Since it is a parallelogram cente at point T,
then the measure of PT is equal to the measure of TR. And the measure of QT is
equal to the measure of TS.
PT = TR
a + 4 = 2a
4 = 2a -a
a = 4
PT = TR = 8 units
QT = TS
b = 2b -3
3 = 2b – b
b = 3
<span>QT = TS = 3 units</span>
Answer:
29
Step-by-step explanation:
<span>7s over 5t to the negative 3rd power 2 to the negative 3rd power times X to the 2nd power times Z to the negative 7th power 7s to the zero power times T to the negative 5th power over 2 to the negative 1st power times M to the 2nd power If you would please simplify these </span>
Answer:
E) 1/2
Step-by-step explanation:
This is no ordinary problem. It actually requires you to solve two different problems in order to figure out the correct answer.
First, we must figure out what the hypotenuse of the triangle is. We have the two small sides (5 and 12), but don't have the larger side. To find this, we must use the Pythagorean theorem: ![a^{2} + b^2 =c^2](https://tex.z-dn.net/?f=a%5E%7B2%7D%20%2B%20b%5E2%20%3Dc%5E2)
Let's plug in our a and b values
![5^2 + 12^2 = C^2](https://tex.z-dn.net/?f=5%5E2%20%2B%2012%5E2%20%3D%20C%5E2)
Simplify
![144 + 25 = c^2](https://tex.z-dn.net/?f=144%20%2B%2025%20%3D%20c%5E2)
![169 = c^2](https://tex.z-dn.net/?f=169%20%3D%20c%5E2)
Square both sides
![c = 13](https://tex.z-dn.net/?f=c%20%3D%2013)
But sadly, we aren't done yet. Now we know the length of the whole hypotenuse side. Time to figure out what X is by a simple equation.
![12x + 14x = 13](https://tex.z-dn.net/?f=12x%20%2B%2014x%20%3D%2013)
Simplify
![26x = 13](https://tex.z-dn.net/?f=26x%20%3D%2013)
Divide by 26
Answer is 1/2
Answer:
0.818
Step-by-step explanation:
Since the shipment has a ton of aspirin tablets, we can assume that we pick 13 of them <em>with</em> <em>reposition, </em>because the probability shoudn't change dramatically from the probability of picking without reposition if we do so.
We call D the amount of defective tablets. If we assume that we pick the tablets with reposition, then we obtain that D is a random variable of Binomial distribution with parameters 13 and 0.6 (the probability of picking a defective tablet).
We want D to be at most one. To calculate the probability of that event we add up the probability of D being equal to 0 and the probability of D being equal to one. Since D is binomial, we have
We conclude that
![P(D \leq 1) = P(D = 0) + P(D = 1) = 0.447+0.371 = 0.818](https://tex.z-dn.net/?f=%20P%28D%20%5Cleq%201%29%20%3D%20P%28D%20%3D%200%29%20%2B%20P%28D%20%3D%201%29%20%3D%200.447%2B0.371%20%3D%200.818%20)
Hence, the shipment will be accepted with probability 0.818
<em>I hope this helps you!</em>