Using data from the previous table, construct an exponential model for this situation.A ( t ) =What will be the value when t=8, rounded to 2 decimal places?
Answers
Answer
• Exponential model
[tex]A(t)=13.60(1+0.25)^{t}[/tex][tex]A(8)\approx81.06[/tex]Explanation
The exponential model equation can be given by:
[tex]A(t)=C(1+r)^t[/tex]where C is the initial value, r is the rate of growth and t is the time.
We can get the initial value by evaluating in the table when t = 0. In this case the value A(0) = 13.60. Then our equation is:
[tex]A(t)=13.60(1+r)^t[/tex]Now we have to get r by choosing any point and solving for r. For example, (3, 26.56). By replacing the values and solving we get:
[tex]26.56=13.60(1+r)^3[/tex][tex]\frac{26.56}{13.60}=(1+r)^3[/tex][tex](1+r)^3=\frac{26.56}{13.60}[/tex][tex]\sqrt[3]{(1+r)^3}=\sqrt[3]{\frac{26.56}{13.60}}[/tex][tex]1+r=\sqrt[3]{\frac{26.56}{13.60}}[/tex][tex]r=\sqrt[3]{\frac{26.56}{13.60}}-1\approx0.2500[/tex]Thus, our rate is 0.25, and we can add it to our equation:
[tex]A(t)=13.60(1+0.25)^t[/tex]Finally, we evaluate t = 8:
[tex]A(8)=13.60(1+0.25)^8=81.06[/tex]Related Questions
1. what is the area of the board shown on the scale drawing? explain how you found the area.2. how can Adam use the scale factor to find the area of the actual electronics board? remember, he uses a different method than Jason.3. what is the area of the actual electronics board?
Answers
Answer:
1. 1800 square cm.
2. See below
3. 45000 square cm.
Explanation:
Part 1
The dimensions of the drawing are 36cm by 50cm.
[tex]\begin{gathered} \text{The area of the board}=36\times50 \\ =1800\operatorname{cm}^2 \end{gathered}[/tex]Part 2
Given a scale factor, k
If the area of the scale drawing is A; then we can find the area of the actual board by multiplying the area of the scale drawing by the square of k.
Part 3
[tex]\begin{gathered} \text{Area of the scale drawing}=1800\operatorname{cm}^2 \\ \text{Scale Factor,k=5} \end{gathered}[/tex]Therefore, the area of the actual drawing will be:
[tex]\begin{gathered} 1800\times5^2 \\ =45,000\operatorname{cm}^2 \end{gathered}[/tex]An excursion boat traveled from the Ferry Dock to Shelter Cove. How many miles did ittravel?
Answers
The situation forms a right triangle:
Where x is the distance traveled.
We can apply the Pythagorean theorem:
c^2 =a^2 + b^2
Where:
c= hypotenuse = x
a & b= the other 2 sides = 5 ,12
Replacing:
x^2 = 5^2 + 12^2
x^2 = 25+144
x^2 = 169
x= √169
x= 13
Distance traveled = 13 miles
Hello! I think this works but I'm not 100% sure
Answers
Given:
1 counsellor for every 9 campers.
Lets' determine the type of variation and write the equation.
Here, we can see that for every 9 campers, there is one extra counsellor. This means that as the number of campers increase, the number of counsellors will also increase.
Since one variable as the other increases, this is a direct variation.
Hence, we have the equation which represents the direct variation below:
y = 9x
Where x represents the number of counsellors and y represents the number of campers.
ANSWER:
Direct variation.
y = 9x
Which of the following natural phenomena follows an elliptical motion?Question content area bottomPart 1Choose the correct answer below.A.A ball thrown from one person to anotherB.The path of marbles when rebounding from a curved surfaceC.Sound wavesD.The motion of the planets around the sun
Answers
The natural phenomena that follows an elliptical motion is:
D.
The motion of the planets around the sun
hello! i need help on this question and the (select) questions have the options of 1997 to 2006
Answers
To find the average rate of change, we use the following formula
[tex]r=\frac{f(b)-f(a)}{b-a}[/tex]Where a = 1998, f(a) = 856, b = 2001, and f(b) = 1591.
