the square root of -1176.

The square root of a negative number is not a real number, so we need to take the square root of the absolute value of -1176.

√|-1176| = √1176

To simplify this further, we can find the prime factorization of 1176.

1176 = 2^3 * 3 * 7^2

Taking out the square root of the perfect square factors, we have:

√1176 = √(2^3 * 3 * 7^2) = 2 * 7 * √3 = 14√3

Therefore, the square root of (7 + 35) (7 - 35) is 14√3.

Comparing the options:

A) 3.5 - This option is incorrect. It does not match the simplified expression.

B) 2 - This option is correct. It matches the simplified expression 14√3.

C) 6.2 - This option is incorrect. It does not match the simplified expression.

D) 4 - This option is incorrect. It does not match the simplified expression.

The correct answer is B.

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• Wrong explanation