Answer:25
Step-by-step explanation:
Answer:
Step-by-step explanation:
The slope of a graph is also known as its gradient, which is the steepness of the graph.
If we are given two points on the line, we can find the slope by taking rise/ run, which is the ratio of the change in y-coordinate against the change in the x-coordinate. This can also be written as a formula:
☆ (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate
In this question, we are given the equation of the line. This equation is already in the slope-intercept form (y= mx +c) since the coefficient of y is 1 and all the other terms are on the other side of the equal sign. In the slope-intercept form, m is the slope while c is the y-intercept.
m= ⅘ since the coefficient of x is ⅘ in the given equation (when the equation is in the slope-intercept form).
Answer:
(a) Test statistic is -2.85 and p-value is 0.0022
(b) Reject the null hypothesis. The population mean of dissolved oxygen content is not equal to 10 mg/L
Step-by-step explanation:
H0: mu equals 10
Ha: mu not equals 10
The test is a two-tailed test because the alternate hypothesis is expressed using not equal to
(a) Test statistic (z) = (sample mean - population mean) ÷ (sd/√n) = (9.14 - 10) ÷ (2/√44) = -0.86 ÷ 0.302 = -2.85
Cumulative area of the test statistic = 0.9978
p-value = 2(1 - 0.9978) = 2(0.0022) = 0.0044
(b) The critical value using 0.02 significance level is 2.422. For a two-tailed test, the region of no rejection of the test statistic lies between -2.422 and 2.422.
Conclusion:
Reject the null hypothesis because the test statistic -2.85 falls outside the region bounded by the critical values -2.422 and 2.422.
The population mean of dissolved oxygen content is not equal to 10 mg/L
Answer:
It will take 4.84 years
Step-by-step explanation:
The initial amount that Matt invested was $1669. It means that principal is
P = 1669
It was compounded 12 times per year. So
n = 12
The rate at which the principal was compounded is 2%. So
r = 2/100 = 0.02
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years.
A = 1,844.38
Therefore
1,844.38 = 1669(1+0.02/12)^(12×t)
1,844.38/1669 = (1.0017)^(12t)
1.1051 = (1.0017)^(12t)
Taking log to base 10 of both sides, it becomes
Log 1.1051 = log 1.0017^(12t)
Log 1.1051 = 12tlog 1.0017
0.043 = 0.00074 × 12t
0.043 = 0.00888t
t = 0.043/0.00888
t = 4.84 years
Let's solve ~
Inequalities change when it is multiplied by -ve number
