how long will it take for the population to reach 5656 fish, according to this model?
Answers
Question:
Solution:
The population growth is given by the following equation:
[tex]P(t)=(707)2^{\frac{t}{3}}[/tex]where P represents the number of individuals and t represents the number of years from the time of introduction. Now, if we have a population of 5656 fish, then the above equation becomes:
[tex]5656=(707)2^{\frac{t}{3}}[/tex]this is equivalent to:
[tex]2^{\frac{t}{3}}\text{ = }\frac{5656}{707}[/tex]this is equivalent to:
[tex]2^{\frac{t}{3}}\text{ = }8[/tex]this is equivalent to:
[tex](2^t)^{\frac{1}{3}}\text{ = }8[/tex]now, the inverse function of the root function is the exponential function. So that, we can apply the exponential function to the previous equation:
[tex]((2^t)^{\frac{1}{3}})^3\text{ = }8^3[/tex]this is equivalent to:
[tex](2^t)^{\frac{3}{3}}^{}\text{ = }512[/tex]this is equivalent to:
[tex]2^t\text{ = }512[/tex]now, we can apply the properties of the logarithms to the previous equation:
[tex]\log _2(2^t)\text{ = }log_2(512)[/tex]this is equivalent to:
[tex]t=log_2(512)\text{ = 9}[/tex]we can conclude that the correct answer is:
9 years
Related Questions
Carlos works a total of 86 hours in four weeks. He works 18.5 hours each week for three weeks. How many hours does Carlos work in the fourth week?
Answers
We are given the following information
Carlos works a total of 86 hours in four weeks.
He works 18.5 hours each week for three weeks.
To determine how many hours Carlos work in the fourth week, we can set up the equation
[tex]86=18.5(3)+x[/tex]We can make x the subject of the formula
[tex]\begin{gathered} x=86-18.5(3) \\ x=86-55.5 \end{gathered}[/tex]Simplifying further
[tex]x=30.5[/tex]Therefore in the fourth week, Carlos will work 30.5 hours
Write a system of two linear equations in two variables that you can
solve by subtracting the equations and that results in a solution of (3, 1).
Answers
The system of two linear equations in two variables that we can solve by subtracting the equations and that results in a solution of (3, 1) is:-
x + y = 4
2x - 3y = 3
Let x + y be equation (1) and 2x - 3y = 3 be equation (2).
Multiplying (1) by 2, we get,
2x + 2y = 8 ...(3)
(3) - (2), we get,
(2x - 2x) + (2y - (-3y)) = 8 - 3
0 + 5y = 5
y = 5/5 = 1
y = 1
Putting y = 1 in (1), we get
x + 1 = 4
x = 4 - 1
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What ratio is equal to 4:18?
Answers
Answer:
2:9
or
8:32
There are many
Answer: 8:36 or 12:54
Step-by-step explanation:
All you have to do is multiply both by 2, so 4 times 2 is 8 and 18 x 2 is 36, and the answer is 8:36.
Given the pre-image coordinates (0, 5), (-3, 2), (4, -1) and transformed image coordinates (2, -5), (-1, -2), (6, 1), what is the coordinate transformation in function notation?
Answers
Given:
The pre-image coordinates (0, 5), (-3, 2), (4, -1) and transformed image coordinates (2, -5), (-1, -2), (6, 1).
Required:
We need to find the transformation in function notation.
Explanation:
Let (x,y) be the pre-image coordinate and (x',y') be the transformed image coordinates.
The transformation is
[tex](x,y)\rightarrow(x^{\prime},y^{\prime}).[/tex]Consider the points (0,5) and (2,-5).
Substitute the values in the transformation.
[tex](0,5)\rightarrow(2,-5)[/tex][tex](0,5)\rightarrow(0+2,-(5))[/tex]Let x =0 and y =5, we get
[tex](x,y)\rightarrow(x+2,-y)[/tex]Consider the points (-3,2) and (-1,-2).
