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.