Answer
If we had a sale price of 30% off of $1,050then the sale price is 70% of $1,050 or 0.7(1050) Then we add 7% sales tax to that making thefinal price paid 107% of [0.7(1050)] ... 1.07[0.7(1050)] = $786.45
Answer:
The probability that the senator was in the Democratic party, given that the senator was returning to office is 0.4715.
Step-by-step explanation:
The complete question is:
Sophia made the following two-way table categorizing the US senators in 2015 by their political party and whether or not it was their first term in the senate.
Democratic Republican Independent Total
First Term 11 28 11 50
Returning 33 26 11 70
Total 44 54 22 120
Find the probability that the senator was in the Democratic party, given that the senator was returning to office.
Solution:
The conditional probability of an event <em>A</em> given that another event <em>X</em> has already occurred is given by:

The probability of an event <em>E</em> is given by the ratio of the number of favorable outcomes to the total number of outcomes.

Compute the probability of selecting an US senator who is a Democratic and was returning to office as follows:

Compute the probability of selecting an US senator who was returning to office as follows:

Compute the conditional probability, P (D | R) as follows:


Thus, the probability that the senator was in the Democratic party, given that the senator was returning to office is 0.4715.
Answer:
last option
Step-by-step explanation:
7pi/6,11pi/6
Answer:
x = 0.72
Step-by-step explanation:
Given
3.8x = 2.736 ( divide both sides by 3.8 )
x = 0.72
Answer:
Congurent triangles are those which map onto them selves perfectly. This means they share the same angle measurements and side lengths. Therefor we can figure out the side lengths by using the information in both triangles.
AD=5x+11
in the congurent triangle, the corresponding side equals:
CM=7x-3
CM and AD are congurent triangles meaning their sidelengths equal the same. Therefore...
5x+11=7x-3
Now we just solve to find the length of AD and CM (equal lengths)
5x+11=7x-3
11=2x-3
14=2x
7=x
x=7
If x=7 then we can plug it in for AD to find the side length.
5(7)+11=46
Notice that CM equals the same 7(7)-3=46
This is because... they are congruent triangles.
These rules also apply for all angle measurements of congruent triangles:
The m<v is equal to the meaasure of E (corresponding angles in congrurent triangles are equal)
We already astablished what x was (x=7) meaning if we find the measure of E then we have the measure of V sicne they are corresponding angles in a congrurent triangle.
(6x7+1)=43°
therefore the m<v is equal to 43°
46 and 43° is your answer
Step-by-step explanation: