Answers
Answer:
10.4
Step-by-step explanation:
So an exponential equation with a decay can be expressed as: [tex]f(x)=a(1-r)^t[/tex] where r is the decay rate. In this case is decreasing at 4% each year, this means that the r is equal to 0.04 (divide the percent by 100 to convert to decimal). So the equation is going to be: [tex]f(x)=a(0.96)^t[/tex]. The reason this works is because whenever you decrease by x%, the new value is (1-x)%, which is expressed in the formula. But the reason the exponent is there is because after 1 year it's going to be 0.96a, but after two years, it's going to be 0.96 the previous year which is 0.96a, so after two years it's going to be 0.96(0.96a), and then the next year it's 0.96 of the second year, which is then 0.96(0.96(0.96a))... and so on. So the amount of 0.96 increases as t increases. the a is going to be the initial amount, since then t=0, 0.96^0 will be equal to 1, which makes the expression a(1), which is just a. So this gives you the complete equation: [tex]p(x)=13000(0.96)^t[/tex]
Now to find when it's equal to 8,500 you need to start by setting it equal to 8,500 so I'll work through each step
Original Equation:
[tex]p(x)=13000(0.96)^t[/tex]
Set the equation equal to 8,500
[tex]8500=13000(0.96)^t[/tex]
Divide both sides by 13,000
[tex]0.653846\approx 0.96^t[/tex]
Rewrite in logarithmic form
[tex]log_{0.96}0.653846=t[/tex]
If you're calculator allows you to enter the base when calculating log, but this expression into your calculator to calculate the value of t, otherwise use the change of base formula
[tex]\text{change of base formula: }log_ba = \frac{log(a)}{log(b)}[/tex]
[tex]t=\frac{log0.653846}{log0.96}\\[/tex]
[tex]t\approx\frac{-0.1845}{-0.0177}[/tex]
[tex]t\approx10.4[/tex]
Related Questions
134 A financial analyst believes that if interest rates decrease in a given period then the
probability that the stock market will go up is 0.08. The analyst further believes that
interest rate have a 0.40 chance of decreasing during the period in question. Given the
above information, what is the probability that the market will go up and interes: rate
will go down during the period in question?
Answers
The probability that the market will go up and interest rate will go down during the period in question is 0.03.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the market will go up and interest rate will go down = 0.08 X 0.40 = 0.03
To learn more about probability, please check: https://brainly.com/question/13234031
#SPJ1
What is the simple interest that is missing from the table?
I
?
p
$375
r
2.2%
t
3 years
Answers
Answer:
SI =PXRXT/100
Step-by-step explanation:
THIS WOULD HELP YOU
which diagram shows a pair of angle measures that prove lines a and b are parallel?
Answers
Answer:
d
Step-by-step explanation:
it's kinda hard to explain
Simplify, using the distributive
property.
5f + 16f = (5 +?)f=?f
Answers
Applying the distributive property, we would simplify the expression as: 5f + 16f = (5 + 16)f = 21f.
How to Apply the Distributive Property?The distributive property states that, ab + ac = (b + c)a.
Using the distributive property, we have:
5f + 16f
= (5 + 16)f
= 21f
Therefore, 5f + 16f is simplified as 21f.
Learn more about the distributive property on:
https://brainly.com/question/2807928
#SPJ1
GIVE EXAMPLE OF ACTION PLAN THAT SHOWS A CONTEXTUALIZED LEARNING PROGRAM
Answers
An example of contextualization in teaching is when writing skills are taught with reference to topics.
How to illustrate the information?It should be noted that the contextualization of basic skills is the instructional approach that gives connections in teaching.
In this case, an example of contextualization in teaching is when writing skills are taught with reference to topics.
Learn more about learning on:
brainly.com/question/26711803
#SPJ1
Un constructor tiene un predio, por lo que está considerando que los terrenos sean rectangulares con un perímetro de 64 metros.
Answers
Based on the perimeter of the rectangle, and the adjustments to make the plot a square, the sides are 13m and 19m.
