Louise deposits $250 into a new savings account.

The account earns 6% simple interest per year.

No money is added or removed from the savings account for 3 years.

What is the total amount of money in her savings account at the end of the 3 years?

The area of the region in which the burro can graze will be 833 pi square feet.

Each interior vertex angle of a regular hexagon is (n - 2)·180°/n  =  (6 - 2)·180°o/6  =  120°

I'll break up the area into three sections.

There is one major section, going 150' along one side in a circular arc to 150' along the adjacent side.

Since the interior angle is 120°, the exterior angle will be 240°.

The area of this section will be:  (240°/360°)·pi·radius2  =  (2/3)·pi·1502  =  15,000 pi

Then, on each end, around the corner of the barn, the goat can go in a circular arc with radius = 50'.

This angle will be 60°, or one-sixth or a circle.

The area of each section will be (1/6)·pi·502  =  416 2/3 pi

Total area:  15,000 pi + 416 2/3 pi + 416 2/3 pi  =  833 1/3 pi square feet.

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I will give you some intuitive remarks for some inspiration on the proofs.

For the first one, notice that if m divides n then n = pm where p is a integer.

Since n and m are both natural numbers p then must be a natural number as well.

Now we know that basically we want to prove that if a is congruent to b mod n then a is congruent to b mod "a factor of n" (this is cause n = pm).

Tell me if you need more clarification.

For the second proof, I would just draw a Venn diagram and prove that the two intersections cover identical regions.

Answer: 3

Step-by-step explanation:

Answer:  3

Step-by-step explanation:

16/4=unit rate =4

1 in 4 hour

3 for 12 hours

let's bear in mind that on the III Quadrant, sine and cosine are both negative, whilst on the IV Quadrant, sine is negative and cosine is positive, that said

[tex]\cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\hspace{5em}\textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=\stackrel{adjacent}{3}\\ o=opposite \end{cases} \\\\\\ o=\pm \sqrt{ 5^2 - 3^2} \implies o=\pm \sqrt{ 16 }\implies o=\pm 4\implies \stackrel{IV~Quadrant }{o=-4} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\tan(\beta )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{3}}\implies \tan(\beta )=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{-3}} \\\\[-0.35em] ~\dotfill\\\\ \tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \\\\\\ \tan(\alpha + \beta)\implies \cfrac{ ~~\frac{-4}{3}~~ + ~~\frac{-4}{-3} ~~ }{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \cfrac{0}{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \text{\LARGE 0}[/tex]

Answer:

$25

Step-by-step explanation:

You round 44.95 to 45 and 68.49 to 70. 70 - 45 = 25.

The radius of the circle with given circumference is 13.

What is circumference?

In mathematics, the circumference of any shape determines the path or boundary that surrounds it. In other words, the perimeter, also referred to as the circumference, helps determine how lengthy the outline of a shape is.

We are given that the circumference of a circle is 81.64 miles.

We know that circumference of a circle is given by 2πr.

So, using this we get

⇒ C  = 2πr

⇒ 81.64  = 2 * 3.14 * r

⇒ 81.64  = 6.28 * r

⇒ r  = 13

Hence, the radius of the circle with given circumference is 13.

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The wire can be divided into five equal parts, where one portion is one-fifth of the total length and the other four parts are four-fifths of the total length. the measure of the longer part of the wire after cutting is 2 meters.

If the wire was cut in a ratio of 1:4, then the total length of the wire can be divided into 5 parts, where one part is 1/5 of the total length, and four parts are 4/5 of the total length. Let's call the length of one part "x".

So, the total length of the wire is:

 [tex]5x = 2.5[/tex] meters

To find the length of the longer part of the wire, we need to find how many parts are in the longer portion. Since the wire was cut in a 1:4 ratio, the longer portion has four parts.

Therefore, the length of the longer part of the wire is:

[tex]4x = 4/5 \times 2.5 meters = 2 meters[/tex]

Therefore, the measure of the longer part of the wire after cutting is 2 meters.

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The perimeter of the figure is approximately 63.6 meters, since the lengths of all the sides add up to the figure's perimeter.

Perimeter is the total length of the boundary of a closed 2-dimensional shape. In other words, it is the distance around the edge of a shape. The perimeter is usually measured in units such as meters, centimeters, feet, or inches depending on the measurement system used. The perimeter can be calculated by adding up the lengths of all the sides of the shape.

Since opposite sides of a parallelogram are equal in length, the length of the straight side of the first parallelogram is:

Length of first parallelogram = 9m

Similarly, the length of the straight side of the second parallelogram is:

Length of second parallelogram = 11m

Now, let's find the length of the straight side of the semicircle segment. We are given that the other side of each parallelogram gets half of the diameter, which is 17m. Therefore, the length of the straight side of the semicircle segment is:

Length of semicircle segment = 17m / 2 = 8.5m

The lengths of all the sides add up to the figure's perimeter. Let's use P to represent the perimeter. Then:

P = 2 (parallelogram length) + semicircle length

When we replace the values we discovered earlier, we obtain:

P = 2(9m + 11m) + π(17m)/2

= 38m + 8.5πm

≈ 63.6m (using π ≈ 3.14)

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Answer:

15 centimeters

Step-by-step explanation:

radius is half of the circles diameter

The new cοοrdinates οf the image οf the pοlygοn are: E'(0, 1), F(4, 0),     G(3, -2) & H(0, 0).

