A person invests 8000 dollars in a bank. The bank pays 4.75% interest compounded daily. To the nearest tenth of a year , how long must the person leave the money in the bank until it reaches 20400 dollars?
The number of days for which the money is left to reach the 20,400$ mark is; 21.28 days
Compound interestThe final amount to be reached is; $20400
The principal amount is; $8,000 and at. rate of 4.75 % compounded.
Hence, it follows that;
20400 = 8000(1+0.045)^(x)Divide both sides of the equation by 8000; we have;
20400/8000= 1.045^(x)2.55 = 1.045^(x)Take log of both sides;
x = 0.4065/0.0191x = 21.28 days.Read more on compound interest;
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What is the area of the triangle below
Consider directed line segment PQ. Point P is located at (-10,3). Point R, which is on segment PQ and divides segment PQ into a ratio of PR:RQ = 2:3, is located at (4,7). What are the coordinates of point Q?
[tex]\textit{internal division of a line segment using ratios} \\\\\\ P(-10,3)\qquad Q(a,b)\qquad \qquad \stackrel{\textit{ratio from P to Q}}{2:3} \\\\\\ \cfrac{P\underline{R}}{\underline{R} Q} = \cfrac{2}{3}\implies \cfrac{P}{Q} = \cfrac{2}{3}\implies 3P=2Q\implies 3(-10,3)=2(a,b)[/tex]
[tex](\stackrel{x}{-30}~~,~~ \stackrel{y}{9})=(\stackrel{x}{2a}~~,~~ \stackrel{y}{2b}) \\\\\\ R=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-30+2a}}{2+3}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{9+2b}}{2+3} \right)}~~ = ~~\stackrel{\textit{and we know that is}}{(4~~,~~7)} \\\\[-0.35em] ~\dotfill[/tex][tex]\cfrac{-30+2a}{5}~~ = ~~4\implies -30+2a=20\implies 2a=50\implies a=\cfrac{50}{2}\implies \boxed{a=25} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{9+2b}{5}~~ = ~~7\implies 9+2b=35\implies 2b=26\implies b=\cfrac{26}{2}\implies \boxed{b=13}[/tex]
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position. The coordinates of the point Q are (25,13).
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
Let the coordinates of the point Q be represented by Q(a,b).
Given the Ratio from P to Q is 2:3.
The internal division of the line segment using the ratios will be,
PR/RQ = 2/3
3P = 2Q
3(-10, 3) = 2(a, b)
Now, the coordinates of R can be rewritten as,
[tex]R = (\dfrac{-30+2a}{2+3},\ \dfrac{9+2b}{2+3}) = (4,7)[/tex]
Comparing the coordinates,
(-30+2a)/(2+3) = 4
a = 25
(9+2b)/(2+3) = 7
b = 13
Hence, the coordinates of the point Q are (25,13).
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!WILL MARK AS BRAINLIEST! I would really appreciate the help!
Answer: 1) 36 m and 60 m^2 2) 15π/2 + 10 m and 75π/4 m^2
Step-by-step explanation:
Using the pythagorean theorem in the first question, we get that the slope is 10 m so the perimeter = 10 + 14 + 6 + 6 = 36 m and the area is
(14 + 6)*6/2 = 60 m^2
So in the next question, the arc of the circle has a length of
2π*5*3/4 = 15π/2
So the perimeter is 15π/2 + 5 + 5 = 15π/2 + 10 m
And the area is 3/4*π*5*5=75π/4 m^2
Hope it helps
Evaluate x + y + z for x = 2, y = -3, z = -4.
Hey there!
x + y + x
= 2 + (-3) + (-4)
= 2 - 3 - 4
= -1 - 4
= -5
Therefore, your answer is: -5
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Please help with this question :`D
Answer:
The 4th term is geometric
Step-by-step explanation:
For geometry series we use Tn = a•r^n-1
r = -3
a = 3
Use the equation Tn = 3(-3)^n-1 and you'll see that it's geometric.
Find ST. Round to the nearest tenth.
HELP PLEASEEEE SHOW WORK!!
