Find the area of the shaded region in the figure below, if the radius of the outer circle is 12 and the radius of the inner circle is 2. Keep your answer in terms of π.

1. After constructing the function according to the question, Q(t) = [tex]35e^{\frac{-ln2}{20}t}[/tex].

2. It will take 50 hours for the amount of Diazepam left in the body to reach 7 mg.

What is a function?

Exactly one element of Y is assigned to each element of X in a mathematical function from a set X to a set Y. Both the set X and the set Y are referred to as the function of the domain and codomain, respectively. Examples include f(x) = x/2 ("f of x equals x split by 2") ("f of x equals x divided by 2") Every input "x" has a single output "x/2," which makes it a function: • f(2) = 1.

Solution explained:

According to the question,

Q(t) = [tex]Pe^{rt}[/tex]

The half-life of Diazepam is 20 hours = t

Q(0) = p = 35 { the initial value}

Q(20) = [tex]35e^{20r} = \frac{1}{2} X 35[/tex]

          =  [tex]e^{20r} = \frac{1}{2}[/tex]

          = [tex]20r = -ln2[/tex]

          = [tex]r = \frac{-ln2}{20}[/tex]

Therefore, Q(t) = [tex]35e^{\frac{-ln2}{20}t}[/tex]

Now, Let

Q(t) = 7

[tex]35e^{\frac{-ln2}{20}t}[/tex] = 7

[tex]e^{\frac{-ln2}{20}t} = \frac{1}{5}[/tex]

[tex]{\frac{-ln2}{20}t} = -ln5[/tex]

After calculating,

t = 50 (hours)

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The day with greater actual attendance is Thursday with 98 students

A percentage is defined as the ratio that can be expressed as a fraction of 100

Given:

Expected numbers: Wednesday= 70 students andThursday= 112 students

20% of Wednesday = 20/100 x 70 = 14 students. That is 14 students are absent on Wednesday but attended on Thursday instead. This means 56 (70 -14) students scheduled for Wednesday attended.

25% of the students who planned to attend on Thursday attended on Wednesday instead:

25% of Thursday = 25/100 x 112 = 28 students.  This means 84 students scheduled for Thursday attended

Actual Wednesday attendance = 56 + 28 = 84 students

Actual Thursday attendance = 14 + 84 = 98 students

Therefore, Thursday had a greater actual attendance with 98 students

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Answer: MO

Step-by-step explanation:

Answer:

4.7 cm

Step-by-step explanation:

Factoring -4 out of -8+20 factored expression is -4(2 + 5).

Factor expressions, also known as factoring, refer to the process of rewriting an expression as the product of factors. 3x + 12y, for example, can be factored into a simple expression of 3 (x + 4y). Calculations become easier in this manner. The terms 3 and (x + 4y) are referred to as factors.

To factor a given expression goes thus:

Each term should be written as the prime factorization.

Determine the factors that all of the terms share.

Multiply those common variables.

In this case, factoring 4 out of -8+20 factored expression is -4(2 + 5).

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Forming the two telephone charge plans in a slope intercept equation form, like Y=mx + b, is as follows:

The slope intercept equation is an equation of a straight-line with its slope (constant unit rate) combining the x and y intercepts.

Generally, the formula y = mx + b depicts the slope intercept equation with the following values:

y = y coordinate

m = slope

x = x coordinate

b = y intercept

                           Plan A   Plan B

Fixed cost (b)      $25        $50

Variable cost (m)  50          25

x = monthly            12          12

y = the total cost for the period

Thus, Plan A will have a total cost of 50x + 25 and Plan B will have a total cost of 25x + 50.

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Value of the expression (a²- 8a - 26) ÷ (a + 2) using synthetic division is given by quotient is a - 10 and remainder is -6.

As given in the question,

Given expression is equal to,

(a²- 8a - 26) ÷ (a + 2)

Simplify the given expression using synthetic division is shown in the attached file,

Another way of division,

(a²- 8a - 26)

= a² -10a + 2a -20 -6

= a (a -10) + 2( a - 10) -6

= ( a + 2 )( a - 10 ) - 6

Quotient of the given division is equal to ( a - 10 )

Remainder of the given division is equal to -6

Therefore, value of the expression (a²- 8a - 26) ÷ (a + 2) using synthetic division is given by quotient is a - 10 and remainder is -6.

The complete question is :

Evaluate the given expression using synthetic division :

(a²- 8a - 26) ÷ (a + 2)

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The statement "A system contains two or more linear equations that can be solved or graphed together at once" is true.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

A system contains two or more linear equations that can be solved or graphed together at once.

This statement is true.

For example,

The two linear equations can be:

ax + by = c ____(1)

dx + ey = F _____(2)

We can solve this equation using the substitution method or elimination method.

We can find the point of intersection.

And we can solve and graph together at once.

Thus,

The statement "A system contains two or more linear equations that can be solved or graphed together at once" is true.

