if the rate of inflation is 3.9% per year, the future price pt (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today.
The current price of the item = 400 dollars
The price in 8 years from today = 543.23 dollars
Given the rate of inflation = 3.9%
The exponential function modelling the future price, p(t) in t years for a certain item is, [tex]p(t)=400(1.039^t)[/tex]
We have to find the current price of the item. This is given by substituting t = 0 in p(t).
That is, p(0) = 400 x 1 = 400 dollars
Therefore current price = 400 dollars
To find the price of the product in 8 years, substitute t = 8 in p(t).
That is, p(8) = [tex]400(1.039^8)[/tex] = 543.23 dollars
Therefore, the future price of the item in 8 years = 543.23 dollars
The question is incomplete. Find out the complete question below:
If the rate of inflation is 3.9% per year, the future price p(t) (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today. p(t)= 400(1.039^t).Find the current price of the item and the price 8 years from today.
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true or false: the difference between cross-sectional and time series data is whether the data is evaluated at a single point in time or multiple points in time
The statement "the difference between cross-sectional and time series data is whether the data is evaluated at a single point in time or multiple factors in time" is true.
The distinction between cross-sectional data and time-series data is that time-series data takes into account the identical variables over a period of time, whereas cross-sectional data makes use of specific records for a specific factor in time.
A data set may be both time series and cross sectional.
When the records of go sectional records is regressed, the defined and explanatory variables are all related to the identical single length or point in time.
Time-series and cross-section (TSCS) data collectively are normally analyzed in political technology and associated disciplines.
Therefore, the statement "the difference between cross sectional and time series data is whether the data is evaluated at a single point in time or multiple factors in time" is true.
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Please procedure and solution
2 x |-6|-3 x |2|+|-14|=
Applying the rule of modulus for given values, the expression will result to 20.
What is Modulus or Absolute ValuesThe modulus of a value for example |a|=a if a is greater than or equal to zero
and also
|a|=-a if a is less than zero
In the expression given; the modulus of -6 written as
|-6|=-(-6) this is because the value is less than zero
The modulus of 2 written as; |2|=2 this is because the value is greater than zero. and;
|The modulus of -14 written as; |-14|= -(-14) since the value is less than zero.
Hence, we can rewrite the expression as;
we deal with multiplication first following the rules of BODMAS
2×-(-6)-3×2+[-(-14)]
2×6-6+14
and thus adding values
12+14-6
and finally we subtract;
26-6
which will results to the solution of 20.
Are these repeating or terminal?
Answer:-5 1/3 is repeating and 1 1/4 is terminal
Step-by-step explanation:
Answer: Terminal
Step-by-step explanation: yw :)
At 1pm,there were 16 seagulls on the beach .At 3 pm, there were 40 seagulls .What is the constant rate of change
Answer:
Step-by-step explanation:
During those 2 hours 24 more seagulls arrived.
Answer:
it is 12 seagulls per hour
Step-by-step explanation:
how to Solve 5 |2x - 1 +20=3
the correct value for x is -1.2, 2.2
Given 5 | 2x - 1 | + 20 = 3
Modulus of a number
The modulus or absolute value, of a number, denoted |x+y| is calculated as
|x + y | =1
x + y = ±1
We need to solve for the value of x
5 | 2x - 1 | = 3 - 20
5 | 2x - 1 | = -17
| 2x - 1 | = - 17 / 5
| 2x - 1 | = - 3.4
2x - 1 = ± (- 3.4)
2x - 1 = -3.4 2x -1 = 3.4
2x = - 3.4 + 1 2x = 3.4 + 1
2x = - 2.4 2x = 4.4
x = - 1.2 x = 2.2
Therefore, the value for x is -1.2, 2.2
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The Sugar Sweet Company is going to transport its sugar to market. It will cost $3500 to rent trucks plus $225 for each ton of sugar transported. The total cost, C (in dollars), for transporting N tons is given by the following function. C(n)=3500+225n)
Answer:to answer this question you have to look at what the relationship is between tones of sugar and the equation C(n) = 6,500 + 225n. The question gave you a hint in parenthesis in the form of (n) tons. This statement means that the amount of sugar is n so for question 1 the 13 tons is the n value.
Q1:
C(13) = 6,500 + 225*13
C(13) = 6,500 + 2,925
C(13) = 9,425
so what does the 9,425 mean? This is the cost to transport 13 tons of sugar.