[tex]r=\frac{1591-856}{2001-1998}=\frac{735}{3}=245[/tex](a) The average rate of change between 1998 and 2001 is 245.We use the same formula between 2002 and 2006, where a = 2002, f(a) = 1483, b = 2006, and f(b) = 745.
[tex]r=\frac{745-1483}{2006-2002}=\frac{-738}{4}=-184.5[/tex](b) The average rate of change between 2002 and 2006 is -184.5.(c) As you can observe, the population was increasing from 1997 to 2001.(d) The population was decreasing from 2001 to 2006.ABCD is a rectangle. Find the length of AC and the measures of a and f.
Answers
SOLUTION
Consider the diagram
We need to obtain the value of length AC
Using the pythagoras rule, we have
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Written as a percent, what is the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5?A.20%B.40%C.60%D.80%
Answers
Given:
There are given that the spinner with 5 equal parts numbered 1 to 5.
Explanation:
In the given spinner, there are given the number: 1, 2, 3, 4, 5.
Now,
From all the given numbers, there are 3 odd numbers: 1, 3, and 5.
So,
From the probability:
[tex]P=\frac{Total\text{ number of odd numbers in the given spinner}}{Total\text{ numbers on the spinner}}[/tex]Then,
[tex]\begin{gathered} P=\frac{3}{5} \\ P=0.6 \end{gathered}[/tex]Now,
For the percentage:
[tex]\begin{gathered} P=0.6\times100\% \\ P=60\% \end{gathered}[/tex]Final answer:
Hence, the correct option is C.
Solve for w. 3w + 2w - 3w = 8
Answers
Answer
w = 4
Explanation
We are asked to solve for w
3w + 2w - 3w = 8
5w - 3w = 8
2w = 8
Divide both sides by 2
(2w/2) = (8/2)
w = 4
Hope this Helps!!!
help meeeeeeeeee pleaseee !!!!!
Answers
The values of the functions are:
a. (f + g)(x) = x² + 3x + 5
b. (f - g)(x) = x² - 3x + 5
c. (f * g)(x) = 3x³ + 15x
d. (f/g)(x) = (x² + 5)/3x.
How to Determine the Value of a Given Function?For any given function, we can evaluate the function by plugging in the equation of each of the functions in the given expression.
Thus, we have the following given functions:
f(x) = x² + 5
g(x) = 3x
a. Find the value of the function for the expression (f + g)(x).
We are required here to add the expression for each of the functions, f(x) and g(x) together, which is:
(f + g)(x) = (x² + 5) + (3x)
(f + g)(x) = x² + 3x + 5
b. Evaluate (f - g)(x) by subtracting the function g(x) from f(x):
(f - g)(x) = (x² + 5) - (3x)
(f - g)(x) = x² - 3x + 5
c. Find (f * g)(x):
(f * g)(x) = (x² + 5) * (3x)
(f * g)(x) = x²(3x) + 5(3x)
(f * g)(x) = 3x³ + 15x
d. Find (f/g)(x):
(f/g)(x) = (x² + 5)/3x
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A credit card bill for $562 was due on September 14. Purchases of $283 were made on September 19, and $12 was charged on September 28. A payment of $350 was made on September 25. The annual interest on the average daily balance is 19.5%. Find the finance charge due (in dollars) on the October 14 bill. (Use 365 for the number of days in a year. Round your answer to the nearest cent.)
Answers
The annual interest on a daily basis with 19.5%, then the finance charge due on October 14 will be $623.
What is interest?In the fields of finance and economics, interest is the payment made at a set rate by a borrower or deposit-taking financial institution to a lender or depositor in excess of the principal amount (the amount borrowed).
