Answer:
The answer is below
Step-by-step explanation:
Let x represent the length of the fence along the stone side and y represent the length of the fence along the wood side. The cost of building the fence C(x) is given by:
C(x) = 100x + 20(2y + x)
C(x) = 100x + 40y + 20x
C(x) = 120x + 40y
Since the area = 7500 ft²,
⇒ xy = 7500
y = 7500/x
[tex]C(x) = 120x + 40(\frac{7500}{x} )\\\\C(x) = 120x+\frac{300000}{x}\\ \\Differentiating\ with\ respect\ to\ x:\\\\C'(x) =120-\frac{300000}{x^2} \\\\At\ minimum\ cost,C(x)=0\\\\hence:\\\\0=120-\frac{300000}{x^2}\\\\\frac{300000}{x^2}=120\\\\120x^2=300000\\\\x^2=\frac{300000}{120}\\ \\x^2=2500\\\\x=\sqrt{2500} \\\\x=50\ ft[/tex]
[tex]C"(x)=\frac{600000}{x^3}\\ \\C"(50)=\frac{600000}{50^3}=4.8>0\\\\y=\frac{7500}{x} =\frac{7500}{50} =150\ ft[/tex]
Hence to minimize cost, 50 ft of fence is used along the stone side and 150 ft of fence along the wood side
Find the inverse of f(x) = 4x + 2.
The inverse of f is g(x) PLSSSS HELPPPPP!!!!!
Answer:
y=(x+2)/4
Step-by-step explanation:
f(x) = 4x +2 is the original equation
x = 4y + 2 is the inverse but we have to solve for y
x+2=4y
4y=x+2
y=(x+2)/4
A bag of popcorn contains 483 calories and serves 3.5 people. How many calories are in each serving?
Answer:
U simply multiply 483 by 3.5
=1690.5
Step-by-step explanation:
A certain forest covers an area of 3200km^2. Suppose that each year this area decreases by 3%. What will the area be after 7 years ?
3200*3%+3200=3296 this means each year it would increase by 96
96*7=672
672+3200=3872km^2
What is 2/3 divided by 1/2
Answer:
1.33333333333
Step-by-step explanation:
There is your answer!
1. A student says that the zeros of y = (x - 2)(x + 7) are -2 and 7. Is the student correct? If not, describe and correct the error the student made.
2. Explain why x^2 + 25 is not equal to (x + 5)^2?
3. Describe how the factoring can help you find the x-intercepts of the graph of the quadratic function y = x^2 - 4x + 3.
Answer: 1) NO. the zeros are: 2 and -7
2) (x + 5)² has a middle term when in expanded form
3) Factoring provides the Intercept form: y = a(x - p)(x - q)
Step-by-step explanation:
1) y = (x - 2)(x + 7)
To find the zeros, set the factors equal to zero:
0 = x - 2 0 = x + 7
x = 2 x = -7
The zeros are 2 and -7.
The student did not set the factors equal to zero.
2) (x + 5)² = (x + 5)(x + 5)
= x² + 5x + 5x + 25
= x² + 10x + 25 ≠ x² + 25
3) The Intercept form of a quadratic equation is: y = a(x - p)(x - q) where p and q are the x-intercepts. Notice that the intercept form IS the factored form. Set the factors equal to zero to find the x-intercepts.
y = x² - 4x + 3
y = (x - 1)(x - 3) --> Intercept form
0 = (x - 1)(x - 3) --> finding the zeros (aka x-intercepts)
0 = x - 1 0 = x - 3
x = 1 x = 3 --> zeros are 1 and 3
1.The zeroes are 2,-7
2.[tex]x^2 + 25\neq ( x + 5)^{2}[/tex]
3. So, factoring can help to find the x-intercepts
1.We have y = (x - 2)(x + 7)
For zeroes of y , Put y=0
(x - 2)(x + 7) =0
x=2,-7
So, the zeroes of y = (x - 2)(x + 7) are 2 and -7.
