A skateboard ramp is 40 feet long and rises from the ground at an angle of 33 degrees. How tall is the ramp?
1 answer:
Answer:
The ramp is 21.8 ft tall.
Step-by-step explanation:
If you convert this into a triangle, 40 ft is the hypotenuse, 33° is the angle next to the right angle (on the horizontal line) and we need to find how tall the ramp is, which will be x. It is very helpful to draw a picture.
We will use the sine ratio because, starting from the given degree of 33, we have the hypotenuse value and need to find the value opposite the degree:
Insert values:
Multiply 40 to both sides to isolate the variable:
Insert the value of x into a calculator:
Round if necessary:
Done.
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Answer:
a) "=T.INV(0.025,10)" and "=T.INV(1-0.025,10)"
And we got
b) "=T.INV(0.025,20)" and "=T.INV(1-0.025,20)"
And we got
c) "=T.INV(0.005,20)" and "=T.INV(1-0.005,20)"
And we got
d) "=T.INV(0.005,50)" and "=T.INV(1-0.005,50)"
And we got
e) "=T.INV(1-0.01,25)"
And we got
f) "=T.INV(0.025,5)"
And we got
Step-by-step explanation:
Previous concepts
The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".
The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.
The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."
Solution to the problem
We will use excel in order to find the critical values for this case
Determine the t critical value(s) that will capture the desired t-curve area in each of the following cases:
a. Central area =.95, df = 10
For this case we want 0.95 of the are in the middle so then we have 1-0.95 = 0.05 of the area on the tails. And on each tail we will have .
We can use the following excel codes:
"=T.INV(0.025,10)" and "=T.INV(1-0.025,10)"
And we got
b. Central area =.95, df = 20
For this case we want 0.95 of the are in the middle so then we have 1-0.95 = 0.05 of the area on the tails. And on each tail we will have .
We can use the following excel codes:
"=T.INV(0.025,20)" and "=T.INV(1-0.025,20)"
And we got
c. Central area =.99, df = 20
For this case we want 0.99 of the are in the middle so then we have 1-0.99 = 0.01 of the area on the tails. And on each tail we will have .
We can use the following excel codes:
"=T.INV(0.005,20)" and "=T.INV(1-0.005,20)"
And we got
d. Central area =.99, df = 50
For this case we want 0.99 of the are in the middle so then we have 1-0.99 = 0.01 of the area on the tails. And on each tail we will have .
We can use the following excel codes:
"=T.INV(0.005,50)" and "=T.INV(1-0.005,50)"
And we got
e. Upper-tail area =.01, df = 25
For this case we need on the right tail 0.01 of the area and on the left tail we will have 1-0.01 = 0.99 , that means
We can use the following excel code:
"=T.INV(1-0.01,25)"
And we got
f. Lower-tail area =.025, df = 5
For this case we need on the left tail 0.025 of the area and on the right tail we will have 1-0.025 = 0.975 , that means
We can use the following excel code:
"=T.INV(0.025,5)"
And we got
