Using an exponential function, we have that:
a) The equation is: [tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex].
b) The house will have a value of $1 million during the year of 2037.
c) The expected value on April 1, 2020, is of $621,520.
What is an exponential function?
An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, the parameters are given as follows:
A(0) = 600000, r = 0.058 each 2 years.
Hence the exponential function is:
[tex]A(t) = 600000(1 + 0.058)^{\frac{t}{2}}[/tex]
[tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex]
Item b:
It is the year 2019 + t, for which A(t) = 1000000, hence:
[tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex]
[tex]1000000 = 600000(1.058)^{0.5t}[/tex]
[tex](1.058)^{0.5t} = 1.6667[/tex]
[tex]\log{(1.058)^{0.5t}} = \log{1.6667}[/tex]
[tex]0.5t\log{1.058} = \log{1.6667}[/tex]
[tex]t = \frac{\log{1.6667}}{0.5\log{1.058}}[/tex]
[tex]t = 18.12[/tex]
The house will have a value of $1 million during the year of 2037.
Item c:
April 1, 2020 is one year and 3 months = 1.25 years after January 1, 2019, hence the value of the home will be given by:
[tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex]
[tex]A(1.25) = 600000(1.058)^{\frac{1.25}{2}}[/tex]
A(1.25) = $621,520.
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For the following exercises, find the x- and y-intercepts of the graphs of each function.
28. f(x) = −2| x +1 | + 6
The x- and y-intercepts of the graphs of the function described are; (2,0) and (4,0) respectively.
What are the x- and y-intercepts of the graph of the function?It follows from the task content that the function given is; f(x) = −2| x +1 | + 6.
Since the x- and y-intercepts corresponds to x and y values for which y and x are zero respectively, it follows that;
x -intercept is;
0 = -2(x+1) + 6
2x = -2 +6
2x = 4
x = 4/2 = 2
y-intercept is;
y = -2(0+1) +6
y = 4.
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math!! please helpp!!!
What is the y intercept of the line below?
( i attached an image)
a) -3
b) 1/3
c) 4
d) (-1.5,0)
e) -1.5
f) (4,0)
g) 3
Answer:
f (4,0)
Step-by-step explanation:
Hope it helps!!!
y=4
x=0
⊱_______________________________________________________⊰
Answer:
4Step-by-step explanation:
[tex]\large\displaystyle\begin{gathered} \sf{The \ y-intercept \ is \ the \ point \ where \ the \ graph \ intercepts \ the \ y \ axis. \\ \sf{Thus, \ assuming \ that \ each \ little \ square \ represents \ one \ unit, \ the \ y-intercept} \\ \sf{is \ 4} \end{gathered}[/tex]
done !!
⊱_______________________________________________________⊰
Cαlligɾαρhγ4. Point P is not on line . Describe the shortest distance from the point to the line
P
8
Answer:
a line that is perpendicular to the line l
Find the number, d, if the sum of five times d and five times five is a
hundred.
The value of d from the given expression is 15
Word problem leading to equationFrom the given statement the sum of five times d and five times five is a
hundred is interpreted as;
5d + 5(5) = 100
5d + 25 = 100
Subtract 25 from both sides
5d = 100 - 25
5d = 75
d =15
Hence the value of d from the given expression is 15
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What is the missing number in this sequence: 1 , 3, ___ , 10 , 15 , 21 ?
Please explain it step-by-step
Answer:
6
Step-by-step explanation:
the sequence increases by 1,2,3,4,5,6 each time, thus it is 6
A farmer has 45 horses and 20 cows.
(i) Write this as a ratio horses : cows.
Give your answer in its simplest form.
Answer: 9 : 4
Step-by-step explanation:
45 : 20
simplify
9 : 4
If the zeros of a quadratic equation are 7 and - 4 , what would be the factors?
