Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C(t) = −2t2 + 8t, where the time, t, is hours after injection.

Part A: What are the domain and range of the function C(t) based on the context of the problem? Show all necessary calculations. (5 points)

Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body. (5 points)

The given logarithmic expression [tex]ln(x^5)[/tex] can be expressed as 5*lnx.

so option (D) is correct.

What is a logarithmic expression?

A logarithmic equation is one that involves the logarithm of a variable-containing expression. To solve exponential equations, first, determine whether both sides of the equation can be written as powers of the same number.

The given logarithmic expression is [tex]ln(x^5)[/tex]

Property of logarithms: [tex]ln(x^n) = nln(x)[/tex]

So by using the above property, we can rewrite the given expression as

                           [tex]=ln(x^5)\\=5ln(x)[/tex]

Hence, the given logarithmic expression [tex]ln(x^5)[/tex] can be expressed as 5*lnx.

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Using percentage, 39% of 80 percent is calculated and given as 31.2.

percentage :

given equation is calculated as:

x = 39 percent of 80

x = 39% of 80

x = 39% x 80

x = (39/100) x 80

x = 31.2

therefore, 39 percent of 80 is 31.2

Using percentage, 39% of 80 percent is calculated and given as 31.2.

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If the equation for a line "u" be represented as [y = (-2x + 10)], then the equation of line "v", being parallel to line "u" and passing through the point (-1, 2) will be [y = (-2x)].

As per the question statement, the equation for a line "u" can be represented as [y = (-2x + 10)],

And we are required to determine the equation of another line "v", which is  parallel to line "u" and passes through the point (-1, 2).

To solve this question, first we need to know about a property of parallel lines, which is, "Any straight line parallel to a line of known slope will also have the same slope"

Now, the formula to determine the equation of a straight line having a known slope, say "m" and a y-intercept of "c" goes as, [y = (mx + c)], also known as the slope-intercept form of line. Comparing the equation of line "u" with this slope-intercept form, we get, [m = (-2)] and [c = 10].

That is, the slope of line "u" is (-2), and hence, the slope of line "v" must also be (-2) since they are parallel to each other.

Also, the formula to determine the equation of a straight line having a known slope, say "m", and passing through a known point, say (x₁, y₁), goes as, [(y - y₁) = {m(x - x₁)],  and using [m = (-2)] and [(x₁, y₁) = ((-1, 2)] in this formula, we get,

[(y - 2) = (-2){x - (-1)}]

Or, [(y - 2) = (-2)(x + 1)]
Or, [(y - 2) = (-2x - 2)]

Or, [y = (-2x - 2 + 2)]

Or, [y = (-2x)]

That is,  the equation of line "v", being parallel to line "u" and passing through the point (-1, 2) will be [y = (-2x)]

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Answer:

interest rate = 0.0400215403 or 4.00215403% or 4%

Step-by-step explanation:

formula

final amount =

initial amount times e^(interest rate times time)

6614 = 4998 times e^(interest rate times 7)

(6614 ÷ 4998) = e^(interest rate times 7)

1.32332933173 = e^(interest rate times 7)

ln means natual log

ln(1.32332933173) = ln(e^(interest rate times 7))

0.28015078214 = interest rate times 7

0.28015078214 ÷ 7 = interest rate

0.0400215403 = interest rate

utub dr ashley godbold

investopedia

Answer:

(fg)'(10)= 3 and the other one is 1.5

Step-by-step explanation:

fg and 10 with the 4x- 10 as the fraction of values of the followings of G-9 so its (fg)'(10)= 3 and the other one is 1.5

The solution for the given logarithmuc function is x = -1 or x = -4.

What is a logarithmic expression?

A logarithmic equation is one that involves the logarithm of a variable-containing expression. To solve exponential equations, first, determine whether both sides of the equation can be written as powers of the same number.

Property of logarithms: log(a) + log(b) = log(ab)

The given function is

                       [tex]log_{2}(x+2) + log_{2}(x+3)=1[/tex]

By using the property of logarithms, we get

                       [tex]log_{2}(x+2) + log_{2}(x+3)=1\\\\log_2{[(x+2)(x+3)]}=1\\\\(x+2)(x+3)=2\\\\x^2+2x+3x+6=2\\\\x^2+5x+6-2=0\\\\x^2+5x+4=0\\\\(x+1)(x+4)=0[/tex]

Simplifying, we get

                   x = -1   (or)  x = -4

Hence, the solution for the given logarithmuc function is x = -1 or x = -4.

