Answer:
Step-by-step explanation:
Let x be the random variable. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 474
σ = 32
x = 514
The probability of being below 514 is expressed as P(x < 514)
For x = 514,
z = (514 - 474)/32 = 1.25
Looking at the normal distribution table, the probability value corresponding to area below the z score is 0.89
Therefore,
P(x < 514) = 0.89
Answer:
90
Step-by-step explanation:
You need to simply add all the given numbers together and enter the missing number that'll make the total 0. So:
-75 + (-25) = -100
-100 + 10 = -90
-90 + <u>90</u> = 0
Thus, adding a 90 in the empty box will make it 0.
Remember that parentheses come first. Follow PEMDAS
Answer:
D. ABE =CBD by SSS.
Step-by-step explanation:
Given that AB = BD and BE = BC, the lengths of AE and CD are equal to each other. Hence, triangles ABE and BCD are congruent by SSS Theorem. The answer is D.
Answer:
Step-by-step explanation:
Given the equation 4x²+ 49y² = 196
a) Differentiating implicitly with respect to y, we have;

b) To solve the equation explicitly for y and differentiate to get dy/dx in terms of x,
First let is make y the subject of the formula from the equation;
If 4x²+ 49y² = 196
49y² = 196 - 4x²

Differentiating y with respect to x using the chain rule;
Let 





c) From the solution of the implicit differentiation in (a)

Substituting
into the equation to confirm the answer of (b) can be shown as follows

This shows that the answer in a and b are consistent.