Answer:
The ages of the children are 6, 9 and 12.
Explanation:
Let x= the age of the youngest child.
If the oldest child is twice the age of the youngest, the age of the oldest child is twice x or 2x.
If the middle child is 3 years older than the youngest, the age of the middle child is x+3.
If the sum of their ages is 27, then
x+2x+x+3=27aaa(Combine like terms)
4x+3=27aaa
aa−3a−3aaa(Subtract 3 from both sides)
4x=24
4x4=24aaa(Divide both sides by 4)
Answer:
B. 0.0122
Step-by-step explanation:
According to the given data the claim is:
"Proportion of students who went to the movie theater last weekend is greater than 0.2"
Since, the word "greater than" is used in the claim, this claim will be our alternate hypothesis and the hypothesis test will be a one-tailed test i.e. Right tailed test because of the word "greater than".
We are given that the hypothesis test was conducted for a random sample of 100 students and it yielded a z-value of 2.25. We have to find the p-value associated with this z-score
So, we have to find p-value corresponding to z-score of 2.25 and Right Tailed Test. We have to use z-table for this purpose and find the probability of z score being greater than 2.25. From the z-table this value comes out to be:
p-value = 0.0122
Therefore, option B gives the correct answer.
Answer:
6x +10
Step-by-step explanation:
Perimeter = 2*(length + width)
= 2* (x+6 + 2x-1)
=2*(3x +5)
=2*3x + 2*5
=6x + 10
Triangles PQR and PSR are right triangles, with both QR = SR = 5 (since these are radii of the circle R).
TR is also a radius of the circle, so TR = 5, making PR = 4 + TR = 9.
Because PQR and PSR are right triangles, we can compute the length of the missing side, which will be equal. By the Pythagorean theorem,
PQ^2 + QR^2 = PR^2
PQ^2 + 5^2 = 9^2
PQ^2 = 56
PQ = √56 = 2√14
Then the perimeter of PQRS is
PQ + QR + RS + SP = 2√14 + 5 + 5 + 2√14 = 10 + 4√14
and so the answer is B.
Answer:
The attached file contains the solution to the question
