The length of the route of a bicylist that has covered 5/7 of his route and an additional 40 miles and yet to cover 118 miles less than 0.75 of his route is 168 miles.
How to form equation and solve for the variable?The bicyclist covered 5 / 7 of his route and an addditional 40 miles.
Let
x = distance of his route in miles
Hence,
distance covered = 5 / 7 x + 40
He has yet to cover 118 miles less than 0.75 of his route. Therefore,
distance not covered = 0.75x - 118
Distance of his route = 5 / 7 x + 40 + 0.75x - 118
x = 5 / 7 x + 40 + 0.75x - 118
x = 1.464x - 78
x - 1.464x = -78
-0.464x = -78
x = 78 / 0.464
x = 168.103448276
x = 168 miles
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Answer:
0.5
Step-by-step explanation:
total no. of tiles
= 3 + 6 + 3
= 12
probability of tile being green
= 6 / 12
= 1/2
= 0.5
hope this helps!
A stereo manufacturer determines that in order to sell x units of a new stereo, the price per unit , in dollars, must be p(x) = 100 - x. The manufacturer also determines that the total cost of producing x units is given by C(x) = 3000 + 2x. a. Express the total revenue function R as a function of x. b. Express the total profit P as a function of x. c. How many units must the company produce and sell in order to maximize profit d. What is the maximum profit? e. What price per unit must be charged in order to make this maximum profit .
Answer: See below
Step-by-step explanation:
a)
[tex]$$The total revenue R(x) is obtained as:\begin{align*} R\left( x \right) &= xp\left( x \right)\\ &= x\left( {100 - x} \right)\\ &= 100x - {x^2} &$$$ R(x) = 100x - {x^2} \end{align*}[/tex]
[tex]$$Thus, {R\left( x \right) = 100x - {x^2}[/tex]
b)
[tex]$$The total profit is obtained as: \begin{align*} P\left( x \right) &= R\left( x \right) - C\left( x \right)\\ &= 1000x - {x^2} - 3000 - 20x\\ &= - {x^2} + 980x - 3000 \end{align*}[/tex]
[tex]$$Hence, P\left( x \right) = - {x^2} + 980x - 3000[/tex]
c)
[tex]$$For maximum profit dP/dx should be equal to zero: \begin{align*} \dfrac{{dP}}{{dx}} &= 0\\ - 2x + 980 &= 0\\ x &= 490 \end{align*}[/tex]
[tex]$$So, the required units to maximize profit is 490[/tex]
d)
[tex]$$The maximum profit is calculated as: \begin{align*} P\left( x \right) &= - {x^2} + 980x - 3000\\ P\left( {490} \right) &= - {490^2} + 980 \times 490 - 3000\\ &= 237100 \end{align*}[/tex]
[tex]$$Accordingly, the maximum profit is \$237100.[/tex]
e)
[tex]$$Calculating the price at maximum profit as: \begin{align*} p\left( x \right) &= 1000 - x\\ p\left( {490} \right) &= 1000 - 490\\ &= 510 \end{align*}[/tex]
[tex]$$Consequently, the price at the maximum profit is \$510.[/tex]
Put the following linear relationships in order from least rate of change to greatest rate of change.
1: y=2x+7
2: y=5x-3
3: y=3x
4: y=4x+6
Answer:
1. 3. 4. 2.
Step-by-step explanation:
All the given linear relationships are given in slope-intercept form
y = mx + b (where m is the slope and b is the y-intercept).
The slope (gradient) of the line represents the rate of change. Therefore, we need to examine the slope of each relationship, and order them accordingly.
Solution
From least rate of change to greatest rate of change:
1. y = 2x + 7
3. y = 3x
4. y = 4x + 6
2. y = 5x - 3
If the area of a rectangle is x4 + 3x3 - 2x2 - 200 and the width is x + 5, find its length.
Answer:
Step-by-step explanation:
Area = 4x + 9 - 4 - 200
= 4x - 195
Since Area is lw, let the width be x + 5 and y be the unknown length.
