What is the solution of the following system of equations: x = y + 9
1 answer:
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The answer is 19
work :
1-multiply the numbers by a submultiple of 10 to remove the decimal points.
2-
now do the division :
so the answer is 19
note: there is no need to get it back to decimal number unless you multiply just one of the numbers or multiply the numbers with different submultiples of 10
good luck
work :
1-multiply the numbers by a submultiple of 10 to remove the decimal points.
2-
now do the division :
so the answer is 19
note: there is no need to get it back to decimal number unless you multiply just one of the numbers or multiply the numbers with different submultiples of 10
good luck
Answer:
The value of this investment at the end of the 5 years is of $662.5.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Dina invests $600 for 5 years at a rate of 2% per year compound interest.
This means that . Thus
Calculate the value of this investment at the end of the 5 years.
This is A(5). So
The value of this investment at the end of the 5 years is of $662.5.
Answer:
Step-by-step explanation:
Hello!
The researcher wants to test if the valve plates manufactured have the expected tensile strength of 5 lbs/mm. So he took a sample of 42 valve plates and measured their tensile strength, obtaining a sample mean of X[bar]= 5.0611 lbs/mm and a sample standard deviation of S=0.2803 lbs/mm.
The study variable is:
X: tensile strength of a valve plate (lbs/mm)
The parameter of interest is the mean tensile strength of the valve plates, μ.
If the claim is that the valve plates of the sample have on average tensile strength of 5 lbs/mm, symbolically: μ = 5
a) The statistic hypotheses are:
H₀: μ = 5
H₁: μ ≠ 5
b) To determine the critical values and rejection region of a hypothesis test you need three to determine three factors of the hypothesis test:
1) The statistical hypothesis.
2) The significance level.
3) The statistic to use for the analysis.
The statistic hypothesis determines the number of critical values and the direction of the rejection region, in this case, the test is two-tailed you will have two critical values and the rejection region will be divided into two.
With the statistic, you will determine the distribution under which you will work and the significance level determines the probability of rejecting the null hypothesis.
To study the population mean you need that the variable of interest has at least a normal distribution, there is no information about the distribution of the study variable but the sample size is large enough n≥30, so you can apply the central limit theorem to approximate the distribution of the sample mean to normal: X[bar]≈N(μ;σ²/n)
Thanks to this approximation it is valid to use an approximation of the standard normal distribution for the test:
≈N(0;1)
The critical values are:
You will reject the null hypothesis if ≤-1.648 or if
≥1.648
You will not reject the null hypothesis if -1.648<<1.648
c)
d) The value of the statistic is between the two critical values so the decision is to not reject the null hypothesis. Then using a significance level of 10% there is no significant evidence to reject the null hypothesis so the valve plates have on average tensile strength of 5 lbs/mm.
e) The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis). If the test is two-tailed, so is the p-value, you can calculate it as:
P(Z≤-1.41) + P(Z≥1.41)= P(Z≤-1.41) + (1 - P(Z≤1.41))= 0.079 + ( 1 - 0.921)= 0.158
p-value: 0.158
I hope it helps!