A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days: f(d) = 11(1.01)°
Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm.
What is a reasonable domain tc plot the growth function?
(4 points)
Part B: What does the y-intercept of the graph of the function f(c) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent? (4 points)
Answers
Answer:
Step-by-step explanation:
a.
f(d)=11(1.01^d
d=6.97 days
b.
t
f(c) represents the size of algae after c days
c.
f(2)=11(1.01)^2
f(7)=11(1.01)^7
[tex]rate=\frac{f(7)-f(2)}{7-2} \\=\frac{11(1.01)^7-11(1.01)^2}{5} \\=\frac{11[(1.01)^7-(1.01)^2]}{5} \\\approx 0.0104 ~mm[/tex]
Related Questions
let f(x) = x-1 graph g(x)=f(3/4x)
Answers
The graph of the function g(x) after putting the value in function f(x) is attached with the answer.
What is function?
A relation b/w a collection of inputs and outputs is known as a function. A function is a relationship between inputs in which each input is connected to precisely one output.
Given function: f(x) = x-1
we have to find: g(x)=f(3/4x)
Putting the value of f(x) in g(x),
g(x) = 3/4x - 1
Now, the graph of the function (3/4)x - 1 is attached in the question.
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b) On the grid draw the graph of x+y=6 for values of c between -2 and 3
Answers
Which of the following is an example of the identity property of 1?
1.11(0)=0
0+2 4/5=2 4/5
11/15(1)=11/15
3-2=1
Answers
Answer:
i think third answer is write
I earn $285/week. There are 4 pays in most months. So, my monthly pay is $285 x 4 or $1140 per month.
Is my calculation of my monthly income accurate? Please explain.
Answers
Answer: Yes
Step-by-step explanation: Most month have 4 weeks so your right.
Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x=9.9 and x = 8.7 and passes through the point ( 0, 8.5 )
Answers
Answer:
ft HD st he do it to we if do ks do just bc
which represents a rotation of 189
degrees?
(X,y) -> (-X,-y)
(X,y) -> (X,-y)
(X,y) -> (y,X)
(X,4) -> (-X,4)
Answers
The required rotation of the 180° is given by, (X,y) -> (-X,-y), option A is correct and the required translation is given by (x + 6, y - 2), option D is correct.
Given that,
To determine which option shows the rotation of 180°, and translation of right 6 units and down 2 units.
Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
Here,
For the rotation of the 180°, the given coordinate undergoes the change in direction so the required coordinate after 180° rotation is given as (-x, -y).
Now, for the translation of 6 units right we must add x with 6 and for 2 units down we must subtract y by 2, the required translation is given as(x + 6, y -2).
Thus, the required rotation of the 180° is given by, (X,y) -> (-X,-y), and the required translation is given by (x + 6, y - 2).
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Cheng is thinking a of a number
what number is Cheng thinking of ?
cheng thinking ;
I multiply my number by 100,hen divide by 10,then multiply by 1000.
My answer is 170'000
Is Cheng's answer is correct or incorrect
Answers
The number is 17
Let the number = x
From the question, we have
(x*100)/10*1000 = 170000
x = 17
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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What is 1 2/3 of 32 in fractions?
Answers
Answer:
53 1/3
Step-by-step explanation:
[tex]1\frac{2}{3} =\frac{3+2}{3} =\frac{5}{3}[/tex]
[tex](32)(\frac{5}{3} )=\frac{(32)(5)}{3} =\frac{160}{3}[/tex]
[tex]\frac{160}{3} =53 +\frac{1}{3} =53\frac{1}{3}[/tex]
Hope this helps
The value of the expression is [tex]\frac{160}{3}[/tex].
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
[tex]1\frac{2}{3}[/tex] of 32
= [tex]\frac{5}{3}[/tex] x 32
[ 5 x 32 = 160 ]
= [tex]\frac{160}{3}[/tex]
Thus,
The value of the expression is [tex]\frac{160}{3}[/tex].
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hi thank you for seeing this
Answers
Each pair of angles should be matched with the correct property (theorem) as follows:
e. Vertical Angles: Angles 7 and 6.
a. Alternate Exterior Angles: Angles 1 and 8.
g. Alternate Interior Angles: Angles 4 and 5.
h. Corresponding Angles: Angles 2 and 6.
d. Supplementary Angles: Angles 6 and 8.
