A function showing the value of the account after t years, where the annual growth rate can be found from a constant in the function is f(t) = 2900 × (1.0624)^t and APY is 6.24%.
What is Compound Interest?Compound interest in simple words is the interest earning for your savings with the interest which those savings earn.
The formula for calculating the amount in Compound Interest is,
A = P( 1 + [tex]\frac{r}{n}[/tex] )ⁿᵇ
where A is the amount, P is the principal, r is the rate of interest, n is the number of times interest compounded in a year and b is the number of years.
Here, P = $2900, r = 6.1% = 0.061, n = 4 (quarterly) and b = t years
A = 2900 (1 + [tex]\frac{0.061}{4}[/tex])^4t
A = 2900 (1.0153)^4t
A = 2900 × (1.0624)^t
So A can be said as a function of t.
f(t) = 2900 × (1.0624)^t
Percentage of growth per year (APY) = ( 1 + [tex]\frac{r}{n}[/tex] )ⁿ - 1
= (1 + [tex]\frac{0.061}{4}[/tex])⁴ - 1
= 1.0624 - 1
= 0.0624 = 6.24%
Hence the function of the value of the account after t years is f(t) = 2900 × (1.0624)^t, where the value 1.0624 is a constant.
Percentage of growth per year is 6.24%.
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HELP ASAAAPPPO! Dawn is making an abstract painting with two triangles. The dimensions of the painting are shown below:
Two triangles share the same height of 8 inches. One triangle has a base of 6 inches and the other is 10 inches.
The total area of the two triangles is
???
square inches.
the total area of the two triangles as shwon in the image is 70 in²
What is area?Area can be defined as the total portion occuppied by a plane fiqure.
To calculate the total area of the two triangles, we use the formula below.
Formula:
Total area of the triangle = Area of the pink triangle+Area of the purple triangleArea of the purple triangle = bh/2.................. Equation 1Where:
b = Base of the purple triangle = 8 inh = Height of the purple triangle = 10 inSubstitute these values into equation 1
Area of the purple triangle = 8×10/2Area of the purple triangle = 40 in²Similarly,
Area of the pink triangle = BH/2........ Equation 1Where:
B = 6 inH = 10 inSubstitute these values into equation 2
Area of the pink triangle = 6×10/2Area of the pink triangle = 30 in²Therefore, the total area of the two triangles is 40+30 = 70 in².
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(2-3)^-1 in indices please answer
Answer:
1
Step-by-step explanation:
First, simplify the parentheses.
2 - 3 = -1
Then, put this simplified value into the original expression.
(2 - 3)^(-1)
= (-1)^(-1)
Finally, execute the exponent function.
(-1)^(-1) = 1/1 = 1
Consider the piecewise function shown on the graph, which is composed of three different function types.
-10 -8 -6 -4 -2
10-
8
6
4
2
-2
-4
6
-8-
02
-10-
4 6
Match each piece of the function with its domain.
8 10
The quadratic is the left-most piece. This exists on the interval (-infty, -2).
The linear piece is the center piece and exists on the interval (-2,6).
The square root piece is the right-most piece and exists on (6, infty).
These intervals are describing how each piece lines up with the x-axis, as illustrated in the picture.
The required description of the given piecewise function are as follows:
quadratic → (-∞, -2); linear → (-2, 6) and square root → (6, ∞).
What is a piecewise function?A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).
The graph is given in the question, as shown
1. quadratic function:
This the sub-function define between the interval (-∞, -2).
2. linear function:
This the sub-function define between the interval (-2, 6).
3. square root function:
This the sub-function define between the interval (6, ∞).
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please help!
The measure of angle J is 120⁰ and is supplementary to the measure of angle K. If the measure of angle K is 12 x , what is the value of x ?
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.
Using the fact that the angles are supplementary, we can write and solve a linear equation to find that x = 5°.
How to find the value of x?
Remember that two angles are supplementary if the addition of their measures is equal to 180°.
Here we know that angles J and K are supplementary, then we know that:
J + K = 180°
Here we also know that:
J = 120°
K = 12x
So we can write a linear equation of the form:
120° + 12x = 180°
12x = 180° - 120°
12x = 60°
x = 60°/12 = 5°
x = 5°
We conclude that the value of x is 5°.
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Can anyone solve this? 30 points (no bots, please)
help meeeeeeeeeee pleaseee
(a) The population of the state was 18.5 million in 2000. (b)The population of the state will reach 26.6 million in the year 2002
What is Population ?A population is a distinct collection of people, whether that group consists of a nation or a population that shares a specific trait. A population is the group of people from which a statistical sample is taken in statistics. As a result, a population can be defined as any group of people who have something in common.
