What percent is represented by the shaded area?

The values of the angles given are: 0,90,180,240,270,360,420,480,540,600,630,660,720 and

he sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle.  It is defined as the length of the opposite side divided by the length of the hypotenuse

The given angles are: 0,30,45,90,120,135,180,210,225,240,270,300,315,330,360

2∅  2*∅ = 0, 90,180,240,270,360,420,480,540,600,630,660,720

sin 2∅ = sin0 = 0; Sin90=1;  sin180=0; sin240= -0.8660; sin270 = -1;

Each angle is multiplied by sine sine360 =1; sin420 = 0.8660; sin480= 0.9848; sin540=1; sin600=-0.8660; sin630=-1; sin660=0.8660; sin720= 0.9397

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The domain of the question is expressed as; 0 ≤ x ≤ 4

The range of the question is expressed as; 100 ≤ f(x) ≤ 207.36

The domain of a graph is defined as the set of all possible input values that makes the function possible while the range is defined as the set of all possible output values that can result from the possible input values.

Now, we are told that the insect population increases by 20% each month from May 1 to September 1.

The function that represents the insect population after x months is;

f(x) = 100(1.2)ˣ

Thus, the domain is from x = 0 to 4 months inclusive. 0 ≤ x ≤ 4

f(0) = 100(1.2)⁰

f(0) = 100

f(4) = 100(1.2)⁴

f(4) = 207.36

100 ≤ f(x) ≤ 207.36

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The image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).

In the given question,

We have to find the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin.

Since we have to find the image after a dilation.

So we learn about it now,

Any scale factor will dilate the image of any coordinate. A specific scale factor can be used to scale the coordinate up or down. To determine the answer, consider the scale factor in the equation and multiply or divide the coordinates of dilation by the appropriate scale factor.

So the given point is (-9,12).

Scale factor is 1/3.

So the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is define as

=(-9×1/3,12×1/3)

Simplifying

=(-3,4)

Hence, the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).

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Answer:

Step-by-step explanation:

Based on the information given, we can conclude that RM = 2, but we cannot determine the lengths of the other sides of the quadrilaterals without further information.

Given that quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation, we can use the information to determine the length of RM.

A translation is a transformation that moves every point of a figure by the same distance and in the same direction. In this case, the translation is such that the corresponding sides of the quadrilaterals are parallel.

Since TY = 2, and the translation moves every point by the same distance, we can conclude that the distance between the corresponding points R and M is also 2 units.

Therefore, RM = 2.

By the properties of a translation, corresponding sides of the two quadrilaterals are congruent. Hence, side YG of quadrilateral YFGT is congruent to side MK of quadrilateral MKNR, and side GT is congruent to NR. However, the given information does not provide any additional details or measurements to determine the lengths of these sides.

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Question↓

Which is a unit rate?

Answer↓

The Correct Answer Is 6 hours: 1 Book

unit rate. • a comparison of two measurements in which. one of the terms has a value of 1.

Hope this helps!! ^ω^

xXxAnimexXx

we know the label is 3 inches wide and since the box is 2 inches tall, is the label is 2 inches tall only on the front and back of the box, namely the sides, the LATERAL area, the lateral area for the label doesn't include the top and bottom.  How many inches is the label laterally?

\(\stackrel{front}{(3\cdot 2)}+\stackrel{back}{(3\cdot 2)}\implies 12\)  and we know that's 75% of the total lateral area.

what about the total lateral area, how many inches is it?

\(\stackrel{front}{(x\cdot 2)}+\stackrel{back}{(x\cdot 2)}\implies 4x\)

so, we know that 4x is the 100% of the lateral area, and we also know that 12 is 75% of it.

\(\begin{array}{ccll} \stackrel{lateral}{area}&\%\\ \cline{1-2} 4x&100\\ 12&75 \end{array}\implies \cfrac{4x}{12}=\cfrac{100}{75}\implies \cfrac{x}{3}=\cfrac{4}{3} \\\\\\ 3x=12\implies x=\cfrac{12}{3}\implies x=4\)

Answer:

Substitution: 3x+10y=1

x+2y=-1

Step-by-step explanation:

Elimination: 3/4x + 5/3y = 11

1/16x - 3/4y = -1

The relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc length s of the arc is

B) C=360 degrees s over A

The relationship between the circumference C of a circle and the degree measure A of a central angle that intercepts an arc length s of the arc can be described by the formula:

s = A / 360 * C

Make C the subject of the formula

s = AC / 360

360s = AC

rearranging

AC = 360s

C = 360 degrees s / A

C = (s / A) * 360°

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Answer:

\(\textsf{B)} \quad C=\dfrac{360^{\circ}\:s}{A}\)

Step-by-step explanation:

In a circle, the ratio of an arc length (s) to the circumference (C) is equal to the ratio of the measure of the arc's central angle (A) to 360°.

