To identify the initial amount (a) and rate of growth in the equation y=100000(1.09)^3, you can use algebra to isolate the variables.
First, divide both sides of the equation by 100000 to get y/100000=(1.09)^3. Then, take the cube root of both sides of the equation to get y/100000=1.09.
Finally, multiply both sides of the equation by 100000 to get y=109000. Therefore, the initial amount (a) is 100000, and the rate of growth is 1.09.
The initial amount, also known as the starting point or the base value, is the value of a variable at the beginning of a given period.
Learn more about the initial amount:
https://brainly.com/question/29045286
#SPJ4
IF F(x) = 29
F(x) = x
X - 26
2
Find x
Answer:
x=291/X
Step-by-step explanation:
it mean 29=xX-262
xX=29+262
xX=291
x=291/X
A series of isosceles triangles are drawn between two red line segments.
a = 11°. Work out x, explaining each stage of your working in the comment box.
The value of x in the isosceles triangles is 169 degrees
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
A series of isosceles triangles are drawn between two red line segments
Also, we have
a = 11°
Because the triangles are isosceles triangles, we have the following equation
x + a = 180
Substitute the known values in the above equation, so, we have the following representation
x + 11 = 180
Evaluate the like terms
x = 169
Hence, the value of x is 169
Read more about triangles at
https://brainly.com/question/14285697
#SPJ1
Which equation represents a liner function? A. y=3x³ B. y=¼x C. Y=x² D. y=|x|
The required Linear function among the following option is D) y=|x|.
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
According to question:A) y=3x³
It is cubic function.
B) y=¼x
It is inverse function.
C) Y=x²
It is a quadratic function.
D) y=|x|
It is a modulus function, but after remove the Mode in x, we get
y = x and y = -x
So, Here power on x is one. It is Linear function as well.
Thus, y=|x| is linear function.
To know more about Function visit:
brainly.com/question/12431044
#SPJ1
Kevin Carter Male Clothing Ltd is a chain of fashion outlets across Birmingham and the
midlands. In quarter 1 they had inflows of £540,000 across their three stores, with outflows
of £495,000. Their opening balance for the quarter was £20,000. For quarter 2 they
anticipate inflows to increase by 7.5% and outflows increase by 5%. Calculate their closing
balance for Quarter 2.
According to the question, the closing balance for quarter 2 is £82,750.
What is the quarter ?A quarter is one fourth of a year. It is typically a three month period, usually consisting of January, February, and March; April, May, and June; July, August, and September; or October, November, and December. The terms of a quarter can vary depending on the context. For example, in the United States, quarters are commonly referred to as “fiscal quarters,” and begin on the first day of October, January, April, and July. In this case, each quarter covers a three-month period.
Inflows for quarter 2: 540,000 x 1.075 = £581,000
Outflows for quarter 2: 495,000 x 1.05 = £519,250
Closing balance for quarter 2:
Opening balance + Inflows - Outflows =
20,000 + 581,000 - 519,250 = £82,750
Therefore, the closing balance for quarter 2 is £82,750.
To learn more about quarter
https://brainly.com/question/26460978
#SPJ1
7. A coin bank contains $12.45 in quarters and dimes. If there are 16 more dimes than quarters,
how many are there of each?
Answer:
x = 40
Step-by-step explanation:
We can set up the following equations to represent the problem:
x = number of quarters
x + 16 = number of dimes
0.25x + 0.1(x + 16) = 12.45
Solving for x, we get:
x = 40
So there are 40 quarters and 56 dimes in the coin bank.
use mathematical induction to prove 9. boole’s inequality, which states: for a sequence of events a1, a2, . . . , an
The mathematical expression boole’s inequality for a sequence of events a1, a2, . . . , an then the bounds are known as Bonferroni inequalities [13].
Arithmetic sequence is [tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1) d ; n > 1
The given equation about an arithmetic sequence is
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1) d ; n > 1
Boole's inequality(or the union bound) states that for any at most countable collection of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the events in the collection.
The objective is to prove the statement using principle of mathematical induction.
The principle of mathematical induction statement that a statement [tex]p_{n}[/tex] about positive integer n, is true if satisfies the following two conditions:
[tex]p_{1}[/tex] is true
If [tex]p_{k}[/tex] is true, then [tex]p_{k+1}[/tex] is true
Consider the statement for n > 1
[tex]p_{n}[/tex] : [tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1) d
Here, it is known that [tex]a_{n}[/tex] is an arithmetic sequence with [tex]a_{1}[/tex] as first term and 'd' as common difference.
Recall that in any arithmetic sequence, each term is determined by adding 'd' to previous term.
Hence, the second term is determined by adding 'd' to first term.
[tex]a_{2}[/tex] = [tex]a_{1}[/tex] + d
For [tex]p_{2}[/tex] , substitute n = 2 in the given statement to verify it for first positive integer.
[tex]p_{n}[/tex] : [tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1) d
[tex]p_{2}[/tex] : [tex]a_{2}[/tex] = [tex]a_{1}[/tex] + (2-1) d
[tex]p_{2}[/tex] : [tex]a_{1} +d[/tex] = [tex]a_{1} +d[/tex]
This has given a true statement.
Hence, the statement is verified for [tex]p_{1}[/tex].
Therefore,
The mathematical expression boole’s inequality for a sequence of events a1, a2, . . . , an then the bounds are known as Bonferroni inequalities [13].
Arithmetic sequence is [tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1) d ; n > 1
To learn more about Boole's inequality visit :
brainly.com/question/29559421
#SPJ4
This shape is being enlarged using a scale factor of 2 and centre (6,3). Work out the coordinates of A' and B'. Y 10+ 9- 8- 7- 6+ 5- 4- 3- 2- 1 0 X 1 2 3 4 A B 5 6 7 8 9 10
The coordinates of the points A and B, after scaling becomes
A(x, y) → A'(2x, 2y)
B(x₁, y₁) → B'(2x₁, 2y₁)
What is scaling? How is it done?Scaling is defined as the process of changing the dimensions of the original figure as per some specific proportional rule.If the initial length is equivalent to {a}. Then, after the scaling by the scale factor of {K}, the length becomes {Ka}. Similarly, if the initial coordinates are (x, y) then after scaling the coordinates would be {Kx, Ky}.Scale factor is a dimensionless quantity that tells by how much time a specific dimension of a figure is enlarged or reduced. Mathematically, it is the ratio of two similar quantities. In case of length scaling, we can write -{K} = L{final}/L{initial}
Given is that shape is being enlarged using a scale factor of 2 and centre (6, 3).
Assume the coordinates of the point are A(x, y) and B(x₁, y₁). After scaling, the coordinates will become -
A(x, y) → A'(2x, 2y)
B(x₁, y₁) → B'(2x₁, 2y₁)
Therefore, the coordinates of the points A and B, after scaling becomes
A(x, y) → A'(2x, 2y)
B(x₁, y₁) → B'(2x₁, 2y₁)
To solve more questions on translations, visit the link below -
brainly.com/question/12463306
#SPJ1
someone help again pls
“write a cubic function who’s graph passes through the given points”
The cubic function whose graph passes through the given points is defined as follows:
y = -2(x³ - 4x² + x + 6).
How to define the cubic function?The cubic function is defined by the Factor Theorem, as a product of it's linear factors.
The x-intercepts of the function are given as follows:
x = -1.x = 2.x = 3.Hence the linear factors of the function are given as follows:
x + 1.x - 2.x - 3.As a product of the linear factors, the function is defined as follows:
y = a(x + 1)(x - 2)(x - 3)
y = a(x² - x - 2)(x - 3)
y = a(x³ - 4x² + x + 6).
When x = 0, y = -12, hence the leading coefficient a is obtained as follows:
6a = -12
a = -2.
Thus:
y = -2(x³ - 4x² + x + 6).
More can be learned about functions at https://brainly.com/question/24808124
#SPJ1
Find what arc
…..mWX
Pleaseeee help me asap I’ll reward/ help you back
The arc angle mWX is 9 degrees.
How to find the arc angles?An inscribed angle is the angle that is formed by the intersection of two chords on the circumference of a circle. Therefore, inscribed angles subtended by the same arc are equal.
Hence,
3x - 20 = 15x - 64
3x - 15x = - 64 + 20
- 12x = -44
divide both sides by -12
x = -44 / -12
x = 3.7
Let's find the arc angle
Hence,
mWX = 3(3.7) - 20
mWX = 11 - 20
mWX = 9 degrees
The answer can't be negative.
learn more on arc here: https://brainly.com/question/1582130
#SPJ1
Please answer will mark brainleast if correct its algebra.
the simple form of the given number will be 8√3.
What is square root?
A value known as the square root of a number is one that, when multiplied by itself, yields the original number. An alternative to square rooting a number is to use it. Therefore, the concepts of squares and square roots are connected. The original number is equal to the square root of any integer, which is equivalent to a number.
Let's assume that m is an integer that is positive, such that (m.m) = (m2) = m.
A square root function in mathematics is described as a one-to-one function that accepts a positive number as input and outputs the square root of the specified input number.
The given number is √192
= √ (2*2*2*2*2*2*3)
=8√3
Hence the simple form of the given number will be 8√3.
Learn more about square roots, by the following link.
https://brainly.com/question/428672
#SPJ1
Suppose ms bush charges $4 per baseball. Would each team pay more if there are 6 teams or 9 teams?
It is going to be more expensive for 9 teams to buy these baseballs.
It has been mentioned in the problem that Ms.Bush charges $4 per baseball. This means that we need to pay $4xn dollars where n is the number of baseballs. According to the question, the member of baseball depends on the number of teams as well. More teams mean more baseballs will be bought.
Since it is obvious that 9 is greater than 6, so, it automatically means that it is going to be more expensive for 9 teams to buy these baseballs as compared to 6 teams.
Learn more about greater than problems on
https://brainly.com/question/29163855?referrer=searchResults
#SPJ4
x-5/10 - 2(x-3)/5 = 3(x-4)/15
Answer:
x-5/10 - 2(x-3)/5 = 3(x-4)/15= x=-15/4
Couple are marrying later. The median age of men who tied the knot for the firt time in 1970 wa 23. 2. In 1998, the median age wa 26. 7. Write an equation, in lope-intercept form to predict the median age that men marry M for any year t. Ue the equation in #9 to predict the median age of men who marry for the firt time in 2005
The equation in slope intercept form is : [tex]y = \frac{1}{8} x - 223.05[/tex]
The slope intercept form is a process used to determine the equation of a straight line in the coordinate plane. It can be used to determine the equation of a line when given the slope of the straight line and the y-intercept
The slope-intercept form of a line is:
y = mx+b
where m is the slope of the line and b is an intercept of the y-axis.
[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
[tex]m = \frac{26.7 - 23.2 }{1998- 1970}[/tex]
[tex]m = \frac{1}{8}[/tex]
So,
[tex]y = \frac{1}{8} x + b[/tex]
To find b we get the point (1970, 23.2) and introduce it in the previous equation.
[tex]23.2= \frac{1}{8} (1970)+ b[/tex]
⇒ 23.2 - 246.25 = b
⇒ b = - 223.05
Then, the equation is : [tex]y = \frac{1}{8} x - 223.05[/tex]
Read more about the line:
https://brainly.com/question/13763238
#SPJ4
Use the transitive property of equality to finish the equation.
-3x+9=7x-5y and 7x-5y=-x-10y
so -x-10y = ?
The graph of y=f(x) is graphed below. What is the end behavior of f(x)?
The required end behavior of the graph of y = f(x) is given as, x → ∞, y→-∞ and when x → -∞, y →∞. Option B is correct.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
As we can see in the graph of y =f(x)
As x approaches -∞ y approaches ∞, and as As x approaches ∞ y approaches -∞
Thus, the required end behavior of the graph of y = f(x) is given as, x → ∞, y→-∞ and when x → -∞, y →∞. Option B is correct.
Learn more about function here:
brainly.com/question/21145944
#SPJ1
On #9, you said your solution was (6,32). What is the
meaning of this solution in terms of this problem?
Hint!
Example response: The solution of (x, y) means
x and y should be your numbers from #9
Remember that x stands for the number of kites, and
y stands for the total cost.
The meaning should reflect that we are buying kites
for a certain cost at 2 different businesses.
Solve for
�
mm.
2
=
�
2
−
7
2=
2
m
−72, equals, start fraction, m, divided by, 2, end fraction, minus, 7
�
=
m=m, equals
The value of m for the given equation is 18. The solution has been obtained by solving the linear equation.
What is a linear equation?
A linear equation is the one with the highest degree of one. This demonstrates that there are no variables in a linear equation with an exponent bigger than one. On the graph, such an equation yields a straight line.
We are given an equation as 2 = m/2 - 7
On solving the equation for m, we get
⇒2 = m/2 - 7
⇒2 = (m - 14)/2
⇒2*2 = (m - 14)
⇒4 = m - 14
⇒m = 18
Hence, the value of m for the given equation is 18.
Learn more about linear equation from the given link
https://brainly.com/question/30092358
#SPJ1
The square root of 9 is how much less than 9 squared? : *
A) 0
B) 3
C) 6
D) 78
The square root of 9 is 78 less than 9 squared
The square root of 9 is calculated as
√9 = √(+ 3)² or√(- 3)²
= + 3 or - 3
Let's calculate the square of 9:
9² = 81
We need to calculate here, how much the square root of 9 is less than the square of 9 or we can say the difference between the square of 9 and the square root of 9. So, let's say that difference is denoted by d
d = 9² - √9
When √9 = +3
d = 81 - 3
d = 78
When √9 = -3
d = 81 - (-3)
d = 81 + 3
d = 84
Hence, the value of the difference between the square of 9 and the square root of 9 is 78 or 84.
To learn more about square root here:
brainly.com/question/29164519
#SPJ4
Lyndie is making reduced copies of a photo that measures 25 centimeters in height. She sets the copy machine to an 80% size reduction.
Part A
Write a percent equation that represents the relationship of the height of the first copy to the height of the original photo.
Part B
Lyndie wants to make another copy that will have a height of 17 cm. The copy machine settings increase or decrease in increments of 5%. Which photo should she make her copy from, the original or her first copy? Explain.
a) The enlargement needed to be done is 25%.
b) The succession time should be at least t=9 to get a final copy that is less than 15% of the original size.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
Let the size of the page be q, when it is reduced to 80%, its size becomes
= 80% x q
= 0.80(q)
= 0.80q
When you want to return it into its original size q,
x(0.80q) = q
x = q / 0.80q
x = 1.25
x= 125%
Hence, the enlargement needed to be done is 25%.
b) The size of the page after t number of copying done is given by
C(t) = [tex]C_0(0.80)^t[/tex]
So, C(t) / [tex]C_0[/tex] = [tex](0.80)^t[/tex]
0.15 ≤ [tex](0.80)^t[/tex]
Taking log on both side
log (0.15) ≤ log [tex](0.80)^t[/tex]
log (0.15) ≤ t log (0.80)
log (0.15) /log (0.80) ≤ t
0.80 ≤ t
Hence, the succession time should be at least t = 9 to get a final copy that is less than 15% of the original size.
Learn more about Percentage here:
https://brainly.com/question/29306119
#SPJ1
are all even numbers prime?
Step-by-step explanation:
Nope. Actually, every single even number except 1 is composite actually
Answer:
No
Step-by-step explanation:
2 is a prime number, but all other even numbers are composite, since they're all multiples of 2
the product of n and 19, increased by 202 is 324
Answer:
n = 6.42105263158
Step-by-step explanation:
324 - 202 = 122
122 ÷ 19 = 6.42105263158
That seems like a very large decimal place for a school related math problem if I'm doing this correctly. When you say increased by you mean addition right?
A rectangular monitor’s size is measured diagonally from one corner to the opposite corner. What is the size of rectangular monitor that is 30 centimeters wide by 24 centimeters hight, to the nearest centimeter?
Answer: 38.3 cm
Step-by-step explanation:
To find the size of a rectangular monitor measured diagonally, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Here are the steps to calculate the diagonal size of the monitor:
Find the length of the hypotenuse by finding the square root of the sum of the squares of the other two sides.The other two sides of the triangle are the width and height of the monitor, which are given as 30 centimeters and 24 centimeters respectively.Apply the formula √(30² + 24²) = √(900+576) = √1476Take the square root of 1476 which is approximately 38.3 cm.Therefore, the size of the rectangular monitor that is 30 centimeters wide by 24 centimeters high is approximately 38.3 cm. to the nearest centimeter.
The size of the given mirror as a rectangular diagonal is 38.41 cm which is almost 39 cm.
We know that;
d=√ {(l)^2 + (w)^2}.........(i), where,
d= diagonal of the rectangle,
l= length of the rectangle = 30 cm
w= width of the rectangle = 24 cm.
Therefore, Substituting the values of each in equation (i), we get;
d=√{(30)^2+(24)^2} cm,
or, d = 38.41 cm
So, the size of the rectangular mirror measured diagonally is 38.41 cm which is almost 39 cm.
Read more about the diagonal of a rectangle;
brainly.com/question/10658174
brainly.com/question/19556570
Find the median of the set of data values.
79, 83, 54, 77, 98, 61, 88
Answer:
The median is 79.
Step-by-step explanation:
Points K and M are points of tangency. Find the value of x
If the points K and M are points of tangency, then the value of x is, 4
What is a circle?In mathematics, the circle is a two dimensional rounded figure which has no corner edges.
Standard form = (x - a)² + (y - b)² = r²
Given that,
A circle, having two pair of lines JK & JM
It is known that,
theorem of a circle,
Lengths of the tangents on the circle from the same point are equal
Length of JK = Length of JM
6x + 5 = 37 - 2x
8x = 32
x = 4
Hence, the value of x is 4
To know more about circle check:
brainly.com/question/17357009
#SPJ1
I really need help with finding the approximate length for this question please and thank you .
Answer:
13.86
Step-by-step explanation:
You have the exact value, just compute it and round the number to get your approximate
Answer:
13.86
Step-by-step explanation:
You'll most likely need the calculator since ✓192 is not a perfect square.
Calculating it
✓192 = 13.856
Rounding it two places would be 13.86
ow many ways are there to put $5$ balls in $3$ boxes if the balls are distinguishable but the boxes are not?
There are 81 different ways to place 5 distinguishable balls in 3 indistinguishable boxes using combinations.
Given that in how many ways we can put 5 balls in 3 boxes if balls are distinguishable, but the boxes are not.
To find the number of ways we will use the concept of combination.
Combinations can be defined as the entire outcomes of an event where the order of outcomes does not matter.
Given Data
The number of balls is 5 balls.
The number of boxes is 3 boxes.
The balls are distinguishable, but the boxes are not distinguishable.
According to the question, the expression for the number of ways is,
P = [tex]\frac{n^N}{n}[/tex]
Putting the values in the formula we get,
P = [tex]\frac{3^5}{3}[/tex]
P = 81
Hence the number of the ways are 81.
Learn more about Combinations click;
https://brainly.com/question/31781540
#SPJ12
Find the missing angles measurements
Please show work and sawer all questions
The following are the respective values of the angles:
∠5 = 44°
∠3 = 117°
x = 60°
x = 157°
How to evaluate for the values of the anglesangles (∠5 + ∠6)° and ∠2 are corresponding angles and are equal so;
∠5 + 90° = 134°
∠5 = 134° - 90°
∠5 = 44°
angles (∠5 + ∠6)° and ∠3 are alternate angles and are equal so;
∠3 = ∠5 + ∠6
∠3 = 27° + 90°
∠3 = 117°
(x + 5) + 90° + (180° - 155°) = 180° {sum of interior angles of a triangle}
x + 5 + 90° + 25° = 180°
x + 120° = 180°
x = 180° - 120°
x = 60°
x = 22° + (180° - 45°) {exterior angle of a triangle equals two opposite interior angles}
x = 22° + 135°
x = 157°
Therefore, the following are the values of the angles: ∠5 = 44, ∠3 = 117°, x = 60°, and x = 157° respectively.
Know more about angle here:https://brainly.com/question/17972372
#SPJ1
find 10% of 70
pls give simple working out :)
Answer: 7 is the 10% of 70
Step-by-step explanation:
1. write 10% as 10/100 as we convert in this form to find the percentage.
2. 10/100 x 70 = 7
therefore the answer is 7
(a)
The prize money from a game show is shared amongst the team in the ratio
A: B: C = 2: 5: 3. If the prize money was £1500, how much more money does person B receive than person A?
(b) Person C donates 40% of his share to charity. State the ratio of the amount
donated to charity, to the total prize money in its simplest form
Step-by-step explanation:
(a)
2:5:3 means that there are 2+5+3 = 10 units of the price money distributed between the team.
£1500 / 10 = £150 per unit.
person A gets therefore 2×150 = £300
person B gets 5×150 = £750
person C gets 3×150 = £450
so, person B gets 750-300 = £450 more money than person A.
(b)
40% of £450 = 450×0.4 = £180
so donated to total prize money is
180/1500 = 3/25
find the solution of the differential equation ″()=⟨12−12,2−1,1⟩ with the initial conditions (1)=⟨0,0,12⟩,′(1)=⟨8,0,0⟩.
The solution to the given differential equation is a 3-dimensional vector function which satisfies the given initial conditions. The vector function consists of three components, one for each dimension in the equation.
The given differential equation is a 3-dimensional vector equation, of the form ()=⟨12−12,2−1,1⟩. The initial conditions are (1)=⟨0,0,12⟩ and ′(1)=⟨8,0,0⟩. The solution to this equation is a 3-dimensional vector function, ()=⟨, ,⟩. The first component of the vector function is a function of the independent variable, and must satisfy the initial condition (1)=⟨0,0,12⟩. This means that the first component of the vector function must be equal to 0 at x=1. The second component must satisfy the initial condition ′(1)=⟨8,0,0⟩. This means that the second component of the vector function must be equal to 8 at x=1. The third component of the vector function must also satisfy the initial condition (1)=⟨0,0,12⟩. This means that the third component of the vector function must be equal to 12 at x=1. Once the initial conditions have been satisfied, the equation can be solved to find the vector function.
Learn more about equation here
https://brainly.com/question/649785
#SPJ4