What are parallel lines?Parallel lines simply refers to two (2) lines that always have the same or equal distance apart and never meet.
What is the alternate exterior angle theorem?The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed are congruent or angles of equal measure and magnitude such as Angles 1 and 8.
What is the alternate interior angles theorem?The alternate interior angles theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent such as Angles 4 and 5.
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I need help please and thank you.
Answers
The inequality that relates [tex]LN[/tex] and [tex]OQ[/tex] is [tex]LN>OQ[/tex].
Apply the distributive property to the following expression: 2n (5m -1)
I need HELP!! ASAP!!
Answers
By using the distributive property, we will rewrite the expression as:
2n*(5m -1) = 10*n*m - 2n
How to apply the distributive property?
The distributive property of the multiplication says that the product:
A*(B + C)
Can be rewritten as:
A*(B + C) = A*B + A*C
So we are "distributing" the product.
In this case, we have the expression:
2n*(5m - 1)
If we apply the distributive property, then we will get:
2n*(5m - 1) = (2n)*(5m) + (2n)*(-1)
Now we can simplify this expression to get:
(2n)*(5m) + (2n)*(-1) = 10*n*m - 2n
That is what we wanted to get.
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Question 10
Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A
pollster contacts 93 people in the 18-21 age bracket and finds that 79 of them respond and 14 refuse to
respond. When 251 people in the 22-29 age bracket are contacted, 219 respond and 32 refuse to respond.
Assume that 1 of the 344 people is randomly selected. Find the probability of getting someone in the 18-21
age bracket or someone who responds.
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
P(18-21 or responds) =
(Hint: It might be helpful to organize the data into a table first.)
Submit Question
%
Answers
The probability of getting someone in the 18-21 age bracket or someone who responds is 28.7%.
The total number of people in the 18-21 age bracket is 93. The number of people in this bracket who responded is 79. The number of people in this bracket who refuse to respond is 14. The total number of people in the 22-29 age bracket is 251. The number of people in this bracket who responded is 219. The number of people in this bracket who refuse to respond is 32.
A person is randomly selected from all the people surveyed. We need to find out the probability of getting someone in the 18-21 age bracket or someone who responds. Let the variables E1 and E2 represent the events.
E1 is the event of getting a person from the 18-21 age bracket.
E2 is the event of getting a person who responds.
P(E1∪E2) = P(E1) + P(E2) - P(E1∩E2)
P(E1∪E2) = (93/344) + [(79 + 219)/344] - (79/93)
P(E1∪E2) = 0.27035 + 0.86628 - 0.84946
P(E1∪E2) = 0.28717
Hence, the probability of getting someone in the 18-21 age bracket or someone who responds is 28.7%.
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I don't know what I'm doing! HELP!!!
Answers
Booker's father amount of commission earned is 668.31 dollars.
Sophia needs to make sells of 16744 dollars in order to earn at least 1800 dollars in commission.
How to find how much commission Booker's father will earn?Booker's father sells computer software and earns a 4.25% commission on every software package he sells.
The amount of commission he will earn after selling a software package of $15, 725 can be calculated as follows:
amount of commission earned = 4.25% of 15725
amount of commission earned = 4.25 / 100 × 15725
amount of commission earned = 66831.25 / 100
Therefore,
amount of commission earned = 668.3125
amount of commission earned = 668.31 dollars
Sophia needs to earn at least 1800 dollars each month to cover her living expenses.
The minimum she needs to sell in order to earn at least 1800 dollars if she earns 10.75% commission can be calculated as follows:
let
x = amount she needs to sell
Therefore,
10.75% of x ≥ 1800
10.75 / 100 x ≥ 1800
multiply both sides by 100
10.75x ≥ 180000
divide both sides by 10.75
x ≥ 16744.1860465
x ≥ 16744
Therefore, she needs to sell 16744 dollars worth of goods.
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The figure is cut into 12 equal pieces. Shade 2/3 of the figure.