What are the sides of the plot?The perimeter is:
2(L + W) = 64
L + W = 32
The adjustment to make the plot a square would mean that both sides can be equal:
L + 3 = W - 3
L = W - 6
Substituting in the original formula gives:
L + W = 32
W - 6 + W = 32
2W = 38
W = 19 m
L would be:
L + W = 32
L + 19 = 32
L = 13m
The rest of the question is:
No obstante, para que los terrenos puedan ser cuadrados, se tendría que aumentar el ancho en 3 m y disminuir 3 m de largo. Entonces, ¿cuánto mediría el ancho y el largo del terreno rectangular?
Find out more on the perimeter of a square at https://brainly.com/question/25092270.
#SPJ1
given the function f(x) shown, sketch the graph of f(x-2)
Answers
Step-by-step explanation:
substitute different values of x inorder to get values of y. so since the value of y will have 2 units substracted from the original function leaving us with shifting. but the graph would be parabolic or slightly curved than my graph.
A store is currently offering a 60% discount on all items purchased. Your cashier is trying to convince you to open a store credit card and says to you, "In addition to the 60% discount you are receiving for purchasing these items on sale today, you will get an additional 20% off for opening a credit card account. That means you are getting 80% off!"
a. What is the mistaken assumption here?
b. Why is that assumption incorrect?
c. If you did truly have 80% discount, explain what should happen when you go to the counter to buy $500 worth of items?
d. If you got your 60% discount and opened the card for an additional 20%, what is the actual % discount you would receive?
e. Is it better to apply the 60% discount first or the 20% discount first?
Answers
Answer:
a the assumption is that after the 60% discount, the 20% will contribute to the old price, not the adjusted price
b this is incorrect because the 20% discount will be added on after the 60% discount has been used
c the 500 dollars would turn to 100 dollars
d 40
e it would be best to first apply the 60% coupon first over the 20% coupon
I’m super confused please help me
Answers
Answer:
See below
Step-by-step explanation:
Look at it from the front and the side as shown in the diagram and draw what you would see:
Find the equation of the line tangent to the graph of f(x)=(lnx)^(4)at x=10
Answers
Hello,
Step-by-step explanation:
[tex]f(x) = ln(x) {}^{4} [/tex]
[tex](ln(u)') = \frac{u'}{u} [/tex]
[tex]f'(x) = \frac{4ln {}^{} (x) {}^{3} }{x} [/tex]
[tex]f'(10) = \frac{4ln {}^{} (10) {}^{3} }{10} = \frac{12ln(x)}{x} [/tex]
[tex]f(10) = ln(10) {}^{4} [/tex]
[tex]y = \frac{12ln(x)}{x} (x - 10) + 4ln(10)[/tex]
[tex]y = f'(a)(x - a) + f(a)[/tex]
A real estate agent is showing homes to a prospective buyer. There are 10 homes in the desired price range listed in the area. The buyer wants to visit only 3 of them. a. In how many ways could the 3 homes be chosen if the order of visiting is considered? b. In how many ways could the 3 homes be chosen if the order of visiting is not important?
Answers
There are 720 ways that the 3 homes could be chosen if the order of visiting is considered. There are 120 ways that the 3 homes could be chosen if the order of visiting is not important.
What is permutation?A permutation is the arrangement or ordering of a finite set of an element.