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Answer: 20 [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

First of all, 5 [tex]\frac{4}{10}[/tex] = 5.4

Remember, 1/10 = 0.1, 2/10 = 0.2, and so on.

This means we can change the equation to 25.92 - 5.4, which gives us 20.52.

This is close to 20.50, which is equivalent to 20 [tex]\frac{5}{10}[/tex], which is equivalent to 20 [tex]\frac{1}{2}[/tex].

Answer:

  (c)  0 – 19, 20 – 39, 40 – 59, 60 – 79, 80 – 99

Step-by-step explanation:

You want to know the intervals suitable for creating a histogram of the given set of 10 data points.

The intervals used to categorize data for a histogram must meet two requirements:

The range of the given data is 8 to 83. All the suggested answer choices include a bin that will contain 8. Choice A does not have a bin that contains 88.

When bins are defined like 0–25, 25–50, the location of the data value 25 is unclear. No data value can fall on a bin boundary, so bins need to be defined to prevent that possibility. For integer data values, bin ranges like 0–14, 15–29, or 0–19, 20–39 are appropriate. This eliminates answer choices B and D, which have ambiguous bin boundaries.

The only reasonable answer choice is C:

  0–19, 20–39, 40–59, 60–79, 80–99

__

Additional comment

Histograms tend to be most useful if they have between 5 and 20 bins. The idea is to produce a picture of the data distribution in a general way, without so much detail that the big picture is obscured.

Here, the selected bin set will have numbers of 3, 3, 2, 1, 1 in the bins. This gives the impression of a data set skewed to the right, as it should.

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The value of 3 less than the quotient of a number y and 4 when y is 20 is 2.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

The expression less than the quotient of a number y and 4 will be:

y/4 - 3

When y is 20, the value will be:

y/4 - 3

20/4 - 3

5 - 3

= 2

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The compound expression (a⁵ · a ÷ a⁻³)⁻¹ is equivalent to the power a⁻⁹.

In this problem we find a compound expression formed by several powers of equal base that must be simplified in a single power with the same base. This can be done by using algebra properties related to powers. First, write the given expression:

(a⁵ · a ÷ a⁻³)⁻¹

Second, multiply the powers of equal base:

(a⁵⁺¹ ÷ a⁻³)⁻¹

(a⁶ ÷ a⁻³)⁻¹

Third, by definition of division and the power of a power:

[a⁶ · (a⁻³)⁻¹]⁻¹

(a⁶ · a³)⁻¹

Fourth, use the multiplication of power of same base:

(a⁶⁺³)⁻¹

(a⁹)⁻¹

Fifth, use the property of a power of a power once again:

a⁻⁹

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Answer:

cot x = 2cot(2x) + tan x

Step-by-step explanation:

[tex] \rm \implies cot \: 2x = \dfrac{cos \: 2x}{sin \: 2x} \\ \\ \rm \implies cot \: 2x = \dfrac{ {cos}^{2}(x) - {sin}^{2}(x) }{2(sin \: x)(cos \: x)} \\ \\ \rm \implies cot \: 2x = \frac{1}{2} \bigg( \frac{cos \: x}{sin \: x} - \frac{sin \: x}{cos \: x} \bigg) \\ \\ \rm \implies cot \: 2x = \frac{1}{2} (cot \: x - tan \: x) \\ \\ \rm \implies 2cot ( 2x )= cot \: x - tan \: x \\ \\ \rm \implies cot \: x = 2cot (2x) + tan \: x[/tex]

The true statements about the circle are the radius of the circle is 3 units, the center of the circle lies on the x-axis and the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9

Given: the equation is x²+y²–2x–8 = 0

In order to determine true statements about the circle, we have to rewrite the given equation and compare it with the standard form of the equation of a circle.

The standard form of the equation of a circle is

(x-a)² + (y-b)² = r²

where (a, b) is the center and r is the radius

using the completing square method on the given equation:

x²+y²–2x–8 = 0

x²-2x + (-1)² + y² + (0)²= 8 + (-1)²

(x-1)² + (y-0)² = 9

(x-1)² + (y-0)²  = 3²

Thus, the center is (0, 1) and the radius is 3

Therefore, the options are the radius of the circle is 3 units, the center of the circle lies on the x-axis and the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9

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Answer: 192.07 mm

Step-by-step explanation:

I don't feel like it rn, so here's an image with the hexagonal prism volume equation.

Answer: x = 9.; B=4

Step-by-step explanation:

AABC = AKLM

AB=LK

8=28 — b= 4

LC=LM

27=3x — x=9

Congruent triangles correspond to equal angles and sides

Answer:

x=11

t=6

Step-by-step explanation:

angle M=angle C

3x=33

/3.  /3

x=11

Side AB= Side KL

18=3t

/3. /3

6=t

Hopes this helps please mark brainliest

Answer:

30 = 6

45 = x

cross multiply

30x = 45*6

30x = 270

divide both sides by

30x/30 = 270/30

X = 9

9-6 = 3 days

What was the question? or was this only meant for your classmates?

