Since the population increases at a rate proportional to the current number of people, the population will be three times of its initial population after 14.27 years.
The population of a community increases at a rate proportional to the number of people present at time t, means:
dP/dt = kP
where k is a constant.
Rearrange it:
(1/P) dP = k dt
Take the integral:
∫ (1/P) dP = ∫ k dt
ln P = kt + C, where C is a constant
Substitute t = 0, from the problem, it is known that P(t = 0) = P₀
Hence,
P(t) = P₀. e^(kt)
The population doubles after 9 years, means if we substitute t = 9
P(9) = P₀. e^(9k)
2P₀ = P₀. e^(9k)
2 = e^(9k)
Take the natural logarithmic:
ln 2 = 9k
k = (ln 2)/9 = 0.077
When the population grows to triple, it means P(t) = 3P₀
3P₀ = P₀. e^(kt)
ln 3 = kt
ln 3 = 0.077 t
t = (ln 3)/0.077 = 14.27 years.
Hence, the population will be three times of its initial population after 14.27 years.
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(0.020) (0.030) / (0.10)x = 2.3 × 10-4
The value of x in the equation is 26. 087
What are algebraic expressions?Algebraic expressions are defined as expressions made up of terms, constants, coefficients, factors and variables.
They may also include certain mathematical or arithmetic operations which includes;
BracketDivisionAdditionSubtractionParenthesesMultiplication and so onGiven the equation;
(0.020) (0.030) / (0.10)x = 2.3 × 10-4
We can simply the equation following the steps;
expand the brackets, we have;
6× 10^-4/ 0.10x = 2.3 × 10^-4
Now, cross multiply
0.10x × 2.3 × 10^-4 = 6× 10^-4
Divide both sides by 2.3 × 10^-4
0. 10x = 6× 10^-4/2.3 × 10^-4
Find the quotient
0. 10x = 2. 608
Let's make the variable 'x' by dividing both sides by it's coefficient
0. 10x/0.10 = 2. 608/0. 10
x = 26. 087
Hence, the value is 26. 087
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given that x=1+2i and y=1-2i calculate x+y x-y x•y and x/y
Answer:
1
Step-by-step explanation:
I like visiting other prisons people up when they are down in the class for lunch
the population standard deviation for the height of college hockey players is 3.2 inches. if we want to estimate 95% confidence interval for the population mean height of these players with a 0.55 margin of error, how many randomly selected players must be surveyed?
Given,
Population Standard deviation = 3.2 inches
Required confidence interval (C) = 95%
Margin of error = 0.55
Let h be the number of randomly selected players surveyed.
∝ = 1 - C = 1 - 0.95 = 0.05
∝/2 = 1 - C / 2 = 0.05/2 = 0.025
Score of ∝/2 = 2.5 - 0.025 = 2.475
We know,
Margin of error = 0.55
Standard deviation = 3.2
∵ 0.55 = 2.475 x 3.2/ √h
√h = √0.144/1000
∴ h = 12
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In a toy store the ratio of the number of dolls to the number of teddy bears is 6:5 if the store has 240 dolls how many teddy bears are in the store
About 200 teddy bears in the store.
Given,
The ratio of the number of dolls to the number of teddy bears is 6:5
and, The store has 240 dolls.
To find the number of teddy bears are in the store.
Now, According to the question:
Total no. of dolls are 240
The ratio of dolls and teddy bears are 6:5
Then, For dolls
= 240/6 = 40dolls
So, Teddy Bears = 40 × 5 = 200
Hence, About 200 teddy bears in the store.
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What is the volume of the following cone?
1. Minimum salary: $160.
Commission: 53% on $2900.
Total income for Minimum salary: $160 and Commission: 53% on $2900 will be $1,697.
Salary and Commission : -A salary is a set earnings that an employee normally gets on a weekly, biweekly or month-to-month foundation. A Commission is greater earnings an worker earns once they promote items or services.
