The concentration C of a drug in a patient's bloodstream t hours after injection is given by C(t) = 100t/2 t^2 + 85.

Use a calculator to approximate the time when the concentration is highest. (Round your answer to two decimal places.)

Answer:

Step-by-step explanation:

We have the following equation:

Which represents a line, and we need to determine the value of x when y = 3.

To achieve that, we can proceed as follows:

1. Substitute the value of y = 3 into the equation:

The surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

To find the increase in surface area, we first need to calculate the initial surface area of the box and then calculate the surface area after increasing the height.

The formula for the surface area of a rectangular prism is given by:

Surface Area = 2*(length width + length height + width*height)

Initial Surface Area:

Length (L) = 13 cm

Width (W) = 8.7 cm

Height (H) = 28 cm

Initial Surface Area = 2*(138.7 + 1328 + 8.7*28)

Next, we calculate the new surface area after increasing the height by 0.2 cm. The new height is:

New Height = Initial Height + Increase in Height = 28 cm + 0.2 cm

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2))

To find the increase in surface area, we subtract the initial surface area from the new surface area:

Increase in Surface Area = New Surface Area - Initial Surface Area

Let's calculate the values:

Initial Surface Area = 2*(138.7 + 1328 + 8.728) = 2(113.1 + 364 + 243.6) = 2*(720.7) = 1441.4 cm²

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2)) = 2*(113.1 + 377.2 + 244.1) = 2*(734.4) = 1468.8 cm²

Increase in Surface Area = New Surface Area - Initial Surface Area = 1468.8 cm² - 1441.4 cm² = 27.4 cm²

Therefore, the surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

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The fraction represented by the point between 1 and 2 on the number line is 5/3.

If the point is between 1 and 2 on the number line, we can determine the fraction it represents by considering the distance between the point and the two adjacent integers.

The point A lies between the numbers 1 and 2, which indicates that the whole number part of the fraction is 1.

Also note that the segment between 1 and 2 is divided into 3 equal parts. A lies on the 2nd part, which implies that the fractional part is 2/3.

                              2

Thus, the point A corresponds to the mixed fraction 1 -

                                                                                     3

 2                             5

1 -  = (1*3)+2 / 3 =  -

 3                             3

So, the fraction represented by the point between 1 and 2 on the number line is 5/3.

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Answer:

\(x = \frac{ - 19}{3} \)

Step-by-step explanation:

\(( - 5x + 5) + ( - 7x + 9) = 90\)

\( = > 5 - 5x - 7x + 9 = 90\)

\( = > 14 - 12x = 90\)

\( = > - 12x = 90 - 14\)

\( = > - 12x = 76\)

\( = > x = \frac{76}{ - 12} = \frac{ - 19}{3} \)

Answer:

1-3 y

Step-by-step explanation:

Subtract the numbers 4 AND 3 WHICH WOULD EQUAL REWRITING THE ADDITON SO IT CHANGES THE MINUS SIGN TO A PLUS.

The mode of the data represented in this line plot will be 8.

Simply counting how several times each number looks in the data set can help you identify the mode, which is the integer that repeats the most frequently in the collected data. The figure with the largest total is the mode.

The value that appears the most frequently in data collection is its mode. By examining the line plot, we can observe that the number 8 and the six Xs above it are the most commonly occurring values. Consequently, 8 represents the data set's mode.

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Hello!

x² - 5x + 6

= (x² - 2x) + (-3x + 6)

= x(x - 2) - 3(x - 2)

= (x - 2)(x - 3)

Answer:

x=75

Step-by-step explanation:

first no.=x

second no.=x+1

third no.=x+2

now,

or,

x+x+1+x+2=228

or,

3x+3=228

or,

3x=228-3

or,

x=225/3

x=75 ans

Answer:

(negative infinity, positive infinity)

Any value of x makes the equation true.

Step-by-step explanation:

-5(3-4x) = -6+20x - 9

-15 + 20x = -15 + 20x

(negative infinity, positive infinity)

Answer:

True for all x

Step-by-step explanation:

-5(3-4x) = -6+20x - 9

Distribute

-15 +20x = -6+20x - 9

Combine like terms

-15 +20x = -15+20x

Subtract 20x from each side

-15 +20x-20x = -15+20x -20x

-15 =-15

This is true for all x

Th

The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

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Answer:

8

Step-by-step explanation:

3/4 cup leaves 1/4 cup from each cup

1/4+1/4+1/4=3/4

so it would be 3/4+3/4+3/4+3/4+3/4+3/4+3/4+3/4=8 cups

Answer

8

Step-by-step explanation:

Ratio: 40 : 60

Total amount - $20

40/100 x 20

= 8  (ANS)

i hope my answer is correct if not i apologize.

Answer:

The correct equation for this situation is: 27 = j + 9, where j represents the number of shells Jamie has collected.

To find out how many shells Jamie has collected, we need to solve this equation for j:

27 = j + 9

Subtracting 9 from both sides of the equation:

27 - 9 = j + 9 - 9

18 = j

Therefore, Jamie has collected 18 shells.

So, the correct answer is A) 27 = j + 9; Jamie collected 18 shells.

Step-by-step explanation:

Answer: 0.07

Step-by-step explanation:

To find the relative frequency of people in the sample whose place of residence is suburban and whose highest degree is a two-year degree, we need to calculate the ratio of the number of people with those characteristics to the total sample size.

Looking at the contingency table, we can see that the number of people in the suburban category with a two-year degree is 21.

