71 divided with 100 times 67
Answer: {-5, 5}. Product is -25, which is the minimum.
Explanation:
let a, b denote the two numbers. We know that b-a=10.
We are looking for a minimum over the product a*b.
One can minimize this using derivatives. In case you have not yet had derivatives, you can also use the vertex of a parabola (since the above is a quadratic form):
The minimum is at the vertex a=-5 and so b=5
Their distance is 10, and their product attains the minimum value of all possiblities -25.
Answer:
Step-by-step explanation:
Hello!
a.
The objective is to study the relationship between the shape of an ibuprofen tablet and its dissolution time.
For these two independent samples of tablets from different shapes where taken and their dissolution times measured:
Sample 1: Disk.shaped tablets
n₁= 6
X[bar]₁= 255.8
S₁= 8.22
Sample 2: Oval-shaped tablets
n₂=8
X[bar]₂= 270.74
S₂= 11.90
Assuming that the population variances are equal and both samples come from normal distributions you need to test if the average dissolution time of the disk-shaped tablets is less than the average dissolution time of the oval-shaped tablets, symbolically:
H₀: μ₁ ≥ μ₂
H₁: μ₁ < μ₂
α: 0.05
Considering the given information about both populations, the statistic to use for this test is a Student t for independent samples with pooled sample variance:
Sa²= 110.76
Sa= 10.52
This test is one-tailed to the left, meaning that you will reject the null hypothesis to small values of t, the p-value has the same direction and you can calculate it as:
P(t₁₂≤-2.63)= 0.0110
Since the p-value= 0.0110 is less than the significance level α: 0.05, the decision is to reject the null hypothesis.
At a 5% significance level you can conclude that the average dissolution time of the disk-shaped ibuprofen tablets is less than the average dissolution time of the oval-shaped ibuprofen tablets.
b.
(X[bar]₁-X[bar]₂)+Sa
(255.8-270.74)+ 10.52*
(-∞;-4.815)
I hope it helps!
Answer:
In both cases, we have similar figures.
This means that the shape of the figures is the same, but the size is different:
PQST is similar to STNR and to NRPQ
VUYZ is similar to YZWX and to VUWX
this means that, for example, in problem 18, the ratio between ST and NR must be the same as the ratio between PQ and ST. This happens because the measure increases by the same scale factor.
With this in mind, we can solve the problem:
18)
ST = 7.5
NR = 5.5
Then the quotient ST/NR is:
ST/NR = 7.5/5.5
And, as we said above:
PQ/ST = ST/NR
PQ/7.5 = 7.5/5.5
PQ = (7.5/5.5)*7.5 = 10.23
19) Here we should have:
YZ/VU = WX/YZ
Then:
22.9/35 = WX/22.9
(22.9/35)*22.9 = WX = 14.98