Jill invest $400 in a savings bond. The value of the bond V(x) in hundreds of dollars after x years is illustrated in the table below. Which equation and statement illustrate the approximate value of the bond in hundreds of dollars over time in years?
Answers
Answer:
V(x) = 4(1.35)x, and it grows.
Step-by-step explanation:
The statement that illustrates the approximate value of the bond in hundreds of dollars over time in years is:
"The value of the bond can be approximated by the quadratic equation V(x) = 0.725x² + 0.675x + 4.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
We can use the given data points to approximate the relationship between the value of the bond and time by fitting a curve that best fits the points.
Based on the given data,
It seems that the value of the bond is increasing at an accelerating rate over time.
We can try to approximate this relationship by fitting a quadratic equation to the data.
Let's assume that the relationship between the value of the bond and time can be approximated by the quadratic equation:
V(x) = ax² + bx + c
where V(x) is the value of the bond in hundreds of dollars after x years, and a, b, and c are constants to be determined.
To solve for a, b, and c, we can use the three data points for which we have values of V(x):
V(0) = 4, V(1) = 5.4, V(2) = 7.29
Substituting these values into the equation.
a(0)² + b(0) + c = 4
a(1)² + b(1) + c = 5.4
a(2)² + b(2) + c = 7.29
Simplifying.
c = 4
a + b + c = 5.4
4a + 2b + c = 7.29
Substituting c = 4.
a + b = 1.4
4a + 2b = 3.29
Solving for a and b.
a = 0.725
b = 0.675
Now,
The equation that approximates the relationship between the value of the bond and time is:
V(x) = 0.725x² + 0.675x + 4
This equation tells us that the value of the bond is increasing at an accelerating rate over time, starting at $400 (or 4 hundred dollars) and increasing by approximately 0.725 hundred dollars for each year squared, plus 0.675 hundred dollars for each year, plus a constant 4 hundred dollars. For example, after 5 years, the value of the bond would be approximately:
V(5) = 0.725(5)² + 0.675(5) + 4 = 23.75
Therefore,
The statement that illustrates the approximate value of the bond in hundreds of dollars over time in years is:
"The value of the bond can be approximated by the quadratic equation V(x) = 0.725x² + 0.675x + 4.
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Related Questions
Which method of calculating finance charge results in the lowest finance charge? a. average daily balance b. previous balance c. ending balance d. adjusted balance Please select the best answer from the choices provided A B C D
Answers
Answer: D
Step-by-step explanation:
adjusted balance
Answer:
above is correct
Step-by-step explanation:
d
Clara has 3 bottles of paint. She buys 5 more bottles of paint. If she uses 1/4 bottle of paint to paint a picture, how many similar paintings can she paint with all the paint?
ANSWER:
She has 3+5=8 bottles of paint. 1/4 bottle paints a picture.
8 divided by 1/4 = 32 paintings possible with all the paint
Answers
Answer:
32 Paintings
Step-by-step explanation:
8 Bottles 4 per one bottle so 8x4 =32
Hoped this helped.
What is the expected value when rolling a fair 12-sided die?
Answers
Answer:
I think 1/12
Step-by-step explanation:
since the question didn't specifically the possibility of a certain number shown.
note this applies to probability related questions
The manager of a fast-food restaurant determines that the average time that her customers wait for service is 3.5 minutes.The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she doesn't want to give away free hamburgers to more than 1% of her customers. What number of minutes should the advertisement use
Answers
Answer:
The advertisement should use 16 minutes.
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
The manager of a fast-food restaurant determines that the average time that her customers wait for service is 3.5 minutes.
This means that [tex]m = 3.5, \mu = \frac{1}{3.5} = 0.2857[/tex]
What number of minutes should the advertisement use?
The values of x for which:
[tex]P(X > x) = 0.01[/tex]
So
[tex]e^{-\mu x} = 0.01[/tex]
[tex]e^{-0.2857x} = 0.01[/tex]
[tex]\ln{e^{-0.2857x}} = \ln{0.01}[/tex]
[tex]-0.2857x = \ln{0.01}[/tex]
[tex]x = -\frac{\ln{0.01}}{0.2857}[/tex]
[tex]x = 16.12[/tex]
Rounding to the nearest number, the advertisement should use 16 minutes.
