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Akimi4 [234]
4 years ago
13

An automobile engineer is revising a design for a conical chamber that was originally specified to be 12 inches long with a circ

ular base diameter of 5.7 inches. In the new design, the chamber is scaled by a factor of 1.5. What is the volume of the revised chamber? Round your answer to two decimal places.
Mathematics
1 answer:
icang [17]4 years ago
4 0

The scale factor is 1.5, which means that the revised chamber is larger. The new dimensions are just the old dimensions times 1.5.

The volume of the revise chamber is:

V = (1/3) (PI) [(D/2)^2] (H)

= (1/3) (PI) {[(5.7)(1.5)/2]^2} [(12)(1.5)]

= 344.4874 in3

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Some students were asked what kinds of animals they have at home.
Nataly_w [17]

(a) Animals by popularity; Dogs, Cats, Others, Horses.

(b) If 250 students were interviewed, 20 students have other pets.

(c) No, it was incorrect.

Step-by-step explanation:

Step 1; We arrange the different pets in chronological order, from the highest percent to the lowest percent;

1. Dogs - 67%,

2. Cats - 20%

3. Others - 8%,

4. Horses - 1%.

None is not included in this list.

Step 2; If 250 students were interviewed, 8% of those have other pets. So we need to calculate how much 8% of 250 is.

8% of 250 = \frac{8}{100} × 250 = 0.08 × 250 = 20.

So 20 students had other pets.

Step 3; 20% of the interviewed students had cats. If 75 students had cats, we need to equate 20% to the 75 and find out how many students were actually interviewed.

20% × x = 75, 0.2 × x = 75,

x = \frac{75}{0.2} = 375.

So if 375 students were interviewed, 75 students would have cats. So the estimate of 250 students being interviewed is incorrect.

8 0
3 years ago
Given that the expression 2x^3 + mx^2 + nx + c leaves the same remainder when divided by x -2 or by x+1 I prove that m+n =-6
Alla [95]

Given:

The expression is:

2x^3+mx^2+nx+c

It leaves the same remainder when divided by x -2 or by x+1.

To prove:

m+n=-6

Solution:

Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).

Let the given polynomial is:

P(x)=2x^3+mx^2+nx+c

It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that

P(2)=P(-1)              ...(i)

Substituting x=-1 in the given polynomial.

P(-1)=2(-1)^3+m(-1)^2+n(-1)+c

P(-1)=-2+m-n+c

Substituting x=2 in the given polynomial.

P(2)=2(2)^3+m(2)^2+n(2)+c

P(2)=2(8)+m(4)+2n+c

P(2)=16+4m+2n+c

Now, substitute the values of P(2) and P(-1) in (i), we get

16+4m+2n+c=-2+m-n+c

16+4m+2n+c+2-m+n-c=0

18+3m+3n=0

3m+3n=-18

Divide both sides by 3.

\dfrac{3m+3n}{3}=\dfrac{-18}{3}

m+n=-6

Hence proved.

7 0
3 years ago
Emmett went to the chocolate store and bought 5 pounds of chocolate. If 2⁄3 of the chocolate was white chocolate, how many pound
AleksandrR [38]
10/3 pounds white chocolate he bought
7 0
4 years ago
Read 2 more answers
Help !! Picture ^^^^
nikitadnepr [17]
The answer is 78

If you multiply 17x6 you get 102
102 equals the whole rectangle after that you need to get rid of the part that’s not there
so you multiply 8x3 which equals 24
you then subtract 24 from 102 and get 78
6 0
3 years ago
A real estate agent earns a 6% commission for the sale of a home. A home sold for $550,000. What was the commission earned by th
Elza [17]

Multiply the sale price by the commission rate:

550,000 x 0.06 = 33,000

He earned $33,000.00

3 0
3 years ago
Read 2 more answers
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