Y = xe^x
dy/dx(e^x x)=>use the product rule, d/dx(u v) = v*(du)/(dx)+u*(dv)/(dx), where u = e^x and v = x:
= e^x (d/dx(x))+x (d/dx(e^x))
y' = e^x x+ e^x
y'(0) = 1 => slope of the tangent
slope of the normal = -1
y - 0 = -1(x - 0)
y = -x => normal at origin
Answer:
P(Y ≥ 15) = 0.763
Step-by-step explanation:
Given that:
Mean =135
standard deviation = 12
sample size n = 50
sample mean 
= 140
Suppose X is the random variable that follows a normal distribution which represents the weekly supermarket expenses
Then,
The probability that X is greater than 140 is :
P(X>140) = 1 - P(X ≤ 140)
From z tables,
Similarly, let consider Y to be the variable that follows a binomial distribution of the no of household whose expense is greater than $140
Then;
∴
P(Y ≥ 15) = 1- P(Y< 15)
P(Y ≥ 15) = 1 - ( P(Y=0) + P(Y=1) + P(Y=2) + ... + P(Y=14) )
P(Y ≥ 15) = 0.763
Answer: dont know sorry
Step-by-step explanation:
Given the equation: (km / 3) - 2x = 4, it is essential to isolate x to obtain the expression to solve it. This is done below:
(km / 3<span>) - 2x = 4
</span>
Adding 2x to both sides:
(km / 3<span>) - 2x + 2x = 4 + 2x
</span>(km / 3<span>) = 4 + 2x
</span>
Subtracting 4 from both sides:
(km / 3<span>) - 4 = 4 + 2x - 4
</span>(km / 3<span>) - 4 = 2x
</span>
Dividing 2 from both sides:
[(km / 3<span>) - 4] /2 = 2x /2
</span>[(km / 3<span>) - 4] /2 = x
</span>x = (km / 6) - 2
Ok so first, the skateboard costs $79.99. The skateboard costs 12% less with discount now so you have to pay 12% less.
You start by finding 12% of 79.99. This can be easily done by hand or with a calculator. Do 0.12 times 79.99. The answer is 9.5988. Since its 12% less we now subtract $9.5988 from $79.99. We get $70.3912. So this is the discounted price.
Now for the state sales tax. The sales tax is 6.75% which is equal to 0.0675. Like we did before, we multiplied .0675 by the value we wanted this percent of. But we can do a short way instead. Instead of getting 6.75% of $70.3912 and then adding it back to $70.3912, we can multiply $70.3912 by 1.0675 and this will do all the work for us.
So now, do $70.3912 times 1.0675 and you will have the answer. The answer is $75.142606, but wait, now we will round this to hundredths place as cents place ends their, and so the final answer will be $75.14.
