Answer:
Step-by-step explanation:
A dime is worth 10 cents. Converting to dollars, it becomes 10/100 = $0.1
A quarter is worth 25 cents. Converting to dollars, it becomes 25/100 = $0.25
Let x represent the number of dimes that Jayden has.
Let y represent the number of quarters that Jayden has.
Jayden has some dimes and some quarters. He has at most 25 coins. It means that
x + y ≤ 25
The coins worth at least $4.60 combined. It means that
0.1x + 0.25y ≥ 4.6 - - - - - - - - - - 1
If Jayden has 7 dimes, then
7 + y ≤ 25
y ≤ 25 - 7
y ≤ 18
Substituting x = 7 into equation 1, it becomes
0.1 × 7 + 0.25y ≥ 4.6
0.7 + 0.25y ≥ 4.6
0.25y ≥ 4.6 - 0.7
0.25y ≥ 3.9
y ≥ 3.9/0.25
y ≥ 15.6
All possible values for the number of quarters that he could have would be
15.6 ≤ y ≤ 18
For a probability distribution the expected value is the summation of product of probabilities with their respective data values. Let x be the probability that Jackson goes gym for 2 days and y be the probability that he goes gym for 3 days.
For the given case we have following values and their probabilities:
0 : 0.1
2 : x
3 : y
So the expected value will be = 0(0.1) + 2(x) + 3(y)
Expected value is given to be 2.05. So we can write the equation as:
2x + 3y = 2.05 (Equation 1)
Also for a probability distribution, the sum of probabilities must always equal to 1. So we can set up the second equation as:
0.1 + x + y = 1
x + y = 0.9 (Equation 2)
From Equation 2 we can write the value of x to be x = 0.9 - y. Using this value in equation 1, we get:
2(0.9 - y) + 3y = 2.05
1.8 - 2y + 3y = 2.05
1.8 + y = 2.05
y = 0.25
Using the value of y in equation 2 we get value of x to be 0.65
Therefore we can conclude that:
The probability that Jackson goes to gym for 2 days is 0.65 and the probability that he goes to gym for 3 days is 0.25
Answer:
sorry but it is wrong the answer is 1,200
Step-by-step explanation:
Answer: The value of x in trapezoid ABCD is 15
Step-by-step explanation: The trapezoid as described in the question has two bases which are AB and DC and these are parallel. Also it has sides AD and BC described as congruent (that is, equal in length or measurement). These descriptions makes trapezoid ABCD an isosceles trapezoid.
One of the properties of an isosceles trapezoid is that the angles on either side of the two bases are equal. Since line AD is equal to line BC, then angle D is equal to angle C. It also implies that angle A is equal to angle B.
With that bit of information we can conclude that the angles in the trapezoid are identified as 3x, 3x, 9x and 9x.
Also the sum of angles in a quadrilateral equals 360. We can now express this as follows;
3x + 3x + 9x + 9x = 360
24x = 360
Divide both sides of the equation by 24
x = 15
Therefore, in trapezoid ABCD
x = 15
