The ratio of cranberry juice to apple juice to orange juice in the fruit punch is = 1 : 2 : 3
Let the total quantity of juice is 60 ml .
Now the apple juice is 1/3 of 60 = 20 ml
The orange juice is 1/2 of 60 = 30 ml
Therefore cranberry juice = 60 -(20+30) ml = 10 ml
Now the ratio of cranberry juice to apple juice to orange juice
= 10 : 20 : 30
= 1 : 2 : 3
We can exactly find out how much of one simple quantity is included in the other by simply comparing two amounts of the same units. Ratios can be divided into two smaller groups.
One is the part to the whole ratio; the other is the part to the part ratio. The exact relationship that is between the two distinct entities or groupings is only exactly depicted by the part-to-part ratio.
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Question 4 of 10
If f(x) = 2(x)² +5√(x+2), complete the following statement (round your
answer to the nearest hundredth):
f(0) =
The function of f(0) =7.0710.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
f(x) = 2(x)² +5√(x+2)
f(0) = 2*0 +5√2
f(0) = 7.0710
Hence the value will be 7.0710.
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We want to construct a box whose base length is 2 times the base width. The material used to build the top and bottom cost $ 11 per square feet and the material used to build the sides cost $ 3 per square feet. If the box must have a volume of 40 cubic feet determine the dimensions that will minimize the cost to build the box.
The dimensions that will minimize the cost, obtained from the cost function are;
Width = [tex]\sqrt[3]{\frac{45}{11} }[/tex] feet
Length = [tex]2\cdot \sqrt[3]{\frac{45}{11} }[/tex] feet
Height = [tex]\dfrac{20}{\left(\sqrt[3]{\frac{45}{11} }\right)^2 }[/tex]
What is a function?A function is a rule, or law or expression that provides the definition between an input variable and an output variable.
Base length of the box = 2 × The base width of the box
Cost of the material used to build the top and the bottom = $11 per square feet
Cost of the material used to build the sides = $3 per square feet
Volume of the box = 40 cubic feet
Let x represent the width of the base of the box, and let y represent the height of the box
The information from the question indicates;
The length of the base of the box = 2·x
The volume of the box, V = x × 2·x × y = 2·x²·y = 40
V = 2·x²·y = 40
[tex]y = \dfrac{40}{2\cdot x^2} = \dfrac{20}{x^2}[/tex]
The cost of the box which can be obtained from the surface area of the box can be found as follows;
Cost of the top and the bottom = 2 × x × 2·x × 11 = 44·x²
Cost of the material for the sides = (2 × x × y + 2 × 2·x × y) × 3 = 18·x·y
Cost of the box, C = 44·x² + 18·x·y
[tex]C = 44\cdot x^2 + 18\cdot x \times \dfrac{20}{x^2} = \dfrac{44\cdot x^2+360}{x}[/tex]
To minimize the cost of the box, we get;
[tex]C' =\dfrac{d}{dx}\left( \dfrac{44\cdot x^2+360}{x}\right) = 0[/tex]
[tex]\dfrac{d}{dx}\left( \dfrac{44\cdot x^3+360}{x}\right) = \dfrac{x\times 44\times 3 \times x^2 - \left(44\times x^3+360\right)}{x^2} = \dfrac{88\cdot x^3-360}{x^2} =0[/tex]
At the minimum cost, [tex]\dfrac{88\cdot x^3-360}{x^2} =0[/tex]
Therefore; 88·x³ - 360 = 0
88·x³ = 360
[tex]x = \sqrt[3]{\dfrac{360}{88} } =\sqrt[3]{\dfrac{45}{11} }[/tex]
The width of the base of the box that minimizes the cost is; [tex]x =\sqrt[3]{\dfrac{45}{11}}[/tex]
The length of the base of the box that minimizes the cost is; [tex]2\cdot x =2\times \sqrt[3]{\dfrac{45}{11}}[/tex]
The height of the box that minimizes the cost is; [tex]\dfrac{20}{x^2} = \dfrac{20}{\sqrt[3]{\dfrac{45}{11} } }[/tex]
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7,17,27,37,47,57 whath other observations you can make about the pattern
The observation I can make of the pattern is that the sequence always increase by 10.