So, the finance charge will be;
(+) $ 562 due on sep 14, $ 562 x (19.5 x31) / (100 x 365) = $ 9.20
(+) purchase $ 283 on Sep 19, $ 283 x (19.5x26 ) / (100 x365) = $ 2.42
(+) finance charge on sep 28, $ 18 x(19.5 x17 ) / (100 x 365) = $ 0.17
(-) Repayment on 25 sep , $ 250 x (19.5 x20 ) / (100 x 365) = (2.745)
Finance charges from 14 sep to 14 oct will be $ 9.7= appr. 10
The Amount due on 14 October = $562 +$283 +$15+$11.855- $250
= $ 623
Therefore, The annual interest on a daily basis with 19.5%, then the finance charge due on October 14 will be $623
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I need help part two and three of this question:A line passes through the following points: (6,3) and (2,9)1. Write the equation of the lineWhich I got y=-3/2 x+122. Write an equation of a line that is perpendicular to the original form. 3. Write the equation of a line that is parallel to the original form.
Answers
Part 2:
To determine an equation that is perpendicular to the line equation y = -3/2x + 12, get the negative reciprocal of the slope of the line equation.
[tex]\begin{gathered} \text{Given slope: }m=-\frac{3}{2} \\ \\ \text{The negative reciprocal is} \\ -\Big(-\frac{3}{2}\Big)^{-1}=\frac{2}{3} \\ \\ \text{We can now assume that any line in the form} \\ y=\frac{2}{3}x+b \\ \text{where }b\text{ is the y-intercept} \\ \text{is perpendicular to the line }y=-\frac{3}{2}x+12 \end{gathered}[/tex]Part 3:
An equation that is parallel to the line y = -3/2x + 12, is a line equation that will have the same slope as the original line.
Given that the slope of the line is m = -3/2, then any line equation in the form
[tex]\begin{gathered} y=-\frac{3}{2}x+b \\ \text{where} \\ b\text{ is the y-intercept} \end{gathered}[/tex]clarissa's division test was a 60% the first six weeks and a 72% the second six weeks. find the percent change.
Answers
The required change in the percentage is 20%.
Given that,
clarissa's division test was 60% in the first six weeks and 72% in the second six weeks. To determine the percent change.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
According to the question,
The change in the percentage = (72 - 60) / 60 × 100
The change in the percentage = 20%
Thus, the required change in the percentage is 20%.
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What is the average rate of change from f(-1) to f(1)?Type the numerical value for your answer as a whole number, decimal or fractionMake sure answers are completely simplified
Answers
The average rate of change of the function is the average rate at which one quantity is changing with respect to another.
Average rate of change = (y2 - y1)/(x2 - x1)
y represents the output values and it is also called f(x)
x represents the input values
For the given interval,
for f(- 1), x = -1 and f(x) = 8
For f(1), x = 1, f(x) = 4
Average rate of change = (4 - 8)/1 - - 1) = - 4/(1 + 1) = - 4/2
Average rate of change = - 2
New York City is a popular field trip destination. This year the senior class at High School A and
the senior class at High School B both planned trips there. The senior class at High School A
rented and filled 2 vans and 6 buses with 244 students. High School B rented and filled 4 vans
and 7 buses with 298 students. Every van had the same number of students in it as did the buses.
Find the number of students in each van and in each bus.
Answers
There are eight students in each van and 38 students are in each bus.
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
Let the number of students fit into a van would be v
And the number of students fit into a bus would be b
School A:
2v + 6b = 244 ...(i)
2v = 244 - 6b
v = 122 - 3b
School B:
4v + 7b = 298 ...(ii)
Substitute the value of v = 122 - 3b in the equation (ii),
4(122 - 3b) + 7b = 298
Solve for b to get b = 38.
Substitute the value of b = 38 in equation (i),
2v + 6(38) = 244
2v + 228 = 244
2v = 16
v = 8
Therefore, eight students are in each van and 38 students are in each bus.
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9 + 4 + (-1) +(-1) +...+ (-546) = 0X X80Σ (-3 + 10) = 0E=1
Answers
Answer
The sum of the sequence = -30072
Explanation
We are given a sequence of numbers and asked to find the sum of the terms up until the last term given. The sequence given is
9, 4, -1,.............., -546
On careful observation of this sequence, we can see that it is an arithmetic progression with a common difference of -5 between consecutive terms.
