Given:
The table of values of an exponential function.
To find:
The function for the given table of values.
Solution:
The general exponential function is:
[tex]y=ab^x[/tex] ...(i)
Where, a is the initial value and b is growth factor.
From the given table it is clear that the function passes through the points (1,9) and (2,36). It means the function must be true for these two points.
[tex]9=ab^1[/tex] ...(ii)
[tex]36=ab^2[/tex] ...(iii)
On dividing (iii) by (ii), we get
[tex]\dfrac{36}{9}=\dfrac{ab^2}{ab}[/tex]
[tex]4=b[/tex]
Putting [tex]b=4[/tex] in (ii), we get
[tex]9=a(4)^1[/tex]
[tex]\dfrac{9}{4}=a[/tex]
Putting [tex]a=\dfrac{9}{4},b=4[/tex] in (i), we get
[tex]y=\dfrac{9}{4}(4)^x[/tex]
[tex]y=9(4)^{x-1}[/tex]
The function notation with variable n is:
[tex]f(n)=9(4)^{n-1}[/tex]
Therefore, the correct option is D.
You are given m =0.4n - 2/3
What is the value of m, when n is 15?
A.0 3.7
B.4.3
C.6.0
D.8.3
Answer:
m = 5.3
Step-by-step explanation:
Given equation,
→ m = 0.4n - (2/3)
Now we have to,
→ Find the required value of m.
We have to use,
→ n = 15
Then the value of m will be,
→ m = 0.4n - (2/3)
→ m = 0.4(15) - (2/3)
→ m = 6 - (2/3)
→ m = (18/3) - (2/3)
→ m = (18 - 2)/3
→ m = 16/3
→ [ m = 5.3 ]
Hence, the value of m is 5.3.
PLEASE HELP THIS ASSIGMENT IS Pythagorean theorem in 3D
I MARK THE BRIANLEST
1.2675 * 10^37 =
help pls its like 3am and for some reason my brain doesn't work :)
Answer:
the answer of the given equation is 1.2675E+37
Step-by-step explanation:
The computation is shown below:
Given that
= 1.2675 × 10^37
The above equation we need to solve
So,
= 1.2675 × 1E+37
= 1.2675E+37
So the answer after solving the equation is 1.2675E+37
The same would be considered and relevant
Hence, the answer of the given equation is 1.2675E+37
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Function g is a transformation of the parent sine function, f(x) = sin(x). g(x) = 1/3sin(2x - 5) +1 the phase shift of function g is ___.
The phase shift is C/B=5/2
We have given that the equation of the sine wave
[tex]f(x)=sinx\\G(x)=\frac{1}{3} sin(2x-5)+1[/tex]
What is the formula for the sine wave?The formula f(x)=A sin(Bx-C)+D
by comparing the g(x) above formula
Phase shift is C/B
C=5 and B=2
Therefore the phase shift is C/B=5/2
To learn more about the phase shift visit:
https://brainly.com/question/1538711
Answer:
5/2
Step-by-step explanation:
I will give you BRAINLIEST for the correct answer
Answer:
126
AS:
If these cubes are to to be placed so that their respective faces are parallel
or perpendicular, as the case may be, to the respective orientations of the
dimensions of the box, without tilting any cubes in any directions,
then choice B) can be justified. This leaves spaces (some volume) in the box
not filled by the cubes.
How many whole number of edges of the cubes fit into 4 cm?
4 / 3 √ 2 must be rounded down to 3.
How many whole number of edges of the cubes fit into 8 cm?
8 / 3 √ 2 must be rounded down to 6.
How many whole number of edges of the cubes fit into 10 cm?
10 / 3 √ 2 must be rounded down to 7.
Then (3)(6)(7) = 126
Which decimal is equivalent to 40 percent
Answer:
40 percentage is 0.4 in decimal . I hope it helps you
an expression that is equivalent to 60x+28y.
Answer:
Step-by-step explanation:
The trick here is to identify the greatest common factor of 60 and 28. 4 is such a factor. We can therefore rewrite 60x + 28y as
4(15x + 7)
There are other possible answers.
600x + 280y
------------------- is an example.
100
find the product (please list step by step)
( 4x^{7}y^{2} ) ( 3x^{3} y^{2} )
Answer:
The answer is 12x¹⁰y⁴.