The slope of the straight line passing through the two given points is undefined which means the line is parallel to the y-axis.

Let us consider the two points A(x₁,y₁) and B(x₂,y₂) be the two points (7,-6) and (6,-6) on the cartesian coordinates.

Let the slope of the line joining A (7,-6)  and B(6,-6)  be m.

We know that the slope of a line is given by:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope of the line

= (6-7) / (-6+6)

= -1 / 0

= undefined

Since the slope is undefined we can say that the straight line is parallel to the y axis.

we know that tan 90° = ∞

So any line parallel to this line will have the same slope as the y axis.

Hence the slope of the given line is undefined or infinity.

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The portion of the graph which does not contain (0, 0) is shaded.

What are Linear Inequalities?

When two mathematical statements or two numbers are compared in an unequal way, it is known as an inequality in mathematics. Inequalities can generally be classified as either algebraic or numerical or as a combination of the two. When a polynomial of degree 1 is compared to another algebraic expression of a degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression.

Given the inequalities :

y ≥>2x + 1

y ≤<2x - 2

From y > 2x + 1 ;

Since the inequality sign is ≥, a solid line is used to draw the straight line graph of  y > 2x + 1

From :

y = mx + c

Where, m = slope ; c = intercept

Hence, a straight line graph with ;

Intercept, c = 1 (where the line crosses the y-intercept)

Slope, m = 2

Consider a point, which isn't on the line ;

Take point (0,0) and use it to test the inequality :

0 > 2(0) + 1

0 >0 + 1

0 >1

This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.

From : y < 2x - 2

Since the inequality sign is ≤, a solid line is used to draw the straight line graph of  y < 2x - 2

Graph the line y < 2x - 2, with ;

Intercept, c = - 2

Slope = 2

Consider a point, which isn't on the line ;

Take point (0,0) and use it to test the inequality y < 2x - 2:

0 < 2(0) - 2

0 < 0 - 2

0 < - 2

This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.

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The solution of the function is x = 12

Trigonometric ratios are the ratios of sides of a right-angle triangle. The most common trigonometric ratios are sine, cosine, and tangent.

Consider a right-angle triangle ABC, right-angled at C. In that case, side AB will be the hypotenuse. Also, if we chose AC as the base and BC as the perpendicular. Then, for ∠BAC, value of sinθ = Perpendicular/ hypotenuse = BC/AB

6cos(5x) = 3

divide both sides by 6, we have

cos(5x) = 3/6

cos(5x) = 0.5

taking the anti cosine of both sides

5x = Arc cos 0.5

5x = 60

x = 60/5

x = 12°

In conclusion, the value of x = 12°

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Slope = m = 2

y = mx + b

y = 2x + b

Plug in (-2, 1) to find b

1 = 2(-2) + b

b = 5

y = 2x + 5

The missing x and y values so that each ordered pair will satisfy the given equation y= −2x +1 is computed to bee

The equation is a linear function representing a straight line

for ordered pair (3, y)

y = −2x + 1

substitute the value of x

y = -2 * 3 + 1

y = -6 + 1

y = -5

hence the ordered pair is (3, -5)

for ordered pair (x, 1)

y = −2x + 1

2x = 1 - y

x = (1 - y) / 2

substitute the value of y

x = (1 - 1) / 2

x = 0

hence the ordered pair is (0, 1)

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Answer:

76.5

Step-by-step explanation:

Volume for prisms is "V = bH", where b = base and H = height.

b = 3 * 3 * 0.5

b = 4.5

H = 17

bH = 4.5 * 17 = 76.5

If the purpose of the awning is to prevent sunlight from entering the house when the angle of elevation of the sun is more than  the length L of the awning is 38.50 in.

Let L represent the length

Hence,

sin 105° / 88 = sin 25° /L

88 × sin 25° / sin 105°

88 × 0.4226 / 0.9659

L= 37.1888/  0.9659

L = 38.50 in

Therefore the length is 38.50 in.

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The complete question is :

An awning that covers a sliding glass door that is 88 inches tall forms an

angle of 50° with the wall. The purpose of the awning is to prevent sunlight

from entering the hours when the angle of elevation of the sun is more than 65°. Find the length L of the awning

Answer:

Step-by-step explanation:

8z-6=-2(-4+3)

8z-6=8z-6

on transposing,

8z-8z-6+6=0

The linear equation with the given slope in the slope-point form is:

y = (1/2)*(x + 1) + 4

We know that for a line with a slope m and a point (a, b), the point-slope form of the line is written as:

y = m*(x - a) + b

In this case, we know that our line has a slope of 1/2 and it passes through the point (-1, 4), so we can replace this on the above formula to get:

y = (1/2)*(x + 1) + 4

This is the linear equation in the point-slope form.

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