When dante was born, his grandparents deposited $10,000 into a special college fund that paid 4% annual interest, compounded monthly. how old was dante when the balance in the account reached$13,000? round your answer to the nearest tenth of a year.

The correct solution method of Kendall's money is 7x = 98. Divide both sides by 7. Kendall had $14

x = Kendall's money

Mateo's money = $98

= 7 × x

The equation:

7 × x = 98

7x = 98

x = 98/7

x = $14

Therefore, the correct answer is option B

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The value of the function (f.h)(x) is 96x⁵ + 132x⁴ + 78x³ + 18x²

f(x) = 3x² + 4x³ + 8x⁴

g(x) = -3x + 12x² - 5x³

h(x) = 12x + 6

Therefore,

(f.h)(x) = f(x).h(x)

Hence,

f(x).h(x) = (3x² + 7x³ + 8x⁴)(12x + 6)

f(x).h(x) = 36x³ + 18x² + 84x⁴ + 42x³ + 96x⁵ + 48x⁴

(f.h)(x) = 96x⁵ + 84x⁴ + 48x⁴ +  36x³ + 42x³ + 18x²

(f.h)(x) =  96x⁵ + 132x⁴ + 78x³ + 18x²

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Answer:

2677.4

Step-by-step explanation:

40161/15

The general rule for each sum is that when you add the tenth term together we will get ten which will make the value an integer. The whole sum is equals to eleven.

Let's sum the decimal numbers to know the general rule,

Therefore,

3.7 + 7.3 = 11.0

6.4 + 4.6 = 11.0

9.1 + 1.9 = 11.0

5.5 + 5.5 = 11.0

Therefore, the  values added are the reverse of the decimals. example is 3.7 and 7.3 or 6.4 and 4.6.

When you add the tenth term together we will get ten which will make the value an integer

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The properties used is [tex]\sqrt[3]{4^{5} } = (4^{5})^{\frac{1}{3} } = 4^{\frac{5}{3} }[/tex]

the correct option is (A).

power can be defined as an expression that represents repeated multiplication of the same number whereas exponent is the quantity that represents the power to which the number is raised.

Given:

[tex]4^{\frac{5}{3} } = \sqrt[3]{4^{5} }[/tex]

We can use the following property

[tex]\sqrt[3]{4^{5} } = (4^{5})^{\frac{1}{3} } = 4^{\frac{5}{3} }[/tex]

By using the property we can find the answer.

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Answer:

4/5

Step-by-step explanation:

In a right triangle such as this one

 cos (angle) = adjacent leg  / hypotenuse

  cos(k) =   KL / 15

You will need to find the leg length KL using Pythagorean Theorem

 15^2 = 9^2 + (KL)^2             KL =  12

then cos k  = 12/15 = 4/5  

The number of quarts of paint did mieko use in the living room is A = 3 quarts

Given data ,

Mieko bought 2 gallons of paint. she used 1/4 of the paint on her bedroom, 3 quarts on the hallway, and the rest of the paint in the living room

Now , on simplifying the equation , we get

Two gallons of paint is equal to 8 quarts (2 x 4 = 8)

Mieko used 1/4 of the paint on her bedroom, which is equal to 2 quarts (1/4 x 8 = 2)

She used 3 quarts of paint on the hallway

Thus, Mieko used a total of 2 + 3 = 5 quarts of paint on the bedroom and hallway

Therefore , she used 8 - 5 = 3 quarts of paint in the living room

Hence , the number of quarts is A = 3 quarts

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Answer:

range is subtracting the highest number from the lowest number. so we want to find the difference

Step-by-step explanation:

all you do is 105-85 which is 15.

The area of rectangle ABCD with side 6 unit by 8 units is  48 unit²

An equation is an expression that shows the relationship between two or more variables or numbers.

