The total amount will be $889123 after 16 years if the starting salary is $350000
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent [tex]y = a^x[/tex]
where a is a constant and a>1
We have:
Starting salary is $350000 and you receive a 6% increase at the end of every year.
We can find the total amount, from the exponential formula:
T = a(1 + r)ⁿ
T is the total amount
a is the starting amount
r is the rate
n is the total number of years
T = 350000(1 + 6%)¹⁶
T = 350000(1 + 0.06)¹⁶
T = 889123.08 ≈ $889123
Thus, the total amount will be $889123 after 16 years if the starting salary is $350000
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Rohan's salary 1200$ per month he spends 75% of it how does he spend in dollars?
Answer:900
Step-by-step explanation:
what is the value of 2/3 + 1/2 of (1/2 - 1/6) / 2/3 + 1/4
Answer:
In fraction form: 77/24
In decimal form: 3.20833
Step-by-step explanation:
That took me a while to solve but that’s the correct answer.
Hope that helps! :)
The number of cars parked in a car park increases from 50 to 73. what is the percentage increase?
73 is a 46% increase of 50.
What is percentage ?
A percentage is a relative value that represents the hundredth part of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given amount.
Percentage is defined as a specific part or amount out of a hundred. It is a fraction with the denominator 100 and is denoted by the symbol "percent."
The percent increase formula is as follows:
Percent increase = [(new value - original value)/original value] * 100.
Number of car parking (original value)=50
Number of car parking(new value)=73
The Percentage increase =[(73-50)/50]*100
= [(23)/50]*100
=.46*100
=46%
73 is a 46% increase of 50.
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what is the midpoint of the line segment that joins -3/4 and 2 1/2
The mid point between the two points is at 13/8 .
What is a Line Segment ?A line segment is a line of fixed measure .
The line segment extends from (-3/4) to [tex]\rm 2 \dfrac{1}{2}[/tex]
i.e the line extends form -3/4 to 5/2
To find the mid point , the total distance needs to be determined
So the distance between the two point is
(5/2) + (3/4) = 13/8
The mid point is at half the distance of this
so it is at 13/8 from both the points
Any point at 13/8 distance from 5/2 towards (-3/4) will be
= (5/2) - (13/8)
= 7/8
So the mid point between the two points is at 13/8 .
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? Question
What are coordinates of the point representing the location of the other end of the string of buoys?
Type the correct answer in each box. Use numerals instead of words.
See below for the explanation on how to determine the coordinates.
How to determine the coordinates?The question is incomplete, and the missing parameters cannot be found.
So, I will give a general explanation on how to determine coordinates.
Assume that the start point of the buoy is
(x, y)
And the length of the buoy is k.
Depending on the position of the bouy on the coordinate plane, the endpoint can be any of the following coordinates (x - h, y), (x + h, y), (x, y + h) and (x, y - h)
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Complete the following chart (check picture below)
The following requires the submission of the details of the parabola related to the equations.
What is a Parabola?A parabola, simply defined, is a plane curve that is created by a point that is moving such that it's distance from a fixed locus is equal to it's distance from a line that is fixed.
What are the details for equation y = -2(x-5)² + 3?Vertex → (5,3)Axis of Symmetry → x = 5Direction of Opening → Opens downMax or Min → (5, 3)Y-intercept → 25/8What are the details for equation y = (x + 2)²Vertex → (-2, 0)Axis of Symmetry → x = -2Direction of Opening → Opens UpMax or Min - (-2, 0)Y-intercept → (0,-47)Learn more about Parabola at;
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Which linear function has the same y-intercept as the one that is represented by the graph? On a coordinate plane, a line goes through points (negative 4, 0) and (0, 3). a y = 2 x minus 4 b y = 2 x minus 3 c y = 2 x + 3 d y = 2 x + 4
The line which is having same y intercept as the line which passes through points (-4,0) and (0,3) is y=2x+3.
Given Points through which the line passes through are (-4,0) and (0,3)
We have to find the equation whose y intercept is equal to the y intercept of the line whose points given above.
First of all we have to find the y intercept of the line which passes through (-4,0) and (0,3). Equation of line is :
y-y1=(y2-y1)/(x2-x1)*(x-x1)
y-0=(3-0)/(0+4) *(x+4)
y=3/4(x+4)
y -intercept exists where x=0
put x=0
y=3
So the options are:
y=2x-4y=2x-3y=2x+3y=2x+4By putting the value of x in all options we will find
y=-4
y=-3
y=3
y=4
So the third option is correct.