We had given the minimum salary of $160 which will be fixed and not depend on the earning of the commission.
Now As given the sale of $2900 and the commission percentage of 53%
∴ Total Commission will be = [tex] \frac{2900\ (53)}{100} [/tex]
∴ Total Commission = 29 (53).
∴ Total Commission = $ 1,537
∴ Total Income will be the addition of base/minimum salary and the commission in total.
∴ Total income will be $160 + $1,537
∴ Total income = $1,697.
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The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 100% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 140 pints of a mixture that is 70% pure fruit juice?
The fruit drink which contains 70 % fruit juice will have 120 pints of 65 % pure fruit juice and 20 pints of 100% pure fruit juice.
Given that:-
Two types of juice are 65 % fruit juice and 100 % pure fruit juice.
The company is attempting to produce a fruit drink that contains 70% pure fruit juice.
We have to find the amount of each of 65% pure fruit juice and 100 % pure fruit juice which contains 70 % fruit juice with 140 pints of total juice.
Let the amount of 65 % pure fruit juice be x pints and,
The amount of 100 % pure fruit juice be y pints
We know that,
x + y = 140 ...(1)
Also,
Using weighted mean, we can write,
(65x + 100y)/(x + y) = 70
65x + 100y = 70x + 70y
5x = 30y
x = 6y
Putting x = 6y in (1), we get
6y + y = 140
7y = 140
y =140/7
y = 20 pints
x = 6y = 6*20 = 120 pints
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9 customers entered a store over the course of 18 minutes. At what rate were the customers entering the store in minutes per customer?
Answer:
2 min
Step-by-step explanation:
18/
a construction company has found it has a probability of 0.10 of winning each time it bids on a project. the probability of winning a given number of projects out of 12 bids could be determined with a binomial distribution.
Every time a construction company submits a bid, the odds of winning are 0.10 percent. With the aid of a binomial distribution, it is possible to calculate the likelihood of selecting a specific number of projects out of 12 bids: TRUE
What is binomial distribution?When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution. The probability of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution. For the trials we are looking at, the probability of receiving success in a binomial distribution must stay constant. Since there are only two possible outcomes when tossing a coin, for instance, the probability of flipping a coin is 1/2 or 0.5 for each trial we conduct.As it is given in the description itself that the probability of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.
Therefore, the statement "every time a construction company submits a bid, the odds of winning are 0.10 percent. With the aid of a binomial distribution, it is possible to calculate the likelihood of selecting a specific number of projects out of 12 bids" is TRUE.
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The complete question is given below:
A construction company has found it has a probability of 0.10 of winning each time it bids on a project. the probability of winning a given number of projects out of 12 bids could be determined with a binomial distribution. TRUE or FALSE.
The depth of the water in a tank after t minutes is modeled by f(t) = 5+1.5t, measured in inches. Find and interpret (10).
A) 20; The depth of the water after 10 minutes is 20 inches.
B) 20; The water reaches a depth of 10 inches after 20 minutes.
C) 65; The depth of the water after 10 minutes is 65 inches.
D) 65; The water reaches a depth of 10 inches after 65 minutes.
The depth of water after 10 minutes is 20 inches which is the option A.
Given that:-
Depth of water in a tank after t minutes is modeled by the function f(t) = 5+1.5t, measured in inches.
Let us check for Option A.
Putting t = 10 min in the given equation, we get,
f(10) = 5 + 1.5*10 = 5 + 15 = 20 inches.
Hence, option A is the right answer.
We can also check the other options to confirm our answer.
Putting t = 20 minutes,
f(20) = 5 + 1.5*20 = 5 + 30 = 35 inches
As 10 inches is written in B, hence, it is not the right answer.
We already know that t = 10 gives 20 inches.
Hence, C is not the answer.
Putting t = 65 minutes,
f(20) = 5 + 1.5*65 = 5 + 97.5 = 102.5 inches
As 10 inches is written in D, hence, it is not the right answer.
