If an investment company pays 6% compounded continuesly, how much should you deposit now to have $10,000 5 years from now?

The ladder needs to make an angle of approximately 54.7 degrees with the house in order for Brigid to reach 18 feet up the side of the house.

To determine the angle the ladder needs to make with the house, we can use the tangent function.

First, we'll need to determine the opposite side (the height that the ladder needs to reach) and the adjacent side (the distance from the base of the ladder to the house) of the triangle formed by the ladder and the house.

Opposite side = 18 feet

Adjacent side = 25 feet

We can then use the tangent function to find the angle:

tan(angle) = opposite / adjacent

Solving for the angle, we get:

angle = arctan(18/25) = approximately 54.7 degrees

Therefore, the ladder needs to make an angle of approximately 54.7 degrees with the house in order for Brigid to reach 18 feet up the side of the house.

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The total quantity of water that the container would have to hold is given as 8.

We know that the container holds 1 gallon of water, and that each bottle holds 1/8 of a gallon. To find out how many bottles the container can hold we need to divide the container size by the size of each bottle.

We can use the following formula to find the number of bottles:

Number of bottles = Container size / Size of each bottle

We can substitute the values into the formula:

Number of bottles = 1 / (1/8) = 8

So the container can hold 8 bottles of water.

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The equation 2x + 3y = 5 has one real solution.

To find it, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable.

For example, you can solve for y to get y = (5 - 2x)/3, and then substitute this into the equation to get 2x + 3((5 - 2x)/3) = 5, which you can then solve for x. Doing this will give you x = 5/4, which means that the solution is (5/4, 5/3).

Linear equations are equations that involve two variables and can be expressed in the form ax + by = c, where a and b are constants and x and y are the variables. These equations have one real solution, which can be found by solving for one of the variables and then substituting the result into the equation to find the other variable. Once both variables are known, the solution to the equation is the point (x,y) that satisfies both equations.

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Answer:

80 ducks (16+64)

Step-by-step explanation:

So if there were 32 brown ducks in the pond at first, then twice the amount of brown ducks (32).

32x2=64 white ducks

So now their are 64 white ducks at the pond. We still have to add how many brown ducks their were so…

64+32=96 ducks in total

But then as the white ducks came in half of the brown ducks flew away.

32/2=16 brown ducks left in the pond.

Lastly add the remaining brown ducks with the white ducks and that is you answer!
16+64=80 total amount of ducks

Final Answer:

80 ducks

I hope this helps! I am sorry if I got it wrong!

By geometric formulas, the gray square has an area of 25 square units.

Squares are quadrilaterals with four right angles. In this question we find a geometric system formed by seven squares with distinct dimensions. By geometry, the area of a square (A), in square units, is equal to following formula:

A = l²

Where l is the length of the side of a square, in units.

All the required lengths are represented in the image attached below. First, determine the side length of the gray square:

7 + x = 12

x = 12 - 7

x = 5

The gray square has four sides with a length of 5 units.

Second, determine the area of the gray square by means of square formula:

A = x²

A = 5²

A = 25

According to area formula for squares, the area of the gray square is equal to 25 square units.

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Answer: The middle number is 15

Step-by-step explanation:

45/3= 15 so the three numbers will be around there.

14+15+16= 45

x = liters of solution at 20%

y = liters of solution at 70%

[tex]\begin{array}{lcccl} &\stackrel{liters}{quantity}&\stackrel{\textit{\% of liters that is}}{\textit{acid only}}&\stackrel{\textit{liters of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{Sol'n at 20\%}&x&0.2&0.2x\\ \textit{Sol'n at 70\%}&y&0.7&0.7y\\ \cline{2-4}&\\ mixture&50&0.4&20 \end{array}~\hfill \begin{cases} x + y = 50\\\\ 0.2x+0.7y=20 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=50\implies x=50-y}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{0.2(50-y) + 0.7y=20} \\\\\\ 10-0.2y+0.7y=20\implies -0.2y+0.7y=10\implies 0.5y=10 \\\\\\ y=\cfrac{10}{0.5}\implies \boxed{y=20}[/tex]

The measures of the angles of the parallelogram are

The measure of ∠A = 72°

The measure of ∠B = 108°

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as ABCD

Now , the measure of ∠A = ( 5y - 3 )°

The measure of ∠C = ( 3y + 27 )°

For a parallelogram , opposite angles are congruent

So , measure of ∠A = measure of ∠C

Substituting the values in the equation , we get

( 5y - 3 )° =  ( 3y + 27 )°

On simplifying the equation , we get

( 5y - 3 ) =  ( 3y + 27 )