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The sales tax is $2.935, and the total due is $51.855 ,Jared has $50 but the cost is $51.855 so he does not have enough money to the purchases.

Given:

jared has $50 to spend on some new clothes for school. if the sales tax rate in his state is 6% the pretax total comes to $48.92.

sales tax = 6% = 6/100 = 0.06.

= 0.06 * 48.92

= $2.935.

Total due = sales tax + pretax total

= $48.92 + $2.935

= $51.855

Jared has $50 but the cost is $51.855 so he does not have enough money to the purchases.

Therefore The sales tax is $2.935, and the total due is $51.855 ,Jared has $50 but the cost is $51.855 so he does not have enough money to the purchases.

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The image of (0, -3) after dilation by a scale factor of 1/3 centered at the origin is : (0, -1)

Given point P (0, -3)

The point is dilated by a scale factor of 1/3 centered at the origin is equivalent to multiplying the point by 1/3 for both the co-ordinates.

Therefore, the new point is given by :

P' = (0×(1/3), (-3)×(1/3))

P' = (0, -1)

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Image of (0,-3) after dilation is (0,-1).

Scale factor = 1/3

Given point = (0,-3)

To find image of a point, we multiply the co-ordinates of the given point by scale factor.

Therefore, image = (0*(1/3),-3*(1/3))

                             = (0,-1)

Hence, image of point (0,-3) is (0,-1).

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The equation of circle that have diameter of 12 cm is x2+(y-3)2=36

What is equation of circle?

The standard equation of a circle is given by:

(x-h)2 + (y-k)2 = r2

Where (h, k) is the coordinates of center of the circle and r is the radius.

Given, diameter = 12 cm

radius = 6 cm

Hence, center is on y-axis hence, x = 0

the point we get (h,k) =(0,3)

Put in equation we get

x2+(y-3)2=36

which is equation of circle.

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Answer:

The correct answer is B. Vertical lines have an undefined slope.

Answer:  " 80 " ; that is, the number: "eighty."

____

Step-by-step explanation:

Note the order of operations:
PE MD AS ;

Please Excuse My Dear Aunt Sally.

____
in which:

Parentheses are the first priority; if they occur.

then:
Exponents are the second priority if they occur.

followed by:
Multiplication and
Division;  if any of these occur; and the priority is from the left-hand side to the right-hand side—if they occur.  So; multiplication does not necessarily take priority over division.  Rather, "Multiplication and Division" are treated equally, as the "next priority", from "left to right"—as they occur/if they occur;

followed by:

Addition and
Subtraction; of any of these occur; and the priority is from the 'left-hand side to the right-hand side—if they occur.  So; addition does not necessarily take priority over subtraction.  Rather, "Addition and Subtraction" are treated equally, as the "next priority", from "left to right"—as they occur/if they occur.
____

So:  For our given problem; we can solve:

  " 8(6 + 4) " ;  which is the same as:
                " 8 * (6 + 4)  ";

 We have a "multiplication" and a "parentheses" ;
    So:  The "parentheses" take first priority:
____

     "(6 + 4) = 10 " ;

now:  " 8 * (6 + 4) " ;

            =    8 * 10 = 80 ; which is our answer:
____
Alternate method:
Note the distributive property of multiplication:
          →   a(b + c) = ab + ac  ;

So:   8 (6 + 4) = (8*6) + (8*4) ;

                      =    48 + 32;

                      =    80 ;  which is our correct answer!
____
Hope this answer was helpful to you!  

Please reply if you have any questions!  Wishing you well!
____

Answer:

0

Step-by-step explanation:

[tex]f(-2)[/tex] is the value of [tex]y=f(x)[/tex] at [tex]x=-2[/tex]

Answer:

20

Step-by-step explanation:

b² - 4ac = (-6)² - 4(1)(4) = 36 - 16 = 20

The gardner is correct Because the total distance traveled by the roller is greater than the length of the bowling green.

A diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.

For the gardener to be correct,

8×Perimeter of the roller = Length of the bowling green

Therefore,

Let use first find the perimeter of the roller

Where:

Substitute these values into equation 1

For 8 full rotation,

Comparing the distance for 8 revolution of the roller with the length of the bowling green,

Therefore, the gardner is correct

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The value of x for the given triangle is 12.

According to the question,

We have the following information:

We have a figure of two triangles joined together and some of the angles are marked.

Now, we observe the figure carefully then the base of both triangles are parallel to each other.

Now, 45° will be the angle of triangle on right hand side because they are vertically opposite angles.

We know that the sum of three angles of triangle is 180°.

