(04.03 MC)
A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days:
f(n) = 8(1.05)n
Part A: When the scientist concluded his study, the height of the plant was approximately 11.26 cm. 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(n) represent? (2 points)
Part C: What is the average rate of change of the function f(n) from n = 2 to n = 6, and what does it represent? (4 points)
(10 points)
Answer:
A) 0 ≤ n ≤ 7
B) initial height of plant = 8 cm
C) average rate of change = 0.475 cm/day.
Plant grew an average of 0.475 cm per day from day 2 to day 6
Step-by-step explanation:
[tex]f(n)=8(1.05)^n[/tex]
Part A
Given height = 11.26 cm
[tex]\implies 8(1.05)^n=11.26[/tex]
[tex]\implies(1.05)^n=\dfrac{11.26}{8}[/tex]
[tex]\implies(1.05)^n=1.4075[/tex]
Taking natural logs:
[tex]\implies \ln(1.05)^n=\ln(1.4075)[/tex]
[tex]\implies n\ln(1.05)=\ln(1.4075)[/tex]
[tex]\implies n=\dfrac{\ln(1.4075)}{\ln(1.05)}[/tex]
[tex]\implies n=7.005819448[/tex]
[tex]\implies n \approx7[/tex]
Therefore, the scientist concluded his study after 7 days, so the domain is 0 ≤ n ≤ 7
Part B
y-intercept is when the curve intersects the y-axis (when n = 0):
[tex]\implies f(0)=8(1.05)&^0=8\times1=8[/tex]
The y-intercept represents the initial height of the plant, which is 8 cm
Part C
Rate of change = change in y ÷ change in x
⇒ rate of change = change in f(n) ÷ change in n
[tex]\implies f(2)=8(1.05)^2=8.82[/tex]
[tex]\implies f(6)=8(1.05)^6=10.72076513...[/tex]
[tex]\implies \textsf{rate of change} \ =\dfrac{f(6)-f(2)}{6-2}=0.4751912813...[/tex]
So the average rate of change was 0.475 cm/day. This indicates that the plant grew an average of 0.475 cm per day from day 2 to day 6 (over a period of 4 days).
ETA: please see attached graph. The gray dotted curve is the function, and the black solid curve is the function with the restricted domain of 0≤n≤7 since the study took 7 days.
The internal dimensions of a fuel can
are:
10 cm by 20 cm by 25 cm.
What is its capacity in litres?
The capacity of this fuel can is equal to 5 liters.
Given the following data:
Length = 10 cm.Width = 20 cm.Height = 25 cm.To calculate the capacity of this fuel can in litres:
How to calculate the capacity of the fuel can.In order to calculate the capacity of this fuel can, we would determine its volume by using this formula:
[tex]Volume = length \times breadth \times height[/tex]
Substituting the given parameters into the formula, we have;
[tex]Volume = 10 \times 20 \times 25[/tex]
Volume = 5,000 [tex]cm^3[/tex].
In liters:
1 [tex]cm^3[/tex] = 0.001 liters.
5000 [tex]cm^3[/tex] = 5 liters.
Capacity = 5 liters.
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please someone solve this problem
I really need answers
Answer:
x = 50°
y = 50°
z = 80°
Step-by-step explanation:
working out x:
angles on a straight line add up to 180°
x + 130° = 180°
subtract 130 on both sides
x = 180° - 130°
x = 50°
working out y:
two vertical lines means that both sides are equal, so both angles are also equal (it's an isosceles triangle). This means that y is the same angle as x = 50°
y = 50°
working out z:
the sum of a triangle add up to 180°
add up the angles of x and y and equate to 180°
50 + 50 + z = 180
100 + z = 180
subtract 100 on both sides
z = 180 - 100
z = 80°
Antonio works at a grocery store. He puts 23 pounds of flour into 5 sacks. He put the same weight of flour into each sack. How much flour did Antonio put into each sack?
A car costs $25,750.00 and depletes in value by 20% per year. How much would the car be worth after 5 years?
