Answer:
b = (4/3), with rounding
Step-by-step explanation:
Area = A, in cm^2
n = days
A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]
------------------
Data:
n = 2, A = 1.8
A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]
1.8 = [tex]A_{0}[/tex][tex]b^{2}[/tex]
n = 3, A = 2.4
2.4 = [tex]A_{0}[/tex][tex]b^{3}[/tex]
Although we are not given the initial area, we can still make the calculation since we have two data points and each has the same initial area, [tex]A_{0}[/tex]. Lets take the first equation and multiply it by b, in order to bring the [tex]b^{2}[/tex] to [tex]b^{3}[/tex]
1.8 = [tex]A_{0}[/tex][tex]b^{2}[/tex]
b(1.8 = [tex]A_{0}[/tex][tex]b^{2}[/tex])
1.8b = [tex]A_{0}[/tex][tex]b^{3}[/tex]
We can know from the second equation that 2.4 = [tex]A_{0}[/tex][tex]b^{3}[/tex] . We can eliminate this term in the above relationship by substituting 2.4:
1.8b = [tex]A_{0}[/tex][tex]b^{3}[/tex]
1.8b = 2.4
b = 1.3333
or (4/3)
Check:
Does the value of (4/3) for b work for both data points? To check this, we do need to assume an initial starting area. Lets assume the starting area, [tex]A_{0}[/tex] = 1.
n = 2, A = 1.8, b = (4/3)
A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]
1.8 = 1*[tex](4/3)^{n}[/tex]
1.8 = 1.78 Close enough?
n = 3, A = 2.4, b = (4/3)
2.4 = [tex]A_{0}[/tex][tex](4/3)^{n}[/tex]
2.4 = 1*[tex](4/3)^{3}[/tex]
2.4 = 2.37 Close enough?
Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral.
The dimension of the rectangle of the largest area in an equilateral triangle is √3/4L.
Here we have to find the dimension of the rectangle of the largest area.
Let the distance from the tip of the base of the triangle to the point that the top of the rectangle meets the triangle be x.
The width of the rectangle is √3/2 x.
By this, we can find the area of the rectangle
Area = √3/2x ( L -x) = √3/2 xL - √3/2x²
To find the maximum area we have:
dA/ dx = 0
dA / dx = √3/2L - √3x = 0
From we have to find the value of x,
√3 x = √3/2L
x = L/2
The dimension of rectangle is √3/2x = √3/2(L/2)
= √3/4 L
Therefore the dimension of the rectangle is √3/4 L.
To know more about the rectangle refer to the link given below:
https://brainly.com/question/15612913
#SPJ4
in order to estimate the proportion of all credit card holders who pay their credit card bills in full each month a credit counseling bureau took a random sample of 450 credit card holders and found that 127 pay all their credit card bills in full each month. a 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is:
A 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is 0.282 + 0.055.
Define confidence interval.Confidence intervals, which describe how closely study results match reality or how dependable they are based on statistical theory, are regularly mentioned in scientific publications. The sample is used to calculate the confidence interval, which represents the range of likely population parameters. In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.
Given,
Number of credit card holders
n = 450
x = 127
p = 127/450
Proportion:
p = 0.2822
99% confidence interval:
C I = 0.2822 ± 2.576 × 0.2122
CI = 0.2822 ± 0.05465
CI = 0.282 + 0.055
A 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is 0.282 + 0.055.
To learn more about confidence interval, visit:
https://brainly.com/question/24131141
#SPJ4
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease y=210(1.092)^x
The change y=210(1.092)^x represent exponential growth
The percentage rate of increase is 9.2 percent increase
How to determine exponential growthExponential functions are functions that consist of three part say c(b)^d
the part that says whether the function is growth or decay is b
b is called the base function and it is used as follows to determine growth or decay function
b < 1 gives a decay functionb > 1 gives a growth functionComparing with the given function 1.092 > 1 hence a growth function
The percentage is solved as follows
1.092 * 100 = 109.2%
109.2% is also referred to as 9.2 percent increase since it is an increment of 9.2%. this is shown below
100% + 9.2% = 109.2%
Learn more about Exponential functions at:
https://brainly.com/question/2456547
#SPJ1
If you translate the square root parent function up three units, and reflect it across the x-axis, what is the equation of the new function?
