a.
The number of outlets in 2007 are 1008 outlets
Since the number of outlets A(t) at these alternative fueling stations t years after 2005 is [tex]A(t) = 233(2.08)^{t}[/tex] with t = 0 corresponding to 2005.
To find the number of outlets in 2007, we substitute t = 2 into the equation.
So,
[tex]A(t) = 233(2.08)^{t}\\A(2) = 233(2.08)^{2}\\A(2) = 233(4.3264)\\A(2) =1008.0512[/tex]
A(2) ≅ 1008 outlets (we round down to the nearest whole number since we can only have a whole number of outlets).
So, the number of outlets in 2007 are 1008 outlets
b.
The number of outlets in 2009 are 4361 outlets
To find the number of outlets in 2009, we substitute t = 4 into the equation.
So,
[tex]A(t) = 233(2.08)^{t}\\A(4) = 233(2.08)^{4}\\A(4) = 233(18.72)\\A(4) =4361.23[/tex]
A(4) ≅ 4361 outlets (we round down to the nearest whole number since we can only have a whole number of outlets).
So, the number of outlets in 2009 are 4361 outlets
c.
The number of outlets in 2010 are 9071 outlets
To find the number of outlets in 2010, we substitute t = 5 into the equation.
So,
[tex]A(t) = 233(2.08)^{t}\\A(5) = 233(2.08)^{5}\\A(5) = 233(38.93)\\A(5) = 9071.36[/tex]
A(5) ≅ 9071 outlets (we round down to the nearest whole number since we can only have a whole number of outlets).
So, the number of outlets in 2010 are 9071 outlets
Learn more about exponential increase here:
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HELP PLEASE I JUST NEED TO KNOW IF THE ANSWER IS AN EXTRANEOUS SOLUTION OR NOT
Solve the rational equation x over 5 equals x squared over quantity 4x plus 2 and check for extraneous solutions.
x = 0; x = −2 is an extraneous solution
x = 2; x = 0 is an extraneous solution
x = 0 and x = 2
x = 0 and x = −2
Answer:
x=0 and x=2
Step-by-step explanation:
[tex]\frac{x}{5} = \frac{x^{2}}{4x+2}[/tex]
4x+2 can't equal 0, is 4x+2=0, then x=-1/2, none of the answers are -1/2 so none are extraneous
x=0 is a solution, but x=-2 isn't, x=2 works (i checked this by plugging the solutions into the equation
Answer:
(C) x = 0 and x = 2
PLS WILL MARK BRAINLIEST DUE TODAY!!!!! Noya needs to determine the number of books that will fit into a box. If the box has a length of 18 inches and each book is StartFraction 2 Over 9 EndFraction of an inch thick, which expression can be used to determine the number of books that will fit into the box?
18 StartFraction 2 Over 9 EndFraction
18 times StartFraction 2 Over 9 EndFraction
StartFraction 2 Over 9 EndFraction divided by 18
StartFraction 9 Over 2 EndFraction divided by 18
Answer:
18 divided by 2/9, or 18/(2/9) (Is this what the first option was meant to say?)
Step-by-step explanation:
18 inches is the amount of space that needs to be filled, or divided up into sections to see how many things can fit.
2/9 is the width of the thing that you need to see how many fit, meaning it's the thing you're dividing by.
Combined, this means your expression is 18 divided by 2/9, or 18/(2/9). I think this is what your first option was meant to say, because if it is what it says, then the first and second option would be the exact same wrong thing.
You DON'T multiply, because if you think about easy numbers, an inch thick book should have 18 fit, and a half-inch thick book should have double that fit. As you get a smaller book, the number that fit increase, which can't happen with multiplication.
You also don't start with 2/9 because that's the width of the book. You're not trying to see how many boxes can fit into each book; that'd be ridiculous.
Answer:
It's A.