From the information given:
If there are 10 homes in the desired price range listed in the area:
Then:
n = 10 and r = 3So, the number of ways of choosing 3 out of 10 (without replacement) and arranging is:
[tex]\mathbf{^nP_r= \dfrac{n!}{(n-r)!}}[/tex]
[tex]\mathbf{^nP_r= \dfrac{10!}{(10-3)!}}[/tex]
[tex]\mathbf{^nP_r= \dfrac{10\times 9\times 8 \times 7!}{(7)!}}[/tex]
= 720 ways
Now, the number of ways of choosing 3 out of 10 if the order of visiting is not important is the combination of the elements and it can be computed as:
[tex]\mathbf{^nC_r= \dfrac{n!}{(n-r)!r!}}[/tex]
[tex]\mathbf{^{10}C_3= \dfrac{10!}{(10-3)!3!}}[/tex]
[tex]\mathbf{\implies \dfrac{10\times 8\times 9 \times 7!}{(7)! \times 3\times 2}}[/tex]
[tex]\mathbf{\implies \dfrac{10\times 8\times 9}{6}}[/tex]
= 120 ways
Learn more about permutation and combination here:
https://brainly.com/question/11732255
#SPJ1
22POINTS PLEAS ANsewer
Answers
Answer:
2y>-y+5
Step-by-step explanation:
because it has a eligible number at the right hand side
an a horizontal number line, positive numbers are____
On a vertical number line, negative numbers are_____
The number 0 is
Answers
Answer:
Positive number are located above 0 and negative numbers are located below 0 on a vertical number line
Answer:
On a horizontal number line, positive numbers are down from ANS= 0 to the left of 0✔ to the right of 0X up from 0.On a vertical number line, negative numbers are ✔ ANS=down from 0 to the left of 0to the right of 0up from 0.The number 0 is a negative numbera positive number✔Ans= neither positive nor negative.
Step-by-step explanation:
yw
For what value of y does 125 =
(1/25)^y-1
Answers
Answer:
[tex] y = -\dfrac{1}{2} [/tex]
Step-by-step explanation:
I assume that y - 1 is an exponent, and the equation is
[tex] 125 = (\dfrac{1}{25})^{y - 1} [/tex]
[tex] 5^3 = (5^{-2})^{y - 1} [/tex]
[tex] 5^3 = 5^{-2y + 2} [/tex]
[tex] -2y + 2 = 3 [/tex]
[tex] -2y = 1 [/tex]
[tex] y = -\dfrac{1}{2} [/tex]
6.62607004081818181818181 X 10^-34
Answers
The solution to this is 6.62607e-34.
How to solve for exponentialsWe have the value is raised to the power of -34
We have to solve this using a calculator
This is similar to
[tex]6.62607004081818181818181*\frac{1}{10000000000000000000000000000000000}[/tex]
The number of zeros are 34
We would have 6.62607e-34 as the final solution.
Read more on exponent here:
https://brainly.com/question/109611
#SPJ1
en un proyecto de innovacion, se deben determinar montos para varios gastos, Se gasta un 25% en equipamiento, un quinto en salarios, un 35% en publicidad, qudando un remanente de $1.500.000 para gastos varios
Answers
The amount that's was attributed to the project from the start based on the percentage is $7,500,000.
How to calculate the percentage?From the information given, the remaining percentage will be:
= 100% - (25% + 20% + 35%)
= 100% - 80%
= 20%
Let the total amount be x.
Therefore, 20% of x = 1,500,000
0.2x = 1,500,000
x = 1500000/0.2
x = 7500000
Learn more about percentages on:
brainly.com/question/24304697
#SPJ1
Review the four points shown on the polar coordinate
system.
5ad6
B
C
76
27/3
4/3
2
3/2
N
4
50/3
A
6
D
11/6
Which point represents (-6.II) ?
Opoint A
Opoint B
Opoint C
Opoint D
Answers
The answer is Point B.
The model for the height of the balloon captured from the ground with a balloon launcher can be represented by the function… how long will it take for the balloon to hit the ground after it’s launched?
Answers
Answer:
2 seconds
Step-by-step explanation:
To find the time it takes for the balloon to reach the ground, you need to set the equation equal to 0. This is because the ground technically has a height of 0.
h(t) = -16² + 128t <----- Original expression
0 = -16² + 128t <----- Plug 0 in for h(t)
16² = 128t <----- Add 16² to both sides
256 = 128t <----- Solve 16²
2 = t <----- Divide both sides by 128
Therefore, if t = 2, it will take the balloon 2 seconds to reach the ground.
==========================================================
Explanation:
The balloon is on the ground when the height is zero.
Replace h with 0 and solve for t.