Answer:
Step-by-step explanation:
sin 44° = [tex]\frac{63}{ST}[/tex]
ST = [tex]\frac{63}{sin44}[/tex]
ST ≈ 90.7
In a right triangle, sin (3x+5)^\circ(3x+5) = cos (8x+9)^\circ(8x+9) Solve for x. Round your answer to the nearest hundredth if necessary.
Right triangles are triangles with a measure of 90 degrees
The value of x is 76/11
How to calculate x in the triangleThe equation is given as:
sin (3x+5) = cos (8x+9)
To solve for x, we make use of the following theorem
If sin(A) = cos(B), then
A + b = 90
So, we have:
3x + 5 + 8x + 9 = 90
Collect like terms
3x + 8x = 90 - 5 - 9
Evaluate the like terms
11x = 76
Divide both sides by 11
x = 76/11
Hence, the value of x is 76/11
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The perimeter of a rectangle bathroom mirror is 24 feet . The mirror is 10 feet wide how tall is it
4. Solve the following equation: 6x + 12 = 4x - 8
Answer:
-10 is the correct answer
Step-by-step explanation:
hope this helps
Answer:
-10
Because I worked it out on paper
Write the ratio for cosB
Answer:
11/61
Step-by-step explanation:
cos b = adj side/hypotenuse
=11/61
Answer:
CosB = B/H
Base(B)= 11
Perpendicular (P)=60.
Hypotenuse (H)= 61
CosB = B/H
CosB= 11/61
Find the value of x.
Answer:
37
Step-by-step explanation:
（x+10)+x+(3x-5)=180
5x=185
x=37
The sum of angles in the triangle is 180 degrees. Therefore, the value of x in the triangle is 35
Angles of a triangleThe sum of angles of a triangle is 180 degrees. This simply implies the sum of the three angles in a triangle is equals to 180 degrees.
Therefore,
x + 10 + 3x - 5 + x = 180
combine like terms
x + x + 3x + 10 - 5 = 180
5x + 5 = 180
subtract 5 from both sides of the equation
5x + 5 - 5 = 180 - 5
5x = 175
divide both sides by 5
5x / 5 = 175 / 5
x = 35
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pls help only if ur sure of the answer!
Answer:
C
Step-by-step explanation:
[tex]12000 \times {1.05}^{4} = 14586[/tex]
The point M(
–
4,
–
6) is rotated 90° clockwise around the origin. What are the coordinates of the resulting point, M'?
will mark branliest
Answer:
M' (- 6, 4 )
Step-by-step explanation:
Under a clockwise rotation about the origin of 90°
a point (x, y ) → (y, - x ) , then
M (- 4, - 6 ) → M' (- 6, 4 )
Order the following numbers from greatest (on top) to least (on bottom). Click on the arrows and drag to move the numbers around.
1 1.
-2/8
-3/7
-0.2
Diamond started the day with $280 in her bank account. She purchased 14 books that were all the same price. After she left the store, she had -$20 in her account. How much did each book cost? (Round your answer to the nearest hundredths place)
Answer:
21.43
Step-by-step explanation:
280+20=300=total spent
300÷14=21.4285714
21.4285714 to the nearest hundredths place= 21.43
the area of rectangle is 18cm².its length is double than of its breath find its length and breadth
find its perimeter
Answer:
length = 6 cm, breadth = 3 cm, perimeter 18 cm
Step-by-step explanation:
Let the breadth be x,
Then the length will be 2x
area of rectangle = length * breadth
using the formula:
(2x * x) = 182x² = 18x² = 9 x = √9x = 3The breadth is 3 cm
Length:
2x2(3)6 cmperimeter of rectangle:
2( length + breadth )2( 3 + 6 )2(9)18 cmFor more length, area, width questions:
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Answer:
Step-by-step explanation:
Let the breadth = x cm
Length = 2x
2x *x = 18
x² = 18/2
x² =9
x = √9
x = 3 cm
Breadth = 3 cm
Length = 2*3 = 6 cm
Perimeter = 2*(length + breadth)
=2*(3+6)
= 2*9
Perimeter = 18 cm
A person walks 4 miles per hour for 2.5 hours. How far do they walk?