Hope this helped!!
Step-by-step explanation:
1. ( 4x⁷y² ) ( 3x³y²)
2. 4x⁷y² ₓ 3x³y²
Please help.
Is algebra.
PLEASE HELP NO LINKS OR FILES
Answer:
i can't see clear
alegbra 2 pls help ill give brainliest
Answer:
it's 1/a3b2 it's C basically
Step-by-step explanation:
I don't know what's equivalent to it but ik the answer
I need to know what the answers are and show work. Please help me! And thank you!
Answer:
x=29
∠C=93°
Step-by-step explanation:
180°-52°-35°=3(x+2)°
180°-87°=(3x)°+6°
93°=(3x)°+6°
(3x)°=87°
x=[tex]\frac{87}{3}[/tex]
x=29
∠C=3(x+2)°
=3(29+2)°
=3(31)°
=93°
Find the missing side length, and enter your answer in the box below. If
necessary, round your answer to 2 decimal places.
9
12
The tree diagram shows the sample space of rolling a cube with faces numbered 1–6 and flipping a fair coin. What is the probability of rolling the number 5 and the coin landing heads up?
Answer:
It’s C 1/12
Step-by-step explanation:
PLEASE HELP. NO LINKS (ALL LINKS WILL BE REPORTED) NEED REAL EXPLANATION AND THE CORRECT ANSWER/ANSWER CHOICES
answer BD is 108
Step-by-step explanation:
60^2+x^2=85^2
3600+x^2=7225
×^2=7225-3600
×^2=3625
Sq root both sides
x= 60
60+48=108
BD=108
The American Water Works Association reports that the per capita water use in a single-family home is 76 gallons per day. Legacy Ranch is a relatively new housing development. The builders installed more efficient water fixtures, such as low-flush toilets, and subsequently conducted a survey of the residences. Twenty-seven owners responded, and the sample mean water use per day was 71 gallons with a standard deviation of 9.5 gallons per day. At the 0.01 level of significance, is that enough evidence to conclude that residents of Legacy Ranch use less water on average
Answer:
Yes, that is enough statistical evidence to suggest to conclude that residents of Legacy Ranch use less water on average
Step-by-step explanation:
The data given by the American Water Works Association are;
The per capita water use in a single-family home, μ = 76 gallons per day
The number of responders in the sample, n = 27
The sample mean water used by the sample, [tex]\overline x[/tex] = 71 gallons
The standard deviation, s = 9.5 gallons per day
The level of significance, α = 0.01
The test statistics is given as follows;
The null hypothesis, H₀; μ ≥ 76 gallons
The alternative hypothesis, Hₐ; μ < 76 gallons
[tex]t=\dfrac{\bar{x}-\mu }{\dfrac{s}{\sqrt{n}}}[/tex]
Therefore, we have;
[tex]t=\dfrac{71-76 }{\dfrac{9.5}{\sqrt{27}}} \approx -2.734817[/tex]
At n - 1 = 27 - 1 = 26 degrees of freedom, the critical-t = 2.5
From the test statistic, of t ≈ -2.734817, the p-value < 0.01, and from a graphing calculator, the p-value is given as Prob = 0.005544418
Therefore, given that the p-value is less the significant level, and less than 0.01, is therefore statistically significant, and therefore, there is sufficient statistical evidence against the null hypothesis, therefore we reject the null hypothesis, and there is enough statistical evidence to suggest to conclude that residents of Legacy Ranch use less water on average.
What is the horizontal asymptote of the function f (x) = StartFraction (x minus 2) Over (x minus 3) squared EndFraction?
y = 0
y = 1
y = 2
y = 3
Answer:
y = 3
Step-by-step explanation:
Here, we want to get the horizontal asymptote
To get this, we have to equate the denominator to 0 and solve for x
Mathematically, we have this as;
x-3 = 0
x = 3
so the horizontal asymptote will be y = 3
Answer:
Its A) y=0
Step-by-step explanation:
find the measure of the missing angle
Answer:
60°
.....................
Answer:
60
Step-by-step explanation:
This is a complementary angle which means two angles that sum up to 90 so 60+30=90
Use the net to find the surface area of the regular pyramid.