A) $5,150
B) $8,437.76
C) $8,240
D) $20,600
Answer : B
First year : 25750 x 80% = 20600
Second year : 20600 x 80% = 16480
Third year : 16480 x 80% = 13184
Fourth year : 13184 x 80% = 10547.2
Fifth year : 10547.2 x 80% = 8437.76
Please help!!!
Please answer two of these questions and I’ll give 20 points!!
12. In a Fibonacci sequence, every term (except the first two) is the sum of the two
preceding terms. For example, 1, 1, 2, 3, 5, 8, 13, 21, ... is a Fibonacci sequence.
Find the sixteenth term of a Fibonacci sequence whose first two terms are -3 and 9.
13. If you buy 31 floops, the total cost will be less than 40$. But if you buy 32 floops, the total cost will be more than 41$. Assuming these prices do not involve tax, what is the cost of one floop?
12. If the first two terms of the sequence are -3 and 9, the next few terms are
-3 + 9 = 6
9 + 6 = 15
6 + 15 = 21
15 + 21 = 36
and so on. Continuing in this way, you'd find the 16th term to be 4359.
13. Let x be the cost of 1 floop.
31 floops cost less than $40, so 31x < 40 or x < 40/31.
32 floops cost more than $41, so 32x > 41 or x > 41/32.
Equivalently,
41/32 < x < 40/31
and
41/32 ≈ 1.28125
40/31 ≈ 1.29032
which means x = $1.29.
Solve the system of equations y = 6x -7
y = 3x + 11
The solution of the given equation will be y = 29 and x = 6.
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If they both are equal to y, they must be equal to each other, therefore,
6x-7 = 3x+11
3x = 18
x=6
Y = 6x - 7
y = 6 x 6 - 7
y = 36 - 7
y = 29
Therefore the solution of the given equation will be y = 29 and x = 6.
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Solve the inequality for x. 1/2 x − 2 > 22
A) x > 12
B) x > 48
C) x > −12
D) x > −48
B is correct
1/2x-2>22
Remember 1/2=0.5
We write the equation as
0.5x-2 >22
Collect like terms
0.5x > 22+2
0.5x>24
Divide through by 0.5
X>24/0.5
X>48
Option b
Answer:
B x > 48
Step-by-step explanation:
1/2x -2 >22
Mulitply both sides of the inequality by 2
x - 4 > 44
Move the constant to the right
x > 44+4
Add the numbers
x>48
A boat is tracking the depths of four divers, as recorded below in the chart. Which diver is farthest from the surface? Audrey What is the depth of the shallowest diver? −10 meters. What is the distance between Steve Z. And Audrey? −53 meters. There is a GPS buoy for fishermen located 30 meters below the surface. How far is Jacques from the buoy? 48 meters
Answer:
Which diver is farthest from the surface? Dave
What is the depth of the shallowest diver? 12.67
What is the distance between Steve Z. and Audrey? 51
There is a GPS buoy for fishermen located 30 meters below the surface. How far is Jacques from the buoy? 1072
Step-by-step explanation:
by solving for v you have to divide 1072 by 12.67 and you get 84.6093133386 so you multiply 51 by 84.6093133386and you get 4315.07498027so you answer is 4315.07498027
If you walk to school at a rate of 3 miles per hour, how long will it take you to walk 6 miles?
Answer:
2 hours
Step-by-step explanation:
3*2=6
bc 3mph times 2 its 6 miles
Answer: 2 hours
Step-by-step explanation:
Arrange the given data so the units cross out:
6 miles * [tex]\frac{1 hour}{3 miles}[/tex]
Solve this multistep equation: 3x+20 = x + 30
Answer:
x=5
Step-by-step explanation:
Subtract 20
from both sides of the equation
2
Simplify
Subtract the numbers
Subtract the numbers
3
Subtract x
from both sides of the equation
Answer:
X = 5
Step-by-step explanation:
To solve for x, you need to get x to one side and everything else to the other side.
3x+20=x+30
Since there is only one positive x on the right, we can subtract it from both sides. This moves it over.
2x+20=30
Since there is a +20 on the same side we put our x, we need to subtract it from both sides to move it over.
