Ethan and Evan are twins. They each deposit $3,000 into separate bank accounts.Their accounts each accrue interest annually as shown in the tables below.
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Part A.
Ethan's account can be model as a linear equation since it is increasing at a constant rate of the form:
[tex]y=240x+3000[/tex]And Evan's account can be model as a exponential equation of the form:
[tex]y=3000(1.08)^x[/tex]Part B:
Evaluate the 1st and 2nd equation for x = 5:
[tex]\begin{gathered} y=240(5)+3000=4200 \\ y=3000(1.08)^5=4407.98 \\ so\colon \\ \frac{4407.98}{4200}=1.05 \end{gathered}[/tex]It would be 1.05 higher
Related Questions
y - y1 = m (x - x1 ) write an equation in point slope form given point ( 4, -3 ) and m = 1
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The point-slope form of a line is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
Replacing with m = 1 and the point (4, -3):
y - (-3) = 1(x - 4)
y + 3 = x - 4
In health class, Leslie is learning about making healthy food choices. For a lesson on digestive health, her teacher asks everyone to track how much fiber they eat daily. At breakfast, Leslie has a banana. She also has raisin bran cereal, which contains 3.8 grams of fiber. In all, Leslie eats 6.7 grams of fiber at breakfast.
Use an equation to find the amount of fiber in the banana.
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The amount of fiber in the banana is 2.9 grams of fiber.
What is a equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
From the. information, she has raisin bran cereal, which contains 3.8 grams of fiber and in all, Leslie eats 6.7 grams of fiber at breakfast.
Let the fiber in banana be b. This will be illustrated as:
b + 3.8 = 6.7
Collect like terms
b = 6.7 - 3.8
b.= 2.9
The fiber is 2.9 grams
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Evaluate (3√2-1) (3√2+1)
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Answer:
9√3 converted is 15.58845727
PLSSS HELPPPPPthe number of stores opened by a coffee company can be modeled by the exponential function graphed on the grid. Based on the graph, which statement does not appear to be true.
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Let's analyze the statements to see which one is not true.
Statement F. The coffee shop company had opened 400 stores by the end of 1992.
The horizontal axis on the graph (the x-axis) represents the number of years that have passed since 1992, thus the year 1992 is at x=0 on the graph.
The vertical axis (the y-axis) represents the number of stores.
As we can see in the following diagram, the red point represents the number of stores at x=0 (at the year 1992):
it is true that the coffee shop had 400 stores by the end of 1992.
Statement G. The coffee shop opened 100 stores in 1 year.
To see if this is true, we look at x=1, which represents 1 year, and check for the number of stores corresponding to 1 year:
This point is at (1,500) --> After 1 year there were 500 stores.
Since they started with 400 stores, this means that it is true that they opened 100 stores in 1 year.
Statement H. Every year the number of stores the coffee company opened increased by 25%.
We can find if this is true just by looking at the form of the graph. This graph has an exponential curve which means that the growth increases at every step. Thus there is an increase in the coffee shop that they open every year. This statement is true.
Statement J. Since 1992 the coffee shop company has opened 250 stores each year.
As we saw with the previous statement, the number of shops opened every year is not constant, it increases with time. Thus, since they do not open the same amount of shops every year, this option the one that is not true.
Answer: Statement J
Andrew constructed a triangle so that the measurement of 1 and 2 were congruent. if angle 3 measured 70 degrees, what is the measure of angle 1?
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Andrew constructed a triangle such that the measurements of angles m<1 and m<2 are congruent.
The above statement can be inferred from concept of congruency of triangles. The oppsoite sides of the two congruent angles in a traingles are also equal.
From the above statement we can deduce the type of a triangle that Andrew drew as follows:
[tex]\text{Andrew drew a isoceles triangle}[/tex]An isoceles triangle has two equal sides and angles i.e congruent sides and interior angles. Hence,
[tex]m\angle1\text{ = m}\angle2\ldots\text{ Eq1}[/tex]The following information is given for the third interior angle m<3 of the isoceles triangle:
[tex]m\angle3\text{ = 70 degrees}[/tex]We need determine the angle measure of the angle 1. Recall that the sum of interior angles of a triangle is given as follows:
[tex]m\angle1\text{ + m}\angle2\text{ + m}\angle3\text{ = 180 degrees }\ldots\text{ Eq2}[/tex]Substitute Eq1 into Eq2 as follows:
[tex]\begin{gathered} m\angle1\text{ + m}\angle1\text{ + m}\angle3\text{ = 180} \\ \\ 2\cdot m\angle1\text{ + m}\angle3\text{ = 180} \end{gathered}[/tex]Substitute the angle measurement of angle ( 3 ) in the expression above and solve for angle ( 1 ) as follows:
[tex]\begin{gathered} 2\cdot m\angle1\text{ + 70 = 180} \\ 2\cdot m\angle1\text{ = 110} \\ m\angle1\text{ = }\frac{110}{2} \\ \\ m\angle1\text{ = 55 degrees }\ldots\text{ Answer} \end{gathered}[/tex]A machine can fill 5,400 bottles in 3 hours. How many bottles can it fill in 8 hours?
