The initial number of bacteria in a culture is found as 200.
What is defined as the population growth?When demographers try to forecast changes in population size, they generally focus on four factors: fertility rates, high mortality (life expectancy), and the population's initial age profile.Using the model P = P₀e^(kt),
Where:
P(t) = the amount of bacteria at time t = 2000.
P₀ = initial amount at time t = 0
r = growth rate
t = time (number of periods)
k is the growth constant.
For t = 3 hours.
400 =P₀e^(k*3) ......eq 1
2000 = P₀e^(k*10) ......eq 2
Re writing eq 1.
400 = P₀e^(k*3)
as (400/P₀) = [e^k]^3,
Solve for e^k,
∛(400/P₀) = e^k
For eq 2.
2000 = P₀e^(k*10)
Rewrite it as;
(2000/P) = [e^k]^10.
Substituting ∛(400/P₀) for e^k, we obtain:
(2000/P₀) = (400/P₀ )^(10/3)
Solved for P.
Raise sides by the power of 3, we get:
(2000/P₀)^3 = (400/P₀)^10.
Therefore,
2000^3/ P₀^3 = 400^10/P₀^10
Solve,
2000^3/ 1 = 400^10/P₀^7
Taking reciprocal.
Solving
P₀^7 = 400^10/2000^3
P₀^7 = 1.31 x 10¹⁶
Take the 7th root of both sides;
P₀ = 200.67
Thus, the initial number of bacteria in a culture is found as 200.
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suppose we take a poll (random sample) of 3604 students classified as juniors and find that 3059 of thembelieve that they will find a job immediately after graduation. what is the 99 % confidence interval for the proportion of gsu juniors who believe that they will,immediately, be employed after graduation.
The 99% confidence interval for the population proportion p is 0.833< p < 0.863.
Given that,
x = 3059
n = 3604
Point estimate = sample proportion = x / n =3059/3604=0.848
[tex]1 - \hat p[/tex] = [tex]1-0.848 =0.152[/tex]
At 99% confidence level the z is ,
[tex]\alpha[/tex] = 1 - 99% = 1 - 0.99 = 0.01
[tex]\alpha[/tex]/ 2 = 0.01 / 2 = 0.005
[tex]Z\alpha[/tex]/2 = [tex]Z*0.005[/tex] = 2.576 ( Using z table )
Margin of error = E = [tex]Z\alpha / 2 * (\sqrt(((\hat p * (1 - \hat p)) / n)[/tex]
= [tex]2.576* (\sqrt((0.848*0.152) /3604 )[/tex]
=0.015
A 99% confidence interval for population proportion p is ,
[tex]\hat p - E < p < \hat p + E[/tex]
0.848-0.015< p <0.848+ 0.015
0.833< p < 0.863
Hence, the 99% confidence interval for the population proportion p is 0.833< p < 0.863.
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solve for x
7x + 12 - 6x = 5(2x+6)
Answer:
7×+12-6×=5(2×+6)=7×-6+12=10×+30=7×-6×-10×=30-12=9×÷9×=18÷9×=×=2
The ratio of mystery books to fantasy books in the library is 7:9.
Fill in the missing values to show the possible number of
mystery and fantasy books.
Mystery Books Fantasy Books
21
Select Answer -
63
Select Answer -
27
54
Select Answer
117
Answer:
42
81
91
Step-by-step explanation:
m = mystery
f = fantasy
[tex]\frac{m}{f}[/tex] = [tex]\frac{m}{f}[/tex]
Compare the ratio with the actual numbers. Solve for the missing number
[tex]\frac{7}{9}[/tex] = [tex]\frac{m}{54}[/tex] you need to multiply 9 by 6 to get 54 so multiply 7 x 6 to get 42.
[tex]\frac{7}{9}[/tex] = [tex]\frac{63}{f}[/tex] Multiply 7 x 9 to get 63,so multiply 9 by 9 to get 81.
[tex]\frac{7}{9}[/tex] = [tex]\frac{m}{117}[/tex] 9 x 13 is 117, so multiply 7 by 13 to get 91.
