Set 9

If the area of the large square is $256 \text{ cm}^2$, then the circumference of the circle is...

Square $ABCD$ has a side length of $24 \text{ cm}$. A circle passes through points $A$ and $D$, and is tangent to side $BC$. The area of the circle is...

If $PQ$ is parallel to $RS$, then the value of $\alpha$ is...

The average test score of class $A$ is $\bar{X}_A$ and the average test score of class $B$ is $\bar{X}_B$. After the scores of both classes are combined, the average score becomes $\bar{X}$. If $\bar{X}_A : \bar{X}_B = 9 : 10$ and $\bar{X} : \bar{X}_A = 84 : 81$, then the ratio of the number of students in class $A$ to class $B$ is...

Inside a box there are $1$ red ball, $6$ green balls, and $2$ white balls. If $7$ balls are to be drawn without replacement, then the probability that the number of green balls drawn is twice the number of white balls drawn is...

If $1 < x < y < 2$ and $z = x - y$, then $z$ is between the values...

Seven years ago, the sum of the ages of the older sibling and the younger sibling was $26$ years. Four years from now, twice the age of the older sibling will be equal to twice the age of the younger sibling plus eight years.

The current age of the younger sibling is...

For the function $f(x) = \frac{\sqrt{5 - x}}{\sqrt{x^2 + x - 6}}$ to be defined in its domain, the domain of function $f$ is...

If the ratio of the volumes of two cubes is $1 : 27$, then the ratio of the surface areas of the two cubes is...

The probabilities of Ali, Bima, and Dika passing the National Exam are $0.75$, $0.8$, and $0.85$ respectively.

The probability that only one person passes among the three is...

A team consists of $12$ people who can finish a job in $15$ days. If the job needs to be completed faster in $9$ days, the percentage increase in workers needed to finish the job is...

A set of data has an average of $24$ and a range of $12$. If each data value is subtracted by $a$ and then the result is divided by $b$, it produces new data with an average of $10$ and a range of $6$. The values of $a$ and $b$ are...

If $x$ is $\frac{3}{4}$ of $34$ and $y$ is $46\%$ of $86$, then...

The fractional form of the repeating decimal $3.15931593...$ is?

A rectangle with length $p$ and width $l$ has an area of $32$. If the perimeter of the rectangle is $6l$, what is the value of $p$?

A rectangular prism has a volume of $12x^2$, length $3x$, and width $2x$. What is the height of the rectangular prism?

The average biology score in a class of $50$ students is $70$. If the average score of male students is $76$ and the number of female students is $4$ more than the number of male students, then the average score of female students in the class is...

In a box, there are $8$ yellow balls and $3$ blue balls. If two balls are taken simultaneously at random, determine the expected frequency of obtaining two blue balls from $110$ trials!