Step-by-step explanation:
jenifer solved 27 problems which is 3/11 of all the problems in her homework. how many problems are in her hommework
Answer:
Her homework has 99 problems
Step-by-step explanation:
27÷3=9
9=1/11
11×9=99
now, if we take into account that a WHOLE is always one, and we can partition it in many ways, say 295/295 = 1, or 313/313 = 1, so the whole amount of homework is 1 fraction wise, thus
[tex]\begin{array}{ccll}amount&fraction\\\cline{1-2}27&\frac{3}{11}\\x&1\end{array}\implies \cfrac{27}{x}=\cfrac{\frac{3}{11}}{~~1~~}\implies \cfrac{27}{x}=\cfrac{3}{11}\implies 27\cdot 11=x\cdot 3\\\\\\297=3x\implies \cfrac{297}{3}=x\implies \boxed{99=x}[/tex]
The perimeter of quadrilateral PQRS is 42 centimeters. The quadrilateral is reflected across
QR
and then translated 6 centimeters to the left and 2 centimeters down. What is the perimeter of the resulting quadrilateral?
Answer:
it’s still 42 centimeters :3
Step-by-step explanation:
this is kind of a trick question. These are transformations that don’t change the shape‘s size such as rotations and translations. Dialations change the shapes size but because in this problem it’s on reflections and translations, you can easily say that the perimeter is still 42 centimeters.
hope this helped :3
:3 byeeeeeeeeeeee
Which of the following scenarios has a speed of 55 miles per hour.
Select all that apply.
Traveling 82.5 miles in 1.5 hours.
Traveling 280 miles in 4 hours.
Traveling 110 miles in 2 hours:
Traveling 165 miles in 3 hours.
Answer:
165 miles in 3 hours
Step-by-step explanation:
1 hour = 55 milles
3hours=?
(3*55)/1
= 165 miles
Hence, correct.
f(x) = x; reflection in the x – axis followed by a translation 3 units down.
Answer:
f(x)=-x-3
Step-by-step explanation:
reflection in the x-axis
f(x) = x ---> f(x) = -x
translation 3 units down:
f(x) = -x ---> f(x) = -x - 3
easy problem.......................................
Answer:
-3/7
Step-by-step explanation:
Ty for points
NO LINKS!!!!!
Part 2: Draw sketches (including several accurate point coordinates) for the following functions. Name all of the transformations.
4. y = -1/3 | x - 2 | - 4
5. y = 1 / ( x + 5) - 3
6. (x - 1)^2 + (y + 2)^2 = 4
Answer:
see below
Step-by-step explanation:
We can use the equation
y = -a f(-b (x-h)) +k
The first negative is a reflection about the x axis
a is a horizontal stretch if it is >1 or a compression if less than 1
The negative inside the function is a reflection about the y axis
b is a horizontal compression if >1 or a compression if less than 1
h shifts the function left ( h<0) or right if (h>0)
k shifts the function up if k>0 or down if k <0
4. y = -1/3 | x - 2 | - 4
parent function |x|
reflection about the x axis
1/3 horizontal compression
shift 2 units to the right
4 units down
y = 1 / ( x + 5) - 3
The parent function is 1/x
shift is 5 units to the left and 3 units down
6. (x - 1)^2 + (y + 2)^2 = 4
(x - 1)^2 + (y + 2)^2 = 2^2
This is a circle of radius 2
The center is shifted from the origin 1 unit to the right and 2 units down
The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. Assume that the population standard deviation is 1.5 gallons. The mean water usage per family was found to be 17.5 gallons per day for a sample of 543 families. Construct the 98% confidence interval for the mean usage of water. Round your answers to one decimal place.
Answer:
The monthly amount of water used per household in a small community is normally distributed with mean 7,069 gallons and standard deviation 58 gallons. Find the three quartiles for the amount of water used.
How do I answer the question -x^2-6x+16=0 using the quadratic formula?
9514 1404 393
Answer:
x = -8 or 2
Step-by-step explanation:
Compare your equation to the standard form equation.
-x^2 -6x +16 = 0 . . . . . . your equation
ax^2 +bx +c = 0 . . . . . . standard form equation
Identify the values of 'a', 'b', and 'c'.
a = -1
b = -6
c = 16
Fill in these values in the quadratic formula and do the arithmetic.
