The true statement is the same distance from the center of the circle is they must be perpendicular.
We have given that,
Two chords in a given circle are the same distance from the center of the circle.
What prerequisites must be met for the chords to be in harmony?The two chords must be equally spaced apart from the circle's center if they are congruent.
A is disregarded because it's possible that the chord won't travel through the circle's center.
Because the chords are not required to be parallel, B is rejected.
Because the chords do not have to be perpendicular, C is rejected.
A chord is any line segment that joins two points on the circle's circumference. While a circle's radius connects the center to the circle's point. As a result, we can conclude that radius is not a chord based on the definitions of both terms.
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Trapezoid W'X'Y'Z' is the image of trapezoid W XYZ under a dilation through point C What scale factor was used in the dilation?
The scale factor is basically by what we need to multiply the original to get the dilated one.
Simple.
We can see that the original one is Trapezoid WXYZ and the dilated one is W'X'Y'Z'.
THe dilated trapezoid is definitely bigger than original. So the scale factor should be larger than 1.
One side of original is "6" and the corresponding side of dilated trapezoid is "14".
So, what we have to do to "6", to get "14"??
This is the scale factor!
To get 14, we have to multiply 6 with, suppose, "x", so:
[tex]\begin{gathered} 6x=14 \\ x=\frac{14}{6} \\ x=\frac{7}{3} \end{gathered}[/tex]Hence, SF is 7/3
what are the terms in 7h+3
Input data
7h + 3
Procedure
A term is a single mathematical expression.
3 = is a single term.
It is simply a numerical term called a constant.
7h = is also a single term. , The coefficient of the first term is 7
H +6g when 9=g and h=4
Hey there!
[tex]g+6g\\g=9,h=4[/tex]
[tex]4(h)+6(9(g))[/tex]
[tex]4+6(9)[/tex]
[tex]=58[/tex]
Hope this helps!
For the function f(x) = 6e^x, calculate the following function values:f(-3) = f(-1)=f(0)= f(1)= f(3)=
Consider the given function,
[tex]f(x)=6e^x[/tex]Solve for x=-3 as,
[tex]\begin{gathered} f(-3)=6e^{-3} \\ f(-3)=6(0.049787) \\ f(-3)=0.2987 \end{gathered}[/tex]Thus, the value of f(-3) is 0.2987 approximately.
Solve for x=-1 as,
[tex]\begin{gathered} f(-1)=6e^{-1} \\ f(-1)=6(0.367879) \\ f(-1)=2.2073 \end{gathered}[/tex]Thus, the value of f(-1) is 2.2073 approximately.
Solve for x=0 as,
[tex]\begin{gathered} f(0)=6e^0 \\ f(0)=6(1) \\ f(0)=6 \end{gathered}[/tex]Thus, the value of f(0) is 6 .
Solve for x=1 as,
[tex]\begin{gathered} f(1)=6e^1 \\ f(1)=6(2.71828) \\ f(1)=16.3097 \end{gathered}[/tex]Thus, the value of f(1) is 16.3097 approximately.
Solve for x=3 as,
[tex]\begin{gathered} f(3)=6e^3 \\ f(3)=6(20.0855) \\ f(3)=120.5132 \end{gathered}[/tex]Thus, the value of f(3) is 120.5132 approximately.
Need help with is math.
For the given polynomial the roots can't have multiplicity, and the polynomial is:
p(x) = (x - 2)*(x - 3)*(x - 5).
How to find the polynomial?Here we know that we have a cubic polynomial (of degree 3) with the following zeros:
2, 3, and 5.
Can any of the roots have multiplicity?
No, because a cubic polynomial can have at maximum 3 zeroes, and here we already have 3.
Now let's get the polynomial
Remember that a cubic polynomial with zeros a, b, and c can be written as:
p(x) = (x - a)*(x - b)*(x - c)
Then the polynomial in this case is:
p(x) = (x - 2)*(x - 3)*(x - 5).
