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Bogdan [553]
2 years ago
12

Carl has new bottle of laundry detergent he uses 0.4 cups of laundry detergent while washing one load of laundry and 0.7 coupon

another load. Use addition to find the total change in the number of cups of detergent in the botttle
Mathematics
2 answers:
Kazeer [188]2 years ago
6 0

Answer:

The change in cups of detergent is -1.1 cup of detergent ( answer should be -1.1 cup in real terms because this cup of detergent have been consumed and we are talking about change)

Step-by-step explanation:

In this question, we are asked to use addition to evaluate the total change in the number of cups of detergent in a bottle.

This is pretty straightforward. To calculate the number of cups of detergent used, we simply add the number of cups used while washing the first laundry load to the number of cups of detergent used while washing the second laundry load.

Mathematically, this is equal to 0.7 + 0.4 = 1.1 cup of detergent

oee [108]2 years ago
4 0

Answer:

-1.1 cups

Step-by-step explanation:

To find out how much was spent on the main bottle of detergent, we must add the expenses that were incurred in the wash.

The statement tells us that first there is an expense of 0.4 cups of laundry detergent while washing one load of laundry and 0.7 coupon another load, therefore this means that the change in the bottle would be:

(-0.4) + (-0.7) = -0.4 - 0.7 = -1.1 cups.

In other words, the main bottle would have 1.1 cups less, that is, -1.1 cups.

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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

4 0
2 years ago
The heights of fully grown sugar maple trees are normally distributed, with a mean of 87.5 feet and a standard deviation of 6.25
Julli [10]

Answer:

20.33%

Step-by-step explanation:

We have that the mean (m) is equal to 87.5, the standard deviation (sd) 6.25 and the sample size (n) = 12

They ask us for P (x <86)

For this, the first thing is to calculate z, which is given by the following equation:

z = (x - m) / (sd / (n ^ 1/2))

We have all these values, replacing we have:

z = (86 - 87.5) / (6.25 / (12 ^ 1/2))

z = -0.83

With the normal distribution table (attached), we have that at that value, the probability is:

P (z <-0.83) = 0.2033

The probability is 20.33%

6 0
2 years ago
Judy’s brother Sam has a collection of 96, but what are the 10 way Sam can divide his comic books equal groups
Ierofanga [76]
He can divide by 2,3,4,6,8,12,16,24,32, and 48 but
8 0
2 years ago
You are at the bottom of a mountain where the temperature is 74°F. The top of the mountain is 5500 feet above you. What is the t
mamaluj [8]

For every 1,000 feet you go up in elevation, the temperature decreases by about 3.3°F

 

Given:

Temperature at the bottom of the mountain is 74°F

The top of the mountain is 5500 feet above you

 

Change (reduction) in temperature is 3.3 X 5500 / 1000

= 18.15°F

 

Temperature at the top of the mountain is 74°F – 18.15°F

= 55.85°F

3 0
2 years ago
Suppose an exponential function is fit to a set of data. Which of the following residual plots indicates that this function was
Zina [86]
The correct answer is the choice that you have selected, the third choice. 

When, we are looking at the residuals for a regression line, we always want to see the points balance like in the third choice. This means that the equation that we found is right in the middle of the points.
7 0
2 years ago
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