Using an exponential function, it is found that it would take 19.68 years for the value of the car to be $3,800.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^\frac{t}{n}[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal, after each n years.In this problem:
The initial value is of $31,000, hence A(0) = 31000.It depreciates by one-half every 6.5 years, hence r = 0.5, n = 6.5.Then, the equation is:
[tex]A(t) = A(0)(1 - r)^\frac{t}{n}[/tex]
[tex]A(t) = 31000(1 - 0.5)^\frac{t}{6.5}[/tex]
[tex]A(t) = 31000(0.5)^\frac{t}{6.5}[/tex]
The value would be of $3,800 at t for which A(t) = 3800, hence:
[tex]A(t) = 31000(0.5)^\frac{t}{6.5}[/tex]
[tex]3800 = 31000(0.5)^\frac{t}{6.5}[/tex]
[tex](0.5)^\frac{t}{6.5} = \frac{3800}{31000}[/tex]
[tex](0.5)^\frac{t}{6.5} = 0.12258064516[/tex]
[tex]\log{(0.5)^\frac{t}{6.5}} = \log{0.12258064516}[/tex]
[tex]\frac{t}{6.5}\log{0.5} = \log{0.12258064516}[/tex]
[tex]t = 6.5\frac{\log{0.12258064516}}{\log{0.5}}[/tex]
t = 19.68.
It would take 19.68 years for the value of the car to be $3,800.
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Answer:
t≈19.7
Step-by-step explanation:
I do not have one, I apologize.
-
Use inverse operations to write the inverse of f(x) = x +
3/2
Answer:
I believe the correct answer is f^-1 (x) = x - 3/2
HELP PLEASE I REALLY SUCK AT MATH
Answer:
D is the answer because 4 goes into all of them.
PLEASE HELP ASAP
EVERYTHING NEEDED IS IN THE PIC BELOW
Answer:
37.69
Step-by-step explanation:
There are 3 circles
Circle A ( radius = 6 cm )
Circle B ( radius = 4 cm )
Circle C ( radius = 2 cm )
the circumference of a circle is C = 2 Pi x r
from each circle we need half of the circumference
Circle A : P = 2pi x 6 / 2 = 6 pi
Circle B : P = 2pi x 4 / 2 = 4 pi
Circle C : P = 2pi x 4 / 2 = 2 pi
the perimetee of the shaded shape is = 6 pi + 4 pi + 2 pi = 12 pi = 37.69 cm
find the value of x in the triangle below
Answer:
√80 (Option A)⠀
Step-by-step explanation:
⠀
This is Right Angled Triangle.⠀
We'll solve this using the Pythagorean Theorem.
Let,
x be AC, where AC is the Hypotenuse.4 be AB, where AB is the Perpendicular.8 be BC, where BC is the Base⠀
We know that,
[tex]{ \longrightarrow \pmb{ \qquad (AC) {}^{2} = (AB) {}^{2} +( BC) {}^{2} }}[/tex]
[tex]{ \longrightarrow \sf{ \qquad (x) {}^{2} = (4) {}^{2} +( 8) {}^{2} }}[/tex]
[tex]{ \longrightarrow \sf{ \qquad (x) {}^{2} = 16 +64 }}[/tex]
[tex]{ \longrightarrow \sf{ \qquad (x) {}^{2} = 80 }}[/tex]
[tex]{ \longrightarrow \it\pmb{ \qquad x {} = \sqrt{80} }}[/tex]
⠀
Therefore,
The value of x is √80The figure is a right angled triangle , where the value 4 is perpendicular , 8 is base and x is hypotenuse.
So, By Pythagoras theorem
[tex]x {}^{2} = 4 {}^{2} + 8 {}^{2} [/tex]
[tex]x = \sqrt{16 + 64} [/tex]
[tex]x = \sqrt{80} [/tex]
Michelle's keeping track of how much time she spends playing video games. She knows she gamed for a total of 60 hours during the past 3 weeks. She played 4 hours more during the 2nd week than the 1st week. Also, she played 2 hours less during the 3rd week than the 2nd week. How many hours did she spend playing video games during the 3rd week?
Answer:
I have no clue.
Step-by-step explanation:
Answer:
What is a appropriately
What is a Procedure
What is a Enthusiasm
What is a Conflict
What is a Technique
What is a Obtain
What is a conflict management
determine if the relationships are linear and if so are they proportional
b= c= Please help asap
Kimberly has 2 1/3 bottles of milk in her refrigerator.
She used 3/4 bottle in the morning and 1 1/8 bottle in the afternoon.
How many bottles of milk does Kimberly have left over?