The equation the function after the transformation is (c) g(x) = -√x - 3
How to determine the transformation of the function?The equation of the function is given as
f(x) = √x ---- i.e the square root parent function
The sequence of transformations is given as follows:-
Translate up by 3 unitsReflection across the x-axisWhen the above transformations are combined, we have:
Translate up by 3 units: g(x) = f(x) + 3
Reflection across the x-axis: g(x) = -(f(x) + 3)
So, we have
g(x) = -(√x + 3)
Expand
g(x) = -√x - 3
Hence, the function g(x) is (c) g(x) = -√x - 3
Read more about transformation at
brainly.com/question/27224272
#SPJ1
Given the following information about the arithmetic sequence an, find a10. A5=24 a8=39
The 10th term of an arithmetic sequence is found as the 49.
Define the term arithmetic sequence?An ordered group of numbers with a shared difference with each consecutive word is referred as an arithmetic sequence. For particular, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression would be another name for an arithmetic sequence.As per the stated values in question.
Fifth term a5 = 24
8th term a8 = 39.
Let the first term be 'a' and the common difference be 'd'.
Then,
a5 = a + 4d
24 = a + 4d .....eq 1
a8 = a + 7d
39 = a + 7d .....eq 2
Solving eq 1 and 2.
3d = 15
d = 5
a = 4
Now,
a10 = a + 9d
a10 = 4 + (9 x 5)
a10 = 4 + 45
a10 = 49
Thus, the 10th term of an arithmetic sequence is found as the 49.
To know more about the arithmetic sequence, here
https://brainly.com/question/6561461
#SPJ4
A,B and C form a triangle where ∠BAC=90∘.AB=7 mm and BC=13.8 mm. Find the length of AC, giving your answer rounded to 1 decimal place.
The length of AC which is the hypothenuse is equal 15.5mm
Pythagoras TheoremThe Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle.
In this question, triangle ABC forms a right-angle triangle at angle B and this makes it possible to use Pythagoras theorem.
AB = leg = 7mmBC = leg = 13.8mmAC = hypothenuse = ?Using the formula;
AC² = AB² + BC²
AC² = 7² + 13.8²
AC = 15.5mm
The length of the hypothenuse is 15..5mm
Learn more on Pythagoras theorem here
https://brainly.com/question/231802
#SPJ1
Bloomington University charges $53,730 for tuition. If they raise their tuition by 8% each
year, how much will tuition be in 2 years?
If necessary, round your answer to the nearest cent.
$
E
Given f(x)=2x+4 , describe how the graph of g compares with the graph of f.
g(x)=2(0.4x)+4
Please help
The function g(x) is a horizontal dilation of scale factor k = 5/2 of function f(x).
How the two graphs compare?We know that f(x) is a linear function:
f(x) = 2x + 4
Here we know that:
g(x) = 2*(0.4x) + 4
Notice that function g(x) can be written as:
g(x) = f(0.4*x)
So we have a horizontal dilation, remember a horizontal dilation of scale factor k can be written as:
g(x) =f(x/k)
Notice that 0.4 = 2/5
Then we have a horizontal dilation of scale factor 5/2.
Learn more about horizontal dilations:
https://brainly.com/question/3457976
#SPJ1
Jared has earned 23% of the $52 he needs to buy a new jacket. Find 23% of $52.
Which expression can you use to find 23% of 52?
0.23 × 52
23% of $52 is $
11.96
.
An easy way to check your answer is to use the friendly
50%
and divide 52 by
2
to get
13
.
Am i right???
Answer:
yeah i think so
Answer:
$11.96
Step-by-step explanation:
Now we have to,
→ find the 23% of $52.