Since t = 0 ,
Then A = 18.5
(b) The population of the state will reach 26.6 million in the year 2002
2002, by using the formula is 18.5e^0.173*t
Given,
A= 26.6
Then,
[tex]A = 18.5 x e^{(0.1708t)} 26.6[/tex]
[tex]= 18.5 x e^{(0.1708t)} \frac{26.6}{18.5}[/tex]
= [tex]e^{(0.1708t)} 1.437838[/tex]
= [tex]e^{(0.1708t)} \ln (\frac{1.437838}{0.1708})[/tex]
t = 2.126116
t =2
Therefore, 2 is the round down to the nearest years. So 2002 is the approximate year the population reached 26.6 million.
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i need help with math please okay help with math pelase
The function [tex]y = (\frac{1}{2})^x[/tex] is a decreasing function.
The function [tex]y = (\frac{1}{2})^x[/tex] is shallower from left to right.
The value of the function [tex]y = (\frac{1}{2})^x[/tex] is unity at the y-intercept.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
The given function is [tex]y = (\frac{1}{2})^x[/tex] which is an exponential function cause the exponent is the variable.
Now, At x = - 2 y = 4 ⇒ (- 2, 4),
x = - 1, y = 2 ⇒ (- 1, 2).
x = 0, y = 1 ⇒ (0, 1).
x = 1, y = 1/2 ⇒ (1, 1/2).
x = 2, y = 1/4 ⇒ (2, 1/4).
x = 3, y = 1/8 ⇒ (3, 1/8).
The function is a decreasing function as the value of x increases the value of the function is decreasing.
The function is shallower from left to right.
The value of the function is unity at y-intercept as anything raised to the zero power is 1.
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help meeeeeeeeeee pleaseee
Step-by-step explanation:
your teacher could have explained this better by telling us that A(t) is the remaining amount of the original isotope.
(a)
we start with 200 g and let it do its thing for 25 years.
all we need to do is enter the number of years into the function formula (as this is a college question you are able to work with functions, right ?) and calculate :
A(25) = 200e^(-0.054 × 25) = 200e^-1.35 =
= 51.84805213... g ≈ 51.85 g
after 25 years, about 51.85 g of the sample will be left.
assuming you have a calculator (at least on your computer) that was really "difficult", don't you think ?
(b)
half of the original amount is 200/2 = 100 g.
so, we need to find the value for t so that A(t) = 100.
100 = 200e^(-0.054 × t)
100/200 = 1/2 = 0.5 = e^(-0.054 × t)
ln(0.5) = -0.054 × t
t = ln(0.5) / -0.054 = 12.8360589... years
I assume you need to round to the nearest hundredth here as well :
after about 12.84 years the sample will decay to half of the original amount.
Caleb went to the grocery store and purchased cans of soup and frozen
dinners. Each can of soup has 200 mg of sodium and each frozen dinner has
500 mg of sodium. Caleb purchased a total of 15 cans of soup and frozen
dinners which collectively contain 4500 mg of sodium. Determine the
number of cans of soup purchased and the number of frozen dinners
purchased.
Answer:
Cans of soup = 10
Frozen dinners = 5
Step-by-step explanation:
To determine the number of cans of soup and frozen dinners Caleb purchased, set up and solve a system of equations based on the given information.
Let x be the number of cans of soup Caleb purchased.
Let y be the number of frozen dinners Caleb purchased.
Each can of soup has 200 mg of sodium and each frozen dinner has 500 mg of sodium. The total amount of sodium in the purchased cans and frozen dinners is 4500 mg. Therefore:
[tex]200x + 500y = 4500[/tex]
Caleb purchased a total of 15 cans of soup and frozen dinners. Therefore:
[tex]x + y = 15[/tex]
To solve the system of equations, rearrange the second equation to isolate x:
[tex]\begin{aligned}x + y &= 15\\x + y -y&= 15-y\\x&=15-y\end{aligned}[/tex]
Substitute this into the first equation to eliminate the term in x, and solve for y:
[tex]\begin{aligned}200(15-y) + 500y &= 4500\\3000-200y + 500y &= 4500\\3000+300y &= 4500\\3000+300y-3000 &= 4500-3000\\300y&=1500\\300y \div 300&=1500 \div 300\\y&=5\end{aligned}[/tex]
Therefore, Caleb purchased 5 frozen dinners.
Substitute the found value of y into the rearranged second equation and solve for x:
[tex]\begin{aligned}x&=15-y\\x&=15-5\\x&=10\end{aligned}[/tex]
Therefore, Caleb purchased 10 cans of soup.