Therefore (x + 5) (y) = 4x - 195
Answer:
x³ - 2x² + 8x - 40
Step-by-step explanation:
Area = length · width
(x⁴ + 3x³ - 2x² + 0x¹ - 200) = length · (x + 5)
length = (x⁴ + 3x³ - 2x² + 0x¹ - 200) ÷ (x + 5)
BRAINLIEST please if this helped!Use the function below to find f(3)
F(x) = (1/4)x
Please help!!
Solve For m
m = - ( 4 + m ) + 2
Which of the following will form the composite function G(F(x)) shown
below?
G(F(x)) = (x-7)2 + (x-7)-1
A. F(x)=(x-7)2 and G(x)=(x-7)-1
B. F(x)=x²+x-1 and G(x) = x-7
C. F(x)=(x-7)-1 and G(x)=(x-7)²
D. F(x)= x-7 and G(x)=x²+x-1
SUBMIT
Answer:
The answer is D.
Step-by-step explanation:
-27 w3 + 125 factorize
[tex]-1(3w-5)(9w^{2} +15w+25)[/tex]
9 to the power of 0 is what number
Answer:
1Step-by step Explanation:
∴ Exponent rule: Any number that has an exponent as 0, the result is 1.
⇒ 9⁰ = 1Thus, the result is 1.
Someone help, please and thank you
Answer:
6√2
Step-by-step explanation:
Given,
θ = 45
Opposite side = 6
To find : - Hypotenuse
Formula : -
sin θ = Opposite side / Hypotenuse
[ The value of sin 45 = 1 / √2 ]
sin 45 = 6 / Hypotenuse
1 / √2 = 6 / Hypotenuse
Cross multiply,
Hypotenuse = 6√2
Answer:
6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
a 45-45-right triangle always has the same relationship between the legs and hypotenuse.
leg:leg:hypotenuse
x:x:x[tex]\sqrt{2}[/tex]
Can you just answer question 23!!! i need help!!!
Answer:
It is Graph A because it has the properties of a cubic graph.
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Case Study 2: Maxing out Matched Savings
Chen's employer will match 50% of their $250 monthly contributions to their 401(k). This
means that Chen's employer will put 50% of $250 = $125 into Chen's 401(k) account each
month in addition to Chen's $250. Free money-- Nice! (this is common!)
How much will Chen have after 40 years of saving $250 their own money if the account
compounds monthly at 3% APR?
hint: Use the TVM Solver on the Tl or this website. Remember, ignore the - sign. Don't forget
about the matching!
Type answer as a number without the $ symbol rounded to the hundredths. Example, if it
the answer was $1234.5687, you would enter 1234.57.
Answer:
The computation of the given question is shown below:-
Total Contributions = Monthly contribution + Amount invested in Ferdinand’s 401(k)
= $250 + $125
= $375
1. Future Value = PMT [((1 + r)n - 1) ÷ r
Future value = 375 × ((1 + 0.03 ÷ 12) × 12 × 40 - 1) ÷ (0.03 ÷ 12)
= $347,272
2. Ferdinand deposit = Given Amount × Total number of months in a year × Number of years
= $250 × 12 Months × 40 Years
= $120,000
3. The Amount put in by the employer = 50% of $250 ×Total number of months in a year × Number of years
= $125 × 12 Months × 40 Years
= $60,000
4. Interest = Future value - Ferdinand deposit - The Amount put in by the employer
= $347,272 - $120,000 - $60,000
= $167,272
Step-by-step explanation:
Please help on the question as attached by providing detailed steps. Tq
Answer:
Step-by-step explanation:
Students and teachers at a school were asked if they preferred blue, green, red, or yellow. The table shows the results of the survey. Blue Green Red Yellow Total Students 5 10 20 15 50 Teachers 15 10 5 20 50 Total 20 20 25 35 100 Choose three statements that can be inferred from the data in the table. A. 20% of all people surveyed chose blue. B. 20% of the students surveyed chose red. C. 20% of the students surveyed chose blue. D. 20% of the teachers surveyed chose green. E. 20% of those who chose red were teachers. F. 20% of those who chose yellow were teachers.
