In 2003, a particular company had 1088 stores and in 2007 there were 1058 stores. Write a linear equation that gives the number of stores in terms of the year. Let t = 3 represent 2003.
y(t) =
Predict the number of stores for the years 2012 and 2014. (Round your answers to the nearest whole number.)
2012 stores
2014 stores
Are your answers reasonable? Explain.
Yes, the number of stores decreases as t decreases.
No, the number of stores increases as t decreases.
No, this company will always have stores.
Yes, the number of stores decreases as t increases.
No, the number of stores increases as t increases.
Answers
The equation is y(t) = yo) e^-kt =
1058 = 1088e^-3k and yes my answer is reasonable , the number of store decreases as t increases
What is exponential function?An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
using the formula;
p(t) = p(o) e^-kt
1058 = 1088e^-3k
e^-3k = 1058/1088
e^-3k = 0.972
-3k = ln 0.972
k = -0.03/-3
k = 0.01
when t = 8
p(t) = 1088e^-kt
= 1088e^-0.08
p(t) = 1088× 0.923
p(t) = 1044
in 10 years
p(t) = 1088e^-0.1
p(t) = 984
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Related Questions
Find g (a + 1 ), if g(x)=5x-3
Answers
Answer:
g(a+1)=5a+2
Step-by-step explanation:
so (a+1) is the value of x
you can write it like this:
x=a+1
using substitution, we can swap out all 'x's for 'a+1's. like so;
g(a+1)=5(a+1)-3 -- given
=5a+5-3 -- distribute
=5a+2 -- simplify!
Hope i helped! have a great day! please mark brainliest!!
How much wire is needed to fence a rectangular garden with measurements 20mmx25m
Answers
Answer:
500000mm
Step-by-step explanation:
First to have to convert the meters into millimeters (25mm×1000mm=25000mm) than you have to times the answer by 20 (25000mm×20mm=500000mm) and your answer is 500000mm
If 50x = 500 then
O A. Xequals 1.
B. x equals 0.
OC. Xequals 5.
OD. * equals 10.
E. I equals 100.
Answers
Answer:
X=10
Step-by-step explanation:
Divide by 50 on both sides so ur left with X alone so 50x/50=500/50
X=10
123^3 as a power of 5
Answers
Answer:
5043
Step-by-step explanation:
If a train traveled 34 miles in 20 minutes. How many miles per hour was it traveling
Answers
Answer:
102 mph
Step-by-step explanation:
1 hour = 60 minutes
(34 miles / 20 minutes) x 3 = (102 miles /60 minutes)
Therefore, the train travels at 102 miles per hour
We know that a train travels a distance of 34 miles in a time of 20 minutes, and from this, we want to find the speed of the train.
We can conclude that the train was travelling at 102 miles per hour.
To solve this, we need to remember the relation:
speed = distance/time
Here we know:
distance = 34mi
time = 20 minutes
But we want the speed in miles per hour, so we need to change the units of the time.
Remember that 1 hour = 60minutes, then:
20 minutes = (20/60) hours = (1/3) hours.
Then we have:
time = (1/3) hours.
Then the speed can be written as:
speed = 34mi/( (1/3) h) = (34*3) mi/h = 102 mi/h
We can conclude that the train was travelling at 102 miles per hour.
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The average (A) of two numbers, m and n, is given by the formula A = m+t/2 . Find
the average of the two numbers 36 and 72.
The solution is
Answers
Answer:
\(54\)
Step-by-step explanation:
Formula for average A of two numbers m and n is:
\(A=\frac{m+n}{2}\)
Substitute the value m=36 and n=72
\(A=\frac{36+72}{2}\)
This is equivalent to:
\(A=\frac{108}{2}\)
The average is:
\(A=54\)
11. Check for Reasonableness Santiago wants to display categorical data
in a circle graph. He divides the circle graph into 5 equal sections because
the data set has 5 groups. Do you agree? Justify your answer,
Answers
Answer: Not necessarily. Dividing the pie chart into 5 equal sections might be a way to display categorical data if the number of categories is 5. However, dividing it into 5 sections might not be the best way to display the data if the number of categories is different than 5 or if any category has a significantly higher or lower proportion than the others. In this case, it may be more appropriate to use a different scale to display the correct ratio. It is important to consider data distribution and visualization clarity before choosing how to display categorical data.
