Following the equation
[tex]V(t) = V_0(1-r)^t[/tex]
We start with an initial price of
[tex]V(0)=V_0[/tex]
and we're looking for a number of years t such that
[tex]V(t)=\dfrac{V_0}{2}[/tex]
If we substitute V(t) with its equation, recalling that
[tex]r = 0.075 \implies 1-r = 0.925[/tex]
we have
[tex]V_0\cdot (0.925)^t=\dfrac{V_0}{2} \iff 0.925^t = \dfrac{1}{2} \iff t = \log_{0.925}\left(\dfrac{1}{2}\right)\approx 8.89[/tex]
So, you have to wait about 9 years.
Final answer:
The expression to determine the number of years it takes for the car to reach a value that is 50% of its purchase price is t = ln(0.5) / ln(1 - 0.075), using the given formula V = Vo(1 - r)^t.
Explanation:
To determine the number of years t after purchase for the car to reach a value that is 50% of its purchase price, we can use the model V = Vo(1 - r)^t where V is the car's value after t years, Vo is the original purchase price, r is the constant annual rate of decrease, and t is the number of years.
V is set to be 50% of Vo, which can be written as V = 0.5Vo, and we know the constant annual rate of decrease r is 0.075. Plugging these values into the formula gives us:
0.5Vo = Vo(1 - 0.075)^t
Dividing both sides by Vo and taking the natural logarithm of both sides, we obtain:
ln(0.5) = ln((1 - 0.075)^t)
Using the properties of logarithms, we can rewrite this as:
ln(0.5) = t * ln(1 - 0.075)
Solving for t yields:
t = ln(0.5) / ln(1 - 0.075)
This expression can be used to find the number of years it takes for the car to be worth half of its purchase price.
Can somebody help me?
Answer:
6
Step-by-step explanation:
Arc length = radius * central angle
s = rθ
A circle is 2π radians, so 1/3 of that is 2/3 π.
Given that s = 12 and θ = 2/3 π:
12 = r (2/3 π)
r = 18/π
r ≈ 6
Best Deal 1
Quantity of Flour Price
3 pounds $5.25
5 pounds $9.75
7 pounds $12.60
10 pounds $14.20
12 pounds $18.24
A baker purchases flour each week from a wholesale warehouse. The chart shows the quantities and prices available this week. If the caterer decides to buy the BEST deal, how much will he save per pound of flour over the most expensive deal?
A) $0.28
B) $0.37
C) $0.47
D) $0.53
d. $0.53 because..
3/5.25 = 1/1.75
5/9.75 = 1.95
7/12.60 = 1.80
10/14.20 = 1.42
12/18.24 = 1.52
then do ;
most expensive deal - least expensive deal = how much he’ll save
1.95 - 1.42 = .53
Answer: The answer would be D.
like she said down there !
!
Step-by-step explanation:
The population of a city has increased by 36% since it was last measured. If the current population is 51000 , what was the previous population?
So if we have the number after the 36% increase in population, we would want to subtract that 36% from 51000.
36% of 51000 can be found by multiplying 51000 by 0.36 (0.36 is the decimal equivalent of 36%)
51000 x .36 = 18360
So you simply subtract 18360 from 51000, which is 32,640.
Enter the equation of the circle described below.
Center (-3, 0), radius 5
Answer:
[tex](x+3)^2 + y^2 =25[/tex]
Step-by-step explanation:
The general equation of a circle has the form:
[tex](x-h)^2 + (y-k)^2 =r^2[/tex]
Where the point (h, k) is the center of the circle and r is the radius
In this case the center is (-3, 0) and the radius is [tex]r=5[/tex]
So [tex]h=-3\\k=0[/tex]
Finally the equation of the circle is:
[tex](x-(-3))^2 + (y-0)^2 =5^2[/tex]
[tex](x+3)^2 + y^2 =25[/tex]
(X+3)^2 +y^2 =25
This is the correct answer
Check on Desmos
Mags is 2 years older than Vector.Which equation will help you find Mags' age (m) if you know Vector's age (v)?
Answer:
Step-by-step explanation:
m = megs age
v = vectors age
meg is 2 years older than vector + 2
therefore
m = v +2
WILL GIVE BRANLIEST! :(
I am so bad at proofs!
It is all on the picture <3
Step-by-step explanation:
The triangles are congruent isosceles, therefore LM ≅ MN ≅ NO ≅ OL.
All four sides are equal, so be definition, quadrilateral LMNO is a rhombus.