[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-(-6)\pm\sqrt{(-6)^2-4(-1)(16)}}{2(-1)}=\dfrac{6\pm\sqrt{100}}{-2}\\\\x=-3\pm5=\{-8,2\}[/tex]
The solutions are x = -8 and x = 2.
GIVING BRAINLIEST IF ANSWRED QUICKLY AND CORRECTLY.
What is the standard deviation depicted on the graph?
-7
-75
-54
-96
Answer:
i think its 96
Step-by-step explanation:
What is 1/2 divided by 5/6
Answer:
3/5
Step-by-step explanation:
1/2 ÷ 5/6 = 1/2 × 6/5 = 6/10 = 3/5
total area of 2 Square Windows is 1025 in squared each side of the larger window is 5 in longer than the size of the smaller window how long are the size of the smaller window
Answer:
B 20in
Step-by-step explanation:
e2021
What causes the phases of the moon? (Select two.)
The Moon changes shape as it moves around Earth.
The Moon's position relative to Earth results in phases.
Earth casts a shadow on the Moon.
The Moon is illuminated on one side by the Sun.
The amount of Moon we see changes over the month — lunar phases — because the Moon orbits Earth and Earth orbits the Sun. Everything is moving. During a lunar eclipse, Earth comes between the Sun and the Moon, blocking the sunlight falling on the Moon.
Answer:
Both 'The Moon is illuminated on one side by the Sun' and 'The Moon's position relative to Earth results in phases.'
Step-by-step explanation:
The Moon has phases because of its position relative to Earth, and also because it is only illuminated on one side by the Sun. As it rotates, some parts of the moon reflects the Sun's light, so it looks as if it's changing shape. The other parts that are blacked out is because it is not reflecting the Sun's light, not because of the Earth.
Find the x- and y-intercepts of the graph of 3x - 5y = 25. State each answer as an
integer or an improper fraction in simplest form.
Answer:
[tex]\bf\mathsf{X-intercept=(\frac{25}{3},\:0)}[/tex]
Y-intercept = (0, -5)
Step-by-step explanation:
Given the linear equation in standard form, 3x - 5y = 25, for which we must determine its x- and y-intercepts.
It is essential to understand what the intercepts mean relative to the given equation and its location on the graph.
X-intercept:The x-intercept is the point where the graph crosses the x-axis. Hence, its coordinates are often represented by (a, 0). Thus, the x-intercept provide the value of x when the value of the y-coordinate is 0.
Now, we can solve the x-intercept by setting y = 0:
3x - 5y = 25
3x - 5(0) = 25
3x - 0 = 25
3x = 25
Divide both sides by 3 to solve for x:
[tex]\large\mathsf{\frac{3x}{3}\:=\:\frac{25}{3}}[/tex]
[tex]\bf\mathsf{x=\:\frac{25}{3}}[/tex]
Therefore, [tex]\bf\mathsf{X-intercept=(\frac{25}{3},\:0)}[/tex] .
Y-intercept:The y-intercept is the point where the graph crosses the y-axis. Hence, its coordinates are often represented by (0, b ). Thus, the y-intercept provide the value of y when the value of the x-coordinate is 0.
Now, we can solve the y-intercept by setting x = 0:
3x - 5y = 25
3(0) - 5y = 25
0 - 5y = 25
-5y = 25
Divide both sides by -5 to solve for y:
[tex]\large\mathsf{\frac{-5y}{-5}\:=\:\frac{25}{-5}}[/tex]
y = -5
Therefore, the y-intercept is (0, -5).
Eddys yard is 12 feet wide and 20 foot long it is covered with grass how many square feet of grass is in eddys yard
Answer:
240 sq feet
Step-by-step explanation:
for a rectangle
area = length * width
a = 20 * 12
a = 240
240 sq feet
Here are the first five terms of an arithmetic sequence.
-1 3 7 11 15
Find, in terms of n, an expression for the nth term of this sequence.