For the RHS triangle, let's take third angle to be y:

45+65+y=180

110+y =180

y =180-110

y = 70°

Now, y will be equal to (6x-2) because they are vertically opposite angles.

6x-2 = 70

6x = 70+2

6x = 72

x = 72/6

x = 12

Hence, the value of x for the triangle is 12.

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The equation of the line y = -x/2 + 6, with slope -1/2,

What is equation straight line?

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

slope m = -1/2.

So the line can be formed by (y-y1) = m (x-x1)

(y-7) =  -1/2* (x+2)

y = -x/2 - 1+7

y = -x/2 + 6

Hence the equation of the line y = -x/2 + 6.

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The height of the sand is 25cm

How to calculate height?

First the volume formula is height × long × wide. So, we can calculate height by dividing the volume by the long and wide.

= 36,000 ÷ 45 ÷ 32

= 25cm

Thus, the height of the sand is 25cm

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Answer:

the slope of the line is -2

Step-by-step explanation:

since the line is going downhill the slope is always negative. The top point is 2 lines above the bottom one and 1 over the slope is -2/1 but simplified is just negative 2

Answer:

Step-by-step explanation:

if you use the rise over run equation the slope would be 3/1

Answer: n

Step-by-step explanation: n!=(n-1)!*n

(n-1)!*n/(n-1)!=n

8/10 as a fraction written in thousands is 8000/10000

This is a term used to refer to fractions that are equal even though they have different values in both he numerator and the denominator

Fractions are class of numbers that are of two parts the upper part is the numerator while the lower part is called the denominator.

In the given problem, 8/10

8/10 is an equivalent form of 8000/10000 in thousands this means that they are equal.

8/10 is shown to be equal to  8000/10000  by dividing, this reduces the fraction to 8/10. Using calculator can still show it that both numbers equal

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Value of y is -14

According to the expressions "" and "y is inversely proportionate to x," y decreases as x increases or vice versa. There are two translations for this idea. The constant of proportionality, k, sometimes known as yx = k, or y = k/x (they are essentially identical though.)

Therefore, in order to solve for either y or x in the future using the knowledge provided, we must first determine the constant k.

As y varies inversely as x

then,

[tex]y=k/x\\\7=k/-4\\\k=-28[/tex]

To find the value of y at x =2

[tex]y=k/x\\\y=-28/2\\\y=-14[/tex]

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By definitions of composite numbers and prime numbers, a total of 117 whole numbers that are less or equal to 300, are divisible by 3, 4 or both, but not by 9.

In this problem we must look for all composite numbers that are divisible by 3, 4 or both, but not by nine. Composite numbers are products of prime numbers, that is, whole numbers that are only divisible by themselves. The set of numbers are formed by three subsets:

Subset 1

n = 3 × x, n ≤ 300, n ≠ 9 · i, i ≥ 1

The elements of the subset are: 3, 6, 12, 15, 21, 24, 30, 33, 39, 42, 48, 51, 57, 60, 66, 69, 75, 78, 84, 87, 93, 96, 102, 105, 111, 114, 120, 123, 129, 132, 138, 141, 147, 150, 156, 159, 165, 168, 174, 177, 183, 186, 192, 195, 201, 204, 210, 213, 219, 222, 228, 231, 237, 240, 246, 249, 255, 258, 264, 267, 273, 276, 282, 285, 291, 294, 300. (67 numbers)

Subset 2

n = 4 × x, n ≤ 300, x ≠ 9 · i, i ≥ 1

The elements of the subset are 4, 8, 12, 16, 20, 24, 28, 32, 40, 44, 48, 52, 56, 60, 64, 68, 76, 80, 84, 88, 92, 96, 100, 104, 112, 116, 120, 124, 128, 132, 136, 140, 148, 152, 156, 160, 164, 168, 172, 176, 184, 188, 196, 200, 204, 208, 212, 220, 224, 228, 232, 236, 240, 244, 248, 256, 260, 264, 268, 272, 276, 280, 284, 292, 296, 300. (50 numbers)

Subset 3

n = 12 × x, n ≤ 300, n ≠ 9 · i, i ≥ 1

The elements of the subset are 12, 24, 48, 60, 84, 96, 120, 132, 156, 168, 204, 228, 240, 264, 276, 300.

There are 117 whole numbers less or equal to 300.

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gof(x) is x/2+3/4 for functions f(x)=2x+3 and g(x)=x/4

A relation is a function if it has only one y-value for each x-value.

Composite functions are when the output of one function is used as the input of another.