Common difference = (n + 1)th term - nth term
= 4 - 9 Or -1 - 4
= -5
For an arithmetic progression, the formula for the last term is given as
Last term = a + (n - 1)d
where
L = last term = -546
a = first term = 9
n = number of terms in the sequence = ?
d = common difference = -5
So, we can solve for the number of terms
-546 = 9 + (n - 1)(-5)
-546 = 9 - 5n + 5
-546 = 14 - 5n
14 - 5n = -546
-5n = -546 - 14
-5n = -560
Divide both sides by -5
(-5n/-5) = (-560/-5)
n = 112
We can now use the formula for the sum of an arithmetic progression to find the sum of this sequence.
[tex]\text{Sum of an A.P. = }\frac{n}{2}\lbrack2a+(n-1)d\rbrack[/tex]We know all of these parameters now
Sum of this AP = (112/2) [(2 × 9) + (112 - 1)(-5)]
= 56 [18 + (111 × -5)]
= 56 [18 - 555]
= 56 [ -537]
= -30072
Hope this Helps!!!
question 18:Evaluate: summation from n equals 2 to 8 of 12 times 4 tenths to the n plus 1 power period Round to the nearest hundredth. (1 point)
Answers
Given:
[tex]\sum_{n\mathop{=}2}^812(0.4)^{n+1}[/tex]Required:
Sum of the numbers
Explanation:
Let
[tex]A_n=\sum_{n\mathop{=}2}^812(0.4)^{n+1}[/tex]when n = 2, Aₙ becomes
[tex]A_2=12(0.4)^{2+1}=12\times(0.4)^3=0.768[/tex]when n = 3, Aₙ becomes
[tex]A_3=12(0.4)^{3+1}=12\times(0.4)^4=0.3072[/tex]when n = 4, Aₙ becomes
[tex]A_4=12(0.4)^{4+1}=12\times0.4^5=0.12288[/tex]
when n = 5, Aₙ becomes
[tex]A_5=12(0.4)^{5+1}=12\times0.4^6=0.049152[/tex]when n = 6, Aₙ becomes
[tex]A_6=12(0.4)^{6+1}=12\times0.4^7=0.0196608[/tex]when n = 7, Aₙ becomes
[tex]A_7=12(0.4)^{7+1}=12\times0.4^8=0.007866432[/tex]when n = 8, Aₙ becomes
[tex]A_8=12(0.4)^{8+1}=12\times0.4^9=0.003145728[/tex]So now,
[tex]\begin{gathered} A=A_1+A_2+A_3+A_4+A_5+A_6+A_7+A_8 \\ \\ A=0.768+0.3072+0.12288+0.049152+0.0196608+0.00786432+0.003145728 \\ \\ A=1.277902848\approx1.28 \end{gathered}[/tex]Final answer:
The
[tex] \sqrt{18} (523 \div 8)[/tex]help I need help
Answers
Solution
Given question
11.85 = 2.1n + 4.5
Requirement
To isolate n
Step 1
Using the subtraction property of equality to isolate the variable
11.85 - 4.5 = 2.1n + 4.5 -4.5
7.35 = 2.1n
Step 2
use the division property of equality to isolate the variable
7.35/2.1= 2.1n/2.1
n = 3.5
Answers are 1 first, then 2 next, those are the 2 steps
umm i need help on my math reducing fractions Im new to them and i dont understand it at all, Btw im in 5th grade not middle school it wont let me change it
Answers
since the smallest number is 2, and 2 can go into itself and 2 also can go into 10, that is the largest common number
[tex]\frac{2}{10}\div\text{ }\frac{2}{2}[/tex][tex]\begin{gathered} 2\text{ divided by 2 = 1} \\ 10\text{ divided by 2 =5} \end{gathered}[/tex]We can not make the number go any smaller since any number divied by one will equal itself
so that means
[tex]\frac{2}{10}\text{ reduced is }\frac{1}{5}[/tex]The graph of f(x) is shown in black.Write an equation in terms of f(x) to match the redgraph.For example, try something like this:f(x)+3, f (x - 2), or 4f(x).
Answers
Notice that the red function is similar to the black function, which means the transformation applied was a translation.
The transformation is 5 units to the right, exactly.
Therefore, the function that represents the red figure is
[tex]f(x-5)[/tex]List the angle measures of △VWX in order from smallest to largest. Assume that t is a positive number.