PLSSS ANSWER JUST PUT THE NUMBER OF THE QUESTION THEN THE ANSWER PLS HELP ITS OVERDUE AND IM GONNA FAIL 7TH GRADE :(
I WILL GIVE BRAINLIEST EVERYONE KEEPS GIVING ME RANDOM LINKS IM CRYIING :( I WOULD BE SO GRATEFUL IF U HELPED UR A LIFE SAVER
Answers
Answer:
11= 21
12= -12
13= -72
14= -1
Step-by-step explanation:
Answer:
11) 21
12) -5
13) 8
14) 9
Step-by-step explanation:
i passed 7th grade (teehee)
ANSWER !!
ILL GIVE 40 POINTS !!
DONT SKIP :((
PLUS BRAINLIEST !
Answers
The dot isn’t shaded so > or <
From -55, it’s showing small than
From -49, it’s showing greater than
x < -55 or x > -49
Answer: x < -55 or x > -49
Step-by-step explanation:
x < -55 or x > -49
They both start with an opened circle, and also these two opened circle dots do not connect to each other. On the left side, the number is going from -55 to the smaller side, -57 or less, so we can say that x is smaller than -55. On the right side, the number goes from -49 to the bigger number, we can say that x is greater than -49.
how many hundred billions in the number 432,845,979,484
Answers
There are 4 hundred billions in the number 432,845,979,484.
To determine how many hundred billions are in the number 432,845,979,484, we need to consider the place value of the hundred billions digit.
The number 432,845,979,484 has 12 digits, and we count the digits from right to left, starting with the units place. The digit in the hundred billions place is the seventh digit from the right.
Let's break down the number:
4 hundred billions (4 x 100,000,000,000)
3 ten billions (3 x 10,000,000,000)
2 billions (2 x 1,000,000,000)
8 hundred millions (8 x 100,000,000)
4 ten millions (4 x 10,000,000)
5 millions (5 x 1,000,000)
9 hundred thousands (9 x 100,000)
7 ten thousands (7 x 10,000)
9 thousands (9 x 1,000)
4 hundreds (4 x 100)
8 tens (8 x 10)
4 units (4 x 1)
As we can see, there are 4 hundred billions in the number 432,845,979,484.
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HELPPP!!!
John is packing a box that is shaped like a cube and
has an edge that is 15 centimeters long. How much
space is available in the box for John to pack?
Answers
Answer:
810
Step-by-step explanation:
multiply them.
Your welcome,
In a popular online role playing game, players can create detailed designs for their
character's "costumes," or appearance. Fatoumata sets up a website where players
can buy and sell these costumes online. Information about the number of people who
visited the website and the number of costumes purchased in a single day is listed
below.
126 visitors purchased no costume.
228 visitors purchased exactly one costume.
34 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase
exactly one costume as a decimal to the nearest hundredth.
Mk
Answers
Answer: 0.59
Step-by-step explanation:
The probability that the next person will purchase exactly one costume is 0.59.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Total number of visitors = 126+228+34 = 388
Total number of visitors who purchased exactly one costume = 228
The probability = 228/388 = 0.587 ≈ 0.59
Thus, the probability that the next person will purchase exactly one costume is 0.59.
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for each of the following find the missing sides
Answers
Answer:
the missing side is 90 because is a right triangle
Fran has 18 paperback books and 24 hardcover books. What is the ratio of hardcover to paperback books?
WILL GIVE BRAINLIEST
3:4
4:3
3:7
7:3
Answers
What is the arc measure of PQ?
Answers
Answer:
47.1
Step-by-step explanation:
l= rø
or, l= 18 × 5π/6
or, l= 15π
l = 47.1
Select the correct answer. 1 -23 1-4 What is the result of the operation 2 O A. 6 -10 -2 -16 4 6 -2 R 5 8 6 _4 Ос. 16 -4 6 4 2 6 -10 2 -16 4 -4 -28
Answers
9514 1404 393
Answer:
D
Step-by-step explanation:
Choices A and D agree in all but one term: row 2 column 3 is (-2)(3) = -6. The term with the correct sign is only found in choice D.
please help mark brainliest ( no attachments please)
Answers
Answer:
I think 3 hours
Answer:
2/6 in 2 hours
Step-by-step explanation:
meteroloogist track severe stoms using Doppler radar. A polar grid is used to measure distances as the storms progress. If the center of the radar screen is the origin and each ring is 10 miles farther from the center, what is the equation of the fourth ring
Answers
Answer:
[tex]$(x-h)^2+(y-k)^2= (r+ 40 )^2$[/tex]
Step-by-step explanation:
It is given that a meteorologist is using a Doppler radar to find out the distance of the storm as it passes using a polar grid.
The origin of the radar screen is its center.
And the distance between each ring is 10 miles from the center.