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Answer:
14400
Step-by-step explanation:
Use the graph of f to describe the transformation that results in the graph of g. Then sketch the graphs of g and f.
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EXPLANATION
Since we have the function:
[tex]f(x)=(\frac{1}{3})^x[/tex]Graphing this an the transformation into a graph calculator we have:
We can see that the transformated function is translated 2 units to the right, and that It is also translated 4 units down.
Thus, the transformations are the following:
g(x) is the graph of f(x) translated 2 units to the right and 4 units down.
John recently purchased $4,106.00 worth of a stock that is expected to grow in value by 8% each year for the next ten years.Assuming this growth forecast holds, which function will show the value of John's stock in tyears?A(t) = 1.08(54,106)A(O) = 54,106(1.1)A(0) = 54,106(1.08)A(t) = $4,106(1.08)
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The exponential growth formula:
[tex]A(t)=A_0(1+r)^t[/tex]Given:
[tex]\begin{gathered} A_0=\text{ \$4106} \\ t=10yrs \\ r=8\%=\frac{8}{100}=0.08 \end{gathered}[/tex]Therefore,
[tex]A(t)=4106(1+0.08)^t=4106(1.08)^t[/tex]Hence, the answer is
[tex]A(t)=\text{ \$}4106(1.08)^t[/tex]if a figure has four corners then it is a quadrilateral and figure has four corners therefore it is a quadrilateral which statement illustrate this to be true the large attachment account example the law of syllogism the law contrapositive
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The given conditions are true:
law of contrapositive
Solve y^3= −125.
y = −5
y = ±5
y = −25
y = ±25
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Answer:
A. y=-5Step-by-step explanation:
Use the order of operations.
PEMDAS stands for:
ParenthesesExponentsMultiplyDivideAddSubtractDo exponents first.
[tex]\sf{y^3=-125}[/tex]
[tex]\sf{x=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\dfrac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\dfrac{-1+\sqrt{3}i}{2}}}[/tex]
[tex]\rightarrow \sf{y=\sqrt[3]{-125},\:y=\sqrt[3]{-125}\dfrac{-1+\sqrt{3}i}{2},\:y=\sqrt[3]{-125}\dfrac{-1-\sqrt{3}i}{2}}[/tex]
[tex]\sf{\sqrt[3]{-125}=\boxed{\sf{-5}}}[/tex]
Therefore, the correct answer is y=-5.
I hope this helps, let me know if you have any questions.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{y^3 = -125}[/tex]
[tex]\large\text{Solve/take the cube root}[/tex]
[tex]\mathsf{(-125)^{^\dfrac{1}{3}}}\mathsf{ = y}[/tex]
[tex]\mathsf{y = (-125)^{^\dfrac{1}{3}}}[/tex]
[tex]\large\text{Simplify it}[/tex]
[tex]\mathsf{y = -5}[/tex]
[tex]\huge\text{Therefore, your answer is: \boxed{\mathsf{y = -5\ (\rm \bold{O}ption\ A.)}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
A store manager records a positive number to show when a deposit is made to the store's bank account and a negative number to show withdrawals.
Which equation could represent how the store manager records making 3 withdrawals of $36 each?
O 3 x 36 108
O 3x-36= -108
-3 x 36 108
O-3 x-36= -108
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Answer:
03*36 108 the positive number
The numerator of the sum 1+1/3+2 is (a) 1 (b) 2 (c) 5 (d) 6.
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The expression is given as,
[tex]\frac{1}{2}+\frac{1}{3}[/tex]Note that the denominator of both the fractions are prime numbers. So their lowest common multiple, LCM(2,3) will be the product of the numbers,
[tex]undefined[/tex]Please help! ♥️I have to get it done by the end of today thank youu sm♥️
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The center of circle is P, diameter of circle is RQ and three radii are PR, PQ, PS.
What is circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.
The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.
From the given figure:
P = Center of circle
RQ = diameter of circle
PQ,PS,PR = radii of circle
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what's the answer?[tex] - 4 \sqrt{15 \times - \sqrt{3} } [/tex]
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In decimal form this is equal to -17.22.
