Fiona invested $1000 at 7% compounded continuously. At the same time, Maria invested $1100 at 7% compounded daily. How long will it take for their investments to be equal in value? Assume there are 365 days in every year.
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Answer:
14,201 years
Step-by-step explanation:
The two compound interest formulas are ...
A = P·e^(rt) . . . . . continuous compounding at rate r for t years
A = P·(1 +r/365)^(365t) . . . . . daily compounding at rate r for t years
We went the amounts to be equal:
1000·e^(0.07t) = 1100·(1+0.07/365)^(365t)
Dividing by 1000(1 +0.07/365)^(365t), we have ...
((e^0.07)/(1+0.07/365)^365)^t = 1.1
The base of the exponential on the left is ...
( e^0.07)/(1+0.07/365)^365 ≈ 1.00000671149321522
Taking logs, we have ...
t×ln(1.00000671149321522) = ln(1.1)
t = ln(1.1)/ln(1.00000671149321522) ≈ 0.09531018/(6.7114704·10^-6)
t ≈ 14,201.09 . . . . . years
It will take about 14,201 years for the investments to be equal.
_____
Additional comment
The investment value at that time will be about $5.269·10^434. (That's a larger number than anything countable in the known universe, including energy quanta.)
These calculations are beyond the ability of many calculators, so might need to be carefully rewritten if the calculator only keeps 10 significant digits, or only manages exponents less than 100.
This shows that daily compounding is very close in effect to continuous compounding. It would take almost 150 years to make a difference of 0.1% in value.
According to the American Academy of Cosmetic Dentistry, 75% of adults believe that an unattractive smile hurts career success. Suppose that 25 adults are randomly selected. What is the probability that 15 or more of them would agree with the claim?
Answer:
0.9703 = 97.03% probability that 15 or more of them would agree with the claim.
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they agree with the claim, or they do not. The probability of an adult agreeing with the claim is independent of any other adult, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
75% of adults believe that an unattractive smile hurts career success.
This means that [tex]p = 0.75[/tex]
Suppose that 25 adults are randomly selected.
This means that [tex]n = 25[/tex]
What is the probability that 15 or more of them would agree with the claim?
This is:
[tex]P(X \geq 15) = 1 - P(X < 15)[/tex]
In which:
[tex]P(X < 15) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 13) + P(X = 14)[/tex]
14 is below the mean, so we start below and go until the probability is 0. Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 14) = C_{25,14}.(0.75)^{14}.(0.25)^{11} = 0.0189[/tex]
[tex]P(X = 13) = C_{25,13}.(0.75)^{13}.(0.25)^{12} = 0.0074[/tex]
[tex]P(X = 12) = C_{25,12}.(0.75)^{12}.(0.25)^{13} = 0.0025[/tex]
[tex]P(X = 11) = C_{25,11}.(0.75)^{11}.(0.25)^{14} = 0.0007[/tex]
[tex]P(X = 10) = C_{25,10}.(0.75)^{10}.(0.25)^{15} = 0.0002[/tex]
[tex]P(X = 9) = C_{25,9}.(0.75)^{9}.(0.25)^{16} \approx 0[/tex]
Then
[tex]P(X < 15) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.0002 + 0.0007 + 0.0025 + 0.0074 + 0.0189 = 0.0297[/tex]
And
[tex]P(X \geq 15) = 1 - P(X < 15) = 1 - 0.0297 = 0.9703[/tex]
0.9703 = 97.03% probability that 15 or more of them would agree with the claim.
What is the difference between these two linear equations?
Y=3x - y=-3x
I need help ASAP thank you guys
Answer:
The fraction is undefined when x=-2
Step-by-step explanation:
The fraction will be undefined when the denominator is zero
x+2 = 0
x+2-2 = 0-2
x = -2
The fraction is undefined when x=-2
Answer:
as to me 5
Step-by-step explanation:
ask someone else to say that I am not sure if you have any questions or need any further information please contact me at the end of the world
Surface Area of Pyramids
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
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Answer:
288 km²
Step-by-step explanation:
The surface area is the sum of the area of the square base and the area of the four triangular faces.