Answer:
10 miles
Step-by-step explanation:
Distance walked in 1 hour = 4 miles
So, distance walked in 2.5 hours
= 4 miles × 2.5
= 10 miles
) An outdoor staircase has a total vertical elevation of 21 feet from the road level to the first floor. The 1st floor to the 2nd floor is also 21 feet. If the angle of elevation is 32 degrees and the landing of each step is 12 inches, answer the following questions showing each step of your work:
a) What is the vertical rise per step (in inches, rounded to the nearest inch)?
b) Find the number of steps needed to climb from road level to the 2nd floor.
Answer:
a) 7 in
b) 72 steps
Step-by-step explanation:
Angle of elevation formula: [tex]tan(\theta)=\dfrac{y}{x}[/tex]
where [tex]\theta[/tex] is the angle of elevation, y is the vertical distance (rise) and x is the horizontal distance.
a) Given:
[tex]x=12[/tex][tex]\theta=32[/tex][tex]\implies tan(32)=\dfrac{y}{12}[/tex]
[tex]\implies y=12tan(32)[/tex]
[tex]\implies y=7 \ \textsf{in (nearest inch)}[/tex]
b) Given:
1st floor = 21 feet2nd floor = 21 feet⇒ Total height = 21 + 21 = 42 feet
1 foot = 12 inches
⇒ 42 feet = 42 x 12 = 504 inches
Using vertical rise of 7 in per step found in part (a):
Number of steps = 504 ÷ 7 = 72
Increased accuracy
Using unrounded vertical rise of 12tan(32):
Number of steps = 504 ÷ 12tan(32) = 67 steps to the nearest step
Please help this is due in 20 minutes. If you get I right I will give you 100 points.
It should cut into
2 right angle traingles.One rectangle for baseOne rectangle for b ack.One rectangle for fronti.e 3 rectangles and 2 right angles2 ne t is accurate
Answer:
A) net A
B) AB = 3 in BC = 5 in CD = 8.6 in
C) 106.6 in²
Step-by-step explanation:
Part A:
net A is the correct net for the prismPart B:
From inspection of the diagram:
AB = 3 inBC = 5 inCD = 8.6 inPart C:
Area of a rectangle = width x length
Area of a triangle = 1/2 x base x height
Surface area = 2(4 x 8.6) + (3 x 8.6) + 2(1/2 x 4 x 3)
= 68.8 + 25.8 + 12
= 106.6 in²
Use the Internet to conduct research on real-world applications of chaos theory. Some examples of search terms to use are chaos theory, the butterfly effect, and fractal. Write 2-3 paragraphs on how chaos theory is used in today's world in various fields.
Chaos theory has a wide range of real-world applications and is used in fields such as weather prediction, finance, and biology.
What is Chaos theory?Chaos theory is a branch of mathematics that studies the behavior of systems that are highly sensitive to initial conditions. The "butterfly effect" is a popular term used to describe the idea that small variations in initial conditions can lead to vastly different outcomes over time. This theory has many real-world applications in various fields.
One of the fields that makes use of chaos theory is weather prediction. Meteorologists use chaos theory to understand how small variations in atmospheric conditions can lead to large-scale weather patterns. They use computer simulations to model how different initial conditions can lead to different weather outcomes. This helps them make more accurate weather predictions and plan for extreme weather events.
Another field that uses chaos theory is finance. Financial analysts use chaos theory to understand how small fluctuations in financial markets can have a significant impact on the economy. They use mathematical models to analyze stock prices and interest rates and determine how small changes can lead to large market movements. This helps them make informed investment decisions and minimize risk.
Chaos theory is also used in biology to study the behavior of populations of animals, plants, and microorganisms. Biologists use chaos theory to understand how small changes in the environment can have a major impact on the growth and survival of populations. This helps them make informed decisions about the conservation and management of natural resources.
In conclusion, chaos theory has a wide range of real-world applications and is used in fields such as weather prediction, finance, and biology. The idea that small variations in initial conditions can lead to vastly different outcomes over time is a powerful tool for understanding complex systems and making informed decisions.
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Complete the table.
Original Price: Percent of discount: Sell Price:
? 25% $40
PLEASE HELP FASTT 100 points
Answer:
you saved $10.00
Step-by-step explanation:
Discount = Original Price x Discount %/100
Discount = 40 × 25/100
Discount = 40 x 0.25
Answer:
10
Step-by-step explanation:
What is 25% of 40?
