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DochEvi [55]
3 years ago
7

A square-based prism made of clay had dimensions of 6 by 6 by 10. A pyramid was removed from the prism as shown below so that th

e prism has no top. If the slant height of the pyramid is 10.5 units, the total surface area of the remaining clay solid is _____ square units. (Round answer to nearest whole number)
Mathematics
1 answer:
guajiro [1.7K]3 years ago
6 0

Answer:

<h2>The total surface area is 402 square units.</h2>

Step-by-step explanation:

Givens

  • The dimensions of the square-based prism are 6 by 6 by 10.(l=6, w=6 and h=10.
  • The slant height of the pyramid is 10.5 units.
  • The base of the pyramid matches the top of the square prism, so it's square-based prism.

Remember tha the slant height refers to the height of sided triangles.

Basically, the resulting form 4 rectangular faces, 1 square face, and four triangular faces.

Rectangular face area:

A_{rectangular}=6 \times 10 = 60 u^{2}

(Remember that the area of a rectangle is defined as b \times h)

Square face area (bottom):

A_{square}=6 \times 6 = 36 u^{2}

(Remember that the area of a square is l \times l)

Triangular faces area:

A_{triangular}=\frac{1}{2}bh=\frac{1}{2}(6)(10.5) =31.5u^{2}

(Remember that the area of a triangle is \frac{1}{2} bh.

Multiplying by the right number of each type, we have the total surface area of the resulting figure:

A=4(60)+36+4(31.5)=240+36+126=402 u^{2}

Therefore, the total surface area is 402 square units.

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Recently, six single-family homes in San Luis Obispo County in California sold at the following prices (in $1,000s): 560, 468, 6
solmaris [256]

The interval for mean sale price is $582

According to statement

The given rates are 560, 468, 685, 534, 658, 593

Now,

Sample mean = X / n

Put the values in it and then

(560+ 468+ 685+ 534+ 658+ 593) / 6 = 582.1667

and use this formula S = sqrt [ X2 - n 2 / (n-1) ]

and put the values in these and

S = sqrt [ X2 - n 2 / (n-1) ] = 95.97179

So, The interval for mean sale price is $582

Learn more about SAMPLE MEAN here

brainly.com/question/16794295

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6 0
2 years ago
A boat on a river travels downstream between two points, 90 mi apart, in 1 h. The return trip against the current takes 2 1 2 h.
docker41 [41]

Answer:

A)63miles per hour.

B)27 miles per hour

Step-by-step explanation:

HERE IS THE COMPLETE QUESTION

boat on a river travels downstream between two points, 90 mi apart, in 1 h. The return trip against the current takes 2 1 2 h. What is the boat's speed (in still water)??b) How fast does the current in the river flow?

Let the speed of boat in still water = V(boat)

speed of current=V(current)

To calculate speed of boat downstream, we add speed of boat in still water and speed of current. This can be expressed as

[V(boat) +V(current)]

It was stated that it takes 1hour for the

boat to travels between two points of 90 mi apart downstream.

To calculate speed of boat against current, we will substact speed of current from speed of boat in still water. This can be expressed as

[V(boat) - V(current)]

and it was stated that it takes 2 1/2 for return trip against the Current

But we know but Speed= distance/time

Then if we input the stated values we have

V(boat) + V(current)]= 90/1 ---------eqn(1)

V(boat) - V(current) = 90/2.5----------eqn(2)

Adding the equations we have

V(boat) + V(current) + [V(boat) - V(current)]= 90/2.5 + 90/1

V(boat) + V(current) + V(boat) - V(current)]=90+36

2V(boat)= 126

V(boat)=63miles per hour.

Hence, Therefore, the speed of boat in still water is 63 miles per hour.

?b) How fast does the current in the river flow?

the speed of the current in the river, we can be calculated if we input V(boat)=63miles per hour. Into eqn(1)

V(boat) + V(current)]= 90/1

63+V(current)=90

V(current)= 27 miles per hour

Hence,Therefore, the speed of current is 27 miles per hour.

7 0
3 years ago
Find the product ( x ≠ ? )
dsp73

Answer:

-3

Step-by-step explanation:

if x= -3

the denominator becomes 0 and the fraction becomes undefined.

8 0
3 years ago
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kompoz [17]

Answer:

a.The quotient is a factor

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What is the inverse of the function f(x) = 2x + 1?
soldier1979 [14.2K]

Answer: The inverse of the linear function f(x)=2x+1 is f^(-1) (x) = (1/2)x-1/2


Solution

f(x)=2x+1

y=f(x)

y=2x+1

Isolating x: Subtracting 1 both sides of the equation:

y-1=2x+1-1

y-1=2x

Multiplying both sides of the equation by 1/2:

(1/2)(y-1)=(1/2)2x

(1/2)y-1/2=x

x=(1/2)y-1/2

Changing "x" by "f^(-1) (x)" and "y" by "x":

f^(-1) (x) = (1/2)x-1/2

8 0
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