How to solve an arithmetic pattern?The sequence above shows an arithmetic pattern. Therefore, the arithmetic formula can be used to solve the next sequence.
7, 17, 27, 37, 47, 57..
Therefore,
aₙ = a + (n - 1)d
where
a = first termd = common differencen = number of termsTherefore,
a = 7
d = 17 - 7 = 10
Hence, the arithmetic formula is as follows:
aₙ = 7 + (n - 1)10
aₙ = 7 + 10n - 10
aₙ = 10n - 3
The sequence always increase by 10.
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Which ordered pair in the form (x, y) is a solution of this equation?
x + 7y= 10
Answer: (3, 1)
Step-by-step explanation:
Plug in each coordinate and see if the equation holds true:
[tex](13, 2)\\13+2(7)=13+14=27\neq 10[/tex]
[tex](2, 1)\\2+7(1)=2+7=9\neq 10[/tex]
[tex](4, 1)\\4+7(1)=4+7=11\neq 10[/tex]
[tex]3+7(1)=3+7=10[/tex]
IXL Please Help Fast!
Find a polynomial function of degree 7 with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.
The polynomial function with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1 will be x³+9x²+16x.
What is a polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
It is given that the polynomial is given with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.
Each zero, such as a, corresponds to a linear factor, such as (x a). The repeating of such components is corresponding to multiplicity. The following polynomial thus meets the requirements in our example:
= (x-(-3))³(x-0)¹
=(x³-3x²(-3)+3x(-3)²-(-3)²)(x)
=x³+9x²+27x-9x
=x³+9x²+16x
Thus, the polynomial function with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1 will be x³+9x²+16x.
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Raina's penny bank is 1/10 full. After she adds 480 pennies, it is 1/2 full. How many pennies can Raina's bank hold?
Answer:
1,200 pennies
Step-by-step explanation:
A monkey gathered 4 coconuts per minute. Is it a rate or unit rate?
Answer: unit rate
Step-by-step explanation:
its obvious
Answer:
I believe it is a unit rate
As a member of the hiking club, you have paid
a total of $51 after 4 months and a total of $105
after 10 months. What is the linear equation in
slope-intercept form that models this situation.
The linear equation in the slope intercept form that models this situation is y = 9x + 15 .
In the question ,
it is given that ,
a member of hiking club paid $51 for 4 months ,
let the number of months be represented on x coordinate , and
the amount paid be represented on y coordinate .
So , the point becomes (4 , 51).
also given that you pay a total of $105 after 10 months ,
the second point becomes (10 , 105).
to find the equation in slope intercept form , we need slope ,
So , Slope = (105-51)/(10-4)
= 54/6
= 9
So , the equation having the point (4,51) and slope as 9 , in slope intercept form is
(y - 51) = 9(x - 4)
y - 51 = 9x - 36
y = 9x - 36 + 51
y = 9x + 15
Therefore , The linear equation in the slope intercept form that models this situation is y = 9x + 15 .
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Samantha invested $660 into a account that paid 3.5% interest compounded annually. Samantha did not make any addition deposits or withdrawals
What is the total amount of interest paid by the investment at the the of 5 years ?
$115.50
$783.87
$123.87
$2,755.50
115.5 is the total amount of interest paid by this investment at the end of 5 years
What is the Percentage?
percentage, a relative value indicating the hundredth parts of any quantity.
Given,
Samantha invested $660 into an account that paid 3.5% interest compounded annually.
