using this module predict when it will take to reach approximately 300 female turtles ? how many female turtles will there be in 7 years?
Answers
Answer
a) It will take 3.54 years for the turtle population to hit 300 female turtles.
b) There will be 78,125 female turtles in 7 years.
Explanation
The model has been give to us as
T(t) = 5ᵗ
where
T(t) = Female turtle population at any time t
t = time in years
First part of the question asks us to find when the turtle population will hit 300 female turtles. That is, find t when T(t) = 300
T(t) = 5ᵗ
300 = 5ᵗ
We can rewrite this as
5ᵗ = 300
We will take the natural logarithms of both sides
In 5ᵗ = In 300
t (In 5) = In 300
t (1.6094) = 5.7038
Divide both sides by 1.6094
t = (5.7038/1.6094)
t = 3.54 years = 3 years, 6.5 months
For the second part of the question, we want to calculate the number of female turtles when t = 7 years
T(t) = 5ᵗ
T(7) = 5⁷ = 78,125 female turtles
Hope this Helps!!!
Related Questions
A scientist begins with 100 milligrams of a radioactive substance, which decays exponentially.after 9 hours 55mg of the substance remains How many milligrams will remain after 21 hours? Round the answer to the nearest whole number and include units
Answers
We have that the general expression for a function with exponential growth or decay is:
[tex]f(t)=ab^t[/tex]where 'a' represents the initial value, 'b' represents the growth or decay and t represents the time.
In this case, we have that a = 100, since that is the initial population (100 mg of radioactive substance). Also, since we have that after 9 hours, 55 mg of the substance remains, we have the following equation:
[tex]f(9)=55[/tex]now, given the exponential function, with a = 100, we have:
[tex]f(t)=100b^t[/tex]then, combining both expressions, we get:
[tex]f(9)=100b^9=55[/tex]solving for b, we have:
[tex]\begin{gathered} 100b^9=55 \\ \Rightarrow b^9=\frac{55}{100} \\ \Rightarrow b=\sqrt[9]{\frac{55}{100}}=0.935 \\ b=.935 \end{gathered}[/tex]then, the function is defined as follows:
[tex]f(t)=100\cdot(0.935)^t[/tex]finally, to find out how many milligrams will remain after 21 hours, we can make t = 21 and evaluate the function:
[tex]\begin{gathered} t=21 \\ \Rightarrow f(21)=100(0.935)^{21}=24.38 \\ f(21)=24.38mg \end{gathered}[/tex]therefore, there will be 24.38mg after 21 hours
Hello all the info I was given is right there
Answers
11.
We can determine the number of real solutions checking the number of times the graph crosses the x-axis, therefore, we can conclude from the graph that the function has 2 real solutions
Is this the right answer to the question. Not 100% sure.
Answers
Answer:
Yes, you are correct. Lines l and m are parallel, so corresponding angles are congruent. It does follow that x = 60.
Saquon Barkley lost 7 2⁄3 yards on the first play, and gained 9 5⁄8 yards on the next play. What was the total gain or loss for the running back during the first two plays?
Answers
If Saquon Barkley lost [tex]7\frac{2}{3}[/tex] yards on the first play, and gained [tex]9\frac{5}{8}[/tex] yards on the next play, then the total gain for the running during the first two plays is [tex]1\frac{23}{24}[/tex] yards
The amount he lost on the first play = [tex]7\frac{2}{3}[/tex] yards
Convert the mixed fraction to the simple fraction
[tex]7\frac{2}{3}[/tex] yards = 23/3 yards
The amount he gained on the second play = [tex]9\frac{5}{8}[/tex] yards
Convert the mixed fraction to the simple fraction
[tex]9\frac{5}{8}[/tex] yards = 77/8 yards
The total gain for the running during the first two plays = The amount he gained on the next play - The amount he lost on the first play
Substitute the values in the equation
= 77/8 - 23/3
= 47/24 yards
Convert the simple fraction to the mixed fraction
47/24 yards = [tex]1\frac{23}{24}[/tex] yards
Hence, if Saquon Barkley lost [tex]7\frac{2}{3}[/tex] yards on the first play, and gained [tex]9\frac{5}{8}[/tex] yards on the next play, then the total gain for the running during the first two plays is [tex]1\frac{23}{24}[/tex] yards.
