Answer:
In 1981 was the building worth double it’s value.
Step-by-step explanation:
Given : A townhouse in San Francisco was purchased for $80,000 in 1975. The appreciation of the building is modeled by the equation : [tex]A=80000(1.12)^t[/tex], where t represents time in years.
To find : In what year was the building worth double it’s value in 1975?
Solution :
The amount is $80,000.
The building worth double it’s value in 1975.
i.e. amount became A=2(80000).
Substitute in the model,
[tex]2(80000)=80000(1.12)^t[/tex]
[tex](1.12)^t=\frac{2(80000)}{80000}[/tex]
[tex](1.12)^t=2[/tex]
Taking log both side,
[tex]t\log (1.12)=\log 2[/tex]
[tex]t=\frac{\log 2}{\log (1.12)}[/tex]
[tex]t=6.11[/tex]
i.e. Approx in 6 years.
So, 1975+6=1981
Therefore, in 1981 was the building worth double it’s value.
The building was worth double its value in [tex]1975[/tex] around the year [tex]1981[/tex]
To determine in what year the building was worth double its value in [tex]1975[/tex], we need to set up the equation based on the appreciation model given:
[tex]\[ A = 80000 \times (1.12)^t \][/tex]
Here, [tex]\( A \)[/tex] represents the current value of the townhouse in dollars, and [tex]\( t \)[/tex] represents the time in years since [tex]1975.[/tex]
We want to find the year [tex]\( t \)[/tex] when the value [tex]\( A \)[/tex] is double the initial value of [tex]\$80,000[/tex]
[tex]\[ A = 2 \times 80000 = 160000 \][/tex]
Now, substitute [tex]\( A = 160000 \)[/tex] into the equation:
[tex]\[ 160000 = 80000 \times (1.12)^t \][/tex]
Divide both sides by [tex]80000[/tex] to solve for [tex]\( (1.12)^t \)[/tex]
[tex]\[ 2 = (1.12)^t \][/tex]
To solve for [tex]\( t \)[/tex], take the natural logarithm ([tex]ln[/tex]) of both sides:
[tex]\[ \ln(2) = \ln((1.12)^t) \][/tex]
[tex]\[ \ln(2) = t \times \ln(1.12) \][/tex]
Now, divide both sides by [tex]\( \ln(1.12) \)[/tex] to solve for [tex]\( t \)[/tex]:
[tex]\[ t = \frac{\ln(2)}{\ln(1.12)} \][/tex]
Using a calculator to find the approximate value:
[tex]\[ t = \frac{0.6931}{0.1178} = 5.88 \][/tex]
Since [tex]\( t \)[/tex] represents years after [tex]1975[/tex], we add this to [tex]1975[/tex] to find the year when the building was worth double its value in [tex]1975[/tex]:
[tex]\[ \text{Year} = 1975 + 5.88 = 1980.88 \][/tex]
In [tex]1981[/tex], the building was worth double its value in [tex]1975.[/tex]
Slope of the line passing through the points (-3,3) and (5,9)
Answer:
m=3/4
Step-by-step explanation:
Slope is equal to the change in y over the change in x, or rise over run.
m=change in y/change in x
The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).
m=y2−y1/x2−x1
Substitute in the values of x and y into the equation to find the slope.
m=9−(3)/5−(−3)
Simplify.
m=3/4
The slope of the line passing through the points (-3,3) and (5,9) is 3/4
The formula for calculating the slope of a line is expressed as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\[/tex]
Given the coordinate (-3,3) and (5,9), substitute the coordinates into the formula as shown below;
[tex]m=\frac{9-3}{5-(-3)}\\m=\frac{6}{5+3} \\m=\frac{6}{8}\\m=\frac{3}{4}[/tex]
Hence the slope of the line passing through the points (-3,3) and (5,9) is 3/4
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In a random sample, 3 out of 400 computer chips are defective. How many chips out of 100000 would be defective?
Answer: x =750
Step-by-step explanation:
Well you just make 3 and 400 a fraction 3/400 and 100,000 and the unknown number a fraction x/100,000. Now you do :
3/400=x/100,000
and figure that out :
3/400=x/100,000
3/400=x/100,000
(3)*(100000)=x*(400)
300000=400x
400x=300000
400x/400=300000/400
x=750 is your answer.
3/400=750/100,000.
Hoped I helped!
Interpret the y-intercept of the graph
Answer:
answer is A
Step-by-step explanation:
An airplane flies a constant speed of 720 km/hour.
e Ilies a constant speed of 720 km/hour. How far can it travel in 4 hours?
Answer:
2880 km
Step-by-step explanation:
(distance) = (rate)*(time).