Subtracting 3y on both sides of the equation , we get

2y - 3 = 27

Adding 3 on both sides of the equation , we get

2y = 30

Divide by 2 on both sides of the equation , we get

y = 15

So , the measure of ∠A = ( 5y - 3 )°

The measure of ∠A = ( 5 ( 15 ) - 3 ) )°

The measure of ∠A = ( 75 - 3 )°

The measure of ∠A = 72°

Now , for a parallelogram , same-side interior angles (consecutive angles) are supplementary

So , the measure of ∠A + the measure of ∠B = 180°

Substituting the values in the equation , we get

72° + the measure of ∠B = 180°

Subtracting 72° on both sides of the equation , we get

The measure of ∠B = 108°

Hence , the measures of angles of the parallelogram are 72° and 108° respectively

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Answer:

sry i dont no

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

to get the equation of any straight line, we simply need two points off of it, let's use (-6,10), (-4,18)

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{18}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{18}-\stackrel{y1}{10}}}{\underset{\textit{\large run}} {\underset{x_2}{-4}-\underset{x_1}{(-6)}}} \implies \cfrac{8}{-4 +6} \implies \cfrac{ 8 }{ 2 } \implies 4[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y -10 = 4 ( x +6) \end{array}} \\\\\\ y-10=4x+24\implies -4x+y=34\implies \stackrel{standard~form}{{\Large \begin{array}{llll} 4x-y=-34 \end{array}}}[/tex]

The collection of values that can be plugged into a function's domain are called its parameters.

A specific area of thinking, action, or interest is referred to as a domain, particularly one over which someone has authority. [formal]...the great artists who experimented with several mediums. Alternative words: region, globe, field, department [informal] More Domain synonyms.

The domain is used to facilitate user navigation and increase accessibility. Slugs are links that consist of the domain plus the text "/text."

Let y = f(x) be a function where x and y are the independent and dependent variables. The chosen x-value is said to fall within the domain of f if a function f offers a means of effectively producing a single value y while using a value for x to that end.

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5k4h 6r + 7k4h 6r + 5k4h 6r + 7k4h 6r = The perimeter of the rectangle is 24k8h 24r.

1. 5k4h 6r + 7k4h 6r = 12k8h 12r

2. 12k8h 12r + 5k4h 6r = 17k12h 18r

3. 17k12h 18r + 7k4h 6r = 24k8h 24r.

Therefore, the perimeter of the rectangle is 24k8h 24r.

The width of a rectangle is represented by 5k4h 6r, and the length of the rectangle is represented by 7k4h 6r. To find the perimeter of the rectangle, we need to add the width and length of the rectangle together. This can be done by adding 5k4h 6r and 7k4h 6r. The answer to this addition is 12k8h 12r. We then need to add the width and length of the rectangle together again. To do this, we add 12k8h 12r and 5k4h 6r. The answer to this addition is 17k12h 18r. Finally, we need to add the width and length of the rectangle together again. This is done by adding 17k12h 18r and 7k4h 6r. The answer to this addition is 24k8h 24r. Therefore, the perimeter of the rectangle is 24k8h 24r.

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The angle measures : m∠1 = 107° and m∠4= 73°

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

There are 2 parallel lines

A transversal cuts them

∠5 and ∠7 are corresponding angles

Corresponding angles are equal in measures

m∠5 = m∠7

m∠7 = 107°

m∠5 = 107°

∠1 and ∠7 formed a pair of alternate exterior angle.

And m∠1 = m∠7

∠1 and ∠4 formed a pair of linear angle.

The sum of the measures of the linear angles is 180°

m∠1 + m∠4 = 180°

Substitute ∠1 by 107°

m∠4 + 107° = 180°

m∠4 = 180 - 107

m∠4= 73°

Therefore, m∠1 = 107° and m∠4= 73°

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The measure of side KL in the given quadrilateral is 31.88 units.

A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.

The Latin words Quadri, a variation of four, and latus, meaning "side," are the source of the name.

A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral.

Convex and concave are the two main forms.

Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.

So, according to the given figure of FGHI and JKLM:

FG/JK = GH/KL = HI/LM = FI/JM

GH/KL = HI/LM

7/KL = 9/41

KL = 7*41/9 = 31.888

Therefore, the measure of side KL in the given quadrilateral is 31.88 units.

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Correct question with a diagram:

Quadrilateral FGHI is similar to quadrilateral JKLM. Find the measure of side KL. Round your answer to the nearest tenth.