Q2:
so this part n is unknown and we are given the C(n) number.
11,450 = 6,500 + 225n
subtract the 6500 from both sides
11,450 - 6,500 = 225n
evaluate
4,950 = 225n
I don't like the n on the right side so I am going to rewrite the equation
225n = 4,950
divide by 225
n = 4,950/225
evaluate
n = 22
So this result means that the company would transport 22 tones of sugar.
Have a great day!
Step-by-step explanation:
I really need help with these and they are due tomorrow... 100 points if you could please answer all
1) The time taken is 2.47 s
2) The time taken is 21.4 s
3) The time taken is 1.2 s
4) The time taken is 81 s
5) The time taken is 5.7 s
What is the time taken for the free fall?Using the equation of kinematics under gravity we knw that;
h = ut + 1/2 gt^2
h = height from which it fell
u = initial velocity
g = acceleration due to gravity
t = time taken
Given the fact that the objects were dropped from a height u = 0 m/s
h = 1/2 gt^2
t = √2h/g
1) √2 * 30/9.8
t =2.47 s
2) t = √2 * 2250/9.8
t = 21.4 s
3) t = √2 * 7/9.8
t = 1.2 s
4) t = √2 * 32000/9.8
t = 81 s
5) t = √2 * 160/9.8
t = 5.7 s
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a hexagon inscribed in a circle has three consecutive sides each of length 3 and three consecutive sides each of length 5. the chord of the circle that divides the hexagon into two trapezoids, one with three sides each of length 3 and the other with three sides each of length 5, has length equal to $m/n$, where $m$ and $n$ are relatively prime positive integers. find $m n$.
According to given conditions, m+n is equal to 409.
Consider the diagram below.
In the hexagon ABCDEF, let
AB = BC = CD = 3;
DE = EF = FA = 5;
Arc BAF is equal to one-third of the circle's circumference.
Hence, ∠BCF = ∠BEF = 60°;
Similarly, ∠CBE = ∠CFE = 60°;
Let the point of intersection of BE and CF be P, BE and AD be Q and CF and AD be R.
∴ Δ EFP and Δ BCP are equilateral, and so Δ PQR is also equilateral.
Also, ∠ BAD and ∠ BED subtend the same arc and so do ∠ ABE and ∠ ADE.
∴ Δ ABQ is similar to Δ EDQ
[tex]\frac{AQ}{EQ} = \frac{BQ}{DQ} = \frac{AB}{ED} = \frac{3}{5}[/tex]
Also,
[tex]\frac{\frac{AD - PQ}{2} }{PQ + 5} = \frac{3}{5}[/tex]
and [tex]\frac{3 - PQ}{\frac{AD + PQ}{2} } = \frac{3}{5}[/tex]
On solving these simultaneous equations, we get AD = 360/49
∴ m + n = 409.
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1. The distance between Earth and Mars is approximately 4.35 × 107 miles.
What is this distance in standard form?
A 435,000 miles
B 4,350,000 miles
C43,500,000 miles
D 435,000,000 miles.
The distance between Earth and Mars in the standard form is 43, 500, 000 miles.
The correct answer is an option (C)
In this question we have been given the distance between Earth and Mars.
The distance between Earth and Mars is approximately 4.35 × 10^7 miles.
We need to write above distance between Earth and Mars in the standard form.
So, we get an expression,
4.35 × 10^7 miles
= 435 × 10^5 miles
= 435 × 100, 000 miles
= 43, 500, 000 miles
Therefore, the distance between Earth and Mars in the standard form is 43, 500, 000 miles.
The correct answer is an option (C)
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The midpoint of overline AB is M(3, 0) If the coordinates of A are (2, 4) what are the coordinates of B?
Answer: B(4,-4)
Step-by-step explanation:
M(3,0) A(2,4) B(x,y)=?
[tex]\displaystyle\\x_M=\frac{x_A+x_B}{2} \\\\Multiply\ both\ parts\ of\ the\ equation\ by \ 2:\\2x_M=x_A+x_B\\2x_M-x_A=x_A+x_B-x_A\\2x_M-x_A=x_B\\x_M=3\ \ \ \ \ x_A=2\\Hence,\\2*3-2=x_B\\6-2=x_B\\4=x_B\\Similarly:\\2y_M-y_A=y_B\\y_m=0\ \ \ \ \ y_A=4\\Hence,\\2*0-4=y_B\\0-4=y_B\\-4=y_B\\Thus,\ B(4,-4)[/tex]
3/6 X 2/4?
