8 4/5 - 2/3 - __

Elevator 1 moved up 15 feet from the ground level. Its position is labeled as +15. Elevator 2 moved down 6 feet from the ground

sergey [27]

The ground level is to be the zero level. When the elevator moves above the ground level, it is moving towards the positive integer and when the elevator moves below the ground level, it is moving towards the negative integer.

Elevator 2 moved down 6 feet from the ground level hence its position is labelled as $-6$

3 0

3 years ago

1. A soccer field has an area (A = LW) that is represented by the polynomial 1 point

matrenka [14]

Answer:

$(x + 6)(x - 6)$

Step-by-step explanation:

Given

See attachment for soccer field

Required

The possible dimension of the field

From the attachment, we have:

$Area = x^2 - 36$

$Length = x +a$

$Width = x + b$

So, we have:

$Length * Width = Area$

This gives:

$(x + a)(x + b) = x^2 - 36$

Express 36 as 6^2

$(x + a)(x + b) = x^2 - 6^2$

Express as difference of two squares

$(x + a)(x + b) = (x + 6)(x - 6)$

Hence, the dimension is: $(x + 6)(x - 6)$

6 0

3 years ago

12% of what number is 42?

Andreyy89

Answer:

350

Step-by-step explanation:

12% = 0.12

42 / 0.12 = 350

3 0

3 years ago

A travel agent currently has 80 people signed up for a tour. The price of a ticket is $5000 per person. The agency has chartered

Nikolay [14]

So hmm let's take a peek at the cost first

so, they chartered the plane for 150 folks with a fixed cost of 250,000
now, incidental fees are 300 per person, if we use the quantity "x", for how many folks, then if "x" persons are booked, then incidental fees are 300x

so, more than likely an insurance agency is charging them 300x for coverage

anyway, thus the cost C(x) = 250,000 + 300x

now, the Revenue R(x), is simple is jut price * quantity

well, the price, thus far we know is 5000 for 80 folks, but it can be lowered by 30 to get one more person, thus increasing profits

so... let's see what the price say y(x) is $\bf \begin{array}{ccllll}
quantity(x)&price(y)\\
-----&-----\\
80&5000\\
81&4970\\
82&4940\\
83&4910
\end{array}\\\\
-----------------------------\\\\$

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 80}}\quad ,&{{ 5000}})\quad 
% (c,d)
&({{ 83}}\quad ,&{{ 4910}})
\end{array}
\\\quad \\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-90}{3}\implies -30
\\ \quad \\\\
% point-slope intercept
y-{{ 5000}}={{ -30}}(x-{{ 80}})\implies y=-30x+2400+5000\\
\left.\qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y=-30x+7400$

so.. now we know y(x) = -30x+7400

now, Revenue is just price * quantity
the price y(x) is -30x+7400, the quantity is "x"

that simply means R(x) = -30x²+7400x

now, for the profit P(x)

the profit is simple, that is just incoming revenue minus costs, whatever is left, is profit
so P(x) = R(x) - C(x)

P(x) = (7400x - 30x²) - (250,000+300x)

P(x) = -30x² + 7100x - 250,000

now, where does it get maximized? namely, where's the maximum for P(x)?

well $\bf \cfrac{dp}{dx}=-60x+7100$

and as you can see, if you zero out the derivative, there's only 1 critical point, run a first-derivative test on it, to see if its a maximum

7 0

3 years ago

if A and B together can do a piece of work in 10 days and B along can do it in 15 days, how many part of the work does A complet

anzhelika [568]

Answer:

1/5

Step-by-step explanation:

Well work can be defined as: $work = rate \ *\ time$

where rate=amount of work that can be done in one unit of time

let a = rate of work A does in a day

let b = rate of work B does in a day

this means that: $10a + 10b=1$ where work=1 and it just means the entire job has been completed.

Since b can do it alone in 15 days, this means that: $15b=1$

If we divide by 15 here, we get the equation: $b=\frac{1}{15}$

We can now use this definition to substitute it into the first equation we made.

$10a + 10(\frac{1}{15}) = 1$

Multiply the 10 and 1/15

$10a+\frac{2}{3}=1$

subtract 2/3 from both sides

$10a=\frac{1}{3}$

Now divide both sides by 10

$a=\frac{1}{30}$

Now multiply this by 6, since we a represents the amount of work that can be done in a day, we want to find how many parts of the work can be done by a in 6 days

$6a=\frac{6}{30}$

Now divide both the numerator and denominator by 6

$a=\frac{1}{5}$

8 0

2 years ago

8 4/5 - 2/3 - ___ = 3 1/10