the following table shows the number of miles a hiker walked on a trail each day for 6 days. day 1 2 3 4 5 6 number of miles 8 5 7 2 9 8 what was the mean number of miles the hiker walked for the 6 days? responses 3.5 3.5 4.5 4.5 6.5 6.5 7.5 7.5 8

Answer:

5x=380

x = 76

Carla made 76 cookies each hours

Step-by-step explanation:

Just make an equation, so the total number of cookies is 380 and she works for 5 hours, so it is just 380/5.

A bowling ball moving at 11 meters per second will have approximately 537.64 joules of energy, rounded to the nearest hundredth.

The kinetic energy (E) of a moving object varies directly with the square of its velocity (v). To write the equation relating E to v, we can use the formula: E = k * v^2, where k is a constant of proportionality. Given a bowling ball traveling at 15 meters per second with 1000 joules of energy, we can find the value of k:

1000 = k * (15^2)
1000 = k * 225
k ≈ 4.44

So, the equation relating the kinetic energy and velocity is: E ≈ 4.44 * v^2.

Now, we want to find the energy of the bowling ball when it's moving at 11 meters per second. Using the derived equation:

E ≈ 4.44 * (11^2)
E ≈ 4.44 * 121
E ≈ 537.64

Therefore, a bowling ball moving at 11 meters per second will have approximately 537.64 joules of energy, rounded to the nearest hundredth.

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Complete question:

The kinetic energy of a moving object varies directly with the square of its velocity. A bowling ball traveling at 15 meters per second has about 1000 joules of energy.

Write the equation that relates the kinetic energy, E, to its velocity, v.

Round your answer to the nearest hundredth.

About how much energy will a bowling ball have if it is moving at 11 meters per second?

Use your answer from part one. Round your answer to the nearest hundredth

Answer: 9/64

Step-by-step explanation:

First, we find the probability of blue in one spin.

One spin: 3/8

Next, we also know that the second spin will also have a probability of 3/8.

To combine these probabilities in both spins, we multiply. This will combine the two independent events. It can be similar to Permutation.

Probability of both spins: 3/8 x 3/8

=9/64

9/64 is the combined probability of both spins.

The value of tan(ф) when cos(ф) = 8/9 in quadrant IV is - √17/8

To solve for the value of tan(ф), we need to use the trigonometric identity: tan(ф) = sin(ф)/cos(ф).

Since ф is in quadrant IV, we know that the cosine value is positive (due to cosine being positive in the adjacent side of quadrant IV) and the sine value is negative (due to sine being negative in the opposite side of quadrant IV).

We are given the value of the cosine, which is cos(ф) = 8/9. To find the sine, we can use the Pythagorean identity: sin²(ф) + cos²(ф) = 1.

Plugging in the given value of the cosine, we get: sin²(ф) + (8/9)² = 1. Solving for sin(ф), we get sin(ф) = - √(1 - (64/81)) = - √(17/81) = - √17/9.

Now that we have the values of sin(ф) and cos(ф), we can substitute them into the tan(ф) equation: tan(ф) = sin(ф)/cos(ф) = (- √17/9)/(8/9) = - √17/8.

Therefore, the value of tan(ф) when cos(ф) = 8/9 in quadrant IV is - √17/8.

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The volume of the fish tank is approximately 3,693,142,608 cubic inches

To find the volume of the rectangular prism-shaped fish tank, we need to multiply its width, length, and height.

Given the dimensions are 2014 inches wide, 1012 inches long, and 1812 inches tall, the calculation is as follows:

Volume = Width × Length × Height

Volume = 2014 in × 1012 in × 1812 in

Upon calculating the product, we get:

Volume ≈ 3,693,142,608 cubic inches

The volume of the fish tank is approximately 3,693,142,608 cubic inches

N.B: None of the answer choices has the correct answer.

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Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

The area of the parallelogram is 8 units², which is option (b).

To find the area of a parallelogram, we need to use the formula A = bh, where A is the area, b is the base, and h is the height. In this case, we can use the distance formula to find the base and height.

Base = distance between points P and Q
= √[(5-3)² + (3-3)²]
= √4
= 2 units

Height = distance between point P and the line containing points R and S. We can find the equation of this line by first finding its slope:

slope = (y2 - y1)/(x2 - x1)
= (7 - 7)/(9 - 7)
= 0

Since the slope is 0, the line is horizontal and has an equation of y = 7. Therefore, the height is the distance between point P and this line, which is:

Height = distance from point P to line y = 7
= |3 - 7|
= 4 units

Now we can plug in the values of b and h into the formula A = bh:

A = 2 x 4
= 8 units²

Therefore, the area of the parallelogram is 8 units², which is option (b).