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The base of a 15-foot ladder is 3 feet from a building. If the ladder reaches the flat roof, how tall is the building?
.
Write the ratio 60: 145 in the form 1: n, where n is a fraction in its simplest form.
Answer:
n = 29/12 is the simplest form
Step-by-step explanation:
145 ÷ 60 = 29/12
Can the numbers 12, 6, 6 be used to form the sides of a triangle? Why or why not
Answer:
No
Step-by-step explanation:
Not because the sum of the measurements of the smaller sides (6, 6) must not be equal to or greater than the measure of the larger side (12) since in these conditions the triangle does not exist.
Hope this helps
Using the numbers 12, 6, 6, the triangle can not be formed.
What is the triangle inequality theorem?The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
Here, we have,
given that,
The given numbers are 12, 6 and 6.
Here, 6 + 6 = 12 but not greater than 12
so, we get,
Therefore, using the numbers 12, 6, 6, the triangle can not be formed.
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Company A charges $25 per day plus $0.25 per mile driven to rent a car. Company B
charges $35 per day plus $0.15 per mile driven to rent a car. How many miles must be
driven for a two-day rental from Company B to be less than a two-day rental from
Company A?
The number of miles that must be driven for the two-day rental from Company B to be less than Company A is 200 miles.
What is the number of miles?The equation that can be used to determine the total cost of renting from Company A is:
Total cost = (cost per day x number of days) + (cost per mile x number of miles)
($25 x 2) + ($0.25 x m)
$50 + $0.25m
The equation that can be used to determine the total cost of renting from Company B is: ($35 x 2) + ($0.15 x m)
$70 + $0.15m
The equation that can be used to determine the number of miles where it would be cheaper to rent for two days from Company B is:
$70 + $0.15m < $50 + $0.25m
$70 - $50 < $0.25m - $0.15m
$20 < $0.10m
m < $20 / 0.10
m < 200
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3 In an election, a good candidate may lose because 40% of voters do not cast their votes due
to various reasons. Form an equation and draw the graph with data. From the graph, find:
(i) The total number of voters, if 720 voters cast their votes.
The total number of voters is 1200, and out of that 720 voters cast their votes.
Let's take total voters = V
The percentage of voters do not cast their votes due to various reasons is 40%.
Therefore, Voters did not cast their votes = (40÷100)V = 0.4V
As 0.4V voters did not cast their votes. To calculate the total number of voters who cast votes, divide (total) by (non-casted-voters):
Voters casted their votes = V - 0.4V = 0.6V
0.6V = 720
=> V = 1200
The total number of voters is 1200 if 720 voters cast their votes.
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A brown bear can run 44 meters in 4 seconds. At this rate, how far could a brown bear run in 20 seconds?
Answer:
220 meters
Step-by-step explanation:
20 seconds is 5 times larger than 4 seconds, so the distance it runs in 20 seconds should be 5 times longer than 44 meters
so:
20/4 = 5
since x is 5 times larger than 44, set up the equation
5 = x/44
multiply both sides by 44
x= 44 * 5 = 220 meters
Which one of these pictures is not like the others? Explain what makes it different using ratios.
M is not like the others. ratio and proportion is used.
What is ratio?
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8 (or 3:4). (or 4:7). Any number of quantities, such as counts of people or objects or measurements of length, weight, or time, etc., can be included in a ratio. In most cases, both numbers must be positive.
Shorter diameter of L is 3:4.
the ratio of M is 4/8= 1:2
the ratio of N is 9/12= 3:4 (count the squares)
so, M is not like the others.
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Find the value of x that makes lines u and v parallel.
3)
78
17x-5
U
21x-5 v
biped
Hello, the correct answer to your question should be 5.
As seen in the photo below, the sum of the given angle values must equal [tex]180^o[/tex].