Answer:
LMNO is a rhombus
Step-by-step explanation:
btw i love ur pfp! BLM
Find the area of right triangle RST
Check the picture below.
Answer:
B. 7.5 square units.
Step-by-step explanation:
We have been given an image of a right triangle. We are asked to find area of our given triangle.
We can see that base of our given triangle is 5 units as difference between point S and point T is 5 units.
[tex]2--3=2+3=5[/tex]
The height of our given triangle (RT) is 3 units.
[tex]1--2=1+2=3[/tex]
[tex]\text{Area of triangle}=\frac{1}{2}\times \text{Base}\times \text{Height}[/tex]
[tex]\text{Area of triangle}=\frac{1}{2}\times \text{5 units}\times \text{3 units}[/tex]
[tex]\text{Area of triangle}=\frac{1}{2}\times 15\text{ units}^2[/tex]
[tex]\text{Area of triangle}=7.5\text{ units}^2[/tex]
Therefore, area of our given triangle is 7.5 square units and option B is the correct choice.
[tex]log_{13} 244=\frac{ln244}{ln13}[/tex] ≈ [tex]2.143[/tex]
A. 2.143
B. 0.453
C. 3.949
D. 2.209
Answer:
A.
Step-by-step explanation:
The question is on laws of logarithms
For example to find the log₁₀ 100
⇒log₁₀ 100 = 2................how?
we take In 100 / 1n l0 = 2
where 10²=100
⇒Thus logₓ y = In y / In x
On a sunny morning, Ishaan rode his bicycle to a farm that sold baskets of apples for $ 9 . 1 2 $9.12dollar sign, 9, point, 12 each and baskets of eggplants for $ 9 . 5 4 $9.54dollar sign, 9, point, 54 each. Ishaan decided to buy a basket of apples and a basket of eggplants . How much did Ishaan need to pay for his produce? $
Answer:18.66
Step-by-step explanation:
Eight white balls and twenty black balls are in a bag. What is the probability of the drawing a black ball in one draw?
Answer:
20/28 which is about 71%
Step-by-step explanation:
so first you add up how many balls there are. 8+20=28. So 28 is the denominator for the fraction. there are 20 black balls, so that is the numerator. so 20/28 is the fraction. then you divide 20 by 28 to get the rounded percent.
Natasha is driving at a rate of 4 miles every 3 minutes how fast is Natasha driving
Answer:
80 mph
Step-by-step explanation:
Since Natasha is driving at a rate of 4 miles every 3 minutes, we are asked to find her speed in mph. Since there are 60 minutes in an hour, we can make a proportion: 4/3 = x/60. Solving for x, we get x to be 80. So Natasha is driving at 80 miles an hour.
Answer:
80 miles per hour
Step-by-step explanation:
60 / 3 = 20
4 x 20 = 80
Which of the following functions has the largest value when x = 3?
c(x) = 3x2 + 5x + 22
j(x) = 12x
a(x) = 9x
All the functions are equal at x = 3.
c(x)
j(x)
a(x)
Answer:
c(3) is the largest
Step-by-step explanation:
For positive values of x, j(x) > a(x), so the comparison is between c(x) and j(x).
Without evaluating the functions, you can subtract 5x from them to get ...
c'(x) = c(x) -5x = 3x² +22
j'(x) = j(x) -5x = 7x
Now the question is whether c'(3) is larger than j'(3). The latter is ...
j'(3) = 7·3 = 21
Since c'(3) has an added constant of 22 and x² will be positive, we know that ...
c(3) > j(3) > a(3)
The function with the largest value at x=3 is c(x).
_____
You can, of course, simply evaluate the functions:
c(3) = (3·3 +5)·3 +22 = 14·3 +22 = 42 +22 = 64j(3) = 12·3 = 36a(3) = 9·3 = 27c(3) > j(3) > a(3) . . . . . . . c(3) is the largest
Answer:
It’s D
Step-by-step explanation:
a(x)
What is the magnitude of the vector (7, -4) to the nearest tenth?
2.4
5.7
8.1
9.0
Answer:
Step-by-step explanation:
Apply the Pythagorean Theorem: hyp² = 7² + (-4)² = 49 + 16 = 65.
The magnitude of this vector <7, -4> is 8.1, to the nearest tenth.
name the property illustrated by (3c x 6)2=3c(6 x 2)
BRAINLIEST REWARD!!!
Answer:
Associative property of multiplication
Explanation:
The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis.