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what is 11/15 + (- 3/5)
Answers
we have
11/15 + (- 3/5)
step 1
REmove the parenthesis
11/15-3/5
Remember that
3/5(3/3)=9/15 ------> is the same number
substitute
11/15-9/15 -----> the fractions have the same deniominator
so
(11-9)/15
2/15
negative 45 minus negative 19
Answers
Answer:
-26
Step-by-step explanation:
Answer:
The answer to this problem is -26
what is the answer too 14:10=:55
Answers
Answer: Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Step-by-step explanation:
There is a proportional relationship between minutes and dollars per minute, shown on a graph of printing expenses. The graph passes through the point (1, 3.40). What is the slope of the graph? What is the unit rate? Complete the explanation The slope is passes through the point (1 The unit rate is $ Vmin. If the graph ofa proportional relationship r), then r equals the slope and unit rate.
Answers
Let:
(x1,y1)=(0,0)
(x2,y2)=(1,3.40)
The slope is:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{3.40-0}{1-0}=\frac{3.40}{1}=3.40[/tex]The unit rate is:
[tex]\frac{3.40}{\min }[/tex]Which picture shows a properreflection across the red dashed line?АB
Answers
When you reflect a point across the red dashed line y = x, the x-coordinate and y-coordinate change places;
If you reflect over the red dashed line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x).
Thus, the picture that shows a proper reflection across the red dashed line is B
The price of a train ticket consists of an initial fee of $5 plus a fee of $2.75 per stop. Julia has $21 and would liketo travel 50 kilometers. She wants to know the largest number of stops she can afford to buy on a ticket
Answers
We have that the price of a train ticket has an initial fee of $5 and $2.75 per stop.
Then, we can represent this using the next inequality:
[tex]5+2.75\cdot S\leq21[/tex]In the inequality, we have some restrictions:
• Julia only has $21, no more than that.
,• In the inequality, we need to talk about the same units. If we have units in money on one side of the inequality, we need to have the same units on the other side of the inequality.
,•
Therefore, the scenario can be described by the inequality presented in the first option (option A).
2f = -12f=??[tex]2f = - 12 \\ \\ f = [/tex]
Answers
Given:
2f = -12
We are required to find the value of f.
To find f, divide both sides of the equation by 2.
We have:
[tex]\begin{gathered} \frac{2f}{2}=-\frac{12}{2} \\ \\ f\text{ = -6} \end{gathered}[/tex]ANSWER:
f = -6
Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line x + 2y = 6?
Drag each choice into the boxes to correctly complete the table.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Parallel Perpendicular Neither
y=−12x−5−2x+y=−4−x+2y=2x+2y=−2
Answers
Answer:
Step-by-step explanation:Base line: x + 2y = 6
Parallel: Continous, never touching
Perpendicular: Create a right angle when touching
y= -1/2x -5 : Parallel
-2x+y=-4 : Pependicular
-x+2y=2 : Neither
x+2y=-2 : Parallel
The bedroom floor is in the shape of a rectangle. It is 14 feet long and 16 feet wide. Your client has requested that you install either oak flooring or maple flooring. The oak flooring costs $5.25 per square foot for materials. The maple flooring costs $7.00 per square foot for materials. The cost you charge for labor will be the same for either flooring options.
How much money will your client save if you install oak flooring instead of maple flooring?
Answers
========================================================
Explanation:
The room is 14 ft by 16 ft.
The floor area is 14*16 = 224 sq ft.
Since oak costs $5.25 per sq ft, this means the total cost of an oak floor is 5.25*224 = 1176 dollars.
Meanwhile, maple flooring will have a total cost of 7*224 = 1568 dollars
If you go with the cheaper option (oak), then the savings is 1568-1176 = 392
----------
Alternative Route:
The difference in per sq ft costs is 7.00-5.25 = 1.75, meaning you save $1.75 per sq ft if you go with the cheaper option.
Multiply this with the total floor area to get 1.75*224 = 392
HELP!!!!!!!
they are 10 to 10. my screen isn't big enough to screenshot it.
A B C or D
Answers
The points (0, 4) , (1, 2) and (2, 0) are shown in figure.
Option 2 is true.
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
In the table,
The values of x = 0 , 1 , 2
The values of y = 4 , 2 , 0
Now,
The coordinates are;
(x , y) = (0, 4) , (1, 2) and (2, 0)
Here, For the value of x shows the coordinates for x - axis.
