The y intercept of the graph of the function f(d) indicates f(d) = 11 and the average rate of change of the function f(d) from d = 2 to d = 7 is 0.114, making 6.97 a reasonable domain to depict the growth function.
What is meant by equation ?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
An equation is a mathematical expression with two equal sides and an equal sign in between. An equation is a mathematical statement proving the equality of two numbers or values.
Equations can be categorized as either identities or conditional equations. For each value of the variables, an identity holds true. Only specific values of the variables make a conditional equation true. An equals symbol ("="), separating two expressions, is used to represent an equation.
Part A:
11.79 = 11(1.01[tex])^d[/tex]
substitute the values in the above equation, we get
[tex]$$& (1.01)^d[/tex] = 11.79 / 11
simplifying the equation, we get
[tex]$$& (1.01)^d[/tex] = 1.071818
d = log 1.071818 / log 1.01
The value of d = 6.97
Part B:
y-intercept is obtained when domain = 0
[tex]$& d=0 \Rightarrow f(0)=11(1.01)^0=11 \times 1=11 \\[/tex]
f(d) = 11
Part C:
Average rate of change,
[tex]$\Delta \mathrm{f} / \Delta \mathrm{d} & =(\mathrm{f}(7)-\mathrm{f}(2)) /(7-2) \\[/tex]
[tex]$& =\left(11(1.01)^7-11(1.01)^2\right) / 5 \\[/tex]
= 0.57 / 5 = 0.114
The y intercept of the graph of the function f(d) indicates f(d)=11 and the average rate of change of the function f(d) from d=2 to d=7 is 0.114, making 6.97 a reasonable domain to depict the growth function.
The complete question is:
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)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) 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?
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6.97 is an appropriate domain in which to represent the growth function because the y intercept of the graph of the function f(d) suggests that f(d) = 11 and the average rate of change of the function f(d) from d = 2 to d = 7 is 0.114 as studied by biologist.
What do you understand by equation ?A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra.
A mathematical expression with two equal sides and an equal sign in the middle is called an equation. A mathematical statement establishing the equality of two numbers or values is called an equation.
Either identities or conditional equations are categories for equations. Each value of the variables corresponds to a specific identity. A conditional equation can only be true for a certain range of variable values. An equation is represented by two expressions being separated by the equals sign ("=").
Part A:
11.79 = 11(1.01
substitute the values in the above equation, we get
[tex](1.01)^{d}[/tex] = 11.79 / 11
simplifying the equation, we get
(1.01)^{0} = 1.071818
d = log 1.071818 / log 1.01
The value of d = 6.97
Part B:
y-intercept is obtained when domain = 0
d = 0
f(0) = 11[tex](1.01^{0} )[/tex] = 11 * 1 = 11
f(d) = 11
Part C:
Average rate of change,
Δf / Δd = (f(7) - f(2)) / 7-2
= 0.57 / 5 = 0.114
The y intercept of the graph of the function f(d) indicates f(d)=11 and the average rate of change of the function f(d) from d=2 to d=7 is 0.114, making 6.97 a reasonable domain to depict the growth function.
The complete question is:
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)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) 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?
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Melanie answered 18 of
24 questions correctly
on a test. What percent
of her answers were
correct?
|GIVING BRAINLIEST| (no links)
75 percent
Megan answered 18 questions correctly on a test. That is 75 percent of the total number of questions (24) which were on the test.
What is the surface area of the square pyramid?
Answer:
16m^2
Step-by-step explanation:
SA = 2bs + b^2
= 2(2m)(3m) + (2m)^2
= 16m^2
HELP ME WITH THIS - FIRST ONE TO ANSWER GETS MARKED BRAINLIEST
Angle A and Angle B are complementary. If Angle A measures 48°, what is the measure of Angle B?
Answer: 42
Step-by-step explanation:
How much water and how much drink mix should Jerome use to make enough energy drink for all the runners? Create a table to show your work and explain your results in writing.
Answer:
well, you didnt give me any numbers or variables, so ill do it like this. if the container is the size of a pint, and there are 8 runners, and a pint equals 16 fluid ounces, in turn it should end as that each runner gets 2 fluid ounces of energy drink
Step-by-step explanation:
Which expression is equivalent to 20x-8y?
Select the correct answer
2(10x+4y)
4(5x-8y)
4(5x-2y)
x(20-8y)
Answer:
4(5x-2y)
Step-by-step explanation:
You can only take out the 4 because 20 and 8 are divisible by 4. You also can't take out x because it's only next to the 20 in the equation.