Answer:
(x - 7) , (x + 4)
Step-by-step explanation:
given the zeros of a quadratic equation x = a and x = b , then
the corresponding factors are (x - a) and (x - b)
here the zeros are x = 7 and x = - 4 then factors are
(x - 7) and (x - (- 4) ) , that is
(x - 7) and (x + 4)
An article marked to give 120% profit originally cost $60. what is the marked price?
Each week, Adam deposits money into his savings account. The graph below models the scenario.
(Graph is in the image below)
A) How much money does Adam deposit each week?
B) How did you determine the answer?
C) Use an alternate strategy to determine the amount of money Adam deposits each week.
Adam's weekly money deposit is a linear relation with a slope of $6 per week.
A) Money deposited by Adam each week is $6.
B) The answer can be determined by observing the graph provided to us, in which the point representing 1 week on the x-axis is intersected by the point representing $6 on the y-axis. This helps us determine that Adam's weekly deposit is $6.
C) An alternative strategy of calculating the slope can be used.
The slope can be calculated in the following way:
m = (y₂ - y₁)/(x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are two points on the line.
Thus slope of this line can be calculated as,
m = (12 - 6)/(2 - 1) = 6/1 = 6 {Since, the line passes through the points (2, 12) and (1, 6)}.
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Which of the following completes the two-column proof below?
Given: ∠1≅∠2, p⊥r
Prove: q⊥r
Proof:
1. ∠1≅∠2 (Given)
2. p∥q (?)
3. p⊥r (?)
4. q⊥r (?)
The figure shows lines p and q and transversal r. The intersection of line p and transversal r forms four angles, the top right angle is labeled as a right angle, the top left angle is labeled as 1. The intersection of line q and transversal r forms four angles, the bottom right angle is labeled as 2.
2. Converse of corresponding angles theorem.
3. Given
4. Perpendicular transverse theorem
What is the Converse of Corresponding Angles Theorem?According to the converse of corresponding angles theorem, if two corresponding angles are congruent, then the lines cut by the transversal that both angles line on are parallel to each other.
Thus, given that ∠1 ≅ ∠2, lines p and q will be parallel based on the converse of corresponding angles theorem.
We are given that lines p and r are perpendicular to each other, therefore, we can conclude that, based on the perpendicular transverse theorem, q⊥r.
The missing reasons in the proof are:
2. Converse of corresponding angles theorem.
3. Given
4. Perpendicular transverse theorem
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Select the correct answer.
The product of two numbers is 21. If the first number is-3, which equation represents this situation and what is the second number?
OA The equation that represents this situation is x-3=21. The second number is 24.
OB. The equation that represents this situation is 3x=21. The second number is 7.
OC. The equation that represents this situation is-3x=21. The second number is-7.
OD. The equation that represents this situation is -3+x=21. The second number is 18.
Option B is correct
Why
3x=21
3(7) =21
21=21
Step-by-step explanation:
Answer:
[tex]-3x=21 , -7[/tex]
Step-by-step explanation:
[tex]-3x=21\\x=\frac{21}{-3} =-7[/tex]
Type the correct answer in the box. Use numerals instead of words.
The graphs of functions f and g are shown.
Graph shows 2 functions. First curve f begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 2), (8, 3) in quadrant 1. Second curve g begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 4), and (8, 6) in quadrant 1.
Function g is defined as . What is the value of k?
The value of k is
.
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words.
The graphs of functions f and g are shown.
Graph shows 2 functions. First curve f begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 2), (8, 3) in quadrant 1. Second curve g begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 4), and (8, 6) in quadrant 1.
Function g is defined as . What is the value of k?
The value of k is
(1,0)
Minerva starts a savings account with $50. The interest on the account balance is compounded annually. The graph below shows the account balance in terms of x ,the number of years since the account was opened.
After 12 years, Minerva's account balance should be about $100, assuming that she does not add or withdraw any money from the account.
Cannot be determined from the information given.
False
True
Minerva's account balance will be about $100 , it is True and Option A is the correct answer.
