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Alexeev081 [22]
2 years ago
5

Multiply. Write your answer as a mixed number in simplest form.

Mathematics
1 answer:
dem82 [27]2 years ago
7 0

Answer:

39/30 = 1 9/30

Step-by-step explanation:

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Suppose that you are to make a rectangular box with a square base from two different materials. The material for the top and fou
saw5 [17]

Answer:

height = 14.5 ft

width = length = 3.2 ft

Step-by-step explanation:

Let the side of the square base is a and the height of the box is h.

The material required to make the box is equal to the total surface area of the box.

Area of base = a²

Cost of square base is $ 2 per ft²

So, the cost of making base = 2a²

Area of four walls + area of top = 2 (a² + ah + ah) + a² =  3a² + 2ah

Cost of making walls and the top is $ 1 per ft²

So, the cost of making walls and the top = 1 x ( 3a² + 2ah)

Total cost of making the box = 2a² + 3a² + 2ah = 5a² + 2ah

According to the question

144 = 5a² + 2ah

h = \frac{144-5a^{2}}{2a}     .... (1)

The volume of the box is V = length x width x height

V = a x a x h

V = 72 a - 2.5 a³     from equation (1)

Differentiate both sides with respect to a.

dV/da = 72 - 7.5 a²

Put, it equal to zero for maxima and minima

7.5 a² = 72

a = 3.2 ft

Put in equation (1)

h = \frac{144-5\times 3.2\times 3.2}{2\times 3.2}

h = 14.5 ft

So, the dimensions of the box are

height = 14.5 ft

width = length = 3.2 ft

6 0
3 years ago
There are 30 names in a hat. If two names are picked without replacement, which expression shows the probability that Jack and J
Darya [45]

Answer: Choice C)

(1/30)*(1/29)

Explanation:

Jack has a 1/30 chance of being picked since he is 1 person out of 30 total. After his name is picked, and not put back, there are 30-1 = 29 names left. The chances Jill is picked is 1/29. The two fractions are multiplied to get the overall probability both are picked.

7 0
3 years ago
In the floor tile pattern, the figure is a square and the two triangles are congruent.
Licemer1 [7]

Answer:

7.1

Step-by-step explanation:

Since it is a square you can use the Pythagorean theorem (a²+b²=c²) by filling in what you know. a²=5 and b²=5 so you have 5²+5²=c². This simplfies to 25+25=c². Now you simplify again to get 50=c². Finally you have to square root everything because the equation can't end in c², it has to be the most simplified it can be. This equals ≈7.1

8 0
3 years ago
What are the intercepts of the line?
zmey [24]
X intercept: (-4)
y intercept: (8)
6 0
2 years ago
2. Please help me with this question will give BRAINLIST to best answer
Sloan [31]

Answer:

>

Step-by-step explanation:

4 0
2 years ago
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