Express 1.27times 10^3 in decimal notation
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1.27 x 10^3
10^3 is 1000
1.27 x 10^3 = 1.27 x 1000 = 1270
[tex]1.27x10^3\text{ = 1.27}x1000\text{ = 1270}[/tex]Answer:
1270
you have torn a tendon and is facing surgery to repair it. the surgeon explains the risks to you: infection occurs in 3% of such operations, the repair fails in 17%, and both infection and failure occur together in 2%. what percentage of these operations succeed and are free from infection? give your answer as a whole number.
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Our required probability is 99.82% or a 100%
%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage.
What is the definition of percentage in statistics?
Percentages. The use of percentages to express statistics is one of the most popular. The word "percent" simply refers to "per hundred," and the sign for percentage is %. By dividing the whole or whole number by 100, one percent (or 1%) is equal to one hundredth of the total or whole.
Given that P(operational infection occurs at a 3% rate)
P(operational repair failures) = 17%
P(infection and failure happen simultaneously) = 2%
The first thing we'll discover is that P(infection or failure) is given by 0.03 + 0.17 - 0.02 = 0.18 = 0.18%.
Therefore, the probability that these procedures will be successful and infection-free is given by 100 - 0.18 = 99.82%.
Consequently, 99.82% of a probability is needed.
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help meeeeeeeeee pleaseee !!!!!
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The total number of toys sold if the daily sales of the toy is $6.50 is 2750 toys.
Functions and valuesEach element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The independent values are known as the domain while the dependent are the codomain.
Given the function that represents the price-sales relationship for number of toys as;
y = 6000 - 500x
If the daily sales of the toy is $6.50, the total toys sold will be:
y = 6000 - 500 (6.50)
y = 6000 - 3250
y = 2750 toys
This gives the total number of toys sold.
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What is the range of the following numbers? 12, 20, 18, 25.6 OA. 5 O B. 167/ O C. 18 O D. 19 E. 25
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
12, 20, 18, 25 , 6
range = ?
We must order the data.
Step 02:
6 , 12 , 18 , 20 , 25
Range = 25 - 6 = 19
The answer is:
The range is 19
I just need someone to show how to brake down and solve this?
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23)Suppose on a certain MTH 101 quiz, you scored a 94%. The mean score in the class was 82.6% with a standard deviation of 12.4%.a)How many standard deviations away from the mean are you?b)Using the following z-table snippet, determine what percent of your classmates you outperformed:
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SOLUTION
Recall the z score formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]The given values are
[tex]x=94,\mu=82.6,\sigma=12.4[/tex]Therefore the score is:
[tex]\begin{gathered} z=\frac{94-86.4}{12.4} \\ z=0.6129 \end{gathered}[/tex]Therefore the score is 0.6129 standard deviations away from the mean.
b. From the table, the required value is 0.729069
Hence the percentage is 72.9069%
Find the length of the legs of a night triangle whose hypotenuse is 25cm and whose area is 84cm use phytagorean theorem.
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Answer:
Explanation:
Here, we want to find the length of the legs of the right triangle given the area and the length of the hypotenuse
We have the sketch of the triangle as shown below:
According to Pythagoras' the square of the length of the hypotenuse equals the sum of the squares of the length of the two other sides
Thus, mathematically:
[tex]a^2\text{ + b}^2\text{ = 25}^2[/tex]Mathematically, we have the area calculated as:
[tex]\begin{gathered} A\text{ = }\frac{1}{2}\times b\times h \\ \\ 84\text{ = }\frac{1}{2}\times a\times b \\ \\ a\text{ = }\frac{168}{b} \end{gathered}[/tex]Now, we have two equations to solve simultaneously
Substitute equation ii into i
We have that as:
[tex][/tex]In ∆PQR, p=13 inches, q=18 inches and r= 12 inches. Find the area of ∆PQR to the nearest square inch.
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Given data:
The first side of the triangle is p=13 inches.
The second side of the triangle is q=18 inches.
The third side of the triangle is r= 12 inches.
The semi-perimeter is,
[tex]\begin{gathered} s=\frac{p+q+r}{2} \\ =\frac{13\text{ in+18 in+12 in}}{2} \\ =21.5\text{ in} \end{gathered}[/tex]The expression for the area of the triangle is,
[tex]\begin{gathered} A=\sqrt[]{s(s-p)(s-q)(s-r)_{}} \\ =\sqrt[]{21.5\text{ in(21.5 in-13 in)(21.5 in-18 in)(21.5 in-12 in)}} \\ =\sqrt[]{(21.5\text{ in)(8.5 in)(3.5 in)(9.5 in)}} \\ =77.95in^2 \end{gathered}[/tex]Thus, the area of the given triangle is 77.95 sq-inches.