From the rectangle ABCD:

AB = 6 units, BC = 8 units

Hence:

Area of ABCD = 6 units * 8 units = 48 unit²

The area of rectangle ABCD with side 6 unit by 8 units is  48 unit²

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Keys:

Step-by-step explanation:

[tex]\left(5\sqrt{3}-\sqrt{27}\right)^3\\\5\sqrt{3}-\sqrt{27}^3=\left(2\sqrt{3}\right)^3\\= 2\sqrt{3}\\\left(2\sqrt{3}\right)^3=2^3\left(\sqrt{3}\right)^3\\=2^3\left(\sqrt{3}\right)^3\\2^3=8\\=8\left(\sqrt{3}\right)^3\\=8\cdot \:3\sqrt{3}\\8\cdot \:3=24\\=24\sqrt{3}[/tex]

Answer:

It is not an integer.

Step-by-step explanation:

[tex](5\sqrt{3} -\sqrt{27} )^3\\\\=(\sqrt{3} *(5-3))^3\\\\=8*3*\sqrt{3} \\\\=24\sqrt{3} \\[/tex]

Answer:

Step-by-step explanation:

If you draw all of the diagonals from one vertex of a regular hexagon we make 5 triangles. This is further explained below.

Generally, the hexagon is simply defined as the hexagon is a polygon with six sides. to be considered a hexagon, the form must have six sides, all of which must be closed.

In conclusion, We get five triangles if we draw the diagonals of a regular hexagon starting at a single vertex.

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Answer:

"Find g to make this statement true".

12 > 4 • g

The answer of the given expression is 1 & 2.

Thus, the answer of the given expression is 1 & 2.

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The purpose of knowing the angle of elevation and depression in relation to the field of surveyor, military/police, aeronautics (pilot), engineers, landscapers, and architects is discussed below

If a person stands and looks up at an object, the angle of elevation is the angle between the horizontal line of sight and the object. If a person stands and looks down at an object, the angle of depression is the angle between the horizontal line of sight and the object.

If the pilot looks straight out, that line of sight is horizontal (focused on the distant horizon). The pilot might see the airport's runway, distant buildings, or even mountains in her field of view.

If the pilot looks down at the ground, the one will see the ground crew. The angle of depression is the angle that is formed between the horizontal and the downward looking angle. It is always a downward view, an angle below the horizon.

For the ground crewmember, looking down would not be much help in communicating with the pilot in her cockpit seat. The crewmember will look up, above the horizontal line, to see the pilot. The ground crewmember's angle of vision if an angle of elevation, the angle above the horizon.

Angle of elevation or depression in a survey can be defined as the angle subtended between the line of sight passing through the scope and the horizontal axis of the instrument.

Engineers, landscapers, architects all use trigonometry in their everyday life to help them efficiently and safely create or design something new.

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Answer:

  x = 6

Step-by-step explanation:

The line of symmetry for the parabola written in the form y=ax²+bx+c is given by the equation x=-b/(2a).

__

Comparing your equation to the above form, we see ...

Then the line of symmetry is ...

  x = -b/(2a) = -(-12)/(2(1)) = 6

The line of symmetry is x=6.

The true statements are

The mean is near the median.

The mean is the best measure of center.

The five-number summary is the best measure of variation

A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.

If the mean is greater than the median, the histogram would be skewed to the right. If the mean is less than the median, the histogram would be skewed to the left.

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[1] n = -2

       We will convert the words given into a mathematical equation and then solve by isolating the variable. Let n be "a number"

19 decreased by four times a number is 17

19 - four times a number is 17

19 - 4 n is 17

9 - 4n = 17

-

9 - 4n = 17

- 4n = 8

n = -2

[2] x = -1, y = 3, or (-1, 3)

      I will plug the first equation into the second from the system of equations given to us because it already has an isolated variable, y.

2y - 2x = 8

2(2x + 5) - 2x = 8

4x + 10 - 2x = 8

2x = -2

x = -1

      Now, I will plug this value back into the equation and solve for y.

y = 2x + 5

y = 2(-1) + 5

y = -2 + 5

y = 3

The scaled size of the thumbnails is 16 pixels per inch of painting

The given parameters are:

The space between adjacent images is 40 inches.

Given that there are two spaces, the remaining space is:

Remaining = 800 - 2 * 40

Remaining = 720

Given that there are three samples of image, the width of each image is:

Image = 720/3

Divide

Image = 240 pixels

The scaled size is then calculated using:

Scale = Image scale width/actual width

This gives

Scale = 240/15

Evaluate

Scale = 16

Hence, the scaled size of the thumbnails is 16 pixels per inch of painting

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Step-by-step explanation:

Select four types of data demographers study to make predictions.

birth rate

death rate

employment

income

marriage

migration

The sum of the interior angles of a regular polygon of 12 sides is 1800°

A polygon is a planar figure characterized by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.