The total sample size is given as 311.

Therefore, the relative frequency can be calculated as:

Relative frequency = (Number of people in suburban category with two-year degree) / (Total sample size)

= 21 / 311

≈ 0.0676

Rounded to two decimal places, the relative frequency is approximately 0.07.

Answer:

0.05333333334

or 5.33333334 percent

Step-by-step explanation:

After divided by before

The triangle ABC is a right triangle

The length of AC is 12.00 cm

From the figure, we have the following parameters:

Length AB = 13 cm

Angle A = 22.6 degrees

Represent the length AC with b.

So, we have the following cosine ratio

\(\cos(A) = \frac{b}{AB}\)

Substitute known values

\(\cos(22.6) = \frac{b}{13}\)

Make b the subject

\(b = 13 * \cos(22.6)\)

Evaluate the product

\(b = 12.00\)

Hence, the length of AC is 12.00 cm

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Answer:

f'(1)=-1

Step-by-step explanation:

You can just find the derivative using the power rule for d/dx (x^-1)=-1x^-2=-1/x^2 then find f'(1)=-1.

I used the limit definition of the derivative to find the slope in the picture attached

Answer:

both elements will be negative in rot.180°

Answer:

18,80,82

Step-by-step explanation:

82^2= 6724

18^2+ 80^2= 6724

The square of the largest number is equal to the sum of the squares of the two smaller numbers.

The number of workers that is closest to but not more than the point of highest MPL is 3. and the number of workers resulting in the highest level of average product of labor is also closest to 3.

To find the marginal product of labor, we need to calculate the additional output produced by each additional unit of labor.

We can calculate this by finding the change in the total product (TP) for each additional unit of labor. The table gives us the following information:

When there are 0 workers, TP = 0

When there is 1 worker, TP = 150

When there are 2 workers, TP = 320

When there are 3 workers, TP = 510

When there are 4 workers, TP = 660

When there are 5 workers, TP = 800

Using this information, we can calculate the marginal product of labor (MPL) as follows:

MPL of the 1st worker = TP of 1 worker - TP of 0 workers = 150 - 0 = 150

MPL of the 2nd worker = TP of 2 workers - TP of 1 worker = 320 - 150 = 170

MPL of the 3rd worker = TP of 3 workers - TP of 2 workers = 510 - 320 = 190

MPL of the 4th worker = TP of 4 workers - TP of 3 workers = 660 - 510 = 150

MPL of the 5th worker = TP of 5 workers - TP of 4 workers = 800 - 660 = 140

We can see that the highest marginal product of labor is 190, which occurs when there are 3 workers. Therefore, the number of workers that is closest to but not more than the point of highest MPL is 3.

complete question:

1. Using the data in the table, the number of workers resulting in the highest level of average product of labor is closest to:

Group of answer choices

3

4

5

Cannot be determined from the information given.

2. Using the data in the table, the marginal product of labor is highest if the number of workers is closest to but not more than:

Group of answer choices

3

4

2

Cannot be determined from the information given.

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The proportion of 1040r tax forms completed in less than 77 minutes = 0.06301

How to find the proportion of the tax forms?

The time required to complete a 1040r tax form = normally distributed

Mean = \(\mu\) = 100 minutes

Standard deviation  = \(\sigma\) = 15 minutes

The proportion of 1040r tax forms completed in less than 77 minutes is given by ,

P( X< 77 ) = P ( Z < \(\frac{77-100}{15}\)  )

                = P( Z < - 1.53 )

                =0.06301

Cumulative probability in the normal distribution =0.06301 or 6.301%

What is normal distribution?

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Answer:

12 x 2+23 x −24=0. Enter an equation ... The first term is, 12x2 its coefficient is 12 . ... B ± √ B2-4AC x = ———————— 2A In our case, A = 12. B = 23. C = -24

Step-by-step explanation:

12 x 2+23 x −24=0. Enter an equation ... The first term is, 12x2 its coefficient is 12 . ... B ± √ B2-4AC x = ———————— 2A In our case, A = 12. B = 23. C = -24

Answer:

13 sips.

Step-by-step explanation:

Divide 22.75 (total) by 1.75 (amount of oz. per sip). You are left with 13, and you can check your answer by multiplying 1.75 (amount of oz. per sip) by 13 (sips). Hope this helped!

Answer: 1.  1*f*(x)-(-(x+4)^2-4)=0

STEP

1

:

Equation at the end of step 1

 fx - x2 - 8x - 12  = 0

STEP

2

:

Solving a Single Variable Equation:

2.1     Solve   fx-x2-8x-12  = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    2*f*(x)-((x-1)^2)=0

STEP

1

:

1.1     Evaluate :  (x-1)2   =    x2-2x+1

Equation at the end of step

1

:

 2fx - x2 + 2x - 1  = 0

STEP

2

:

Solving a Single Variable Equation:

2.1     Solve   2fx-x2+2x-1  = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

The commission for the sale of $33000 worth of items at 6 percent is $1980 and if the sale doubles than the commission would be $3960

Given that the commission rate is 6%

If the sales done is 33000 dollars then the commission received by the agent would be:

33000 * 0.06 = 1980

Now if the sale doubles we would have 33000 x 2

= 66000 dollars

then the commission received would be

66000 x 0.06

= $3960

Hence we would say that the commission for the sale of $33000 worth of items at 6 percent is $1980 and if the sale doubles than the commission would be $3960

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