This problem is asking you to apply the *Pythagorean Theorem*, given the information you’ve been given.
In case you’ve forgotten, the Pythagorean Theorem states that, in any given right triangle, the sum of the squares of the lengths of its legs is equal to the square of the length of its hypotenuse (the side opposite its right angle). If we call the lengths of the legs a and b, and the length of the hypotenuse c, this can be expressed in notation as a^2+b^2=c^2 (it doesn’t matter in this case which leg you pick for a and which you pick for b). Here, if we choose the left leg as a and the bottom leg as b, we’re given that a^2 (the area of a square with sides of length a) is 25 sq. in, and b is 3.5 in. Plugging those values into the equation, we have:
25 + (3.5)^2 = c^2
From here, you don’t even need to solve for c, you just need to find the value of c^2 (since you’re trying to find the area of a square with side lengths c). Just solve the left side of the equation, and you’ll have your answer in square inches.
Remember when you learning about the "Least Common
Multiple" and you wondered when in the world you would
ever need to use it ?
Well, here you are ! Hello !
The next time they will cross the starting line together is the
LCM (Least Common Multiple) of 30 and 40 .
Do you remember how to find it ?
Here's one easy way:
Count by 30s until you come to a number that's divisible by 40 .
Laura's first lap. . . . . . . . 30 seconds . . . not divisible by 40
Laura's two laps . . . . . . . 60 seconds . . . not divisible by 40
Laura's three laps. . . . . . 90 seconds . . . not divisible by 40
Laura's four laps. . . . . . 120 seconds . . . divisible by 40
After 120 seconds, Laura has completed four laps,
Shelby has completed only three laps.
3/4 of the juice from a 2 L bottle is 1.5 L.
There is only half a litre left after the party.
Answer:
The answer is "between 0.10 and 0.05".
Step-by-step explanation:
For sample 1:
For sample 2:
Calculating the null and alternative hypotheses:
Calculating the test statistic:
Calculating the conservative degrees of freedom:
by using Excel the p-value for left tailed test and for test statistic will be with .