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
The sequence is geometric. Any exponential function models geometric growth. Recall the general nth term of a geometric sequence is a*(r)^(n-1) which is very similar to the form y = a*b^x. The big difference is that the x function is continuous while the function in terms of n is discrete. In this case, the common ratio is r = 1.10 to indicate we have 10% growth. Notice how 100%+10% = 1.00+0.10 = 1.10
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The first quadrant is where x and y are both positive. Since x is the time in years, it doesn't make sense to talk about negative years or negative years have passed by. We can have a negative balance in a bank account, so it makes sense to have y be negative. However, Mr Sullivan starts with some positive amount and his account grows every year. So there's no way that y can be negative in this case.
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The point (0,200) is the y intercept. It represents the starting amount he deposited into the account, which was the $200. Keep in mind that no other deposits were made, and he cannot pull money out of the account if he wants his account to grow according to the graph. Also, the interest rate must remain at 10%.
Answer:
(a) 
Step-by-step explanation:
Given
Required
Determine the time in each lap
The unit time in each lap is calculated by dividing the total time by the number of laps; i.e.;
Substitute values for Time and Lap
Answer:
8) -8, -9
9) 4, 
Step-by-step explanation:
8) x² + 12x + 27
Solutions of a polynomial means the values of 
such that the polynomial becomes zero. 
.
We use the following formula to determine the solutions of a quadratic equation of the form: 
In this equation, 
Substituting in the formula, we have:
Taking 2 common outside we get:
Therefore, we get two solutions viz, x = -3, -9.
9) 2x² - 9x + 4 = y
X- intercepts of a polynomial means the value of x such that y = 0. It means the roots of the polynomial.
Solving the equation using the formula above, we get:
The values of x = 4, .
Hence, the answer.
