Answer:
probability that all of the sprinklers will operate correctly in a fire: 0.0282
Step-by-step explanation:
In order to solve this question we will use Binomial probability distribution because:
- In the question it is given that the sprinklers activate correctly or not independently.
- The number of outcomes are two i.e. sprinklers activate correctly or not.
A binomial distribution is a probability of a success or failures outcomes in an repeated multiple or n times.
Number of outcomes of this distributions are two.
The formula is:
b(x; n, P) = 
b = binomial probability also represented as P(X=x)
x =no of successes
P = probability of a success on a single trial
n = no of trials
is calculated as:
= n! / x!(n – x)!
= 10! / 10!(10-10)!
= 1
According to given question:
probability of success i.e. p = 0.7 i.e. probability of a sprinkler to activate correctly.
number of trials i.e. n = 10 as number of sprinklers are 10
To find: probability that all of the sprinklers will operate correctly in a fire
X = 10 because we have to find the probability that "all" of the sprinklers will operate correctly and there are 10 sprinklers so all 10 of them
So putting these into the formula:
P(X=x) =
= C₁₀,₁₀ * 0.7¹⁰ * (1-0.7)¹⁰⁻¹⁰
= 1 * 0.0282 * (0.3) ⁰
= 1 * 0.0282 * 1
P(X=x) = 0.0282
The slope of a function is the ratio of the rise (y2 - y1) and the run (x2-x1) of a function, In this case the slope would be (1 - 0) / (1-0) = 1. The y-intercept would be the y value when x is zero. From the table we see this will have a value of zero. The equation for this function would be y = x. We use the said equation to fill the blanks in the table.
Length = 4x
width = 7x
perimeter is 2length+2width= 352
2(4x)+2(7x) = 352
8x+14x =352
22x = 352
x = 16
then length = 4*16=64
width =7*16=112
Answer:
a. rad27
Step-by-step explanation:
we can use a2+b2=c2 where c is the hypotonuse.
we plug in 3^2+b2=6^2
9+b^2=36
b^2=27
then do a rad over each to get rid of the ^2 on the b
b=rad 27
answer is rad27
To answer this question, first
let ∫ √(t³+1) dt = g(t) + C
<span>Then g'(t) = √(t³+1) </span>
<span>F(x) = ∫₀ˣ √(t³+1) dt = g(t) |₀ˣ = g(x) - g(0) </span>
<span>Now g(x) is some function of x, while g(0) is a constant </span>
<span>F(x) = g(x) - g(0) </span>
<span>Differentiate both sides: </span>
<span>F'(x) = g'(x) - 0 = √(x³+1) </span>
<span>So you are correct, in this case, we simply replace t with x (this is not always the case) </span>
<span>F'(2) = √(2³+1) = √9 = 3 </span>
<span>You MUST remember that when dealing with square roots, we have: </span>
<span>x² = 4 -----> x = -2 or 2 </span>
<span>x = √4 ----> x = 2 </span>
<span>That's why in the quadratic formula: x = (-b ± √(b²-4ac)) / (2a), we use a ± sign in front of square root, otherwise, if we could willy-nilly assign positive and negatives value to √(b²-4ac), then we would have no need for the ± sign. </span>
<span>Also, when solving x² = 4, we usually have intermediate step </span>
<span>x = ± √4, where +√4 (or simply √4) = 2, and -√4 = 2
</span>
