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2 years ago

15

Noah fills a soap dispenser from a big bottle that contains 2 1/3 liters of liquid soap. That amount of soap will fill 3 1/2 dis

pensers. How many liters of soap fit into one dispenser?

1 answer:

kakasveta [241]2 years ago

6 0

Answer:

1 1/2

Step-by-step explanation:

3 1/2 / 2 1/3

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Let f(x) = 1/x . Find the number b such that the average rate of change of f on the interval [2, b] is − 1/8

vekshin1

Answer:

b=4

Step-by-step explanation:

So, we have the function $f(x)=1/x$ . We need to find b such that the average rate of change or the slope is -1/8 between the intervel [2, b]. First, let's find f(2).

f(2) = 1/(2) = 1/2

So, we have the point (2, 1/2)

At point b, f(b) = 1/b.

Let's plug this into the slope formula:

$\frac{y_2-y_1}{x_2-x_1}=\frac{.5-\frac{1}{b} }{2-b} =-1/8$

Now, we just need to solve for b. First, let's multiply both the numerator and denominator by b (to get rid of the annoying fraction in the numerator).

$\frac{.5b-1}{2b-b^2} =\frac{-1}{8}$

Now, cross multiply.

$4b-8=b^2-2b$

$b^2-6b+8=0$

Solve for b. Factor using the numbers -4 and -2.

$=(b-4)(b-2)=0$

Thus, b=4 or b=2.

However, b=2 is not a possible solution since the interval [2,2] means nothing. Thus, b=4.

4 0

2 years ago

A trapezoid has an area of 50 square units. The lengths of the bases are 10 units and 15 units. find the height.

Lera25 [3.4K]

Step-by-step explanation:

area = ( base 1 + base 2 ) ÷ 2 x height

50 = ( 10 + 15) ÷2 x height

50 ÷ 12.5 = height

height = 4

5 0

2 years ago

The formula used to calculate the value of a savings accounty =(1+)120What does theafter t years is A(t)=0.04= 1500 1+120.04frac

yulyashka [42]

We have here the formula for Compound Interest:

$A=P(1+\frac{r}{n})^{nt}$

Where:

• A is the accrued amount.

,

• P is the Principal (the original amount of money, the starting amount of money).

,

• r is the interest rate.

,

• n is the number of times per year compounded.

,

• t is the time in years.

When we have that n is equal to 12, we are talking here about that the amount of money is being compounded monthly (we have 12 months in a year, 12 periods, n = 12). <em>Therefore, we are dividing the rate, r, by the number of compoundings per year, n, and this is the rate per each new compounding period of time, r/n, and, in this case, n = 12 (monthly interest rate). </em>

Therefore, in few words, the fraction (0.04/12) is the monthly interest rate (option C).

[If we see the other options, we have:

• The daily interest rate would be given by 0.04/365.

,

• How long the money has been in the account is time, t.

,

• The starting balance in the account is the Principal, P. ]

7 0

1 year ago

Which is the simplified form of the expression 3(7/5x + 4) - 2(3/2 - 5/4x)

faltersainse [42]

Answer:

Step-by-step explanation:

I think you meant 3([7/5]x + 4) - 2(3/2 - [5/4]x). If that's the case, then identify the LCD: It is 20. Multiply both [7/5]x + 4 and 3/2 - [5/4]x by 20 and then divide the resulting expression by 20:

3(28x + 80) - 2(30 - 25x)

------------------------------------

20

Next, perform the indicated multiplication:

84x + 240 - 60 + 50x

----------------------------------

20

This simplifies to:

34x + 180 17x + 9

---------------- = ----------------

20 10

Next time, please share the answer choices.

6 0

3 years ago

Two baseball teams, Team A and Team B need to play a series of games. The series end either if a team wins two consecutive games

Nimfa-mama [501]

Answer:

3

Step-by-step explanation:

The Series,The Games,and the amount of games to play

7 0

2 years ago