Given,

f(x)=2x+3 and g(x)=x/4

g circle f of x equal to g of f of x.

and gof(x)=g(f(x))

g circle f of x equal to g of two times of x plus three.

gof(x)=g(2x+3)

gof(x)=(2x+3)/4

=2x/4+3/4

gof(x)=x/2+3/4

Hence gof(x) is x/2+3/4 for functions f(x)=2x+3 and g(x)=x/4

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Option (B) is the correct one and -3x - 6 < -33 and -3x - 6 ≥ −36 is an equivalent form of the given compound inequality

Given, a compound inequality

−33 > (−3x − 6) ≥ −36

Now, we can interpret the given inequality separately also,

−33 > (−3x − 6)

On simplifying, we get

-33 > -3x - 6

-33 + 6 > -3x

-27 > -3x or -3x - 6 < -33

also, (−3x − 6) ≥ −36

On simplifying, we get

-3x - 6 ≥ −36

-3x ≥ −36 + 6

-3x ≥ −30 or -3x - 6 ≥ −36

So, -3x - 6 < -33 and -3x - 6 ≥ −36 is an equivalent form of the given compound inequality.

Hence, Option (B) is the correct one and -3x - 6 < -33 and -3x - 6 ≥ −36 is an equivalent form of the given compound inequality.

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Answer:

12.573%

Step-by-step explanation:

Percent means "parts per 100".

Therefore, to convert a decimal to a percent, multiply the decimal by 100.

When multiplying a decimal by a multiple of 10, simply move the decimal point to the right the same number of places as there are zeros.

Therefore, to multiply a decimal by 100, simply move the decimal point 2 places to the right.

⇒ 0.12573 × 100 = 12.573%

Answer: log7 21 /  log7 5

I took one for the team and guessed, and got it right.

You are welcome future students.

The expression that correctly shows how to rewrite the logarithm [tex]\log_5{21}[/tex], using a logarithm of base 7, with change of base, is given as follows:

[tex]\frac{\log_7{21}}{\log_7{5}}[/tex]

To change the base of a logarithm, a new fraction is written, in which:

In this problem, the logarithm that will be calculated is:

[tex]\log_5{21}[/tex]

Hence the number and the base of the logarithm are presented as follows:

With the change of the base to base 7, the numerator and the denominator of the fraction are given as follows:

Hence the simplified logarithm is presented as follows:

[tex]\frac{\log_7{21}}{\log_7{5}}[/tex]

Meaning that the correct option is the second option.

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Answer: D is the correct answer.

Step-by-step explanation:

The pythagoras theorum states that in a right angled triangle, the sum of the squares of the two smaller sides is equal to the square of the hypotenuse ( the largest side.)

The number of nonreal complex nineteenth roots is 1

Here we have to find the nonreal complex nineteenth roots of 1

we know that nth root ⇒ n roots

Therefore,

[tex]1^{1/19}[/tex] ⇒ -1,1

[tex]-1^{19}[/tex] ⇒ -1

[tex]1^{19}[/tex] ⇒ 1

we get 1 real root exist.

The number of non real complex nineteenth roots is 1.

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The test that does not include scales for assessing test taker response biases and faking is D. Meyers-Briggs Type Indicator.

A popular objective personality measure is the Millon Clinical Multiaxial Inventory—Third Edition (MCMI-III). The MCMI-III assesses the presence of psychological disorders, including personality disorders.

The MMPI-2 is a 567-item true/false self-report questionnaire that assesses a person's psychological state. It includes nine validity scales (or 'lie' scales) that assess lying, defensiveness, faking good, and faking bad, among other things.

The MMPI-2-RF provides accurate measurement of 40 dimensional constructs related to personality and psychopathology in the context of the new paradigm (with an additional nine scales measuring protocol validity, or the individual's test-taking approach).

The Myers-Briggs Type Indicator is an introspective self-report questionnaire used in personality typology to identify different psychological preferences in how people perceive the world and make decisions. Introversion/extraversion, sensing/intuition, thinking/feeling, and judging/perceiving are the four categories. Unlike others, this first use a scale.

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Answer:

rental cost of each movie is $2.5

rental cost of each video game is $5.5

Step-by-step explanation:

use x for movie and y for video game. Then you get the equations
2x+12y=71 and 5x+3y=29

then you solve each equation for either x or y.
when you solve for y you will get
y = (71 -2x) / 12    and y = (29 -5x) / 3

because y is the same, you put those equations together
(71-2x) / 12 = (29 -5x) / 3
then solve for x and you get x = 2.5

then you put 2.5 for x in either of the original equations and solve for y.
for both equations you will get y = 5.5