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3 years ago

Cost of an oil change: $19.95 Discount: 33% What is the new cost?

Mathematics

2 answers:

marysya [2.9K]3 years ago

5 0

Answer:

$13.95

Step-by-step explanation:

valina [46]3 years ago

3 0

Answer:

The new cost is 13.37

Step-by-step explanation:

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Evaluate-2x3 - 2x2 - 4x-2 for x=-2.<br> A.-18<br> B. 16<br> C. -2<br> D. 14

dmitriy555 [2]

Answer:

Step-by-step explanation:

-2x^3 - 2x^2 - 4x-2

Let x = -2

-2 (-2)^3 - 2 (-2)^2 -4(-2) -2

Exponents first

-2 (-8) -2 (4) -4(-2) -2

Then multiply

16 -8 +8 -2

Then add and subtract

4 0

3 years ago

A ; 1/2. B ; 1/3. C ; 2/3 D ; 4/9

hichkok12 [17]

Option B, 1/3

Since pepper topping can be in any size pizza, it remains as a 1/3 probability, since there are three toppings per size.

3 0

3 years ago

Which function is equivalent to the inverse of y=sec(x)

kipiarov [429]

From the identity:

$sec(x)= \frac{1}{cos(x)}$

$f(x)=sec(x)= \frac{1}{cos(x)}$

the inverse of f is g such that f(g(x))=x,

we must find g(x), such that $\frac{1}{cos[g(x)]}=x$

thus, $cos[g(x)]= \frac{1}{x}$

$g(x)=cos^{-1} (\frac{1}{x})$

Answer: b. g(x)=cos^-1(1/x)

6 0

4 years ago

A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int

Wittaler [7]

Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}$

By expanding the previous equation:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)$

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

$V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0$

Since there is no accumulation within the tank, expression is simplified to this:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}$

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

$V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}$ , where $c(0) = 0 \frac{pounds}{gallon}$ .

$\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}$

The solution of this equation is:

$c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})$

The salt concentration after 8 minutes is:

$c(8) = 0.166 \frac{pounds}{gallon}$

The instantaneous amount of salt in the tank is:

$m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds$

3 0

3 years ago

Which of the following is equivalent to the inequality shown below?

VARVARA [1.3K]

Answer:

$4x + 0.9 \geq 0.1$ is equivalent to the inequality $40x+9 \geq 1$

Step-by-step explanation:

Given inequality : $4x + 0.9 \geq 0.1$

We are supposed to find Which of the following is equivalent to the inequality

$4x + 0.9 \geq 0.1$

$\Rightarrow 4x+\frac{9}{10} \geq \frac{1}{10}$

Multiply both sides by 10

$\Rightarrow 4(10)x+\frac{9}{10}(10) \geq \frac{1}{10}(10)$

$\Rightarrow 40x+9 \geq 1$

$4x + 0.9 \geq 0.1$ is equivalent to the inequality $40x+9 \geq 1$

So, Option B is true

B) $40x+9 \geq 1$

7 0

4 years ago