We need to find the total amount of interest paid by this investment at the end of 5 years
A=P(1+rt)
A is the final amount
P is the principal amount
r is the rate of interest
t is time
A=?,P=660,r=3.5%=0.035, t=5
A=660(1+0.035(5))
=660(1+0.175)
=660(1.175)
A=775.5
To check the total amount of interest paid by this investment at the end of 5 years
We need to find the difference between the initial amount and the final amount
775.5-660 =115.5
Hence 115.5 is the total amount of interest paid by this investment at the end of 5 years
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Princess can sel an average of
21 muffins per day She needs to earn
$30 per day to meet her fundraising goal.
How much does she need to charge for
each muffin to reach her goal? Round to the
hearest cent.
Step-by-step explanation:
x = price per muffin
21 × x = 30
x = 30/21 = 10/7 = $1.428571429... ≈
≈ $1.43
she needs to charge $1.43 per muffin.
The population of a city has increased by 28% since it was last measured. If the current population is 80,000, what was the previous population?
The previous population of the city is 62500
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 3x + 4y = 14, 5x − 4y = 4.
if the previous population is represented by x and the increment by y, then
y= x×28/100
y = 28x/100 equation 1
the new population = previous population+ increment
therefore x+y= 80,000
represent 28x/100 for y in equation 2
x+28x/100= 80000
making the LHS a single fraction
(100x+28x)/100= 80000
128x= 80000×100
divide both sides by 128
x= 8000000/128
x= 62500
therefore the previous population is 62500
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A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. the premium antifreeze solution contains 60% pure antifreeze. the company want to obtain 180 gallon of a mixture that contain 35% pure antifreeze. how many gallon of water and how many gallon of the premium antifreeze solution must be mixed
The gallons of water and gallons of the premium antifreeze solution that must be mixed are 60 gallons and 120 gallons respectively.
How to determine the gallons of water and premium antifreeze solution?In order to solve this word problem, we would assign a variable to the gallons of water and premium 60% antifreeze that is required, and then translate the word problem into algebraic equation as follows:
Let the variable w represent the gallons of water.Let the variable p represent the premium 60% antifreeze.Since the premium antifreeze solution contains 60% premium antifreeze, we have the following mathematical expression:
w + p = 180 ....equation 1.
0.60p = 0.40(180) ....equation 2.
From equation 2, we have:
0.60p = 0.40(180)
0.60p = 72
Premium antifreeze, p = 72/0.60
Premium antifreeze, p = 120 gallons.
For the gallons of water, we have:
w + p = 180
Water, w = 180 - p
Water, w = 180 - 120
Water, w = 60 gallons.
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-2.5f+0.8f-16-9=
(Simplify your answer. Use integers or c
Answer:
[tex]-1.7f+-25[/tex]
Step-by-step explanation:
1 ) To simplify combine like terms...
[tex]=-2.5f+0.8f+-16+-9[/tex]
[tex]=(-2.5f+0.8f)+(-16+-9)[/tex]
[tex]=-1.7f+-25[/tex]
Hope this helps! :)
A customer at the store wanted to buy a different watch that was listed at $88 but had a 15% discount. Then the customer had to pay a sales tax of 5% on the dis...
The customer have to pay $87.9 for the watch.
A customer at the store wanted to buy a different watch that was listed at $88 but had a 15% discount.
Given the information is
Watch is listed at $88 and had a discount of 15%
The customer had to pay a sales tax of 5%
Than, by reducing the discount from the price listed
= $88 - 15%
= 88 - [tex]\frac{15}{100}[/tex]
= 87.85
Now we have to add 5% tax to the discounted price
= 87.85+5%
= $87.9
Hence the answer is the customer have to pay $87.9 for the watch.
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somebody answer, please?
The table displays data collected, in meters, from a track meet.
one fourth 6 2 4
3 two thirds one third nine halves
What is the median of the data collected?
2.5
4.5
2
3
The median of the data collected from a track meet is 2 meters.
What is median?The median is the middle number in a sorted, ascending or descending list of numbers.
To calculate the median of the given date, we folloe the steps below.
Collected date: 1, 4, 6, 2, 4, 3, 2/3, 1/3, 1/2
Step 1: Rearreange the date in accending order.
