Answer:
64√2 or 64 StartRoot 2 EndRoot
Step-by-step explanation:
A 45-45-90 traingle is a special traingle. Let's say one of the leg of the triangle is x. The other one is also x because of the isosocles triangle theorem. Therefore, using the pytagorean theorem, you find that x^2+x^2=c^2. 2(x)^2=c^2. You then square root both sides and get c= x√2.
Therefore, the two legs are x and the hypotenuse is x√2. x√2=128 because the question says that the hypotenuse is 128. Solve for x by dividing both sides by √2. X=128/√2. You rationalize it by multiplying the numberator and denominator of the fraction by √2. √2*√2= 2.
X=(128√2)/2= 64√2 cm.
Since X is the leg, the answer would be 64√2
The temperature when Emily went to bed was -4°F.
Step-by-step explanation:
8°F + 3°F = 11°F (noon)
The temperature had risen by 3°F by noon. This means to add 3.
noon + 6°F = the day's high temperature
11°F + 6°F = 17°F (the day's high temperature)
The temperature rose another 6°F in the afternoon. This means add 6 to the temperature from noon.
high temperature - 21°F = temperature at bed
17°F - 21°F = -4°F
The temperature dropped by 21°F when Emily went to bed. This means to subtract 21 from the day's high temperature.
Risen, rose, and increase mean addition.
Decrease, dropped, and decline mean subtraction.
Hope this helps :)
Solve the inequality for x:
5x - 3 ≤ 7x +7
Subtract 7x from each side:
-2x -3 ≤ 7
Add 3 to each side:
-2x ≤ 10
Divide both sides by -2, also when dividing both sides of an inequality you flip the direction of the inequality sign:
x ≥ -5
The dot will be on -5, because the inequality includes equal to, the dot is solid and is greater than, the arrow will point to the right.
The correct answer is D.
Answer:
4.11% probability that he has lung disease given that he does not smoke
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Does not smoke
Event B: Lung disease
Lung Disease/Nonsmoker 0.03
This means that 
Lung Disease/Nonsmoker 0.03
No Lung Disease/Nonsmoker 0.7
This means that 
What is the probability of the following event: He has lung disease given that he does not smoke?
4.11% probability that he has lung disease given that he does not smoke