Hence the line whose y-intercept matched with the given line is y=2x+3.
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Answer:
a
Step-by-step explanation:
Find x
Help me please thank u
Step-by-step explanation:
ATTACHED IS THE SOLUTION!!!The coordinate grid shows points A through K. What point is a solution to the system of inequalities? y < −2x + 10 y < 1 over 2x − 2 coordinate grid with plotted ordered pairs, point A at negative 5, 4 point B at 4, 7 point C at negative 2, 7 point D at negative 7, 1 point E at 4, negative 2 point F at 1, negative 6 point G at negative 3, negative 10 point H at negative 4, negative 4 point I at 9, 3 point J at 7, negative 4 and point K at 2, 3 I B A F
The point that is a solution to the system of inequalities on the coordinates grid is A.
How to illustrate the information?It should be noted that form the information given, the expression is y < −2x + 10. In this case, draw the solid line y = -2x + 10.
Shade the region below the like for x = 5.
y = -2(5) + 10
= -10 + 10
= 0
For x= 0
y = -2(0) + 10
= 0 + 10
= (0, 10)
The diagram is attached.
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Knowing that sin 30° = 1, what is a?
OA. 3.5
OB. 14
OC. 12.12
OD. 7
30⁰
7
a
60⁰
Answer:
B
Step-by-step explanation:
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{a}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
a = 7 × 2 = 14
Determine the value of x.
घ
55°
yo
E
(11x + 4)º
Answer: 6
Step-by-step explanation:
Because [tex]\overline{DE} \cong \overline{EF}[/tex], [tex]y=55[/tex]. So, because angles in a triangle add to 180 degrees, [tex]11x+4=70 \longrightarrow x=6[/tex]
Functions and Transformations
The new translated function will be more towards the origin , as the value of length is decreased , Option C is the right answer.
What is a Function ?A function is a mathematical statement used to relate a dependent and an independent variable.
It is given that
Area of a Rectangle is 10 sq. unit
Width of the Rectangle is x unit
Length is given by
l(x) = 10 / x
When the length of the Rectangle is increased by 1 ,
The new function will be
l(x) = 10 /(x+1)
The new translated function will be more towards the origin , as the value of length is decreased ,
This is represented by Graph 3 ,
This can be proved by keeping the value of x
let x = 2
y = 10 /3 = 3.333
This is only in the graph 3 , Therefore Option C is the right answer.
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If 9: x= x4, then x=
Answer:
x = ±6
Step-by-step explanation:
9 : x = x : 4
9/x = x/4
Cross multiply.
x² = 9 × 4
x² = 36
x = ±√36
x = ±6
Identify the term that means the difference of the minimum and maximum values of a data set and the term that means the difference of the first quartile and third quartile of a data set.
Answer:
Range: Difference of minimum and maximum values of a data set
Interquartile Range: Difference of first quartile and third quartile of a data set
Step-by-step explanation:
Answer: what he said
Step-by-step explanation:
Thé nth term rule for a sequence is 4n + 7 what is the 3rd term of this sequence?
Answer:
a₃ = 19
Step-by-step explanation:
to find the third term substitute n = 3 into the nth term rule
a₃ = 4(3) + 7 = 12 + 7 = 19
Answer:
a₃ = 19
Step-by-step explanation:
the relationship between any two terms of an arithmetic sequence (in our case the relationship between the 3rd term and nth term) gives us this equality :
[tex]a_n - a_3 = 4(n-3)[/tex]
Then
4n + 7 - a₃ = 4n - 12
Then
7 - a₃ = - 12
Then
7 + 12 = a₃
Then
a₃ = 19
What is the best first step in solving the equation 3+√6x=5?
O Subtract 3 from both sides.
O Find the cube of Vex.
O Cube both sides of the equation.
O Subtract 5 from both sides.
WHICE group of domain-specific words belongs only to math domain
Answer:
The major field of anthroplogy and evolutionary and paleo anthropological perspectives on the origin of humankind
The average monthly temperature T(m), in degrees Celsius, in a particular city varies according to the model T of m equals 4 times sine of the quantity pi over 6 times m end quantity plus 2 comma where m represents the months of the year and January begins at m = 0. Between what months will the temperature be below 0°C?
The months with temperature below 0° is August and October.
GIven,
T(m) = 4 sin (π/6 m)₊2
In the above equation, T(m) is the average temperature in a month in degrees Fahrenheit, and m is the month of the year.