Answer:
Caleb purchased 10 cans of soup and 5 frozen dinners.
Step-by-step explanation:
Caleb purchased 10 cans of soup and 5 frozen dinners.
Let no. of can of soup be x and no. of frozen dinner be y.
To solve this, we can set up the following system of equations:
[tex]\tt x + y = 15[/tex]......[i]
[tex]\tt 200x + 500y = 4500[/tex]......[2]
Let's find the value by elimination method:
Multiplying equation one by 200.
we get,
[tex]\tt 200 x+ 200 y = 15*200[/tex]
[tex]\tt 200x +200 y =3000[/tex]
Subtracting equation 2 with equation 1.
[tex]\tt (200x+500y)-(200x +200 y) =4500-3000[/tex]
[tex]\tt \tt 300y = 1500[/tex]
[tex]\tt y =\dfrac{1500}{300}[/tex]
[tex]\tt y = 5[/tex]
Substitute the value of y into the first equation to find x.**
[tex]\tt x + 5 = 15[/tex]
[tex]\tt x = 15 - 5[/tex]
[tex]\tt x = 10[/tex]
Therefore, Caleb purchased 10 cans of soup and 5 frozen dinners.
Evaluate 3×sup(2,4)+1.
Answer:
49
hope this helps!!
PLEASE ANSWER NEED THIS REALLY SOON!!!! OFFERING 100 PTS
A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive states that the revenues for online ads have more than doubled that of the revenues for printed ads since starting the online version of the paper. Use the graph below to justify the lead executive’s statement and to determine the approximate year that the two ad revenues were equal.
Graph with x axis labeled years. Y axis labeled revenue in dollars. The line for printed ad revenue starts at 0, 3 and goes through the10, 2. The line for online ad revenue starts at 0, 0 zero and goes through the 10, 3.
A) The lead executives statement has been justified below considering the fall and rise of the graph line.
B) Between the years 7 and 8.
How to Interpret Linear Graphs?A) Looking at the attached graph, we can trace that the printed ad's revenue peaked at $3 million and then began to fall steadily. The online ad revenue started with nothing and thereafter gradually increased in value to millions of dollars. Now, since the printed ad revenue has been declining and online ad revenue is seen to be increasing, it means that the lead executive's assertion is accurate.
B) Both curves are seen to intersect between the seventh and eighth year, I would say around the middle of year 7, and both online ads and printed ads generated an approximate revenue of $2.2 million each
Between the years 7 and 8.
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Pls help I forgot how to do this.
find the solution to the following system substitution y=-2 x -3 y= 3 x + 12
The solution to the system substitution is (x , y) = (-3,3).
What is substitution?The substitution operation in algebra is used to systematically replace instances of a symbol with a given value in various settings involving formal objects containing symbols (commonly called variables or indeterminates).A fundamental operation in computer algebra is substitution.In computer algebra systems, it is frequently abbreviated as "subs" or "subst."Here it is given that,
y=-2 x -3 and y= 3 x + 12
Take y=-2 x -3 as equation 1,
y= 3 x + 12 as equation 2'
by equating both equations,
-2x-3=3x+12
-3-12=3x+2x
5x=-15
x=-15/5
=-3
substituting the value of x in the equation1
y=-2x-3
y=-2(-3)-3
=3
Hence, The solution to the system substitution is (x , y) = (-3,3).
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Which choice is the solution to the inequality below?
6x>72
OA. x< 12
OB. x> 12
OC. x2 72
OD. x>72
The solution to the inequality 6x > 72 is option B x > 12
What is an inequality?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
A is not equivalent to b in any scenario. Since a is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.
There are two forms of inequality relations that are not strict, in contrast to strict inequalities:
The notation a ≤ b or a ⩽ b means that a is less than or equal to b (or, equivalently, at most b, or not greater than b).
The notation a ≥ b or a ⩾ b means that a is greater than or equal to b (or, equivalently, at least b, or not less than b).
Given, the inequality is 6x>72
6x > 72
Dividing by 6 on both sides of inequality, we get,
6x/6 > 72/6
⇒ x > 12
Hence, option B is correct.
The solution to the inequality 6x > 72 is option B, x > 12
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Trapezoid ABCD where AB║CD is shown below
diagonals AC and DB intersect MN at E
and AD ≅ AE
If m∠ DAE =35° and m∠ DCE=25°
m∠ NEC=30° determine and state m∠ ABD
By using various properties of triangles, we get the value of [tex]\angle[/tex]ABD is 47.5°.
