You traveled 11 miles because if you did use 28.00 and $1.50 then you take that answer and then add the $4.00 and $3.00 you will get $7 so you just subtract that for the other number and you get 11 miles because it is $1.50 per mile
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Answer: Choice A) 0.20</h3>
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Explanation:
Let's say there are 1000 students. The students must take math, science or they can take both simultaneously.
- 65% of them are in math. So there are 0.65*1000 = 650 math students.
- 43% are in science, leading to 0.43*1000 = 430 science students.
- 13% are in both so we have 0.13*1000 = 130 students who are in both.
Now onto the sentence that says "Suppose a high school student who is enrolled in a math class is selected at random"
This means we only focus on the 650 math students and ignore the 1000-650 = 350 students who aren't in math.
Of those 650 math students, 130 are also in science (since 130 are in both classes).
The probability we're after is therefore 130/650 = 0.20
Let x=ab=ac, and y=bc, and z=ad.
Since the perimeter of the triangle abc is 36, you have:
Perimeter of abc = 36
ab + ac + bc = 36
x + x + y = 36
(eq. 1) 2x + y = 36
The triangle is isosceles (it has two sides with equal length: ab and ac). The line perpendicular to the third side (bc) from the opposite vertex (a), divides that third side into two equal halves: the point d is the middle point of bc. This is a property of isosceles triangles, which is easily shown by similarity.
Hence, we have that bd = dc = bc/2 = y/2 (remember we called bc = y).
The perimeter of the triangle abd is 30:
Permiter of abd = 30
ab + bd + ad = 30
x + y/2 + z =30
(eq. 2) 2x + y + 2z = 60
So, we have two equations on x, y and z:
(eq.1) 2x + y = 36
(eq.2) 2x + y + 2z = 60
Substitute 2x + y by 36 from (eq.1) in (eq.2):
(eq.2') 36 + 2z = 60
And solve for z:
36 + 2z = 60 => 2z = 60 - 36 => 2z = 24 => z = 12
The measure of ad is 12.
If you prefer a less algebraic reasoning:
- The perimeter of abd is half the perimeter of abc plus the length of ad (since you have "cut" the triangle abc in two halves to obtain the triangle abd).
- Then, ad is the difference between the perimeter of abd and half the perimeter of abc:
ad = 30 - (36/2) = 30 - 18 = 12
Answer:
She made She made 100 grams of 45% sugar syrup.
Step-by-step explanation:
Genna added 45 grams of sugar into 55 grams of water.
Total amount she mixes = 45 + 55 = 100 grams.
Percentage of sugar in total mixture (sugar syrup) = 45 grams sugar in 55 grams syrup.
Here, Solute is sugar and Solvent is water.
mass of solute = 45
mass of solute + mass of solvent = 100
Putting values, we get,
Thus, She made She made 100 grams of 45% sugar syrup.
