Answer: -3
Step-by-step explanation: substitute y and x into the formula y=k/x, and that is 4=k/-12. Then you multiply the -12 over, you get that k=-48. Then you substitute that into the same equation getting y=-48/x, but then you see that y should be 16, so then it would be 16=-48/x. Then, you flip the two fractions to make it more simpler looking like 1/16=x/-48x. Then you multiply the -48 over, getting x=-3.
Answer:
17
Step-by-step explanation:
4 × 5 - 3² x 2 ÷ 6
20 - 3² × 2 ÷ 6
20 - 9 × 2 ÷ 6
20 - 18 ÷ 6
20 - 3 = 17
<em>H</em><em>O</em><em>P</em><em>E</em><em> </em><em>T</em><em>H</em><em>I</em><em>S</em><em> </em><em>H</em><em>E</em><em>L</em><em>P</em><em>S</em><em> </em><em>A</em><em>N</em><em>D</em><em> </em><em>H</em><em>A</em><em>V</em><em>E</em><em> </em><em>A</em><em> </em><em>N</em><em>I</em><em>C</em><em>E</em><em> </em><em>D</em><em>A</em><em>Y</em><em> </em><em><</em><em>3</em>
Answer: a. 8% ; b. Not independent; c. See tree diagram; d. Yes
Step-by-step explanation:
a. Let F = Females
M = Males
C = Those that attend college
P(F) = 80% = 0.8
P(M) = 20% = 0.2
P(C/F) = 90% = 0.9
P(C/M) = 78% = 0.78
If 90% of the females go to college, it means that 10% don't go to college.
We then use the multiplication rule and we'll get:
= 80% × 10%
= 0.8 × 0.1
= 0.08
= 8%
b. An independent event is one that the occurence of one event doesn't affect the other event from happening. However, this is not independent as the occurence of the events affect each other.
c. See attachment
The joint probability on the tree diagram will be:
= 0.72 + 0.08 + 0.156 + 0.044
= 1.00
The question is asking us to find the dimensions of the rectangle, which would be the length and width. So, to find this, we must first state our givens, as it is Geometry.
Given: Length of rectangle = 59 + twice the width, diagonal = 2 inches longer than the width
Let's first translate all our givens to numbers. We'll start off by assigning variables that are easy to work with (x, y and z).
x = width
y = length
z = diagonal
Now that we have done that, we need to translate all our givens into numbers. Here is how that would look like:
y = 2x + 59 ←59 plus twice the width (x)
z = y + 2 ←Diagonal = 2 inches more than width
If we draw a diagram, we can see that the diagonal, length, and width all create a right triangle, which means that we can use the Pythagorean Theorem. By using right triangle postulates and theorems, we can deduce that the diagonal is the hypotenuse. Here is what our setup looks like:
x² + y² = z²
<em />Now, all we need to do is plug in the expressions we created for y and z:
x² + (2x + 59)² = [2 + (2x + 59)²]
When we solve for x, we get x = 20. Now, we just plug the x value back into the y equation to get 99. Therefore, the length equals 99 inches and the width equals 20 inches. Hope this helps and have a great day!