SA = (10 km)² + 4(1/2)(10 km)(9.4 km) = 288 km²
____
The area formulas for a square and a triangle are ...
A = s² . . . . area of a square of edge length s
A = 1/2bh . . . . area of a triangle with base b and height h
a. 312
b. 317
c. 315
d. 316
Answer:
B.) 317
Step-by-step explanation:
100/2 = 50
124/2 = 62
180/2 = 90
634/2 = 317
A lady wearing a McDonalds t-shirt with a delicious-looking Big Mac on it asks which fast food restaurant is your favourite. This leads to which type of bias?
a) Response Bias
b) Sampling Bias
c) Measurement Bias
d) Non-response Bias
what are the answers to the questions below?
Answer:
You have to follow PEMDAS or parenthesis, exponents, multiplication, division, addition, and subtraction. It's an order to solve equations. I listed the steps and the answers for you below :) I have throughly checked them so they should be correct! yw :D
Step-by-step explanation:
1. 5x + 4x - 6x = 24
9x - 6x = 24
3x = 24
24/3 = 8
x = 8
2. 8y + 5 - 4y + 1 = 46
8y - 4y = 4y
5 + 1 = 6
4y + 6 = 46
4y = 46 - 6
4y = 40
40/4 = 10
y = 10
3. 33 = 5 ( x + 8 ) + 3
33 = 5x + 40 + 3 (because we distributed)
33 = 5x + 43
5x + 43 = 33 (just rewriting it to make it easier)
5x = 33 - 43
5x = -10
-10/5 = -2
so x = - 2
4. 2m + 3 ( m - 8 ) = 1
2m + 3m - 24 = 1
we got 3m - 24 because we distributed the 3
5m - 24 = 1
5m = 25
25/5 = 5
m = 5
5. p + p - 2p + 4p = - 48
2p - 2p + 4p = - 48
4p = - 48
- 48 / 4 = - 12
p = - 12
6. 2 ( y + 5 ) + 3y = 25
2y + 10 + 3y = 25
5y + 10 = 25
5y = 25 - 10
5y = 15
15/5 = 3
y = 3
7. 1/4 h + 3/4 h + 1/2 h + 2 = 5
1/4 h + 3/4 h + 1/2 = 3/2 h
3/2 h + 2 = 5
3/2 h = 5 - 2
3/2 h = 3
h = 2
8. 60 = 4 ( k + 3 ) + 2 ( k - 3 )
60 = 4k + 12 + 2k - 6
4k + 12 + 2k - 6 = 60
6k + 6 = 60
6k = 60 - 6
6k = 54
k = 9
9. - 2 ( d + 1.4 ) - 1.8 = 20.6
-2d + - 2.8 - 1.8 = 20.6
-2d - 2.8 = 22.4
-2d = 25.2
d = - 12.6
10. 8 - 2 ( w + 4 ) = 10
8 + - 2 w + - 8 = 10
-2w + 9 + - 8 = 10
-2w = 10
10 / -2 = -5
w = -5
Name
MATH 1342
Lab 12 - Ch.10 - Hypothesis Testing
Critical Thinking, Communication Skills, Empirical/Quantitative Skills
2. A machine is designed to fill jars with 16 ounces of coffee. A quality control inspector
suspects that the machine is not filling the jar with the full 16 ounces. A sample of 20 jars has
a mean of 15.8 ounces and a standard deviation of 0.32 ounce. Is there enough evidence to
support the inspector's claim that the mean number of ounces of coffee in the jars is less than
16? Use a = .05.
1.
Hand H
2.
3.
Critical value(s)
4.
Graph
5.
Test Statistic
6.
P-value
7.
Reject H. or Do Not Reject H.
8.
Conclusion
1 & 2:The null and alternate hypotheses are
H0 : u = 16 vs Ha: u < 16
The null hypothesis is that the mean is 16 ounces against the claim that it is less than 16 ounces.