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perpendicular lines homework
I need help with system B. I have one right. And if the answer is infinitely. It asks to satisfy and it has Y=
We have the next system of equations
[tex]\begin{gathered} -5x-y=5 \\ -5x+y=5 \end{gathered}[/tex]We can sum both equations we can eliminate one variable
[tex]\begin{gathered} -10x=10 \\ \end{gathered}[/tex]then we isolate the x
[tex]x=\frac{10}{-10}=-1[/tex]Therefore x=-1 then we substitute the value of x in order to find the value of y in the second equation
[tex]-5(-1)+y=5[/tex]Then we simplify
[tex]5+y=5[/tex]Then we isolate the y
[tex]y=5-5[/tex][tex]y=0[/tex]ANSWER
x=-1
y=0
Mary Anne wants the professor to build a ramp to make it easier to get things into the cook hut. The ramp has to rise 2 feet and will have anangle of 12 degrees with the ground.Calculate how far out from the hut the ramp will go. Round to the nearest 1 decimal. _____What length of timbers will be needed to build the ramp (how long is the distance along the ramp) Round to the nearest 1 decimal. _____
The next figure illustrates the problem
x is computed as follows:
tan(12°) = opposite/adjacent
tan(12°) = 2/x
x = 2/tan(12°)
x = 9.4 ft
y is computed as follows:
sin(12°) = opposite/hypotenuse
sin(12°) = 2/y
y = 2/sin(12°)
y = 9.6 ft
Suppose that 27 percent of American households still have a traditional phone landline. In a sample of thirteen households, find the probability that: (a)No families have a phone landline. (Round your answer to 4 decimal places.) (b)At least one family has a phone landline. (Round your answer to 4 decimal places.) (c)At least eight families have a phone landline.
Answer:
(a) P = 0.0167
(b) P = 0.9833
(c) P = 0.0093
Explanation:
To answer these questions, we will use the binomial distribution because we have n identical events (13 households) with a probability p of success (27% still have a traditional phone landline). So, the probability that x families has a traditional phone landline can be calculated as
[tex]\begin{gathered} P(x)=nCx\cdot p^x\cdot(1-p)^x \\ \\ \text{ Where nCx = }\frac{n!}{x!(n-x)!} \end{gathered}[/tex]Replacing n = 13 and p = 27% = 0.27, we get:
[tex]P(x)=13Cx\cdot0.27^x\cdot(1-0.27)^x[/tex]Part (a)
Then, the probability that no families have a phone landline can be calculated by replacing x = 0, so
[tex]P(0)=13C0\cdot0.27^0\cdot(1-0.27)^{13-0}=0.0167[/tex]Part (b)
The probability that at least one family has a phone landline can be calculated as
[tex]\begin{gathered} P(x\ge1)=1-P(0) \\ P(x\ge1)=1-0.167 \\ P(x\ge1)=0.9833 \end{gathered}[/tex]Part (c)
The probability that at least eight families have a phone landline can be calculated as
[tex]P(x\ge8)=P(8)+P(9)+P(10)+P(11)+P(12)+P(13)[/tex]So, each probability is equal to
[tex]\begin{gathered} P(8)=13C8\cdot0.27^8\cdot(1-0.27)^{13-8}=0.0075 \\ P(9)=13C9\cdot0.27^9\cdot(1-0.27)^{13-9}=0.0015 \\ P(10)=13C10\cdot0.27^{10}\cdot(1-0.27)^{13-10}=0.0002 \\ P(11)=13C11\cdot0.27^{11}\cdot(1-0.27)^{13-11}=0.00002 \\ P(12)=13C12\cdot0.27^{12}\cdot(1-0.27)^{13-12}=0.000001 \\ P(13)=13C13\cdot0.27^{13}\cdot(1-0.27)^{13-13}=0.00000004 \end{gathered}[/tex]Then, the probability is equal to
P(x≥8) = 0.0093
Therefore, the answers are
(a) P = 0.0167
(b) P = 0.9833
(c) P = 0.0093
Question 2 of 10The one-to-one functions g and h are defined as follows.g={(-8, 6), (-6, 7), (-1, 1), (0, -8)}h(x)=3x-8Find the following.g-¹(-8)=h-¹(x) =(hoh− ¹)(-5) =
Answer: We have to find three unknown asked quantities, before we could do that we must find the g(x) from the coordinate points:
[tex]\begin{gathered} g=\left\{\left(-8,6\right),(-6,7),(-1,1),(0,-8)\right\}\Rightarrow(x,y) \\ \\ \text{ Is a tabular function} \\ \end{gathered}[/tex]The answers are as follows:
[tex]\begin{gathered} g^{-1}(-8)=0\text{ }\Rightarrow\text{ Because: }(0,-8) \\ \\ \\ h^{-1}(x)=\frac{x}{3}+\frac{8}{3} \\ \\ \\ \text{ Because:} \\ \\ h(x)=3x-8\Rightarrow\text{ switch }x\text{ and x} \\ \\ x=3h-8 \\ \\ \\ \\ \text{ Solve for }h \\ \\ \\ h=h^{-1}(x)=\frac{x}{3}+\frac{8}{3} \end{gathered}[/tex]The last answer is:
[tex]\begin{gathered} (h\text{ }\circ\text{ }h^{-1})(-5) \\ \\ \text{ Can also be written as:} \\ \\ h[h^{-1}(x)]\text{ evaluated at -5} \\ \\ h(x)=3x-8 \\ \\ h^{-1}(x)=\frac{x}{3}+\frac{8}{3} \\ \\ \\ \therefore\Rightarrow \\ \\ \\ h[h^{-1}(x)]=3[\frac{x}{3}+\frac{8}{3}]-8=x+8-8=x \\ \\ \\ \\ h[h^{-1}(x)]=x \\ \\ \\ \\ h[h^{-1}(-5)]=-5 \end{gathered}[/tex]A very large bag contains more coins than you are willing to count. Instead, you draw a random sample of coins from the bag and record the following numbers of eachtype of coin in the sample before returning the sampled coins to the bag. If you randomly draw a single coin out of the bag, what is the probability that you will obtain apenny? Enter a fraction or round your answer to 4 decimal places, if necessary.Quarters27Coins in a BagDimes21Nickels24Pennies28
Given:
The number of quarters = 27
The number of dimes = 21
The number of Nickels = 24
The number of Pennies = 28
Required:
Find the probability to obtain a penny.
Explanation:
The total number of coins = 27 + 21 + 24 +28 = 100
The probability of an event is given by the formula:
[tex]P=\frac{Number\text{ of possible outcomes}}{Total\text{ number of outcomes}}[/tex]The number of penny = 28
[tex]\begin{gathered} P(penny)=\frac{28}{100} \\ P(penny)=0.28 \end{gathered}[/tex]Final Answer:
The probability of obtaining Penny is 0.28.
b) A survey on the nationality of the student in the St Thomas international school is conducted and the results are shown below:i) if two students are randomly selected, what is the probability that both of them are European (correct to 4 decimal places)ii) if one student is randomly selected, what is the probability that a student is not Asian. (correct to 4 decimal places)
Given:-
A survey on the nationality of the student in the St Thomas international school is conducted and the results are shown.
To find if two students are randomly selected, what is the probability that both of them are European and if one student is randomly selected, what is the probability that a student is not Asian.
So now the total number of students are,
[tex]230+110+85+25=450[/tex]So now the probability of getting European is,
[tex]\frac{110}{450}=\frac{11}{45}[/tex]So the probability is,
[tex]\frac{11}{45}[/tex]So now the probability is asian is,
[tex]\frac{230}{450}=\frac{23}{45}[/tex]So the probability that it is not asian is,
[tex]1-\frac{23}{45}=\frac{45-23}{45}=\frac{22}{45}[/tex]so the required probability is,
A country's population in 1994 was 182 million.In 2002 it was 186 million. Estimatethe population in 2004 using the exponentialgrowth formula. Round your answer to thenearest million.
we have the exponential formula
[tex]P=Ae^{(kt)}[/tex]so
we have
A=182 million ------> initial value (value of P when the value of t=0)
The year 1994 is when the value ot t=0
so
year 2002 -----> t=2002-1994=8 years
For t=8 years, P=186 million
substitute the value of A in the formula
[tex]P=182e^{(kt)}[/tex]Now
substitute the values of t=8 years, P=186 million
[tex]\begin{gathered} 186=182e^{(8k)} \\ e^{(8k)}=\frac{186}{182} \\ \text{apply ln both sides} \\ 8k=\ln (\frac{186}{182}) \\ k=0.0027 \end{gathered}[/tex]the formula is equal to
[tex]P=182e^{(0.0027t)}[/tex]Estimate the population in 2004
t=2004-1994=10 years
substitute the value of t in the formula
[tex]\begin{gathered} P=182e^{(0.0027\cdot10)} \\ P=187 \end{gathered}[/tex]therefore
the answer is 187 millionPLEASE ANSWER ASAP ! Thanks :)
The inverse function table of the function is given by the image at the end of the answer.