So let :
r = radius
h and k = be the coordinates of the center.
So the equation of a circle is :
[tex]$(x-h)^2+(y-k)^2= r^2 $[/tex]
Now the equation of the fourth circle when the radius changes by 10 miles is :
[tex]$(x-h)^2+(y-k)^2= (r+ 40 )^2$[/tex]
Please need help thank you
Answers
Answer:
12 miles
Step-by-step explanation:
Area=length*width
To find the length using the area, do area/width.
96/8=12
. Find the cost of lodging: Four people staying for three nights at a cabin priced at $36.00 per night for two people, plus $3.50 per additional person
Answers
Luke's answer makes sense or is nonsense.His model is correct or incorrect. There are [blank] not 3 inches, in a foot.
Answers
Can anyone help me please:)
Evaluate the expressions below.
14x + 2 and 2(7x + 1)
x = 10
Answers
Explanation: 14x + 2 and 2(7x + 1)
14(10) + 2 = 142 and 2(7(10) + 1) = 142
Hope this helped! :)
Answer:
142
Step-by-step explanation:
14x+2
(14)(10)+2
=142
2(7x+1)
2((7)(10)+1)
=142
hope this helped! :]
The function f(x) models the value of imported goods into the United States, and the function g(x) models the value of exported
goods from the United States, where x is the number of years since 1990.
Which statements are correct?
A) g(x) appears to be a linear function
B) f(x) appears to be an exponential function
C)Exports increase more quickly around the year 2041
D) Exports eventually exceed imports from the united States
E) A quantity increasing exponentially eventually exceeds a quantity
increasing linearly
Answers
Answer:
C, D, E
Step-by-step explanation:
I did the USATESTPREP
5th grade math. correct answer will be marked brainliest
Answers
Answer:
8
Step-by-step explanation:
4/5 of 10 is 8
4/5*10
Answer:
zack has 8 stamps.
Step-by-step explanation:
total stamps: 10
fifths: 10 divided by 5 = 2
so each part is worth 2 stamps.
so now : 2 x 4 = 8
therefore 8 is answer.
im not wrong
im am a high schooler
now mark me brainlist please.
hope it helps.
CONVERT THE PERCENTAGES FRACTION 120%
Answers
Answer:
[tex]\frac{6}{5}[/tex]
Step-by-step explanation:
Answer:
6/5
Step-by-step explanation:
Its 6/5..
1 = 20%
Please give brainliest
Help please question in the picture
Answers
Answer:
81 m²
Step-by-step explanation:
The area of the figure = area of the rectangle + area of the triangle
= Length*Width + ½*base*height
Length = 10 m
Width = 6 m
base = 6 m
height = 7 m
Thus:
Area = 10*6 + ½*6*7
Area = 60 + 21 = 81 m²
Help please and why
Answers
Because with you divided 16 1.25
it takes Emma 18 minutes to type 14 pages of a manuscript. find how long it takes her to type 77 pages
Answers
Answer:
99 minutes
Step-by-step explanation:
18/14 = 1.286 minutes per page
1.286 x 77 = 99 minutes
If your weekly salary is $1780 and taxes takes out $440, then what percent do you pay in taxes?
Round your answer to 1 decimal place.
Answers
Answer:
24.7
Step-by-step explanation:
If your weekly salary is $1780 and taxes takes out $440, then 24.7% you pay in taxes.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that the weekly salary is One thousand seven hundred and eighty $1780.
Taxes takes out is four hundred and forty $440.
We need to find the percent of tax we have paid.
This can be found by as below.
1780x=440
Divide both sides by 1780
x=440/1780
x=0.247
Now multiply with 100 as it is a hundredth part
0.247×100=24.7%
Hence, 24.7% is the percentage of tax we have paid.
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7.3 Times 10 to the power of two
Answers
Answer: the answer is 730
Step-by-step explanation:
Hope this helps you! Have a good day! :)
Choose all lengths that are equal to
6 feet 12 inches.
Answers
Answer:
Can you show a picture? Or like tell us the options?
1.
Which equation has a solution of 8?
A = 16
C 8
B =
r
8
B 4r = 16
D-2r= -16
Answers
Answer:
it's x + 2 = 10 ,x - 4 = 4 , 3 x =24 and x over 8 = 1
Step-by-step explanation:
I guess that's the right answer
12x^3-8x^2-32x factoring
Answers
Answer:
= 4x (3x+4) (x−2)
Step-by-step explanation:
12x^3−8x^2−32x
= 4x (3x+4) (x−2)