Answer:
1 3/20
Step-by-step explanation:
convert 15cm ^ 3 into m * m ^ 3
Answer:
15 ×10^-6
Step-by-step explanation:
1 m = 100 cm
1m^3 = 100^3 cm^3
1m^3 = 1×10^6 cm^3
15 cm^3 = 15 / 1×10^6 = 15×10^-6 m^3
Lily wants to do fencing around a circular garden that has a radius of 70m. If the cost of fencing is $12 per meter, find the total cost of fencing for the entire garden (use pi=22/7
Answer:
$5280
Step-by-step explanation:
Since the radius of the circle is 70m, the perimeter or circumference of the circle is 2πr --> 2 * 70 * 22/7 which is 440 meters. Since each meter of fencing costs $12, the total cost of the fencing is $5280
why are the cars values modeled by exponential functions and not linear function?
prove that
[tex] \frac{1 }{ \sin(x) \times \cos(x) } [/tex]
equals 2csc2x
Answer:
See below for proof
Step-by-step explanation:
[tex]2csc(2x)\\\\2[\frac{1}{sin(2x)}]\\ \\2[\frac{1}{2sin(x)cos(x)}]\\ \\\frac{2}{2sin(x)cos(x)}\\ \\\frac{1}{sin(x)cos(x)}[/tex]
Thus, the identity is proven
1
2. Four friends are on a boating excursion on the Gulf of Mexico. One is parasailing in the air, above
sea level. Two are scuba diving in the water, below sea level. One is swimming on the surface, at
sea level.
Which integer represents the elevation of the friend who is swimming on the surface?
A.-2
B. O
C. 1
D.4
The integer that represents the elevation of the friend who is swimming on the surface is 0.
What are integers?An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a set of integers that consists of the following:
Positive Numbers: If a number is greater than zero, it is considered positive. For instance, 1, 2, 3, etc.Negative numbers are those that are less than zero. For instance: 1, 2, 3, etc.Zero is described as being neither a positive nor a negative number. A whole number, that is.Given:
Two are scuba diving in the water, below sea level. One is swimming on the surface, at sea level.
We know that the the region below sea level represented by negative integers and the region above sea level represented by positive integers.
Thus, if the scuba driver is on the surface then it neither negative nor positive.
So, it would be represented by zero.
Hence, the integer that represents the elevation of the friend who is swimming on the surface is 0.
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the students in mr reed's english class are reading the same 760 page novel. Three friends alice, bob and chandra, are in the class. Alice reads a page in 20 seconds, bob reads a page in 45 seconds and chandra reads a page in 30 seconds. Before chandra and bob start reading. Alice says she wants to team read with them. If they divide the book into three sections so that each reads fore the same amount of time, how many seconds will each have to read?
Answer:
please rate and mark as brainlest.
Step-by-step explanation:
alice will have 5067 seconds,
bob will have 11400 seconds
chandra will have 7600 seconds.
first, divide 760 by 3 to get 253.33, then just multiply each value of seconds for each person to get their value, and round.
please rate and mark as brainlest.
Rotate shape A 90° clockwise with centre of rotation (0,0).
What are the coordinates of the vertices of the image?
Step-by-step explanation:
(3,3)====(3,-3)
(3,2)====(2,-3)
(5,2)====(2,-5)
Which graph best represents the equation created when the slope of y = 6x is changed to 0?
The graph with an equation y = 6x has a slope of 6. If the slope is changed to 0, the equation becomes y = 0.
What is a linear function?A linear function is in the form:
y = mx + b
Where m is the slope (rate of change) and b is the y intercept
The graph with an equation y = 6x has a slope of 6. If the slope is changed to 0, the equation becomes y = 0.
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12. A bakery has five different types of cookies in its display case as listed.
. Chocolate chip
. Oatmeal raisin
• Peanut butter
• Sugar
• Macadamia nut
If Cameron selects one cookie from the display case at random, what is the probability that it will be a peanut butter or sugar cookie?
Answer:
2/5
Step-by-step explanation:
Information we need to solve
Portion of peanut butter cookiesPortion of sugar cookiesTotal number of cookiesProbaility
No. of sugar and peanut butter cookies / Total cookies1 + 1 / 52/5Solve for x.
0.2x – 3.2
= 1.8
1
5
X = ?
Answer:
X = 25
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable
Use the distributive property (expand) to write an equivalent expression for: 3(4x-2t). Type your answer ( I NEED THIS RIGHT AWAY PLS)
Answer:
The distributive property here is to just multiply each value by tree number outside the parenthesis.
3 ( 4x - 2t)
12x - 6t
That would be your answer.
Mathamatics What decimal is being represented by the decimal grid?
100/100 + 100/100 + 26/100 = 2 + 0,26 = 2,26
Assume that the following data were generated using a valid and appropriate methodology. XYZ Data Analytics, Inc. Received properly completed surveys from 523 members of the target population for a new product. One hundred seventy nine of those respondents indicated they would buy the new product at the proposed price
Using the z-distribution, as we are working with a proportion, the 95% confidence interval for the proportion of consumers who would buy the product at it's proposed price is (0.3016, 0.3830).
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
179 out of 523 members indicated they would buy the new product at the proposed price, hence:
[tex]\pi = \frac{179}{523} = 0.3423[/tex]
Then the bounds of the interval are found as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3423 - 1.96\sqrt{\frac{0.3423(0.6577)}{523}} = 0.3016[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3423 + 1.96\sqrt{\frac{0.3423(0.6577)}{523}} = 0.3830[/tex]
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Which of the following is not an exponential function?