Answers
Explanation
To begin with, we will first have to obtain the length of side VX
[tex]VX^2=WX^2+VW^2-2\times WX\times VWcosw[/tex]In our case
[tex]\begin{gathered} WX=28t \\ VW=95t \\ w=94^0 \end{gathered}[/tex]Thus
[tex]\begin{gathered} VX^2=(28t)^2+(95t)^2-2\times(28t\times95t)cos94 \\ \\ VX^2=784+9025+371.104 \\ VX^2=100180.10 \\ \\ VX=100.90t \end{gathered}[/tex]Next, we will determine the angles at V and X
using sine rule
[tex]\begin{gathered} \frac{sin94}{100.9t}=\frac{sinV}{28t} \\ \\ sinV=\frac{28t\times sin94}{100.9t} \\ \\ sinV=0.27683 \\ \\ V=16.07^0 \\ \end{gathered}[/tex]Then, we will get the measure at X
[tex]180^0-16.07^0-94=69.93^0[/tex]Therefore, the order from smallest to largest angles will be
m
OR
m
Substitute the given values into the given formula and alone the unknown variable if necessary round to one decimal place
Answers
c = 15
Explanation:The perimter, P = 37
The side lengths of the triangle are:
a = 10, b = 12, c = ?
The perimeter of the triangle is given by the formula:
P = a + b + c
Substitute a = 10, b = 12, and P = 37 into the formula P = a + b + c and solve for c
37 = 10 + 12 + c
37 = 22 + c
c = 37 - 22
c = 15
Use the table to write an equation that relates the cost of lunch Y and the number of students X
Answers
In order to determine what is the equation which describes the values of the table, consider that the general form of the equation is:
y = mx
where m is the constant of proportionality between both variables x and y.
To calculate m you calculate the quotient between any pair of data from the table.
If you for example use the following values:
Students = 8.00
Lunch cost = 2
the constant of proportionality is:
m = 8.00/2 = 4.00
Next, you replace the value of m in the equation y=mx:
y = $4.00x
how do i solve the equation?
Answers
Answer: 7x=63 and 12x+9= 117
Step-by-step explanation:
add those two equations and set it to 180 degree
7x+12x+9=180
19x=171
x= 9
7x = 7 (9) = 63
12x+9 = 12 (9)+9 = 117
graph the line passing through (-6,1) whose slope is m= -6
Answers
As given by the question
There are given that the point (-6, 1) and slope (m) is -6.
Now,
To graph, the line, first, finds the equation of the line by using the given point and slope.
Then,
From the formula of point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]Where,
[tex]x_1=-6,y_1=1,\text{ and m=-6}[/tex]Then, put all given values into the above formula:
So,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-1_{}=-6(x-(-6)_{}) \\ y-1=-6(x+6) \end{gathered}[/tex]Then,
[tex]\begin{gathered} y-1=-6(x+6) \\ y-1=-6x-36 \\ y-1+1=-6x-36+1 \\ y=-6x-35 \end{gathered}[/tex]Then, the graph of the above equation is shown below:
A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solution contains 65%pure antifreeze. The company wants to obtain 260 gallons of a mixture that contains 45% pure antifreeze. How many gallons of water and how many gallons of the premium antifreeze solution must be
Answers
Answer:
80 gallons of water
180 gallons of premium antifreeze solution.
Explanation:
Let's call X the number of gallons of water and Y the number of gallons of the premium antifreeze solution.