A. 6/24
B. 18/8
C. 8/18
What is an equivalent form of 12(p + 5) − 11(3q + 4)?
−21pq + 1
60p − 77q
12p − 33q + 16
12p − 33q + 9
Answer:
12p − 33q + 16
Step-by-step explanation:
Let's simplify step-by-step.
12(p+5)−11(3q+4)
Distribute:
=(12)(p)+(12)(5)+(−11)(3q)+(−11)(4)
=12p+60+−33q+−44
Combine Like Terms:
=12p+60+−33q+−44
=(12p)+(−33q)+(60+−44)
=12p+−33q+16
=12p−33q+16
Order the following fractions from greatest to least 3/4 4/6 4/8
Answer:
4/8, 4/6, 3/4
Step-by-step explanation:
3/4 = 18/24
4/6 = 16/24
4/8 = 12/24
18>16>12
Find the value of k in the data set so that f(x) is a linear function.
x = {-7, -2, 2, 5}
f(x) = {-15, k, 3, 9}
In order for f(x) to be a linear function, determine the value of k in the data set.
x = {-7, -2, 2, 5}
f(x) = {-15, k, 3, 9}
The value of k is {-5}.
Given that to find the value of k in the data set such that the data set represents a linear function.
Linear Function is a straight line on the coordinate plane is represented by a linear function. The formula for a linear function is f(x) = mx + b, where m and b are real values.
Here, f(x) or y is the dependent variable, m is a slope of the line, x is the independent variable and b is the y-intercept.
Here,(x,f(x)) are {(-7,-15),(-2,k),(2,3),(5,9)}
The slope of the function,
(x, f(x)) = (2,3) and (5,9)
Slope formula is m=[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
Slope m= [tex]\frac{9-3 }{5-2}[/tex]
Slope m=[tex]\frac{6}{3}[/tex]
Slope m=2.
Using the point slope form, determine the linear function's equation.
[tex]y-y_{1} =m(x-x_{1})[/tex]
Here, [tex](x_{1},y_{1})=(-7,-15)[/tex] and m=2
We get
y + 15 = 2 (x + 7)
y = 2x - 1
Now at x = -2 and f(x) = k
k = 2(-2) - 1
k = -4-1
k=-5
Therefore, the value of k is -5.
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Freida is a clothing factory manager and wants to minimize her costs in the upcoming production cycle.
Her bosses have ordered that at least 100 shirts (s) and more than 150 pairs of pants (p) must be made to
meet inventory requirements. The factory cannot produce more than 800 garments in total and at east as
many pants as shirts produced. The total garments produced must also be at least 300. Shirts cost $8 each
to manufacture and sell for $22 while pants cost $5 to make and sell for $15. The factory costs $600 to run no
matter how many garments are made. How many shirts and pants should be made in order to minimize
costs?
1. Fill in the chart with the inequalities that come from this problem.
PROBLEM CONSTRAINTS
...at least 100 shirts
...more than 150 pairs of pants
. cannot produce more than 800 garments
„.at least as many pants as shirts produced
garments produced must be at least 300
2. Write the cost minimization equation.
3. Graph the system Of inequalities on the following graph or in Desmos.
4. How many Of each product should Freida make to minimize her costs?
5. profit is revenue minus costs. Write the profit equation (don't forget to include the $600 cost
independent of how many garments are produced)
6. Would your answer of what to produce be different if you were trying to maximize profit
instead of minimize costs? If so, what would be the new optimal production numbers?
Answer:
Step-by-step explanation:
f+an=g Solve for 'f'.
Answer:
f = g - an
Step-by-step explanation:
f + an = g
To isolate f, we need to do inverse (opposite) operation for an.
The opposite of +an is -an
f = g - an
Hope this helps :)
Have a great day!
Can someone please help me i'm running out of time please!!!!
Answer:
10 and 1/2 for the first, and 3 and 3/4 for the second
Step-by-step explanation:
if my new price is 54 and my old price was 68 what is the difference between my new and old price
Answer:13
Step-by-step explanation:
68-54=14
14-1=13
Solve the equation. Check the solution
11-10x-7-4x=6
X= =(Type an integer or a
(Type an integer or a simplified fraction.)