1/3, 1/2, 2/3, 1, 2, 3, 4, 4, 6Step 2: Pick the middle of the number in the arranged data
Median = 2 meters.Hence, the median of the data collected is 2 meters.
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Answer:
2.5
Step-by-step explanation:
Solve the system. 2x + y = 3 −2y = 14 − 6x Write each equation in slope-intercept form. y = -2 x + 3 y = 3 x + -7 How do the slopes and y–intercepts of the two equations compare?
The slopes and the y-intercepts of two equations are different.
How to calculate the slope-intercept form of the equation?Mathematically, the slope-intercept form of a line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the y-intercept.How to determine the slopes and y–intercepts of the two equations?From the information provided, we have the following equations:
2x + y = 3 ....equation 1.
−2y = 14 − 6x ....equation 2.
In slope-intercept form, the first equation can be written by subtracting 2x from both sides as follows:
2x + y - 2x = 3 - 2x
y = 3 - 2x
y = -2x + 3
Therefore, m = -2 and c = 3.
For the second equation, we would divide both sides by -2 as follows:
−2y/-2 = 14/-2 − 6x/-2
y = -7 + 3x
y = 3x - 7
Therefore, m = 3 and c = -7.
In this context, we can reasonably and logically deduce that the slopes and the y-intercepts are quite different.
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Answer:
y = -2x + 3
y = 3x + -7
The slopes and the y-intercepts are different.
The system represents lines that Intersect at one point
Exactly one solution
Step-by-step explanation:
Edge2022
get me brainliest
What is the equation of the line shown in the graph?
The equation of the given line is y = 2x + 4
What is the equation of a line?The equation y = mx + c is the general equation of any straight line, where m is the slope of the line and c is the y -intercept.
Given a line passing through points (-1, 2) and (-3, -2)
We know (y - y1) = [(y2−y1)/(x2−x1)](x - x1).
Therefore, y - 2 = [(-2-2)/(-3+1)](x+1)
y-2 = 2x + 2
y = 2x + 4
Hence, The equation of the given line is y = 2x + 4
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Mai has 5 loves of bread and jeff has 3 loves.Mia and Jeff decide to share their bread witha hungry stranger.they all sit down and they have an equal amount of bread. the stranger gives them 8 coins to split for there generosity. describe the most equitable way mia and jeff should split the coins based on how much bred they gave
The most equitable way to share the coin between Mai and Jeff is ratio 5:3. Mai will have 5 coins and Jeff 3 coins
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b.
Mai dropped 5 loaves and Jeff 3 loaves. This means that the ratio of brad dropped by Mia and Jeff is 5:3.
The stranger dropped 8coins. the most equitable way to share the coin is to share it in ratio 5:8
Using this ratio, the total ratio is 8
therefore Mia will have 5/8×8=5coins
Jeff will have 3/8×8= 3coins
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If you want easy access to your money for paying bills, eating out, etc, it is best to use a ____________ account.
If you want easy access to your money for paying bills, eating out, etc, it is best to use a checking account.
What is checking account?A checking account is a sort of bank account that enables simple deposits and withdrawals of cash for everyday use.
For instance, you may use your debit card to withdraw cash, deposit a check you receive, or set up direct deposit to get your paychecks.
It is advisable to utilize a checking account if you want quick access to your money for things like paying bills and dining out.
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Last year, Amy deposited $1000 into an account that paid 2% interest per year and $3000 into an account that paid 7% interest per year. No withdrawals were made from the accounts.
Answer the questions below. Do not do any rounding.
(a) What was the total interest earned at the end of 1 year?
(b) What was the percent interest for the total deposited?
If no withdrawals were made from the accounts. The total interest earned at the end of 1 year is $230 and the percent interest for the total deposited is 5.75%.
How to find the total interest earned?a. Total interest earned :
Total interest earned = (0.02)($1000)+(0.07)($3000)
Total interest earned =$20+$210
Total interest earned =$230
b. Percent interest amount deposited
Percent interest amount deposited = Total interest earned / Total amount deposited
Percent interest amount deposited = $230 /( $1,000 + $3,000)
Percent interest amount deposited = $230 / $4000
Percent interest amount deposited = 0.0575 × 100
Percent interest amount deposited =5.75%
Therefore $230 is the interest earned and 5.75 is the percent interest.
