X is the number of dog
y is the number of cats , y=40
25% of x is 25*x /100=25x/100=x/4
<span>and there are 25% more cats than dogs means y+ x/4=x implies 40=(3/4)x
</span>x=160/3=53
so the number of dogs is 53 and the number of cats is 40
the total number is 53+40=93
Answer:
The beam will bend by 50 mm with a mass of 100kg?
Step-by-step explanation:
The first step in solving the problem of direct variation is setting up the relation mathematically.
We can do this as follows:
The bending of the beam varies directly as its mass.

here is the symbol representing direct variation. To remove this and replace it with an equality sign, we have to introduce a constant of proportionality, k

k = 20 /40 = 0.5
We can now use this to find the distance the beam will bend with a mass of 100kg?
This will be

There fore, the beam will bend by 50 mm with a mass of 100kg?
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:
2. Substitution property
3. Given
4. Definition of congruent angles
5. Substitution property
6. Subtraction property of equality
7. Definition of congruent angles
8. Given
9. Definition of equilateral triangle
11. SAS (10, 7, 9)
Step-by-step explanation:
Answer:
The slope is 6/5 and the y intercept is -13/5
Step-by-step explanation:
6x-5y=13
Solve for y
Subtract 6x from each side
6x-6x-5y=-6x+13
-5y = -6x+13
Divide by -5
-5y/-5 = -6x/-5 +13/-5
y = +6/5x -13/5
This is in slope intercept form y = mx+b where m is the slope and b is the y intercept
The slope is 6/5 and the y intercept is -13/5