To solve this problem, let us first assign some variables.
Let us say that:
v1 = velocity of airplane = 180 mph
t1 = time travelled by airplane
v2 = velocity of jet = 330 mph
t2 = time travelled by jet
Since we know that distance is the product of velocity and
time, and that the distance travelled by the two must be equal for the jet to
catch up to the plane, hence:
v1 * t1 = v2 * t2
But we know that:
t1 = t2 + 1
Therefore:
180 (t2 + 1) = 330 t2
180 t2 + 180 = 330 t2
150 t2 = 180
t2 = 1.2 hours
<span>Therefore the jet can catch up to the plane after 1.2
hours it takes off.</span>
Answer:
a. We reject the null hypothesis at the significance level of 0.05
b. The p-value is zero for practical applications
c. (-0.0225, -0.0375)
Step-by-step explanation:
Let the bottles from machine 1 be the first population and the bottles from machine 2 be the second population.
Then we have 
, 
, 
and 
, 
, 
. The pooled estimate is given by
a. We want to test 
vs 
(two-tailed alternative).
The test statistic is 
and the observed value is 
. T has a Student's t distribution with 20 + 25 - 2 = 43 df.
The rejection region is given by RR = {t | t < -2.0167 or t > 2.0167} where -2.0167 and 2.0167 are the 2.5th and 97.5th quantiles of the Student's t distribution with 43 df respectively. Because the observed value 
falls inside RR, we reject the null hypothesis at the significance level of 0.05
b. The p-value for this test is given by 
0 (4.359564e-10) because we have a two-tailed alternative. Here T has a t distribution with 43 df.
c. The 95% confidence interval for the true mean difference is given by (if the samples are independent)
, i.e.,
where 
is the 2.5th quantile of the t distribution with (25+20-2) = 43 degrees of freedom. So
, i.e.,
(-0.0225, -0.0375)
Answer:
The value of f(30) is equal to 2.
Step-by-step explanation:
The given expression is :
We need to find the value of f(30)
Put x = 30 in above expression.
So,
Hence, the value of f(30) is equal to 2.
Answer:
false
Step-by-step explanation:
A reasonable function is W = 7F + 5000
Where W is the weight of the plane and F is the number of gallons of fuel.
The domain is the set of possible values for F. That is from 0 (empty tank) to 400 (full tank).
So the domain is F = [0,400], or what is equivalente 0 ≤ F ≤ 400.
The range is the set of values of W.
The minimum value of W is when F = 0 => W = 7(0) + 5000 = 5,000.
The maximum value of W is when F = 400 => W = 7(400) + 5000 = 7,800
So the range is W = [5,000 ; 7,800], pr 5000 ≤ W ≤ 7,800.