Consider the hyperbola represented by the equation: (picture)
The center of the hyperbola is _______
The left vertex, if the hyperbola opens horizontally, or the bottom vertex, if it opens vertically, is ______
The other vertex is ______
Answer:
- The center of hyperbola is (-2 , 3)
- The left vertex, if the hyperbola opens horizontally, or the
bottom vertex, if it opens vertically, is (-6 , 3)
- The other vertex is (2 , 3)
Step-by-step explanation:
* Lets study the equation of the hyperbola
- The standard form of the equation of a hyperbola with
center (h , k) and transverse axis parallel to the x-axis is
(x - h)²/a² - (y - k)²/b² = 1, Where
- The length of the transverse axis is 2a
- The coordinates of the vertices are (h ± a , k)
- The length of the conjugate axis is 2b
- The coordinates of the co-vertices are (h , k ± b)
- The coordinates of the foci are (h ± c , k), where c² = a² + b²
* Now lets solve the problem
∵ (x + 2)²/4² - (y - 3)²/5² = 1
∵ (x - h)²/a² - (y - k)²/b² = 1
∴ a = 4 , b = 5
∴ h = -2 , k = 3
∵ The center of the hyperbola is (h , k)
∴ The center of hyperbola is (-2 , 3)
∵ The coordinates of the vertices are (h + a , k) , (h - a , k)
∴ The coordinates of the vertices are (-2 + 4 , 3) , (-2 - 4 , 3)
∴ The coordinates of the vertices are (2 , 3) , (-6 , 3)
∴ The left vertex, if the hyperbola opens horizontally, or the
bottom vertex, if it opens vertically, is (-6 , 3)
∴ The other vertex is (2 , 3)
The center of a hyperbola is determined by the coordinates (h, k) in its equation. The vertices are the points where the hyperbola intersects its major axis, and their positions depend on whether the hyperbola opens horizontally or vertically. If it opens horizontally, the left vertex is at (h - A, k), and if it opens vertically, the bottom vertex is at (h, k - B).
Explanation:In the equation of a hyperbola, the center of the hyperbola can be found by identifying the coordinates (h, k). These are the constants in the denominators of the fractions on the left-hand side of the equation. For instance, in the equation ((x-h)²/A²) - ((y-k)²/B²) = 1, the center would be at the point (h, k).
The vertices of the hyperbola are the points where the hyperbola intersects its major axis. If the hyperbola opens horizontally, the left vertex will be located at the coordinate (h - A, k), and the other vertex will be at (h + A, k). If the hyperbola opens vertically, the bottom vertex will be at the coordinate (h, k - B), with the other vertex at (h, k + B).
Remember, A represents the distance from the center to a vertex along the major axis, and B represents the distance from the center to a vertex along the minor axis.
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3 less than 3 times a number is 12, what is it?
The number is 3.
3x3 is 9, which is 3 less than 12.
Answer:
The number is 5.
Step-by-step explanation:
12 plus 3 is 15.
5 x 3 = 15
15 - 3 = 12
3 less than 3 times a number is 12.
It sounds like 3 less from a number IS 12. So adding 3 to 12 will get 15, and 15 divided by 3 equals 5.
I hope this is correct and that it helps! :)
Which expression gives the volume of a sphere with radius 5?
Answer:
it is d
Step-by-step explanation:
formula of sphere=4/3* pi*r cubed
Answer:
D
Step-by-step explanation:
A is nothing.
B is the surface area
C is nothing
D is the volume of a sphere.
Devaughn is 11 years younger than Sydney. The sum of their ages is 83. What is Sydney's age?
To solve for Sydney's age, we used an equation based on the relationship that Devaughn is 11 years younger than Sydney and the sum of their ages is 83. Solving the equation 2S - 11 = 83, we found that Sydney is 47 years old.
To find Sydney's age, we need to set up and solve an equation based on the information given: Devaughn is 11 years younger than Sydney, and the sum of their ages is 83.
Let's let Sydney's age be represented by S and Devaughn's age be represented by D. Given that Devaughn is 11 years younger than Sydney, we can express Devaughn's age as D = S - 11.
The sum of their ages is given as 83, so we can write the following equation: S + D = 83.
Substituting Devaughn's age in terms of Sydney's age, we get: S + (S - 11) = 83. This simplifies to 2S - 11 = 83. Solving for S, we add 11 to both sides, resulting in 2S = 94, and then we divide by 2 to find S = 47.
Therefore, Sydney's age is 47 years old.