Using the conjugate zeros theorem to find all zeros of a polynomial
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We know that 1+i is a root of the polynimial. This also implies that 1-i is also a root of the polynomial. In other words, the term
[tex](x-1+i)(x-1-i)[/tex]is a factor of our polynomial. This last expression can be written as
[tex](x-1+i)(x-1-i)=x^2-2x+2[/tex]so, in order to find the remaining zero, we can compute the following division of polynomials,
which gives
Therefore, the remaining root is x=1.
In summary, the answer is:
[tex]1+i,1-i,1[/tex]Solve for 5x - 3y = -45the equations beside it are the answer choices.
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You have the following equation:
5x - 3y = -45
In order to solve the previous equation for y, you proceed as follow:
5x - 3y = -45 subtract 5x both sides
- 3y = -45 - 5x multiply by -1 both sides
(-1)(-3y) = (-1)(-45 - 5x)
3y = 45 + 5x divide by 3 both sides
y = 45/3 + 5/3 x order the right side
y = 5/3 x + 15
Hence, the solution for y is y = 5/3 x + 15
Solve the direct variation problemsJohn is working at a bank and receives 25 dollars an hour. a. Write an equation that relates x and y.b. what is the constant of proportionality?
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Let "x" represent the number of hours that John works and "y" represent John's earnings after working x hours.
b) John receives $25/hour → this value represents the change in John's earnings for every unit increase of x, which is, the constant proportionality (k) of the relationship.
a) If x and y have a direct relationship, you can express it as follows:
[tex]y=25x[/tex]Find the slope and y-intercept of the graph of the linear equation. Give the y intercept in point form in the space provided. Use the equation editor to enter the slope if there are fractions. 5x - y = -5
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The general equation of a line is:
y = mx + b
Here, y refers to how far up and x refers to how far along.
m is slop, that is the change in y to the change in x
and b is y intercept or the point where the value of x is zero.
So,
The given equation is:
5x - y = -5
The simplest step is to map the given equation with the standard equation (y = mx + b).
So,
- y = -5 -5x
Multiplying both sides by -1, we get
y = 5 + 5x
or
y = 5x + 5
Now, if we map this form with the standard equation (y = mx + b), we get
m = 5 and b = 5
Therefore, the slope (m) is equal to 5.
Also, y-intercept (b) is equal to 5.
Select your answer to the question below: * AABC is shown below. Suppose the triangle is translated 5 units to the right and 7 units down. What are the coordinates of the image of vertex B after this transformation? : Y 6 B'C 2 A C. 8 G 2 4 A (8-6) B (2-6) c (-3.-6) D (2.0)
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From the given graph,
The coordinates of point B are (-3, 7)
The triangle ABC has translated 5 units to the right and 7 units down
That means the x coordinate of B must add by 5 and the y-coordinate must subtract by 7
The rule is (x + 5, y - 7)
The image of point B is B'
B' = (-3 + 5, 7 - 7)
B' = (2, 0)
The image of point B is (2, 0)
If two lines intersect to form a right angle, then they are
..(perpendicular, parallel, obtuse
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quilt squares are cut on the diagonal to form triangular quilt pieces. the hypotenuse of the resulting triangles is 16 inches long.what is the side of each piece. A.8in B.8and 3 in C.16and 2in D. 8and2in.
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The right triangle formed is shown below
From the diagram,
x represents the side of the square. Recall that a square has equal sides
To find x, we would apply the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
From the diagram,
hypotenuse = 16
one leg = other leg = x
By substituting these values into the formula,
16^2 = x^2 + x^2
16^2 = 2x^2
256 = 2x^2
Dividing both sides by 2,
2x^2/2 = 256/2
x^2 = 128
Taking square root of both sides, we have
[tex]\begin{gathered} x\text{ = }\sqrt[]{128}\text{ = }\sqrt[]{2\times64}\text{ = }\sqrt[]{2}\text{ }\times\text{ }\sqrt[]{64} \\ x\text{ = 8}\sqrt[]{2} \end{gathered}[/tex]The correct option is 8√2 in
A car has 34,000,miles on its odometer and accumulates an average of 100 more each week. What is the function rule that represents the total m miles the car will have on the odometer after w weeks?
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Answer:
Step-by-step explanation:
M= 100m +34,000w
Answer: it would be A. for you, but for me it was C.:
m = 34,000 + 100w
what I mean is the answers were jumbled around.