Answer: x=-1/7
Step-by-step explanation:
11-10x-7-4x=6
11-7-10x-4x=6
4-14x=6
-14x=2
x=-1/7
find the radius r of the circle if an arc of length 20 cm on the circle subtends a central angle of 40°. (round your answer to two decimal places.)
From the arc length given radius yielded is 22.91 cm.
What is the arc length?
The arc period estimate for a circle equals the radius of the circle. whilst r is in radians, the system for arc length may be written as arc length = r. Arc period = (/180) r, wherein r is the radius and L is the length of an arc.The radius is inversely proportional to the arc period.The length of an arc is the space between its ends measured along a circle (in units like inches or centimeters).The primary angle:
40°
Arc size
20 cm
Recall the arc length formula.
[tex]l=(\frac{Theta}{360} )*(2\pi r)[/tex]
Inserting the values:
20 =[tex]\frac{40}{360} *(2\pi r)[/tex]
[tex]r=\frac{36(20)}{10\pi }[/tex]
=72/π
=22.918cm the radius is.
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9 + k + 5 = 21
pls help
Answer:
k= 7
Step-by-step explanation:
First let's add like terms: a+b+a=c: a²+b=c
k+9+5=21
k+14=21
Subtract 14 from both sides of the equation
k+14-14=21-14
K=7
Hi!
[tex]\tt{9+k+5=21}[/tex]
Step 1: Combine like terms.
[tex]\tt{9+5+k=21}[/tex]
[tex]\tt{14+k=21}[/tex]
Step 2: Subtract 14 from both sides.
[tex]\tt{k=7}[/tex] [tex]\checkmark[/tex]
Have a great day!
Hope that helps. :)
-Stargazing & daydreaming -
Answer number 12 please thank you
Answer:
D. (A U C) ∩ B
Step-by-step explanation:
12.
A = {-2, -1, 0, 1}
B = {0, 1, 2, 3}
C = {-2, 0, 2, 4}
A. A U B = {-2, 1, 0 , 1, 2, 3}
B. A U (C ∩ B} = A U {0, 2} = {2, 1, 0, 1, 2}
C. B ∩ C = {0, 2}
D. (A U C) ∩ B = {-2, -1, 0, 1, 2, 4} ∩ {0, 1, 2, 3} = {0, 1, 2}
please help with these 2 questions in math!! thank uu!!
Answer:
sorry if wrong again but for a put (r+y) (a+b)
for b put (pq-[tex]r^{2}[/tex]) x (9-1)
Step-by-step explanation:
pansy measured the height of a window frame as 5.12 feet, but the actual height was 6 feet. what is the percentage of error in pansy's measurement?
The percentage of error in Pansy's measurement is 14.67%
In the given statement is :
Pansy measured the height of a window frame as 5.12 feet, but the actual height was 6 feet.
We know that
Percentage error can be calculated using the formula: (what was measured - the actual measurement) / actual measurement × 100%.
Thus:
The height that was measured = 5.12 feet
Actual measurement of the height = 6 feet
Percentage error = (6 - 5.12) / 6 × 100
Percentage error = 14.67
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Simplify.
H+
1 to the power of 1/4
Answer:
noooo
Step-by-step explanation:
Someone Help please
Answer:
is B espero que esto te ayude yo también estoy nececicando ayuda con mis trabajos
The sum of 3 consecutive even numbers is 60. What are they?
Answer:
18, 20 and 22.
Step-by-step explanation:
Let the lowest number be n, then:
n + n + 2 + n + 4 = 60
3n + 6 = 60
3n = 54
n = 18.
So the other 2 are 20 and 22.
can anyone help me solve this (-5z)³
Answer:
-125z³
Step-by-step explanation:
cube each value
(-)³x(5)³x(z)³
negative sign multiplied by three is negative
- x - x - = -
5 x 5 x 5 = 125
z x z x z = z³
answer = -125z³
Find the equation of a line using y = mx + b given the slope is 2 and the y-intercept is (0,2).
Answer:
y=2x+2
Step-by-step explanation:
y=mx+b where:
m=slope; b=y intercept
Therefore, simply plug in values for (m) and (b)
(m=2); (b=2)
and you're left with the equation (y=2x+2)