An equation is shown below: 2(7x − 3) = 9 Which of the following correctly shows the beginning steps to solve this equation? (4 points)
Answer:
2(7x-3)=9
14x-6=9
14x=9+6
14x=15
x=15/14
Hey there!
Let's solve this equation!
We have
2(7x-3)=9
Use the Distributive Property & distribute 2:
14x-6=9
Now, add 6 to both sides:
14x=15
Divide both sides by 14:
x=15/14
Hope everything is clear.
Let me know if you have any questions!
#ILoveLearning
:-)
Sofia has been saving money to buy a new computer. For her birthday, Sofia’s mother gave her twice what she had already saved. Now she has $135.
How much money did Sofia have before her birthday ?
Answer:
67.5
Step-by-step explanation:
135/2=67.5
answer is $67.50
In circle S with the measure of arc \stackrel{\Large \frown}{RT}= 156^{\circ} RT ⌢ =156 ∘ , find \text{m} \angle RSTm∠RST
The measure of arc RT in the circle S is about 60 degrees.
What is a circle?A circle is the locus of a point such that the distance from its fixed point is always constant.
The question is not complete. A similar question is attached.
From the diagram:
arc RT = 2 * ∠RUT(angle at circle center is twice angle at circumference)
arc RT = 2 * 30
arc RT = 60°
The measure of arc RT in the circle S is about 60 degrees.
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multiply .( p + q ) ( p + q )
Answer:
[tex](p + q)(p + q) \\ = {p}^{2} + pq + pq + {q}^{2} \\ = {p}^{2} + {q}^{2} + 2pq \\ = {(p + q)}^{2} \\ thankyou[/tex]
Question 1
The purpose of the sales director's study is to determine whether attending the training program caused an increase in sales
for representatives from the two regions. So the sales director collected sales data from both groups (those receiving training
and those receiving no training) for three months after the one-month program and compared the number of orders secured
by those who attended the training program with the number of orders secured by those who didn't attend.
Part A
? Question
Select the correct answer from each drop-down menu.
because a treatment
applied to the sales
The sales director conducted
representatives
This is the best statistical study for this situation because the sales director is trying to establish
Based on the above scenario, the sales director conducted an experiment.
Because a treatment was applied to the sales representatives.The the best statistical study for this situation because the sales director is trying to establish correlation.What is an experiment?An experiment is known to be a method that is et up with the aim to test a given hypothesis as a component of a scientific method.
In an experiment, there are the two key variables which are the independent and dependent variables. The independent variable is known to be a controlled or it is tested against the dependent variable.
See full question
Part A.
The sales director conducted a.) an experiment b.) a survey c.)an observational study because a treatment a.) was not b.)was applied to the sales representatives.
This is the best statistical study for this situation because the sales director is trying to establish a.) causality b.) correlation.
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Dion is performing a hypothesis test in which the population mean is 92 and the standard deviation is 2. His sample size is 7 with a mean of 93. 5. Which of the following correctly depicts the z-statistic for this data? 0. 28 0. 36 1. 98 2. 63.
The value of the z statistic for the considered data is given by: Option C: 1.98 approximately.
How to find the z score (z statistic) for the sample mean?If we're given that:
Sample mean = [tex]\overline{x}[/tex] Sample size = n Population mean = [tex]\mu[/tex] Sample standard deviation = sThen, we get:
[tex]z = \dfrac{\overline{x} - \mu}{s}[/tex]
If the sample standard deviation is not given, then we can estimate (in some cases) it by:
[tex]s = \dfrac{\sigma}{\sqrt{n}}[/tex]
where [tex]\sigma[/tex] = population standard deviation
For this case, we're specified that:
Sample mean = [tex]\overline{x}[/tex] = 93.5Sample size = n = 7Population mean = [tex]\mu[/tex] = 92Population standard deviation = [tex]\sigma[/tex] = 2Thus, the value of the z-statistic is evaluated as:
[tex]z = \dfrac{\overline{x} - \mu}{\sigma/\sqrt{n}} = \dfrac{93.5 - 92}{2/\sqrt{7}} \approx 1.98[/tex]
Thus, the value of the z statistic for the considered data is given by: Option C: 1.98 approximately.
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Find A and the reason
We see that Triangle ABC is an isosceles triangle which means:
Sides BA and BC are equal in lengthAngle BAC and BCA are equalWe see that Angle BCD and Angle BCA are on a straight line, which means that both of the angles' measures are equal to 180 degrees
--> in equation form:
Angle BCD + Angle BCA = 180
118 + Angle BCA = 180
Angle BCA = 62 degrees
Since Angle BCA and BAC are equal, then Angle BAC or Angle A in this case is 62 degrees
Hope that helps!
What is the solution to y=-2x+7 and y=5x-7
Answer:
x-2,y= 3, it can also be written as (2 ,3)
Step-by-step explanation:
2x-7y=5x-7-2x-7=5x-75x+2x=
7+77x=14x=2y=5x-7=5*2-7=10-..