Answer:
The standard deviation of weight for this species of cockroaches is 4.62.
Step-by-step explanation:
Given : A different species of cockroach has weights that are approximately Normally distributed with a mean of 50 grams. After measuring the weights of many of these cockroaches, a lab assistant reports that 14% of the cockroaches weigh more than 55 grams.
To find : What is the approximate standard deviation of weight for this species of cockroaches?
Solution :
We have given,
Mean 
The sample mean x=55
A lab assistant reports that 14% of the cockroaches weigh more than 55 grams.
i.e. P(X>55)=14%=0.14
The total probability needs to sum up to 1,



The z-score value of 0.86 using z-score table is z=1.08.
Applying z-score formula,

Where,
is standard deviation
Substitute the values,





The standard deviation of weight for this species of cockroaches is 4.62.
Answer:
Step-by-step explanation:
X^2+7x+63=63
<=> x^2+7x=63-63=0
<=> X(x+7)=0
<=> x1=0
X2=-7
Answer: 
Step-by-step explanation:
Given
The temperature of the liquid is
placed in an oven with temperature of
.
Initially difference in temperature of the two

According to the question
![\Rightarrow \dfrac{dT(t)}{dt}=77\cdot \Delta T\\\\\Rightarrow \dfrac{dT(t)}{dt}=77\times (450-T)\quad [\text{T=75}^{\circ}F\ \text{at t=0}]](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7BdT%28t%29%7D%7Bdt%7D%3D77%5Ccdot%20%5CDelta%20T%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7BdT%28t%29%7D%7Bdt%7D%3D77%5Ctimes%20%28450-T%29%5Cquad%20%5B%5Ctext%7BT%3D75%7D%5E%7B%5Ccirc%7DF%5C%20%5Ctext%7Bat%20t%3D0%7D%5D)