How to calculate the inverse function?A function y = f(x) is composed by the following set of cartesian points:
(x,y).
In the inverse function, the input of the function represented by x and the output of the function represented by y are exchanged, meaning that the coordinate set is given by the following rule:
Thus, the points that will belong to the inverse function table are given as follows:
x = -8, f^(-1)(x) = -2, as the standard function has x = -2 and f(x) = -8.x = -4.5, f^(-1)(x) = -1, as the standard function has x = -1 and f(x) = -4.5.x = -4, f^(-1)(x) = 0, as the standard function has x = 0 and f(x) = -4.x = 0, f^(-1)(x) = 2, as the standard function has x = 2 and f(x) = 0.More can be learned about inverse functions at https://brainly.com/question/3831584
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Answer:
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} \vphantom{\dfrac12} x &-8 &-4.5 & -4&0 \\\cline{1-5} \vphantom{\dfrac12} f^{-1}(x) &-2 & -1& 0&2 \\ \cline{1-5}\end{array}[/tex]
Step-by-step explanation:
The inverse of the graph of a function is its reflection in the line y = x.
Therefore, the mapping rule to find the inverse of the given ordered pairs is:
(x, y) → (y, x)Therefore:
The inverse of (-2, -8) is (-8, -2)The inverse of (-1, -4.5) is (-4.5, -1)The inverse of (0, -4) is (-4, 0)The inverse of (2, 0) is (0, 2)Completed table:
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} \vphantom{\dfrac12} x &-8 &-4.5 & -4&0 \\\cline{1-5} \vphantom{\dfrac12} f^{-1}(x) &-2 & -1& 0&2 \\ \cline{1-5}\end{array}[/tex]
Watch help videoGiven the matrices A and B shown below, find – B - A.318154B12be-12
Given two matrices
[tex]A=\begin{bmatrix}{-18} & {3} & {} \\ {-15} & {-6} & {} \\ {} & {} & {}\end{bmatrix},B=\begin{bmatrix}{-4} & {12} & {} \\ {8} & {-12} & {} \\ {} & {} & {}\end{bmatrix}[/tex]We will solve for the resultant matrix -B - 1/2A.
This operation is represented as
[tex]-B-\frac{1}{2}A=-\begin{bmatrix}{-4} & {12} & {} \\ {8} & {-12} & {} \\ {} & {} & {}\end{bmatrix}-\frac{1}{2}\begin{bmatrix}{-18} & {3} & {} \\ {-15} & {-6} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Let's simplify the matrices further based on scalar operations that can be done here. The B matrix will be multiplied by -1 while the A matrix will be multiplied by 1/2. We now have
[tex]-B-\frac{1}{2}A=\begin{bmatrix}{4} & {-12} & {} \\ {-8} & {12} & {} \\ {} & {} & {}\end{bmatrix}-\begin{bmatrix}{-9} & {\frac{3}{2}} & {} \\ {\frac{-15}{2}} & {-3} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Now, we apply the subtraction of matrices to the simplified matrix operation above. We have
[tex]\begin{gathered} -B-\frac{1}{2}A=\begin{bmatrix}{4-(-9)} & {-12-\frac{3}{2}} & {} \\ {-8-(-\frac{15}{2})} & {12-(-3)} & {} \\ {} & {} & {}\end{bmatrix} \\ -B-\frac{1}{2}A=\begin{bmatrix}{4+9} & {-12-\frac{3}{2}} & {} \\ {-8+\frac{15}{2}} & {12+3} & {} \\ {} & {} & {}\end{bmatrix} \\ -B-\frac{1}{2}A=\begin{bmatrix}{13} & {\frac{-27}{2}} & {} \\ {-\frac{1}{2}} & {15} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex]Hence, the resulting matrix for the operation -B - 1/2A is
[tex]-B-\frac{1}{2}A=\begin{bmatrix}{13} & {\frac{-27}{2}} & {} \\ {-\frac{1}{2}} & {15} & {} \\ {} & {} & {}\end{bmatrix}[/tex]What is the solution to the equation below ? 0.5x = 6 A . 3 B . 12 C . 60