Answer:
19, 23, 27, 31, 35, 39, 43, 47
Step-by-step explanation:
is this what you meant? if not tell me what you meant and I'll change it
Mr Miller is having a party. he needs to rent some tables for his guest. he will rent 1 table for every 8 guests. Each table costs $4.50 to rent. If Mr.Miller will have 72 guests at his party, how much will it cost to rent the tables for his party?
A. $13.50
B.$16.00
C.$36.00
D.$40.50
Answer:
D.) $40.50
Step-by-step explanation:
If he is having 72 guests over, then he'll need nine tables.
(72 guests divided by eight guests, [each table] equals the need for nine tables)
If each table is $4.50 and he needs nine tables then we shall multiply nine by 4.50
9 x 4.50 = 40.50
$40.50
Hope this helped! Please mark brainliest!
The small copier makes 437 copies each day. The large copier makes 4 times as many copies each day.
How many copies does the large copier make each week?
Answer:
1,748x7=12,236
Step-by-step explanation:
i think this is right...
A 2 kg cart traveling 0.3 m/s runs into a 4 kg cart at rest. What is the momentum of each cart before the
collision?
A. The small cart has a momentum of 0 kg · m/s and the large cart has a momentum of
0.6 kg . m/s.
B. The small cart has a momentum of 0.6 kg · m/s and the large cart has a momentum of
0 kg . m/s.
C. The small cart has a momentum of 0 kg · m/s and the large cart has a momentum of
2.4 kg . m/s.
D. The small cart has a momentum of 0.6 kg · m/s and the large cart has a momentum of
1.2 kg. m/s.
Answer:
The small cart has a momentum of 0.6 kg ⋅ m/s and the large cart has a momentum of 0 kg ⋅ m/s
I just took the test.
0.6 kg and 0 kg p=mv100 kg * m/sThe train cars move together in the direction the large car was movingM1V1 i + M2V2 f = M1V1 f +m2 v2 felastic collision, because the law of conservation of momentum was followed.The ratio of useful energy output to energy input.80%Ethan measured a line to be 14 inches long. If the actual length of the line is 14.5
inches, then what was the percent error of the measurement, to the nearest tenth of a
percent?
Answer: Estimate the length of each line segment in inches. Then
measure it to the nearest —
1
2
— inch.
2.
Estimate: Actual:
Estimate the length of each line segment. Then
measure it to the nearest —
1
4
— inch.
3.
Estimate: Actual:
4.
Estimate: Actual:
Draw a line segment that has the given length.
5. 4 inches
6. 3—1
4
— inches
7. 4—
1
2
— inches
8. —3
4
— inch
9. Marta wants to make 4 necklaces that are the same
length. She asks her friends to cut the string for the
necklaces 15 paper clips long. Would all the
lengths be the same? Explain your thinking.
Answers will
vary.
Answers will
vary.
Answers will
vary.
3 inches
2—
1
2
— inche
Step-by-step explanation:
Answer:
0.036 or 3.6%
Step-by-step explanation:
First you must set up the equation:
(|14.5 - 14|) / 14
0.5 / 14
0.036 x 100%
3.6%
Another Problem For Help With More Explanation:
Mathew goes to the store and gets 10 bananas, which he expects to be 4.1 pounds, however it turned out the actual weight was 3.9 pounds. What was the percent error of the measurement, to the neartest tenth of a percent?
So first you must take the 2 values you need out, which would be 4.1 pounds (the expected value) and 3.9 pounds (the actual value).
You then must set up the equation which is (|X-Y|)/Y.
X is the actual value, which would be 3.9 pounds and Y is the expected value, which would be 4.1.
You then plugin the numbers so you get (|3.9-4.1|) / 4.1.
Then follow PEMDAS, which would be the parantheses, so it would be |-0.2| / 4.1.
The absolute value of -0.2 is 0.2, since the absolute value makes it positive, no matter if it was already negative or positive.
You are then left with 0.2 / 4.1, which you then do the math for, with it equaling 0.048780.