Answer:
40 in²
Step-by-step explanation:
There are four triangles for each side of the pyramid, and the height is three inches. The area of a triangle is base times height divided by 2, so each triangle is 6 in².
4(base) x 3(height) ÷ 2 = 6
Multiply 6 by 4 because there are four triangles, which is 24.
Once you have that, the only surface left is the bottom of the pyramid. You can find this by multiplying 4 by 4, since it's a square.
4 x 4 = 16
If you add 16 and 24 together, that's your answer.
Answer:
40
(its right i did this)
please help solve h(t) =-16t^2+40t+20
Answer: el último
Step-by-step explanation:
Seth owns a local ice cream parlor. He designed a new sign in the shape of an ice cream cone and cut it from plywood. He wants to attach LED lights around the PERIMETER of the sign. A diagram of the sign made from a TRIANGLE and a SEMICIRCLE is shown below. What is the length of LED lights he will need to span the PERIMETER of the sign?
Answer:2 feet i think?
Step-by-step explanation:
sorry need points
What is the answer please!
Answer:
rectangle
Step-by-step explanation:
Answer:
b!
Step-by-step explanation:
a. does not have a base or hight
c. is BxHxL
d. not sure
The equation of a circle is x2 + y2 - 12y + 20 = 0
What are the coordinates of the center and the length of the radius of the circle?
Answer:
Center: (0, 6); radius = 4
Step-by-step explanation:
x^2 + y^2 - 12y + 20 = 0
We must complete the square in y.
x^2 + y^2 - 12y = -20
x^2 + y^2 - 12y + 36 = -20 + 36
x^2 + (y - 6)^2 = 16
(x - 0)^2 + (y - 6)^2 = 4^2
Center: (0, 6); radius = 4
Which is the graph of the equation y - 1 =[tex]\frac{2}{3}(x-3)[/tex]
Answer:
Step-by-step explanation:
Ten deer were introduced into a protected preserve. Their expected population doubles each year. Which function represents the same relationship?
Answer:
y(t)= 10 (2)^t
Step-by-step explanation:
If t is the number of years given then the expected number can be found by
y(t)= 10 (2)^t
where t takes the value 0,1,2,3, and so on.
Putting t= 0
y(t)= 10 (2)^t
y(0)= 10 (2)^0
y(0)= 10 For the start the number of deer are 10.
Putting t= 1
y(t)= 10 (2)^t
y(1)= 10 (2)^1
y(1)= 20 After 1 year it has doubled to 20
Putting t= 2
y(t)= 10 (2)^t
y(2)= 10 (2)^2
y(2)= 40 After 2 years it has again doubled to 40
Putting t= 3
y(t)= 10 (2)^t
y(3)= 10 (2)^3
y(3)= 80 After 3 years it has again doubled to 80
PLEASE HELP I WILL GAVE BRAINIEST. How much people scored at least four goals?
porfa es pa hoy les doy 26 puntos
hola como esta no veo bien las preguntas
456*43-53(45)................help
Answer: 17223
Step-by-step explanation:
You have to multiply your
Step-by-step explanation:
456×43-53(45)=
19608-53(45)
19608-2385
17223 Answer
Please answer correctly! I will mark you as Brainliest
Answer:
33,333 ft^3
Step-by-step explanation:
A pyramids volume can be defined by V=lwh/3. We know the base is 1000 ft^2, so we multiply that by an additional 100 for the height. We then have 100,000 ft^3. After that, we simply divide it by three, which is 33,333.3 repeating, and round it to 33,333 ft^3
reduse this fractions 4/8 and 6/10
Answer:
1/2 and 3/5
Step-by-step explanation:
I dunno how to explain this, but I hope it helps!
Evaluate the numerical expression.
(5 + 3) x 2 - 6
please help!
Answer:
10
Step-by-step explanation:
Please use " * " or " · " to indicate multiplication; " x " is a variable, not an operator.
(5 + 3) x 2 - 6 => (5 + 3)·2 - 6
Order of operations rules require that we do first any work inside parentheses. So we have:
(5 + 3)·2 - 6 => (8)·2 - 6
Those same rules dictate that we must multiply before subtracting. So now we obtain:
16 - 6 = 10