The equations are;

a) y = -7/2x - 13

b) -2/7x - 46/7

We know that the equation of the line that we have here can be written in the general form as the equation that is given as; y = mx + c

We have that

m = slope of the line

c = intercept of the line

As such, we have;

-7x-2y=6 or y = 6 + 7x/-2

or

y = -3 - 7x/2

For the parallel line m = - 7/2

y - (-6) = -7/2(x - (-2))

y + 6 = -7/2x - 7

y = -7/2x - 13

For the perpendicular line m = - 2/7

y - (-6) = -2/7(x - (-2))

y + 6 = -2/7x - 4/7

y = -2/7x - 46/7

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The correct answer is option c as DE/AE=BC/AC

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate. The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx. Where “m” is the slope of a line. So, tan θ to be the slope of a line.

Given here ΔADE ≈ΔABC and thus  DE/AE=BC/AC

but tanθ = DE/AE=BC/AC where tan θ is the slope of the line thus both the lines have identical slopes.

Hence, The correct answer is option c)  ΔADE ≈ΔABC thus DE/AE=BC/AC Therefore the slope of AD is the same as the slope of AB

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Solving the modular arithmetic will result to

The term modular arithmetic is the arithmetic that works with whole numbers in a such that, following division by a modulus, all numbers are replaced by their remainders.

Solving the modular arithmetic: 2 + n = 0 (mod 6)

2 + n = 0 (mod 6)

n = -2

Solving the modular arithmetic: 2 + (3 + n) = 1 (mod 6):

2 + (3 + n) = 1 (mod 6)

5 + n = 1 (mod 6)

n = 1 - 5

n = -4

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Pat needs 16[tex]\sqrt{1200}[/tex]cm of trim for each placemat to braid trim around the edges.

To find out how much trim Pat needs for each placemat, we need to first find the perimeter of the rectangle.

The area of the rectangle is given as 1200 [tex]cm^2[/tex].

The perimeter of the rectangle is the sum of all four sides of the rectangle. If the length and breadth of the rectangle are L and B respectively, then the perimeter P can be calculated using the formula:

P = 2(L+B)

Now, let's find the length and breadth of the rectangle using the area formula,

Area = LB = 1200 [tex]cm^2[/tex]

so LB = 1200 [tex]cm^2[/tex]

Now we can substitute the value of L and B in the perimeter formula

P = 2(L+B) = 2(sqrt(1200)+sqrt(1200))

As the area of the rectangle is given as 1200[tex]cm^2[/tex] , the length and breadth can be calculated as [tex]\sqrt{1200}[/tex]cm.

So the perimeter of the rectangle is

P = 2*([tex]\sqrt{1200}[/tex] + [tex]\sqrt{1200}[/tex])

  = 2*2[tex]\sqrt{1200}[/tex]

  = 4[tex]\sqrt{1200}[/tex]cm

To find the total length of trim Pat needs for the placemat, we need to multiply the perimeter by the number of edges that need a trim. Since the edges are around the rectangular placemat, so it will be 4 edges.

So, the total length of trim Pat needs for the placemat is

P4 = 4[tex]\sqrt{1200}[/tex]*4 = 16[tex]\sqrt{1200}[/tex]cm

So Pat needs 16[tex]\sqrt{1200}[/tex]cm of trim for each placemat.

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The values that can be eliminated from the solution set of the inequality are given as follows:

Values of x ≤ 0.

The perimeter of a rectangle of length l and height h is given by the formula presented as follows:

P = 2(l + h).

The dimensions for this problem are given as follows:

The perimeter must be less than 120, hence the inequality is given as follows:

2(x + 4 + x) < 120

4x + 8 < 120

4x < 112

x < 28.

However, a side length must assume positive values, meaning that values of x ≤ 0, that is, zero and negative values, are eliminated from the solution.

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The required maximum volume of the box is 2ft³.

Volume is a measurement of how much space an object takes up.

We can calculate the amount of something needed to fill it, like water for a bottle, tank, or aquarium.

Amount of space that stuff takes up - that's what we mean when we talk about volume.

Stuff is anything that has mass and takes up room.

When scientists are measuring volume, they usually use cubic meters.

So, calculate as:

V=x·y²

2x+y=3

y=3-2x

V = x·(3-2x)² = x·(9-12x+4x²) = 9x - 12x²+4x

V ` = 9-24x+12x² = 3(4x²-8x+3) = 3(4x²-6x-2x+3)

= 3[2x(2x-3)-(2x-3)] = 3(2x-3)(2x-1)

When the most amount is present: V ` = 0

Then,

2x-3 = 0  

2x = 3              

x = 1.5 (That's wrong, 'cause y = 0.)

or: 2x-1 = 0

2x = 1

x = 0.5,  y = 3 - 2 · 0.5 = 3 - 1 = 2

V max = 0.5 · 2² = 0.5 · 4 = 2 ft³

Therefore, the required maximum volume of the box is 2ft³.