You then do 0.048780 x 100%, to get the percent, which would be 4.8780%, however you would just need to round to the tenth of a percent, so it would be 4.9%. Hope this extra problem helps you understand the topic more! :}
A fishing pond loses an average
2/3 inches of water each week.
Find the total change in the water
level of the pond after 5 weeks.
Answer as an improper fraction = 10/3 inches
Answer as a mixed number = 3 & 1/3 inches
=============================================================
Explanation:
Multiply the two given values to get (2/3)*5 = (2/3)*(5/1) = 10/3
Optionally, you can convert that to a mixed number
10/3 = (9+1)/3 = (9/3) + (1/3) = 9 + (1/3) = 3 & 1/3
A parabola can be drawn given a focus of (−5,3) and a directrix of
y=1. Write the equation of the parabola in any form.
Answer:
Step-by-step explanation:
y = 1 is a horizontal line
Vertex is halfway between the directrix and focus on a vertical line through x = (-5, 3).
(1 + 3)/2 = (-5, 2)
The shortest distance from the directrix to the focus is 3 - 1 = 2 units
so points (-5 - 2, 3) = (-7, 3) and (-5 + 2, 3) = (-3, 3) are on the parabola.
The vertex form of a parabola is
y = a(x - h)² + k
y = a(x - (-5))² + 2
y = a(x + 5)² + 2
plugging in one of the other known points
3 = a(-7 + 5)² + 2 or 3 = a(-3 + 5)² + 2
1 = a(-2)² 1 = a(2)²
a = 1/4 a = 1/4
y = ¼(x + 5)² + 2
to find the standard form, expand the vertex form
y = ¼(x² + 10x + 25) + 2
y = 0.25x² + 2.5x + 6.25 + 2
y = 0.25x² + 2.5x + 8.25
or
4y = x² + 10x + 33
Find each of the following differences by changing them into sums with multiplication by a negative number
8(x+3)-2(x+5)
The difference of given expressions is 6x+14.
What is the subtraction of expressions?To subtract an algebraic expression from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.
Given that, 8(x+3)-2(x+5)
8x+24-2x-10 (By distributive property of multiplication)
(8x-2x)+(24-10) (Grouping like terms)
6x+14
Therefore, the difference of given expressions is 6x+14.
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Three siblings are each 3 years apart. If the total number of years between them is 90 years, how old is the oldest sibling
Answer:
33 years old
Step-by-step explanation:
x = youngest sibling
y = oldest sibling
x + (x + 3) + (x + 3 + 3) = 90
3x + 9 = 90
3x = 81
x = 27
y = 27 + 3 + 3 = 33
(4.05)^2
Help me please I really don’t under stand what I’m supposed to do with the brackets and exponent
Step-by-step explanation:
The power 2 after 4.05 means that 4.05 should times itself twice, which means
[tex] {4.05}^{2} = (4.05)(4.05) \\ = 16.4025[/tex]
Simplify fully 24(x−2)^2 + 6 (x−2) PLEASE HELP ME!!!!!
it is 24x² - 90x + 84
Step-by-step explanation:
it cuz I'm smart lolz
Answer:
6(x-2) x (4x-7)
Step-by-step explanation:
the pictures attached have the working there
Find the product of the following. Write your answer on the line. 21. 713.1 x 10 22. 943.843 x 100 23. 1.999 x 4.12 = 24. 60.09 x 0.0123 = 25. 0.10002 x 0.411=_
Answer:
The numbers are best written as,
(1.2 x 10⁻²)(3.65 x 10⁸)
If we multiply the bases of the scientific notations, we get an answer of 4.38. There exists a rule which states that for exponents of the same number which are multiplied, we add up the exponents. Thus, our final answer would be,
4.38 x 10⁶
Step-by-step explanation:
ratio of 5/20 to 9/20
Answer:
5:20 to 9:20
Step-by-step explanation:
11. Angelina did not pay her credit card bill in full, so her bill has a finance charge added on.
The average daily balance is $520.39 and the monthly periodic rate is 1.2%. What should her
finance charge be on her statement?