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Therefore, Tariq has collected 201.09 g trace element.

We are given that Tariq uses a container that is in the shape of a cylinder. The radius of the cylinder is 7.6 cm and the height of the cylinder is 17 cm.

Firstly, we will find the volume of the cylinder by applying the formula

The volume of the cylinder = [tex]\pi r^{2} h[/tex]

As we know the values of r and h, we will substitute these values in the given formula

The volume of cylinder = 3.14 * 17.6 * 7.6 *7.6

The volume of cylinder = 55.264 * 57.76

Volume = 3192.04 [tex]cm^{3}[/tex]

We are given that the water sample shows 0.063 grams of some trace element for every cubic centimeter of water. Therefore, we will multiply the volume of the cylinder by 0.063 to calculate the number of trace elements collected.

= 3192.04 * 0.063

= 201.09

Therefore, a total of 201.09 g of trace elements was collected by Tariq.

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the rock will be going 89.9 m/s just before it hits the bottom of the chaste on a certain plaats moon.

To answer your question, we need to use the formula for the acceleration due to gravity, which is:

a = g

where a is the acceleration, and g is the gravitational constant. In this case, we know that the acceleration due to gravity on the moon is 2.9 m/sec^2, so we can substitute that into the formula:

a = 2.9 m/sec^2

Now we need to use the formula for calculating the speed of an object that is falling under the influence of gravity, which is:

v = gt

where v is the speed, g is the gravitational constant, and t is the time. We know that the rock takes 31 seconds to hit the bottom of the chivaste, so we can substitute that into the formula:

t = 31 s

Now we can calculate the speed of the rock just before it hits the bottom:

v = gt
v = 2.9 m/sec^2 x 31 s
v = 89.9 m/s

So the rock will be going 89.9 m/s just before it hits the bottom of the chivaste on the certain plaats moon.

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Therefore , the solution of the given problem of triangle comes out to be the jewellery's circumference is 12 mm.

If a polygon contains at least one more segment, it is a hexagon. It is a simple rectangle in shape. Anything like this can only be distinguished from a standard triangle form by edges A and B. Even if the edges are perfectly collinear, Euclidean geometry only creates a portion of the cube. A triangle is made up of a quadrilateral and three angles.

Here,

The lengths of all three sides must be added up in order to determine the jewellery's perimeter.

=> c²= a² + b²

where a and b are the lengths of the other two sides, and c is the length of the hypotenuse.

=> A = 3mm, and B = 4mm.

Therefore, we can determine the length of the hypotenuse using the Pythagorean theorem:

=> c² = a²+ b²

=> c² = 3² + 4²

=> c² = 9 + 16

=> c² = 25

=> c = √25)

=> c = 5 mm

As a result, the hypotenuse is 5 mm long.

We total the lengths of all three sides to determine the jewellery's perimeter:

=> perimeter = 4mm, 3mm, and 5mm.

=> 12 mm is the diameter.

Therefore, the jewellery's circumference is 12 mm.

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Therefore, the measure of line segment XC is 3.75 cm.

In geometry, two lines or planes are said to be perpendicular if they intersect each other at a right angle (90 degrees). The term "perpendicular" is also commonly used to describe the relationship between a line and a surface, where the line is at a right angle to the surface at the point of intersection. In general, the concept of perpendicularity is fundamental to many mathematical and scientific fields, such as trigonometry, physics, and engineering. It is also a commonly used term in everyday language to describe objects or structures that intersect at right angles, such as the corners of a square or the legs of a chair.

Here,

In the given diagram, let O be the center of the circle and let XC = a.

Since AB is perpendicular to XY at C, we have AC = BC = 8 m (using Pythagoras theorem). Also, since AB is a radius of the circle, we have AB = r, where r is the radius of the circle.

By the power of a point theorem, we have:

AC × XC = BC × XY

Substituting the given values, we get:

8 m × a = 8 m × 30 cm

Simplifying and converting units, we get:

a = 3.75 cm

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The equation of line passing through the points (8, 6) and (-3, 6) is y = 6. Since the y-coordinate is the same for both points, the line is a horizontal line at y = 6.

