Answers
Answer:
1) f(x) = 500·(1.1)ˣ
2) f(x) = 500·(0.9)ˣ
Step-by-step explanation:
1) The given values in the table are;
x; 0, 1, 2, 3
f(x); 500, 550, 605, 665.5
By observation, we have that each two subsequent term of f(x) have a common ratio, given as follows;
550/500 = 11/10 = 1.1 = 605/550 = 665.5/605
From which we have;
The values of f(x) are in a geometric progression
The nth of a geometric progression = a·rⁿ
The common ratio, r = 1.1
The first term, a = 500
The number of terms, n = x
Therefore, xth term, f(x) = a×(r)ˣ
Substituting the values gives;
The equation for the data shown in the table is f(x) = 500·(1.1)ˣ
2) The given table of values is presented as follows;
x; 0, 1, 2, 3
f(x); 500, 450, 405, 364.5
The common ratio, f(xₙ)/f(xₙ₋₁) = 450/500 = 9/10 = 0.9 = 405/450 = 364.5/405
The terms of f(x) are in a geometric progression
The first term. a = 500
The common ratio, r = 9/10 = 0.9
The nth term of a geometric progression, G.P. = a·rⁿ
By plugging in the values of 'a', 'r', and 'n', the value of the xth term, f(x), therefore;
The equation for the data shown in the table is f(x) = 500·(0.9)ˣ.
Related Questions
if 1/3 of a number is added to 1/5 of the same number.the result is 8. find the number. I am
Answers
Answer:
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
The length of a rectangle is 5 less than
the width. Which polynomial describes
the area of the rectangle?
Answers
Answer:
Let length = x
Let width = x + 5
Let Area = A
A = x(x + 5)
A = x2 + 5x
The sum of a number and 3:
Answers
Answer:
x+3?
Step-by-step explanation:
honestly, there is not alot of information present here. so when a hear "a number" i think variable.... which would be set up as x+3
Earth is the third planet from the Sun, with an average distance of
93,000,000 miles. It takes light about 8 minutes to travel from the Sun
to Earth.
Pluto, a dwarf planet, has an average distance of 3.7 X10° miles
from the Sun. How many times farther from the Sun is Pluto than
Earth? How long does it take light to reach Pluto?
Answers
Answer:
The ratio of the distance of Pluto and the earth to the Sun is 40.
Time taken by light to travel from Sun to Pluto is 5.3 hours.
Step-by-step explanation:
Distance between Earth an Sun = 93,000,000 miles
Time from Sun to Earth = 8 minutes
Distance beteen Pluto and Sun = 3.7 x 10^9 miles
The ratio of the distance between Pluto and Sun to the Earth and Sun is
[tex]\frac{3.7\times 10^9}{93000000}\\\\=39.8 =40[/tex]
Now let the time taken by the light to move from Sun to Pluto is t.
[tex]\frac{93000000}{8}=\frac{3.7\times 10^9}{t}\\\\t =318.28 minutes = 5.3 hours[/tex]
The radius of the circle is 7 cm. What is the area of the shaded part? Use π = 227
Answers
Answer:
227 * 7^2
Put into calculator
Step-by-step explanation:
Area of a circle is pi * r^2 (pi times radius squared)
Just put the numbers in
227 * 7^2
Put into calculator and there you go
consider the following sequence at 87;84;81 which term will be the first negative term in the sequence
Answers
Answer:
"31st in the sequence"
87/3 = 29 .. 29 subtractions needed to get to zero
the 30th position in the sequence will be zero
the 31st is the first negative term
1 87
2 84
3 81
4 78
5 75
6 72
7 69
8 66
9 63
10 60
11 57
12 54
13 51
14 48
15 45
16 42
17 39
18 36
19 33
20 30
21 27
22 24
23 21
24 18
25 15
26 12
27 9
28 6
29 3
30 0
31 -3
Step-by-step explanation:
Write 2.073 in expanded form.
Answers
Answer:
2 + 0.0 + 0.07 + 0.003
Step-by-step explanation:
Pretty much just adding the whole number and decimal.
2 (whole number) + 0.073
Expanded forms require showing which place the numbers are in (i.e. 0.07 is the hundredths place)
Two workers paint lines for angled parking spaces. One worker paints a line so that m∠1=65. The other worker paints a line so that m∠2=65. Are their lines parallel? Explain your answer.
Answers
The image of the car park showing the 2 angles is attached.
Answer:
Their lines are parallel.
Step-by-step explanation:
From the attached image, we can see that ∠1 and ∠2 form a pair of alternate exterior angles. Thus; ∠1 = ∠2.
Now since they are congruent, it means that their lines will be parallel.
Thus, we can conclude that their lines are parallel.
how do u factor..
x^2 + 10× - 2400 = 0
Answers
Answer:
[tex]{ \bf{ {x}^{2} + 10x - 2400 = 0}} \\ { \bf{ \red{it \: has \: no \: rational \: factors}}} \\ x = - 54.2 \: \: and \: \: 44.2[/tex]
x^2-24000=0
x^2=24000
take the square root of 24000
find the perimeter of this figure to the nearest hundredth. Use 3.14 to approximate π.
Answers
Answer:
P = 40.56 ft.
Step-by-step explanation:
Answer:
40.56
Step-by-step explanation:
Answer plsssss………………
Answers
Answer:
The corresponding angles theorem works for cases where we have two parallel lines intersecting another line.
Two lines are parallel if, at any point, the distance between these two lines is always the same.
Now, if we look at the image, we can see that the distance between the two horizontal lines changes (is smaller at the right and larger at the left)
Thus, these lines are not parallel.
Then the corresponding angles theorem can not be used here, and we have that:
∠9 ≠ ∠10
Find the measure of a single exterior angle of the regular polygon shown below. If necessary, round to the nearest tenth.
Answers
Answer:
32.7 degrees
Step-by-step explanation:
The total exterior angle of any polygon is 360 degrees
Each exterior angle can be calculated by dividing this total by the number of sides
So we have each measure as 360/n
where n is the number of sides
here, we have n = 11
So we have each exterior angle as:
360/11 = 32.7 degrees
Answer:
40
Step-by-step explanation:
calculate the area of the shape
Answers
Answer:
which shape tho and it's easy if there is more than one shape than find the formula for each shape and combine them!
Answer:
the formula for the rectangle is LxW or BxH (however your teacher taught it) which is just 4x15=60. The triangle is bxh÷2 which means 4x15=60 then 60÷2= 30. Add 30+60 which gives you Area=90formula for a circle πxr^22
3
4
5
8
10
TIME REMAINING
49:29
C D
Hal is asked to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually.
What multiplicative rate of change should Hal use in his function?
0.02
0.98
01.02
1.98
Save and Exit
Answers
Answer: .98
Step-by-step explanation:
Yk help me bru In the straight edge and compass construction of the angle bisector below which of the following reasons can be used to prove that angle DGB = angle EGB
Answers
Answer:
The correct Option is B
Step-by-step explanation:
Two Angles that are equal to the same angle must themselves be equal (Transitive property of equality)
BD = BE, because they are radii of the same circle. DG = EG because they are sides f equilateral triangle DEG. Therefore, the correct option is option A.
What is angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.
We refer to these as dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves.
Angle can also refer to the size of such an angle or maybe a rotational angle. The length of such a circular arc divided by its radius is the traditional definition of this metric, which may also be signed. BD = BE, because they are radii of the same circle. DG = EG because they are sides f equilateral triangle DEG.
Therefore, the correct option is option A.
To know more about angle, here:
https://brainly.com/question/15277238
#SPJ7
What is the first step in solving for w in the equation 3W + 5 = 14?
Answers
I really need help, please.
Answers
7.
y=118, z=15, because when 2 shapes are similar, the ratios of the sides relative to each other remain the same, and the angles also remain the same. This property can be used to solve the rest of the questions
8.
15*2/3=10
9.
Always
10.
Sometimes
Can someone help me please
Answers
Answer:
yes what would u like help with
Calculate the Kinetic Energy when the mass of the car is 1,200kg and the speed
is 11.11 m/s.
Answers
Answer:
74059.3 J
Step-by-step explanation:
KE = I/2mv²
KE = 1/2(1200)(11.11)²
KE = 1/2(1200)(123.4321)
KE = 74059.26 J
Answer
74059.26J
Explanation
Formula
EK=mv^/2
m=1200kg
v=11.11m/s
E=1200kg×(11.11m/s)^/2
E=74059.26J
Find the second number
Answers
[tex]\huge\bold{Given :}[/tex]
Product of two numbers = 1.875
One of the number = 2.5
[tex]\huge\bold{To\:find :}[/tex]
The second number.
[tex]\huge\bold{Solution :}[/tex]
[tex]\sf\blue{The \:second\:number \:is\:0.75 .}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
Let the second number be [tex]x[/tex].
As per the question, we have
[tex]Product \: \: of \: \: the \: \: two \: \: numbers = 1.875 [/tex]
[tex]⇢ \: 2.5 \times x = 1.875[/tex]
[tex]⇢x = \frac{1.875}{2.5} [/tex]
[tex]⇢x = 0.75[/tex]
[tex]\sf\purple{Therefore,\:the\:second\:number\:is\:0.75.}[/tex]
[tex]\huge\bold{To\:verify :}[/tex]
[tex]2.5 \times x = 1.875[/tex]
[tex]➪ \: 2.5 \times 0.75 = 1.875[/tex]
[tex]➪ \: 1.875 = 1.875[/tex]
➪ L. H. S. = R. H. S.
Hence verified.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]
An aeroplane travels on a bearing of 295o so that it is 200 km west of its starting point. How far has it travelled on this bearing?
please use diagrams to explain
Answers
The more accurate value is roughly 220.675583792499 km but even that isn't an exact value.
===============================================
Explanation:
Refer to the diagram below.
The plane starts at point A, which is the origin (0,0)
Directly north is the bearing 0 degrees, which it sometimes written as triple zeros and a degree symbol at the end, so we'd write 000° to mean directly north.
Let's say we face directly north. When turning clockwise (turn toward the east), the bearing angle increases. That means directly east is the bearing 090° and 180° is directly south.
The bearing 270° is directly west. Another 25 degrees gets us to 270+25 = 295°
This plane is facing the northwest direction, as the diagram indicates below (the plane is aimed at point C while it's located at point A initially).
------------
Triangle ABC has the horizontal component AB = 200 km, since we're told that the plane is 200 km west of its starting point (and some unknown distance north of the starting point).
We use the cosine ratio to help determine the hypotenuse length AC
cos(angle) = adjacent/hypotenuse
cos(A) = AB/AC
cos(25) = 200/x
x*cos(25) = 200
x = 200/cos(25)
x = 220.675583792499 which is approximate.
x = 221
I'm rounding to the nearest whole number since every other value given to you is a whole number. Round as your teacher instructs.
This means the plane is roughly 221 km away from its starting point. In other words, side AC is about 221 km long.
Point CC is located at (4,3)(4,3) on the coordinate plane. Point CC is reflected over the xx-axis to create point C'C ′ . Point C'C ′ is then reflected over the yy-axis to create point C''C ′′ . What ordered pair describes the location of C''?C ′′ ?
Answers
Answer:
[tex]C" = (-4,-3)[/tex]
Step-by-step explanation:
Given
[tex]C = (4,3)[/tex]
Required
The coordinates of C"
From the question, we understand that:
C is reflected over x-axis to give C'
The rule to this is:
[tex]C(x,y) \to C'(x,-y)[/tex]
So, we have:
[tex]C(4,3) \to C'(4,-3)[/tex]
Next, C' is reflected over y-axis to give C''
The rule to this is:
[tex]C'(x,y) \to C"(-x,y)[/tex]
So, we have:
[tex]C'(4,-3) \to C"(-4,-3)[/tex]
the graph of y=-3x+4 is?
Answers
Answer:
B
Step-by-step explanation:
that is a linear equation, therefore it makes a line, eliminating choices C and D.
Lines can literally Any x or y. So it would be B, a set of all the solutions to the equations.
Need helppp pls!!!!
Answers
Answer:
130º
Step-by-step explanation:
it seems like this would make a circle which adds up to 360º so first add the two numbers (150+80=230) then subtract from the amount it should be (360-230=130)
There is a bag with only milk and dark chocolates. The probability of randomly choosing a dark chocolate is 5/12. There are 40 dark chocolates in the bag and each is equally likely to be chosen. Work out how many milk chocolates there must be
Answers
Answer: the total number of milk chocolate is 6
Step-by-step explanation:
help asap pls -=-=-=-=--------------
Answers
Answer:
-1/3
Step-by-step explanation:
at x=0 y= 5
at x=3 y= 4
y=ax+b
b= 5
4=3x+5
3x= -1
x= -1/3
[tex]y = - \frac{x}{3} + 5[/tex]
What percentage of the data values falls between the values of 27 and 45 in the data set shown?
VX
25
30
35
40
45
50
25%
O 50%
оооо
O 75%
100%
Answers
Answer:
75%
Step-by-step explanation:
Looking at the plot, we can see that the number 27 represents the minimum value while the number 45 represents the upper quartile
Between the minimum value and the upper quartile, there is 75% of all the values on the plot
So, we can conclude that between the numbers 27 and 45, we have 75% of all the data values present.
Kindly note;
There are five points in a box plot
minimum
lower quartile (0-25%)
Median (0-50%)
Upper quartile (0-75%)
Maximum number (0-100%)
Can you please help me. It says to find each product
Here is the question
There is a picture
Answers
Answer:
-3/5
Step-by-step explanation:
7 * -3/7 * 1/5
Rewritng
7/7 * -3/5 *1
Simplifying fractions
1 * -3/5 *1
-3/5
Description:- Note down postal pin code of your place where you reside. Take x times of last 2 digits of that pin code and add number of family members to it. Put it equal to your age and solve for x.
Answers
Answer:
x = 2/3
Step-by-step explanation:
The last two digit of postal code here is 12
We multiply this by x
so we have x * 12 = 12x
The number of family members is 6 ; and we are to equate it to my age which is 14
thus, we have the equation as;
12x + 6 = 14
12x = 14-6
12x = 8
x = 8/12
x = 2/3
find'x' 2log_5x = 1+log_5(x-6/5)
Answers
Answer:
x = 2 and x = 3
Step-by-step explanation:
Formulas used :
[tex]log_5 \ 5 = 1[/tex]
[tex]log_5 \ x + log_5 \ y = log_5 \ (xy)[/tex]
[tex]log_5 \ x = log_5 \ y => x = y[/tex]
Steps :
[tex]2 \ log_5 \ x = 1 + log_5 (x - \frac{6}{5} )\\\\2 \ log_5 \ x = log_5 \ 5+ log_5 (x - \frac{6}{5} )\\\\2 \ log_5 \ x = log_5 \ ( 5(x - \frac{6}{5} ))\\\\x^2 = 5(x - \frac{6}{5})\\\\x^2 = 5x - 6\\\\x^2 - 5x + 6 = 0\\\\x^2 - 2x - 3x + 6 = 0\\\\x(x - 2 ) - 3 (x - 2) = 0\\\\(x - 3)(x-2) = 0\\\\x = 3 , x = 2[/tex]
