The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.
To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.
In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.
The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.
The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.
Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.
First, we need to standardize the value of 60.8 using the formula:
Z = (X - μ) / σ
Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.
In this case, the standardized value is:
Z = (60.8 - 60) / sqrt(0.16)
Z = 0.8 / 0.4
Z = 2
Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.
Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.
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Write an equation for the function graphed below
The rational function graphed in this problem is defined as follows:
y = -2(x - 1)/(x² - x - 2).
How to define the rational function?The vertical asymptotes of the rational function for this problem are given as follows:
x = -1 and x = 2.
Hence the denominator of the function is given as follows:
(x + 1)(x - 2) = x² - x - 2.
The intercept of the function is given as follows:
x = 1.
Hence the numerator of the function is given as follows:
a(x - 1)
In which a is the leading coefficient.
Hence:
y = a(x - 1)/(x² - x - 2).
When x = 0, y = -1, hence the leading coefficient a is obtained as follows:
-1 = a/2
a = -2.
Thus the function is given as follows:
y = -2(x - 1)/(x² - x - 2).
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21x² - 2x + 1/2 =0
find the following quadratic equation by factorization method
PLESE SOMEONE HELP
Step-by-step explanation:
21x²-2x +1/2 = 0
x² - 2x ×21 + 1/2× 21 = 0
Sandro would like to retire at age 60 with an income of $1500 per month from his
retirement savings. If he is to receive these payments until he is 90 years old, what
amount would he need in his retirement savings account at age 60, if the account
earns 4.5% compounded monthly?
The amount (present value at age 60) that Sandro would neet in his retirement savings account in order to have a monthly income of $1,500 until he is 90 years old, compounded at 4.5% monthly is $296,041.74.
How the present value is computed:The present value is computed using an online fiance calculator that discounts the future withdrawals (monthly income) for a 360-months period.
End of withdrawal period = 90 years old
Beginning of withdrawal period = 60 years old
The number of years between 60 and 90 = 30 years
N (# of periods) = 360 months (30 years x 12)
I/Y (Interest per year) = 4.5%
PMT (Periodic Payment) = $-1,500
FV (Future Value) = $0
Results:
Present Value (PV) = $296,041.74
Sum of all periodic payments = $540,000 ($1,500 x 360 months)
Total Interest = $243,958.26
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Find the value of y.
Answer:
y = [tex]\sqrt{55}[/tex]
Step-by-step explanation:
using the Altitude- on- Hypotenuse theorem
(altitude)² = product of parts of hypotenuse
then
y² = 11 × 5 = 55 ( take square root of both sides )
y = [tex]\sqrt{55}[/tex]
Can someone help me please? ASAP
Answer:
triangle XYZ is similar to triangle RPQ
scale factor = 2/5
Step-by-step explanation:
Angles X and R are given as congruent.
Angles Z and Q are right angles, so they are congruent.
Then, angles Y and P must be congruent.
The similarity statement is
triangle XYZ is similar to triangle RPQ
To find the scale factor, divide the length of a side of the image by the length of the corresponding side in the original.
10/25 = 2/5
The scale factor is 2/5.