3/5 pound of pasta feeds 6 people how many lbs does each person get
Answers
Answer:
0.1 lbs or 1/10 lbs
Step-by-step explanation:
3/5 = 6/10 =
0.6 / 6 =
0.1
Certain advertisers would like to estimate the proportion of viewers who spend the majority of their television time
watching alone. The consensus is that this percentage has been increasing over the years due to the increased
number of television sets in households.
a. Determine the sample size needed to construct a 90% confidence interval with a margin of error of no more than
6% to estimate the true proportion of viewers who watch television alone.
b. What impact would a pilot sample that showed that 44% of viewers spend the majority of their television time
watching alone have on your on results.
a. The sample size needed is
(Round up to the nearest integer.)
b. The new sample size needed would be 0
(Round up to the nearest integer.)
Answers
Answer:
Step-by-step explanation:
A rectangle has a length of 3x + 5 and a width of 2x. The
perimeter is 60 inches. What is the value of x?
Answers
Answer:
Hi there
Your answer is
x is equal to 5
Step-by-step explanation:
L=3x+5
W=2x
P=60
Perimeter formula
W+W+L+L=P
Plug in values
2x+2x+(3x+5)+(3x+5)=60
10x+10=60
-10
10x=50
/10
x=5
Consider the following distribution: 5, 5, 8, 9, 10, 10, 11. Which of the following is a correct statement about this distribution?
The mode is 9.
The median is 7.
The distribution is bimodal.
The mean is 6.5.
Answers
The distribution is bimodal. - this is a correct statement.
According to the question, the following distribution is 5, 5, 8, 9, 10, 10, and 11.
In statistics, the mode is the value that is being occurred frequently in a given set.In the above distribution, there are two modes i,e 5 and 10.
In statistics and probability theory median is the value separating the higher half from the lower half of a data sample. It is the point above and below which half (50%) of the observed data falls and so represents the midpoint of the data.Median: Middle value
In the above distribution, the median is - 9.
A data set is called bimodal if it has two modes which means that there is not a single data value that occurs with the highest frequency. Instead, there are two data values that tie in having the highest frequency.In statistics mean is the sum of a collection of numbers divided by the count of the numbers.Mean = \(\frac{5 + 5 + 8 + 9 + 10 + 10 + 11}{7}\) = \(\frac{58}{7}\) = 8.28
Hence,
The distribution is bimodal. - this is a correct statement.
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Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answers
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
If the prime factorization of 600 is 2 x 2 × 2 × 3 × 5 × 5, what would you need to multiply it by to get the prime factorization of 3000?
Answers
To get the Prime factorization of 3000 we need to multiply by 5.
What is Prime Factorization:When the number is factored using prime numbers, or primes, the process is known as prime factorization. The easiest method to determine the prime factors of a given number is to keep dividing the given number by the prime factors until we will get 1.
For example, the Prime factorization of 45 is given below
=> 45/5 = 9, 9/3 = 3, 3/3 = 1
=> 45 = 5 × 3 × 3
Here we have
The prime factorization of 600 is 2 x 2 × 2 × 3 × 5 × 5
Let us assume that on multiplying with p,
we will get the factorization of 3000
=> 2 x 2 × 2 × 3 × 5 × 5 × p = 3000
=> p = \(\frac{3000}{2\times 2 \times 2 \times 3 \times 5 \times 5}\)
Her 2 x 2 × 2 × 3 × 5 × 5 = 600
=> p = \(\frac{3000}{600}\)
=> p = 5
Therefore,
To get the Prime factorization of 3000 we need to multiply by 5.