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As per the decimal number system, the cost of 25 tickets is $32.5

The term decimal in math is defined as the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point.

Here we have given that the product of 3 student tickets at $4.

Here we have know that the ticket cost for 3 students is $4.

Then the cost of one person is calculated by dividing the cost by the number of students then we get,

=> 4/3

=> 1.3

So, if the cost for one person or ticket is $1.3 then the cost of 25 tickets is calculated as,

=> 25 x 1.3

=> 32.5

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Answer:

Jane has 251

Step-by-step explanation:

Stickers Initially = 27 Jane bought stickers on 1st day = 3 Remaining days = 13 Each next day she bought 2 more stickers than the previous day, so: Stickers bought in the last 2 weeks (14 days) = n+(n+2)+(n+2+2)+(n+2+2+2)+.............+(n+2(13))here n =3 So:Stickers bought in the last 2 weeks (14 days) = 3+5+7+9+11+13+15+17+19+21+23+25+27+29Stickers bought in the last 2 weeks (14 days) = 224 At Present Jane has Total Stickers = Stickers Initially+ Stickers bought in the last 2 weeks (14 days)At Present Jane has Total Stickers = 27+224

Answer: Commutative property.

Step-by-step explanation: Basically, the commutative property can be expressed as a + b = b + a, which matches this scenario pretty well. You are correct.

Let me know if this is right! :)

Answer:

Mark the sides BC and DF as congruent---------------------------------------------------We are given a side and an adjacent angle and need to identify the missing side or angle for proof by SAS .SAS is side-angle-side and requires two sides and the included angle to be congruent on both triangles.The missing bit is the other side of the marked angle B and D:sides BC or DF.

Step-by-step explanation:

Answer:

it takes 110 minutes

Step-by-step explanation:

Answer:

it takes approximately 110 minutes

Exponential graph is identified by its curve.

An exponential graph is a graph that shows a rapid increase or decrease of a value over time, where the rate of change is proportional to the current value. It is usually represented by a curve that bends upward or downward.

The key characteristic of an exponential graph is that the Y-axis is on a logarithmic scale, and the curve of the graph is a steep curve going either up or down. The equation of an exponential graph is usually of the form y = ab^x, where a is the initial value, b is the growth or decay factor, and x is the independent variable.

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Answer:

  (a)  (5, 9)

Step-by-step explanation:

You want the solution to the system ...

The value of x is already given, so no work is required to find that.

The value of y is found by using that value of x in the equation for y:

  y = 2x -1

  y = 2·5 -1 = 10 -1 = 9

The solution is (x, y) = (5, 9).

The predicted winning time in year 10 of the race is 2.83 minutes.

The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.

Given:

From the scatter plot, the points are given as follows:

(1, 5.4), (2, 5), (3, 4.6), (4, 4.9), (5, 4.1), (6, 3.9), (7, 3.6), (8, 3.3).

Inserting these points into the linear regression calculator, we get

y = -0.29x + 5.67.

Now, for x= 10 year

y = -0.29(10) + 5.67 = 2.77 minutes.

which is closest to 2.83 minutes.

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A trapezoid will appear smaller than the original trapezoid if it is dilated with a scale factor between 0 and 1.

An open, flat shape with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel.

What three characteristics do trapezoids have? An isosceles trapezoid has equal base angles and diagonals. The midpoints of the two opposing sides are parallel to the point where the diagonals intersect. An isosceles trapezoid has opposite sides that are congruent to one another or have the same length.

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Answer: An increase of a population doubling every year can be modeled using repeated multiplication. The expression for the increase after five years would be:

2 * 2 * 2 * 2 * 2 = 2^5 = 32

This can also be written as an exponential expression, with 2 as the base and 5 as the exponent:

2^5 = 32

This notation expresses that 2 is multiplied by itself 5 times to get 32, which represents the population size after 5 years with the rate of doubling every year.

It's also worth mentioning that exponential notation is used to represent the quantity of growth (doubling every year) , and using exponents makes it easy to see how much the population has grown over a certain period of time.

Step-by-step explanation:

Answer:

Step-by-step explanation:

2^5= 32

=2 x 2 x 2 x 2 x 2

= 2^5

= 32