Answer:
= ![\dfrac{1}{5^{9}}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B5%5E%7B9%7D%7D)
Step-by-step explanation:
When dividing values with exponents, we simply need to subtract the numerators exponent to the denominators exponent.
So we have:
= ![5^{-6 - 3}](https://tex.z-dn.net/?f=5%5E%7B-6%20-%203%7D)
= ![5^{-9}](https://tex.z-dn.net/?f=5%5E%7B-9%7D)
Now since we have a negative exponent, we can get the reciprocal of the value to make it positive.
= ![\dfrac{1}{5^{9}}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B5%5E%7B9%7D%7D)
Using the SSA formula:
X = SQRT ( 40^2 + 26^2 - 2*40*26*cos(65))
X = SQRT(2276 - 2080*cos(65))
X = SQRT(1396.954)
X = 37.37 = 37.4 ft.
<h2>
Answer</h2>
Distributive Property
The distributive property states that when a factor is multiplied by the sum of two numbers, you can multiply each of the two numbers by that factor and then add them.
<h2>Example</h2><h3>Equation </h3>
10(x + 2) = 45
Apply the distributive property to the left side of the equation by multiplying
two numbers inside the parentheses by 10
10(x) + 10(2) = 45
Now add them
10x + 20 = 45
Rearrange the like terms
10x = 45 -20
10x = 25
x = 25/10
x = 2.5
Answer:
X=the smaller
y=the larger
The bigger of two numbers is four more than the smaller, then:
y=x+4
one more than twice the smaller is the same as the larger, then
1+2x=y
We have the following system of equations:
y=x+4
y=2x+1
We solve this system by equal values method:
x+4=2x+1
x-2x=1-4
-x=-3
x=3
We find the value of "y"now:
y=x+4
y=3+4
y=7
the values of x and y are:
x=3
y=7
Step-by-step explanation:
Answer: 0.5
Step-by-step explanation:
Binomial probability formula :-
, where P(x) is the probability of getting success in x trials , n is the total trials and p is the probability of getting success in each trial.
Given : The probability that the adults follow more than one game = 0.30
Then , q= 1-p = 1-0.30=0.70
The number of adults surveyed : n= 15
Let X be represents the adults who follow more than one sport.
Then , the probability that fewer than 4 of them will say that football is their favorite sport,
![P(X\leq4)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)\\\\=^{15}C_{0}\ (0.30)^0(0.70)^{15}+^{15}C_{1}\ (0.30)^1(0.70)^{14}+^{15}C_{2}\ (0.30)^2(0.70)^{13}+^{15}C_{3}\ (0.30)^3(0.70)^{12}+^{15}C_{4}\ (0.30)^4(0.70)^{11}\\\\=(0.30)^0(0.70)^{15}+15(0.30)^1(0.70)^{14}+105(0.30)^2(0.70)^{13}+455(0.30)^3(0.70)^{12}+1365(0.30)^4(0.70)^{11}\\\\=0.515491059227\approx0.5](https://tex.z-dn.net/?f=P%28X%5Cleq4%29%3DP%28x%3D0%29%2BP%28x%3D1%29%2BP%28x%3D2%29%2BP%28x%3D3%29%2BP%28x%3D4%29%5C%5C%5C%5C%3D%5E%7B15%7DC_%7B0%7D%5C%20%280.30%29%5E0%280.70%29%5E%7B15%7D%2B%5E%7B15%7DC_%7B1%7D%5C%20%280.30%29%5E1%280.70%29%5E%7B14%7D%2B%5E%7B15%7DC_%7B2%7D%5C%20%280.30%29%5E2%280.70%29%5E%7B13%7D%2B%5E%7B15%7DC_%7B3%7D%5C%20%280.30%29%5E3%280.70%29%5E%7B12%7D%2B%5E%7B15%7DC_%7B4%7D%5C%20%280.30%29%5E4%280.70%29%5E%7B11%7D%5C%5C%5C%5C%3D%280.30%29%5E0%280.70%29%5E%7B15%7D%2B15%280.30%29%5E1%280.70%29%5E%7B14%7D%2B105%280.30%29%5E2%280.70%29%5E%7B13%7D%2B455%280.30%29%5E3%280.70%29%5E%7B12%7D%2B1365%280.30%29%5E4%280.70%29%5E%7B11%7D%5C%5C%5C%5C%3D0.515491059227%5Capprox0.5)
Hence, the probability rounded to the nearest tenth that fewer than 4 of them will say that football is their favorite sport =0.5