Using compound interest, it is found that Dante was 6.6 years old when the balance in the account reached $13,000.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.In this problem, we have that the parameters are given as follows:
A(t) = 13000, A(0) = 10000, r = 0.04, n = 12.
Hence the time in years is found as follows:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]13000 = 10000\left(1 + \frac{0.04}{12}\right)^{12t}[/tex]
[tex](1.0033)^{12t} = 1.3[/tex]
[tex]\log{(1.0033)^{12t}} = \log{1.3}[/tex]
[tex]12t\log{1.0033} = \log{1.3}[/tex]
[tex]t = \frac{\log{1.3}}{12\log{1.0033}}[/tex]
t = 6.6
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A rectangle is 29 feet long and 7 feet long. What is the area of this rectangle?
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!
HELP ON 1 & 2 THANK YOU
[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
Select the correct solution method below, where x represents Kendall’s money
The correct solution method of Kendall's money is 7x = 98. Divide both sides by 7. Kendall had $14
How to write equation?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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What is 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?
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
What is angle of elevation and depression?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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Help me I’m confused
The properties used is [tex]\sqrt[3]{4^{5} } = (4^{5})^{\frac{1}{3} } = 4^{\frac{5}{3} }[/tex]
the correct option is (A).
What is exponents and power?
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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Do these two statements contradict
each other?
aurt is scalene
and aurt is obtuse.
yes
no
What is the sum of the interior angles of a regular polygon with 12 sides?
A. 1260
B. 1800
C. 2160
OD. 360
The sum of the interior angles of a regular polygon of 12 sides is 1800°
What is a polygon?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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HELP PLS question is in picture along with answers
In the given diagram, the measure of angle B (m∠B) is 40°
Exterior angle theoremFrom 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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pick one of the following sums and investigate these
What happens?
what is the general rule for each sums?
how does the rule work?
3.7+7.3=
6.4+4.6=
9.1+1.9=
5.5+5.5=
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.
How to find the general rule for a sum?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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In circle B below, diameter RT, radius BE, and chord RE are drawn.
If m2TRE = 15° and BE = 9, then the area of sector EBR is
The area of sector EBR in the given diagram attached below is: 33.75π units².
What is the Area of a Sector?Area = θ/360º × πr²
Given the following:
m∠TRE = 15° BE = 9Measure 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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Find the values of the six trig functions for theta on each triangle.
Step-by-step explanation:
Select four types of data demographers study to make predictions.
birth rate
death rate
employment
income
marriage
migration
pushpa Rajkgf chapter 2VOLINCE VOLINCE VOLINCERRRWhat is the line of symmetry for the parabola whose equation is y=x^2-12x+7
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 ...
a=1b=-12c=7Then the line of symmetry is ...
x = -b/(2a) = -(-12)/(2(1)) = 6
The line of symmetry is x=6.
Parville surveys every 15th person in the
town to see if there is support for a new
library and there are 40,161. How many people are surveyed?
Answer:
2677.4
Step-by-step explanation:
40161/15
Given f(x) = -x + 5, find f(-3).
Answer:
[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]
What we need to do:-Replace x with -3:-[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]
Good luck with your studies. [tex]\ddot\smile[/tex]#TogetherWeGoFar ~
[tex]\rule{300}{1}[/tex]
Hey there!
Find f(-3) :
Answer :f(-3) = 8 ✅
Explanation :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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find the length for point a to point
b
HELP ASAP ILL MAKE YOU THE BRAINIEST
find the value of c
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.
PLEASE HELP ASAP ILL MAKE YOU THE BRAINIEST Find the area of the rhombus
Answer:
the answer is 40
Step-by-step explanation:
A = 10 x 8 over 2 which is 40
The temperatures for the summer in California are 105, 90, 85, 89, and 100.
What is the range of the temperature
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.
If you draw all of the diagonals from one vertex of a regular hexagon, how
many triangles do you make?
If you draw all of the diagonals from one vertex of a regular hexagon we make 5 triangles. This is further explained below.
What is a hexagon?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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Determine the area, in square units, of rectangle ABCD.
Enter the area of rectangle ABCD.
The area of rectangle ABCD with side 6 unit by 8 units is 48 unit²
What is an equation?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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An artist is designing a website to showcase his 15-inch-wide paintings. The website will include scaled-down images of the paintings called thumbnails. For ease of viewing and to keep the thumbnail images large enough to show some detail, the artist decides to put three thumbnail images in a row so that any two adjacent images are separated by a space of 40 pixels, as shown in the figure above. If the website is 800 pixels wide, what should be the scaled size (in pixels per inch of painting) of the thumbnails?
The scaled size of the thumbnails is 16 pixels per inch of painting
How to determine the scaled size?The given parameters are:
Width = 15 inchesWebsite = 800 pixelsThe 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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Sketch the graph of y= (x-3)2 - 25, then select the graph that corresponds
to your sketch.
The graph of the given quadratic equation is graph C.
How to sketch the quadratic equation?
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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Perform the indicated operation
Answer:
Step-by-step explanation:
Given the following f(x) = 3x² + 7x³ + 8x^4; g(x) = -3x + 12x² - 5x³; and h(x) = 12x +
6
Complete the following: (f.h)(x)
96x5 +132x4+78x³ + 18x²
96x +132x4+78x³ + 18x²
96x5 + 122x + 78x³ + 18x²
96x5 +132x4+84x³ + 18x²
The value of the function (f.h)(x) is 96x⁵ + 132x⁴ + 78x³ + 18x²
How to solve function?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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Express cos K as a fraction in simplest terms.
9
M
15
Answer: cos K=
K
Submit Answer
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
i can figure out
12 is greater than four times a number g
Answer:
"Find g to make this statement true".
12 > 4 • g
The answer of the given expression is 1 & 2.
Concept:Firstly, convert word form into numerical expression.Then Simplify the given expression.How to solve the given question?Convert word form into numerical expression.Thus, the answer of the given expression is 1 & 2.
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The histogram shows the results of a survey that asked people how many hours of sleep they get each night. Which
statements are true?
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
What is a histogram?
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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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. how many quarts of paint did mieko use in the living room?
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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Volume of a triangular prism with numbers 3 4 5 6
Answer:
Step-by-step explanation:
V=14h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4aBase sidebBase sidecBase sidehHeight
(5√3-√27)^3
how do you prove that this is an integer?
Keys:
[tex]\left(a\cdot \:b\right)^n=a^nb^n[/tex]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]