What is the solution to this equation

Juanita spent $9 on each of her 6 grandchildren at the fair. How much money did she spend? Juanita gastó $9 en cada uno de sus 6

Elena-2011 [213]

Answer:

$54

Step-by-step explanation:

she had 6 grandchildren and she used $9 for one grandchild so we multiply

9 x 6 = $ 54

6 0

3 years ago

A one-parameter family of solutions of the DE P' = P( 1 - P) is given below. P = c1et/1 + c1et Does any solution curve pass thro

topjm [15]

Answer:

a. The curve $P(t) = -\frac{6e^t}{5-6e^t}$ passes through the point (0, 6)

b. No solution of the curve $P(t)$ passes through the point (0, 1)

Step-by-step explanation:

Consider the family of the solution of DE $P' = P(1 - P)$ is $P = \frac{c_1e^t}{1 + c_1e^t}$

a. If any solution passes through the point (0, 6), then there is $c_1$ such that the point (0, 6) satisfies the solution $P = \frac{c_1e^t}{1 + c_1e^t}$

Substitute $t = 0, P = 6$ in $P = \frac{c_1e^t}{1 + c_1e^t}$ and then solve the equation to obtain $c_1$

$P(t) = \frac{c_1e^t}{1 + c_1e^t}\\P(0) = \frac{c_1e^0}{1+c_1e^0}\\ 6 = \frac{c_1}{1 + c_1}\\ c_1 = -\frac{6}{5}$

Therefore, the curve $P(t) = -\frac{6e^t}{5 - 6e^t}$ passes through the point (0, 6)

b. If any solution passes through the point(0, 1), then there is $c_1$ such that the point (0, 1) satisfies the solution $P = \frac{c_1e^t}{1+c_1e^t}$

$P(t) = \frac{c_1e^t}{1 + c_1e^t}\\ P(0) = \frac{c_1e^0}{1 + c_1e^0}\\ 1 = \frac{c_1}{1+c_1} \\1 + c_1 = c_1$

this is not possible

Hence, there is no curve $P(t)$ that exists which passes through the point (0, 1)

4 0

3 years ago

The legth of a rectangle is 15 inches less then twice its width, w. If the perimeter of the rectangle is 96 inches what is the l

KATRIN_1 [288]

Answer:

length of the rectangle=27"

Step-by-step explanation:

length be = l; width be = b

2b-15= l

perimeter= 2(l+b)

=2(2b-15+b)=96

=2(3b-15) =96

3b-15 .=48

3b=48+15=63

b=21. Therefore l = (2 x 21) - 15=42-15 =27"

8 0

3 years ago

A survey found that 60% of shoppers at My-Way-Store like chocolate ice cream. If 240 boppers like chocolate ice cream, how many

erastovalidia [21]

Answer:

400

Step-by-step explanation:

240/60=4, meaning 4 people per every percentage. Which when 4 is multiplied by 100, you get 400=100%

4 0

3 years ago

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Sixty percent of the books at a library are non-fiction. The library has about 15000 books. How many of the library’s books are

ddd [48]

There are 9000 non-fiction books in the library.

$100:60::15000:x\\$ represents the situation.

Step-by-step explanation:

Given,

Total books at library = 15000

Percent of non-fiction books = 60

Percent of all books = 100

Ratio of percent of books to non-fiction books = 100:60

Let,

x represent the number of non-fiction books.

Ratio of number of all books to non-fiction books = 15000:x

Using proportion

Ratio of percent of books :: Ratio of number of books

$100:60::15000:x\\$

Product of extreme = Product of mean

$100*x=15000*60\\100x=900000$

Dividing both sides by 100

$\frac{100x}{100}=\frac{900000}{100}\\x=9000$

There are 9000 non-fiction books in the library.

$100:60::15000:x\\$ represents the situation.

Keywords: ratio, proportion

Learn more about proportion at:

#LearnwithBrainly

4 0

3 years ago