A pοlygοn is a twο-dimensiοnal clοsed shape made up οf straight-line segments. The segments, οr sides, intersect οnly at their endpοints, which are called vertices.

Tο graph pοlygοn EFGH, we first plοt the given cοοrdinates:

E(-1, 3)

F(1, 4)

G(3, 3)

H(0, 0)

Tο find the image οf the pοlygοn after a clοckwise rοtatiοn οf 90 degrees abοut vertex H, we can use the fοllοwing transfοrmatiοn matrix:

| cοs(-90)  -sin(-90)  0 |   | x - 0 |   |  y  |

| sin(-90)   cοs(-90)  0 | * | y - 0 | = | -x  |

|    0         0       1 |   |   1   |   |  1  |

Simplifying this matrix, we get:

|  0  -1  0 |

|  1   0  0 |

|  0   0  1 |

Tο apply this transfοrmatiοn tο each pοint οf the pοlygοn, we can multiply the matrix by the cοlumn vectοr (x, y, 1) fοr each pοint.

Therefοre, the new cοοrdinates οf the image οf the pοlygοn are:

E'(0, 1)

F(4, 0)

G(3, -2)

H(0, 0)

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Answer:

Step-by-step explanation:

Let's assume that the width of the flag is "w" ft.

According to the problem, the length of the flag is 400 ft greater than the width, which means it can be expressed as:

length = w + 400

Now, we know that the perimeter of the flag is 2,120ft. The perimeter of a rectangle is given by:

perimeter = 2(length + width)

Substituting the values, we get:

2120 = 2[(w+400) + w]

2120 = 2[2w + 400]

2120 = 4w + 800

4w = 1320

w = 330

Hence, the width of the flag is 330ft.

From our equation for the length, we have:

length = w + 400

length = 330 + 400

length = 730

Therefore, the length of the flag is 730ft.

Answer:

+4

Step-by-step explanation:

F(x,y)   = 3x+y      and y <= -2x+ 4     sub in for 'y'

          = 3x  + (-2x+4)

          = x + 4

If you look at the graph for   y <= - 2x+4   ( see below)

    you will see that the domain (x values ) can only go from 0 to 4 and the max value is +4     ( rememeber too that y is restricted to >= 0  as is x )

The inequality can be solved to get 2 > x, and the graph on the number line can be seen in the image at the end.

Here we have an inequality and we want to sole it, to do so, we just need to isolate the variable in the inequality.

Here we have:

10 > 5x

To isolate the variable we can divide both sides of the inequality by 5, then we will get:

10/5 > 5x/5

2 > x

So x is the set of all values smaller than 2.

That is the inequality solved, to graph this, drawn an open circle at x = 2 and a line that goes to the left. The graph is the one you can see in the image below.

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In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are listed and explained:

An year is composed by 365 days, hence the daily mean of the number of checks written is given as follows:

120/365 = 0.3288 checks.

The variance has the same value of the mean for the Poisson distribution, in units squared, while the standard deviation is the square root of the variance, hence:

sqrt(0.3288) = 0.5734 checks.

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Answer:

3x + 4 < 13

2y - 5 > 7

6n - 1 ≤ 23

8m + 2 ≥ 18

4a - 7 < 5a + 2

9b + 3 > 6b + 10

Step-by-step explanation:

I dunno if this is what you're asking for

Answer:

ok.....

x + 2 < 5

|x - 4| > 4

x + 7 [tex]\geq[/tex] 8

-x < -5

x - 5 < 9

5x + 18 > 2

|3x - 1| < 8

The brace measures 50 inches in length.

The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, which is the side opposite the right angle, equals the sum of the squares on the legs of the triangle, a2 + b2 = c2.

The other two sides of the picture frame are its length and width. We thus have:

Length of the hypotenuse (brace)² = Length² of the picture frame + Width² of the picture frame

Let's enter the picture frame's specified dimensions:

Length of the brace² = 30² + 40²

Length of the brace² = 900 + 1600

Length of the brace² = 2500

Taking the square root of both sides, we get:

Length of the brace = √(2500)

Length of the brace = 50

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Answer:

22

Step-by-step explanation:

first you would add all books from the book store to get 66

Then you would divide that by 3 to get

66÷3=22

The amount of time needed for this capital to triple would be 50 months, the letter "d" being correct. We arrive at this result using simple interest.

Simple interest is a type of financial calculation that is used to calculate the amount of interest on borrowed or invested capital for a given period of time.

In order to find the amount of time required for the principal to be equal to three times the redemption, we have to note that the amount will be equal to three times the principal, using this information in the formula. Calculating, we have:

M = C * (1 + i * t)

3C = C * (1 + 0.04t)

3 = 1 + 0.04t

0.04t = 3 - 1

0.04t = 2

t = 2/0.04

t = 50

Answer: top two goes together, middle left goes to bottom right, bottom left goes to middle right

Step-by-step explanation:

Substitute x for an easy number like 2 and solve.

x - 2/3 - 1/2x = 1/2x - 2/3

x - 1/2 - 3/4x = 1/4x- 1/2

1/3x - 3/4 - 2/3x = -1/3x - 3/4

The angle made by one chord and tangent of the circle is 32.5 degrees.