[tex](-3,2)\rightarrow(-1,-2)[/tex][tex]Use\text{ }-3+2=-1.[/tex][tex](-3,2)\rightarrow(-3+2,-(2))[/tex]Let x =-3 and y=2.
[tex](x,y)\rightarrow(x+2,-y)[/tex]Consider the points (4,-1) and (6,-1).
[tex](4,-1)\rightarrow(6,1)[/tex][tex]Use\text{ }4+2=6.[/tex][tex](4,-1)\rightarrow(4+1,-(1))[/tex][tex](x,y)\rightarrow(x+2,-y)[/tex][tex]f(x,y)=(x+2,-y)[/tex]Final answer:
[tex](x,y)\rightarrow(x+2,-y)[/tex][tex]f:(x,y)\rightarrow(x+2,-y)[/tex]Complete each equation below so that it shows equivalent fractions.
Answers
4/5 would be 8/10 because you’re multiplying by 2
1/6 can be many, but the answer would be 2/12 because you multiplied by two
Answer:
[tex]\frac{3}{12}, \frac{8}{10},\frac{2}{12}[/tex]
Step-by-step explanation:
→ Find the multiplier in the first one
12 ÷ 4 = 3
→ Multiply onto top
[tex]\frac{3}{12}[/tex]
→ Find multiplier for second one
10 ÷ 5 = 2
→ Multiply
2 × 4 = 8
Which box plot represe nts the data sei {1,3,5,7,9,11)? -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 © 2018 Songlind Created using Geogebra -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 6 7 2018 Song Crested using GeoGebra 1 2 3 4 5 6 7 8 9 10 11 © 2018 Songs Created using GeoGebra -1 0 1 2 3 4 5 6 7 8 9 10 11 12-13 2018 StrongMind Created using GeoGebra
Answers
The graphs represents the box plot of the data, then it divides the data in fourths.
Since we have 6 data, the median must be the average
[tex]\frac{5+7}{2}=6[/tex]Since the only option where the median is in the number 6 is the third one then that is the correct answer.
But we can analyse more about the data, since
[tex]\begin{gathered} \frac{1}{6}\cong0.167 \\ \frac{2}{6}\cong0.33>0.25 \end{gathered}[/tex]Then, the firs quartile must be at the second number, that is, the number 3, and the third quartile at the fifth number, that is, 9.
A jar of sweet pickles contains 650 grams of pickles. There are 12 jars in a case. How many kilograms of pickles are in a case?
Answers
Find the missing angle measures. PLS HELP IM SO CONFUSED AND I HAVE A TEST TOMMROW
Answers
Answer:
7. x = 35 y = 25
6. m = 129
10. 30
Step-by-step explanation:
The sum of the interior angles of a tringle is 180°. The smaller tringle on the right adds up to 180.
One angle is 90, that is the angle that has a small square. Another angle is 55 so the last angle needs to be 35 (90+ 55+35 = 180)
The larger triangle is 25 (90 + 55 + 10 + 25 = 180)
6 m= the sum of the other two angles that are given
10 140 = 90 + 1
1 = 30
Answer:
Step-by-step explanation:
I think you are trying to answer #7 ? I'll do that one
I see that you knew X =35°
and you knew that b/c it's always 180° around the inside, or interior , or minor angles of the RIGHT triangle (i'm making a big point out of the triangle being a "Right" one, b/c it matters for what we know about the triangle.)
so now you can add 10° to the 55° to get the next bigger RIGHT triangle.
65° is the upper angle so the ∠z = 25°
also you know [tex]y^{0}[/tex] b/c you know [tex]x^{0}[/tex] = 35° and
[tex]y^{0}[/tex] + [tex]x^{0}[/tex] = 180 , again
[tex]y^{0}[/tex] = 180-35
[tex]y^{0}[/tex] = 145°
what is the name of this system? consistent and dependent, consistent and independent, or inconsistent?
Answers
If a system has at least one solution, it is said to be consistent .
For system to be independent,
If a consistent system has exactly one solution, it is independent .
