How can you tell if a linear system of equations has an infinite number of solutions?

1 answer:

4 0

The graph of a linear equation with two variables, x and y, is a line. There are an infinite number of solutions for a line

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Solve the problem. The half-life of plutonium-234 is 9 hours. If 50 milligrams is present now, how much will be present in 6 day

MaRussiya [10]

Answer:

4) 0.001

Step-by-step explanation:

The amount (a) present in h hours is ...

a(h) = (initial value)×(1/2)^(h/(half-life))

6 days is 6×24 hours, so the amount remaining is ...

a(6×24) = 50×(1/2)^(6×24/9) = 50/2^16 ≈ 0.001 . . . . milligrams

3 0

3 years ago

The mayor is interested in finding a 98% confidence interval for the mean number of pounds of trash per person per week that is

saul85 [17]

Solution :

Given :

Sample mean, $\overline X = 34.2$

Sample size, n = 129

Sample standard deviation, s = 8.2

a. Since the population standard deviation is unknown, therefore, we use the t-distribution.

b. Now for 95% confidence level,

α = 0.05, α/2 = 0.025

From the t tables, T.INV.2T(α, degree of freedom), we find the t value as

t =T.INV.2T(0.05, 128) = 2.34

Taking the positive value of t, we get

Confidence interval is ,

$\overline X \pm t \times \frac{s}{\sqrt n}$

$34.2 \pm 2.34 \times \frac{8.2}{\sqrt {129}}$

(32.52, 35.8)

95% confidence interval is (32.52, 35.8)

So with $95 \%$ confidence of the population of the mean number of the pounds per person per week is between 32.52 pounds and 35.8 pounds.

c. About $95 \%$ of confidence intervals which contains the true population of mean number of the pounds of the trash that is generated per person per week and about $5 \%$ that doe not contain the true population of mean number of the pounds of trashes generated by per person per week.