2x = 10
Now x is being multiplied by 2. To get rid of it, we divide both sides by 2.
x = 5
The slope of this line is . (If the slope does not exist, enter DNE or NONE.)
Answer:
0
Step-by-step explanation:
The slope is 0 because the y value stays the same
Find the area of the rectangle with measurements shown; reduce to lowest terms:
Length: 2 2/5 feet; Width: 1/3 feet
4/5 square feet
5 7/15 square feet
1 12/15square feet
4/5 feet
Answer:
4/5
Step-by-step explanation:
the area of rectangle is length × breadth
length = 2 2/5 breadth = 1/3
2 2/5 × 1/3 = 12/15
reducing to the lowest term =4/5
Step-by-step explanation:
2 2/5 × 1/3 = 12/15
Reduced is 4/5
Hope this helps
Brainliest
A university has 39,930 students. in a random sample of 270 students, 18 speak three or more languages. predict the number of students at the university who speak three or more languages.
Answer:
65 students speak 3 or more languages
Step-by-step explanation:
15×30
Select each correct answer.
There were 30 people in a room. One-fifth of the people had blue eyes. How many people had blue eyes?
Evan's mother drove 30 miles on Wednesday and another 15 mile on Wednesday. How many miles did she drive in all?
Jada had 30 crayons. She lost 15 of the crayons. How many crayons does she have left?
Amelie read 30 pages of a book. She read 15 of the pages on Monday. How many pages did she read on Monday?
Answer:
6 people had blue eyes
45 miles
15 crayons
15 pages
Step-by-step explanation:
Q: There were 30 people in a room. One-fifth of the people had blue eyes. How many people had blue eyes.
A: total number of people x 1/5 = 30 x 1/5 = 6
Q: Evan's mother drove 30 miles on Wednesday and another 15 mile on Wednesday. How many miles did she drive in all?
A: total miles = 30 + 15 = 45 miles
Q: Jada had 30 crayons. She lost 15 of the crayons. How many crayons does she have left?
A: total number of crayons - number lost = 30 - 15 = 15 crayons left
Q: Amelie read 30 pages of a book. She read 15 of the pages on Monday. How many pages did she read on Monday?
A: 15 pages, as the question states "She read 15 of the pages on Monday"
ANSWER:
450
6 of them had Blue eyes
Evan's mother drove 45 miles in total.
Jada had 15 crayons left
Amelie read 15 pages on monday.
PLEASE SOLVE ASAP I WILL CROWN BRAINLIST
B
To find the area you multiply width times height, here for the bigger rectangle, to find the area you multiply 7*6 and then add that with 6 * x because those are the width and height of the smaller rectangle.
Second part
I believe that Wiliam chose C because he accidentally thought that adding everything was correct. He added 7+6 to get 13 for the bigger rectangle and then for the smaller rectangle decided that to find the area you would add 6 and x.
Answer:
Step-by-step explanation:
a, b and d all represent the combined area of the gardens
(6*7) + (6*x) is equivalent to 6(7+x) and 42 + 6x
Check:
(6*7) + (6*x)
42 + 6x
6(7+x)
42 + 6x
42 + 6x
William chose C because he added the length and width of the vegetable garden (7 + 6 = 13), and then added the length and width of the flower garden (6 + x = 6 + x).
Hope this helps!
Select the correct answer. A square field has an area of 10 square miles. What is the approximate length, to the nearest thousandth, of one side of this field? A. 2. 5 miles B. 3 miles C. 3. 162 miles D. 3. 612 miles.
The approximate length, to the nearest thousandth, of one side of this field is 3.162 miles. Then the correct option is C.
What is a square?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a square, opposite sides are parallel and all sides are equal and each angle is 90 degrees. And its diagonals are also equal and intersect at mid-point at right-angle.
A square field has an area of 10 square miles.
Let the side of the square be x.
We know that the area of the square will be
[tex]\rm (Side)^2 = Area[/tex]
Then we have
[tex]\rm x^2 = 10\\\\\rm x \ = \sqrt{10}\\\\\rm x \ = 3.162[/tex]
The approximate length, to the nearest thousandth, of one side of this field is 3.162 miles. Then the correct option is C.