To find the equation of the line passing through the points (8, 6) and (-3, 6), we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

First, we need to find the slope, which is given by

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (8, 6) and (x2, y2) = (-3, 6)

m = (6 - 6) / (-3 - 8)

m = 0 / -11

m = 0

Since the slope is zero, the line is a horizontal line. We can see from the given points that the line passes through y = 6. Therefore, the equation of the line is

y = 6

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Mr. Bilo received 8 P50-bills, 5 P100-bills, and 5 P20-bills.

The number of P50, P100, and P20 bills Mr. Pilo got is calculated as follows;

Amount from P50-bills: 2/5 x P1,000 = P400

Amount from P100-bills: 1/2 x P1,000 = P500

The total amount he received from the P50-bills and P100-bills = P400 + P500

The total amount he received from the P50-bills and P100-bills = P900. The amount left to be changed into P20-bills = P1,000 - P900

The amount left to be changed into P20-bills = P100.

The number of bills will then be:

Number of P50-bills: P400 ÷ P50 = 8

Number of P100-bills: P500 ÷ P100 = 5

Number of P20-bills: P100 ÷ P20 = 5

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Complete question:

Mr Bilo has a P1,000-bill and asked someone to exchange in to 2/5 P50-bill and 1/2 P100-bill and the rest into 20-bill. How many P50,P100 and P20 bills did he get.

1. The growth factor for the number of customers over a year is approximately 1.4266.

2. the growth factor in customers over a decade period is approximately 5.927.

Factors that affect how many consumers there are in a year are

c(12)/c(0) = (400 x (1.03)¹²) / (400 x (1.03)⁰)

= (1.03)¹²

= 1.4266....

Therefore, the growth factor for the number of customers over a year is approximately 1.4266.

2. To write an equation for the number of customers c as a function of the number of years y, we can substitute m = 12y into the original equation

[tex]c(y) = 400 x (1.03)^{12y}[/tex]

one decade = 10 years

= 120 months

We must calculate the value of the equation at m=120 and divide it by the equation's value at m=0.

c(120) / c(0) = [400 x (1.03)¹²⁰] / [400 x (1.03)⁰]

= (1.03)¹²⁰

= 5.927...

Therefore, the growth factor in customers over a ten-year period is approximately 5.927.

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Given Question is incomplete, complete question is given below:

A small printing company launched an online ordering system to expand its business. The equation [tex]c=400(1. 03)^m[/tex] represents the number of customers c it has in terms of the number of months m since it launched the ordering system.

1. By what factor does the number of customers grow in one year? Write your answer as an expression and a numerical value

2. If y is time in years, write an equation for the number of customers c as a function of the number of years y after the introduction of the ordering system. If this model continues to apply for a decade, by what factor will the number of customers grow in one decade?

Part a: f(x) = (x-3)^2 + 5

Part b: f(x) = (x+10)^2 + 5

Part a: To shift the function f(x) = x^2 + 5 right 3 units, we need to subtract 3 from the x-coordinate of the vertex. The vertex form of a quadratic function is given by f(x) = a(x-h)^2 + k, where (h,k) is the vertex. Thus, the function in vertex form that shifts f(x) right 3 units is:

f(x) = (x-3)^2 + 5

Part b: To shift the function f(x) = x^2 + 5 left 10 units, we need to add 10 to the x-coordinate of the vertex. Using the same vertex form as before, the function in vertex form that shifts f(x) left 10 units is:

f(x) = (x+10)^2 + 5

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The solution of the trigonometric equation

cos(2x) = cos(x) + 2

is x = 180°

Here we want to solve the equation:

cos(2x) = cos(x) + 2

First, we know that:

cos(2x) = 2cos(x)²  - 1

Then we can rewrite:

2cos(x)²  - 1 = cos(x) + 2

We can define:

cos(x)= y

2y² - 1 = y + 2

Then we need to solve the quadratic:

2y² - 1 - y - 2  =0

2y² - y - 3 = 0

Using the quadratic formula we will get:

[tex]y = \frac{1 \pm \sqrt{(-1)^2 - 4*2*2*-3} }{2*2} \\\\y = \frac{1 \pm 5}{4}[/tex]

so the solutions are:

y = (1 + 5)/4 = 6/4

y = (1-  5)/4 = -1

And remember that y = cos(x), then y =  6/4 can be discarded.

Then the solution comes from:

cos(x) = -1

then x = pi = 180°

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The images of points B and C are B'(x, y) = (- 2, 6) and C'(x, y) = (- 1, 7), respectively.