30% of a sum of money is rupees 300. what is the total amount?
step by step explanation please
subject: linear equations in math
the total amount is 9000
an article suggests the uniform distribution on the interval (6.5, 21) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. (a) what are the mean and variance of depth? (round your variance to two decimal places.)
The meand and variance are 13.75 cm and 17.52 respectively.
Each possible outcome is equally likely when there is a uniform probability.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The mean of the uniform distribution is:
M = ( a + b ) / 2
The variance of the uniform distribution is given by:
V = ( b - a )² / 12
Uniform distribution on the interval ( 6.5, 21 )
Therefore, a = 6.5 and b = 21
Hence, the mean will be:
M = ( 6.5 + 21 )/ 2
M = 27.5 / 2
M = 13.75
The mean of depth is 13.75 cm.
The variance will be:
V = ( b - a )² / 12
V = ( 21 - 6.5 )² / 12
V = 210.25 / 12
V = 17.52
The variance of depth is of 17.52 cm².
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Solve for x
2(5x+3)=6x-3
Linear equations
2(5x + 3) = 6x -3Apply the multiplicative law of distribution.
10x + 6 = 6x - 3Rearrange the unknown terms on the left side of the equation.
10x - 6x = -3 - 6Combine as terms
4x = -3 - 6Calculate the sum or difference.
4x = -9Divide both sides of the equation by the coefficient of the variable.
x = - 9/4The answer is x = - 9/4. Because if we do the division, the result is not exact; means that the result is decimal.
Answer:
x = -9/4
Step-by-step explanation:
2(5x+3)=6x-3
10x + 6 = 6x - 3
10x - 6x = -3 - 6
4x = -3 - 6
4x = -9
The answer is x = -9/4
A construction company takes 1/8 hours to remove 1/4 metric tons of dirt from a construction site.
A construction company takes 1/8 hours to remove 1/4 metric tons of dirt from a construction site 2 metric tons in an hour.
What do you mean by tons?Ton is the name of a number of different measurement units. It has a lengthy history and a variety of meanings and applications.
It mostly discusses weight units. Due to the ambiguous nature of what ton might mean.
2,240 pounds, or the long ton, the tonne, also known as a metric ton, which is 1,000 kilograms, and the short ton, which is 2,000 pounds.
Its original use as a volume measurement has persisted in terminology like the freight ton and several other units, with capacities ranging from 35 to 100 cubic feet (0.99 to 2.83 [tex]m^{3}[/tex]). The ton has recently been used for specialized purposes such as energy measurement and vehicle classification. It can also be used as a measure of energy or as a power unit in refrigeration; this is commonly referred to as a ton of refrigeration.
Due to the fact that the ton (of any system of measuring weight) is typically the heaviest unit specified in informal speech, its word also has figurative usage, singular and plural, figuratively signifying a big amount or quantity, or to a great degree, as in "We have a ton of homework, there are a ton of bees in this hive, and I really, really adore you."
The best way to do this is to convert all fractions to decimals. Problem starts out looking like this.
Formula
Rate = Tons removed / hours
Tons Removed = 1/4 metric ton
Time taken = 1/8 hour
rate = [tex]\frac{\frac{1}{4} }{\frac{1}{8} }[/tex]
Rather than doing it with the fractions, it is much easier to do it with decimals
1/4 = 0.25
1/8 = 0.125
Now what we get is rate = 0.25 / 0.125 = 2
So, now 2 metric tons can be removed in an hour
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Simplify the expression using the Distributive Property and explain each step.
70[2.50+(−0.60)]+25[3.75+(−0.70)]
The new expression by using distributive property is: 209.25
What is distributive property?
In mathematics, the distributive property tell the solution method for the expression who are in the form of a(b + c). In this, first add the expression which are in the parenthesis and later multiply it.
According to the question, the given expression is as follows:
70[2.50+(−0.60)]+25[3.75+(−0.70)]
Using distributive property, whose list contains parenthesis, exponents, multiplication/division, addition/subtraction. This is the list in which the given expression need to simplify.
First parenthesis calculation,
2.5 + - 0.6 = 1.9 and 3.75 + - 0.7 = 3.05
Now, substitute the values:
70(1.9) + 25(3.05)
Multiply it: 133 + 76.25;
Add it: 209.25
Hence, the new expression by using distributive property is: 209.25
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I’m 2020 summer camp registration was $15 more than it was in 2021 in 2020 registration was $285 by what percentage did the summer camp registration decrease in 2021
The summer camp registration decreased in 2021 by 5.26 percent.