20% of all people surveyed chose blue and 20% of the teachers surveyed chose green. Then the correct options are A and D.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Students and teachers at a school were asked if they preferred blue, green, red, or yellow.
The table shows the results of the survey.
[tex]\begin{matrix}&\rm Blue &\rm Green &\rm Red &\rm Yellow &\rm Total \\\\\rm Students &5 &10 &20 &15 &50 \\\\\rm Teachers &15 &10 &5 &20 &50\\\\\rm Total &20 &20 &25 &35 &100\end{matrix}[/tex]
A. The probability of the people who chose blue will be
[tex]\rm P = \dfrac{20}{100} = 0.2 \ or \ 20\%[/tex]
B. The probability of the student who chose red will be
[tex]\rm P = \dfrac{20}{50} = 0.4 \ or \ 40\%[/tex]
C. The probability of the student who chose blue will be
[tex]\rm P = \dfrac{5}{50} = 0.1 \ or \ 10\%[/tex]
D. The probability of the teachers who chose green will be
[tex]\rm P = \dfrac{10}{50} = 0.2 \ or \ 20\%[/tex]
E. The probability of the teachers who chose red will be
[tex]\rm P = \dfrac{5}{50} = 0.1 \ or \ 10\%[/tex]
F. The probability of the teachers who chose yellow will be
[tex]\rm P = \dfrac{20}{50} = 0.4 \ or \ 40\%[/tex]
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Latasha reads 9 pages in 3 minutes. Latasha reads at a rate of
per minute. She reads at a rate of ?
minute per page.
Answer:
3 pages per minute.
Step-by-step explanation:
If we know that she reads 9 pages in 3 minutes, then we can divide the whole speed by 3 to get how much she reads in one minute.
3 pages in 1 minute.
a bike requires 2 hours of assembly and a swing 3 hours. a maximum of 250 hours of assembly time are available. the profit is $50 on a bike and $20 on a swing. if no more than 100 items can be produced how many of each should be assembled for maximum profit?
The assemble for maximum profit is mathematically given as
For maximum profit, 100 tire and 0 strings must be assembled.
How many of each should be assembled for maximum profit?Generally, the equation for the max number is mathematically given as
Mx=50x+20y
Therefore
2x+3y \leq 250
x1+x\leq=100
Therefore
with cordinates of
(0,0)
(100,0)
(50,50)
(0,250/3)
In conclusion, The mx of 50x+20y is (100,0)
Hence, for maximum profit 100 tire and 0 strings must be assembled.
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Need help with math please
(3+2a)² alguien sabe la respuesta?
Answer:
3(3+2a)+2a(3+2a)
9+6a+6a+4a^2
9+12a+4a^2
ANS 4a^2+12a+9
Which of the functions below could possibly have created this graph?
O A. F(x) - –** – x2 – 3x2 +3
O B. F(x) = x + 13** + 12x
C. F(x) = -x + 2x* +6x
D. F(x)= x4 – x2 – 3x +3
Answer:
D
Step-by-step explanation:
All you have to do is put it in desmos, hope this helped :)))
The graph of the equation is f ( x ) = x⁴ - x³ - 3x² + 3
What is Equation of Graph of Polynomials?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
Let the equation of the graph be represented as A
Now , the value of A is
f ( x ) = x⁴ - x³ - 3x² + 3
There are no asymptotes for the function
And , the graph of the function is plotted below
Hence , the equation is f ( x ) = x⁴ - x³ - 3x² + 3
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I need help ASAP!!!! Worth 20 points!
Answer:
x in (-oo:+oo)
(5/4)*x-(3/7) = 0
(5/4)*x-3/7 = 0
5/4*x-3/7 = 0 // + 3/7
5/4*x = 3/7 // : 5/4
x = 3/7/5/4
x = 12/35
x = 12/35
Step-by-step explanation:
A self-serve car wash charges $5.52 to use its facilities, plus an additional $0.95 for each minute the customer is at the self-serve
car wash. If Tiffany was at the car wash for 5 minutes, how much was she charged?