3:The significance level is 0.05
4. Critical Value:
The critical region for significance level = 0.05 for one tailed test is z< ± 1.645
5.The test statistic
The test statistic to be used is
z= x- μ/σ/√n
z= 15.8-16/0.32/√20
z= -0.2/ 0.071556
z= -2.7950
6. The p-value ≈ 0.00259 for one tailed test.
7. Reject H0
Since the calculated value of z= -2.7950 is less than z∝= -1.645 we reject the null hypothesis.
8. Conclusion:
There is enough evidence to support the inspector's claim that the mean number of ounces of coffee in the jars.
https://brainly.com/question/15980493
Graph
1. (02.01)
Solve -4(x + 10) - 6 = -3(x - 2). (1 point)
-40
-46
-52
52
Answer:
-52
Step-by-step explanation:
-4(x + 10) - 6 = -3(x - 2)
Distribute the left side to get:
(-4x + -40) - 6
Now distribute the right side to get:
-3x + 6
Arrange the equation as the following:
-4x - 40 - 6 = -3x + 6
Add the like terms on each side:
-4x - 46 = -3x + 6
Do the inverse operation of each term:
-x = 52
Now we need to get x to become a positive, so we just divide -x by -1 to get x.
And 52/-1 to get our final answer of -52.
Answer: -52
Step-by-step explanation:
-4(x + 10) - 6 = -3(x - 2)
Distribute the left side to get:
(-4x + -40) - 6
Now distribute the right side to get:
-3x + 6
Arrange the equation as the following:
-4x - 40 - 6 = -3x + 6
Add the like terms on each side:
-4x - 46 = -3x + 6
Do the inverse operation of each term:
-x = 52
Now we need to get x to become a positive, so we just divide -x by -1 to get x.
And 52/-1 to get our final answer of -52.
Jessica combines 1/3 cups of blue paint and 1/2 cups of red paint.
A photographer bought 35 rolls for $136.44 what was the price of one roll
Answer:
$3.90
Step-by-step explanation:
136.44/35= (rounded tot the nearest hundredth) $3.90
Answer:
136.44÷36 =3.79
3.79×36=136.44
Step-by-step explanation:
So one ball cost 3. 79
If f(x) = 5x - 1, then f^-1(x)=
Answer:
[tex]f^{-1}[/tex](x) = [tex]\frac{x+1}{5}[/tex]
Step-by-step explanation:
let y = f(x) and rearrange making x the subject , that is
y = 5x - 1 ( add 1 to both sides )
y + 1 = 5x ( divide both sides by 5 )
[tex]\frac{y+1}{5}[/tex] = x
Change y back into terms of x , with x = [tex]f^{-1}[/tex] (x) , then
[tex]f^{-1}[/tex] (x) = [tex]\frac{x+1}{5}[/tex]
For the graph find a) b) c) and d)
Answer:
[tex]f(0) = -1[/tex]
[tex]f(\pi) = 1[/tex]
Domain: All real numbers
[tex]Range = [-1,1][/tex]
Step-by-step explanation:
Given
The attached graph
Solving (a): f(0)
On the attached graph
[tex]f(x) = -1[/tex] when [tex]x =0[/tex]
So:
[tex]f(0) = -1[/tex]
Solving (b): f(pi)
On the attached graph
[tex]f(x) = 1[/tex] when [tex]x =\pi[/tex]
So:
[tex]f(\pi) = 1[/tex]
Solving (c): Domain
There is no restriction on x.
Hence, the domain is the set of all real numbers
Solving (d): Range
In the attached graph
[tex]y_{min} = -1[/tex]
[tex]y_{max} = 1[/tex]
So, the range is:
[tex]Range = [-1,1][/tex]
7
Abdul's gas tank is
1
3
full. After he buys 12 gallons of gas, it is
full. How many gallons can Abdul's tank hold?
9
Answer:
27
Step-by-step explanation:
Let T be the capacity of the tank.
Since the tank was 1/3 full and ends up 7/9 full.
[tex]\frac{7}{9}[/tex]T - [tex]\frac{1}{3}[/tex]T = 12
Simplifying the left side of the equation, tells us how much 12 gallons fills.
