Answer:
Step-by-step explanation:
Let us assume that the length of fishes in the tank is normally distributed. Thus, x is the random variable representing the length of fishes in the tank. Since the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = standard deviation
number of samples
From the information given,
µ = 15
σ = 4
n = 31
We want to find the probability that x is between (15 - 0.5) inches and (15 + 0.5) inches. The probability is expressed as
P(14.5 ≤ x ≤ 15.5)
For x = 14.5
z = (14.5 - 15)/(4/√31) = - 0.7
Looking at the normal distribution table, the probability corresponding to the z score is 0.2420
For x = 15.5
z = (15.5 - 15)/(4/√31) = 0.7
Looking at the normal distribution table, the probability corresponding to the z score is 0.7580
Therefore,
P(14.5 ≤ x ≤ 15.5) = 0.7580 - 0.2420 = 0.5160
5,000 × 3.8%= 19,000×18= 342,000 × 40 = 13,680,000
At the end of the January the balance of credit card need to be $498+$35=$533
$533 is more than one half of the $900. So at the end of the January.
Answer:
x = 7
Step-by-step explanation:
-3 (x - 1) + 8 (x - 3) = 6x + 7 - 5x
-3 (x - 1) + 8 (x - 3) = 6x - 5x + 7
-3 (x - 1) + 8 (x - 3) = x + 7
-3x + 3 + 8x - 24 = x + 7
-3x + 8x + 3 - 24 = x + 7
5x - 21 = x + 7
+21 +21
--------------------------------------------------
5x = x + 28
-x -x
---------------------------------------------------
4x = 28
/2 /2
----------------------------------------------------
x = 7
Answer:
Step-by-step explanation:
Given: 
To choose: the correct option
Solution:
Power refers to a number of times, a number is multiplied by itself. Another name for power is exponent.
As per rule of exponents, 
Here,
Therefore,
![(-32)^{(\frac{3}{5}) }=[(-2)^5]^{(\frac{3}{5}) }=(-2)^{5(\frac{3}{5}) }](https://tex.z-dn.net/?f=%28-32%29%5E%7B%28%5Cfrac%7B3%7D%7B5%7D%29%20%7D%3D%5B%28-2%29%5E5%5D%5E%7B%28%5Cfrac%7B3%7D%7B5%7D%29%20%7D%3D%28-2%29%5E%7B5%28%5Cfrac%7B3%7D%7B5%7D%29%20%7D)
Here, 
So,
![(-32)^{(\frac{3}{5}) }=[(-2)^5]^{(\frac{3}{5}) }=(-2)^{5(\frac{3}{5}) }=(-2)^3=-8](https://tex.z-dn.net/?f=%28-32%29%5E%7B%28%5Cfrac%7B3%7D%7B5%7D%29%20%7D%3D%5B%28-2%29%5E5%5D%5E%7B%28%5Cfrac%7B3%7D%7B5%7D%29%20%7D%3D%28-2%29%5E%7B5%28%5Cfrac%7B3%7D%7B5%7D%29%20%7D%3D%28-2%29%5E3%3D-8)