Given the equation:
[tex]0.5x=6[/tex]Multiplying both sides by 2
[tex]\begin{gathered} 2\cdot0.5x=2\cdot6 \\ x=12 \end{gathered}[/tex]So, the answer will be option B) 12
solve the quadratic equation below.3x^2-9=0
What’s the correct answer answer asap for brainlist
Answer: serbia
Step-by-step explanation:
Hello! I need some help with this homework question, please? The question is posted in the image below. Q6
Step 1
Given;
[tex]g(x)=3x^2-5x-2[/tex]Required; To find the zeroes by factoring
Step 2
Find two factors that when added gives -5x and when multiplied give -6x
[tex]\begin{gathered} \text{These factors are;} \\ -6x\text{ and x} \end{gathered}[/tex][tex]\begin{gathered} -6x\times x=-6x^2 \\ -6x+x=-5x \end{gathered}[/tex]Factoring we have and replacing -5x with -6x and x we have
[tex]\begin{gathered} 3x^2-6x+x-2=0 \\ (3x^2-6x)+(x-2)_{}=0 \\ 3x(x-2)+1(x-2)=0 \\ (3x+1)(x-2)=0 \\ 3x+1=0\text{ or x-2=0} \\ x=-\frac{1}{3},2 \\ \text{The z}eroes\text{ are, x=-}\frac{1}{3},2 \end{gathered}[/tex]Graphically the x-intercepts are;
The x-intercepts are;-1/3,2
Hence, the answer is the zeroes and x-intercepts are the same, they are;
[tex]-\frac{1}{3},2[/tex]i need some help list the integers in the set
Solution
The integers are the set of real numbers consisting of the natural numbers, their additive inverses and zero. {...,−5,−4,−3,−2,−1,0,1,2,3,4,5,...} The set of integers is sometimes written J or Z for short. The sum, product, and difference of any two integers is also an integer.
The whole numbers are set of real numbers that includes zero and all positive counting numbers. Whereas, excludes fractions, negative integers, fractions, and decimals. All the whole numbers are also integers, because integers include all the positive and negative numbers
The integers are real numbers
Therefore the numbers are list of integers
[tex]-8,9,\frac{0}{7},\frac{12}{4}[/tex]Comparing Two Linear Functions (Context - Graphically)
start identifying the slope and y-intercept for each high school.
The slope represents the growth for each year, in this case for high school A is 25 and for high school B is 50.
The y-intercept is the number of students that are enrolled currently, in this case for A is 400 and for B is 250.
The complete equations in the slope-intercept form are
[tex]\begin{gathered} A=25x+400 \\ B=50x+250 \end{gathered}[/tex]Continue to graph the equations
High school B is projected to have more students in 8 years.
Please help me answer the following question with the picture below.
Answer:
9x+b
Step-by-step explanation:
What is the opposite of the number −12?
A(-1/12
B(1/12
C(0
D(12
Answer: D(12)
Step-by-step explanation: To find the opposite it the number you would do -12= -12 x -1 = 12
29 graph in desmos and label points of inflection, critical points, local extremes, absolute extremes, asymptotes, etc
Given:
There are given the function:
[tex]f(x)=\frac{3x}{x^2-1}[/tex]Explanation:
According to the question:
We need to draw the graph of the given equation:
So,
The graph is:
vertical asymptotes are (-1,1)
And,
The horizontal asymptotes is
y = 0.
PLEASE HELP ME!! a shoe company is going to close one of its two stores and combine all the inventory from both stores these polynomials represented the inventory in each store. which expression represents the combined inventory of the two stories?