[tex]\frac{4}{9}[/tex]T = 12
Now we solve for T:
T = 12*9/4
T = 27
A group of friends will go on a weekend camping trip and split the cost of gas
equally. The cost that each person will pay for gas is inversely proportional to the
number of people who go on the trip. If four friends go on the trip, each person pays
$23 for gas. Write an equation that describes the relationship between cost (c) that
each person pays for gas, and the number of people on the trip (n).
C = 92/n
C= n/0.17
C = 5.75n
C = 5.75/n
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Answer:
(a) C = 92/n
Step-by-step explanation:
The "inversely proportional" relation is represented by the equation ...
C = k/n
The value of k can be found from the given values of C and n.
23 = k/4
23×4 = k = 92
Then the relationship is ...
C = 92/n
The volume of a rectangular prism (shown below) is 48x^3+56x^2+16x Answer the following questions:
(1) What are the dimensions of the prism?
(2) If x = 2, use the polynomial 48x^3+56x^2+16x to find the volume of the prism.
(3) If x = 2, use the factors found in part a to calculate each dimension.
(4) Using the dimensions found in part c, calculate the volume. Show all work.
Answer:
(a)
[tex]Length = 8x\\Width = 3x + 2\\Height = 2x + 1[/tex]
(b)
[tex]P(2) = 640[/tex]
(c)
[tex]Length= 16[/tex]
[tex]Width = 8[/tex]
[tex]Height =5[/tex]
(d)
[tex]Volume = 640[/tex]
Step-by-step explanation:
Given
[tex]P(x) = 48x^3 + 56x^2 + 16x[/tex]
Solving (a): The prism dimension
We have:
[tex]P(x) = 48x^3 + 56x^2 + 16x[/tex]
Factor out 8x
[tex]P(x) = 8x(6x^2 + 7x + 2)[/tex]
Expand 7x
[tex]P(x) = 8x(6x^2 + 4x + 3x + 2)[/tex]
Factorize
[tex]P(x) = 8x(2x(3x + 2) +1( 3x + 2))[/tex]
Factor out 3x + 2
[tex]P(x) = 8x(3x + 2)(2x + 1)[/tex]
So, the dimensions are:
[tex]Length = 8x\\Width = 3x + 2\\Height = 2x + 1[/tex]
Solving (b): The volume when [tex]x = 2[/tex]
We have:
[tex]P(x) = 48x^3 + 56x^2 + 16x[/tex]
[tex]P(2) = 48 * 2^3 + 56 * 2^2 + 16 * 2[/tex]
[tex]P(2) = 640[/tex]
Solving (c): The dimensions when [tex]x = 2[/tex]
We have:
[tex]Length = 8x\\Width = 3x + 2\\Height = 2x + 1[/tex]
Substitute 2 for x
[tex]Length=8*2[/tex]
[tex]Length= 16[/tex]
[tex]Width = 3*2+2[/tex]
[tex]Width = 8[/tex]
[tex]Height = 2*2 + 1[/tex]
[tex]Height =5[/tex]
So, we have:
[tex]Length= 16[/tex]
[tex]Width = 8[/tex]
[tex]Height =5[/tex]
Solving (d), the volume in (c)
We have:
[tex]Volume = Length * Width * Height[/tex]
[tex]Volume = 16 * 8 * 5[/tex]
[tex]Volume = 640[/tex]
17 Geometry question: Use an algebraic equation to find the measurement of each angle that is represented in terms of X
Answer:
2x + 30° = 40°
4x + 30° = 50°
Step-by-step explanation:
2x + 30° and 4x + 30° are complementary angles.
Complementary angles sum up to give 90°.
Therefore,
2x + 30° + 4x + 30° = 90°
Add like terms
6x + 60 = 90
6x = 90 - 60
6x = 30
6x/6 = 30/6
x = 5
✔️2x + 30°
Plug in the value of x
2(5) + 30
10 + 30
= 40°
✔️4x + 30°
4(5) + 30°
20 + 30
= 50°
math can you guys help me PLS
Answer:
The surface area of the triangular prism is 84 square centimeters.