Answers
Answer:
Step-by-step explanation:
OK:
I won't be able to draw this but if I can I will
1. Find 2/3 of the 12 pieces
2/3*12=
24/3=
8
2. Answer: Shade 8 out of 12 pieces
How far up the wall does the ladder reach (round your answer to the nearest tenth) enter only the numerical answer no label
Answers
Answer: 8.7m
Step-by-step explanation:
We can use the Pythagorean theorem to solve this,
[tex]a^2+b^2 = c^2[/tex]
We have a (5m) and c (10m) so we're looking for b.
We can rearrange the equation to find b into,
[tex]b^2 = c^2-a^2[/tex]
[tex]b^2=10^2-5^2[/tex]
[tex]b^2 = 100-25[/tex]
[tex]b^2=75[/tex]
[tex]b=8.66025404[/tex]
Rounded to the nearest tenth is 8.7m.
PLEASE PLEASE HURRY What is −12÷2/3? Responses −36 negative 36 −24 negative 24 −18 negative 18 −8 negative 8
Answers
Answer: -18
Step-by-step explanation:
im not 100% sure but good luck :)
Answer: -12/2/3=-2
Step-by-step explanation:
A right triangle has a leg that measures 7 in. The angle opposite this side measures
62°. What is the length of the hypotenuse of this triangle? Round to the nearest tenth.
(Remember to include the correct units in your answer)
Please help
Answers
The hypotenuse of the right triangle is 7.93 inches.
According to the question,
We have the following information:
A right triangle has a leg that measures 7 in. The angle opposite this side measures 62°.
Now, the hypotenuse can be easily found using the trigonometric function.
(More to know: in a right triangle, we can use the Pythagoras theorem. This theorem can not used in any other triangle.)
We will use sin 62 to find hypotenuse.
Sin 62 = perpendicular/hypotenuse
Hypotenuse = perpendicular/sin 62
Hypotenuse = 7/0.88295
Hypotenuse = 7.93 inches
Hence, the hypotenuse of the right triangle is 7.93 inches.
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A shelf and bracket are shown below. The shelf is
perpendicular to the wall.
Note: The figures is not drawn to scale
What angle (x), in degrees, does the bracket make with the wall?
Answers
60 degrees is he angles which are made by bracket with the wall
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The shelf is perpendicular to the wall.
The shelf makes an angle of 90 degree to the wall because when the shelf is perpendicular then the wall and shelf should be ninety degrees.
From the shelf edge to wall there creates an angle x.
We need to find the angle x.
As it forms a right angle triangle one angle is 90 degrees and the other angles should be 60 degrees and 60 degrees.
Hence 60 degrees is the angles which are made by bracket with the wall
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Find three even numbers less than 400, each of which can be expressed as a sum of consecutive positive odd numbers in at least six different ways.
Answers
Answer:
394, 396 and 398
Step-by-step explanation:
U= {2, 3, 4, 5, 7}
C= {2, 4}
D= {2, 7}
(a) (C n D)’=
(b) C’ U D=
Answers
The value of (CnD)'= {3,5} and the valueof C' U D = { 2,3,5,7}
What is complement of a set?The complement of a set is the set that includes all the elements of the universal set that are not present in the given set. Let's say A is a set of all coins which is a subset of a universal set that contains all coins and notes, so the complement of set A is a set of notes (which do not includes coins).
if U = { 2,3,4,5,7}
C= { 2,4}
D= { 2,7}
therefore (CnD)= { 2,4,7}
the complement of set (CnD) that is, (CnD)' = {3,5}
complement of set C (C')= { 3,5,7}
Therefore the union of C' and D(C' U D) = { 2,3,5,7}
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find the values of x, y, and z.
Answers
To find x, you would do 180-36-63, which would be 81.
Then you would do 180-81 to find z, which is 99.
To find y, would do do 180-99-13, which is 68.
Answer:
x=81
y=68
Z=99
Step-by-step explanation:
to find x we have to remember the rule that all 3 angles sum up to be 180 in a triangle
So we use this to find x
180-(63+36)=x
180-99=x
81=x
Now to find z since it is on a flat plane you just subtract 81 from 180 to find z
180-81=z
99=z
Now to find y we add all the angles of the second triangle and then subtract that sum by 180
180-(13+99)=y
180-112=y
68=y
Hopes this helps please mark brainliest
See picture-multiple choice.