What is meaning of Compounded annually ?Compounded Annually means when the interest is given even on the interest accrued from the principal amount . This is done once a year.
It is given that
Principal Amount = $50
From the graph attached in the answer which was missing in the question ,
It can be confirmed that after 12 years
Minerva's account balance should be about $100.
Therefore it is True and Option A is the correct answer.
The graph missing is attached
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In the diagram, JKLM∼EFGH. Find the perimeter of each polygon.
The perimeter of polygon JKLM = 85 units
The perimeter of polygon EFGH = 34 units.
What is the Perimeter of a Polygon?The perimeter of polygon JKLM = JK + KL + LM + JM
The perimeter of polygon EFGH = EF + FG + GH + EH
Find the missing lengths using the similarity theorem:
JK/EF = KL/FG = LM/GH = JM/EH
Plug in the values
20/8 = KL/11 = LM/3 = 30/EH
20/8 = KL/11
KL = (20 × 11)/8 = 27.5
20/8 = LM/3
LM = (20 × 3)/8
LM = 7.5
20/8 = 30/EH
EH = (30 × 8)/20
EH = 12
The perimeter of polygon JKLM = 20 + 27.5 + 7.5 + 30 = 85 units
The perimeter of polygon EFGH = 8 + 11 + 3 + 12 = 34 units.
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Suppose that $x$ is a multiple of 6 (not necessarily positive). If the square of $x$ is less than 200, how many possible values of $x$ are there
All multiple of 6 under 14 are: -12, -6, 0, 6, 12
How do we get 14 here:
√200= 14.142 (Round to thousandth place)
This is how many x we have found.
A multiple in math is the number you get when you multiply a certain number by using an integer. for example, multiples of 5 are: 10, 15, 20, 25, 30…, and so forth. Multiples of 7 are 14, 21, 28, 35, 42, 49…and many others.
In math, the meaning of a multiple is the product result of one number multiplied by another number. Here, 56 is a multiple of the integer 7. Here is an example of multiples: Fun facts. 0 is a multiple of every number as the product of 0 multiplied by any number is 0.
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4^x + 3 = 7 using the change of base formula log y =
log y/log b
Answer:
x=1
Step-by-step explanation:
It's pretty obvious to see that x equals 1 after you subtract 3 from both sides, but this question specifies using change base, so:
log(b)a means log base b with a as the contents
1.
4^x+3-3=7-3
4^x=4
log(4)4^x=log(4)4 (both logs are base 4 in this case to free the x)
x=log(4)4
x=log(10)4/log(10)4 (both logs are base 10 in this case)
x=1
Change base is definitely unnecessary in this problem
Find the polar equation of the conic with focus at the pole, directrix y=3, and eccentricity of 2. a. r= 6/1+2 sin theta b. r= 6/1-2 sin theta c. r= 3/ 1- 2 cos theta d. r= 1/3+2 cos theta
The required polar equation of a conic is given be: [tex]r = \frac{6}{1-2sin\Theta }[/tex]. option b is correct.
For a conic we have directrix = 3 and eccentricity = 2
What is polar equation?Polar equation can be identified as of the form of x= a+b.sinФ.
Which contain simple variable along with trigonometric operators.
Here,
Standard polar equation for the conic is given as,
[tex]r=\frac{ep}{1-esin\theta}[/tex]
By putting given values
[tex]r = \frac{6}{1-2sin\Theta }[/tex].
Thus, the required polar equation for the conic is [tex]r = \frac{6}{1-2sin\Theta }[/tex].