Step-by-step explanation:
The surface area of a figure is exactly what it means, the area of its outer surface or the added areas of each face that makes the figure.
Nets are a way to find surface area easier because it is an outline of the faces of the 3d figure.
But since we don’t have a net, we will just find the area of each face that forms this right triangular prism:
The two congruent triangular bases:
1/2 x 4 x 3 = 6 cm^2
6 x 2 = 12 cm^2
Lateral bottom rectangular face:
6 x 3 = 18 cm^2
Lateral to the right rectangular face:
5 x 6 = 30 cm^2
Lateral to the left rectangular face:
4 x 6 = 24 cm^2
Add up all the values:
12 + 18 + 30 + 24 = 84
The SA is 84 square centimeters
I NEED HELP ASAP!!! convert 0.252525 to a fraction and convert 2.454545 to a fraction
Answer:
1. What is 0.252525 as a fraction?
0.252525 as a fraction equals 252525/1000000
2. 2.454545 as a fraction equals 2454545/1000000
Step-by-step explanation:
To write 0.252525 as a fraction you have to write 0.252525 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
0.252525 = 0.252525/1 = 2.52525/10 = 25.2525/100 = 252.525/1000 = 2525.25/10000 = 25252.5/100000 = 252525/1000000
And finally we have:
0.252525 as a fraction equals 252525/1000000
2. What is 2.454545 as a fraction?
To write 2.454545 as a fraction you have to write 2.454545 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
2.454545 = 2.454545/1 = 24.54545/10 = 245.4545/100 = 2454.545/1000 = 24545.45/10000 = 245454.5/100000 = 2454545/1000000
And finally we have:
2.454545 as a fraction equals 2454545/1000000
Thanks
Translate into an algebraic expression:
n-1 increased by 110%
Answer:
Step-by-step explanation:
(n-1)1.1
What is the expected value of the two investments? Type the correct answer in each box. Round your answers to the nearest whole dollar value. The expected value of the Computer Co. stock is $ 5,040 0], and the expected value of the US Treasury bond is $ 5,085
THE AWNSER IS IN THE QUESTION
Answer: $5,040 & $5,085
Step-by-step explanation:
The expected value of the Computer Co. stock is $5,040, and the expected value of the US Treasury bond is $5,085
The expected value of both the stocks Computer Co. and US Treasury bond is $5,062.5.
What is the weighted average?When the average is not of any individual rather it is an average of two or more groups or sets it is called a weighted average.
To obtain the weighted average we multiply no. of individuals by their averages and sum the next group in the previous procedure and divide them by the total no. of individuals.
The expected value is the weighted average also known as the mean.
Given, The expected value of the Computer Co. stock is $ 5,040, and the expected value of the US Treasury bond is $ 5,085.
Therefore the expected value of both stocks is,
= (5040 + 5085)/2.
= $5,062.5
learn more about expected values here :
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Question
Express all real numbers less than -2 or greater than or equal to 3 in interval notation.
Real numbers can be expressed using the following interval,
[tex]\mathbb{R}=(-\infty,\infty)[/tex]
Of course infinities are not just normal infinities but thats out of the scope of this question.
Real numbers less than two can be expressed with,
[tex](-\infty,\infty)\cap(-\infty,-2)=\boxed{(-\infty,-2)}[/tex]
The [tex]\cap[/tex] is called intersection ie. where are both intervals valid. First we took real numbers then we intersected them with real numbers valued less than -2 and we got real numbers which are less than -2.
Similarly we can perform with "greater than or equal to 3" real numbers,
[tex](-\infty,\infty)\cap[3,\infty)=\boxed{[3,\infty)}[/tex]
So we have one interval stretching from negative infinity to (but not including) -2, and another interval stretching from including 3 to positive infinity.