Here we have:
(distance traveled) = (720 km/hr)(4 hrs) = 2880 km
I could use some help on this, please! :)
i dont wanna just give away the answer so heres a hint
#x stands for # X x or # times x
x is a vairable so the x+13 part will be #+13
figure out what the number is then if you still need help ask me again
In dealing with surface area what is net?
Answer:
Step-by-step explanation:
A net is a drawing that shows the edges and faces of a solid in two dimensions. You can think of a net as what you would get if you “unfolded” a solid. ... The net is made of three congruent rectangles and two congruent equilateral triangles. The surface area is the sum of the areas of the five shapes.
Answer:
three-dimensional figure that represents a cylinder
Step-by-step explanation:
Ture or False
The median better represents
the data than the mean.
Answer:
False
Step-by-step explanation:
What is the constant of proportionality in the equation, Y=4.50x?
Solution:
Given that,
[tex]y = 4.50x[/tex]
We have to find the constant of proportionality in the equation
We know that,
When y varies directly with x, then
[tex]y \propto x\\\\y = kx ---- eqn\ 1[/tex]
Where, "k" is constant of proportionality
From given,
y = 4.50x
Compare the above equation with eqn 1,
k = 4.50Thus, constant of proportionality in the equation y = 4.50x is 4.50
Divide the number in the thousands place by itself and then multiply the answer by 0. Write your answer in the tenths place
To divide the number in the thousands place by itself and then multiply the answer by 0, we can follow a simple process. Let's consider an example where the number in the thousands place is 5. Dividing 5 by 5 gives us 1. Multiplying 1 by 0 gives us 0, which is the answer in the tenths place.
Explanation:To divide the number in the thousands place by itself, we can consider a specific number for better understanding. Let's say the number in the thousands place is 5. Dividing 5 by 5 gives us 1. To find the answer in the tenths place, we need to multiply 1 by 0. The product of 1 and 0 is 0. Therefore, the answer in the tenths place is 0.
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The formula for the surface area of a cube is S 5 6x2
where x is the length of one side. Find the length of the
side of a cube with a surface area of 150 square inches.
Chase plans to buy a new car and determines he can budget $725 monthly for four years. His bank is
offering an 8.25% annual interest rate. What is the maximum loan he can afford to stay in his budget?
Use the formula, A – P/(1+) -11
, where P is the month payment, r is the annual interest rate, n is
the nur
the number of times interest is compounded in one year, and t is the number of years.
O A. $26,000.50
B. $29,555.50
C. $37.425.75
O
D. $52,500.00
Answer:
The correct answer is B. $ 29,555.50
Step-by-step explanation:
Let's calculate A, using the formula provided, this way:
A = P * [(1 + r)ⁿ - 1]/r * (1 + r)ⁿ, where:
P is the month payment = 725
r is the monthly interest rate = 0.0825/12 = 0.006875
n is the the number of months to pay = 4 * 12 = 48
Replacing with the values we know, we have:
A = P * [(1 + r)ⁿ - 1]/r * (1 + r)ⁿ
A = 725 * [(1 +0.006875 )⁴⁸ - 1]/0.006875 * (1 +0.006875 )⁴⁸
A = 725 * 0.38939833/0.006875 * 1.38939833
A = 282.313789/0.009552114
A = 29,555.50
The correct answer is B. $ 29,555.50
The correct option is B. [tex]\$29555.50[/tex]. The maximum loan Chase can afford, while making monthly payments of [tex]\$725[/tex] for [tex]4[/tex] years at an [tex]8.25\%[/tex] annual interest rate.
Given:
Monthly payment [tex]\( P = $725 \)[/tex]
Annual interest rate [tex]\( r = 8.25\% \)[/tex] or [tex]\( 0.0825 \)[/tex] as a decimal
Number of payments per year [tex]\( n = 12 \)[/tex] (since monthly payments)
Number of years [tex]\( t = 4 \)[/tex]
The formula to calculate the present value [tex]\( A \)[/tex] of the loan is:
[tex]\[ A = P \times \frac{1 - (1 + \frac{r}{n})^{-nt}}{\frac{r}{n}} \][/tex]
Now, substitute the given values
[tex]\[ A = 725 \times \frac{1 - (1 + \frac{0.0825}{12})^{-12 \times 4}}{\frac{0.0825}{12}} \][/tex]
First, calculate [tex]\( \frac{r}{n} \)[/tex]
[tex]\[ \frac{0.0825}{12} = 0.006875 \][/tex]
Next, calculate [tex]\( (1 + \frac{r}{n})^{-nt} \)[/tex]
[tex]\[ (1 + 0.006875)^{-48} = 0.7221 \][/tex]
Now substitute these values into the formula for [tex]\( A \)[/tex]
[tex]\[ A = 725 \times \frac{1 - 0.7221}{0.006875} \][/tex]
[tex]\[ A = 725 \times \frac{0.2779}{0.006875} \][/tex]
[tex]\[ A = 725 \times 40.4218 \][/tex]
[tex]\[ A = 29555.50 \][/tex]
Mrs.Roberts charges 25 for a basic cake that serves 12 people. If you want a large cake, it costs an additional $1.25 per serving. Write equation for the total cost or a cake, where y represents total cost and x represents the number of additional servings. How much would a cake that serves 20 people cost?
