Sari estimated the quotient of 120.78 ÷ 9.9 to be 12. She said that her estimate is slightly greater than the actual answer. Is

B refers to the base of the triangle,
and a signifies the length of the two identical sides.

The measurement labeled as 'a' is larger than 'b' since those equal sides are longer than the base. Given "one of the longer sides measures 6.3 cm," we assign a = 6.3.

Substitute 6.3 for each 'a' in the equation and solve for b:
2a + b = 15.7
2(6.3) + b = 15.7
12.6 + b = 15.7
b = 15.7 - 12.6 (applying subtraction property of equality)
b = 3.1

To determine the rates at which the inlet and outlet pipes fill and empty the reservoir, we remember that work done equals rate multiplied by time. Let’s denote the inlet rate as i and for the outlet pipe as 0. Therefore,
i(24) = 1
o(28) = 1
In this context, the '1' represents the total number of reservoirs, since the problem states the time needed for each pipe to either fill or empty a singular reservoir. Solving for rates yields:
i = 1/24 reservoirs/hour
o = 1/28 reservoirs/hour

Over the first six hours, the inlet pipe fills (1/24)(6) = 1/4 reservoirs and during the same period, the outlet pipe empties (1/28)(6) = 3/14 reservoirs. To calculate the net volume of the reservoir filled, we subtract the emptying total from the filling total:
1/4 - 3/14 = 1/28 reservoirs (note that if emptying exceeds filling, a negative value results. In such cases, treat that negative value as zero, indicating that the outlet rate surpasses the inlet rate, leading to an empty reservoir).
Now we need to find out how long it will take to fill up one reservoir since we’ve already partially filled 1/28 of it, after closing the outlet pipe. In simpler terms, we need to determine the time required for the inlet pipe to finish filling the remaining 27/28 of the reservoir. Fortunately, we have already established the filling rate for the inlet pipe, leading to the equation:
(1/24)t = 27/28
Solving for t gives us 23.14 hours. Remember to add the initial 6 hours to this result since the question seeks the total time. Thus, the final total is 29.14 hours.

Please ask me any questions you may have!

Jada intends to provide milk and nutritious cookies at a gathering for her book club. She has planned to offer 12 ounces of milk and 4 cookies for each participant. With her included, the total number of club members is 15. Each package of cookies has 24 cookies and is priced at $4.50. A gallon of milk has 128 ounces and costs $3. Let n denote the club members, m for the ounces of milk, c for the cookies, and b for Jada's budget in dollars. Identify all equations that could represent the relevant quantities and constraints in this scenario.

â m = 12(15)

n refers to the club members

b. 3m + 4.5c = 6

c. 4n =

m stands for ounces of milk

& 44.50) = C

c indicates the cookies

e b=2(3) + 3(4.50)

b denotes Jada's budget in

currency

The equations applicable for representing the quantities and constraints in this scenario are:

a) m = 12(15)

c)4n = c

e) b = 2(3) + 3(4.50)

Detailed explanation:

Jada is set to provide milk and nutritious cookies for her book club meeting

She plans to prepare 12 ounces of milk and 4 cookies for each individual

She has 15 members in total

A pack of cookies contains 24 cookies and costs $4.50

A gallon of milk has 128 ounces and costs $3

Designate the total members by n

Ounces of milk = m

The number of cookies = c

Jada's budget in dollars = d

y = 12(15)

Each individual will receive 4 cookies

4n = c

As one pack contains 24 cookies

She requires = 15 × 4 = 60 cookies

60 ÷ 24 = 2.5

Thus, she would need to purchase 3 packs of cookies

She needs = 15 × 12 = 180 ounces of milk

A gallon of milk contains 128 ounces

180 ÷ 128 = 1.406

She will need to acquire 2 gallons of milk

It's noted: from the prompt

Each gallon of milk costs $3

Each package of cookies costs $4.50

b serves as Jada's dollar budget

b = 2(3) + 3(4.50)

<pThe relevant equations that could signify the quantities and constraints in this scenario are:

Options a, c and e are valid

Answer:

No solution

Step-by-step explanation:

Given: and  

Handle each inequality separately.

             Utilizing the subtraction property of inequalities

and

              Utilizing the addition property of inequalities

Thus, the solution to the combined inequality is the overlap of both solutions.

Refer to the attached image for the number line representation.

No solution

As of 12:04 EST in the U.S.

$1=<span>112.624847 Yen

Thus:

100USD(112.624847Y/1USD)=11262.62 Yen</span>