The sum of the all the interior angles of a polygon with 'n' number of sides is given by the formula,

Sum of all the angles = (n-2) × 180°

Since the number of sides in the polygon is 12, the sum of the angles will be,

Sum = (12-2) × 180° = 10 × 180° = 1800°

Hence, the sum of the interior angles of a regular polygon of 12 sides is 1800°.

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Answer:

Step-by-step explanation:

V=14h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4aBase sidebBase sidecBase sidehHeight

          [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

       Given f(x)=-x+5, find f(-3).

    [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]

We have the function

[tex]\longmapsto\sf{f(x)=-x+5}[/tex]

We need to find

[tex]\longmapsto\sf{f(-3)=}[/tex]

[tex]\longmapsto\sf{f(x)=-(-3)+5}[/tex]

Simplifying,

[tex]\longmapsto\sf{f(x)=3+5}[/tex]

(which is the exact same thing as 5-3)

Henceforth, We conclude that the answer is

[tex]\longmapsto\sf{f(-3)=8}[/tex]

#TogetherWeGoFar ~

[tex]\rule{300}{1}[/tex]

Hey there!

Find f(-3) :

f(-3) = 8 ✅

f(x) = -x + 5

>> Substitute -3 for x in f(x) :

f(-3) = -(-3) + 5

f(-3) = 3 + 5

f(-3) = 8

Therefore, your answer is f(-3) = 8

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Answer:

the answer is 40

Step-by-step explanation:

A = 10 x 8 over 2 which is 40

In the given diagram, the measure of angle B (m∠B) is 40°

From the question, we are to determine the measure of angle B

By the exterior angle theorem,

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Then, we can write that

m∠A + m∠B = 155° (Exterior angle theorem)

115° + m∠B = 155°

m∠B = 155° - 115°

m∠B = 40°

Hence, the measure of angle B (m∠B) is 40°

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The graph of the given quadratic equation is graph C.

Remember that for a quadratic equation with a vertex (h, k), the vertex form is given by:

[tex]y = a*(x - h)^2 + k[/tex]

Where a is the leading coefficient, in this case we have a = 1.

Here we have:

[tex]y = (x - 3)^2 - 25[/tex]

So the vertex is at (3, -25).

From that function we can also get the y-intercept, that is given by evaluating the function in x = 0, so we get:

[tex]y = (-3)^2 - 25 = -16[/tex]

So this function passes through (3, -25) and (0, -16). The sketch can be seen below.

Notice that from the given options only the third graph intercepts the y-axis on the negative region, so from that, we conclude that the third graph is the correct option.

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Work Shown:

tan(angle) = opposite/adjacent

tan(61) = x/9

x = 9*tan(61)

x = 16.2364298 approximately

Your calculator needs to be in degree mode. One quick way to check is to type in something like tan(45) and the result should be 1.

The area of sector EBR in the given diagram attached below is: 33.75π units².

Area = θ/360º × πr²

Given the following:

Measure of arc TE = 2(m∠TRE) = 2(15) [inscribed angle theorem]

Measure of arc TE = 30°

Arc RE = 180 - arc TE = 180 - 30 [semicircle]

Arc RE = 150°

m∠EBR = Arc RE = 150°

Area of sector EBR = m∠EBR/360 × π(BE²)

Area of sector EBR = 150/360 × π(9²)

Area of sector EBR = 33.75π units²

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Answer:   203

Step By Step Explanation: Just multiply the numbers.

Answer:

Area = 203 [tex]ft^{2}[/tex]

Step-by-step explanation:

The area of a rectangle can be found using this equation:

Area = length x width

The length given is 29 feet, and the width is 7 feet.

Let's plug these into the equation:

Area = (29)(7) = 203 [tex]ft^{2}[/tex]

Therefore, the area of the rectangle is 203 [tex]ft^{2}[/tex].

Hope this helps! If you have any questions about my work, please let me know down in the comments!