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2 years ago

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Bruno solved the following equation: 4x + one half(10x − 4) = 6 Step Work Justification 1 4x + 5x − 2 = 6 2 9x − 2 = 6 3 9x = 8

4 x = eight ninths Which of the following has all the correct justifications Bruno used to solve this equation? 1. Multiplication Property of Equality 2. Combine like terms 3. Subtraction Property of Equality 4. Division Property of Equality 1. Distributive Property 2. Combine like terms 3. Subtraction Property of Equality 4. Division Property of Equality 1. Distributive Property 2. Combine like terms 3. Addition Property of Equality 4. Division Property of Equality 1. Multiplication Property of Equality 2. Combine like terms 3. Addition Property of Equality 4. Division Property of Equality

1 answer:

beks73 [17]2 years ago

4 0

Answer:

Statement Reason

1. $4x+5x-2=6$ 1. Distributive Property

2. $9x-2=6$ 2. Combine like terms

3. $9x=8$ 3. Addition Property of Equality

4. $x=\dfrac{8}{9}$ 4. Division Property of Equality

Step-by-step explanation:

The given equation is

$4x+\dfrac{1}{2}(10x-4)=6$

Using distributive property, we get

$4x+\dfrac{1}{2}(10x)+\dfrac{1}{2}(-4)=6$

$4x+5x-2=6$

$9x-2=6$ (Combine like terms)

Using Addition Property of Equality, add 2 on both sides.

$9x=6+2$

$9x=8$

Using Division Property of Equality, divide both sides by 9.

$x=\dfrac{8}{9}$

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valentina_108 [34]

Answer: 10 t -0.5 t is the total cost of the ticket for the group of 10 people after getting discount.

Where 10 t is the initial cost of ticket without discount and 0.5 t is the total discount.

Step-by-step explanation:

Here, t represents the cost of one ticket.

Therefore, For 10 person the cost of the ticket = 10 t

And, According to the question, there is a discount of 5% percent per ticket if a group buys 10 tickets.

Thus, the discount for the group of ten people = 5% of 10 t = 0.5 t

The the total cost for the group of ten people after getting the discount = 10 t - 0.5 t

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2 years ago

Read 2 more answers

The length of time that an auditor spends reviewing an invoice is approximately normally distributed with a mean of 600 seconds

Bumek [7]

Answer: 11.5%

Explanation:

Since 1 minute = 60 seconds, we multiply 12 minutes by 60 so that 12 minutes = 720 seconds. Thus, we're looking for a probability that the auditor will spend more than 720 seconds.

Now, we get the z-score for 720 seconds by the following formula:

$\text{z-score} = \frac{x - \mu}{\sigma}$

where

$t = \text{time for the auditor to finish his work } = 720 \text{ seconds}
\\ \mu = \text{average time for the auditor to finish his work } = 600 \text{ seconds}
\\ \sigma = \text{standard deviation } = 100 \text{ seconds}$

So, the z-score of 720 seconds is given by:

$\text{z-score} = \frac{x - \mu}{\sigma}
\\
\\ \text{z-score} = \frac{720 - 600}{100}
\\
\\ \boxed{\text{z-score} = 1.2}$

Let

t = time for the auditor to finish his work
z = z-score of time t

Since the time is normally distributed, the probability for t > 720 is the same as the probability for z > 1.2. In terms of equation:

$P(t \ \textgreater \ 720) 
\\ = P(z \ \textgreater \ 1.2)
\\ = 1 - P(z \leq 1.2)
\\ = 1 - 0.885
\\ \boxed{P(t \ \textgreater \ 720) = 0.115}$

Hence, there is 11.5% chance that the auditor will spend more than 12 minutes in an invoice.

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2 years ago

Rewrite the interval 11-20 using inequalities

Svetach [21]

If you're meaning a value between 11 and 20, write
11<x>20 and put a line under the < and > which indicates that x could also equal 11 or 20. x doesnt only have to be a value between 11 and 20, but it can equal the numbers too.

i dont think that makes a lot of sense but if you were to say the answer out loud, the answer would be "x (which is any value) is more than or equal to 11 and less than or equal to 20"

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2 years ago

A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like

mixas84 [53]

Answer:

a) $\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) $\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) the steady state mass of the drug is 2000 mg

d) t ≅ 153.51 minutes

Step-by-step explanation:

From the given information;

At time t= 0

an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500

The inflow rate is 0.06 L/min.

Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant.

The objective of the question is to calculate the following :

a) Write an initial value problem that models the mass of the drug in the blood for t ≥ 0.

From above information given :

$Rate _{(in)}= 500 \ mg/L \times 0.06 \ L/min = 30 mg/min$

$Rate _{(out)}=\dfrac{x}{4} \ mg/L \times 0.06 \ L/min = 0.015x \ mg/min$

Therefore;

$\dfrac{dx}{dt} = Rate_{(in)} - Rate_{(out)}$

with respect to x(0) = 0

$\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) Solve the initial value problem and graph both the mass of the drug and the concentration of the drug.

$\dfrac{dx}{dt} = -0.015(x - 2000)$

$\dfrac{dx}{(x - 2000)} = -0.015 \times dt$

By Using Integration Method:

$ln(x - 2000) = -0.015t + C$

$x -2000 = Ce^{(-0.015t)$

$x = 2000 + Ce^{(-0.015t)}$

However; if x(0) = 0 ;

Then

C = -2000

Therefore

$\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) What is the steady-state mass of the drug in the blood?

the steady-state mass of the drug in the blood when t = infinity

$\mathbf{x = 2000 - 2000e^{-0.015 \times \infty }}$

x = 2000 - 0

x = 2000

Thus; the steady state mass of the drug is 2000 mg

d) After how many minutes does the drug mass reach 90% of its stead-state level?

After 90% of its steady state level; the mas of the drug is 90% × 2000

= 0.9 × 2000

= 1800

Hence;

$\mathbf{1800 = 2000 - 2000e^{(-0.015t)}}$

$0.1 = e^{(-0.015t)$

$ln(0.1) = -0.015t$

$t = -\dfrac{In(0.1)}{0.015}$

t = 153.5056729

t ≅ 153.51 minutes

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2 years ago

I would like to purchase 20 products at the cost of $65 per product the state sales tax is 3.5% what is the total

Ivanshal [37]

1,650 is the answer to your question

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