T(8) = 4 sin (8π/6 m)₊2
= 4 sin (4π/3 )₊2
= 4 sin (π₊π/3 )₊2
= ₋4 sin π/3 ₊2
= ₋4×√3/2 ₊2
= ₋2√3 ₊ 2 <0
The function for the average monthly temperature, in m months from january is given by
T(0) = 4 sin(10π/6) ₊ 2
= 4 sin(5π/3) ₊ 2
= 4 sin(2π ₋ π/3) ₊ 2
= - 4sin π/3 ₊ 2 = ₋4 × √3/2 ₊ 2
= ₋2√3 ₊2<0
we can notice that after january, from august till october the months will face temperature below 0 degrees.
So the answer is August and October.
Your question is incomplete. Please find the missing content here.
The average monthly temperature T(m), in degrees Celsius, in a particular city varies according to the model T of m equals 4 times sine of the quantity pi over 6 times m end quantity plus 2 comma where m represents the months of the year and January begins at m = 0. Between what months will the temperature be below 0°C?
July and NovemberJuly and OctoberAugust and NovemberAugust and OctoberLearn more about "temperature problems" here-
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Hi I need help with the question in the image. Step by step, thank you!
The exponential function is [tex]f(x) = 18(12)^{-x-4} + 2[/tex]
How to determine the equation?An exponential function is represented as:
y = b^x
Where b represents the base.
The base is given as:
b = 12
So, we have:
y = (12)^x
It is vertically compressed by a factor of 1/8.
So, we have:
y = 18(12)^x
When reflected across the y-axis, we have:
[tex]y = 18(12)^{-x}[/tex]
The horizontal asymptote is y = 2.
So, we have:
[tex]y = 18(12)^{-x} + 2[/tex]
It passes through the point (-3, 4).
So, we shift the function to the right by 4 units
[tex]y = 18(12)^{-x-4} + 2[/tex]
Express as a function
[tex]f(x) = 18(12)^{-x-4} + 2[/tex]
Hence, the exponential function is [tex]f(x) = 18(12)^{-x-4} + 2[/tex]
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( this is my summer math homework, please help!)
Find the selling price of each item.
1. Original price of a bunny: $46.00
Text: 2%
2. Original price of a CD: $14.99
Tax: 2%
3. Original price of a CD: $16.50
Tax: 4%
4. Original price of a car: $19,500.00
Tax: 4%
Using proportions, the selling prices are given as follows:
1. $46.92.
2. $15.29.
3. $17.16.
4. $20,280.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
To find the selling prices, we have to multiply the original prices by either 1.02(2% sales tax) or 1.04(4% sales tax), hence they are given as follows:
1. 46 x 1.02 = $46.92.2. 14.99 x 1.02 = $15.29.3. 16.50 x 1.04 = $17.16.4. 19500 x 1.04 = $20,280.More can be learned about proportions at https://brainly.com/question/24372153
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Abbot Tools is designing a new toolbox. The length of the toolbox will be three times its width, w, and the length of the diagonal of the top cover will be 30 inches.
Use this information to determine the length, l, of the box. Select the correct answer from the drop-down menu.
The length and width of the toolbox given the diagonal is 45 inches and 15 inches respectively.
TriangleWidth of the triangle = wLength of the triangle = 3wDiagonal = 30 inchesHypotenuse ² = opposite ² + adjacent ²
30² = w² + (3w²)
30² = 4w²
900 = 4w²
w² = 900/4
= 225
w = √225
w = 15
Therefore,
Width of the triangle = w
= 15 inches
Length of the triangle = 3w
= 3(15)
= 45 inches
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A correlation coefficient of 0.08 indicates strong positive correlation. Group startsTrue or False
Since the correlation coefficient has an absolute value that is less than 0.6, it is not a strong relationship, hence the statement is False.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.In this problem, the correlation coefficient is of 0.08, hence:
The coefficient is positive, hence the is a positive correlation.The coefficient is of 0.08, which is less than 0.6, hence the correlation is not strong.Thus, the given statement is False.
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the answer the answer
Answer:
the answer
Step-by-step explanation:
Answer:
K?
Step-by-step explanation:
The answer of the answer is the answer.
Hope this helped :D
Which of the following demonstrates the correct first step in copying an angle?
Create a line that intersects the angle.
Draw a ray with one endpoint.
Create a point outside of the angle.
Swing an arc that intersects the angle's rays.
"Draw a ray with one endpoint" demonstrates the correct first step in copying an angle. This is further explained below.
What is the angle?In general, the distance (which is sometimes stated as a degree) that occurs between two crossing lines or surfaces at or near the point where they meet. This distance might be positive or negative.