What are the properties of a triangle?
A triangle's sides and angles serve as the foundation for all of its characteristics. Triangular closed polygons with three sides and three vertices are what the word "triangle" means. The three internal angles of a triangle add up to 180°.
Let us first name a few angles that we will be using throughout the solution.
Let, [tex]\angle[/tex]DEN=a
[tex]\angle[/tex]ENC=c
[tex]\angle[/tex]MEB=b
[tex]\angle[/tex]EMB=d
Now, since it is given that AD ≅ AE, let us assume that triangle ADE is an isosceles triangle, with AD=AE.
Hence we get
[tex]\angle[/tex]DAE+[tex]\angle[/tex]ADE+[tex]\angle[/tex]AED=180° (angle sum property)
35°+2[tex]\angle[/tex]ADE=180°
[tex]\angle[/tex]ADE=[tex]\angle[/tex]AED=72.5°
Next, we know that
[tex]\angle[/tex]AED+a+[tex]\angle[/tex]NEC=180° (linear pair property of angles on a straight line)
72.5°+a+30°=180°
a=77.5°
Since a=b (opposite angles)
we get, a=b=77.5°
Now in triangle ENC, if we take the sum of angles, we get
[tex]\angle[/tex]NEC+[tex]\angle[/tex]NCE+c=180° (angle sum property)
30°+25°+c=180°
c=125°
We also know that the sum of interior angles made by an intersecting line between 2 parallel lines (given shape is a trapezoid) is 180, hence we get
c+d=180°
d=55°
In triangle MBN, we have
d+b+[tex]\angle[/tex]MBD=180° (angle sum property)
55°+77.5°+[tex]\angle[/tex]MBD=180°
[tex]\angle[/tex]MBD=47.5°
Therefore, we get the value of [tex]\angle[/tex]ABD=47.5°
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An amount of $250 is contributed at the end of each month, and the balance earns interest at an APR of 6.2%. What is the total amount accrued after 7 years?
The required amount at the end of the 7 years is given as $32,340
Given that,
An amount of $250 is contributed at the end of each month, and the balance earns interest at an APR of 6.2%.
Investment is defined as when an individual spends money on something that returns him or her higher money than the money they or invest.
here,
According to the question,
The total amount accrued after 7 years is given as,
[tex]y\:=\:250\cdot12\cdot 7\left[1\:+\:\frac{0.062}{12}\right]^{12\cdot 7}\\y = $32,340[/tex]
Thus, The required amount at the end of the 7 years is given as $32,340.
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Find 8 * 3 1/2 using the distributive property
The value of the expression upon evaluation by using the distributive property as required is; 28.
What is the value of the given expression using the Distributive property?It follows from the task content that the distributive property is to be used to determine the value of the expression given.
Since the given expression is; 8 • 3 ½.
It follows that the expression can be written as follows;
8 ( 3 + ½ )
Hence, by the distributive property, it follows that we have;
( 8 × 3 ) + ( 8 × ½ )
= 24 + 4
= 28.
On this note, the value of the expression is; 28.
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Kim has $45 to spend for a day at the zoo. She pays $17 for admission, $8 for lunch, and $4 for a snack. Use integers to write an expression that represents the amount of money Kim has left and determine how much she has.
I need help guys I don’t know what to do or how to do it can someone help me out?
Answer:
I'll help
Step-by-step explanation:
the entrance fee to the skating rink=$5
each minute the skater uses the rink costs=$0.25
The temperature in Austin is 33.5◦F and rising at a rate of 2.5◦F per hour. The temperature in San Antonio is 37.5◦F and rising at a rate of 1.5◦F per hour. Write an inequality that shows how long the temperature in Austin will remain colder than that in San Antonio.
The inequality that shows how long the temperature in Austin will remain colder than that in San Antonio is 33.5 + 2.5t < 37.5 + 1.5t and the time is less than 4 hours
How to determine the inequality and the intervalsFrom the question, we have the following parameters that can be used in our computation:
Austin
Initial temperature = 33.5 degrees Fahrenheit
Rate of increment = 2.5 degrees Fahrenheit
San Antonio
Initial temperature = 37.5 degrees Fahrenheit
Rate of increment = 1.5 degrees Fahrenheit
The above parameters mean that
Current temperature = Initial temperature + Rate of increment x Number of hours
So, we have
Austin: A(t) = 33.5 + 2.5t
San Antonio: B(t) = 37.5 + 1.5t
When Austin is colder than San Antonio, we have
A(t) < B(t)
Substitute the known values in the above equation, so, we have the following representation
33.5 + 2.5t < 37.5 + 1.5t
Evaluate the like terms
t < 4
Divide both sides by 1
t < 4
Hence, the interval is less than 4 hours
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g(x)=3(2)^x find g(3)
Answer:
g(3) is 24
Step-by-step explanation:
To find the value of g(3), we need to plug 3 into the function g(x) and evaluate the resulting expression. The function g(x) is defined as g(x) = 3(2)^x. When we plug 3 into this function, we get g(3) = 3(2)^3. To evaluate this expression, we need to calculate 2^3, which is 8. Therefore, g(3) = 3 * 8 = 24.