The total cost of a cake that serves 20 people is $35.
Step-by-step explanation:
Total cost = yNumber of additional servings = xThe number of additional servings = 20 - 12 = 8. (x=8)The equation can be formed as:
Total cost = basic cost + (No. of additional serving [tex]\times[/tex] cost per additional serving)y = 25 + x1.25Substitute x=8 in the above equationy = 25 + 8(1.25)y =25+10y = 35Therefore, the total cost of a cake that serves 20 people is $35.
-10 + 20p + 6p = -16
Answer: p = 0.23
Step-by-step explanation:
-10 + 20p + 6p =-16
To find the value of p
Step 1: combine like terms
20p + 6p = -16 + 10
26p = 6
Divide both sides by 26
p = 6/26
P= 0.23
I hope this helps.
Answer:
p = -3/13
Explanation:
1. add 10 onto right side
2. combine like terms
3. divide by 26 to get p by itself
4. simplify
Find the value of 10! / (10-2) !
Answer:
The answer is 90
The value of the 10!/(10 - 2)! is 90 after simplification of the factorial option (C) 90 is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have given an expression:
10!/(10 - 2)!
The sign '!' represents the factorial of the number.
As we know,
If factorial of any number can be evaluated:
n! = n(n - 1)(n - 2)(n - 3)(n - 4).......1
10! = 10×9×8×7×6×5×4×3×2×1
or
10! = 90(8!)
(10 - 2)! = 8!
= 90(8!)/(8)!
90
8! is canceled out from the numerator and denominator
Thus, the value of the 10!/(10 - 2)! is 90 after simplification of the factorial option (C) 90 is correct.
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An athlete plans to row upstream a distance of 6 kilometers and then return to his starting point in a total time of 4 hours. If the rate of the current is 2 km/hr, how fast should he row.
Answer:
3.5 kilometers per/hour
Step-by-step explanation:
6/4= 1.5
1.5+2=3.5
genas new outfit originally cost 75. she received 20% off how much did genas outfit cost
Answer:
$75 x .20=$15
75-15=$60
To find out how much Gena's outfit cost after the 20% discount, subtract the discount amount from the original price.
Explanation:To find out how much Gena's outfit cost after the 20% discount, we can use the formula:
The discount amount = original price x discount percentage
In this case, the discount amount = $75 x 0.20 = $15.
Therefore, Gena's outfit cost after the discount is:
Original price - discount amount = $75 - $15 = $60.
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What is 1099 divided by 54
Answer:
20.4
Step-by-step explanation:
20.35185185185185
You have to round it because in the hundredth place #5 is over 5 so, it rounds so the answer is 20.4.
Anything more than 5, 6, 7, 8, 9 ^ rounds.
The perimeter of a rectangle is 15x + 17y
If the length is 7/2x + 7y then find the width of the rectangle.
Answer choices:
A. 4x + 3/2y
B. 8x + 3y
C. 8x + 10y
D. 4x + 3y
The width of the rectangle, given its perimeter and length, is calculated using the formula for the perimeter of a rectangle. By reorganizing the terms and isolating the width, we find that the width is 4x + 3/2y, which is Answer Choice A.
Explanation:The perimeter of a rectangle is given as 15x + 17y. The length is provided as 7/2x + 7y. To find the width, we need to remember that the perimeter of a rectangle is twice the sum of its length and width (P = 2l + 2w). Let's denote the width of the rectangle as 'w'.
So, the equation representing the perimeter is:
15x + 17y = 2(7/2x + 7y) + 2w
Now let's multiply out the factors on the right side:
15x + 17y = 2(7/2x) + 2(7y) + 2w
15x + 17y = 7x + 14y + 2w
To find 'w', we need to move all terms involving 'w' to one side of the equation and all other terms to the other side:
2w = 15x + 17y - (7x + 14y)
2w = 15x - 7x + 17y - 14y
2w = 8x + 3y
Divide throughout by 2 to find 'w':
w = 4x + 3/2y
The width of the rectangle is 4x + 3/2y, which corresponds to Answer Choice A.
six episodes of a tv series last total of five hours, How many minutes on average does an episode last
Step-by-step explanation:
[tex]5 \: hours \: = 5 \times 60 = 300 \: min \\ minutes \: per \: episode = \frac{300}{6} \\ = 50 \\ [/tex]
Hence, each episode lasted for 50 minutes on an average.