What is the distance of 2/3 from the horizontal axis in Cartesian plane?
Distance of 2/3 from the horizontal axis is 2 for a cartesian plane.
What is cartesian coordinate system?
The coordinate system in where the location of a point is identified by a pair of numerical terms and that has two reference axis is termed as cartesian coordinate system.
In cartesian plane the reference axis are named as X - axis and Y -axis.
In this system, location of a point p is identified by p (x, y) that means x is the x coordinate of point p and y is the y coordinate of point p. Generally, X-axis is horizontal, and Y-axis is vertical. Both axes are intersected at the origin.
What is the distance of 2/3 from the horizontal axis in cartesian plane?The point coordinate 2/3 denotes the location of a point with respect to a reference direction in the polar coordinate system. In the polar coordinate system, the angle between horizontal axis and a reference point is called polar angle. we know tan angle = vertical coordinate / horizontal coordinate.
hence, tan angle = 2/3
for this reason, if we imagine a cartesian coordinate system 2 is the y coordinate and 3 is the x coordinate.
Finally, the distance of 2/3 from the horizontal axis is 2.
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Find the area of the shape shown below.
Answer:
12.5
Step-by-step explanation:
So this is basically a rectangle. You make the 2 triangles a square.
2.5x2.5=6.25
6.25x2=12.5
Please help if the answer is right I will give brainliest. Simplify the radical
Answer:
[tex]\frac{2\sqrt{6}}{3n^{\frac{3}{2}}}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt{8}}{\sqrt{3n^3}}==\frac{\sqrt{8}}{\sqrt{3}n\sqrt{n}}=\frac{2\sqrt{2}}{\sqrt{3}n\sqrt{n}}=\frac{2\sqrt{6}}{3n^{\frac{3}{2}}}[/tex]
HELP PLEASE!!!
The circumference of a circular field is 276 yards. What is the diameter of the field?
Round your answer to the nearest hundredth.
Round 7.3084 to 2 decimal places.
Answer:
[tex] \sf \: 7.31[/tex]
Step-by-step explanation:
Now we have to,
→ round a number to 2 decimal places.
The number is,
→ 7.3084
Let's solve the problem,
→ 7.3084
→ ≈ 7.308
→ [tex] \boxed{ \sf ≈ 7.31} [/tex]
→ ≈ 7.3
Hence, the answer is 7.31.
A square rug measures 8 feet by 8 feet. find the diagonal distance of the rug to the nearest whole number
The box plot below describes a data set. Which of the following has a value of 18?
Answer:
the answer is third quartille
Step-by-step explanation
Solve the equation −14 - 1 4 (x – 26) = –200 for x.
Hello there!
Answer:
x = 39 2/7
Step-by-step explanation:
-14 - 14(x - 26) = -200
- 14 + 14 - 14(x - 26) = -200 + 14
-14(x - 26) = -186
-14(x - 26)/(-14) = -186/(-14)
x - 26 = 93/7
x - 26 + 26 = 93/7 + 26
x = 275/7
x = 39 2/7
1. An open box is to be made from a sheet of card 40cm by 30cm. A square of side x cm is to be
cut from each corner, as shown in the diagram, and then the sides will be folded up so that the
depth of the box will be x cm.
(a) Find in terms of x the length and width of the base of the box (ie AB and AD).
(b) The volume of the box is y. Write down an equation expressing y in terms of x.
Step-by-step explanation:
AB = DC = 40 - 2x
AD = BC = 30 - 2x
there is not more explanation possible, I think.
we cut off from each side 2 pieces of x cm. so, AB, DC, AD, BC are the the remaining lengths.
the volume of the box is ground area times height (x is the length of the remaining flaps after the cut, so, when folding up these flaps/sides, they will be x cm high).
Volume = y = AB×AD×x
=> y = (40-2x)×(30-2x)×x = (1200 - 60x - 80x + 4x²)×x =
= (1200 - 140x + 4x²)×x = 4x³ - 140x² + 1200x
How to answer this question
The value of x to the nearest degree will be 112°.
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
There are three angles are shown in figure.
That is,
⇒ 59°, 108°, and 81°.
Now, We know that;
Sum of all four angles is 360°.
So, We can formulate;
⇒ 59° + 108° + 81° + x = 360°
⇒ 248° + x = 360°
⇒ x = 360° - 248°
⇒ x = 112°
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Help Plz :)
Hehehehehehehee
Answer:
Step-by-step explanation:
.
.
find the measure of angle 1
Determine whether each number is prime or composite.
