Answer: 5,760
Step-by-step explanation:
It was given that each dog is distinct from other dogs and each cat is distinct from other cats, Also from the hint given, the First position is for the dogs. Let D represent the dogs and C represent the Cat , then we have
D C D C D C D C D D or
D D C D C D C D C D or
D C DD C D C D C D or
D C D C D D C D C D or
D C D C D C DD C D
Each of the arrangements above could be done in
2 x 4! x 4! ( it is constant that D is starting , so I am only left with the arrangement of the remaining 5 D's , out of the remaining 5 D's it is also constant that tow of them will be together and this could be done in 2 ways, so I have 4! left for the D's and 4! also for the C's )
= 2 x 24 x 24
= 1 , 152
The total arrangement = 5 x 1 , 152
= 5,7 60 ways
Answer: 
Step-by-step explanation:
1. To find the equation asked, you must add the times:
Where 
is the time takes Lilly in her path to work and 
is the time takes Lilly in her path to home.
2. You must use the following formula of speed and solve for the time
Where n is the distance, V is the speed and t is the time.
3. You know that Lilly takes a train each day to work that averages 35 miles per hour, then, you can write the following expression:
4. And her train ride follows the same path at 45 miles per hour:
5. Then, you obtain the following equation:
Answer:
456.2 units²
Step-by-step explanation:
The area of the square base is ...
base area = w² = (10 units)² = 100 units²
The lateral area is 4 times the area of one rectangular face:
lateral area = 4wx = 4(10 units)(5 units) = 200 units²
The area of one triangular face is half the product of its base length (w) and its slant height (h). The latter is found using the Pythagorean theorem:
h² = y² +(w/2)² = (6 units)² +((10 units)/2)² = 61 units²
h = √61 units
So, the area of 4 triangles is ...
area of triangular faces = 4(1/2)wh = 2(10 units)(√61 units) ≈ 156.2 units²
__
Now we have the areas of the parts, so we can add them together to get the total surface area:
surface area = base area + lateral area + area of triangular faces
= 100 units² + 200 units² + 156.2 units²
surface area = 456.2 units²
The formula for volume of a cone is V=(1/3)*h*π*(r^2)
our height is 7.5 feet, and since the length of the base of the cone (diameter) is 22 feet long, the radius is 11 feet long.
(1/3)*7.5*π*(11^2)=302.5*π=950.3
so the volume of the house is about 950 feet cubed.
Answer:
D) y = -1/3x - 7
Step-by-step explanation:
This graph has a negative slope, so immediately you can eliminate A.
Let's find the slope first. One point is (0,-7) and the other can be (-3,-6).
(-6+7)/(-3-0) = 1/(-3) = -1/3
Because the slope is -1/3, you can eliminate C.
Let's look at the y-intercept next. When x = 0, y = -7.
