The equation represents the proportional

Father can do the job on the farm in 6 hours. The older son can do it in 8 hours. The younger son can do same job in 12 hours. H

FrozenT [24]

Answer: it will take a combined rate of 2.67 hours

Step-by-step explanation:

Father can do the job on the farm in 6 hours. This means that the father's unit rate of working will be 1/6

The older son can do it in 8 hours. This means that the older son's rate of working will be 1/8

The younger son can do same job in 12 hours. This means that the younger son's working rate is 1/12

When they work together, they will be working simultaneously. It means that their unit rates are additive. The combined unit rates will be

1/6 + 1/8 + 1/12 = (20 + 15 + 10)/120

45/120

Assuming it takes t hours for them to complete the work while doing it together. Their combined unit rate will be 1/t

45/120 = 1/t

45t = 120

t = 120/45 = 2.67 hours

3 0

3 years ago

The cost of admission to the bayton zoo is 10.50 for each senior citizen $15.75 for each adult , and 8.50 for each child

alex41 [277]

Yes, and what is the problem?

5 0

2 years ago

A salad bar offers vegetable platters in 4 sizes (small, medium, large, and super-sized) and 6 different vegetables to choose fr

quester [9]

Answer: She could create 60 platters.

Step-by-step explanation:

Given: A salad bar offers vegetable platters in 4 sizes (small, medium, large, and super-sized) and 6 different vegetables to choose from.

Number of combinations of selecting <em>r</em> things from <em>n</em> things is given by:-

$^nC_r=\dfrac{n!}{r!(n-r)!}$

So, the number of combinations of selecting 2 different vegetables from 6 = $^6C_2=\dfrac{6!}{2!4!}=\dfrac{6\times5}{2}=15$

Now, By Fundamental counting principle, the number of different platters she could create = (number of ways of selecting 2 different vegetables from 6) x (Number of sizes)

= 15 x 4

= 60

Hence, she could create 60 platters.

6 0

2 years ago

Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is proportional to the product o

Keith_Richards [23]

Answer:

32.1 g

Step-by-step explanation:

In each 3 grams of C, there are 2 grams of A and 1 gram of B. So, for some amount C, the amount remaining of A is 40 -(2C/3), and the amount remaining of B is (50 -C/3). Since the reaction rate is proportional to the product of these amounts, we have ...

C' = k(40 -2C/3)(50 -C/3) = (2k/9)(60 -C)(150 -C) . . . for some constant k

This is separable differential equation with a solution of the form ...

ln((150 -C)/(60 -C)) = at + b

We know that C(0) = 0, so b=ln(150/60) = ln(2.5). And we know that C(10) = 20, so ln(130/40) = 10a +ln(2.5) ⇒ a = ln(1.3)/10

Then our equation for C is ...

ln((150 -C)/(60 -C)) = t·ln(1.3)/10 +ln(2.5)

__

For t=20, this is ...

ln((150 -C)/(60 -C)) = 2ln(1.3) +ln(2.5) = ln(2.5·1.3²) = ln(4.225)

Taking antilogs, we have ...

(150 -C)/(60 -C) = 4.225

1 +90/(60 -C) = 4.225

C = 60 -90/3.225 ≈ 32.093 . . . . . grams of product in 20 minutes

In 20 minutes, about 32.1 grams of C are formed.

7 0

2 years ago

Help me pls due 9-24-18

ANTONII [103]

26. Tuesday -5 is colder than all the others
27. Friday 0degrees is the warmest day there
28. 20 degreases on Saturday adding the positive 25 to negative five makes it 20 degrees

8 0

2 years ago