The value of y shows the coordinates for y - axis.
So, The points (0, 4) , (1, 2) and (2, 0) are draw on the graph as given in figure.
Thus, The points (0, 4) , (1, 2) and (2, 0) are shown in figure.
Option 2 is true.
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Given a triangle with a = 1, A = 17°, and B = 32°, what is the length of c? Round to the nearesttenth.
Answers
a=1
A=17°
B=32°
c=?
[tex]\frac{a}{\sin A}=\frac{c}{\sin C}[/tex][tex]C=180-17-32=131[/tex][tex]\frac{1}{\sin 17}=\frac{c}{\sin 131}[/tex][tex]\frac{1}{0.2924}\cdot0.7547=c[/tex][tex]2.58=c[/tex]a hotel manager has 12 diferent promotional events,plans to run 4 weeks, how many events can she run
Answers
Answer: 3 per week.
Step-by-step explanation: 3 x 4 = 12.
HELP PLEASEEEEEEEEE!!!!!!!! ILL MARK BRAINLIEST
Answers
Answer:
(3.11), (310/100),(1/3),(3/10),(2/-3) Hope I helped
Step-by-step explanation:
310/100 when divided gives us 3 10/100 or in simple form 3.1
1/3 is the smallest rational number but in simple form it is equal to 0.3(3) never ending multiplication of 3
3.11 is displayed in simple form so there is no need to change the number
3/10 can be displayed in simple form as 0.3( remember when dividing by a multiplication of 10 move the decimal point to the left of the lumber by the amount of zeros)
2/-3 since we are dividing the number by a negative number the result will end up in the negatives so lets think of it as 2/3 and later add the negative sign. 2/3 is equal to 0.6(6) and since we are dividing by a negative the result will be -0.6(6)
Alyssa paints 3 walls blue. Each of the walls is 8.3 feet tall and 7.5 feet wide. Round the length and width to the nearest whole number. Then estimate the area that Alyssa will paint. Write equations to show your work. Once, you have done everything find the exact area. Write equations to show your work. Then, compare your estimate to the exact answer. Why is your answer reasonable?
Answers
The equation to show the area Allysa will paint is Area = 3(Height x Width) = 3( 8.3ft * 7.5ft) and the area is 186.75 ft²
How to solve Algebraic Word Problems?We are given the dimensions of wall as 8.3ft by 7.5ft.
Thus;Height of wall = 8.3 ft
Width of wall = 7.5 ft
Now, there are total 3 walls in the bedroom to be painted blue.
The formula to calculate the area of one wall is;
A = Height x WidthFormula to calculate the area of four walls will be;
Area = 3(Height x Width) = 3( 8.3ft * 7.5ft)
= 3 (62.25 ft²)= 186.75 ft²
Thus, an area that Alyssa will paint = 186.75 ft²
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Find the quotient.0.56/−0.7
Answers
ANSWER
-0.8
EXPLANATION
The division between a positive number and a negative number gives as a result a negative number. With this in mind, we can do the division as if the numbers were both positive and then add the minus sign to the result:
Adding the minus sign, the result is -0.8
This is a multi-part Item. Make note of your answer(s) to this part for use in the remaining part(s).Kara and Nathan participated in a 60-minute maze race.Kara:32 minutesNathan:40 minutesPart AUse ratio notation and decimal notation to describe the relationship between Kara's time and the total time of the race.Enter the correct answers in the box. For the decimal, enter the digit that repeats 3 times.Hint(s): Write the ratio of Kara's time over the total time.Use long division to write the fraction as a decimal.ratio:decimal:
Answers
Answer:
Kara's rate over the total time is 0.5333
Step-by-step explanation:
Kara finished the race in 32 minutes.
The total duration of the race was 60 minutes.
So the ratio is:
32/60 = 16/30 = 8/15 = 0.5333
Kara's rate over the total time is 0.5333
Make the following conversions. Round your answers to 2 decimal places, where necessary.5 hours 10 minutes toa. Minutes: ? minb. Hours: ? hr
Answers
Let's do the math for this question.
The area of the scale model of a playground is 6 square yards. The scale model is enlarged by a scale factor of 3 to create the actual playground. What is the area of the actual playground?
