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1. How many minutes are there in a week?

2. The measure of angles of quadrilateral ABCD form the arithmetic sequence ∠A, ∠B, ∠C, ∠D. If the measure of angle B is 75 degrees what is the degree measure of angle D?

3. January 1st of a year is a Monday. What day of week is the 31st of the same month?

4. What is the value of n if 2^10 × 4^20 × 8^30 = 2^n ?

5. There were 30 cans of soda in the fridge. 60% were Coke and the rest were Pepsi. Noah drank a few cans of Coke and now 60% of the soda cans in the fridge are Pepsi. How many cans of Coke did Noah drink?

6. What is the positive solution to the equation x = 1 2 + 1 x − 2 ?

Randomly selecting a page in a booklet, the chance to get an even page number is 48%. How many pages does the booklet have?

8. What is the units digit of the sum of all positive multiples of 6 smaller than 500?

9. If each dimension of a rectangle decreases by 1, its area will decrease from 2017 to 1717. What will be the area of the rectangle if each of its dimensions increases by 1?

10. There are several flyers that need to be printed. Working alone, Printers A, B, and C can finish the task in 3, 4, and 6 hours, respectively. If we use all three printers simultaneously, how many minutes will it take to finish the printing task?

Jan 22, 2021

#1
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Please, I need help with these problems too!!!!!!!!!11  Please, hurry!!!!!!!!!!!!!  I need the answers really soon!!!!!  Like right now!!!!!!!

11. If x + 1/x = 2, then find x^2 + 1/x^2

12. what are the last two digits of 7^2010?

13. What is smallest number of integers needed to be selected from the set {1,2,3,...,2020} to guarantee 2 of selected numbers relatively prime?

14. Three consecutive integers form the sides of a right triangle.  What are the three integers?

15. Solve 4^x + 2^x = 12.

16. How many ordered triples of positive integers (a,b,c) are there such that 1<= a <= b <= c <= 10?

17. How many perfect squares are factors of 79!?

18. What is the sum of all proper fractions with a denominator less than or equal to 10?

19. How many three-digit numbers are divisible by 8?

20. Triangle ABC is an isosceles triangle with AC=BC and angle C =120°. Points D and E are chosen on segment AB so that AD=DE=EB. Find angle CDE

Pleeez, I really need the answers!!!!!!!!!!!!!!!!!!!!!!  Hurrry!!!!!!!!!!!!!!!!!!!!!!!!!!!!!  HURRY!!!!!!!!!!!!!!!!!!!!!

Jan 22, 2021
#2
+266
+4

1)  There are 60 minutes in an hour, therefore 60 * 24 = minutes in a day and, 60 * 24 * 7 = minutes in a week, so 60 * 24 = 1440. and 60* 24 * 7 → 1440 * 7 = 10080 minutes in a week.

4)

$$2^{10}\cdot \:4^{20}\cdot \:8^{30}=2^n$$

$$2^{140} = 2^n$$

$$\mathrm{True\:for\:all}\:x;\quad \:2^{140}=2^n$$

6)

x = 12+1*x-2

x = 12 + x - 2

x = x + 12 -2

x = x+10

x - x = x + 10 - x

0 = 10

No Solution

Jan 22, 2021
#3
+266
+4

19) There are 112 three digit numbers divisible by 8.

12) For $$7^{2010}$$ we have to multiply by 7 so this gives 49 for the last two digits.

14) I memorized this: 3, 4, and 5 are lengths of a right triangle

15) $$\left(2^x\right)^2+2^x=12$$

$$\left(u\right)^2+u=12$$

$$u=3,\:u=-4$$

Thats a lot of questions, so I think you should at least try some of them, they aren't so hard. Just give them a try!

Jan 22, 2021