On average, each episode of the TV series lasts 50 minutes, calculated by converting the total viewing time of five hours to 300 minutes and dividing that by the number of episodes, which is six.
To calculate the average duration of an episode, we need to convert the total time of all episodes from hours to minutes and then divide by the number of episodes.
There are 60 minutes in one hour, so five hours equates to 300 minutes (5 hours × 60 minutes/hour = 300 minutes). With six episodes in total, we divide the total minutes by the number of episodes to find the average length of one episode.
300 minutes / 6 episodes = 50 minutes per episode.
Therefore, on average, each episode of the TV series lasts 50 minutes.
Which expression is equivalent to 30 divided by (3+x )
The expression 30 divided by (3+x) is already presented in its simplest form which is 30 / (3 + x).
The question which expression is equivalent to 30 divided by (3+x) pertains to the simplification of algebraic expressions, a basic concept in algebra. To solve or simplify this expression directly, it remains 30 / (3 + x), as there is no further simplification that can be done without additional context or constraints on the variable x. In algebra, expressions are simplified or manipulated using algebraic rules, but in this case, the expression is already in its most simplified form unless specific values are provided for x.
Tamiko got a check for 109.60 and a small bonus check for 34.15.What is the net result of her transactions using the result from part A.She wants to save 3/5 of this amount.How much will she save?
a) Net result of Tamiko's transactions = $143.75
b) Total amount she can save = $86.25
Step-by-step explanation:
Step 1 :
Given,
Amount Tamiko got in her first check = $109.60
Amount of the bonus check = $34.15
Fraction of the amount she wants to save = [tex]\frac{3}{5}[/tex]
We need to find the net results of her transactions and the amount she will save
Step 2 :
The new result of her transactions can be computed by adding the amount she has received through both the check.
Total amount she received = 109.60 + 34.15 = 143.75
Total amount she can save = [tex]\frac{3}{5}[/tex] × 143.75 = 86.25
Step 3 :
Answer :
a) Net result of Tamiko's transactions = $143.75
b) Total amount she can save = $86.25
Solve.
The answer must be a fraction. Solve by substituting.
Answer: x = -14/5
Step-by-step explanation: We shall begin by expanding the brackets for both sides of the equation
-2/3 (x + 2) = 1/6 (x + 6)
(-2x/3) -4/3 = (x/6) + 1
By collecting like terms we now have
(-2x/3) - (x/6) = 1 + 4/3
(-4x - x)/6 = 7/3
-5x/6 = 7/3
By cross multiplication we now have
-5x (3) = 7 (6)
-15x = 42
x = -(42/15) {simplify further by dividing the RHS by 3}
x = -14/5
Therefore x equals, minus fourteen over five (-14/5)
You jump off a 24 foot high cliff and your fall is modeled by the function:
h(t) = -16t2 + 8t + 24
When would you reach 16 feet above the water?
A. 1/4 second
B. 1 second
C. 1/2 second
D. 8 seconds
Answer: B) 1 second
Step-by-step explanation:
plug 16 (final height) into the equation given:
16=-16t^2+8t+24, and solve for t.
x will equal -1/2 or 1
disregard the negative because you can’t have time.