Jean throws a ball with an initial velocity of 64 feet per second from a height of 3 feet. Write an equation and answer the questions below. Show all your work for full credit. Use the correct units with your answers
Answer:
Step-by-step explanation:
From what I understand about parabolic motion in the English system, the equation for flight is
[tex]s(t)=-16t^2+v_{0}t+h_{0}[/tex]
where [tex]v_{0}t[/tex] is the initial upwards velocity and
[tex]h_{0}[/tex] is the initial height from which the object was launched. Filling in that equation with those values gives you
[tex]s(t)=-16t^2+64t+3[/tex]. That's a.
In order to determine how long it will take the ball (or rocket...the problem is mixing up the 2) to reach its max height you need to put the equation into vertex form, since the vertex of a parabola is the absolute max (or min depending upon the parabola) of the function. The absolute max is the heighest that the ball will go. Completing the square is the way to solve this. Begin by setting the equation equal to 0, the moving the 3 over by subtraction:
[tex]-16t^2+64t=-3[/tex]
Now factor out the -16 since the leading coefficient HAS to be a positive 1:
[tex]-16(t^2-4t)=-3[/tex]
Now take half the linear term (half of 4t which is 2), square it (4) and add it into the parenthesis:
[tex]-16(t^2-4t+4)=-3[/tex]
BUT since you added in a 4*-16 on the left you have to add it in on the right:
[tex]-16t^2(t^2-4t+4)=-3-64[/tex]
which simplifies to
[tex]-16(t-2)^2=-67[/tex]
Now bring the 67 over by addition and you have your vertex:
[tex]s(t)=-16(t-2)^2+67[/tex].
The vertex is (2, 67). The 2 stands for time, so 2 seconds, and the 67 stands for feet, so at 2 seconds the max height is 67 feet.
How long it will be in the air is found by factoring to find the zeros. These can be found by plugging the quadratic into the quadratic formula and getting that the zeros are -0.046 and 4.046
So the quadratic starts a tiny tiny bit to the left of the origin, but for all intents and purposes we can say it starts at the origin (x = 0) and ends at
x = 4.05 seconds. Which makes sense if you know anything about parabolic motion and physics. The vertex indicates not only the time and the max height at that time, it also is indicative of the halfway mark. Meaning that if it takes 2 seconds to reach its max height, it will hit the ground at 4 seconds. And 4.05 is close enought to 4 (but since you were told to round to the nearest hundredth, that .05 matters). Sorry it's so long, but it's not a question that can be answered with just a few sentences.
PLEASE HELP ASAP 50 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Answer:
C
Step-by-step explanation:
Using the coefficients of each term and evaluating for h = - 4
- 4 | 1 - 7 - 7 20
↓ - 4 44 - 148
---------------------------
1 - 11 37 - 128 ← remainder
Quotient = x² - 11x + 37 , R - 128
Measure the sides and angles of the two triangles. Are the two triangles similar? Yes, corresponding angles are congruent. Yes, all sides have been increased by 1 unit. Yes, corresponding sides are proportional. No, corresponding angles are not congruent and corresponding sides are not proportional.
Answer:
D) No, corresponding angles are not congruent and corresponding sides are not proportional.
;]
Step-by-step explanation:
Answer:
the answer is D i just answered it with D and its correct
good luck on your assignment :)
Step-by-step explanation:
HELP ASAP!!!!! PLEASE
Find the area of the square, which has a side length of 2.
Area of square = 2 x 2 = 4
Now multiply the area by the length b
Volume = 4 x 5 = 20 square units total.
Whats this answer ? Help
Answer:
True
Step-by-step explanation:
A negative exponent turns into positive when it is put into fraction form.
5^-2 = 1/5^2
5^-2 = 1/25
Answer:
Step-by-step explanation:
It's true. A minus power means that you put the denominator in the numerator and the numerator in the denominator. For example
(5/3)^(-2) = (3/5)^2 = 9/25
Ava and Kelly ran a road race, starting from the same place at the same time. Ava ran at an average speed of 6 miles per hour. Kelly ran at an average speed of 8 miles per hour. b If Kelly finished the race in 1 1/2 hours, how long did it take Ava to finish the race?
Answer:
2
Step-by-step explanation:
Kelly ran at an average speed of 8 miles per hour. If she finished the race in one and a half hours that means she ran 12 miles.
8=x
?=3/2x
12=x
We now know the road is 12 miles long. Ava has an average speed of 6 miles so she will finish it in 12/6 hours.
12/6=2
It takes Ava to finish the race in 2 hours.
Kelly ran at an average speed of 8 miles per hour.
If she finished the race in one and a half hours that means she ran 12 miles.
What is the formula for the average speed?
The average speed is the distance traveled divided by the time taken.