A. $10.52
B. $6.47
C. $10.27
D. $4.75
How to do this one ?
The volume of the conical mountain, to the nearest whole number, is approximately 143 cubic kilometers.
What is the Volume of a Cone?Volume of a cone = 1/3πr²h, where h os the height, r is the radius.
Given the following dimensions of the conical mountain:
Height (h) = 3.8 kmRadius (r) = 6 kmVolume of the mountain = 1/3πr²h = 1/3π(6²)(3.8)
Volume of the mountain ≈ 143 km³
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What’s 1+2?
Answer fasttttt
I will mark you as branly
Answer:
3
Step-by-step explanation:
uhhhhhhhhhhhhh yeah
image Which absolute value equation represents the graph? Question 7 options: A) ƒ(x) = –|3x| – 5 B) ƒ(x) = 5|x| – 3 C) ƒ(x) = |5x – 3| D) ƒ(x) = 3|x – 5|
The function f(x) = |x| shift horizontally to the right by 5 units with a stretch of 3 units. The resulting function will be f(x) = 3|x - 5|
Transformation of functionsTransformation is a technique used to change the position of an object on an x-plane.
The parent function of the shown graph is f(x) = |x|
The attached graph shows that the function f(x) = |x| shift horizontally to the right by 5 units with a stretch of 3 units. The resulting function will be f(x) = 3|x - 5|
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How many hours would it take to watch 170 episodes of a show, each episode is about 23 minutes long.
Answer:
Around 65 hours(2 days and 17 hours)
Each episode is 23 minutes long, and there's 170 episodes, so multiply 23 by 170 being 23 minutes for each episode.
[tex]23 * 170 = 3,910[/tex]
Now, convert 3,910 minutes to hours by dividing for every 60 minutes.
[tex]3,910 / 60 = about~65[/tex]
Therefore, the answer is ≈65
the exact value is 65.16667
Wilbur has homework assignments in seven subjects. He only has time to do five of them.
Answer:
21 waysStep-by-step explanation:
Given
Wilbur has 7 subjects' homeworkHe can only do 5 of themCombination Formula
ⁿCₓ = n! / (n - x)! x!Number of possible ways
⁷C₅ = 7! / 2! x 5!⇒ 7 x 6 x 5! / 2! x 5!⇒ 7 x 6 / 2⇒ 7 x 3⇒ 21 waysWrite the inverse variation function given that y varies inversely with x, and y = 0.5 when x = 24.
[tex]\large{\text{Refer\:to\:explanation\:pls}}[/tex]
Calculation ↓If y varies inversely with x, we divide :
y = [tex]^k/_x[/tex]
Where
k = constant of proportionality
We are given that :
y = 0.5
x = 24
So we write :
0.5 = [tex]\Large\text{$^k/_{24}$}[/tex]
Multiply by 24 on [tex]\Large{\text{both\:sides\::}}[/tex]
12=k
[tex]\Large{\text{The\:constant\:of\:proportionality\:is\:12.}}[/tex]
So we havey = 12/x
[tex]\footnotesize{\text{hope\:helpful}}[/tex]
There is 1/2 of a pizza left for 4 friends to
share. What fraction of a pizza will each
friend get to eat?
will make brainlest and rate 5 stars and say thanks
you could solve this problem one of two ways-
1)
100/4 25/2 12.5
100, equals the entire pizza. 4, is the number of people. 25, is the amount they all get. They you divide by 2 since it is only a half pizza.
-or-
2)
100/2 50 50/4 12.5
100, equals the entire pizza. Divide that by 2 since it half a pizza. 100/2 equals 50. Then, since there is 4 friends you divide 50 by 4. Which equals 12.5.
In conclusion, the final answer is 12.5% of the pizza each.
Hope this helps!!
Look at the following ratio:
3:8
Write an equivalent ratio if it was three times greater:
24 out of 50 children prefer the color blue. what
percentage of children prefer the color blue?
Answer:
48%
Step-by-step explanation:
as a fraction is 24/50
make denominator 100 so times by 2
24 x 2 = 48 so
48/100 = 48%