This is because:

Therefore, this can be expressed as:

\(\dfrac{s}{C}=\dfrac{A}{360^{\circ}}\)

Cross multiply:

\(360^{\circ} \cdot s=C \cdot A\)

Now, divide both sides by A to isolate C:

\(\dfrac{360^{\circ} \cdot s}{A}=C\)

Therefore, the relationship between the circumference (C) of the circle in which the degree measure (A) of a central angle of a circle intercepts an arc length (s) of the arc is:

\(\large\boxed{\boxed{C=\dfrac{360^{\circ}\:s}{A}}}\)

Answer:

Not 100% sure

Step-by-step explanation:

Image result for how to simplify 5(2x-8) using distributive property

The formula for the distributive property is expressed as, a × (b + c) = (a × b) + (a × c); where, a, b, and c are the operands. Here, the number outside the brackets is multiplied with each term inside the brackets and then the products are added.

Answer:

x = 16°

Step-by-step explanation:

What we know:

∠JML = 47°

∠JKL = (7x + 21)°

∠JML is an inscribed angle

∠JKL is an inscribed angle

Inscribed angles are half of the value of their intercepted arc

So if m∠JML = 47° then mArc JL is double that or 94°

And ∠JKL is intercepted by Arc JML which is the rest of the circle not intercepted by ∠JML so

mArc JL + Arc JML = 360°

94 + Arc JML = 360

Subtract 94 from both sides to isolate Arc JML

Arc JML = 266°

So if Arc JML = 266° then it's intercepted inscribed angle is half of that.

Arc JML ÷ 2 = ∠JKL

266 ÷ 2 = ∠JKL

133 °= ∠JKL

Now we can use this value and set it equal to the expression to find the value of x

(7x + 21) = 133

Subtract 21 from both sides to isolate the x

7x = 112

Divide both sides by 7

x = 16

For least amount of fencing, length and width of rectangular area should be 14 feet and 7 feet respectively.

Let us consider length and width are l and w respectively.

Area of rectangular region = l x w

l x w = 98

w = 98/l

Since, no fencing needed along the river.

So, perimeter of rectangular region, P = 2w + l

Substituting the value of w in above expression.

We get,    

P = 2(98/l) + l

= 196 /l + l

For least amount of fencing, perimeter should be minimum

Differentiate perimeter expression with respect to length l.

dP/dl = -196/l^2 +1 =0

l^2 = 196

l= sqrt(196)

l= 14 feet

so, w= 98/14

w = 7

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To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

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

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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Answer:

true i think

Step-by-step explanation:

Answer:

The smallest angle is 30 degrees, the second angle is 80 degrees and the third angle is 70 degrees

Step-by-step explanation:

let x = the smallest angle

This means that one angle is x+40, and the third angle is 3x-10. This make our equation:

x + 40 + 3x - 10 + x = 180

Combine like terms

5x + 30 = 180

Subtract 30 from both sides

5x = 150

Divide both sides by 5

x = 30

Plugging this in:

3x - 10 =

90 - 10 =

80

And for the other:

x + 40 =

30 + 40 =

70

The equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

1. Start with the given equation: 2-3cos(x) = 5+3cos(x).

2. Subtract 3cos(x) from both sides to isolate the constant term: 2-3cos(x) - 3cos(x) = 5.

3. Combine like terms: 2-6cos(x) = 5.

4. Subtract 2 from both sides: -6cos(x) = 3.

5. Divide both sides by -6: cos(x) = -1/2.

6. To find the solutions for cos(x) = -1/2 in the range of 0° to 180°, we need to determine the angles where cos(x) equals -1/2.

7. These angles are 120° and 240°, as cos(120°) = cos(240°) = -1/2.

8. However, the given equation states that 2-3cos(x) equals 5+3cos(x), which is not satisfied by cos(x) = -1/2.

9. Therefore, the equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

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Answer:  9c²

Step-by-step explanation:

To find the Greatest Common Factor of 207c³ and 108c², first factor them down to their primes and see what they have in common.

                207c³                     108c²

                 ∧   ∧                        ∧  ∧

             9·23  c·c·c              9·12   c·c

            ∧                            ∧  ∧

           3·3                         3·3 3·4

                                                  ∧

                                                 2·2

207c³: 3·3·23  c·c·c

108c²:  2·2·3·3·3·4 c·c

GCF = 3·3 c·c

        = 9c²

The GCF of 207c^3 and 108c² is 9c²

Given the expressions \(207c^3 \ and \ 108c^2\)

We are to find the GCF of both terms

First, we need to get the factors as shown::

207c³ = 9 * 23 * c² * c

108c² =  9 * 12 * c²

From the factors, we can see that 9 and c² are common to both terms:

The GCF of 207c^3 and 108c² is 9c²

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The monthly PMI Payment for Christina's loan is $37.50.The correct answer is option B.