Answers
From the given graph the correct statement is option (B) " As x approaches - ∞, f(x) approaches - ∞ and x approaches + ∞, f(x) approaches - ∞
From the given graph
The x axis represents the values of x, and the y axis represents the value of y
From the graph,
When the value of x moves from 0 to - ∞, then the value of f(x) is moves from 0 to - ∞
Similarly, when the value of x moves from 0 to ∞, the the value of f(x) is increased to positive values and then decreased to - ∞.
Hence, from the given graph the correct statement is option (B) " As x approaches - ∞, f(x) approaches - ∞ and x approaches + ∞, f(x) approaches - ∞
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Solve the following system of linear equations by graphing:
4x + 2y = -4
4x + 2y = -20
Graph the linear equations by writing the equations in slope-intercept form:
y= ___x + ___
y= ___x + ___
Identify the appropriate number of solutions. If there’s a solution, give the point.
Answers
Answer:
No solution. The lines are parallel
Step-by-step explanation:
I graphed with Desmos. It is a free.
The temperature gauge in your car records the temperature to be 27°C. What is that temperature to the nearest degree Fahrenheit?
Answers
===============================================
Work Shown:
F = (9/5)*C + 32
F = (9/5)*27 + 32
F = 80.6
F = 81
Side note: 9/5 = 1.8
Answer:
81 degrees Fahrenheit.
Step-by-step explanation:
Using the standard Fahrenheit-Celsius conversion formula.
27 * 9/5 = 48.6.
48.6 + 32 = 80.6.
Rounded to 81.
Therefore 81 degrees Fahrenheit.
Carter shared his post with 10 friends, who each share with only 2 people each day. Carter shared his post with 10 friends, who each share with only 2 people each day.
write an exponential function to represent the spread of carters social media post.
Answers
The exponential function will be equal to y = 20ˣ.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Carter shared his post with 10 friends, who each share with only 2 people each day.
The exponential function will be written as,
y = abˣ
y = 10(2)ˣ
y = 20ˣ
Therefore, the exponential function will be equal to y = 20ˣ.
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Answer:
f(x) = 10(2)^x
Step-by-step explanation:
Rule for solving: The first number is the first part of the equation, and the second number is in parenthesis.
4.8 is what percent of 12
Answers
Answer:
40%
Step-by-step explanation:
4.8 * 100 = 480
480 / 12 = 40
= 40%
I hope this helps.
Helppp!
Triangle FJE and GKH are similar right triangles. Which statements about the slopes of FE and GH is true?
Answers
G(-2,1)
H(4,9)
F(-5,-3)
E(-8,-7)
Therefore we can find the slope by using the formula : y1-y2/x1-x2
Let’s find slope GH
1-9/-2-4=-8/-6=4/3
Let’s find slope FE
-3-(-7)/-5-(-8)=4/3
The slope FE is equal to the slope of GH
B) is the right answer
A rectangular plece of carpet covers 180 yd². The width is 7 yd less than the length. Find the length and width.
Round your answers to the nearest tenth of a yard.
The length is approximately
yd.
The width?
Answers
THE LENGTH AND WIDTH WILL BE = length: 5.7 yd
width: 1.7 yd.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.We are aware of the quantity of apples and the amount of money in the aforesaid problem.According to our question-
w(w +4) = 10
w² +4w = 10 . . . . . eliminate parentheses
w² +4w +4 = 14 . . . . . . add the square of half the w-coefficient to complete the square
(w +2)² = 14 . . . . . . . . . rewrite as a square
w +2 = √14 . . . . . . . . . take the square root
2 = -2 +√14 ≈ 1.7 . . . . yards (width)
Then the length is 4 more yards than this, so is ...
length = 1.7 +4 = 5.7 . . . yards
The length and width are 5.7 and 1.7 yards, respectively.
In the attached graph, we let x represent the length. As you can see, the magnitudes of the two zeros are width and length.
HENCE,THE LENGTH AND WIDTH WILL BE = length: 5.7 yd width: 1.7 yd.
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Hi can someone please help me? Thank you so much have a good day/night! ;)
Answers
Answer:
136 cm
Step-by-step explanation:
area of rectangle-- width x length--- 112
area of triangle-- base x height divided by 2--- 24
please mark brainiest
What is answer? Tell me pls :)
Answers
Answer:
when y=20
x=unknown number
x-y=16
x=16+y
x=16+20
x=36
Step-by-step explanation: