Answer:
Since the calculated value of Z does not fall in the critical region we accept our null hypothesis that mean = 60 seconds
Step-by-step explanation:
State the null hypothesis
H0: u = 60against the claim
Ha u≠ 60 (this is a two tailed test)
Sample size n= 36
Sample mean=X`= 55
Population mean = u= 60
The significance level α = 0.05
Standard deviation= Sd = 22 seconds
Z= X`- u / Sd /√n
Z= 55- 60 / 22/√6
z= - 5/22/6
Z= -1.3635
The value of z from the table is Z∝/2= ±1.96
The critical region is less than - 1.96 and greater than 1.96.
Since the calculated value of Z does not fall in the critical region we accept our null hypothesis that mean = 60 seconds
8x-12 = 5+15
8x-12 = 20
8x = 32 +12
x = 4 ÷8
Answer:$1655.22
Step-by-step explanation:
The total distance from Oakland California to Erlanger Kentucky is 2,364.6 miles. The gas tank gets 25 miles per gallon on the highway. It means that total number of gallons required to cover the distance from Oakland California to Erlanger Kentucky would be
2364.6/25 = 472.92 gallons
If the gas cost $3.50 per gallon, it means that the total amount that it will cost to drive from Oakland California to Erlanger Kentucky would be
472.92 × 3.5 = $1655.22
You can focus on the two sub-triangles ABC and ACD
We know that they are both right triangles, because we're given that AC and BD are perpendicular.
The sides AB and AD are the hypothenuses of these triangles, so we know their length through the pythagorean theorem:
But since we're given 
, the expressions for AD and AB are actually the same expression. This proves that AD=AB, and thus that the triangle is isosceles.
We know that she spent $39, and has 3/4 of the original amount left. Our goal is to find the original amount. We can use the equation. x - 39 = 3/4x. Once we subtract x on the left hand side, we get -39 = -1/4x. Once we multiply -39 by -4, we get 146. She originally had $156.