The summer camp registration fee in 2020 was $285.We are given that the summer camp registration fee in 2020 was $15 more than it was in 2021.From the above data, we can find the summer camp registration fee in 2021.The summer camp registration fee in 2021 was $285-$15.The summer camp registration fee in 2021 was $270.We need to find the percentage decrease in the summer camp registration fee.The percentage decrease is (decrease/initial value)*100.The percentage decrease is (15/285)*100.The percentage decrease in the summer camp registration fee is 5.26 percent.To learn more about percentage, visit :
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what is the slope of a line that runs through the points (10,10) and (5,10)
The slope of the line that passes through the points (10,10) and (5,10) is 0
How to determine slope of a line?Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1 ( 10,10 )
x₁ = 10y₁ = 10Point 2 ( 5,10 )
x₂ = 5y₂ = 10To determine the slope, plug these coordinates into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 10 - 10 )/( 5 - 10 )
Slope m = ( 0 )/( 5 - 10 )
Slope m = ( 0 )/( -5 )
Slope m = 0
Therefore, the slope of the line is 0.
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371 + 18x ≥ 566 solve for X
[tex]18x \geqslant 566 - 371 \\ 18x \geqslant 195 \\ \frac{18x}{18} \geqslant \frac{195}{18} \\ x \geqslant 10.8333333333[/tex]
YOU CAN EVEN WRITE IT IN THE FRACTION FORM .
BE REMINDED THAT <> CHANGE SIGN WHEN YOU DIVIDE OR MULTIPLY A NEGATIVE NUMBER ONLY.
HOPE THIS HELPS
Answer:
Step-by-step explanation:
18x ≥ 195 if equal to the answer is 10.83(3)
Geometry lvl 1 stuff but im dum
Answer:
A
Step-by-step explanation:
Point A
:] its ok we all dum sometimes lol
Multiply.
3y^2(-5y^4)
Simplify your answer as much as possible.
Answer:
[tex]\boxed{\sf{-15y^6}}[/tex]
Step-by-step explanation:
To solve this, you have to use a distributive property to multiply the numbers from left to right.
Distributive property:
A(B+C)=AB+AC
A(B-C)=AB-AC
[tex]\sf{3y^2\left(-5y^4\right)=-3y^2* 5y^4}[/tex]
Multiply.
-3*5=-15
-15y²y⁴
[tex]\sf{y^2y^4=y^2^+^4=y^6}[/tex]
=-15y⁶
Therefore, the final answer is -15y⁶.
I hope this helps, let me know if you have any questions.
Given measurement of angle 8= 86° and measurement of angle 4= (4x + 2)°, what is the value of x ?
The value of x is 21 °.
What are the properties of parallel lines ?1. The vertically opposing angle pairs are equal.
2. The related angle pairs are equivalent.
3. The alternative outside angle pairs are equivalent.
4. There is equality between the alternate interior angle pairs.
In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical. We can see parallel lines examples in our daily life like a zebra crossing, the lines of notebooks, and on railway tracks around us.
Given: ∠ 8 = 86° and ∠ 4= (4x + 2)°
Since ∠4 = ∠8 { Because angles on the same side of the parallel sides are equal }
Thus when we equate these two we get ;
86 = 4x +2
4x = 84
x= 21
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Determine the domain of the function f(x) = 1/√x-1 + 1/√2-x
The domain of the function is 1 ≤ x < 2.
What is domain ?The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.
The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates).
We have f : [tex]\frac{1}{\sqrt{x-1} } + \frac{1}{\sqrt{2-x} }[/tex]
[tex]\sqrt{x-1}[/tex] ≥ 0
x- 1 ≥ 0
x ≥ 1
Similarly , [tex]\sqrt{2-x}[/tex] > 0
2 - x > 0
2 > x
So our domain is 1 ≤ x < 2.
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A bag contains five white balls and four black balls. Your goal is to draw two black balls.
You draw two balls at random. What is the probability that they are both black?