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For sake of simplicity, let us assume that you have won exactly three punches for the game AND that no
prizes are removed after each punch. You are then shown the punching board, which contains 50 slots
with the following dollar amounts: (5) $100, (10) $250, (10) $500, (10) $1000, (8) $2500, (4) $5000, (2)
$10000, (1) $25000. You get to punch one slot at a time and either keep the amount you found or
continue with your other punches.
Working backwards, if you have already used and thrown away your first two punches, there is no
strategy for the third punch. You take whatever you get. Now examine the second punch.
QUESTION 1: What is the expected value of your third punch? Again, for sake of simplicity, assume that
your first two punches were put back into the mix. (Essentially no prizes are removed so there are still
50 holes to punch) Show all calculations necessary for you answer.
Also the question in the picture
The expected value of your third punch is 5660.
What is probability?
A linear scale from 0 (impossibility) to 1 (certainty) or as a percentage between 0 and 100% expresses the likelihood that a specific event (or series of events) will occur.
Given that,
This is the third and last punch and also there is no removal of prizes after each punch. Hence, the expected value would be equal to the mean of all the possibilities available.
E(third punch) = Σ x p(x)
= 100× (5/50) + 250 × (10/50) + 500 × (10/50) + 1000 × (10/50) + 2500 ×(8/50) + 5000 × (4/50) + 100000 × (2/50) + 25000 × (1/50)
= 5660
Let us find the median of the given possibilities,
5 100's, 10 250's, 10 500's, 10 1000's, 8 2500's, 4 5000's, 2 100000's, 1 25000
There is a total of 50 possibilities and hence the median will be the average of the 25th and 26th terms.
25th term = 500
26th term = 1000
Median = (500 + 1000) / 2 = 750
The next available possibility greater than 750 is 1000.
Probability of getting more than 1000 in third punch = P (x > 1000) = (No. of terms greater than 1000) / Total no. of possible outcomes = 15 / 50 = 0.3
Probability of getting less than 1000 in third punch = P (x > 1000) = (No. of terms lesser than 1000) / Total no. of possible outcomes
= 25 / 50 = 0.5
Hence, in the second chance of punch, 1000 or anything greater than 1000 is preferred because the probability of getting more than 1000 in the next chance is less than the probability of getting less than 1000.
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10% of your grade is participation, 30% is class work/homework, 60% is test /projects. a student had an average of 100 for participation, 95 for class work/homework and 75 for test/projects. What the is the grade in the class?
The overall weighted average grade for this student in the class is 83.5%.
How is the weighted average grade computed?The weighted average grade is a function of the multiplication of each rate by the average score for each grading category.
The class grades are added to obtain the total grade that the student received for the different categories, involving class participation, classwork/homework, and tests/projects.
Grade Average Class Grade
Participation 10% 100 10% (10% x 100%)
Classwork/Homework 30% 95 28.5% (30% x 95%)
Test/projects 60% 75 45% (60% x 75%)
Total grade in class 83.5%
Thus, from the student's participation, classwork/homework, and tests/projects, we can summarize that they scored an average weighted grade of 83.5%.
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Order these numbers from least to greatest. 7.209, 7.23, 7.3, 7.1032
Answer:
7.1032,7.209,7.23,7.3.
so we can not put the dot and imagine like 71032 72090 we not put the 0 but it's can not be with no 0 72300 and we not put 0 73000 it most greatest so
i write answer on the top!
Compare the following functions:
Function A: y = 4x −5
Function B: _______.
What is the slope/rate of change of Function A? ______.
What is the slope/rate of change of Function B between f(0) and f(1)? ______.
What is the slope/rate of change of Function B between f(1) and f(2)? ______.
What is the slope/rate of change of Function B between f(2) and f(3)? _____.
