<u>Given</u>:
The given balanced scale is represented by the equation
----- (1)
We need to determine the process that balance the scale.
<u>Process to balance the scale:</u>
Given that the if one x block is subtracted from the right side and three numbered blocks are subtracted from the left side.
Thus, the equation (1) becomes
----- (2)
Now, to balance the scale, let us subtract one block x from the left side and subtract three numbered blocks from the right side.
Thus, the equation (2) becomes,
------ (3)
Thus, the equation (3) is the same as the equation (1).
Hence, the process required to balance the scale is to subtract one x block from the left side and subtract three numbered blocks from the right side.
Therefore, Option B is the correct answer.
Answer:
The probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.
Step-by-step explanation:
Let the random variable <em>X</em> represent the time a child spends waiting at for the bus as a school bus stop.
The random variable <em>X</em> is exponentially distributed with mean 7 minutes.
Then the parameter of the distribution is,
.
The probability density function of <em>X</em> is:
Compute the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning as follows:
![=\int\limits^{9}_{6} {\frac{1}{7}\cdot e^{-\frac{1}{7} \cdot x}} \, dx \\\\=\frac{1}{7}\cdot \int\limits^{9}_{6} {e^{-\frac{1}{7} \cdot x}} \, dx \\\\=[-e^{-\frac{1}{7} \cdot x}]^{9}_{6}\\\\=e^{-\frac{1}{7} \cdot 6}-e^{-\frac{1}{7} \cdot 9}\\\\=0.424373-0.276453\\\\=0.14792\\\\\approx 0.148](https://tex.z-dn.net/?f=%3D%5Cint%5Climits%5E%7B9%7D_%7B6%7D%20%7B%5Cfrac%7B1%7D%7B7%7D%5Ccdot%20e%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%20x%7D%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B7%7D%5Ccdot%20%5Cint%5Climits%5E%7B9%7D_%7B6%7D%20%7Be%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%20x%7D%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%5B-e%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%20x%7D%5D%5E%7B9%7D_%7B6%7D%5C%5C%5C%5C%3De%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%206%7D-e%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%209%7D%5C%5C%5C%5C%3D0.424373-0.276453%5C%5C%5C%5C%3D0.14792%5C%5C%5C%5C%5Capprox%200.148)
Thus, the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.
Answer:
The mass of the block is 
Step-by-step explanation:
we know that
The density is equal to the mass divided by the volume
step 1
Find the volume of the granite block
we know that
The volume of a rectangular prism (granite block) is equal to
substitute the values
step 2
Find the mass of the block
we have
substitute the values and solve for the mass
The 3 inside angles of a triangle need to equal 180 degrees.
This is a right triangle so the bottom left corner is 90 degrees.
This means the other two angles when added need to equal 180-90 = 90 degrees.
Now you have 8x + 7x = 90
Combine like terms:
15x = 90
Divide both sides by 15
X = 6
Now you have the value for x solve the two angles:
8x = 8(6) = 48
7x = 7(6) = 42
Top left = 48 degrees
Bottom right = 42 degrees
