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3 years ago

10. What is the solution to the proportion? 3 7 42

Mathematics

2 answers:

Tamiku [17]3 years ago

6 0

W=18 because to get 4070 to multiply 7 by 6 so then to get your numerator you then multiply the 3 by 6

cupoosta [38]3 years ago

4 0

Answer: w=18

Explanation: 7×6 = 42 so to get W you have to multiply 3 by 6. 3×6 = 18.

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The arc of the parabola y = x^2 from (3,9) to (4,16) is rotated about the y-axis. Find the area of the resulting surface. Please

Hitman42 [59]

Answer:

156.5

Step-by-step explanation:

Thinking process:

The area can be calculated using the formula:

$S = \int\limits^4_3 {2\pi x\sqrt{1+}(2x)^{2} } \, dx$

We let the substitution take place.

Therefore, we let $u = 1 + 4x^{2}$

Thus, $du = 8dx.$

So,

$xdx = \frac{1}{8}du$

Also, the interval of the integration changes to [ 37, 65]

Thus,

$S = \int\limits^4_3 {2\pi \sqrt{1+4x^{2} } } \, dx \\= \int\limits^65_35 {2\pi \sqrt{\frac{1}{8}u } } \, dx$

= $\frac{1}{6} [ 65^{\frac{3}{2}-37^{\frac{3}{2} } }$

= 156.5 units²

8 0

3 years ago

A bag contains 4 white, 3 blue, and 6 red marbles. A marble is drawn from the bag, replaced, and another marble is drawn. Find t

PilotLPTM [1.2K]

First find the probability of each color being drawn.

We need to find the total number of marbles first.

4 + 3 + 6 = 13

So everything will be over 13.

Probability of a white marble being drawn --> $\frac{4}{13}$

Probability of a blue marble being drawn --> $\frac{3}{13}$

Probability of a red marble being drawn --> $\frac{6}{13}$

Now to find the probabilities of more than one being drawn, we can multiply.

Part a :

$\frac{6}{13}*\frac{6}{13}=\frac{36}{169}$

Part b :

$\frac{3}{13}*\frac{3}{13}=\frac{9}{169}$

Part c :

$\frac{6}{13}*\frac{3}{13}=\frac{18}{169}$

Part d :

$\frac{7}{13}*\frac{7}{13}=\frac{49}{169}$

5 0

3 years ago

A cruise line is planning its menu for the next trip. Vacationers like eating steak, lobster, and chicken. The cruise line has d

pychu [463]

Answer: They should order 160 steak, 80 lobster and 260 chicken. The total cost for the meals would be $4460

Step-by-step explanation:

The cruiser will have 400 passangers on board. By taking into account that the cruise line decided to buy 25% more of meals than bookings, we can conclude that in order to calculate the ammount of meals they will order, we have to take the number of passangers on board, 400, and add to it 25% more. So the number of meal orders will be 400 + (1/4 * 400) = 500.

Let's use the letter S to simbolize the ammount of steak they should buy, with L the ammount of lobster, and with C the ammount of chicken. The sum of those ammounts should be 500, so we deduce this formula

$S + L + C = 500$

we can replace C with 500 - S - L. Since at least forty percent of the passangers will have steak dinner and at least twenty percent will have lobster, we obtain this relations:

$S \geq 400*0.4 = 160$
$L \geq 400*0.2 = 80$

We note $f$ the total cost of the meals (in $). The value of $f$ will depend on the values of S and L. Using the information we are given about the cost of each dinner, and recalling that C was 500- S - L, we can represent $f$ by this formula

$f(S,L) = 10*S + 13*L + (500-S-L) * 7$

Which is equal to $10*S + 13*L + 3500 - 7*S - 7*L = 3500 + 3*S + 6*L$

We want to minimaze the value of $f$ , since 3*S + 6*L will get bigger as we use bigger values of S and L, then we will be in a good position if we take the values of S and L as low as possible.

With the restriction we obtained, the lowest values of S and L we can take are 160 and 80 respectively; so we take those values. In conclusion