The slope of Function A is _______.
The slope of Function B is _______.
The slope of the function A which is presented as an equation and the slope of function B presented as a table are presented as follows;
The slope of function A is 4
The slope of function B are;
Between f(0) and f(1), the slope is 1
Between f(1) and f(2), the slope is 3
Between f(2) and f(3), the slope is 5
What is the slope of a graph of a function?The slope is found by the ratio of the rise to the run of the graph.
The function A is; y = 4·x - 5
Function A is of the form y = m·x + c
Where;
m = The slope of the function = 4
Therefore;
The slope of function A is 4
The first difference of the values of function B is not a constant.
The value of f(0) in function B is 0
The value of f(1) in function B is 1
The slope between f(0) and f(1) is m = (f(1) - f(0))/(1 - 0)
Which indicates that m = (1 - 0)/(1 - 0) = 1
The slope of function B between f(1) and f(2) is found as follows;
f(2) = 4, f(1) = 1, from which we get;
m = (4 - 1)/(2 - 1) = 3
The slope between f(2) and f(1) is 3
The slope of the function B between f(2) and f(3) is found as follows;
f(2) = 4, f(3) = 9, from which we get;
m = (9 - 4)/(3 - 2) = 5
The slope of the function B between f(2) and f(3) is 5
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The Johnson's purchased a car. If the total price, including a 6% sales tax, was $19,674, find the price of the car before tax
Answer:
Step-by-step explanation:
The price of the car before tax was $18,560.3
Let the price of the car be x. Then,
x + 6% of x = $19,674
106x/100 = $19,674
x = $ 19,673*100/106
with BODMAS, we get
x= $18560.3
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A bottle holds 96 fluids ounce of lemonade. How much is this in pints?
Answer:
12 pints
Step-by-step explanation:
[tex]\frac{1}{8}[/tex] = [tex]\frac{8}{96}[/tex]
8 ounces is equal to 1 pint. 8 x 12 = 96, so 1 x 12 is 12
You are on vacation in New York City, and you need to get around town to different locations. Below are the rates for 2 different cab companies, locally dubbed "The Red Cabs" and "The Green Cabs".
How many miles would you travel for the cost to be the same for both cabs and how much will that cost you?
What is the difference in cost between the two companies if you need to travel 8 miles?
After seeing all your vacation photos on S n a p b o o k, your cousin decided they wanted to visit New York City also. They asked for some general advice on traveling around the city. What advice would you give them about which cab company they should use when they travel around the city?
Answer:
The costs are equal at 3 miles. It coest $8 for either company
At 8 miles the green cost 13 and the red cost 18.
My advice would be to use the Red compnay if traveling less than 3 miles and the green company is traveling more than 3 miels. At 3 miles the costs are the same.
Step-by-step explanation:
1. Which function below is an exponential function?
Answer:
D
Step-by-step explanation:
On his trip to meet Clare, Kiran brought his dog with him. At the same time Kiran
and Clare started walking, the dog started running 6 miles per hour. When it got to
Clare it turned around and ran back to Kiran. When it got to Kiran, it turned around
and ran back to Clare, and continued running in this fashion until Kiran and Clare
met. How far did the dog run?
According to the given distance, the dog can run on 22.5 miles
Distance:
Distance refers the the length of the line joining the two points. Here the two points lie on the same horizontal or same vertical line, the distance can be found by subtracting the coordinates that are not the same.
Given,
On his trip to meet Clare, Kiran brought his dog with him.
Here at the same time Kiran and Clare started walking, the dog started running 6 miles per hour.
When they got to Clare it turned around and ran back to Kiran. And when it got to Kiran, it turned around and ran back to Clare, and continued running in this fashion until Kiran and Clare met.
Here we know that they meet after 3.75 hours.
And we know that the dog was running 6 miles per hour
So, for 3.75 hours, it can be calculated as,
=> 3.75 x 6
=> 22.5
Therefore, then the dog can ran 22.5 miles.
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