This is the concept of volumes of solid figures;
volume=length*width*height
the dimensions of our figure is:
length=15 1/2 in=31/2 in
width=10 1/4 in=41/4 in
height= 12 in
thus the volume will be:
volume=(31/2*41/4*12)
volume=1906 1/2 in^3
the answer is 1906 1/2 in^3
Answer:
Step-by-step explanation:
1. 655.84
x <u>0.0062</u>
131168
+ 393504
000000
<u>0000000 </u>
0004066208
there are 5 numbers after the decimal point,we count from the back and place our point = 40.66208
Answer:
4 inches
Step-by-step explanation:
Actual dimensions:
Length = 15 feet
Width = 12 feet
Scale dimensions:
Length = 5 inches
Width = x inches
Write a proportion:
![\dfrac{\text{Actual length}}{\text{Scale length}}=\dfrac{\text{Actual width}}{\text{Scale width}}\\ \\ \\\dfrac{15\ feet}{5\ inches}=\dfrac{12\ feet}{x\ inches}\\ \\x=\dfrac{5\ inches\times 12\ feet}{15\ feet}=4\ inches](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctext%7BActual%20length%7D%7D%7B%5Ctext%7BScale%20length%7D%7D%3D%5Cdfrac%7B%5Ctext%7BActual%20width%7D%7D%7B%5Ctext%7BScale%20width%7D%7D%5C%5C%20%5C%5C%20%5C%5C%5Cdfrac%7B15%5C%20feet%7D%7B5%5C%20inches%7D%3D%5Cdfrac%7B12%5C%20feet%7D%7Bx%5C%20inches%7D%5C%5C%20%5C%5Cx%3D%5Cdfrac%7B5%5C%20inches%5Ctimes%2012%5C%20feet%7D%7B15%5C%20feet%7D%3D4%5C%20inches)
The probability that he first chooses an advanced book and then chooses a beginner book is 6/121.
<h3>Probability</h3>
Given:
Beginner book=2
Intermediate book=6
Instructional piano books=11
Advanced books=3
Hence:
Probability=(2×3)÷(11×11)
Probability=6/121
Therefore the probability that he first chooses an advanced book and then chooses a beginner book is 6/121.
Learn more about probability here: brainly.com/question/24756209
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Answer:
-4
+3
12
-0.5, 12.25
x = -0.5
Step-by-step explanation:
The x intercepts are the values of x when y = 0 ie the roots of the equation
![-x^2 -x +12 = 0](https://tex.z-dn.net/?f=-x%5E2%20-x%20%2B12%20%3D%200)
or
![x^2 + x - 12 = 0](https://tex.z-dn.net/?f=x%5E2%20%20%2B%20x%20%20-%2012%20%3D%200)
We can re-write the above as:
(x+4) (x-3) = 0
This gives the two roots as x = -4 and x = +3. Leftmost (smallest) root is -4 and rightmost(largest) root is +3
y intercept is when x = 0. Plugging into the original equation, y value at x = 0 is 12
Vertex x value is given by the formula -b/2a where a is the coefficient of x^2 and b the coefficient of x
Here a = -1, b= -1 so vertex x value = - (-1)/(-1).2 = - 1/2 = -0.5
Plugging this value of x into the original function gives the vertex y value
![y = - (0.5^{2}) - (-0.5) + 12\\= -0.25 + 0.5 + 12 = 12.25](https://tex.z-dn.net/?f=y%20%3D%20-%20%280.5%5E%7B2%7D%29%20-%20%28-0.5%29%20%2B%2012%5C%5C%3D%20-0.25%20%2B%200.5%20%2B%2012%20%3D%2012.25)
The line of symmetry is the vertical line corresponding to the vertex x value so line of symmetry is at x = -0.5
The graph of the quadratic function shows these values