What is the Alternate Segment Theorem?

The Alternate Segment Theorem is a theorem in geometry that relates the angles formed by a line that is tangent to a circle and a chord of that circle. The theorem states that the angle formed by a tangent and a chord of a circle is equal to the angle that is subtended by the chord in the opposite segment of the circle

In a circle, the angle formed by a chord and a tangent that intersect at a point on the circle is equal to half the measure of the arc intercepted by the chord.

Therefore, if the arc intercepted by the chord is 65 degrees, then the angle formed by the chord and the tangent is half of 65 degrees, which is:

65 degrees / 2 = 32.5 degrees

So, the angle X made by the chord and the tangent is 32.5 degrees.

Therefore, the angle made by one chord and tangent of the circle is 32.5 degrees.

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[tex]x^{0}[/tex] has a value of [tex]27.5[/tex] degrees.

Values are the benchmarks or ideals by which we judge the acts, traits, possessions, or circumstances of others. Values that are embraced by many include those of beauty, honesty, fairness, harmony, and charity. When considering values, it might be helpful to categorise them into one of three categories: Personal values are those that an individual upholds.

Values come in two varieties. They serve as either terminal or auxiliary values for Rokeach. Terminal values always are end-states whereas qualities are always forms of conduct. Individuals think that acting in line with cognitive factors and reaching terminal values are always related.

We find the value of [tex]x^{0}[/tex]

[tex]Angle P = 1/2 (mAC-AB)[/tex]

[tex]x^{0}=\frac{1}{2} (120^{0}- 65^{0} )[/tex]

[tex]x^{0} =\frac{1}{2}*55^{0}[/tex]

Therefore, [tex]x^{0}= 27.5^{0}[/tex]

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The table that represents the function for a lawn being mowed more quickly than by Killian's rate is given as follows:

Second table.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.

Killian can cut grass at a rate of 1000 square feet each 10 minutes, hence his average rate of change is given as follows:

1000/10 = 100 square feet per minute.

For the second table, in 7 minutes, 1100 square feet of lawn is mowed, hence the rate is given as follows:

1100/7 = 157 square feet per minute.

It is more quickly than Killian's as the rate of change is greater.

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Answer:

20.8

Step-by-step explanation:

Let h be the height of the ladder. We know that the distance BC is 8 ft, and the angle of elevation BAC is 69 degrees. Therefore, we have:

tan(69) = h/8

Multiplying both sides by 8, we get:

8*tan(69) = h

Using a calculator, we get:

h ≈ 20.8 ft

Therefore, the height of the top of the ladder from the ground is approximately 20.8 feet.

Answer:

∠w = 50°

∠y = 130°

Step-by-step explanation:

Angles ∠w and ∠y are supplementary angles, which means their sum is 180.

4x + 6 + 12x - 2 = 180

16x + 4 = 180

16x = 176

x = 11

To find the angle measures replace x with 11

∠w = 4x + 6

∠w = 4*11 + 6

∠w = 50°

Now, ∠y

∠y = 12x - 2

∠y = 12*11 - 2

∠y = 130°

The exponential equation represents a growth, and the rate of increase is 9%.

The general exponential equation is written as:

y = A*(1 + r)^x

Where A is the intial value, and r is the rate of growth or decay, depending of the sign of it (positive is growth, negative is decay).

Here we have:

y = 38*(1.09)^x

We can rewrite this as:

y = 38*(1 + 0.09)^x

So we can see that r is positive, thus, we have a growth, and the percentage rate of increase is 100% times r, or:

100%*0.09 = 9%

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Answer:

To find the coordinates of A' after the translation, we need to apply the motion rule to the coordinates of A:

(x, y) → (x + 2y - 5, y - 6)

Substituting the coordinates of point A, which is (4, -4), into this motion rule, we get:

A' = (4 + 2(-4) - 5, -4 - 6) = (-3, -10)

Therefore, the coordinates of A' after the translation are (-3, -10).

Answer: He has one left

Step-by-step explanation: 2-1=1

The circle E with diameter CD and radius EA having the length of AC is approximately 4.2 units.

What is Pythagoras' Theorem?

In a right-angled triangle, the square of the hypotenuse side equals the sum of the squares of the other two sides.

Since EA is a radius of circle E, and AB is tangent to E at A, we know that AB is perpendicular to EA. Thus, triangle EAB is a right triangle.

Let x be the length of AC. Then, by the Pythagorean Theorem in triangle EAC, we have:

[tex]AC^{2} = EA^{2} +EC^{2}[/tex]

[tex]AC^{2} = 3^{2} + 3^{2}[/tex]

[tex]AC^{2} = 18[/tex]

AC ≈ 4.2 (rounded to the nearest tenth)

Therefore, the length of AC is approximately 4.2 units.

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