[tex]h(t) = -16t^2 + 128t\\\\0 = -16t^2 + 128t\\\\-16t^2 + 128t = 0\\\\-16t(t - 8) = 0\\\\-16t = 0 \ \text{ or } \ t-8 = 0\\\\t = 0/(-16) \ \text{ or } \ t = 0+8\\\\t = 0 \ \text{ or } \ t = 8\\\\[/tex]
Ignore t = 0 because this is when the balloon is initially on the ground. In other words, the balloon starts on the ground, so it makes sense that t = 0 leads to h = 0.
The other solution t = 8 is what we're after. The balloon touches the ground again at the 8 second mark. This is the length of time the balloon is in the air.
A quick way to determine and confirm the answer is to use graphing software. Check out the diagram below. We have a parabola with x intercepts of 0 and 8.
!!!!!!!A dress pattern uses the scale 2 inches : 1 foot.if the model is 12 inches long how long is the dress!!!!!!pls Hurry
Answers
Using the scale ratio, the length of the dress is: 6 ft.
How to Apply Scale to Measurement?Given a scale for the dress pattern as, 2 inches : 1 foot, it means 2 inches of the model equals 1 foot of the actual dress.
Therefore, using the scale ratio, let x represent the length of the dress. We would have:
2/1 = 12/x
x = (12 × 1)/2
x = 6 ft.
The length of the dress is: 6 ft.
Learn more about scale on:
https://brainly.com/question/2429309
#SPJ1
What is the end behavior of the function f of x equals negative 2 times the cube root of x? as x → –[infinity], f(x) → 0, and as x → [infinity], f(x) → 0. as x → 0, f(x) → –[infinity], and as x → [infinity], f(x) → 0. as x → [infinity], f(x) → [infinity], and as x → –[infinity], f(x) → –[infinity]. as x → –[infinity], f(x) → [infinity], and as x → [infinity], f(x) → –[infinity].
Answers
The end behavior of the function is as:
as [tex]x[/tex]→∞, f(x)→+∞ and as x→-∞, f(x)→+∞
What is end behavior?The end behavior of a function will describe the behavior of the graph of the function at the "ends" of the x-axis.
How do determine the end behavior of a function?By determining the highest degree of the polynomial function. As the highest degree term will grow faster than the other terms as x gets very large or very small, its behavior will dominate the graph.
The graph of the function is f(x)=2∛x
the function leads to infinity so the end behavior of the function is
as [tex]x[/tex]→∞, f(x)→+∞ and as x→-∞, f(x)→+∞
Learn more about the end behavior function here:
https://brainly.com/question/13393745
#SPJ4
The value of x. if (3x +3) : (9x + 7) is duplicate ratio of 3:5 is
Answers
Answer:
(3x + 3) (9x + 7) is the duplicate ratio of 3:5 . the value of x is 2.
Pls answer for brainlest and 50 points PLEASE EXPLAIN
In image
Answers
First, let's complete the angles in the triangle. Remember that the sum of the angles in a triangle is 180 degrees.
73 + 90 + x = 180
163 + x = 180
x = 17
So, the angle that completes the triangle is 17 degrees. If we look at that angle in the triangle and the one adjacent to it, we can see that those two angles form a linear pair (or are supplementary, both meaning that they add up to 180 degrees).
17 + x = 180
x = 163
So, 17's supplement is 163 degrees. The 163 degree angle corresponds with angle r, and corresponding angles are congruent.
Therefore, angle r is 163 degrees. The correct answer is option C.
Hope this helps!
Step-by-Step Solution:
In the Right Triangle formed to the extreme right, lets mark the angles as
∠1, ∠2 and ∠3.
Therefore, from the Figure :-
∠1 = 73°
∠2 = 90°
By Angle Sum Property :-
∠3 = 180 - (73 + 90)
∠3 = 180 - 163
=> ∠3 = 17°
The Angle which forms a Linear Pair with ∠3 is the Corresponding Angle of ∠r, and Corresponding Angles are Equal.
Therefore,
=> 180 - ∠3
= 180 - 17
=> 163°
Therefore, the Angle that forms the Linear Pair with ∠3 is 163°
This Angle is Corresponding to ∠r and hence they are Equal ie. ∠r = 163°
Hence, ∠r = 163°
What is the volume of the pyramid shown
in the diagram?