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Matthew thought he could make 19 free throws, but he only made 13. What was his percent error? Hint: Percent error = Prediction - Actual Actual x 100 Round to the nearest percent. [ ? 1% Matthew thought he could make 19 free throws , but he only made 13 . What was his percent error ? Hint : Percent error = Prediction - Actual Actual x 100 Round to the nearest percent . [ ? 1 %
Answer:
[tex]\huge\boxed{\sf 46.2\%}[/tex]
Step-by-step explanation:
Prediction = 19 throws
Actual = 13 throws
Percent Error:[tex]\displaystyle =\frac{Predication -Actual}{Actual} \times 100 \%\\\\= \frac{19-13}{13} \times 100 \%\\\\= \frac{6}{13} \times 100 \%\\\\= 0.462 \times 100 \%\\\\= 46.2\%\\\\\rule[225]{225}{2}[/tex]
A survey of 150 people at a local high school about playing video games was conducted, and the results are posted in the table.
Play Video Games Do Not Play Video Games
Juniors 48 12
Seniors 45 25
Teachers 6 14
What is the probability of choosing a person at random who is a teacher and plays video games? Are these independent events?
The P(teacher and video games) = 4%; the two events are not independent.
The P(teacher and video games) = 4%; the two events are independent.
The P(teacher and video games) = 9%; the two events are not independent.
The P(teacher and video games) = 9%; the two events are independent.
The P(teacher and video games) = 4%; the two events are not independent.
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.
P(teacher and video games) = number of teachers who play video game / total number of respondents
6/150 = 0.04 = 4%
Independents events are events whose occurrence do not depend on each other. They are random events.
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Answer:
The P(junior and video games) = 32%; the two events are not independent.
Step-by-step explanation:
i got it right aswell
If 3x + 7 =22, what is the value of x
Answer:
x=5
Step-by-step explanation:
solution,
3x+7=22
or,3x=22-7
or,3x=15
or,x=15/3
:×=5
The value of x in the equation 3x + 7 = 22 is x = 5.
To find the value of x in the equation 3x + 7 = 22, we can solve for x as follows:
Subtract 7 from both sides of the equation:
3x + 7 - 7 = 22 - 7
3x = 15
Divide both sides of the equation by 3 to isolate x:
(3x)/3 = 15/3
x = 5
Therefore, the value of x in the equation 3x + 7 = 22 is x = 5.
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Write an equation in slope intercept form for the line with slope -1/2 and y-intercept -5
Answer: -1/2x - 5 = Y
Step-by-step explanation:
- slope intercept form is mx + b = Y
- m is the slope
- b is the y intercept
- leave x and y as variables
- since your y intercept is negative the + will be a -
- so the equation becomes -1/2x - 5 = Y
hope this helps :)
What is the circumference of the given circle in terms of л
Answer:
30π in
Step-by-step explanation:
Circumference of a circle = 2πr
Where r is the radius
In the given diagram, the radius is 15 in
2×π×15 in = 30π in
Evaluate 3 × 5². A. 30 B. 75 C. 150 D. 225
Answer:
B: 75
Step-by-step explanation:
5^2 is 5 times itself twice, so 5 times 5 = 25
3 times 25 is 75
Answer:
Hello! The answer to your question is B. 75.
Step-by-step explanation:
To solve this question, you have to first convert the exponents:
[tex]5^2 = 25[/tex]
Now that you have converted the exponents, you can multiply:
3 × 25 = 75
A trapezoid has bases measuring 5cm and 9cm, and an area of 42cm. Find the height
The height of the trapezoid is 6 cm
How to find the height?The given parameters are:
Bases = 5cm and 9cm
Area = 42 square cm
The height is calculated using
Area = 0.5 * (Sum of bases) * Height
So, we have:
42 = 0.5 * (5 + 9)* Height
This gives
42 = 7* Height
Divide through by 7
Height= 6
Hence, the height of the trapezoid is 6 cm
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He length of the hypotenuse of a right triangle is 24 inches. if the length of one leg is 8 inches, what is the approximate length of the other leg? 16.0 inches 18.4 inches 22.6 inches 25.3 inches
Answer:
22.6
Step-by-step explanation:
a^2 + b^2 = c^2 We know one of the legs and the hypotenuse. The hypotenuse must be c. The leg that we do know can be a or b. It is our choice. I am going to let it be a
8^2 + b^2 = 24^2 Plug in the numbers that I know
64 + b^2 = 576 Square the numbers that I know
b^2 = 512 Subtract 64 from both sides
b = 22.6 Put this in your calculator to find the square root and round.