[tex](17x-5)+(21x-5)=180[/tex]Therefore, when we add these two values, we get the number [tex]"38x-10"[/tex]. If we equalize this number to [tex]180^o[/tex], we find the value of our [tex]x[/tex] as [tex]5[/tex].
[tex]38x-5=180[/tex][tex]38x=190[/tex][tex]x=5[/tex]Write an equation of a line that is perpendicular to y = 3x + 3 and passes through (−6, 3).
y equals negative one-third times x plus 1
y equals negative one-third times x minus 5
y = 3x + 21
y = 3x − 15
The equation of a line that is perpendicular to y = 3x + 3 is option A y equals negative one-third times x plus 1(-1/3x + 1)
Given,
The equation of line, y = 3x + 3
The line passes through (-6, 3)
We have to find the equation of the line that is perpendicular to y = 3x + 3
Slope of the line, m = 3
Here, in perpendicular case, slope is negative of its reciprocal.
That is, m = -1/3
Now, we can find the equation
y - y₁ = m(x - x₁)
Here,
y₁ = 3
x₁ = -6
m = -1/3
So,
y - 3 = -1/3(x - (-6))
y - 3 = -1/3(x + 6)
y - 3 = -1/3x + -1/3(6)
y - 3 = -1/3x - 6/3
y - 3 = -1/3x - 2
y = -1/3x - 2 + 3
y = -1/3x + 1
That is, the equation of a line that is perpendicular to y = 3x + 3 is y equals negative one-third times x plus 1(y = -1/3x + 1)
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Answer:A is the answer
Step-by-step explanation:
i got it right on the test
What percentage is 55cm of 4 metres ?
55cm is 13.75% of 4 meters.
Answer: 12.5%
Step-by-step explanation:
There are 100 CM in 1 M.
4×100=400
50/400=12.5
Simplify the expression (x12)3
Answer:
36x
Step-by-step explanation:
Quinn is baking sweet potato pies. The table shows the ratio of cups of sugar to number of pies. Number of Pies 3 5 9 Cups of Sugar 1 and one half 2 and one half 4 and one half How many cups of sugar will Quinn need to make 16 pies? 8 cups 8 and one half cups 9 and one half cups 11 cups
The number of cups of sugar that is required to make 16 pies is equal to 8 cups.
What is a direct proportion?Mathematically, a direct proportion can be represented the following mathematical expression:
y = kx
Where:
x represents the number of pies.y represents the cups of sugar.k represents the constant of proportionality.Since the cups of sugar varies directly (direct proportion) with the number of pies, the cups of sugar and number of pies must remain in a constant ratio.
Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = (1 1/2)/3
Constant of proportionality (k) = 0.5 or 1/2
From the above mathematical expression for direct proportion, an equation which models the situation or relationship is:
y = kx
y = 0.5x
Now, we can determine the number of cups of sugar at x = 16:
y = 0.5 × 16
y = 8 cups of sugar.
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Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. N=4; i and 4i are zeros; f(-1)=102
Answer:
[tex]f(x)=3x^4+51x^2+48[/tex]
Step-by-step explanation:
As n = 4, the degree of the polynomial is 4.
Therefore, the function cannot have more than 4 distinct roots.