The company wants to obtain 260 gallons of the mixture, so our first equation is:
X + Y = 260
Additionally, the mixture should contain 45% of pure antifreeze and the premium antifreeze solution contains 65% pure antifreeze. So, our second equation is:
0.45(X + Y) = 0.65Y
Now, we need to solve the equations for X and Y. So, we can solve the second equation for X as:
[tex]\begin{gathered} 0.45(X+Y)=0.65Y \\ 0.45X+0.45Y=0.65Y \\ 0.45X=0.65Y-0.45Y \\ 0.45X=0.2Y \\ X=\frac{0.2Y}{0.45} \\ X=\frac{4}{9}Y \end{gathered}[/tex]Then, we can replace X by 4/9Y on the first equation and solve for Y as:
[tex]\begin{gathered} \frac{4}{9}Y+Y=260 \\ \frac{13Y}{9}=260 \\ 13Y=260\cdot9 \\ 13Y=2340 \\ Y=\frac{2340}{13} \\ Y=180 \end{gathered}[/tex]Finally, replacing Y by 180, we get that X is equal to:
[tex]\begin{gathered} X=\frac{4}{9}Y \\ X=\frac{4}{9}\cdot180 \\ X=80 \end{gathered}[/tex]Therefore, the solution should have 80 gallons of water and 180 gallons of premium antifreeze solution.
Find the length of the third side. If necessary, write in simplest radical form.
4
4√5
Answers
Help math help math
What is this answer?
Answers
Answer:
24/25
Step-by-step explanation:
We are dividing 3/10 by 5/16
Kala the trainer had two solo workout plans that she offers her clients. PlanA and plan B. Each client does either one or the other (not both) on Friday there were 3 clients who did plan A and 5 who did plan B. On Saturday there were 9 clients who did plan A and 7 who did plan B. Kala trained her Friday clients for a total of 6 hours and her Saturday clients for a total of 12 hours. How long does each of the workout plans last?
Answers
Answer:
Each of the workouts plans lasts 45 minutes.
Explanation:
Let the duration for Plan A workout = x
Let the duration for Plan B workout = y
Friday
• Plan A --> 3 clients
,• Plan B --> 5 clients
,• Kala trained her Friday clients for a total of 6 hours
[tex]3x+5y=6[/tex]Saturday
• Plan A --> 9 clients
,• Plan B --> 7 clients
,• Kala trained her Saturday clients for a total of 12 hours
[tex]9x+7y=12[/tex]The system of equations is solved simultaneously.
[tex]\begin{gathered} 3x+5y=6\cdots(1) \\ 9x+7y=12\cdots(2) \end{gathered}[/tex]Multiply equation (1) by 3 in order to eliminate x.
[tex]\begin{gathered} 9x+15y=18\cdots(1a) \\ 9x+7y=12\cdots(2) \end{gathered}[/tex]Subtract.
[tex]\begin{gathered} 8y=6 \\ y=\frac{6}{8}=0.75\text{ hours} \\ 0.75\times60=45\text{ minutes} \end{gathered}[/tex]Substitute y=0.75 into equation (2) to solve for x.
[tex]\begin{gathered} 9x+7y=12 \\ 9x+7(0.75)=12 \\ 9x+5.25=12 \\ 9x=12-5.25=6.75 \\ x=\frac{6.75}{9} \\ x=0.75 \end{gathered}[/tex]x=y=0.75 hours = 45 minutes,
Each of the workouts plans lasts 45 minutes.
a store sells gift cards in preset amount. You can purchase gift cards for $20 or $30 . You spent $380 on gift cards. let x be the number of gift cards for $20 And let y be your gift cards for $30 . Write an equation in standards for to represent this situation
ANSWER= 20x+30y=380
but what ab this one
What are three combinations of gift cards you could have purchased?
Answers
The equation that represent the situation is as follows:
20x + 30y = 380The three combination of the gift cards you can purchase is as follows:
13 and 410 and 67 and 8How to represent equation in standard form?The store sells gift cards. One can purchase gift cards for $20 or $30 .
You spent $380 on gift cards. let x be the number of gift cards for $20 And let y be your gift cards for $30 .
The equation in standard form to represent the situation is as follows:
The standard form of a linear equation is A x + By = C. A, B, and C are
constants, while x and y are variables.
Therefore,
x = number of gift cards for 20 dollars
y = number of gift card for 30 dollars
Hence,
20x + 30y = 380
The three combination one could have purchased is as follows:
20(13) + 30(4) = 38020(10) + 30(6) = 38020(7) + 30(8) = 380learn more on equation here: https://brainly.com/question/7222455
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need help assap look at file attached
Answers
Answer:
length is 27, width is 9
Step-by-step explanation:
72/4= 18
2x27+ 2x9 = 54 + 18 = 72
