Anita can paint 25 wooden slats in 5.5 hours. If she continues to work at the same pace without any breaks, how many slats can she paint in 9.9 hours?
In one hour, Anita can paint 25 / 5.5 = <<25/5.5=4.54>>4.54 wooden slats.
So, in 9.9 hours, she can paint 4.54 x 9.9 = <<4.54*9.9=44.946>>44.946 wooden slats.
Since Anita can't paint a fraction of a slat, then she can paint 44 wooden slats in 9.9 hours. Answer: \boxed{44}.
NO
I apologize for the mistake. Let's correct the solution.
If Anita can paint 25 wooden slats in 5.5 hours, then her rate of painting is 25 slats / 5.5 hours = 4.545454545 slats per hour.
To find out how many slats Anita can paint in 9.9 hours, we multiply her rate by the number of hours:
Number of slats = rate of painting * number of hours = 4.545454545 * 9.9 = 44.999999995 slats.
Since we can't have a fraction of a slat, we round down to the nearest whole number. Therefore, Anita can paint 44 slats in 9.9 hours. Answer: \boxed{44}.
In a right triangle, two sides are12 and 13. Find the measure of the third side. Consider ALL cases.
To find the measure of the third side in a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's denote the third side as x. According to the Pythagorean theorem, we have the equation:
x^2 = 12^2 + 13^2.
Simplifying this equation, we get:
x^2 = 144 + 169,
x^2 = 313.
To find the value of x, we take the square root of both sides:
x = √313.
Since square roots can be either positive or negative, there are two possible values for x:
x = ±√313.
So, the measure of the third side can be √313 or -√313, depending on which direction we consider positive in the triangle.
A two digit number has twice as many ones as tens. Twice the original number is nine more than the reversed number. Find the original number.
Let's assume the tens digit of the two-digit number is "x" and the ones digit is "y".
We are given the information that the number has twice as many ones as tens, so we can represent this as:
y = 2x
The original number can be written as 10x + y. Reversing the digits gives us 10y + x.
Twice the original number is 2(10x + y) = 20x + 2y.
Nine more than the reversed number is 10y + x + 9.
We are given that twice the original number is nine more than the reversed number, so we can write this as an equation:
20x + 2y = 10y + x + 9
Simplifying this equation, we have:
19x = 8y + 9
Since we are looking for a two-digit number, the tens digit cannot be zero. We can try different values of x and solve for y to find the correct value.
Let's try x = 1:
19(1) = 8y + 9
19 = 8y + 9
8y = 10
y = 10/8 = 5/4, which is not a valid solution since y should be an integer.
Let's try x = 2:
19(2) = 8y + 9
38 = 8y + 9
8y = 29
y = 29/8, which is not a valid solution since y should be an integer.
Let's try x = 3:
19(3) = 8y + 9
57 = 8y + 9
8y = 48
y = 48/8 = 6
Therefore, the original number is 10x + y = 10(3) + 6 = 36 + 6 = 42.
So, the original number is 42.
WRONG!
Apologies for the mistake. Let's try again to find the correct answer.
Let's assume the tens digit of the two-digit number is "x" and the ones digit is "y".
We are given the information that the number has twice as many ones as tens, so we can represent this as:
y = 2x
The original number can be written as 10x + y. Reversing the digits gives us 10y + x.
Twice the original number is 2(10x + y) = 20x + 2y.
Nine more than the reversed number is 10y + x + 9.
We are given that twice the original number is nine more than the reversed number, so we can write this as an equation:
20x + 2y = 10y + x + 9
Simplifying this equation, we have:
19x - 8y = 9
Now, let's explore different values of x and y.
Let's try x = 1:
19(1) - 8y = 9
19 - 8y = 9
-8y = -10
y = -10/-8
y = 5/4, which is not an integer.
Let's try x = 2:
19(2) - 8y = 9
38 - 8y = 9
-8y = 9 - 38
-8y = -29
y = -29/-8
y = 29/8, which is not an integer.
Let's try x = 3:
19(3) - 8y = 9
57 - 8y = 9
-8y = 9 - 57
-8y = -48
y = -48/-8
y = 6
Therefore, the original number is 10x + y = 10(3) + 6 = 30 + 6 = 36.
So, the original number is 36.
A brave knight travelled on his horse from one kingdom to another in 2 days. The first day he rode 10 mph, the second day he rode 8 mph. If he traveled the exact same amount of time each days and went 180 miles, find how many hours it took the knight to travel from one kingdom to another.
Let's denote the time the knight traveled on each day as "t" hours.
On the first day, the knight traveled at a speed of 10 mph for "t" hours, so the distance covered on the first day is 10t miles.
On the second day, the knight traveled at a speed of 8 mph for "t" hours, so the distance covered on the second day is 8t miles.
According to the problem, the total distance covered during the two days is 180 miles.
So, we can set up the equation: 10t + 8t = 180
Combining like terms, we have: 18t = 180
Dividing both sides by 18, we get: t = 180 / 18 = 10
Therefore, the knight traveled for 10 hours each day.
Since he traveled for 10 hours each day, the total time it took him to travel from one kingdom to another is 2 * 10 = <<2*10=20>>20 hours.
Hence, it took the knight 20 hours to travel from one kingdom to another.
Each side of a pentagon is 10 cm greater than the previous side. If the perimeter is 500 cm, find each side of the pentagon.
Let's denote the lengths of the sides of the pentagon as follows:
x: length of the first side
x+10: length of the second side
x+20: length of the third side
x+30: length of the fourth side
x+40: length of the fifth side
The perimeter of the pentagon is the sum of the lengths of all the sides.
Perimeter = x + (x+10) + (x+20) + (x+30) + (x+40) = 500
Combining like terms, we have: 5x + 100 = 500
Subtracting 100 from both sides, we get: 5x = 400
Dividing both sides by 5, we have: x = 400 / 5 = 80
Therefore, the lengths of the sides of the pentagon are:
First side: x = 80 cm
Second side: x+10 = 80+10 = 90 cm
Third side: x+20 = 80+20 = 100 cm
Fourth side: x+30 = 80+30 = 110 cm
Fifth side: x+40 = 80+40 = 120 cm
Hence, the lengths of the sides of the pentagon are 80 cm, 90 cm, 100 cm, 110 cm, and 120 cm.