To determine Christina's monthly PMI (Private Mortgage Insurance) payment, we need to find the corresponding interest rate for her loan-to-value (LTV) ratio. The LTV ratio is calculated by dividing the loan amount by the property value.

The loan amount can be calculated by subtracting the down payment from the property value:

Loan amount = Property value - Down payment

           = $170,000 - $20,000

           = $150,000

Now we can calculate the LTV ratio:

LTV ratio = Loan amount / Property value * 100

         = $150,000 / $170,000 * 100

         = 88.24%

Since Christina is obtaining a 30-year mortgage, we need to look at the interest rates for LTV ratios between 85.01% and 90%. According to the table, the interest rate for this range is 0.30%.

To calculate the PMI payment, we multiply the loan amount by the PMI rate and divide it by 12 months:

PMI payment = (Loan amount * PMI rate) / 12

           = ($150,000 * 0.30%) / 12

           = $450 / 12

           = $37.50

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The Probable question may be:
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.

Use the table to find her monthly PMI payment

Base to loan% = 95.01% to 97%,90.01% to 95%,85.01% to 90%,80.01% to 85%.

30-year fixed-rate loan = 0.55%,0.41%,0.30%,0.19%

15-year fixed-rate loan = 0.37%,0.28%,0.19%,0.17%.

A. $51.25

B. $37.50

C. $23.75

D. $42.50

Since our assumption holds for all values between 6 and k, and we have shown it also holds for k+1, we can conclude by strong induction that it is possible to cut a square into n smaller squares for any n ≥ 6.

To prove this using strong induction, we will first establish a base case and then prove that if the statement holds true for any value k, then it also holds true for k+1.
Base Case: n = 6
Divide the square into four equal smaller squares by drawing two lines, one vertical and one horizontal, each passing through the center.

Then, divide one of these smaller squares into two equal rectangles by drawing a line parallel to the side.

We have now divided the original square into 6 smaller squares.
Inductive Step:
Assume the statement is true for all values n = 6, 7, ..., k,

where k ≥ 6.

We want to prove that the statement is true for n = k+1.
Consider a square that is divided into k smaller squares.

We will show that it is possible to divide this square into k+1 smaller squares.

Choose one of the k squares and label it S.

If S is a rectangle, divide it into two smaller squares by drawing a line parallel to the shorter side.

If S is a square, divide it into two equal rectangles by drawing a line through the center parallel to a side.
In either case, we have replaced one of the original k squares with two smaller squares, resulting in a total of k+1 squares.

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Answer:

Nothing, cause it isn't possible:)

Answer:

then you would be driving at the speed of light with your headlights on

Step-by-step explanation:

Answer:

Option 3

Step-by-step explanation:

Rewriting input as fractions if necessary:

3/8, 3/20

For the denominators (8, 20) the least common multiple (LCM) is 40.

LCM(8, 20)

Therefore, the least common denominator (LCD) is 40.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

3/8 = 3/8 × 5/5 = 15/40

3/20 = 3/20 × 2/2 = 6/40

Answer:

Below

Step-by-step explanation:

Line AB is of the form y = mx + b    where m is the slope = 2

 Line BC is perpendicular to this and will have slope - 1/m = - 1/2   and includes the point C (0,6)

 The point slope form of line BC will then be

     ( y-6) = - 1/2 ( x - 0)    which can be re-arranged to

       y = - 1/2x + 6     < ==== equation for line BC

Answer:θ ≈ 2.57 radians

θ ≈ 0.58 radians

Step-by-step explanation:We can solve this quadratic equation in sin(θ) by factoring:

4sin^2(θ) + 7sin(θ) - 5 = 0

(4sin(θ) - 1)(sin(θ) + 5) = 0

Therefore, either:

4sin(θ) - 1 = 0

sin(θ) = 1/4

or:

sin(θ) + 5 = 0

sin(θ) = -5 (not possible, since sin(θ) is between -1 and 1)

So, we have sin(θ) = 1/4. Since 0 ≤ θ < 2π, we can find the two solutions in the interval [0, 2π) by using the inverse sine function:

θ = arcsin(1/4)

Using a calculator, we find:

θ ≈ 0.2531 or θ ≈ 2.8887

Therefore, in radians, the solutions for θ are approximately:

0.2531 (which is less than 2π)

2.8887 (which is greater than 2π)

So the only answer that satisfies 0 ≤ θ < 2π is:

Answer:

0.75p=c

Step-by-step explanation:

answer:

minimum = 20 inches

maximum = 49 inches

Step-by-step explanation:

The height data in the question is

10 15 20 25 30 35 40 45 50.

From above we have the classes as:

10-14, 15-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49,

The minimum tree height bus from the first class. While the maximum tree height is from the last class.

The first class is 10-14, so the minimum height = 10 inches

The last class is 45-49 so the maximum height inches = 49 inches.

The maximum tree height from the classes I have grouped is 49 inches since 49 is the upper limit from the last class.

The minimum tree height is 10 inches