8=x
12=x
We now know the road is 12 miles long.
Ava has an average speed of 6 miles so she will finish it in 12/6 hours.
12/6=2hours
Therefore, It takes Ava to finish the race in 2 hours.
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Which statement describes a strong U.S. dollar?
Answer:
I can tell you that B is NOT correct as I got it wrong. I bet the right answer is C as it is holding steady at 1:95.
Step-by-step explanation:
These are the choices for Plato
A. The exchange rate between the U.S. dollar and the yen changes from 1:95 to 1:102.
B. The exchange rate between the U.S. dollar and the euro changes from 1:95 to 1:92. - Wrong answer
C. The exchange rate between the U.S. dollar and the euro remains 1:95
Which statement is true about the ray passing
through points B and C?
The ray extends infinitely in one
direction
The ray extends infinitely in both
directions
The ray has a finte length that can
be measured
There are only two points on the
entire ray
Cosidering the ray BC.
It is clear that:
1) A ray starts from one point and extends infinitely in ONE direction.
2) The ray BC cannot be measured. But the line-segment BC can be Measured.
3) B and C are the only two points on the given ray.
Hence the statement: "There are only two points on the entire ray" is the correct one.
Hope it helps...
Regards;
Leukonov/Olegion.
The ray given in the figure is passing in one direction and does not have a finite length as far as the ray segment is considered so options (A), and (D) are true.
What is a line segment?A line section that can connect two places is referred to as a segment.
In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
Given,
A ray is passing through points B and C.
(A) The ray extends infinitely in one direction which is True.
(D) There are only two points on the entire ray which is also true.
Hence, The ray given in the figure is passing in one direction and does not have a finite length as far as the ray segment is considered.
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Write the equation of the line, in slope-intercept form, that contains the points (-1, -2) and (1, 2). Use the box provided or the upload option to submit all of your calculations and final answer.
Quadrilateral KLMN has vertices of K(-4,-1), L(-1,-1) M(-2,-5) and N(-4,-4) Find the length of MN
Answer:
The length of MN is [tex]\sqrt{5}[/tex] units.
Step-by-step explanation:
The given Quadrilateral KLMN has vertices at K(-4,-1), L(-1,-1) M(-2,-5) and N(-4,-4).
We use the distance formula to find the length of MN.
[tex]|MN|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We plug in the values to get
[tex]|MN|=\sqrt{(-4--2)^2+(-4--5)^2}[/tex]
[tex]|MN|=\sqrt{(-2)^2+(1)^2}[/tex]
[tex]|MN|=\sqrt{4+1}[/tex]
[tex]|MN|=\sqrt{5}[/tex]
The length of MN is [tex]\sqrt{5}[/tex] units.
Answer:
B
Step-by-step explanation:
PLEASE HELP!
Find the function inverse ,f-1(x) , of y = 2x + 1.
Answer:
[tex]f^{-1}(x)=\frac{x}{2}-\frac{1}{2}[/tex]
Step-by-step explanation:
It is called an inverse or reciprocal function of [tex]f[/tex] to another function [tex]f^{-1}[/tex] that fulfills that:
If [tex]f(a)=b[/tex], then [tex]f^{-1} (b)=a[/tex]
To calculate the inverse of the function [tex]y=2x+1[/tex]
[tex]f(x)=y[/tex]
So, rewritting the function
[tex]f(x)=2x+1[/tex]
Changing the x for y
[tex]x=2y+1[/tex]
Let's clear y
[tex]y=\frac{x-1}{2}[/tex]
Ordering the function above
[tex]y=\frac{x}{2}-\frac{1}{2}[/tex]
So, the inverse of the function [tex]f(x)=2x+1[/tex] is:
[tex]f^{-1}(x)=\frac{x}{2}-\frac{1}{2}[/tex]
.
-0.18x + y = -6.54
-2.8x - y = -2.4
Answer:
The solution is (-3, 10.8)
Step-by-step explanation:
While it's rather obvious that you want to solve this system of linear equations, you should share that instruction when you post the problem.
To solve this system using elimination by addition and subtraction, combine the two equations as shown below (to eliminate y):
-0.18x + y = -6.54
-2.8x - y = -2.4
--------------------------
-2.98x = -8.94
Dividing both sides by -2.98, to isolate x, yields: x = -8.94 / (-2.98) = -3.
Then x = 3. Find y from -2.8x - y = -2.4: -2.8x + 2.4 = y, and here,
y = -2.8(-3) + 2.4 = 8.4 + 2.4 = 10.8
Then the solution is (-3, 10.8)