To reach 16 feet above the water, you would reach that height after approximately 1/2 second. Option C
To find when you would reach 16 feet above the water, set the function h(t) equal to 16 and solve for t:
-16t2 + 8t + 24 = 16
Combine like terms to get:
-16t2 + 8t + 8 = 0
Now, you can use the quadratic formula to solve for t:
t = (-b ± √(b2 - 4ac)) / (2a)
Plug in the values of a, b, and c from the equation:
t = (-8 ± √(82 - 4(-16)(8))) / (2(-16))
Simplify the expression inside the square root and solve for t to get the answer:
t ≈ 1/2 second
Option C
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you are asked to draw a triangle with side length of 10in,7in and 2in how many triangles like this can you draw
15 points: can someone help me with this thank you. (all separate equations)
solve for y: 6x+3y=12
solve for k: 2p-k=3
solve for w: 6v-2w=10
Step-by-step explanation:
[tex]6x+3y=12\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\6x-6x+3y=12-6x\\\\3y=12-6x\qquad\text{divide both sides by 3}\\\\\dfrac{3y}{3}=\dfrac{12}{3}-\dfrac{6y}{3}\\\\\large\boxed{y=4-2y}\\\\===================[/tex]
[tex]2p-k=3\qquad\text{subtract}\ 2p\ \text{from both sides}\\\\2p-2p-k=3-2p\\\\-k=3-2p\qquad\text{change the signs}\\\\k=-3+2p\\\\\large\boxed{k=2p-3}\\\\===================[/tex]
[tex]6v-2w=10\qquad\text{subtract}\ 6v\ \text{from both sides}\\\\6v-6v-2w=10\\\\-2w=10-6v\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2w}{-2}=\dfrac{10}{-2}-\dfrac{6v}{-2}\\\\w=-5+3v\\\\\large\boxed{w=3v-5}\\\\===================[/tex]
evaluate expression 5a+b for A=6 and b=3
Answer:
33
Step-by-step explanation:
5a+b
if a = 6 and b = 3, substitute these values into the expression:
5a+b
= 5(6) + 3
= 30 + 3
= 33
Hope This Helps!!!!!!!!!!!!!!
Answer:
33
Step-by-step explanation:
5a+b
if a = 6 and b = 3, substitute these values into the expression:
5a+b
= 5(6) + 3
= 30 + 3
= 33
How long is AB please explain how you answered
Answer:
AB = [tex]4\sqrt{3}[/tex]
Step-by-step explanation:
30-60-90 theorem, usually x is used to explain but I will use y since x is in your problem, just substitute any variable for y
in a 30 -60 -90 triangle
the length opposite the 30 degrees is y
the length opposite the 60 degrees is y[tex]\sqrt{3}[/tex]
the length opposite the 90 degrees is 2y
since y[tex]\sqrt{3}[/tex] = 6
y = 6/[tex]\sqrt{3}[/tex]
rationalizing the denominator
[tex]\frac{6}{\sqrt{3} } *\frac{\sqrt{3}}{\sqrt{3}}[/tex] = [tex]\frac{6\sqrt{3} }{3} = 2\sqrt{3}[/tex]
if y = [tex]2\sqrt{3}[/tex], 2y = [tex]4\sqrt{3}[/tex]
Which expression is equivalent to (18x + 9k) + (2x + 6k)? 16 x + 3 k 20 x + 15 k 20 x + 16 k 36 x + 54 k. Need it soon. Thx!
Answer: 20x + 15k
Step-by-step explanation:
Lose the parentheses and add the like terms. Add 18x and 2x, then add 9k and 6k. That's all there is to it.
The equivalent expression of (18x + 9k) + (2x + 6k) is 20x + 15k.
The correct option is A.
What are the equivalent expressions?Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
We have an expression,
(18x + 9k) + (2x + 6k).
To find the equivalent expressions:
Simplifying,
(18x + 9k) + (2x + 6k),
= 20x + 15k
This is the equivalent expression.
Therefore, 20x + 15k is the equivalent expression.
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company 2 charges 4600$ for the first 550 feet of fence and 29 for each additional feet.find the cost if company 2 completes the job the total fence is 660
To calculate the total cost for a 660 feet fence by Company 2, subtract the initial 550 feet covered by the flat fee from the total length, multiply the additional feet by the per-foot cost, and add the flat fee to get the final cost, which is $7790.
Explanation:The student is asking about calculating the total cost for installing fencing, which involves initial fees and additional per unit costs. In this case, Company 2 charges a flat fee for the first 550 feet of fence and then an additional fee for each foot beyond that.
To find the total cost when Company 2 installs a fence of 660 feet, we first calculate the number of feet beyond the initial 550 feet. This is 660 - 550 = 110 feet. Then, we multiply the additional feet by the cost per additional foot: 110 feet x $29/foot = $3190.
Lastly, we add the initial flat fee of $4600 to the cost for the additional feet to get the total cost: $4600 + $3190 = $7790.
linear, exponential, or neither?
Answer:
A) Linear
Step-by-step explanation:
For a linear relation, there will be a constant rate of change
For an exponential relationship, there will be a multiplicative rate of change.
For x-values, there is a constant difference of
[tex]d = 4 - - 3 = 11 - 4 = 18 - 11 = 7[/tex]
For the y-values, there is a constant difference of
[tex]b = 1 - - 3 = 5 - 1 = 9 - 5 = 4[/tex]
The rate of change of the function represented by the table is
[tex]m = \frac{change \: in \: y}{change \: in \: x} = \frac{4}{7} [/tex]
The equation can be derived as:
[tex]y + 3 = \frac{4}{7} (x + 3)[/tex]
This is a linear relationship