Answer:
The probability that you draw two balls that are both black is [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
To find probability, take the number of desirable outcomes over the total number of possible outcomes.
In this case, the black balls are desirable. There are four of them.
this means the numerator of the first fraction is 4. The denominator is the total possible outcomes or in this case the total number of black and white balls. This number is 9. The first probability fraction is [tex]\frac{4}{9}[/tex]
Lets say that the first one was black. Now we need to find the probability of drawing another one. Now there are black balls left in the bag. This means that the number of desirable outcomes is 3. There are also 8 balls total. This means the number of total possible outcomes is 8. The second probability is [tex]\frac{3}{8}[/tex]
To get the total probability you multiply both of the individual probabilities together.
[tex]\frac{4}{9} *\frac{3}{8} =\frac{1}{6}[/tex]
Evaluate 8x - 4y when x = 2 and y = 3(b) o
EXPLANATION
Given the equation 8x -4y
When x=2 and y=3 the resulting expression would be as follows:
8*2 -4*3=
=16 - 12
= 4
The answer is 4
Order the number least to greatest 1 8/25 1.3 5/4
When the given numbers are ordered from least to greatest, the result would be 8/25, 1, 5/4, 1.3
How to order numbers?To be able to order the numbers, it would be best to convert them to the same form. In order words, all the numbers should either be decimals or fractions.
Decimals are easier to compare so convert them to decimals:
= 8 / 25 = 5 / 4
= 0.32 = 1.25
The numbers are:
1, 0.32, 1.3, 1.25
The order from least to greatest is:
0.32, 1, 1.25, 1.3
or:
8/25, 1, 5/4, 1.3
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……………………………
3x + 7 = 2(x+1)+x
its 0=-5
ur mom lolololololoOLOOLOLLLLO
Write three fractions equivalent to \frac{9}{15}
Scale the numerator and denominator up for the first two and down for the third.
Scale up by: __ Equivalent fraction: __
Scale up by: __ Equivalent fraction: __
Scale down by: __ Equivalent fraction: __
(a) On scaling up by a factor of 2 , the equivalent fraction is 18/30.
(b) On scaling up by a factor of 3 , the equivalent fraction is 27/45.
(c) On scaling down by a factor of 3 , the equivalent fraction is 3/5 .
In the question ,
a fraction 9/15 is given ,
Part(a)
to scale up the fraction by a factor of 2 , we multiply the numerator and denominator by 2 .
On multiplying , we get
9/15 = (9*2)/(15*2) = 18/30 .
Part(c)
to scale up the fraction by a factor of 3 , we multiply the numerator and denominator by 3 .
On multiplying , we get
9/15 = (9*3)/(15*3) = 27/45 .
Part(c)
to scale down the fraction by a factor of 3 , we divide the denominator and numerator by 3 .
On dividing , we get
9/15 = (9/3)/(15/3) = 3/5 .
Therefore , (a) On scaling up by a factor of 2 , the equivalent fraction is 18/30.
(b) On scaling up by a factor of 3 , the equivalent fraction is 27/45.
(c) On scaling down by a factor of 3 , the equivalent fraction is 3/5 .
The given question is incomplete , the complete question is
Write three fractions equivalent to 9/15 .
Scale the numerator and denominator up for the first two and down for the third.
(a) Scale up by: __ Equivalent fraction: __
(b) Scale up by: __ Equivalent fraction: __
(c) Scale down by: __ Equivalent fraction: __
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5х +2y=10
5x+2y=20
Solve system by using either elimination or substitution
Answer:
No solution
Step-by-step explanation:
The method that will use is substitution
ill use the equation 5x+2y=10 and substitute into the other one
5x+2y=10
2y=10-5x
y=5-2.5x
Now we must insert this equation into another
5x + 2(5-2.5x) = 20
5x+10-5x = 20
10=20
10 does not equal to 20 so it has no solution
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David leaves the house to go to school. He walks 200 m west and 45 m north. how far away is he from his starting point?
Step-by-step explanation:
...............
............
