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.
Learn more about equations here:
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Related Questions
Ms. Vasquez's daughter lives 1,650 miles away. Ms. Vasquez won a gift card for 100 gallons of gas. If her car can travel 35 miles on each gallon, can she travel roundtrip to see her daughter on free gas? Explain how you know.
Answers
Answer:
yes, since it takes 48 gallons of gas to go one direction to go back it is 96
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
If her daughter lives 1,650 miles away, and her gift card is for q00 miles of gas, and her car can travel 35 miles on each gallon, it would take about 47 gallons to make the 1,650 mile trip to her daughter. Leaving 53 gallons on her car.
To make the 1,650 mile trip back to her own home, it would take another 47 gallons. Since she still has 53 gallons left from her trip there, she will be able to make the trip back with still 6 gallons in her tank.
Tell whether b=6 is a solution of 8b=48
Answers
Answer:
b= 6 for sure
Step-by-step explanation:
what is 2 x 2? answer dumly
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What is 10×25 to the sixth power
Answers
Answer:
2.4414063e+14 (wow such a large number)
Step-by-step explanation:
10x25= 250
250 to the 6th power = 2.4414063e+14
A tutor earns $220 for 4 hours of tutoring. At the same rate, how much would the tutor earn for 3 hours of tutoring?
A. $150
B. $155
C. $165
D. $180
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C
Write the additive inverse and multiplicative inverse of 3-7i?
Answers
Step-by-step explanation:
additive inverse means multiplying 3-7i by it's conjugate which would be
(3-7i)(3+7i)=3^2+7^2=9+49=58
the multiplicative inverse of a number z is 1/z
1/(3-7i)
multiply numerator and denominator by 3-7i's conjugate and it equals 58
(3-7i)/58
3/58-7/58i
Hope that helps :)
what is the domainof f(x)=4^x
Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Domain of given function is set of real numbers
1) Solve 2 + 7x + 12 = 0 using factoring and the zero product property.
a) Factor2+7x+12
b) Use the zero product property to solve for x
b) Use the zero product property to solve for x
Answers
Answer:
7x+14=0, 7x=-14, x= -2
Step-by-step explanation:
add like terms, then get x on one side, number on the other, then divide both sides by 7
What is the range for the set of data?
A. 4
B. 6
C. 3.5
D. 0
I don’t want a link, so if you were gonna send one, ignore this instead
Answers
800:2 in the simplest form
Answers
Answer:
400:1
Step-by-step explanation:
800:2
800/2:2/2
400:1
A hexagonal prism has a base with an area of 15 square inches and the volume is 105 cubic inches.
.
Complete the sentence about the height of the prism.
The height of the prism is _____ inches,square inches,cubic inches
Answers
Answer:
I believe the answer would be 1575 cubic inches. Sorry if i'm wrong!
Answer:
The answer is 7 square in
Step-by-step explanation:
Do this formula
V=Bh
105=15h
h=7 square in
can anyone solve these and show work? please help a girl out lol
Answers
45 | 45 | 90
n | n | n root 2
15 | x
n=n=x=15 u
y is hypotenuse, since 15 is n, hypotenuse is gonna be n root 2 so 15 root 2
18) 30-60-90 triangle
30 | 60 | 90
n | n root 3 | 2n
x | y | 15
2n=15
n=7.5=x
7.5 root 3=y
who is the current vice president of the us? is this a statistical question or a non statistical question why or why not? Explain your answer
Answers
Answer:
The current vice president (as of 4-16-2021) of the U.S. is Kamala Harris. This is a non-statistical question.
Step-by-step explanation:
A statistical question can be answered by collecting data and where there will be variability in that data. The proposed question (Who is the current vice president of the U.S.?) does not allow for variability in the data as there is only one legitimate answer to the question, thus it is NOT a statistical question.
Answer: statistical question
Step-by-step explanation:
cause your asking the current vice president.
Write and solve an equation to determine the height of a rectangular prism
with a width of 6 millimeters, a length of 20.5 millimeters, and a volume
of 984 cubic millimeters.
PLEASE HELP
Answers
Answer/Step-by-step explanation:
H = V/lw
H = 984/20.5*6
H = 984/128
H = 8
ANSWER:
H = 8
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 434 gram setting. It is believed that the machine is underfilling the bags. A 9 bag sample had a mean of 431 grams with a variance of 144. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled
Answers
Answer:
No, there is not sufficient evidence to support the claim that the bags are underfilled
Step-by-step explanation:
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 434 gram setting.
This means that the null hypothesis is:
[tex]H_{0}: \mu = 434[/tex]
It is believed that the machine is underfilling the bags.
This means that the alternate hypothesis is:
[tex]H_{a}: \mu < 434[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
434 is tested at the null hypothesis:
This means that [tex]\mu = 434[/tex]
A 9 bag sample had a mean of 431 grams with a variance of 144.
This means that [tex]X = 431, n = 9, \sigma = \sqrt{144} = 12[/tex]
Value of the test-statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{431 - 434}{\frac{12}{\sqrt{9}}}[/tex]
[tex]z = -0.75[/tex]
P-value of the test:
The pvalue of the test is the pvalue of z = -0.75, which is 0.2266
0.2266 > 0.01, which means that there is not sufficient evidence to support the claim that the bags are underfilled.
Can you please help me do a and b I will reward brainliest
Answers
a) 640.32 cm^3
b) 98.4 cm^3
Step-by-step explanation:Part a)Cylinder volume:(3.14) × 2^2 × 12 = 150.72 cm^3
Triangular prism:We need to find the height of the base so we use the Pythagorean theorem.