1. 41
2. 29
3. 87
4. 36
5. 57
6. 61
7. 71
8. 103
9. 39
10. 91
11. 47
12. 67
please!!!!Can somebody help me
1.)41 is prime
2.29 is prime
3.87 is composite
4.36 is composite
5.57 is composite
6.61 is prime
7.71 is prime
8.103 is prime
9.39 is composite
10. 91 is composite
Can u please helppppppppp
Answer:
Draw a vertical line that goes through the point given. This will make the two lines perpendicular. The line given is horizontal, a vertical like would be 90° o the horizontal line.
Step-by-step explanation:
HELP ME ASAP!!!!
A vertical mast is on top of building and is positioned 6' from edge of building. The mast casts a 90' shadow from front of building. Another building 24' tall casts a shadow 64'. What is the height of the mast?
a. 7ft 6in
b. 9ft 9in
c. 12ft
d. 33ft
Answer:
33.75
Step-by-step explanation:
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please help me out thank you so much whoever does !!
Answer: Angle c is 80 degrees
Equation: 60+40+x = 180
Step-by-step explanation: First of all, know a triangle equals 180 degrees. You add the angles you already know together and then subtract that number from 180. Then you get angle c. :)
(a) What is the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50
Using the normal distribution and the central limit theorem, it is found that there is a 0.0901 = 9.01% probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.
What is probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.To learn more about distribution refer to:
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√2x – 1- x = −8
How do I solve this equation?
The solution for the given equation would be [tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex].
What is an equation?
An equation is a statement that two expressions are equal to each other. It is a mathematical sentence that asserts the equality of two expressions. An equation can be written in the form of:
expression_1 = expression_2
The given equation is √2x – 1- x = −8.
[tex]2x=x^2-14x+49[/tex]
[tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex]
Hence, the solution for the given equation would be [tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex].
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please help: find m∠LHF
Answer:
17
Step-by-step explanation:
5y - 8 = 9y - 28
-8 = 4y - 28
4y = 20
y = 5
9(5) - 28
45 - 28
17
Riders must be at least 42 inches tall to ride the coaster. Write an addition inequality to determine how much taller William must be to ride the coaster. Let x be the variable representing how much taller
An addition inequality to determine how much taller William must be to ride the coaster is, Height of William + x ≥ 42.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Riders must be at least 42 inches tall to ride the coaster, and 'x' be the variable representing how much taller William should be.
Therefore, Height of William + x ≥ 42 is an inequality that may be used to calculate how much taller William has to be in order to ride the coaster.
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A recipe for 2 dozen cookies requires 3 cups of flour. The number of cookies baked varies directly with the amount of flour used.
Question:
How many cups of flour are needed to make 75 cookies?
A) 600
B) 8
C) 938
D) 3618
2 dozen = 24
24 cookies = 3 cups
24 x 2 = 48
48 cookies = 6 cups
24 x 3 = 72
72 cookies = 9
9 ~ 8
~
i think the anwser is b. 8
what is the mode of this data set? 4, 69, 84, 69, 90, 75, 94, 90, 90, 1, 5
Answer:
90
Step-by-step explanation:
90 because it occurs most in the data set.
Answer:
90
Step-by-step explanation:
The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!
Three line segments have measures of 18 units, 12 units, and 10 units. Will the segments form a triangle?
Does it form a triangle?
No, the segments will not form a triangle based on the line segments provided.
For three line segments to form a triangle, they must satisfy the triangle inequality theorem. The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides of the triangle must be greater than the length of the third side.
This is because if the sum of the lengths of any two sides is less than or equal to the third side, it would not be possible to form a triangle with those side lengths, as the two shorter sides would not be able to reach the longer side to form the triangle.
In this case, the sum of the two shorter segments (12 units + 10 units) is 22 units, which is less than the measure of the longest segment (18 units). Therefore, the three segments will not form a triangle.
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Q1) A car travels 145 miles in
3 hours and 38 minutes. How
fast did it travel?
38 minutes / 60 minutes = 0.63
The car traveled for 3.63 hours
Speed = distance/ time
Speed = 145 / 3.63 = 39.94 miles per hour
Round the answer as needed.
HELP!
4(2x-3)=6x+2
I thought when I simplify it 22x=14 but its wrong
Answer:
the answer is 1
Step-by-step explanation:
4(2x-3)=6x+2
8x-12=6x+2
+6x +6x
14x-12 =2
+12 +12
14x=14
x=1 and don't worry we all make mistakes