[tex]\implies f(x)=a(x-p)(x-q)(x-r)(x-s)[/tex]
If a complex number z is a root of f(z) = 0 then its complex conjugate is also a root. Therefore:
If i is a root, then -i is also root.If 4i is a root, then -4i is also root.[tex]\implies f(x)=a(x-i)(x+i)(x-4i)(x+4i)[/tex]
[tex]\implies f(x)=a(x^2-i^2)(x^2-16i^2)[/tex]
[tex]\implies f(x)=a(x^2-(-1))(x^2-16(-1))[/tex]
[tex]\implies f(x)=a(x^2+1)(x^2+16)[/tex]
Given f(-1) = 102, then:
[tex]\begin{aligned}\implies f(-1)=a((-1)^2+1)((-1)^2+16)&=102\\a(1+1)(1+16)&=102\\a(2)(17)&=102\\34a&=102\\a&=3\end{aligned}[/tex]
Therefore:
[tex]\implies f(x)=3(x^2+1)(x^2+16)[/tex]
[tex]\implies f(x)=3(x^4+17x^2+16)[/tex]
[tex]\implies f(x)=3x^4+51x^2+48[/tex]
which small digit represent M so that the number 2m234 and is divisible by 3
Answer:
m = 1
Step-by-step explanation:
A number is divisible by 3 if the sum of the digits is a multiple of 3
the given number is 2m234 and we are asked to find the smallest m
Adding up known digits gives 2 + 2 + 3 + 4 = 11
The next multiple of 3 is 12
So 11 + m = 12
m = 1
The other possibilities are
m = 4, m = 7
Reuters reports that 15 percent of australians smoke. by introducing tough laws banning brand labels on cigarette packages, australia hopes to ultimately reduce the percentage of people smoking to 10%. answer the following questions based on a sample of 240 australians..
The mean of the sampling distribution of proportion is 0.15
The probability the sample proportion will be within 0.04 of the population proportion is 0.9182
The probability the sample proportion that will be within 0.02 of the population proportion is 0.6157
P(Smokers) in Australia= 15/100=0.15
Sample, n =240
Part a, The mean of the sampling distribution of proportion:
μ₂ = P(Smokers)
= 0.15
The mean of the sampling distribution of proportion is 0.15
The standard deviation of the sampling distribution of proportion is,
δ [tex]=\sqrt{p\frac{(1-p)}{n} }[/tex]
[tex]=\sqrt{0.15\frac{(1-0.15)}{240} }[/tex]
[tex]=0.0230[/tex]
The standard deviation of the sampling distribution of proportion is 0.0230
Part b, The probability the sample proportion will be within +/-0.04 of the population proportion:
To find this, we first, compute the z score then find probability based on standard normal table.
For 0.15-0.04, p=0.11 and converts to:
[tex]z=\frac{p-u_{p} }{standard deviation} \\[/tex]
[tex]=\frac{0.11-0.15}{0.0230}[/tex]
= -1.74
For 0.15+0.04, p=0.19, and converts to:
[tex]z=\frac{0.19-0.15}{0.0230}[/tex]
= 1.74
From the standard normal distribution table, the associated probability for z values and subtracts the probability is,
[tex]=p(-1.74\leq z\leq 1.74)[/tex]
[tex]=0.9591-0.0409[/tex]
[tex]=0.9182[/tex]
Hence, the probability the sample proportion will be within 0.04 of the population proportion is 0.9182
Part c, the probability the sample proportion will be within 0.02 of the population proportion:
First, compute the z score then find probability based on standard normal table.
For 0.15-0.02, p=0.13, and converts to:
[tex]=\frac{0.13-0.15}{0.0230}[/tex]
=-0.87
For 0.15+0.02, p=0.17, this converts to:
[tex]=\frac{0.17-0.15}{0.0230}[/tex]
=0.87
From the standard normal distribution table, the associated probability for z values and subtracts the probability is,
[tex]=p(-0.87\leq z\leq 0.87)[/tex]
[tex]=0.8079-0.1922[/tex]
[tex]=0.6187[/tex]
Hence, the probability the sample proportion will be within 0.02 of the population proportion is 0.6157
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Rafael rented a truck for one day. There was a base fee of 15.95, and there was an additional charge of 74 cents for each mile driven. Rafael had to pay 220.19 when he returned the truck. For how many miles did he drive the truck?
