Set 10

Observe the image above. The correct letter to replace the question mark (?) in the second triangle is...

Based on the figure above, if $x^\circ = y^\circ$, what is the measure of angle $z$ in terms of $x$?

At an Independence Day event attended by $3000$ people, the committee provides $20$ prizes to be drawn during the event. What is the probability that a participant gets a prize?

Set $A$ contains all negative integers, set $B$ contains all positive even integers, and set $C$ contains all positive integers divisible by $3$.

Which of the following numbers is NOT included in the product of two members of sets $A$, $B$, or $C$?

If the maximum value of $x + y$ on the set $\{(x,y)|x \ge 0, y \ge 0, x + 5y \le 10, 5x + y \le a^2 - 5\}$ is $5$, then the value of $a = \dots$

The price of a math book at ABC store is $85,000$ rupiah and a biology book is priced at $40,000$ rupiah. Because the store is having an anniversary, all books are given an $x\%$ discount. If on that day the price of a math book is $28,900$ rupiah. What is the price of the biology book?

If the quadratic function $y = kx^2 + 8x + (k-1)$ has an axis of symmetry $x = 4$, then the maximum value of the function is...

Given:

1. $x > 2$
2. $-3 < x < 2$
3. $x < -3$
4. $x > -3$

If $x^2 + x - 6 > 0$, then the inequality is satisfied by...

Suppose a contractor is going to build an apartment. The probability of a public protest occurring is $0.7$. If there is no protest, the probability that the construction finishes on time is $0.8$. If there is a protest, the probability that the construction finishes on time is $0.4$.

Determine the probability that the construction finishes on time!

Nina runs at a constant speed of $5 \text{ km/h}$. And she walks at a speed of $1 \text{ km/h}$. If Nina travels $3 \text{ km}$ by running for half of the total travel time and walking for the rest, what is the total time taken by Nina?

Putri and Tina are celebrating their birthdays today. Currently, Tina's age is $2$ times Putri's age. If in $6$ years, Putri's age is $\frac{2}{3}$ of Tina's age, what is Putri's current age?

To build a house, a contractor needs $33$ workers for $21$ days. If only $14$ workers arrive, how long will they take to complete the job?

The recurring decimal number $1.5454545454...$ in common fraction form is...

The correct values to complete the number sequence are...

In a class of $50$ students, each student has at least one favorite subject among three subjects: Mathematics, Biology, and Physics.

The data is as follows:

• $35$ students like Mathematics
• $20$ students like Biology
• $15$ students like Physics
• $5$ students like Physics and Biology
• $13$ students like Mathematics and Biology
• $7$ students like Mathematics and Physics

How many students like Mathematics, Biology, and Physics?

A basket contains $10$ duck eggs and $20$ chicken eggs. Half of the duck eggs are broken, and one-fourth of the chicken eggs are broken.

If one egg is taken from the basket, what is the probability that the taken egg is a duck egg or a broken egg?

Given two sets:

The intersection of these two sets is...

In Semester $I$, Hani took $5$ Mathematics exams and obtained an average score of $7.5$. In one academic year, Hani took a total of $11$ mathematics exams and obtained an average score of $8.0$.

What is the increase in Hani's average mathematics exam score from Semester $I$ to Semester $II$?

The relationship between the values of $x$ and $y$ from the following equations is...