For system to be dependent,
If a consistent system has an infinite number of solutions, it is dependent .
The graph is given in the question tab which has exactly one solution.
So the given system is consistent and independent.
look at picture! thank you!
Answers
Answer:
middle, last, first
What is the answer???
Answers
9.7=9(theta) solve for theta
theta equals 1.078 rad
If you need the answer in degrees multiply 1.078 by 180 over pi
Answer: Approx. 62 degrees
Find the equation of a circle with the center at ( 0, 0 ) and a radius of 1.
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given details
[tex]\begin{gathered} center:(0,0) \\ radius:1 \end{gathered}[/tex]STEP 2: Write the formula for equation of a circle
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ Where\text{ }(h,k)\text{ is the center} \\ r\text{ is the radius} \end{gathered}[/tex]STEP 3: Find the equation of the circle
[tex]\begin{gathered} By\text{ substitution,} \\ (x-0)^2+(y-0)^2=1^2 \\ x^2+y^2=1^2 \\ x^2+y^2=1 \end{gathered}[/tex]Hence, the equation of the circle is given as:
[tex]x^2+y^2=1^[/tex]of the 1800 students enrolled in school 55% are girls of the girls attending the school 30% take the bus to school of the boys attending the school 70% take the bus to school how many boys take the bus to school
Answers
If 55% of the students are girls, 45% of the students are boys
[tex]1800\cdot0.45=810[/tex]It means there are 810 boys. From this number, 70% take the bus to school
[tex]810\cdot0.70=567[/tex]It means 567 boys take the bus to school.
Trey drew a map of the summer camp he is staying at this summer. He graphed the point D(-4.5, 4.5) for the dining
hall. The flag pole is located at D', a reflection of D across the y-axis. The campfire is located at D", a reflection of D'
across the x-axis.
Identify the ordered pair that describes the location of the campfire. Express your answer using decimal notation.
Answers
The coordinates of the campfire is D'' ( x₂ , y₂ ) = D'' ( 4.5 , -4.5 )
What is Reflection?
Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images
The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of the point (x, y) across the y-axis is (-x, y)
Given data ,
Let the coordinates for the dining be = D (x , y )
Let the coordinate of the point D (x , y ) be = D ( -4.5 , 4.5 )
Now ,
The coordinates for the flag pole is D'
where D' ( x₁ , y₁ ) is the reflection of D (x , y ) across the y-axis
So , When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of the point (x, y) across the y-axis is (-x, y)
Therefore , D' ( x₁ , y₁ ) = D' ( 4.5 , 4.5 )
Now ,
The coordinates for the campfire is D'' ( x₂ , y₂ )
where D'' ( x₂ , y₂ ) is the reflection of D' ( x₁ , y₁ ) across the x-axis
So , When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of the point (x, y) across the x-axis is (x, -y)
Therefore , D'' ( x₂ , y₂ ) = D'' ( 4.5 , -4.5 )
Hence , The coordinates of the campfire is D'' ( x₂ , y₂ ) = D'' ( 4.5 , -4.5 )
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Find the slope of the line. Write your answer in simplest form.
-5-4-3-2-1
(1, -3)
(-5,-4)
The slope is
45
y
1 x
Answers
The slope of the line is 1/6 when the graph has a line with points (1,-3) and (-5,-4).
Given that,
In the picture we have a graph with lines with 2 points.
We have to find the slope of the graph of line.
We have points (1,-3) and (-5,-4)
Slope of the line is m
m is rise/run
Rise is y₂-y₁
Run is x₂-x₁
Slope is (-4+3)/(-5-1)
Slope is (-1)/(-6)
Slope is 1/6
Therefore, The slope of the line is 1/6 when the graph has a line with points (1,-3) and (-5,-4).
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help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: 10.8 seconds
Step-by-step explanation:
[tex]-16t^2 +170t+40=10\\\\16t^2 -170t-30=0\\ \\ t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]
find the length of one side of a solid cube given that its
volume is 8 cm cube
total surface area is 54 cm square.
