Δ = 1 + 4*20 = 81
x' = (-1 + 9)/2 = 4
x'' = (-1 - 9)/2 = -5
4² + 4 - 20 = 0
(-5)² - 5 - 20 = 0
Ok !
Answer:
1/3
Step-by-step explanation:
1/3 can be used as an expression that is exactly the same as 2/3x5.
When you multiply 2/3 x 5-
Look here if you need help solving 2/3 X 5: (2/3 x 5/1...is the simplest way to multiply the two, make sure to multiply 2 by 5 and 3 by 1 to get your answer.)(5x2=10...3x1=3)
-you get 10/3. This answer simplified is 1/3. So in the end, 1/3 is a great expression or answer to use as an equivalent to the equation 2/3 x 5.
Hoped this helped! :)
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:
111 / 190
Step-by-step explanation:
Total biscuits = 20
Plain, P = 12
Chocolate, C = 5
Currant, K = 3
Assume without replacement :
Probability that biscuit are of the same type :
P(plain) :
12 / 20 * 11 / 19 = 132 / 380
P(chocolate) :
5/ 20 * 4 / 19 = 20/ 380
P(currant) :
3/20 * 2 /19 = 6 / 380
Therefore,
Probability that biscuit is of the same type :
P(plain) + P(chocolate) + P(currant)
132/380 + 20/380 + 6/380
158 / 380 = 79 / 190
Therefore, probability that biscuit aren't of the same type :
1 - P(biscuit is of same type)
1 - 79/190
(190 - 79) / 190
111 / 190
Answer:
The simple interest is $300.
Step-by-step explanation:
<em>Find the Interest amount.</em>
I: Interest ?
P: Principle Amount $2500
R: Rate 6% = .06
T: Time Period (in years) 2 Years
<em>Convert into equation to find Simple Interest</em>
I = Prt
I = (2500)(.06)(2)
<em>Calculate</em>
I = 300
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