Let's solve the problem,
→ 23% of $52
→ (52/100) × 23
→ 0.52 × 23
→ $11.96
The similar expression is,
→ 0.23 × 52
→ $11.96
Hence, answer is $11.96.
What is the value of the expression c²a + 2a÷b, when a = -3, b=2, and c = 3?
03
09
O
O 12
O
18
Answer:
-30 I don't see -30 as an answer option. Please check the problem.
Step-by-step explanation:
c²a + 2a÷b
c²a + 2a/b Enter values for a, b and c for a = -3, b= 2 and c = 3.
(3)²(-3) + 2(-3)/(2)
(9)*(-3) + (-6)/(2)
-27 + (-3)
-27 - 3 = - 30
A hippopotamus can run 6 kilometers in 15 minutes. At this rate, how far can the hippopotamus run in 1 minute?
Answer:
400meters
Step-by-step explanation:
Find the speed of the hippopotamus by dividing distance with time
6000 meters ÷15minutes =400meters/minutes
how do you simplify the distributive property ?
Answer:
for example 2(3+1)
to solve with the distributive property you multiply the number outside the parentheses(2) with each inside number(3 and 1) individually.
2(3)+2(1)
now solve
6+2=8
now to check it by solving the regular way
2(3+1), 3+1=4 so
2(4)
8
we can see that the answers are the same.
to use the distributive property with x in it
for example, -3(x-6)
multiply the outside number(-3) with each inside number(x and -6)
-3(x)+(-3)(-6)
simplify
-3x-(-18)
-3x+18
hope this helps!
two cars are traveling in the same direction along the same route. the red car travels at a constant speed of 40 miles per hour, and the black car is traveling at a constant speed of 50 miles per hour. if the red car is 20 miles ahead of the black car, how many hours will it take the black car to overtake the red car?
Balck car can overtake the red car in 2 hrs
Relationship between Speed, Distance and Time:
The Relationship between Speed, Distance & Time can be understood by the following formulas
Speed = Distance/Time
Time = Distance / Speed
Distance = Speed X Time
Constant speed:
Constant speed is also called the uniform rate which involves something traveling at a fixed and steady pace or something moving at some average speed.
Here we have
Two cars are traveling in the same direction along the same route.
The speed of the Red car = 40 miles per hr
The speed of the Black car = 50 miles per hr
From above data
The difference between speeds of cars = 50 - 40 = 10 miles per hr
Which means the Black car is chasing the Red car at 10 miles per hr
Given that distance between two cars = 20 miles
The time taken by the Black car to cover 20 miles
=> Distance/ speed = 20/10 = 2hrs
Balck car can overtake the red car in 2 hrs
Learn more about Speed, Distance, and Time at
https://brainly.com/question/10566304
#SPJ4
What is the absolute value of −9.4?
Answer:
9.4
Step-by-step explanation:
Given the following function, find the vertex, y=5x^2-8x+6
Answer:
The vertex is (0.8, 2.8)------------------------------------
GivenFunction y = 5x² - 8x + 6Find the x-coordinate of the vertexx = - b/(2a)x = - (-8)/(2*5) = 8/10 = 0.8Find the y-coordinate of the vertexy = 5(0.8²) - 8(0.8) + 6 = 2.8Ojojo and fifi shared an amount of
ratio 3. 4 respectively.
money
If frifi had 140000 had much was
Shared ?
The total amount that was shared $245000 .
In the question ,
the ratio of amount shared by JoJo and Frifi is given
the ratio is given as 3:4 .
the amount that JoJo get = 3x
the amount that Frifi get = 4x
given that Frifi got $140000 .
So , 4x = 140000
Dividing both sides by 4 ,
we get ,
x = 140000/4
x = 35000
total amount shared = 3x + 4x = 7x
Substituting the values of x = 35000 , we get
total amount shared = 7*35000
= 245000
Therefore , The total amount that was shared $245000 .