Answers
Step-by-step explanation:
I assume you mean as second question "what is the volume of a cube with the surface area of 54 cm² ?".
first question :
volume is 8 cm³
the volume of a cube is side³.
8 cm³ = side³
side = cubic root(8) = 2 cm
add-on : the surface of a cube (6 sides) is 6 times the area of side² squares.
surface = 6 × 2² = 6 × 4 = 24 cm²
second question :
54 cm² = 6 × side²
9 = side²
side = sqrt(9) = 3 cm
and the volume would be
side³ = 3³ = 27 cm³
Using the digits 1 to 10 at most one time each, fill in the boxes to make the result is closest to 1
Answers
Answer:
Using the digits 1 to 10 at most one time each to fill the given boxes, the value that makes the expression closest to 1 is;
[tex]\frac{(\frac{10}{5})^6}{(\frac{4}{1})^3}[/tex]Explanation:
Given the question in the attached image.
To make sure the result of the expression is closest to 1, we must make sure the value of the denominator and the numerator of the fraction is as close as possible.
[tex]\text{ denominator }\approx\text{ numerator}[/tex]Picking a set of values for the numerator, we must also try to select a separate set of values for the denominator that gives a result that is almost equal to the numerator.
Using this method we can arrive at a possible solution;
[tex]\frac{(\frac{10}{5})^6}{(\frac{4}{1})^3}[/tex]Let us simplify this expression to confirm;
[tex]\frac{(\frac{10}{5})^6}{(\frac{4}{1})^3}=\frac{(2)^6}{(4)^3}=\frac{64}{64}=1[/tex]Therefore, Using the digits 1 to 10 at most one time each to fill the given boxes, the value that makes the expression closest to 1 is;
[tex]\frac{(\frac{10}{5})^6}{(\frac{4}{1})^3}[/tex]which description shades length of the number line below?
Answers
Given the number line, it appears that in every 1/2 of a number, there are 5 bars in it. And in every 5 bars, 4 bars were shaded.
Adding the number of shades, we get:
4 + 4 + 4 = 12
Adding the total number of bars, we get:
5 + 5 + 5 = 15
The total number of bars sums up to be 3/2 in the number line.
Putting this into an equation, we get:
[tex]\text{ }\frac{12}{15}\text{ of }\frac{3}{2}\rightarrow\frac{\frac{12}{3}}{\frac{15}{3}}\rightarrow\frac{4}{5}of\frac{3}{2}\text{ }[/tex]Therefore, the answer is 4/5 of 3/2. It is letter B.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
To the nearest tenth, the sides measure 4.5, 9.5, and 10.5 units.
Step-by-step explanation:
[tex]{x}^{2} + {(x + 5)}^{2} = {(x + 6)}^{2} [/tex]
[tex] {x}^{2} + {x}^{2} + 10x + 25 = {x}^{2} + 12x + 36[/tex]
[tex]2 {x}^{2} + 10x + 25 = {x}^{2} + 12x + 36[/tex]
[tex] {x}^{2} - 2x - 11 = 0[/tex]
x = 4.5, so x + 5 = 9.5 and x + 6 = 10.5
(Lesson 12.2) Graph the system of linear inequalities. Give two ordered pairs that are solutions andtwo that are not solutions. (2 points)9.sy 3x + 3w<-286I422 46 8-8 -6 -4 -20-2
Answers
ANSWER :
Two ordered pairs (Solution) : (-4, -4) and (-3, -3)
Two ordered pairs (Not a solution) : (1, 1) and (2, 3)
EXPLANATION :
From the problem, we have :
[tex]\begin{gathered} y\ge3x+3 \\ y<-2 \end{gathered}[/tex]Note that the boundary line is dashed or broken if the inequality symbol is < or >.
Otherwise, the boundary line is a solid line.
Graph the first inequality :
Change the symbol to "="
[tex]y=3x+3[/tex]Solve for the x and y intercepts.