12 cm³
15 cm³
21 cm³
45 cm³
Please help urgent
Answers
Answer:
volume = 15 cm^3
Step-by-step explanation:
Volume of pyramid = 1/3 base area * height
= 1/3 ( 3 x 3 ) * 5 = 15 cm^3
if 3²× = 27 what is x
Answers
Answer:
3
Step-by-step explanation:
whenever solving for x, you have to work backwards…like so:
3 squared is 9
27 divided by nine is 3
x=3
To double check the answer, substitute the value that we just found into x
(3x3)x3=27
Answer:
[tex]x=\dfrac{3}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]3^{2x}=27[/tex]
Rewrite 27 in exponential form with base 3:
[tex]\implies 3^{2x}=3^3[/tex]
As both exponents have the same base,
[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]
[tex]\implies 2x=3[/tex]
Divide both sides by 2:
[tex]\implies x=\dfrac{3}{2}[/tex]
You enter an elevator on the ground floor, which is labeled 0. You get off on the floor labeled +4. What is your location?
A four floors above the ground floor
B. four floors below the ground floor
C. four floors near the ground floor
D. four floors around the ground floor
Answers
Answer:
A. four floors above the ground floor
Step-by-step explanation:
if you start at 0 which is the ground floor and go up 4, that would be +4, since, in theory, going up would be considered positive. So the answer is A.
need help with this question.
Answers
We have this equation:
[tex]\log(x) + \log(x + 99) = 2[/tex]
First, combine both logarithms using the multiplication property and simplify the expression.
[tex]\log[x(x + 99)] = 2[/tex]
[tex]\log[ {x}^{2} + 99x ] = 2[/tex]
Now, use the definition of logarithm to transform the equation.
[tex] {10}^{2} = {x}^{2} + 99x[/tex]
[tex] {x}^{2} + 99x - 100 = 0[/tex]
Finally, use the quadratic formula to solve the equation.
[tex]x = \frac{ -99 ± \sqrt{ {99}^{2} - 4 \times 1 \times ( - 100)} }{2 \times 1} [/tex]
With this, we can say that the solution set is:
x = 1x = -100We cannot choose x = -100 as a solution because we cannot have a negative logarithm. The only solution is x = 1.
if f(x)=4x-x^2 find f(x+h)-f(x+h)/2h
Answers
Answer:
0
Step-by-step explanation:
numerator are the same the difference between same number or variable will be zero
What is the solution to the system of equations?
O (5, 0)
O (0,5)
O (0-5)
O (-5, 0)
Answers
Answer: (0, -5) which is choice C
Explanation:
The solution is where the lines cross or intersect. This point is on both lines at the same time to make both equations true.
brainliest!!!!!!
Question 4(Multiple Choice Worth 1 points)
(06.05 MC)
Given the functions k(x) = 2x² - 5 and p(x) = x - 3, find (k. p)(x).
(kop)(x) = 2x² - 6x + 4
(kop)(x) = 2x² - 12x + 13
(kop)(x) = 2x² - 12x + 18
(kop)(x) = 2x² - 8
Answers
Answer:
2x² - 12x + 13
Step-by-step explanation:
Given following:
k(x) = 2x² - 5p(x) = x - 3Start solving from right to left across the function.
Steps:
k[p(x)]k[x - 3]2(x - 3)² - 52(x² - 6x + 9) - 52x² - 12x + 18 - 52x² - 12x + 13Answer:
2x² - 12x + 13
Step-by-step explanation:
Steps:
k[p(x)]
k[x - 3]
2(x - 3)² - 5
2(x² - 6x + 9) - 5
2x² - 12x + 18 - 5
2x² - 12x + 13 pls brainlest
what is the lcd of 1/4 and 1/6
Answers
Answer:
12
Step-by-step explanation:
LCD of 1/4 and 1/6 is the least common denominator that is divisible by 4 and 6 at the same time and is the least.
So it the same to find least common multiple of 4 and 6 that is 12.
The answer is 12.