The formation of an angle is caused by the conjunction of two rays at a single point in space. The split or 'opening' that can be seen between these two rays is referred to as a 'angle,' and the symbol denotes this particular angle. The degree is the standard unit of measurement for angles, and its values include things like 60 degrees and 90 degrees, amongst other possible combinations.
In conclusion, "Draw a ray with one terminal" illustrates the correct first step in duplicating an angle. This step shows how to replicate an angle.
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Given that is the angle bisector of A, determine the length of x. (SHOW YOUR WORK PLEASE!!!)
The length of x will be 4 cm if is the angle bisector of A.
What is an angle bisector?A straight line that splits an angle in a triangle into two congruent angles is known as the angle bisector.
Given sides;
AB=12
AE=8
BD=6
DE=x
From the triangle angle bisector theorem;
[tex]\rm \frac{BD}{DE} = \frac{AB}{AE} \\\\ \frac{6}{x} =\frac{12}{8} \\\\ x=4[/tex]
Hence the length of x will be 4 cm.
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If y is inversely proportional to z^4, when y = 16 and z = 3, then 16 = k/81
true or false
Answer: 65
Step-by-step explanation:
1 + 64 = 65
Pedro Fernández es gerente de Avon Chic, Pedro estaba interesado en las tasas de rendimiento de los últimos cinco años de dos diferentes fondos mutuos. Trujix, Inc., mostro un periodo de cinco años, tasas de rendimiento del 12; 10; 3; 9 y 11%, mientras que Fondo Corporation arrojo 13; 12:14:10 y 6%. Un cliente se acercó a Pedro y expreso su interés uno de estos fondos mutuos. ¿cuál debería escoger Pedro para su cliente?
Pedro Fernández should advice his client to go with the second mutual fund named as Fund Corporation. This is because, it showed an higher average return over the five-year period at an average of 11% beating Trujix Inc by 3%.
What is the calculation that supports the above?To get the better fund, Pedro must calculate a simple average of the interest rates of the various funds over the past 5 year period.
Trujix Inc 5-Year Average
(12 + 10+ 3 +9 + 11)/5
= 45/5
=9%
Fund Corporation 5-Year Average
(13 + 12 +14 + 10+ 6)/5
= 55/5
= 11%
Hence, the better investment is the one by Fund corporation.
Full Question
Pedro Fernández is a manager at Avon Chic, Pedro was interested in the rates of return for the last five years of two different mutual funds. Trujix, Inc., showed a five-year period, rates of return of 12; 10; 3; 9 and 11%, while Fund Corporation showed 13; 12:14:10 and 6%. A client approached Pedro and expressed his interest in one of these mutual funds. Which one should Pedro choose for his client?
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The jones family and the Connor family both bought the same boxed package of sugar cubes at the store, in which the cubes were arranged in 5 layers. After drinking of 61 cups of tea, the Joneses found that they were out of sugar. The Connors' sugar box was enough to last them thought 88 cups of tea. Both families put either 2 or 3 pieces of sugar per cup. How many sugar cubes were in the box
The number of sugar cubes in the box is 180
How to determine the number of sugar cubes?The given parameters are:
Layers = 5Pieces = 2 or 3Cups of tea = 61 and 88Multiply 61 and 88 by 2 and 3
61 * 2 = 122
61 * 3 = 183
88 * 2 = 176
88 * 3 = 264
The number of sugar cubes cannot be 122 and 264, because they are out of the range
So, we have:
183 and 176
There are 5 layers.
This means that the number of sugar cubes is divisible by 5.
The only number between 176 and 183 that is divisible by 5 is 180
Hence, the number of sugar cubes is 180
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Abigail poured 8 x 10 milliliters of water into a beaker to use for an experiment. How is 8 x 10 written as a whole number?
Answer:
80?
hshsshjsjsjjsjajjsjsnnsnsnnw
Step-by-step explanation:
hhddussisusuis
Calculate the angle of depression from the
top of the flag pole to point A.
Give your answer to 1 d.p.
A
31 feet
25 feet
The angle of depression from the top of the flag pole to point A is 36.2 degrees.
What is the angle of depression?From trigonometric ratio: cos(θ) = Adjacent / Hypotenuse
Given that;
Adjacent = 25ftHypotenuse = 31ftAngle of depression θ = ?cos(θ) = Adjacent / Hypotenuse
Cos(θ) = 25ft/31ft
Cos(θ) = 0.80645
θ = cos⁻¹( 0.80645 )
θ = 36.2°
Therefore, the angle of depression from the top of the flag pole to point A is 36.2 degrees.
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