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Devon’s bike has wheels that are 26 inches in diameter. After the front wheel picks up
a tack, Devon rolls another 100 feet (1200 inches) and stops. How far above the ground in inches is the tack?
Answers
To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.
First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:
C = π × 26
C ≈ 81.64 inches
This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.
Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:
1200 / 81.64 ≈ 14.68 revolutions
Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.
Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.
Therefore, the tack is located 13 inches above the ground.
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Find two numbers which add to give 0 and multiply to give -16
Answers
Answer:
4 and -4
Step-by-step explanation:
Which of the following is the equation of a line with a slope of -5/9
Answers
Answer:
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Step-by-step explanation:
Please help me important question Please help me important question in image
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The age in United States has a normal distribution with a mean 46 years and standard deviation 13 years. The children are classified as those younger than 18 years and the middle age citizens are those in the age group 18-55. If a citizen is randomly chosen, what is the probability that he/she is middle age
Answers
Answer:
0.74
Step-by-step explanation:
The middle age citizens are those in the age group of 18-55.
We solve this question using z score formula
z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
Mean 46 years
Standard deviation 13 years
For x = 18 years
z = 18 - 46/13
z = -2.15385
Probability value from Z-Table:
P(x = 18) = 0.015626
For x = 55 years
z = 55 - 46/13
= 0.69231
Probability value from Z-Table:
P(x = 55) = 0.75563
The probability that he/she is middle age is
P(x = 55) - P( x = 18)
= 0.75563 - 0.015626
= 0.740004
Approximately = 0.74
Adult tickets for an art exhibit cost $15. Tickets for students cost $8.
Martin has $180 to buy 2 adult tickets and 20 student tickets.
Martin says he has enough money to buy all of the tickets because $8 × 20 = $160 and $160 is less than $180.
Critique Martin's reasoning. Which statements are correct? Choose all that apply.
A.
Martin correctly found the total cost of the tickets.
B.
Martin did not include the cost of the adult tickets.
C.
The cost of the two adult tickets is $15.
D.
Martin correctly concludes that he has enough money to buy all of the tickets.
E.
The total cost is $190, so Martin does not have enough money.
Answers
Answer:
The correct answers are B & E
Step-by-step explanation:
The cost of adult tickets: 15$ * 2= 30$
The cost of student tickets: 8$ * 20= 160$
=> All the tickets cost 30$ + 160$= 190$
=> Martin still needs 10$ more to buy all of the tickets
QUESTIONS IN PICTURE/ATTACHMENT:
Answers
The domain of the question is expressed as; 0 ≤ x ≤ 4
The range of the question is expressed as; 100 ≤ f(x) ≤ 207.36
How to find the domain and range of the graph?
The domain of a graph is defined as the set of all possible input values that makes the function possible while the range is defined as the set of all possible output values that can result from the possible input values.
Now, we are told that the insect population increases by 20% each month from May 1 to September 1.
The function that represents the insect population after x months is;
f(x) = 100(1.2)ˣ
Thus, the domain is from x = 0 to 4 months inclusive. 0 ≤ x ≤ 4
f(0) = 100(1.2)⁰
f(0) = 100
f(4) = 100(1.2)⁴
f(4) = 207.36
100 ≤ f(x) ≤ 207.36
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what is the property of 3x(5x7)=(3x5)7
Answers
The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.
In the equation you provided: 3x(5x7) = (3x5)7
The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.
Last week, Jada ran 2 7/10 miles. This week, she plans to run 5 times as far as last week.
How many miles does Jada plan to run this week?
Write your answer as a fraction or as a whole or mixed number.
Answers
Answer:
13.5 miles or 27/5 miles
Step-by-step explanation:
2 7/10 is equal to 2.7 If she plans to run 5 times as much as last week, multiply 2.7 by 5.
2.7*5=13.5
A company that manufactures and sells consumer video cameras sells two versions of their popular
hard disk camera, a basic camera for $750, and a deluxe version for $1250. About 75% of customers
select the basic camera. Of those, 60% purchase the extended warranty for an additional $200. Of
the people who buy the deluxe version, 90% purchase the extended warranty.
a) Sketch the probability tree for total purchases.
b) What is the percentage of customers who buy an extended warranty?
c) What is the expected revenue of the company from a camera purchase (including warranty if
applicable)?
d) Given that a customer purchases an extended warranty, what is the probability that he or she bought
the deluxe version?
Answers
The probability that he or she bought the deluxe version is 0.5
a) Here is the probability tree for total purchases:
0.75
┌─────────────┐
│ Basic │
│ Camera │
└───────┬─────┘
│
│0.6
│
▼
┌──────────────┐
│Extended │
│Warranty │
└─────┬────────┘
│
│0.4
│
▼
┌──────────────┐
│ │
│ No │
│Warranty │
└──────────────┘
b) To calculate the percentage of customers who buy an extended warranty, we need to consider both branches of the probability tree that lead to purchasing an extended warranty.
From the probability tree, we can see that 75% of customers select the basic camera, and of those, 60% purchase the extended warranty. Additionally, 25% of customers select the deluxe camera, and of those, 90% purchase the extended warranty.
Now we can calculate the percentage of customers who buy an extended warranty:
Percentage = (Percentage of Basic Camera Customers x Percentage of Basic Camera Customers with Extended Warranty) + (Percentage of Deluxe Camera Customers x Percentage of Deluxe Camera Customers with Extended Warranty)
Percentage = (0.75 x 0.6) + (0.25 x 0.9)
Percentage = 0.45 + 0.225
Percentage = 0.675 or 67.5%
Therefore, 67.5% of customers buy an extended warranty.
c) To calculate the expected revenue of the company from a camera purchase, we need to consider the different scenarios: customers who buy the basic camera without the warranty, customers who buy the basic camera with the warranty, customers who buy the deluxe camera without the warranty, and customers who buy the deluxe camera with the warranty.
Expected Revenue = (Percentage of Basic Camera Customers x Price of Basic Camera) + (Percentage of Basic Camera Customers with Extended Warranty x (Price of Basic Camera + Price of Extended Warranty)) + (Percentage of Deluxe Camera Customers x Price of Deluxe Camera) + (Percentage of Deluxe Camera Customers with Extended Warranty x (Price of Deluxe Camera + Price of Extended Warranty))
Expected Revenue = (0.75 x $750) + (0.75 x 0.6 x ($750 + $200)) + (0.25 x $1250) + (0.25 x 0.9 x ($1250 + $200))
Expected Revenue = $562.50 + $382.50 + $312.50 + $337.50
Expected Revenue = $1,595.00
Therefore, the expected revenue of the company from a camera purchase, including the warranty if applicable, is $1,595.00.
d) To calculate the probability that a customer bought the deluxe version given that they purchased an extended warranty, we can use conditional probability.
Probability (Deluxe Version | Extended Warranty) = Probability (Deluxe Version and Extended Warranty) / Probability (Extended Warranty)
From the probability tree, we can see that the probability of buying the deluxe version and extended warranty is 0.25 x 0.9 = 0.225, and the probability of purchasing an extended warranty is 0.45 (as calculated in part b).
Probability (Deluxe Version | Extended Warranty) = 0.225 / 0.45
Probability (Deluxe Version | Extended Warranty) = 0.5 or 50%
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2 + 2. what is the sum
Answers
Answer: 4
Step-by-step explanation:
Answer:4
2+2=4 if I have two apples and pick up two more I now have 4 total
tell how you can use the structure of mathematics to complete the task
Answers
Answer: It is crucial for students to look for and make use of a structure because this practice requires them to reason about the underlying mathematical structure and unity of mathematics ideas.
The average amount of money spent for lunch per person in the college cafeteria is $6.4 and the standard deviation is $2.03. Suppose that 48 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.
Answers
The average amount of money spent for lunch per person in the college cafeteria is $6.45 and the standard deviation is $2.55. Suppose that 44 randomly selected lunch patrons are o
population mean is 6.45
population standard deviation is 2.55.
sample size is 44.
z-score is indicated because you are using population standard deviation and sample size is greater than 30.