Answers
The actual area of the playground is 54 square yards
How to determine the area?The given parameters are
Area of the scale model = 6 square yardsScale factor of dilation = 3The actual area of the playground is calculated as
Actual area = Area of the scale model * Scale factor of dilation^2
Substitute the known values in the above equation
So, we have
Actual area = 6 * 3^2
Evaluate the exponent
Actual area = 6 * 9
Evaluate the product
Actual area = 54
Hence, the value of the area is 54
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Use the graph below for this question: graph of parabola going through 2, negative 3 and 3, negative 1. What is the average rate of change from x = 2 to x = 3? (1 point) a) 2 b) 3 c) 0 d)5
Answers
From x = 2 to x = 3 the average rate of change is 2.
The graph of the parabola passes through 2, negative 3 and 3, negative 1 or ( 2, - 3) and ( 3, - 1 ).
Let's say y = f(x) represents the function of the parabola.
Then f( 2 ) = - 3 and f( 3 ) = - 1
Now, for a function y = f(x) the average rate of change from x = a to x = b is given by the expression [ f( b ) - f( a ) ] / ( b - a)
When x changes from x = 2 to x = 3,
The average rate of change will be:
[ f( 3 ) - f( 2 ) ] / ( 3 - 2 ) = [ - 1 - ( - 3 ) ] / 1 = 2
The average rate of change from x = 2 to x = 3 is 2.
The correct option is (a).
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Find compatible numbers to find two estimates.
2518 divided by 32
Answers
Answer: 78.6875
Step-by-step explanation:
math
The function g is defined as follows.
g(x)=x² +1
If the graph of g is translated vertically upward by 4 units, it becomes the graph of a function h.
Find the expression for h (x).
Answers
Answer:
Use that steps to find your answer
Answer:
h(x) = g(x) + 5 = x² + 5
Step-by-step explanation:
Since the graph is translated vertically upward by 4 units, there is no change in the x values; for the same x value the new y value is +4 times the old y value
In the expression 5^2, the 2 represents the _________________.
A: product
B: sum
C: base
D: exponent
Answers
The number, 2, in the given expression represents the exponent. The correct option is D: exponent
The exponent in a mathematical expressionFrom the question, we are to determine what the number, 2, represents in the given expression
The given expression is
5^2
That is,
5²
An exponent is a number or letter written above and to the right of a mathematical expression called the base
In the given expression, the number 2 is written above and to the right of 5. The number 5 is the base in the expression.
Thus,
The 2 represents the exponent
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Question Let f(x) = -531+4. Evaluate f(-1). Do not include 'f(-1) =' in your answer.
Answers
Note that the function f(x) = -531+4 is a function that doesn't depend on x. Hence, it is a constant function. We have that f(x) = -531+4 = -527. This means that the function assigns to any input value the number -527. So, in this case
f(-1) = -527.
Simplify the expression
10 - 2(-10x + 7)
Answers
Answer: 20x - 4
Step-by-step explanation:
10 - 2(-10x+7)
Distribute the -2:
10 + 20x -14
Combine Like Terms:
20x - 4
Angela purchase a shirt for $14.65 a pair of jeans for $21.99 and she was charged $2.93 tax how much change should she receive if she paid with a $50 bill
Answers
The cost of the shirt = $14.65
The cost of the pair of jeans = $21.99
Tax = $2.93
Amount paid = $50
Change = Amount paid - (Cost of shirt + Cost of jeans + tax)
Change = 50 - (14.65 + 21.99 + 2.93)
Change = 50 - 39.57
Change = $10.43
elenas bed measures 3‘ x 6‘ on the scale drawing what are the actual measurements of her bed
Answers
Using proportions, supposing a scale of 1 inch = 3 feet, the actual measurements of her bed are given by: 9 ft x 18 ft.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division, from the relations built in the problem.
One example of application of proportions is for scale problems, as the actual scale and the drawing length are compared to find the actual length of the object drawn.
In the context of this problem, the scale is given by:
1 inch = 3 feet.
The drawn length of the bed is given by:
3 inches x 6 inches.
Hence the actual length is given by:
9 feet x 18 feet.
As:
3 x 3 = 9.6 x 3 = 18.What is the missing information?The scale of the drawing is missing, hence we are going to suppose that it is 1 inch = 3 feet.
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