If we want numbers in both intervals we can express this two ways,
First way is to use [tex]\cup[/tex] union operator to denote we want numbers from two intervals,
[tex]\boxed{(-\infty,2)\cup[3,\infty)}[/tex]
The second way is to specify which numbers we do not want, we do not want -2 and everything up to but not including 3, which is expressed with the following interval
[tex][-2,3)[/tex]
Now we just take out the not wanted interval from real numbers and we will remain with all wanted numbers,
[tex]\boxed{(-\infty,\infty)-[-2,3)}[/tex]
Hope this helps.
Valerie set out to bicycle from TBLS to the beach, a distance of 10 miles. After going a short while at 15 miles per hour, the bike developed a flat tire, and the trip had to be given up. The walk back to TBLS was made at a dejected 3 miles per hour. The whole episode took 48 minutes. How many miles from TBLS did the flat occur
Answer:
I think it is 3 miles becos the bicycle broke at 15miles per hour and the walk from the current place to the TBLS is 3 miles per hour
In a study of 806 randomly selected medical malpracticeâ lawsuits, it was found that 513 of them were dropped or dismissed. Use a 0.01 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed. What is the hypothesis test to beâ conducted?
Solution :
[tex]$H_0: p = 0.5$[/tex]
[tex]$H_a: p > 0.5$[/tex]
Alpha, α = 0.01
The sample proportion is :
[tex]$p'=\frac{x}{n}$[/tex]
[tex]$=\frac{513}{806}$[/tex]
= 0.636
Test statistics, [tex]$z=\frac{p'-p}{\sqrt{\frac{pq}{n}}}$[/tex]
[tex]$z=\frac{0.636-0.5}{\sqrt{\frac{0.5\times 0.5}{806}}}$[/tex]
[tex]$z=\frac{0.136}{0.0176}$[/tex]
z = 7.727
The p value = 0.00001
Here we observe that p value is less than α, and so we reject the hypothesis [tex]H_0[/tex].
Therefore, there is sufficient evidence,
In a standardized normal distribution the mean is ____ while the standard deviation is ____.
A. 0; 1
B. 1; 0
C. 0; 0
D. 1; 1
Answer:
A. 0; 1
Step-by-step explanation:
Required
Mean and standard deviation of a standardized normal distribution
A standardized normal distribution is represented as:
[tex](\mu,\sigma) = (0,1)[/tex]
This implies that:
[tex]\mu = 0[/tex] -- mean
[tex]\sigma = 1[/tex] --- standard deviation
Hence, (a) is true
Which graph has the solutions -1 and 4?
a.
On a coordinate plane, a parabola opens up and goes through (negative 4.2, 0) and (0, negative 1).
c.
On a coordinate plane, a parabola opens up and goes through (negative 4, 0) and (1, 0).
b.
On a coordinate plane, a parabola opens up and goes through (0, negative 3) and (4.5, 0).
d.
On a coordinate plane, a parabola opens up and goes through (0, negative 1) and (4, 0).
Please select the best answer from the choices provided
A
B
C
D
Answer:
graph d
in graph d, the line intersects the x axis twice at (-1,0) and (4,0), so those two are the solutions of the graph
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“””” HELP PLEASE “”””
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9514 1404 393
Answer:
x = 14 cm
Step-by-step explanation:
We can only solve for x if the triangles are similar. The arrows on the left and right legs say those are parallel. Since alternate interior angles at each of the transversals are congruent, the triangles are AA similar.
ΔABC ~ ΔDEC, so we have ...
EC/ED = BC/BA
x/(18 cm) = (35 cm)/(45 cm)
x = (18 cm)(7/9) = 14 cm
A decreasing inventory turnover ratio indicates:_______
a. a longer time span between the purchase and sale of inventory.
b. a shorter time span between the purchase and sale of inventory.
c. a longer time span between the ordering and receiving of inventory.
d. a shorter time span between the ordering and receiving of inventory.
help me with this questions please!
9514 1404 393
Answer:
r = 18
Step-by-step explanation:
Let d represent the number of districts. The given information lets us write two equations:
3d = 27 . . . . . the number of state senators
d +r = 27 . . . . the number of representatives
The first equation tells us ...
d = 27/3 = 9
The the second equation tells us ...
r = 27 -d = 27 -9 = 18
The number of at-large representatives is r = 18.