Compare the sample mean to the population mean.The z-score formula is \((x - m) / s\)
in this case, x is the sample mean, m is the population mean, s is the standard error.
\(standard error = standard deviation / sqrt(sample size0 = 2.55 / sqrt(44) = .3844\) rounded to 4 decimal places.
z-score formula becomes \(z = (x - 6.45) / .3844\)
solve for x to get:
\(x = .3844 * z + 6.45\)
since you don't have a z-score, you can't find x.
the best you can do is find the critical z-scores, and hence, the critical raw scores.
In order to do that you need to to know the confidence level.
if you know that, you can find the critical z-scores and, from that, the critical x-scores.
we'll compare two confidence levels.
the first is at 99% confidence level.
the second is at 90% confidence level.
with a 99% two-tail confidence level, the critical z-scores are plus or minus 2.5758 rounded to 4 decimal places.
the critical raw scores are found by using the z-score formula.
you get \(x = .3844 * 2.5758 + 6.45 = 7.4401\) for the high score.
you get x = \(.3844 * -2.5758 + 6.45 = 5.4599\) for the low score.
the 99% two-tail confidence level tells you that 99% of your samples of size 44 will have the sample mean between 5.4599 and 7.4401.
that's your 99% confidence interval.
with a 95% two-tail confidence level, the critical z-scores are plus or minus 1.9600 rounded to 4 decimal places.
the critical raw scores are found by using the z-score formula.
you get \(x = .3844 * 1.9600 + 6.45 = 7.2034\) for the high score.
you get\(x = .3844 * -1.9600 + 6.45 = 5.6966\) for the low score.
the 95% two-tail confidence level tells you that 95% of your samples of size 44 will have the sample mean between 5.6966 and 7.2034.
that's your 95% confidence interval.
the higher the confidence level, the wider the confidence interval when you are dealing with the same population mean and population standard deviation and same sample size.
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Correct and complete question:
The average amount of money spent for lunch per person in the college cafeteria is $6.45 and the standard deviation is $2.55.
Suppose that 44 randomly selected lunch patrons are observed.
Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.
b. What is the distribution of x?
x-N(6.45,_________________)
Aisha organized her books for 5 hour and her coin collection for 3 hour. 7 What is the best estimate for the total time Aisha spent organizing?
Answers
Answer:
about 8 hours
Step-by-step explanation:
8 hours. It is Five hours plus Three hours.
Missing numbers
, 9.8 , 9.1
Answers
Answer:
10.5
Step-by-step explanation:
Missing number, 9.8, 9.1
We see that each time it subtracts 0.7
We take
9.8 + 0.7 = 10.5
So, the missing number is 10.5
How do you do this question?
Answers
Answer:
Correct integral, third graph
Step-by-step explanation:
Assuming that your answer was 'tan³(θ)/3 + C,' you have the right integral. We would have to solve for the integral using u-substitution. Let's start.
Given : ∫ tan²(θ)sec²(θ)dθ
Applying u-substitution : u = tan(θ),
=> ∫ u²du
Apply the power rule ' ∫ xᵃdx = x^(a+1)/a+1 ' : u^(2+1)/ 2+1
Substitute back u = tan(θ) : tan^2+1(θ)/2+1
Simplify : 1/3tan³(θ)
Hence the integral ' ∫ tan²(θ)sec²(θ)dθ ' = ' 1/3tan³(θ). ' Your solution was rewritten in a different format, but it was the same answer. Now let's move on to the graphing portion. The attachment represents F(θ). f(θ) is an upward facing parabola, so your graph will be the third one.
someone help me if you can :)
Answers
Answer:
the answer is 126,321,000
Multiply.
8×35
Enter your answer as a mixed number in simplest form by filling in the boxes
PLS HELP
Answers
Answer:
280
Step-by-step explanation:
Answer:
8×35=280.
This is the best I can give to you