How do you solve this equation
2 answers:
Remember the order of operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction
Solve the expressions in parentheses first.
There is an expression within parentheses that is also in an expression within brackets. Solve that expression first:
The expression in brackets will now read:
Multiply 3(-4):
Solve the expression:
The problem should now look like this:
Solve the expression in parentheses that has an exponent:
Solve the term with 1/4 as a coefficient:
The expression should now look like this:
The answer is 40.
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Answer:
a) The 95% confidence interval would be given by
b) No contradict the result obtained since the confidence interval contains the value 0, so we don't have enough evidence to conclude that we have a significant effect in the colling rate and the hardness.
Step-by-step explanation:
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean 1
represent the sample mean 2
n1=50 represent the sample 1 size
n2=40 represent the sample 2 size
sample standard deviation for sample 1
sample standard deviation for sample 2
parameter of interest.
Part a
The confidence interval for the difference of means is given by the following formula:
(1)
The point of estimate for is just given by:
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,88)".And we see that
The standard error is given by the following formula:
And replacing we have:
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by
Part b
No contradict the result obtained since the confidence interval contains the value 0, so we don't have enough evidence to conclude that we have a significant effect in the colling rate and the hardness.
Answer:
1) La serie geométrica formada es
4, 2, 1,..., ∞
2) La suma al infinito de las áreas de los cuadrados es 8 in.²
Step-by-step explanation:
1) El área del primer cuadrado, a₁ = 2² = 4 pulgadas²
El área del siguiente cuadrado, a₂ = (√ (1² + 1²)) ² = (√2) ² = 2 pulg²
El área del siguiente cuadrado, a₃ = ((√ (2) / 2) ² + (√ (2) / 2) ²) = 1 pulg²
Por lo tanto, la razón común, r = a₂ / a₁ = 2/4 = a₃ / a₂ = 1/2
Las áreas de los cuadrados progresivos forman una progresión geométrica como sigue;
4, 4×(1/2), 4 ×(1/2)²,...,4×
De donde obtenemos la serie geométrica formada de la siguiente manera;
4, 2, 1,..., ∞
2) La suma de 'n' términos de una progresión geométrica hasta el infinito para -1 <r <1 se da como sigue;
Por lo tanto, la suma de las áreas de los cuadrados hasta el infinito se obtiene sustituyendo los valores de 'a' y 'r' en la ecuación anterior de la siguiente manera;
La suma al infinito de las áreas de los cuadrados, = 8 in.²