PLEASE HELP!!!!!!!!!!!!!!
Answer:
The first answer is correct:
[tex]\{\frac{1}{3},-3.45,\sqrt{9}\}[/tex]
Step-by-step explanation:
Since [tex]\frac{1}{3}, -3.45, \sqrt{9}=3[/tex] are all rational numbers, the set that contains those numbers is the set of rational numbers.
In the second set, number [tex]\sqrt{37}[/tex] is irrational number since it can not be written as quotient.
Also in the third and fourth set, numbers [tex]\sqrt{44}[/tex] and [tex]\sqrt{2}[/tex] are irrational numbers.
Therefore, the first answer is correct.
Which of the following best describes a parabola?
A.The locus points equidistant from a given line of symmetry and focus.
B.The locus of points equidistant from two given points.
C.The locus of points equidistant from a given directrix and focus.
D.The locus of points equidistant from a center.
The Parabola is a locus of points equidistant from a single point called focus and a line called Directrix. The correct option is C.
What is a Parabola?A parabola is a U-shaped figure, all the point on the parabola is equidistant from the focus, and a line called Directrix.
The Parabola is a locus of points equidistant from a single point called focus and a line called Directrix.
Therefore, The correct option is C.
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Using the quadratic formula, solve for "t" in
the function: 0= -16t2 + 5t + 104. Keep in
mind that time CANNOT be "negative'!!!
t = 1.1 s
t = 1.9 s
t=2.71 s
t=2.2 s
If x is inversely proportional to y, then as x decreases, y decreases.
Answer:
Yes
Step-by-step explanation:
Let's assume that x=1/y.
For y=1, x=1
For y=2, x=0.5
For y=4, x=0.25
And so on
Two different cubes of the same size are to be painted, with the color of each face being chosen independently and at random to be either black or white. What is the probability that after they are painted, the cubes can be rotated to be identical in appearance
Answer:
Step-by-step explanation:
Define two ways of painting to be in the same class if one can be rotated to form the other.We can count the number of ways of painting for each specific class .
Case 1: Black-white color distribution is 0-6 (out of 6 total faces)
Trivially [tex]1^{2}[/tex]=1 way to paint the cubes.
Case 2: Black-white color distribution is 1-5
Trivially all [tex]\frac{6}{5}[/tex] =6 ways belong to the same class , so [tex]6^{2}[/tex] ways to paint the cubes.
Case 3: Black-white color distribution is 2-4
There are two classes for this case: the class where the two red faces are touching and the other class where the two red faces are on opposite faces. There are 3 members of the latter class since there are 3 unordered pairs of 2 opposite faces of a cube. Thus, there are [tex]\frac{6}{4}[/tex]-3=12 members of the former class . Thus, [tex]12^{2} + 3^{2}[/tex] ways to paint the cubes for this case.
Case 4: Black-white color distribution is 3-3
By simple intuition, there are also two classes for this case, the class where the three red faces meet at a single vertex, and the other class where the three red faces are in a "straight line" along the edges of the cube. Note that since there are 8 vertices in a cube, there are 8 members of the former class and [tex]\frac{6}{3} -8=12[/tex] members of the latter class. Thus, [tex]12^{2} - 8^{2}[/tex] ways to paint the cubes for this case.
Note that by symmetry (since we are only switching the colors), the number of ways to paint the cubes for black-white color distributions 4-2, 5-1, and 6-0 is 2-4, 1-5, and 0-6 (respectively).
Thus, our total answer is[tex]\frac{2*(6^{2} + 1^{2}+ 12^{2}+ 3^{2})+12^{2}+8^{2}}{2^{12} } =\frac{588}{4096} = \frac{147}{1024}[/tex]