[tex]\begin{gathered} \text{ when x = 0 :} \\ y=3(0)+3=3 \\ \\ \text{ when y = 0 :} \\ 0=3x+3 \\ -3x=3 \\ x=-\frac{3}{3}=-1 \end{gathered}[/tex]Test the inequality at the origin (0, 0)
The region will pass through the origin if it satisfy the inequality.
[tex]\begin{gathered} y\ge3x+3 \\ 0\ge3(0)+3 \\ 0\ge3 \\ \text{ False!} \end{gathered}[/tex]Therefore, the region will NOT pass through the origin.
Plot the points (0, 3) and (-1, 0).
Connect it with a solid line.
The region will NOT pass the origin.
Graph the second inequality :
Change the symbol to "="
[tex]y=-2[/tex]Since y must be less than -2, the region is from y = -2 to the negative infinity.
Plot the point (0, -2) and draw a horizontal dashed line since the symbol is <.
That will be :
The solution to the inequality is the overlapping region.
Any point in the overlapping region is a solution.
Two ordered pairs solution are (-3, -3) and (-4, -4)
Two ordered pairs that are NOT a solution : (1, 1) and (2, 3)
The table lists the locations of four underwater camreas relative to sea level which camrea is the farthest from the surface of the water
Answers
The fish camera will farthest from from the surface of water as it is -15 1/3 feet away that is 15 1/3 feet below the sea level. so correct option is B.
What is number line?A number line is a diagram of a graduated straight line used to represent real numbers in elementary mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point. A number line is a visual representation of numbers on a straight line in mathematics. A number line's numbers are arranged in a sequential manner at equal intervals along its length. It is typically represented horizontally and can extend indefinitely in any direction. A number line is exactly what it sounds like—a horizontal, straight line with numbers spaced evenly apart along its length.
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Let f(x) = 4x-5 and g(x) = 3x, find (f+g)(x).
Answers
Answer:
7x-5
Step-by-step explanation:
A group of 6 students was asked, "How many hours did you watch television last week?" Here are their responses.11, 11, 4, 9, 10, 17Find the mean number of hours for these students.If necessary, round your answer to the nearest tenth.hours
Answers
The mean number of hours for these students 10.3
Explanation:Given the following data:
11, 11, 4, 9, 10, 17
The mean is the sum of the data divided by the number of elements in the data.
Sum of data is:
11 + 11 + 4 + 9 + 10 + 17 = 62
Number of elements in the data is:
6
The mean is now:
62/6 = 10.3
Colette earned a total of $15 for 3 hours of yard work. How many hours in all will it take Colette to earn $20? Assume the relationship is directly proportional.
Answers
Answer:
Step-by-step explanation:
It would take four hours because you divide fifteen dollars by three hours which would be five per hour. If each hour is five dollars, then four hours would be twenty dollars.
I need know the answer and how to write out my answer as well
Answers
5 . 3
6 I 3 1 . 8
- 3 0
1 8
- 1 8
0
Therefore, the answer is 5.3
A box of cereal costs $3.59 for 30 oz. Find the unit cost, round to the nearest hundredth. ?
Answers
Someone answer this?
Answers
Answer:
lawsuits
Step-by-step explanation:
Roster method The set of n negative integers greater than -7
Answers
Remember that
The Roster Method is a way to show the elements of a set by listing the elements inside brackets.
In this problem we have
The set of n negative integers greater than -7
so
the negative integers greater than -7 are
-6,-5,-4,-3,-2 and -1
therefore
The elements are
{-6,-5,-4,-3,-2,-1}Emma drew 11 hearts and 20 cycles.What is the ratio of circles to hearts in simplified form?
Answers
The ratio of a to be is expressed as a/b or a:b
Given that Emma drew 11 hearts and 20 cycles, the ratio of circles to hearts would be
20/11
Looking at the above ratio, there are no common factors. This means that it cannot be simplified further. Therefore, the ratio of circles to hearts in simplified form is
20/11