Question

What digit can be written in place of x so that 4508π‘₯ number divisible by 12?

278

likes
1388 views

Answer to a math question What digit can be written in place of x so that 4508π‘₯ number divisible by 12?

Expert avatar
Esmeralda
4.7
101 Answers
Solution:
1. A number is divisible by 12 if and only if it is divisible by both 3 and 4.
2. Check divisibility by 4:
- The last two digits of the number 4508x must be divisible by 4.
- Possible last two digits can be 80, 81, 82, 83, 84, 85, 86, 87, 88, \text{or} 89.
- From these, 80, 84, \text{and} 88 are divisible by 4.

3. Check divisibility by 3:
- The sum of the digits of the number 4508x must be divisible by 3.
- The sum of the digits 4 + 5 + 0 + 8 = 17.
- We seek x such that 17 + x is divisible by 3.

4. Check which x among 0, 4, 8 makes 17 + x divisible by 3:
- If x = 0, then 17 + 0 = 17 (not divisible by 3)
- If x = 4, then 17 + 4 = 21 (divisible by 3)
- If x = 8, then 17 + 8 = 25 (not divisible by 3)

5. The digit x that makes 4508x divisible by 12 is 4.

Frequently asked questions (FAQs)
Find the equation of a circle with center (h, k) = (2, -3) and radius r = 5.
+
What is the value of f(2) for the function f(x) = 1/x?
+
What is the period, amplitude, and range of the sine function f(x) = sin x?
+
New questions in Mathematics
𝑦 = ( π‘₯2 βˆ’ 3) (π‘₯3 + 2 π‘₯ + 1)
A college believes that 22% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 5 percentage points?
90 divided by 40
Derivative of x squared
An integer is taken at random from the first 40 positive integers. What is the probability that the integer is divisible by 5 or 6?
Suppose SAT reading scores are normally distributed with a mean of 496 and a standard deviation of 109. The University plans towards scholarships for students who scores are in the top 7%. What is the minimum score required for the scholarship round your answer to the nearest whole number.
A pair of die is thrown and the absolute difference of the two scores is recorded. What is the probability of the absolute difference being 4 or more?
Find the equation of the line perpendicular to βˆ’5π‘₯βˆ’3𝑦+5=0 passing through the point (0,βˆ’2)
-3(-4x+5)=-6(7x-8)+9-10x
Emma is on a 50 m high bridge and sees two boats anchored below. From her position, boat A has a bearing of 230Β° and boat B has a bearing of 120Β°. Emma estimates the angles of depression to be about 38Β° for boat A and 35Β° for boat B. How far apart are the boats to the nearest meter?
form a key for your lock containing the numbers 2 2 5 8 How many different keys can you form?
0.1x8.2
30y - y . y = 144
A bag has 4 green lollipops, 3 white lollipops, and 1 black lollipop. What is the probability of drawing a white lollipop?
A buyer purchased a North Carolina home for $475,250. The seller allowed the buyer to assume his first small mortgage with a loan balance of $110,000. How much is the excise tax paid in the transaction? $951 $729.50 $950.50 $221 none of the above
The average weekly earnings in the leisure and hospitality industry group for a re‐ cent year was $273. A random sample of 40 workers showed weekly average ear‐ nings of $285 with the population standard deviation equal to 58. At the 0.05 level of significance can it be concluded that the mean differs from $273? Find a 95% con‐ fidence interval for the weekly earnings and show that it supports the results of the hypothesis test.
2 - 6x = -16x + 28
A nondegenerate ideal gas of diatomic molecules with a kilomolar mass of 2 kg/kmol and a characteristic rotational temperature of 86 K is adsorbed on the walls of a container, where the binding energy is 0.02 eV. The adsorbed molecules move freely on the walls, and their rotation is confined to the plane of the walls. Calculate the surface density of adsorbed molecules at 12 K if the gas pressure is 103 Pa! What result would you get at 68 K and the same pressure?
4m - 3t + 7 = 16
A small box measures 10 in. by 4 in. by 6 in. high. Find the volume of the box.