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2 years ago

6

The sum of two numbers is 3. When you take twice the smaller number and add it to 6 times the larger number you get 16. What are

the two numbers?

1 answer:

ss7ja [257]2 years ago

8 0

2(x + y = 3)
2x + 6y = 16
2x + 2y = 6
Subtract
4y = 10, y = 10/4
10/4 + x = 3, x = 1/2
The two numbers are 10/4 and 1/2

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Dominic makes and sells salsa. The function C = 2n + 200 represents his costs, in dollars, for producing n jars of salsa. His re

Elan Coil [88]

Answer:the function representing profit, P = 3n + 200

Step-by-step explanation:

The function C = 2n + 200 represents his costs, in dollars, for producing n jars of salsa.

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Therefore,

The function representing Dominic's profit, P, for selling n jars of salsa will be

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3 years ago

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1 year ago

Find the probability of a least one birthday match among a group of 44 people.

Cerrena [4.2K]

Answer:

0.1137= 11.37%

Step-by-step explanation:

Assuming there are 365 days in one year and every people have 1 birthday, then the chance for two people to have the same birthday is 1/365 and the chance they are not is 364/365. We are asked the chance for at least one match among 44 people. The opposite of the condition is that we have 0 matches and easier to calculate. The calculation will be:

P(X>=1)= ~P(X=0) = 1

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2 years ago

cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material for the sides of the can costs 0

Dafna11 [192]

Answer:

Radius=2.09 cm

Height,h=14.57 cm

Step-by-step explanation:

We are given that

Volume of cylinderical shaped can=200 cubic cm.

Cost of sides of can=0.02 cents per square cm

Cost of top and bottom of the can =0.07 cents per square cm

Curved surface area of cylinder= $2\pi rh$

Area of circular base=Area of circular top= $\pi r^2$

Total cost,C(r)= $0.02\times 2\pi rh+2\pi r^2\times 0.07$

Volume of cylinder, $V=\pi r^2 h$

$200=\pi r^2 h$

$h=\frac{200}{\pi r^2}$

Substitute the value of h

$C(r)=0.02\times 2\pi r\times \frac{200}{\pi r^2}+2\pi r^2\times 0.07$

$C(r)=\frac{8}{r}+0.14\pi r^2$

Differentiate w.r.t r

$C'(r)=-\frac{8}{r^2}+0.28\pi r$

$C'(r)=0$

$-\frac{8}{r^2}+0.28\pi r=0$

$0.28\pi r=\frac{8}{r^2}$

$r^3=\frac{8}{0.28\pi}=9.095$

$r=(9.095)^{\frac{1}{3}}=2.09$

Again, differentiate w.r.t r

$C''(r)=\frac{16}{r^3}+0.28\pi$

Substitute the value of r

$C''(2.09)=\frac{16}{(2.09)^3}+0.28\pi=2.63>0$

Therefore,the product cost is minimum at r=2.09

h= $\frac{200}{\pi (2.09)^2}=14.57$

Radius of can,r=2.09 cm

Height of cone,h=14.57 cm

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V125BC [204]

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