The given question is incomplete , the complete question is
JoJo and Frifi shared an amount in the ratio 3:4 respectively , if Frifi had $140000 , then find the total amount that was shared ?
Learn more about Ratio here
https://brainly.com/question/14793091
#SPJ1
How would you write the work to get the answer to the problem your neighbor pays you $20 every two hours you work you work for eight hours on saturday how much does your neighbor owe you
The neighbour us an amount of $160 for the work that we did for him.
As per the agreement the never will pay 20 dollars were every hour that we work.
We worked for a total of 8 hours on Saturday.
So, according to the unitary method,
Total amount of money owned by the neighbour = number of hours for which we work x the amount received for working per hour.
Total amount of money owned by the neighbour = 8 × 20
Total amount of money owned by the neighbour = 160 dollars.
The total amount of money owned by the neighbour to us is 160 dollars.
To know more about unitary method, visit,
https://brainly.com/question/24587372
#SPJ4
equivalent expressions
it’s due tmr and i don’t understand
thank you if you are willing to help
Answer:
c) x+4
Step-by-step explanation:
1. The original expression can be re-written as (I just rewrote each fraction so that there are no mixed numbers):
[tex]\frac{x}{2}+\frac{9}{2}+\frac{x}{2}-\frac{1}{2}[/tex]
2. Next, you want to group all the terms with the variable x, and all the terms without a variable. All the fractions should be rearranged:
[tex]\frac{x}{2}+\frac{x}{2}+\frac{9}{2}-\frac{1}{2}[/tex]
3. You can now simplify and add the variable terms and the non-variable terms.
[tex]\frac{x+x}{2}+\frac{9-1}{2}[/tex]
Simplify further:
[tex]\frac{2x}{2}+\frac{8}{2}[/tex]
[tex]x+4[/tex]
So your answer is choice c
X = 4/2, y=-3/4 find X+Y
x-y
Step-by-step explanation:
X+Y=4+2=6X-Y=4-2=2OR
X+Y=3+4=7X-Y=3-4=-1marrisa bought 3 packages of balloons and 4 packages of party favors for a total of 14.63. Ray bought 2 packs of balloons and 4 packs of party favors for a total of 16.03. find the price of a pack of balloons and the price of a pack of party favors
The price of a pack of balloons is 4. 39
The price of a pack of party favors is 0. 36
How to determine the valuesWe have that;
Let the cost of balloons be x
Let the cost of party favors by y
From the information given, we have that;
3x + 4y = 14. 63 (1)
2x + 4y = 16. 03 (2)
Now, let's make 'x' the subject from equation (1)
x = 14. 63 - 4y/ 3 (3)
Substitute in equation (2)
3( 14. 63 - 4y/ 3) = 16. 03
expand the bracket
43. 69 - 12y /3 = 16. 03
cross multiply
43. 69 - 12y = 48. 09
collect like terms
- 12y = - 4. 4
make 'y' the subject
y = 0. 36
substitute in equation (3)
x = 14. 63 - 4(0. 36)/ 3
x = 13. 1/ 3
x = 4. 39
Hence, the prices are 4. 39 and 0. 36 respectively.
Learn more about simultaneous equations here:
https://brainly.com/question/16863577
#SPJ1
A 5-kilogram bag of cat food costs $14.85. What is the unit price?
Answer:
I believe the unit price would be $2.97
Step-by-step explanation:
Hope this helps! :))
Please let me know if its incorrect.
GHLJ and GSTU are both parallelograms. Why is
∠L ≅ ∠T?
Parallelogram G S T U is inside of larger parallelogram G H L J. Side G S in on side G H, and side G U is on side G J.
The angle L is congruent to angle T ∠L ≅ ∠T and the reason is that opposite angles of a parallelogram are congruent.
How to identify congruent angles?We are given the parallelograms GHLJ and GSTU in such a manner that the parallelogram GSTU is inscribed right inside parallelogram GHLJ with angle G coinciding on the two parallelograms.
Now, we can remember that property of parallelogram states that the opposite angles of a parallelogram are congruent.
Thus, angle G is congruent to angle T and angle L .
Therefore, ∠L ≅ ∠T
Read more about congruent angles at; https://brainly.com/question/1675117
#SPJ1
Answer:
By the parallelogram angle theorem, opposite angles of a parallelogram are congruent. Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.
Step-by-step explanation:
got it right on edge2
I need to know before I can perform a rotation.
the size of the coordinate plane
the degree of rotation
which way to flip the point, line, or figure
which way to slide the point, line, or figure
To perform Rotation in coordinate plane the following information may help you.
What is Geometric Rotation ?
In geometry, rotation is a type of rigid motion or transformation that involves the movement of a shape about a point while preserving the shape, size, and distance between the points on the shape.The center of rotation is the location around which the shape is rotated.
To perform Rotation in coordinate plane
The size of the coordinate plane - the points or graph is mention in question so no need to worry about size of coordinate plane.The degree of rotation : This describes the extent to which a shape is rotated, and can vary from 0° to 360°. This is a required condition to know when to stop rotating the figure.Last two questions sum up and I'm explaining like that,
Reflection in the line y = 0 [x - axis]When a point is reflected in the x-axis then signs of it's ordinate (y-axis) change.
Mₓ (x, y) = (x, - y)
Reflection in the line x = 0 [y - axis]When a point is reflected in the y-axis then signs of it's abscissa (x-axis) change.
My (x, y) = (-x, y)
Reflection in the originWhen a point is reflected in the origin , the signs of it's Abscissa and ordinate change.
M₀ (x, y) = (-x, -y) (in origin the sign become opposite if there is '+' then it changes to '-' and vice versa)
To read more about Geometric Rotation.
https://brainly.com/question/26249005
#SPJ13
HELP!
Identify the dependent events.
A. spinning a prime number on a spinner three times in a row
B. drawing a black card and then a red card from a well shuffled 52-cards deck
C. drawing a green jelly bean from a packet of jelly beans and then drawing a red
jelly bean after replacing the first
D. getting two heads when a coin is tossed twice
As replacing a draw is an independent event, the dependent events are
B. drawing a black card and then a red card from a well-shuffled 52-cards deck.
D. Getting two heads when a coin is tossed twice.
What are dependent events?If the outcome of one event has an impact on the outcome of another, then two events are dependent. For instance, if you draw two colored balls at random from a bag and don't replace the first ball before drawing the second, the result of the second draw will be influenced by the result of the first.
From the given options we conclude that the dependent events are
Drawing a black card and then a red card from a well-shuffled 52-cards deck.
Getting two heads when a coin is tossed twice.
learn more about dependent events here :
https://brainly.com/question/12138721
#SPJ1
The unit rate is cup of milk to
1 cup of flour, so the constant of
proportionality is 2. Let y
represent the number of cups of
milk, and x represent the
number of cups of flour.
3
y = 2x
y=2(3), or 21
4
The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality.Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.
Find the solution ?Therefore, let's examine the provided graph first in order to locate the solution.We can see that 1 batch of cookies need 2 cups of flour
This provides us with a ratio of 2:1.
Constant proportionality is the ratio of two proportional quantities having a constant value.
Since the batch of cookies grows by 1 for every 2 cups added, we have a constant proportionality of 2 cups.
3y=2x
Divide each term in 3y=2x
by 3
and simplify.
Tap for more steps...
y=2x3
Since the equation can be written in the form y=kx
, y varies directly with x and k. The constant of variation, k, is 23
23
To learn more about constant of proportionality refer
https://brainly.com/question/1835116
#SPJ1
PLEASE HELP ASAP ILL GIVE BRAINLIEST
Find x and y
*image is linked*
The values of x and y in the similar triangles are 3 and 2 respectively.
What are similar triangle?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
In similar triangles, corresponding sides are always in the same ratio.
Therefore, using similar triangle ratio, let's find the value of x and y.
x / 6 = 1.5 / 3
cross multiply
3x = 1.5 × 6
3x = 9
divide both sides by 3
x = 9 / 3
x = 3
Let's find y.
y / 4 = 1.5 / 3
cross multiply
3y = 6
divide both sides by 3
y = 6 / 3
y = 2
learn more on similar triangle here: https://brainly.com/question/25882965
#SPJ1
help meeeeeeeeeeeeeee pleaseee
The table of solutions for this quadratic equation (y = -2x²) include the following:
x y_
-2 -8
-1 -2
0 -0
1 -2
2 -8
Also, a graph of the solution of this quadratic equation is shown in the image attached below.
How to determine the solution and plot the graph?In Mathematics, the valid and true solutions to the given quadratic equation (y = -2x²) are referred to as ordered pairs and they can be determined by substituting the x-values contained in the table into the quadratic equation as follows;
When x = -2, the y-value for this quadratic equation is given by:
y = -2x²
y = -2(-2)²
y = -2 × 4
y = -8
When x = -1, the y-value for this quadratic equation is given by:
y = -2x²
y = -2(-1)²
y = -2 × 1
y = -2
When x = 0, the y-value for this quadratic equation is given by:
y = -2x²
y = -2(0)²
y = -2 × 0
y = 0
When x = 1, the y-value for this quadratic equation is given by:
y = -2x²
y = -2(1)²
y = -2 × 1
y = -2
When x = 2, the y-value for this quadratic equation is given by:
y = -2x²
y = -2(2)²
y = -2 × 4
y = -8
In conclusion, you would notice that a graph of this quadratic equation is parabolic (u-shaped) in nature with a slope of -2.
Read more on graphs here: brainly.com/question/4546414
#SPJ1
Divide. Write 5/8 as a fraction, a whole number, or a mixed number.
Answer: 5/8
Step-by-step explanation:
5/8 is already a fraction
Can anyone state the vertex of the graph?
The graph has no vertex
The transformations from the parent function are
Vertical shift down 2Horizontal shift left 4How to determine the vertex?To determine the vertex of a graph, we look for the location of the maximum or the minimum point of the graph
Because the graph is a cubic function, the graph has no maximum or minimum (by definition)
This means that there is absence of a vertex in the graph
The transformation from the parent functionIn (a), we have
We can see that the graph is a cubic function
This function is represented as
y = ∛x
In this graph, we can see that the graph is 4 units to the left i.e. y = ∛(x - 4)
And 2 units below the origin i.e. y = ∛(x - 4) + 2
Read more about vertex and transformations at
brainly.com/question/15709421
brainly.com/question/4289712
#SPJ1
One day in 2014, 1 euro was worth x rand.
One year later, 1 euro was worth (x+1) rand.
Winston changed 1000 rand into euros in both years.
In 2014 he received 4.50 euros more than in 2015.
Write an equation in terms of x and show that it simplifies to 9x²+9x-2000=0.
1000/x - 1000/(x + 1) = 4.5 is an equation in terms of x that simplifies to this quadratic equation 9x² + 9x - 2000 = 0 as shown below.
What is a quadratic equation?In Mathematics, the standard form of a quadratic equation is given by this mathematical expression:
ax² + bx + c = 0.
Since Winston changed 1000 rand into euros in both 2014 and 2015, this can be represented by this mathematical expression:
1000/x - 1000/(x + 1) = 4.5
Taking the lowest common multiple (lcm), we have:
1000/x(x + 1) = 4.5
1000/(x² + x) = 4.5
Cross-multiplying, we have the following:
1000 = 4.5(x² + x)
1000 = 4.5x² + 4.5x
Multiplying both sides of the equation by 2, we have:
2 × (1000 = 4.5x² + 4.5x)
2000 = 9x² + 9x
Rearranging the terms and equating to zero, we have:
9x² + 9x - 2000 = 0.
Read more on quadratic equation here: https://brainly.com/question/3404535
#SPJ1