A coin is tossed twice, find the probability of getting no tails.

The possible outcomes are: Head-Head (HH), Head-Tail (HT), Tail-Head (TH), Tail-Tail (TT).
There are 4 total possible outcomes.

The only outcome with no tails is Head-Head (HH).
There is 1 favorable outcome.

The correct option is B.

• B. $\frac{1}{4}$

$P = \text{N}5000$
$r = 5\% = 0.05$
$n = 2$ years

The correct option is C.

• C. N512.50

MMXXVII: M = 1000, M = 1000, X = 10, X = 10, V = 5, I = 1, I = 1.
MMXXVII $= 1000 + 1000 + 10 + 10 + 5 + 1 + 1 = 2027$.
MCMXII: M = 1000, CM = 900 (1000 - 100), X = 10, I = 1, I = 1.
MCMXII $= 1000 + 900 + 10 + 1 + 1 = 1912$.

$115 = 100 + 10 + 5 = \text{CXV}$.
The correct option is B.

• B. CXV

A hexagon has 6 sides, so $n=6$.

$(n-2) \times 180^\circ$.

The correct option is B.

• B. $720^\circ$

The diagram shows an angle being bisected. The question asks for the approximate measure of the original angle.

The angle appears to be obtuse (greater than $90^\circ$). Comparing it to the options, $45^\circ$ is too small, and $90^\circ$ would be a right angle. Between $120^\circ$ and $135^\circ$, the angle looks closer to $120^\circ$.
The correct option is D.

• D. $120^\circ$

Total problems: 75. Passing grade: $60\%$ of $75 = 0.60 \times 75 = 45$ problems.
Arithmetic: 10 problems. Correct: $70\%$ of $10 = 0.70 \times 10 = 7$ problems.
Algebra: 30 problems. Correct: $40\%$ of $30 = 0.40 \times 30 = 12$ problems.
Geometry: 35 problems. Correct: $60\%$ of $35 = 0.60 \times 35 = 21$ problems.

Total correct $= 7 + 12 + 21 = 40$ problems.

Problems needed $= \text{Passing score} - \text{Current correct score}$
Problems needed $= 45 - 40 = 5$ problems.
The correct option is B.

• B. 5

3 fishes $= 2$ loaves of bread
1 loaf of bread $= 4$ bags of rice

Since 1 loaf of bread $= 4$ bags of rice, then 2 loaves of bread $= 2 \times 4 = 8$ bags of rice.

3 fishes $= 8$ bags of rice

1 fish $= \frac{8}{3}$ bags of rice.
The correct option is D.

• D. $\frac{8}{3}$

(Assuming the variable is $x$ instead of $y$ as per the options).

Subtract 6 from both sides:

Divide by $-3$. Remember to reverse the inequality sign when dividing by a negative number:

The values are $0, 1, 2$.
The correct option is D.

• D. 1, 2, 3 (Note: The option D is 1, 2, 3. The first three non-negative integers are 0, 1, 2. If the question implies positive integers, then 1, 2, 3 would be correct. Given the options, 0, 1, 2 is not an option, but 1, 2, 3 is. Let's re-evaluate. If $x \ge 0$, then $0, 1, 2$ are the first three. If the options are strictly positive, then $1, 2, 3$ would be the first three positive integers. However, $x \ge 0$ includes 0. Let's assume the question implies the smallest three distinct integer values that satisfy the inequality. Option C is $0, -1, -3$ which is incorrect. Option D is $1, 2, 3$. This is the closest if 0 is excluded or if the question implies positive integers. Given the options, $0, 1, 2$ is not available. Let's assume the question implies the first three positive integer values, or that 0 is not considered one of the "values" in the context of the options. However, $x \ge 0$ means $x$ can be 0. If 0 is included, then $0, 1, 2$ would be the answer. Since $0, 1, 2$ is not an option, and $1, 2, 3$ is, it implies that 0 might be excluded from the "first three values" in the context of the options provided, or there's a slight discrepancy. Let's stick to the mathematical solution $x \ge 0$ and the smallest integers are $0, 1, 2$. If we must choose from the options, and 0,1,2 is not there, then 1,2,3 is the next logical choice if 0 is implicitly excluded. However, the most accurate answer for $x \ge 0$ is $0, 1, 2$. Let's re-check the options. Option C is $0, -1, -3$. Option D is $1, 2, 3$. If $x \ge 0$, then 0 is a valid value. So $0, 1, 2$ are the first three. Since $0, 1, 2$ is not an option, and $1, 2, 3$ is, there might be an error in the question or options. However, if we consider the smallest positive integers, then $1, 2, 3$ would be correct. Given the options, and the fact that 0 is often treated differently, $1, 2, 3$ is the most plausible intended answer among the choices if 0 is not considered one of the "first three values" in the context of the options. Let's assume the question implies positive integers for the "values". Let's re-evaluate the options. A. $-2, -1, 0$ (Incorrect, as $x$ must be $\ge 0$) B. $-3, -2, -1$ (Incorrect) C. $0, -1, -3$ (Incorrect, as $x$ must be $\ge 0$) D. $1, 2, 3$ (These values satisfy $x \ge 0$. If the question implicitly asks for the first three positive integer values, this would be correct. If it asks for the first three non-negative integer values, it should be $0, 1, 2$. Since $0, 1, 2$ is not an option, and $1, 2, 3$ are all $\ge 0$, this is the best fit among the given choices, assuming 0 is not counted or the question implies positive integers.) Let's choose D based on the available options, acknowledging the slight ambiguity.
• D. 1, 2, 3

Ages: $y, (y-1), 2, 6, (y+3)$.

The mean age is 5 years.

Multiply both sides by 5:

Subtract 10 from both sides:

Divide by 3:

Ages: $5, (5-1), 2, 6, (5+3)$
Ages: $5, 4, 2, 6, 8$.

Arrange the ages in ascending order: $2, 4, 5, 6, 8$.
The median is the middle value in an ordered set. Since there are 5 ages, the median is the $3^{rd}$ value.
Median age $= 5$ years.
The correct option is A.

• A. 5years

Angle A $= 25^\circ$.
Side AC (adjacent to angle A) $= 52$ cm.
We need to find side BC (opposite to angle A).

Using a calculator, $\tan(25^\circ) \approx 0.466307658$.

The correct option is C.

• C. 24cm

Numbers: $8, 9, 7, 4, 8, 9, 10, 8, 7, 12$.
There are 10 numbers.

Sum of numbers $= 8+9+7+4+8+9+10+8+7+12 = 82$.

First, arrange the numbers in ascending order: $4, 7, 7, 8, 8, 8, 9, 9, 10, 12$.
Since there is an even number of values (10), the median is the average of the two middle values (the $5^{th}$ and $6^{th}$ values).
The $5^{th}$ value is 8. The $6^{th}$ value is 8.

The correct option is B.

• B. 65.6

Area $A = \pi r^2$, where $r$ is the radius.
So, for two circles, $A_1 = \pi r_1^2$ and $A_2 = \pi r_2^2$.

Take the square root of both sides:

The correct option is A.

• A. 4:5