In summary, the value of g(3) is 24.
Answer:
g(3) = 24
Step-by-step explanation:
Given information,
→ g(x) = 3(2)^x
Then the value of g(3) will be,
→ g(x) = 3(2)^x
→ g(3) = 3(2)³
→ g(3) = 3(8)
→ [ g(3) = 24 ]
Hence, the value of g(3) is 24.
Helpppppp pleasee due soon
Answer:
[tex]y = \sqrt{34} \\\\x = \sqrt{106}[/tex]
Step-by-step explanation:
Is the following statement linear or exponential?
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week. HELP PLEASE
Answer:
exponential
Step-by-step explanation:
the 14% of a number will be always greater because the numbers themselves will be greater
Question
the value of 2 cos x - cos 3x - cos 5x is
not spam
Required Answer -:
16cos³ x sin² x
Let's Begin2cos x - ( cos 3x + cos 5x )
= 2cos x - 2 cos 4x cos x
= 2cos x 2sin² 2x
= 4 cos x ( 2sin x cos x)²
= 16cos³ x sin² x
Thus,, the value of 2 cos x - cos 3x - cos 5x is = 16cos³ x sin² x
Which of the following makes NO distinction between an explanatory variable X and a response variable Y (i.e., you can interchange the roles of X and Y and get the same result)?CorrelationOnly correlation makes no distinction between the X and Y variables. With regression the line would be flipped.
The term that makes NO distinction between an explanatory variable X and a response variable Y is Correlation , the correct option is (a) .
In the question ,
four options are given ,
we have to select the option that makes no distinction between explanatory variable X and a response variable Y .
Response Variable is the (dependent variable) measures the outcome of the study.
Explanatory Variable is the (independent variable) helps to explain or influence changes in a response variable.
So , Correlation makes no distinction between explanatory and response variables.
So , it makes no difference in calculating the correlation , which variable you call x and which you call y .
Therefore , the correct option is (a) .
The given question is incomplete , the complete question is
Which of the following makes NO distinction between an explanatory variable X and a response variable Y (i.e., you can interchange the roles of X and Y and get the same result) ?
(a) Correlation
(b) Regression
(c) Both correlation and regression make no distinction between X and Y.
(d) Both correlation and regression make distinction between X and Y.
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A new ramp is being built at the school. It will be two meters long and one meter high. What will the slope of the ramp be?
Answer:
1/2
Step-by-step explanation:
Slope is rise (height)/run(length)
Slope is 1 meter/2 meters
Solve the following inequalities 1/2(3x - 2) ≤ (x+4)
Answer:
x ≤ 10
Step-by-step explanation:
3/2 x - 1 ≤ x +4
3/2 x - x ≤ 1 + 4
(3-2)/2 x ≤ 5
1/2 x ≤ 5
2 * 1/2 x ≤ 2 * 5
x ≤ 10
URGENT HELP PLeASE please just answer b and c
Answer:
b) 2/9
c) 1/3
Step-by-step explanation:
The probability of a desired event happening is the number of ways the desired event can happen divided by the total number of possible outcomes.
a) Correct
b)
There are 9 possible outcomes.
2 outcomes are negative.
p(negative) = 2/9
c)
There are 3 outcomes that are more then 3.
p(more than 3) = 3/9 = 1/3
Give the quotient and remainder.
355÷8
Answer:
355 ÷ 8 = 44 with remainder 3
Step-by-step explanation:
44
-------------------------
8 | 355
- 32
--------
35
- 32
------
3
"Marsha has 54% left on her phone. Every 1 minute her battery life decreases by 1/2%. Write an equation to represent marshas phone battery life."
The answer to this Question based on Linear Relation is given below
What is Linear Relation?
It is a relation between two variables in which one variable has linear behaviour as other
means if one variable increases or decreases then other variables does same behaviour linearly
Solution:
let us denote the battery by b and time by t
b = 54 - t/2
this relation satisfies all the conditions that are given in Question and gives variation of battery with time and this if plotted on graph will give a linear straight line
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