Add the two expressions together;
[tex]\begin{gathered} (\frac{1}{2}g^2+\frac{7}{2})+(3g^2-\frac{4}{5}g+\frac{1}{4}) \\ =\frac{1}{2}g^2+3g^2-\frac{4}{5}g+\frac{7}{2}+\frac{1}{4} \\ =3\frac{1}{2}g^2-\frac{4}{5}g+(\frac{14+1}{4}) \\ =\frac{7}{2}g^2-\frac{4}{5}g+\frac{15}{4} \end{gathered}[/tex]The first option is the correct answer
Determine which of the following lines, if any, are perpendicular • Line A passes through (2,7) and (-1,10) • Line B passes through (-4,7) and (-1,6)• Line C passed through (6,5) and (7,9)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
Line A:
point 1 (2,7)
point 2 (-1,10)
Line B:
point 1 (-4,7)
point 2 (-1,6)
Line C:
point 1 (6,5)
point 2 (7,9)
Step 02:
perpendicular lines:
slope of the perpendicular line, m’
m' = - 1 / m
Line A:
slope:
[tex]m\text{ = }\frac{y2-y1}{x2-x1}=\frac{10-7}{-1-2}=\frac{3}{-3}=-1[/tex]Line B:
slope:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{6-7}{-1-(-4)}=\frac{-1}{-1+4}=\frac{-1}{3}[/tex]Line C:
slope:
[tex]m\text{ = }\frac{y2-y1}{x2-x1}=\frac{9-5}{7-6}=\frac{4}{1}=4[/tex]m' = - 1 / m ===> none of the slopes meet the condition
The answer is:
there are no perpendicular lines
A population of values has a normal distribution with u = 203.6 and o = 35.5. You intend to draw a randomsample of size n = 16.Find the probability that a single randomly selected value is greater than 231.1.PIX > 231.1) =Find the probability that a sample of size n = 16 is randomly selected with a mean greater than 231.1.P(M > 231.1) =Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or Z-scores rounded to 3 decimal places are accepted.
Part 1:
The probability that a single randomly selected value is greater than 231.1 equals one minus the probability that it is less or equal to 231.1:
P(x > 231.1) = 1 - P(x ≤ 231.1)
Now, to find P(x ≤ 231.1), we can transform x in its correspondent z-score, and then use a z-score table to find the probability:
x ≤ 231.1 => z ≤ (231.1 - 203.6)/35.5, because z = (x - mean)/(standard deviation)
z ≤ 0.775 (rounding to 3 decimal places)
Then we have:
P(x ≤ 231.1) = P( z ≤ 0.775)
Now, using a table, we find:
P( z ≤ 0.775) ≅ 0.7808
Then, we have:
P(x > 231.1) ≅ 1 - 0.7808 = 0.2192
Therefore, the asked probability is approximately 0.2192.
Part 2
For the next part, since we will select a sample out of other samples with size n = 16, we need to use the formula:
z = (x - mean)/(standard deviation/√n)
Now, x represents the mean of the selected sample, which we want to be greater than 231.1. Then, we have:
z = (231.1 - 203.6)/(35.5/√16) = 27.5/(35.5/4) = 3.099
P(x > 231.1) = 1 - P(x ≤ 231.1) = 1 - P(x ≤ 231.1) = 1 - P( z ≤ 3.099) = 1 - 0.9990 = 0.0010
Therefore, the asked probability is approximately 0.0010.
i inserted a picture of the question state whether it’s a b c or d please don’t ask tons of questions yes i’m following
The possible values for any probability are between zero and one. With this in mind we conclude that A, B, C and E are allowed probabilities
Given the special right triangle, find the value of x and y. Express your answer in simplest radical form.
Austin and carly despoit 500.00 into a savings account which earns 1% interest compounded monthly they want to use the money in the account to go on a trip in 2 years how much will they be able to spend
EXPLANATION
Let's see the facts:
Austin and Carly deposit: $500
Interest rate= 1%
Compounding period = monthly
Total number of years = 2
Given the Compounding Interest Rate formula:
[tex]\text{Compound amount = P (1+r/n)\textasciicircum{}nt}[/tex]n is the compounding period
t is the number of years
r is te interest rate in decimal form
Replacing the given values will give us:
[tex]\text{Compound amount = 500 (1+}\frac{0.01}{12})^{12\cdot2}[/tex]Solving the power:
[tex]\text{Compound amount = 500 }\cdot1.020192843[/tex][tex]\text{Compound amount = \$510.09}[/tex]Answer: Austin and Carly will be able to spend $510.09.