In this problem we find must determine the image of two points by translation, whose formula is introduced below:

T(x, y) = P'(x, y) - P(x, y)

Where:

First, determine the translation vector:

T(x, y) = (1, 4) - (0, 0)

T(x, y) = (1, 4)

Second, determine the images of points B and C:

B'(x, y) = (- 3, 2) + (1, 4)

B'(x, y) = (- 2, 6)

C'(x, y) = (- 2, 3) + (1, 4)

C'(x, y) = (- 1, 7)

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(a) The quadrant in which u/2 lies is either Quadrant I or Quadrant II.

(b) The exact values of sin(u/2), cos(u/2), and tan(u/2) are:
sin(u/2) = √10/5
cos(u/2) = 3√10/10
tan(u/2) = 2/3

(a) To determine the quadrant in which u/2 lies, we need to look at the value of sin u. Since sin u is positive (3/5 is positive and π/2 is in Quadrant I), we know that u is in either Quadrant I or Quadrant II.

To find u/2, we divide u by 2, which means u/2 will be in either Quadrant I or Quadrant II as well. Therefore, the answer is either Quadrant I or Quadrant II.

(b) We can use the half-angle formulas to find the values of sin(u/2), cos(u/2), and tan(u/2):

sin(u/2) = ±√[(1 - cos u)/2]
cos(u/2) = ±√[(1 + cos u)/2]
tan(u/2) = sin(u/2)/cos(u/2)

Since sin u = 3/5, we can find cos u using the identity sin^2 u + cos^2 u = 1:

cos u = ±√[(1 - sin^2 u)] = ±√[(1 - 9/25)] = ±4/5

Since u/2 is in either Quadrant I or Quadrant II, we know that sin(u/2) and cos(u/2) are positive. Therefore, we can choose the positive square roots for sin(u/2) and cos(u/2):

sin(u/2) = √[(1 - cos u)/2] = √[(1 - 4/5)/2] = √[1/10] = √10/10 = √10/5
cos(u/2) = √[(1 + cos u)/2] = √[(1 + 4/5)/2] = √[9/10] = 3/√10 = 3√10/10

Finally, we can use these values to find tan(u/2):

tan(u/2) = sin(u/2)/cos(u/2) = (√10/5)/(3√10/10) = 2/3

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The total cost of the trip in U.S. dollars as per given rates and conversion is equal to approximately USD 3,232.58.

Total cost of the trip in U.S. dollars,

Convert the Australian dollars to U.S. dollars.

Using the exchange rate of 0.7752 USD per 1 AUD.

The cost of the hotel is,

7 nights × A$110/night = A$770

To convert this to U.S. dollars, multiply by the exchange rate,

A$770 × 0.7752 USD/AUD

= USD 596.904

Expected cost of meals, tours, souvenirs, etc. is,

A$3,400

Convert this to U.S. dollars, we again multiply by the exchange rate,

A$3,400 × 0.7752 USD/AUD

= USD 2,635.68

Total cost of the trip in U.S. dollars is the sum of these two amounts is,

USD 596.904 + USD 2,635.68 = USD 3,232.584

Rounding to two decimal places = approximately USD 3,232.58.

Therefore, the cost of the trip in the U.S. dollars is equal to approximately USD 3,232.58.

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The above question is incomplete, the complete question is:

You are planning a trip to Australia. your hotel will cost you a$110 per night for seven nights. you expect to spend another a$3,400 for meals, tours, souvenirs, and so forth. How much will this trip cost her in U.S. dollars if the USD equivalent is .7752?

The answer is B) - (11x² - 6x)ln(3) + 2ln(3) - 6ln(x) + C, where C is the constant of integration.

To solve this problem, we are given a function h(x) and asked to find its antiderivative or indefinite integral, which is denoted by H(x) and is defined as the function whose derivative is h(x). We are also given a specific value of H(x) at x = 6 and asked to use it to find the constant of integration, denoted by C.

The given function is h(x) = 22x - 3x² - 6/x, and we want to find H(x), which is the antiderivative of h(x). Using the power rule of integration, we can integrate each term of h(x) separately:

where C is the constant of integration. Note that we need to include an absolute value sign around x in the natural logarithm term because the function is not defined for x = 0.