List 2 ways that will not prove two triangles are congruent
Answer:
first way: 2 Angles and one side
second way: 2 sides and one angle
Answer:
Step-by-step explanation:
congruent triangles
how to tell if triangles are congruent using SSS, SAS, ASA, and AAS rules
why AAA and SSA do not work as congruence shortcuts
the Hypotenuse Leg Rule for right triangles
how to use CPCTC (corresponding parts of congruent triangles are congruent)
5ljhgfghjkjhghjkjhgfghjhi xbhljxjhgv sgdx
Determine the length of the missing side in the triangle shown.
right triangle with one leg labeled 11 and hypotenuse labeled 15
square root of 346
square root of 104
square root of 26
square root of 4
aspa pls thanks!
Answer: square root of 104
Step-by-step explanation:
The length of the missing side in the right triangle is approximately √104.
Given is a right triangle with one leg labeled 11 and hypotenuse labeled 15.
We need to find length of the missing side.
To determine the length of the missing side in the right triangle, we can use the Pythagorean theorem.
It states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's denote the missing side as "x".
According to the given information:
One leg (one of the shorter sides) is labeled as 11.
The hypotenuse (the longest side) is labeled as 15.
Using the Pythagorean theorem, we can set up the equation:
11² + x² = 15²
Simplifying this equation:
121 + x² = 225
Subtracting 121 from both sides:
x² = 225 - 121
x² = 104
To find the value of "x," we can take the square root of both sides of the equation:
x = √104
Therefore, the length of the missing side in the right triangle is approximately √104.
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10k²=50 quadratic equation
Answer:
see my photo. hope it can help
Rashon has a dimes and y nickels. He has no less than 12 coins worth at most $0.95
combined. Solve this system of inequalities graphically and determine one possible
solution.
A possible solution of the system of inequalities is 5 dimes and, 8 nickels
How to determine a possible solution?From the question, the given parameters are:
Number of coins = Not less than 12
Worth = At most $0.95
Represent dime with x and nickels with y
So, we have the following inequalities
x + y >= 12
0.1x +0.05y <= 0.95
Next, we plot the graph of the inequalities (see attachment)
From the graph, we have a possible solution to be (5, 8)
This is so because this point is in the shaded region
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In Exercises 76, find an equation of the tagent line to
the graph of the function f through the point (xo, yo not on the
graph. To find the point of tangency (x, y) on the graph of f
solve the equation
76.
f(x) = 2/x
(xo, Yo) = (5,0)
The most appropriate choice for tangent to a curve will be given by- 2x + 25y = 10 is the required equation of tangent.
What is tangent to a curve?
In geometry, a tangent line is a straight line that most closely resembles (or "clings to") a curve at a particular point. It could be thought of as the limiting role of straight lines that pass through the specified point and a nearby curve point as the second point gets closer to the first. If two curves share the same tangent at a given point, they are said to be tangent. Similar definitions apply to the tangent plane to an exterior at a point and two surfaces that are tangent at a point.
Equation of tangent to a curve at a point [tex](x_1, y_1)[/tex] is given by
[tex]y-y_1 = \frac{dy}{dx}|_{(x_1, y_1)}(x - x_1)[/tex]
Here,
f(x) = [tex]\frac{2}{x}[/tex]
f'(x) = [tex]\frac{d}{dx} (\frac{2}{x})[/tex]
= [tex]2(-1)x^{-1-1}\\-2x^{-2}[/tex]
[tex]f'(x)|_{(5, 0)} = -\frac{2}{5^2}[/tex]
[tex]= -\frac{2}{25}[/tex]
Equation of tangent
[tex]y - 0 = -\frac{2}{25}(x - 5)\\\\25y = -2x +10\\2x + 25y = 10[/tex]
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Latoya works mowing lawns and babysitting. She earns $9.40 an hour for mowing and $8.10an hour for babysitting. How much will she earn for 4 hours of mowing and hour of babysitting?
Answer:
$45.70
Step-by-step explanation:
$9.40 four times and $8.10 1 time so 9.40 x 4 = 37.6 + 8.10 = 45.70
Write the equation of a line using the given information:
Same slope as x=-2 and passes through the point (7,-1)
Answer:
y-y1=m(x-x1)
y+1=-2(x-7)
y+1=-2x+14
-1 -1
y=-2x+13
Step-by-step explanation: