If the exponential model f(x)=3(2)x is written with the base e, it will take the form A0ekx. What is A0 and what is k?
Answers
Answer:
Answer in pic
Step-by-step explanation:
The required value of A₀ = 3 and k = ln 2, as of the given exponential model.
What is an exponential function?The function which is in format f(x) =a^x where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
here,
Since.
[tex]a^x = e^{xlna}[/tex]
According to the question,
[tex]3(2)^x = A_oe^{kx}\\3e^{xln2} = A_oe^{kx}[/tex]
Now
Compare the values,
A₀ = 3 and k = ln 2,
Thus, According to the stated exponential model, A0 = 3 and k = ln 2.
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Related Questions
In the last six months, Sonia's family used 529, 499, 651, 652, 1,163, and 310 minutes on their cell phone plan. To save money, Sonia's family wants to keep their mean cell phone usage below 600 minutes per month.
By how many minutes did they go over their goal in the last six months?
Answers
Answer:
They went over their goal for the last six months by 34 minutes per month.
Step-by-step explanation:
Mean of a data-set:
The mean of a data-set is the sum of all values in the data-set divided by the size of the data-set.
529, 499, 651, 652, 1,163, and 310 minutes on their cell phone plan.
The mean is:
[tex]M = \frac{529+499+651+652+1163+310}{6} = 634[/tex]
By how many minutes did they go over their goal in the last six months?
The mean was of 634 minutes, and they wanted to keep it below 600. So
634 - 600 = 34
They went over their goal for the last six months by 34 minutes per month.
Do you have any practice questions for grade 1 and 8 of math
Answers
Answer:
dear please focus on other subjects not only on math
on a tv game show,omar needs answer 7 out of every 10 questions correctly. There will be 30 questions in all
Answers
in the diagram, the measure of angle 3 is 105°
which angle must also measure 105°?
A.1
B.4
C.6
D.8
Answers
Answer:
it's angle 1.
Reason:
vertically opposite angles are equal
Which additional facts prove that RST and
WXY are congruent? (Geometry)
Answers
Answer:
Option C
Step-by-step explanation:
In the given triangles ΔRSW and ΔWXY,
m(∠S) = m(∠X) = 60° [Given]
Properties of congruence of two triangles applicable in this question,
SAS or ASA
For the congruence of two triangles by the property SAS,
"Two corresponding sides and the included angle should be congruent"
RS ≅ WX, ST ≅ XY and ∠S ≅ ∠X
Which is not given in any option.
For the congruence of two triangles by the property ASA,
"Two consecutive angles and the side having these angles should be congruent"
∠R ≅ ∠W, ∠S ≅ ∠X and RS ≅ XY
Option C will be the correct option.
Help. Urgent. Skenekeks
Answers
Answer:
D
Step-by-step explanation:
Plug in the numbers for the x-value and solve the equation.
| 3(80/3)/4 + 1 | = 16
| 3(-40/3)/4 + 1 | = 16
Create a tree diagram that shows all the possible outcomes for tossing a coin and spinning a spinner with six equal sections numbered 1 through 6.
Answers
Step-by-step explanation:
We can use a tree diagram to help list all the possible outcomes.
probability tree coin dice
From the diagram, n(S) = 12
This may help you....
plzzz mark me as brainlist....
Which function results after applying the sequence of transformations to
f(x) = x5?
• reflection over the x-axis
• vertically stretch by a factor of 2
• shift down 1 unit
Answers
Answer:
A. g(x) = -2x^5 - 1.
Step-by-step explanation:
Reflection over the x axis results in the function -x^5.
Vertical stretch of 2 gives -2x^5
Finally a shift down of 1 unit gives -2x^5 - 1
The function results after applying the sequence of transformations to
f(x) = x⁵ is,
⇒ g(x) = -2x⁵ - 1.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Now,
After Reflection over the x axis results in the function is,
g (x) = - x⁵
And, After Vertical stretch of 2 gives,
g (x) = -2x⁵
Then, Finally a shift down of 1 unit gives,
g (x) = -2x⁵ - 1
Thus, The function results after applying the sequence of transformations to f(x) = x⁵ is,
⇒ g(x) = -2x⁵ - 1.
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When an airplane is 35,000 feet from an air traffic control tower, the angle of elevation between the tower and the airplane is.
What is the approximate altitude, a, of the plane at this point?
A. 45,689 feet
B. 26,812 feet
C. 29,369 feet
D. 41,711 feet
Answers
Answer:
26,812 ft
Step-by-step explanation:
The drawing given is very helpful in this case. When solving problems like this, it's important to realize what trigonometric ratio we're going to use. From the given angle (50°), we are given the hypotenuse (35,000 ft) and we're trying to solve for the opposite side ([tex]a[/tex]).
So since we're trying to find the opposite side side and we have the hypotenuse, we should try to find a trigonmetric ratio between the opposite side and the hypotenuse. Using SOH-CAH-TOA, hopefully you can see that we should pick SOH (i.e. [tex]\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]). Therefore, we can set up our equation given the angle [tex]\theta=50^\circ[/tex].
[tex]\sin(50^\circ)=\frac{a}{35000}[/tex]
Since we're solving for [tex]a[/tex], we can just rearrange to get [tex]a=35000\sin(50^\circ)=26812[/tex]
Therefore, the plane's altitude [tex]a[/tex] is 26,812 ft.
The approximation altitude of the plane at 35,000 feet from an air traffic control tower will be 26812 feet hence option (B) will be correct.
What is a trigonometric function?the trigonometric functions are real functions for only an angle of a right-angled triangle to ratios of two side lengths.
The domain input value for the six basic trigonometric operations is the angle of a right triangle, and the result is a range of numbers.
The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.
Given that 35000 feet are the distance between a plane and the air traffic control tower.
Hypotaneous = 35000 feet
The angle of elevation is 50°
By trigonometric function sin
Sinx = perpendicular/hypotaneous
Sin50° = Altitude/35000
Altitute = 35000 × sin50°
Altitude = 26811.55 ≈ 26812 feet will be the correct answer.
For more information about the trigonometric function
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(07.04 LC)What is the solution to the equation ax = 2?
Ox= 1
Ox=1
- کی
Ox= 3
O x = 12
Plz helppp
Answers
Answer:
x=12 .
Step-by-step explanation:
See image below:)
X+ 5
If m(x) =x-1 and n(x) = x-3, which function has the same domain as (mon)(x)?
X+5
O (x)=
11
11
o h(x)=
X-1
11
O (X)=
X-4
11
Oh(x) =
X-3
Answers
Answer:
third option
Step-by-step explanation:
m(n(x)) =
[tex] \frac{x - 3 + 5}{x - 3 - 1} = \frac{x + 2}{x - 4} [/tex]
the domain of this is R/(4)
so as the third option
The function that has the same domain as (m o n)(x) is
h(x) = 11 / (x - 3)
Option D is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
m(x) = (x + 5)/ (x - 1) and n(x) = x - 3,
Now,
(m o n)(x)
= m (n(x)
= m (x - 3)
= (x - 3 + 5) / (x - 3 - 1)
= (x + 2) / (x - 3)
We can not have x = 3.
So,
The domain can not have x = 3.
From the options,
h(x) = 11 / (x - 3) can not have x = 3.
Thus,
The function that has the same domain as (m o n)(x) is
h(x) = 11 / (x - 3)
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WILL GIVE BRAINLIESTTT!!!! PLS HELP
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Create a proportion using the form %/100 = is/of to represent the following word problem.
Seven is what percent of 30?
Answers
Pa help po plssssss
Sana po meron Ang maka-sagot ☺️☺️
Answers
Answer:
The answer is below
Step-by-step explanation:
a) the volume of the pit = length * width * depth = 9 dm * 6 dm * 7 dm = 378 dm³
Hence to fil the pit, 378 dm³ of sand is needed.
b) Volume of the room = length * width * height = 2.3 m * 0.59 m * 3.74 m = 5.08 m³
The cabinet would occupy 5.08 m³ of space.
c) volume = length * width * height
210 dm³ = 3.5 dm * 6 dm * width
width = 210 dm³ / (3.5 dm * 6 dm) = 10 dm
d) Volume of the room = length * width * height = 15 m * 15 m * 15 m = 3375 m³
The stockroom has a space of 3375 m³
e) volume = length * width * height = 5 dm * 5 dm * 5 dm = 125 dm³
The container has a space of 125 dm³
f) volume = length * width * height = 41 cm * 13 cm * 24 cm = 12792 cm³
The box has a space of 12792 cm³
g) volume of prism = length * width * height
72 m³ = 4 m * 3 m * length
length = 72 m³ / (4 m * 3 m) = 6 m
h) volume = length * width * height = 8 cm * 8 cm * 8 cm = 512 cm³
The figure has a volume of 512 cm³
i) volume = length * width * height = 5 ft * 2 ft * 3 ft = 30 ft³
The cabinet has a space of 30 ft³
The height of a square pyramid with a that has 12 cm edges and a lateral area of 240cm sq.
Answers
Answer:
The height of the pyramid = 8 cm
Step-by-step explanation:
Given that,
The edges of a pyramid, a = 12 cm
The lateral area of a pyramid, A = 240 cm²
The formula for the lateral area of a square pyramid is given by :
[tex]A=a\sqrt{a^2+4h^2}[/tex]
Where
h is the height
Squaring both sides,
[tex]A^2=a^2\times (a^2+4h^2)\\\\\dfrac{A^2}{a^2}=a^2+4h^2\\\\\dfrac{A^2}{a^2}-a^2=4h^2\\\\4h^2=\dfrac{(240)^2}{12^2}-12^2\\\\4h^2=256\\\\h^2=64\\\\h = 8\ cm[/tex]
So, the height of the pyramid is equal to 8 cm.
Given the system of equations, what is the solution? 2x+y = -1 х- у = -5
Answers
Answer:
x=-2, y=3
Step-by-step explanation:
make it easy first, solve for x in the second equation: x= -5+y.
then sub that in for the other x: 2(-5+y)+y= -1
now combine like terms: -10+3y= -1
solve for y: 3y=9, y= 3
then replace y for your second equation: x-3= -5
solve for x= -5+3.... so then its -2
check by replacing all variables with your new solutions:
2(-2), which is -4+3 does equal -1
(-2) -3 does equal -5.
your answers are x=-2, y=3
Solve for x. Round to the nearest tenth if necessary.
A. 28
B. 30.1
C. 41.1
D. 30
Answers
Answer: 41.1
Step-by-step explanation:
To find the value of x, we need to use SOH-CAH-TOA. SOH-CAH-TOA is since, cosine, and tangent. The O, A, H stands for opposite, adjacent, and hypotenuse respectively.
Looking at the figure, we see 47°. The labelled angles are adjacent and the hypotenuse. Therefore, we use CAH or cosine.
[tex]cos(47)=\frac{28}{x}[/tex] [multiply both sides by x]
[tex]xcos(47)=28[/tex] [divide both sides by cos(47)]
[tex]x=\frac{28}{cos(47)}[/tex]
When we plug that into a calculator, we get x=41.1.
Answer:
ans: 41.1
Step-by-step explanation:
in given figure 47° is reference angle so considering the given sides and reference angle use cosine
I.e
cos47° = 28/x
x = 28 / cos47°
x = 41.1
help i got to pee!!!!!!!!!!!!1
Answers
Answer:
23s - 7
Step-by-step explanation:
17s - 10 + 6s + 3
=23s - 7
Answer:
[tex]23s-7[/tex]
Step-by-step explanation:
Given:
[tex]17s-10+3(2s+1)[/tex]
Distribute the parenthesis
[tex]17s-10+6s+3[/tex]
Combine like terms
[tex]23s-7[/tex]
Hope this helps
In an attempt to clean up your room, you have purchased a new floating shelf to put some of your 17 books you have stacked in a corner. These books are all by different authors. The new book shelf is large enough to hold 10 of the books.
(a) How many ways can you select and arrange 10 of the 17 books on the shelf? Notice that here we will allow the books to end up in any order. Explain.
(b) How many ways can you arrange 10 of the 17 books on the shelf if you insist they must be arranged alphabetically by author? Explain.
Answers
Answer:
19448 ways
70572902400 ways
Step-by-step explanation:
(a)
To arrange 17 books on a shelf from a possible we use the combination formula :
nCr = n! ÷ (n-r)!r!
17C10 = 17! ÷ 7! 10!
17C10 = 19448 ways
To arrange the books in alphabetical order :
2)
In question, 2, the order of arrangement matters ; hence, we use permutation ;
nPr = n! ÷ (n-r)!
17P10 = 17! ÷ (17 - 10)! = 17! ÷ 7!
17P10 = 70572902400
The cost of 8 chalk markers in a store is $12.20. Ava buys 20 chalk markers from the store. How much will Ava pay at the store?
Answers
Answer: 0.61
Step-by-step explanation:
Divide 12.2 by 20
I am not sure if this is the answer you can try it
Answer:
$30.50
Step-by-step explanation:
20 x 12.20 = 244
244 divided by 8 = $30.50
what is 7x+3y=9 in y-intercept form?
Answers
Answer:
y = -2 1/3+3
Step-by-step explanation:
-Subtract 7x from each side of equation
-divide by 3 on each side
7x+3y = 9
3y = -7x+9
y = -7/3+3
:) ur welcome
point o is the center of this circle what is m angle CAB
a 55
b 48
c 45
d 35
Answers
Answer:
m< CAB = ½× 96° = 48° (option b)
The equation y = 50(1.05)x models the growth of a mule deer population introduced into Guadalupe National Park in December 2015. "X" represents the number of years after December 2015 while "y" represents the population at time "x". In what year will the mule deer population first reach 1500?
F. 2084
G. 2044
H. 2043
J. 2086
Answers
Answer: (f)
Step-by-step explanation:
Given
The growth equation is [tex]y=50(1.05)^x[/tex]
When population becomes 1500
[tex]\Rightarrow 1500=50(1.05)^x\\\Rightarrow 30=(1.05)^x\\\text{Taking log both sides}\\\Rightarrow \ln (30)=x\ln (1.05)\\\\\Rightarrow x=\dfrac{\ln (30)}{\ln (1.05)}\\\\\Rightarrow x=69.71[/tex]
Thus, after 69.71 years of year 2015 i.e. [tex]2015+69.71=2084.71[/tex]. In year 2084, it becomes 1500.
option (f) is correct.
I need help please, i dont understand
Answers
9514 1404 393
Answer:
(a) none of the above
Step-by-step explanation:
The largest exponent in the function shown is 2. That makes it a 2nd-degree function, also called a quadratic function. The graph of such a function is a parabola -- a U-shaped curve.
The coefficient of the highest-degree term is the "leading coefficient." In this case, that is the coefficient of the x² term, which is 1. When the leading coefficient of an even-degree function is positive, the U curve has its open end at the top of the graph. We say it "opens upward." (When the leading coefficient is negative, the curve opens downward.)
This means the bottom of the U is the minimum value the function has. For a quadratic in the form ax²+bx+c, the horizontal location of the minimum on the graph is at x=-b/(2a). This extreme point on the curve is called the "vertex."
This function has a=1, b=1, and c=3. The minimum of the function is where ...
x = -b/(2·a) = -1/(2·1) = -1/2
This value is not listed among the answer choices, so the correct choice for this function is ...
none of the above
__
The attached graph of the function confirms that the minimum is located at x=-1/2
_____
Additional comment
When you're studying quadratic functions, there are few formulas that you might want to keep handy. The formula for the location of the vertex is one of them.
The ratio of girls to boys in a particular classroom is 8: 7. How many boys are in the class if there are 45 students?
ONLY ANSWER IF YOU KNOW THE ANSWER
Answers
9514 1404 393
Answer:
21
Step-by-step explanation:
Rearranging the given ratio, we can find the ratio of boys to the total.
boys : (boys +girls) = 7 : (7+8) = 7 : 15
Then the number of boys is ...
(7/15)(45) = 21
There are 21 boys in the classroom.
2 Vince worked 506 hours in 11 weeks. At what rate did he work in hours per week?
Answers
Answer:
46 hours per week
Step-by-step explanation:
diide 506 by 11 weeks!
A. 11.1
B. 6.7
C. 13
D. 4.1
Answers
Answer:
C. 13Line AE & Line AD have the same in measurement.If a regular polygon has exterior angles that measure 36° each, how many sides does the polygon have? O A. 12 O B. 6 O c. 10 O D.8
Answers
Answer:
A decagon with has 10 sides.
The polygon has 10 sides.
What are Polygons?Polygons are closed figures which has at least three set of line segments joined together.
The polygon with least number of sides is triangle.
Regular polygons are polygons which are having all the sides and interior angles equal to each other.
Given that,
Each exterior angle of the polygon = 36°
Sum of the exterior angles of a polygon is always 360°.
So,
Each exterior angle of a regular polygon = 360° / Number of sides
Number of sides of the polygon = 360° / measure of each exterior angle
Substituting,
Number of sides = 360° / 36°
= 10
Hence there are 10 sides for the polygon.
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Find the value of x° in rhombus ABCD.
Answers
29. In the 2010-2011 NBA regular season, the Los Angeles Lakers won 7 more than twice as many games as they lost. The Lakers played 82 games. How many wins and losses did the team have?
Answers
Answer:
Loss 25 Games & Win 57 Games
Step-by-step explanation:
According to question,we have
The Los Angeles Lakers won 7 more than twice as many games as they lost.
Assume Total Loss=L & Thus Total Win = 2L + 7Total Win + Total Loss = Total Games Played
2L + 7 + L = 82
3L = 82-7
3L = 75 ⇔ L = 25
Thus, Total Loss=25 Games & Thus Total Win = 57 Games
the cost price of an articles was 4000 find the marked price of the article so that there will be profit of 20%after allowing a discount of 20%
Answers
Answer:
The marked price of the article was $ 6000.
Step-by-step explanation:
Since the cost price of an article was $ 4000, to find the marked price of the article so that there will be profit of 20% after allowing a discount of 20%, the following calculation must be performed:
4000 x X x 0.8 = 4000 x 1.2
4000 x X x 0.8 = 4800
4000 x X = 4800 / 0.8
4000 x X = 6000
X = 6000/4000
X = 1.5
4000 x 1.5 = 6000
Therefore, the marked price of the article was $ 6000.