5^2 + x^2 = 14.1^2
25 + x^2 = 198.81
x^2 = 173.81
x = 13.184
After finding height, we can use the equation for a normal triangular prism:
[tex]\frac{1}{2}[/tex] × Base × Height × Length
[tex]\frac{1}{2}[/tex] × 13.184 × 10 × 12= 791.04cm^3
Total Volume: 791.04 - 150.72 = 640.32 cm^3
Part b)Small Sphere Volume:[tex]\frac{4}3[/tex] × 3.14 × 1^3 = [tex]\frac{314}{75}[/tex]cm^3
Half Sphere Volume :0.5([tex]\frac{4}3[/tex]× 3.14 × 3^3) = 56.52cm^3
Cone Height:5^2 = 3^2 + h^2
25 = 9 + h^2
16 = h^2
h = 4
Cone Volume:(3.14) × 3^2 × [tex]\frac{4}{3}[/tex] = 37.68 cm^3
Total Volume = 98.4 after rounding
Scott wants to put soil in his garden shown below. If soil comes in bags that fill 3 square yards each, how many bags of soil should Scott buy
Answers
Answer:
5
Step-by-step explanation:
Becuase his backyard is 15 square yards.
Kristy is going to a college where tuition is $8,000 per year. She has a scholarship that pays 80% of tuition. Her aunt is giving her $1,000 per year. How much will Kristy need to borrow to pay tuition each year?
Answers
8,000-6,400= 1,600
1,600-1,000= 600 that is the amount of tuition she will need to pay each year.
PLSS help me ☝............
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Answer:
New Coordinates: G'(0,4) Y'(3,3) M(3,7)
Movement: Translation 3 units up
Step-by-step explanation:
Since you're adding to the y-coordinate, your points will move up which makes this a translation
Find the volume of the sphere. Round to the nearest tenth.
The volume is about _____ cubic meters.
Answers
find the rate of change of the linear function from the point (0,8) to the point (24,4)
Answers
9514 1404 393
Answer:
-1/6
Step-by-step explanation:
The slope (rate of change) is given by ...
m = (y2 -y1)/(x2 -x1)
m = (4 -8)/(24 -0) = -4/24 = -1/6
The rate of change of the linear function is -1/6.
_____
The equation is y = -1/6x +8.
Xavier writes a ratio out of 18 as the decimal 0.22222222.
Answers
Answer: 4/18
Step-by-step explanation:
The ratio 4:18 can be written as the decimal 0.22222222, so the value in the numerator is 4.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We have:
Xavier writes a ratio out of 18 as the decimal 0.22222222.
Let's suppose the x out of 18 can be written as 0.22222222
x/18 = 0.22222222
x = 3.999999 ≈ 4
It means 4/18 can be written as 0.22222222
Thus, the ratio 4:18 can be written as the decimal 0.22222222, so the value in the numerator is 4.
Learn more about the ratio here:
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Find the perimeter of the semicircular region
22 mm
Answers
Answer:
The permiter is 22mm since its still the same
Step-by-step explanation:
A coffee shop recently sold 10 drinks, including 4 mochas. What is the experimental
probability that the next drink sold will be a mocha?
Simplify your answer and write it as a fraction or whole number.
P(mocha) =
Submit
Work it out
Not feeling ready yet? These can help:
Answers
Answer:
2/5
Step-by-step explanation:
IXl answer
The experimental probability that the next drink sold will be a mocha is 2/5.
Number of mochas =4
Total drinks =10
What is probability?Probability is the quantification of possibilities.
P(event) = Favorable outcomes/ Total outcomes
P(mocha) = 4/10
P(mocha) =2/5 =0.4 or 40%
Thus, the experimental probability that the next drink sold will be a mocha is 2/5.
To get more about probability visit:
https://brainly.com/question/24756209
Solve for x.
109= -x + 267
X=
x 5
?
Answers
Answer:
x=158
Step-by-step explanation:
109=-x+267
-267 -267
-158=-x
x=158
(also i noticed part of your question says x=(?)*5 and 31.6*5 is 158 so that would be 31.6)
find the circumference and the area of a circle with the diameter of 8 m.
Answers
Answer:
circumference = 8 x 3.14 = 25.12 m
area = 3.14(4²) = 50.24 m²
Step-by-step explanation:
Answer:
C= about 25.13
A= about 50.27
Step-by-step explanation:
The formula for circumference is 2* pi* r
The formula for area is pi *r^2
Tristian has 35 rock songs, 50 dance songs and 15 rap songs on his play list. If his music player randomly selects a song, what is the probability that it is a dance song?
Answers
Answer:
1/2
Step-by-step explanation:
35+50+15 = 100
probability of the dance song = 50/100 = 1/2
Answer:50%
Step-by-step explanation:
35+15+50=100
50 divided by 100 is 0.5 or you can do it as a fraction and get 50/100
Helpppppppppppppooopp
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Answer:
I can't see clearly
Step-by-step explanation:
CAn someone help me plsss
Answers
13.76
Divide 27.52 by 2 to get 13.76
Ed's dog Zoe ate almost 18% of the 4 dozen cookies he baked.
Which is the best estimate of the number of cookies Zoe ate?
Answers
Answer:
.72 or 1
Step-by-step explanation:
it is .72 in decimals but if you wanna round up to a whole number it's 1