Answer: He drove 276b miles with the truck
Step-by-step explanation: 220.19 - 15.95 = 204.24
204.24 / .74 = 276
Simple function problem (will mark brainliest to correct answer)
From the given quadratic function ff(x) = (x² + cx - 1)/(2x² - 3x + 2), we can tell that the possible values for which the function lies on the interval (-1, 2) is; c c ≤ 12
What is the solution to the quadratic function?We are given the quadratic function f(x) as;
f(x) = (x² + cx - 1)/(2x² - 3x + 2)
Now, we want to find the possible values of c for which the function belongs to the interval (-1, 2). Thus, we will plug in -1 for x and equate the function to 2;
f(-1) = ((-1)² + c(-1) - 1)/(2(-1)² - 3(-1) + 2) = 2
(1 - c - 1)/6 = 2
-c/6 = 2
c = -12
Thus, the possible values for which the given function f(x) belongs to the interval (-1, 2) are; c ≤ 12
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The compositions f(g(x)) and g(f(x)) of functions f and g are shown on the graph. Which statements describe the compositions? Check all that apply. f(g(x)) = g(f(x)) for at least one value of x. The composition of f and g is commutative. f(g(0)) = 5 and g(f(–2.5)) = 5. Both f(g(x)) and g(f(x)) have the same domain. The graphs show that function composition is not commutative.
Given the Graph functions above, the option that applies in the above scenario are:
f(g(x)) = g(f(x)) for at least one value of x. [Option A]f(g(0)) = 5 and g(f(–2.5)) = 5. [Option C]Both f(g(x)) and g(f(x)) have the same domain. [Option D]The graphs show that function composition is not commutative. [Option E]What is a Graph function?A function's graph is the set of all points in the plane of the form (x, f(x)). The graph of f might similarly be defined as the graph of the equation y = f. (x). As a result, the graph of a function is a subset of the graph of an equation.
Explanation for Option A:
Note that both functions intersect at some point. That one is where f(g(x)) = g(f(x)) for at least one value of x. Note, this is for the value of x and not y;
Explanation for Option C:
This simply means that on the if f(g) where y = 5,x is 0; for g(f) where y = 5, x = -2.5. This is also observable in the graph
Explanation for Option D
If two functions f and g have the same domain and codomain, and f(a)=g for every an in the domain, we say they are equal (a).
Explanation for Option E
If a graph is cummulative, there will be a noticeable trend either as an upward trajectory or a negative one with the line crossing the origin. This is not the case here.
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Answer:
The expert answer is correct. But here is the short answer.
1, 3, 4, 5.
Kim cuts 2 2/3 yards from a roll of ribbon to make one bow.
They have 22 5/8 yards of ribbon available to make bows.
Use the drop-down menus to answer each question.
22 5/8÷2 2/3 will tell us the number of bows that is there will be some ribbon left over once we have enough to make 8 full bows but not a ninth.
Given that,
To construct one bow, Kim uses 2 2/3 yards of ribbon from a roll.
22 5/8 yards of ribbon can be used to create bows.
We have to find 22 5/8÷2 2/3 will tell us the number of bows.
Take the mixed fractions,
A mixed number is a representation of both a whole number and a legal fraction. In most cases, it denotes a number that falls between any two whole numbers.
=22 5/8÷2 2/3
=181/8÷8/3
Change to improper fractions
=181/8×3/8
Multiply by the reciprocal. Nothing cancels.
=543/64
Change into a mixed number
=8 31/64
Therefore, There will be some ribbon left over once we have enough to make 8 full bows but not a ninth.
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10x - 26 = 3x + 23
x= ?
10x - 26 = 3x + 23
x = 7
To find out x
10x - 3x = 23 + 26
7x = 49
x = 7
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Answer: x=7
Step-by-step explanation
[tex]10x-26=3x+23\\[/tex]
First you want to get the x's to one side you would subtract 3x from both sides.
Then your equation should be:
[tex]7x-26=23[/tex]
Then you want to add 26 to both sides.
[tex]7x=49[/tex]
Then you would divide both sides by 7, making your answer:
[tex]x=7[/tex]