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3 years ago

13

The ratio of raisins to all M&M's in one bag of trail mix is 1:4. The ratio of peanut M&M's to plain M&M's is 2:3. I

f there are 20 raisins in the trail mix, how many plain M&M's are there?

1 answer:

antoniya [11.8K]3 years ago

3 0

Answer:

48

Step-by-step explanation:

Multiplying the ratio of raisins to M&Ms by 20, we find there are a total of 80 M&Ms in the bag.

raisins : M&Ms = 1 : 4 = 20 : 80

The ratio of peanut to plain M&Ms is 2 : 3, a total of 2+3 = 5 ratio units. These stand for a total of 80 M&Ms, so each ratio unit of M&Ms stands for 80/5 = 16 M&Ms. That is ...

peanut : plain = 2 : 3 = 32 : 48

There are 48 plain M&Ms in the bag.

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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

4 0

3 years ago

The vertices of triangle rst are r(–1,–2), s(2,–1), and t(4,2). If δjkl ∼ δrst and the length of kl is units , what is the lengt

NemiM [27]

Answer:

3.16 units

Step-by-step explanation:

It has been given that the triangles JKL and the triangle RST are congruent.

That implies that, the length of the side JK, KL, and JL is equivalent to the length of the sides RS, ST, and RT respectively.

Now, to find the length of JK we need to find the length of the side RS. The coordinates of the points R and S are $(-1,-2)$ and $(2,-1)$ .

The length of the side RS is equal to the distance between point R and S.

RS $=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$= \sqrt{(2-(-1))^2+(-1-(-(-2))^2}$

$=\sqrt{3^2+(-1+2)^2}$

$=\sqrt{9+1}=\sqrt{10}=3.16$

Now that we have the length of the side RS, and the triangles JKL and RST are congruent therefore, the length of the side JK is 3.16 units.

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3 years ago

Read 2 more answers

What is 1/2 to the negative power of 2 using exponent rules

Otrada [13]

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2/1^2 = 2

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2 years ago

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Leno4ka [110]

Answer:

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Step-by-step explanation:

8x = 48,

Divide each side by 8 to isolate x

8x/8 = 48/8

x = 6

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Kiera pays $1.95 per song<br> she downloads.

Step2247 [10]

Answer:

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Explanation:

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2 years ago