Y is 25% of 40
Equation: Y = P% * X
Solving our equation for Y
Y = P% * X
Y = 25% * 40
Converting percent to decimal:
p = 25%/100 = 0.25
Y = 0.25 * 40
Y = 10
8x+14y=4
-6x-7y=-10
Please help by solving the problem as a system of equation by elimination
Step-by-step explanation:
8x+ 14y= 4
-6×-7y= -10
For elimination method we can decide to eliminate either the y or x variable I'm going to eliminate the x variable so either of the one am eliminating we multiply the first equation by the coefficient of the variable we are eliminating in other words
8x +14y=4.....*-6
-6×-7y= -10......*8
-48x-84y= -24
-48x-56y= 80
then we multiply the second equation all through by -1
-48x-84y= -24
48x+ 56y= -80
28y=-104
y= 26/7
x= 8/3
Griffin’s General Store is having a 30% off sale on fans. Robert paid $24. 50 for a fan that was on sale. What is the original price of the fan?.
100 Points!!!
The table shows the number of calories in different numbers of apples.
Number of apples 3 5 8
Number of calories 195 325 520
How many calories are in 9 apples?
Answer:
585 calories are in 9 apples
Step-by-step explanation:
Number of apples : 3 || 5 || 8
Number of calories: 195 || 325 || 520
Find the unit rate:
[tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{325-195}{5-3}[/tex]
[tex]\frac{130}{2}[/tex]
[tex]65[/tex]
Find equation:
y - 325 = 65( x -5)
y = 65x - 325 +325
y = 65x .....this is the equation to find any number of calories.
put x as 9 here:
y = 65x
y = 65(9)
y = 585 calories
Select the correct solution for the expression.
Answer:
= B
[tex]\frac{16}{40} +\frac{15}{40} = \frac{31}{40} \\\\\frac{2}{5} +\frac{3}{8} =\frac{31}{40}[/tex]
help!?!?!?!?!?!!?!?!?!?!?!
you took time typing help that you forgot your Question :D
What are the sine and cosine ratios for a 30°–60°–90° triangle with a hypotenuse of 6, when θ = 60°?
Answer:
There are two ways to do this problem algebraically or trigonometrically.
Algebraically/geometrically
The ratios of the sides of a 30/60/90 tri. are x, x√3, 2x (short leg, long leg, hyp). Therefore, if the long leg is 6 'units'. then 6 = x√3. x = 6√3.
The hyp is 2x then the hypotenuse is 2(6√3) = 12√3, rationalizing is 12√3/3 = 4√3
Using Trig.
We can use sinx = y/r = opp/hyp. The long leg of 6 is opposite 60 degrees (pi/3).
Therefore, sin(pi/3) = 6/r =
r = 6/sin(pi/3) = 6/(√3/2) = 12/√3, when you rationalize you get 12√3/3 = 4√3
The sine and cosine ratios for a 30°–60°–90° triangle with a hypotenuse of 6, when θ = 60° are 6√3 and 4√3.
What is a Hypotenuse?This is defined as the longest side of a right-angled triangle and is opposite to the right angle.
The ratios of the sides of a 30/60/90 triangle are x, x√3, 2x (short leg, long leg, hyp). We can infer that the long leg is 6 'units' which is
6 = x√3
x = 6√3.
The hypotenuse is 2x then the hypotenuse is 2(6√3)
= 12√3 when rationalized
= 12√3/3 = 4√3.
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A parallelogram's area is given by the expression 4x2 2x 6. The height of the parallelogram is 2x2. Which expression represents the base of the parallelogram? 2 x 2 2 2 x.
Answer:
The answer is B!!HOPE THIS HELPS :)
Step-by-step explanation:
I just guessed it and its right :)
Answer:
b
Step-by-step explanation:
Sasha likes to run on a track that is 58 of a mile. If she runs 7 laps. How many miles did she run? 758 678 548 438
Answer:
4 miles
Step-by-step explanation:
4 miles because if if if 58 of mile which is just a half mile basically and she does 7 laps
7 x 0.58=4.06 which is 4 miles
Have a good day :}