More about the square link is given below.
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What is the value of (32)4 ?
Answer:
128
Step-by-step explanation:
Dolores spent $13.00 of the $20.00 in her wallet. Which decimal represents the fraction of the $20.00 Dolores spent? Answer in a complete paragraph
Answer:
0.65 can I have branliest please?
What is the circumference of the circle? Answer in terms of pi
Answer:
10π
Step-by-step explanation:
The circumference of a circle is the distance of the outside of the circle. The formula for circumference is C=2πr.
In the question, you are given the diameter. Diameter is the radius times 2. So, to find the radius you can divide the diameter by 2. Since, 10cm/2 is 5 cm, 5cm is the radius.
Then, plug this information into the formula to solve for C.
2*5π = 10πThis means that, in terms of pi, the circumference is 10π cm.
n=3;
-3 and 9 + 2i are zeros;
f(2)=265
Answer:
6 inches wide and a row of 7 stamps how wide is each stamp
I need help on 8 9 and 10
9. x + (y - 3 - 4x + 2( 3x - (-y - 1) + 2y) - 3x)
= x + (y - 3 - 4x + 2 (3x + y - 1) + 2y - 3x)
= x + (y - 3 - 4x + 6x + 2y - 2 + 2y - 3x)
= (x - 4x + 6x - 3x) + (y + 2y + 2y) - (3+2)
= 0 + 5y - 5
= 5y - 5 (or simplified as 5(y-1)
10. 6 + (-a -3(b + 6(a - b)+4a) - 2b)
= 6 + (-a - 3(b + 6a - 6b + 4a) -2b)
= 6 + (-a - 3b + 18a - 18b + 12a - 2b)
= 6 + (-a + 18a + 12a) + (-3b - 18b - 2b)
= 6 + 29a - 23b
Lmk if it's wrong, I'll try to edit it.
the area of a trapezium with parallel sides 18cm 12cm and height is 8cm
Trapezium
parallel sides = 18 cm, 12cm
Height = 8cm
____Area of trapezium =
[tex] \frac{1}{2} \times (a + b) \times h[/tex]
____[tex] \frac{1}{2} \times (a + b) \times h[/tex]
[tex] \frac{1}{2} \times (18 + 12) \times 8[/tex]
[tex] \frac{1}{2} \times (30) \times 8[/tex]
[tex] \frac{1}{1} \times (15) \times8[/tex]
[tex]120 \: cm ^{2} [/tex]
____Therefore, Area of trapezium is [tex]120 \: cm {}^{2} [/tex]
Answer:
Area of Trapezium = 120 cm³
Step-by-step explanation:
Trapezium = 1/2 * (a+b) * h [Formulae]
A & b = Sum of parallel sides
Given that,
Height H = 8Sum of parallel sides = 18 and 12, 18+12Solved:
1/2(18+12)8 cm²1/2 * 30 * 8 cm²15 * 8 cm²120 cm²Therefore,the area of trapezium is 120 sq. cm or 120 cm².
i need answer please
It is centered at (h,k) --> (0,0) and has a radius 9
The equation of the circle is
[tex](x-h)^{2} +(y-k)^{2} =r^{2} \\(x-0)^{2} +(y-0)^{2} =r^{2}\\x^{2} +y^{2} = 9^{2}[/tex]
Hope that helps!
The total bill for the drinks and pizza comes out to be $17.28. How much should each person pay if they are to share the total bill equally among the three of them?
pls help yall are soo smart
Answer:
5.76
Step-by-step explanation:
17.28/3
14. There are 11 boys and 10 girls in a classroom. A teacher chooses a student at random and puts that student
at the head of a line, chooses a second student at random and makes that student second in the line, and
so on, until all 21 students are in the line. What is the probability that the teacher puts them in a line
alternating boys and girls? where no two of the same gender stand together?