Next, we are given that H(6) = 31, which means that when x = 6, the value of H(x) is 31. Substituting x = 6 and H(x) = 31 into the above equation, we get:

Simplifying, we get:

Therefore, the antiderivative of h(x) is:

We can simplify the expression by using the identity ln|a/b| = ln|a| - ln|b|:

where C is the constant of integration. Thus, the final answer is:

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The reduction form is [tex]I_4 i= cot^3 x =ln |sin x| - 3 cot x + 3x + C[/tex].

To find the reduction formula for ∫cot^n x dx, we can use integration by parts. Let u = cot^(n-1) x and dv = cot x dx, then[tex]du = (n-1)cot^(n-2) x csc^2[/tex]x dx and v = ln |sin x|. By the formula for integration by parts, we have:

∫cot^n x dx = ∫u dv = uv - ∫v du

= [tex]cot^(n-1) x ln |sin x| - (n-1) ∫cot^(n-2) x csc^2 x ln |sin x| dx.[/tex]

This gives us the reduction formula:

[tex]I_n = ∫cot^n x dx = cot^(n-1) x ln |sin x| - (n-1) I_(n-2).[/tex]

Using this formula, we can find I_4 as follows:

[tex]I_4 = ∫cot^4 x dx = cot^3 x ln |sin x| - 3 I_2\\= cot^3 x ln |sin x| - 3 ∫cot^2 x dx\\= cot^3 x ln |sin x| - 3 (cot x - x) + C,\\[/tex]

where C is the constant of integration. Therefore, the solution for I_4 is [tex]cot^3 x ln |sin x| - 3 cot x + 3x + C.[/tex]

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The relation has been plotted on the graph where the first quadrant has (1, 2) and (2, 4), while the second quadrant contains (-1, 3) and (-2, 4).

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

You can compare various data sets using bar graphs.

In a line graph, the data is represented by tiny dots, and the line that connects them indicates what happens to the data.

So, we have the coordinates:

(-1, 3); (-2, 4); (1, 2); (2, 4)

Now, plot it on the graph as follows:

(Refer to the graph attached below.)

(-1, 3) and (-2, 4) are in the 2nd quadrant, and (1, 2) and (2, 4) are in the 1st quadrant.

Therefore, the relation has been plotted on the graph where the first quadrant has (1, 2) and (2, 4), while the second quadrant contains (-1, 3) and (-2, 4).

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Correct question:

Express the relation (-1, 3); (-2, 4); (1, 2); (2, 4) on the graph.

Answer: 5 hours of service

Step-by-step explanation:

25 + x(15) = 20x

⇒ 25 = 20x - 15x

⇒ 25  = 5x

⇒ x = 5

The number name of 346. 725 is three hundred forty-six point seven two five.

A number name refers to the name that is used to describe the number in words. This is helpful in communicating it orally.

To convert the given number to word form, we do as follows:

1. We check the digits of the number before decimals

In this case, the number of digits in the question is 3

2. The highest place value is then checked.

It comes out to be hundreds

3. We name it accordingly and add a suffix to the face value

This is 3 and the name comes out to be Three hundred

4. We continue it till we encounter the decimal

We get the number as Three hundred forty-six

5. Then we mention the word decimal or point

The result is Three hundred forty-six point

6. The number after the decimal is written as it is

Hence, the name comes out to be Three hundred forty-six point seven two five.

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Answer:

Blue = 4

Red = 24

Green = 4

All = 32

Step-by-step explanation:

Area of a triangle: 1/2 * base * height, so for both blue and green:

1/2 * 2 * 4

1 * 4

4

Area of an object with 4 sides: length * width, so for red:

6 * 4

24

Area of everything: blue + red + green, so for all:

4 + 4 + 24

8 + 24

32

The probability of drawing a diamond or a spade card from a standard deck of cards and rolling a 2 on a six-sided die is 8.33%

To calculate the probability of drawing a diamond or a spade card from a standard deck of cards, we need to find the total number of diamond and spade cards in the deck. There are 13 cards in each suit, so there are 26 diamond and spade cards in total. The deck has 52 cards in total, so the probability of drawing a diamond or a spade card is:

P(diamond or spade) = 26/52 = 1/2 = 50%

To calculate the probability of rolling a 2 on a six-sided die, we need to find the total number of possible outcomes, which is 6 (since there are 6 sides on the die), and the number of favorable outcomes, which is 1 (since there is only one face with a 2 on it). Therefore, the probability of rolling a 2 on a six-sided die is:

P(rolling a 2) = 1/6 = 16.67%

To find the probability of both events happening together (drawing a diamond or a spade card and rolling a 2 on a six-sided die), we multiply the probabilities of each event:

P(diamond or spade AND rolling a 2) = P(diamond or spade) * P(rolling a 2)
= 50% * 16.67%
= 8.33%

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(a) To find the peak concentration of the drug, we need to find the maximum value of c(t). Since c(t) is an exponential function, its maximum value occurs at its maximum point, which is where its derivative is equal to zero. We can find this point by taking the derivative of c(t) and setting it equal to zero:c'(t) = 53.2e^{-0.26} - 13.832te^{-0.26} = 0Solving for t, we get t = 3.870 hours. Therefore, the peak concentration of the drug is c(3.870) = 109.2 ng/ml.(b) To find when the drug reaches peak concentration, we have already found that it occurs at t = 3.870 hours. Therefore, the drug reaches peak concentration 3.870 hours after it is administered.

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The peak concentration of the drug is approximately 42.83 ng/ml, and it occurs around 3.85 hours after the drug is administered.

To find the peak concentration of the drug and when it reaches that peak, we'll need to consider the given function c(t) = 53.2te^(-0.26t), where t is the time in hours.

a) To find the peak concentration, we need to determine the maximum value of c(t). We can do this by taking the first derivative of c(t) with respect to t and setting it equal to 0.

c'(t) = 53.2(-0.26)e^(-0.26t) + 53.2e^(-0.26t) = 0

Now, solve for t:

t ≈ 3.85 hours

b) Plug the value of t back into the c(t) function to find the peak concentration:

c(3.85) = 53.2(3.85)e^(-0.26(3.85)) ≈ 42.83 ng/ml

So, the peak concentration of the drug is approximately 42.83 ng/ml, and it occurs around 3.85 hours after the drug is administered.

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Answer:

Step-by-step explanation:

2 x 36 ÷ 3 + 9 - 4

= 72 ÷ 3 + 9 - 4 (perform multiplication first)

= 24 + 9 - 4 (perform division)

= 29 (perform addition and subtraction)

Therefore, 2x36 ÷ 3 + 9 - 4 = 29.

Answer:

29

Step-by-step explanation:

2×36=72

72/3=24

24+9=33

33-4=29

Check the picture below.

Answer:

250 degrees

Step-by-step explanation:

For any circle tangent to line FG at point F, as shown in the diagram, and for any point E on the circle, the relationship between the measure of angle GFE and the arclength of FE is given by [tex]m~\text{arc}~FE=2m \angle GFE[/tex].

So, the measure of the arc FE is 110 degrees.  Since a circle is fully 360degrees, the missing arc represented by the question mark is given by the following equation:

? + 110 = 360

Solving for the ?

? = 250 degrees

After the duration of 2 hours the distance between the first pair and the second pair is 3.07 km, under the condition that the second pair decide to head 60° west of north travelling at the same pace.

In order to evaluate the distance between two points with given coordinates, we can apply the distance formula. The distance formula is

d = √ [ (x₂ − x₁)² + (y₂ − y₁)² ]

Here,

(x₁, y₁) and (x₂, y₂) = coordinates of the two points.

For the given case, we can consider that the first pair of team members start at the origin (0, 0) and cover the distance towards  north for 2 hours at a pace of 4 km/h.

Hence, their final position is (0, 8).

The second pair of team members take  the origin (0, 0) and travel 60° west of north for 2 hours at a pace of 4 km/h.

Now to evaluate their final position, we have  to find their coordinates. Let us consider their final position (x, y).

We can apply trigonometry to find x and y.

The angle between their direction of travel and the y-axis is 60°.

sin(60°) = y / d

cos(60°) = x / d

Here,

d = distance travelled by the second pair of team members.

It is given that they travelled for 2 hours at a pace of 4 km/h.

d = 2 hours × 4 km/h

= 8 km

Staging this value into the above equations

y = d × sin(60°) = 8 km × sin(60°)

≈ 6.93 km

x = d × cos(60°) = 8 km × cos(60°)

≈ 4 km

Hence, the final position regarding the second pair of team members is approximately (4 km, 6.93 km).

Now we can apply the distance formula to evaluate the distance between the two pairs of team members

d = √ [ (x₂ − x₁)² + (y₂ − y₁)² ]

d = √ [ (4 − 0)² + (6.93 − 8)² ]

d ≈ 3.07 km

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