Yes because if she's going one in one out it is a chance thats what shes doing
The probability that the teacher puts them in a line alternating boys and girls is 1/352714
What is probability?Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Given: There are 11 boys and 10 girls in a classroom.
A teacher chooses a student at random and puts at the head of a line.
Number of students= [tex]^{21}P_{21}[/tex]/ 11 ! * 10!
= 21 !/11!*10!
= 21*20*19*18*17*16*15*14*13*12*11!/11!* 10*9*8*7*6*5*4*3*2*1
= 352714
P(alternate boys and girls)= n(A)/n(S)
= 1/ 352714
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Consider x2 10x _____. How many unit tiles need to be added to complete the square and form a perfect square trinomial expression? unit tiles.
The number of unit tiles need to be added to complete the square and form a perfect square trinomial expression is 25.
What is algebra tile?Algebra tiles used to represent the algebraic expression in the table form. The shape of algebra tile is square and rectangle, in which the variables represented.
A trinomial which is expressed as the square of the binomial equation is a perfect square trinomial.
Let the missing number for the given expression is g. Therefore,
[tex]x^2 +10x+g[/tex]
Now, to make the above expression the perfect square trinomial expression, this has to be make such that it can be written in the squared form.
To find the value of g, half the middle term and square it. As the value of the middle term is 10. Thus, the value of the g is,
[tex]g=\left(\dfrac{10}{2}\right)^2\\g=5^2\\g=25[/tex]
Put this value in the above expression as,
[tex]x^2 +10x+25\\(x+5)^2[/tex]
Hence, the number of unit tiles need to be added to complete the square and form a perfect square trinomial expression is 25.
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HELP ME QUICKLY LLEASE IM BEGGING ANYONE ESS
Which source is the most credible?
A. New guidelines from the government about how much sugar
people should eat
B. A report by the sugar industry saying sugar can be a safe and
healthy part of people's diets
C. An article from 2001 stating that diets high in fat are more harmful
than diets high in sugar
D. A blog by someone who worked hard to remove sugar from her
diet and now feels much more energetic
Step-by-step explanation:
Option C. Even though it's not Mathematics
Answer:
A. It's new, so it's recent and probably more applicable
Please help me quickly!!
Answer: The 2nd choice.
Step-by-step explanation:
The y-intercept is the y coordinate when x = 0. Based on the table, we can see that the y coordinate is 12 when x is 0.
The slope is equal to (y2-y1)/(x2-x1) for any given points (x1,y1) and (x2,y2).
We can choose the point (0,12) to represent (x1,y1) and the point (6,0) to represent (x2,y2).
Therefore, the slope is (0-12)/(6-0) = -12/6 = -2
Pls hurry ASAP! U will get Brainly
Answer:
- 9 and 28
Step-by-step explanation:
substitute the given values for x, y, z into the expressions
1
- (3 - 2) - 4(3 + 1) + 1 + (2(3) + 2)
= - 1 - 4(4) + 1 + 6 + 2
= - 1 - 16 + 9
= - 17 + 9
= - 8
2
4(2) - 6(- 3 + 1²) + 4(2)
= 8 - 6(- 3 + 1) + 8
= 8 - 6(- 2) + 8
= 8 + 12 + 8
= 28
Answer:
-8 28Step-by-step explanation:
You want to evaluate these expressions when (x, y, z) = (3, 2, 1).
-(x -y) -4(x +z) +z +(2x +y)4y -6(-x +z²) +4ySimplifyWe find it easier to evaluate the expression when it is simplified to a form that minimizes that amount arithmetic we need to do. So, our evaluation does that first. Then the corresponding values are put where the variables are in the expression, and the arithmetic is carried out.
1.Simplifying, we find the sum to be ...
-x +y -4x -4z +z +2x +y = x(-1-4+2) +y(1+1) +z(-4+1)
= -3x +2y -3z = 2y -3(x +z)
= 2(2) -3(3 +1) = 4 -12
= -8
2.Simplifying, we find the sum to be ...
4y +6x -6z² +4y
= 6x +8y -6z²
= 6(x -z²) +8y
= 6(3 -1²) +8(2) = 12 +16
= 28
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