2. We have [tex]x^2 + 25[/tex]
[tex]x^2 + 25= x^2 + 5^{2}[/tex]
And
[tex](x+ 5)^{2} \\=x^{2} +5^{2} +10x\\=x^{2} +25 +10x\\\neq x^{2} +25[/tex]
So, [tex]x^2 + 25\neq ( x + 5)^{2}[/tex]
3.We have the quadratic function [tex]y = x^2 - 4x + 3[/tex]
[tex]y=x^2 - 4x + 3\\=(x-3)(x-1)\\[/tex]
For x-intercept put y=0, we get
[tex](x-3)(x-1)=0\\x=3,x=1[/tex]
So, factoring can help to find the x-intercepts of the graph of the quadratic function [tex]y = x^2 - 4x + 3.[/tex]
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A bicycle manufacturing plant is producing the first few frames for their new electric bicycle design. The first batch of 60 frames has some issues: 1/3 of the frames had a weak junction where top tube meets the seat tube. After some fine tuning, a second batch of 120 frames is made, of which 1/4 are bad, still having the weak junction. Finally, another bug is fixed and a third batch of 180 frames is made and only 1/5 of these are bad. Unfortunately, due to a clerical error, all 360 frames were combined, unlabeled, into the same shipping bin. You have access to a quick test that checks if a bike frame is defective, which is correct with probability 9/10. That is, if the bike frame is defective, the test will say it is defective with probability 9/10. If the bike frame is not defective, the test will say it is defective with probability 1/10.
A) Determine the probability that the test returns "defective," P[D].B) Determine the probability that, given the test returns "not defective," the bike frame is not bad P[Bc |Dc].
Answer:
a) 131/450
b) 1233/1276
Step-by-step explanation:
P(bad) = P(1st batch)*P(bad 1st batch ) + P(2nd batch )*P(bad 2nd batch) + P(3rd batch )*P(bad 3rd batch)
p(bad) =(60/360)*(1/3) + (120/360)*(1/4 ) + (180/360)*(1/5)
= 43/180
And that of P(good )
= 1 - 43/180
= 137/180
a)
P(defective) = P(bad)*P(defective /bad) + P(good)*P(defective /good)
= (43/180)*(9/10) + (137/180)*(1/10)
= 131/450
b)
P(Bc I Dc ) = P(good)*P(not defective |good) / P(not defective)
= (137/180)*(1 - 1/10) / (1 - 131/450)
= 1233/1276
Let the Universal set be the letters a through J:
Answer:
{a, b, d}Step-by-step explanation:
A= {a, b, d, e}B = {a, d, h, j}C = {a, b, g, h}A ∩ (B ∪ C) = {a, b, d, e} ∩ {a, b, d, g, h, j} = {a, b, d}
(01.05 MC)Taylor bought 6 tickets to a movie. The price of each ticket was
the same. After he bought the tickets, his account balance showed a change
of -$68.04. What would have been the change to Taylor's account balance
had he only bought 1 ticket to the movie?
Answer:
-$11.34
Step-by-step explanation:
Each of these tickets have been said to have the same costs of buying them.
If 6 tickets = -68.04 dollars
1 ticket = ?
We cross multiply to get the unknown
6 x ? = 1 x -68.04
Such that
? = -68.04/6
= -$11.34
So in conclusion if Taylor had not bought these 6 tickets and had only gotten 1 for the movie, the change to his account balance would be $-11.34
three medium apples have about 285 calories
Answer:
3 apples = 885 calories
Step-by-step explanation:
3 x 285 = 885
Answer:
95 calories per apple
Step-by-step explanation:
285 / 3
= 95
Best of Luck!
Madison’s band used to practice for 50 minutes every Tuesday. Now they practice 130% as many minutes as they used to. How many minutes do they play on Tuesdays now?
Answer:
it is 65 :)
Step-by-step explanation:
Answer:
Answer is 65.
Step-by-step explanation:
I got it right on Time4Learning
Amy spent $6.00 for 2 gallons of gas. Bobby paid $15.00 for 6 gallons of gas. Carlos paid $32.00 for 8 gallons of gas. List the people in order of how much they paid for one gallon of gas, from the cheapest to the most expensive cost per gallon.
Answer:From cheapest to most expensive: Bobby, Amy, Carlos
-Hope this helped!
Step-by-step explanation:
Amy pays $3. 6/2=3
Bobby pays $2.50. 15/6=2.5
Carlos pays $4. 32/8=4
Triangle ABC was translated to form triangle A'B'C'. Which describes the transformation? Check all that apply.
A.
It is non rigid
B.
The size is preserved
C.
It is rigid
D.
The angles are not preserved
E.
It is isometric
Answer:
B, C, E
Step-by-step explanation:
Translation is a rigid transformation. As such, it preserves sizes and angles. "Isometric" is another way to say "the size is preserved."
What is g^-1(x)? What is the domain of g^-1(x)?
Answer:
g⁻¹(x) = 1/x - 4
(-∞, 0)∪(0, ∞)
Step-by-step explanation:
To find g⁻¹(x), switch the places of x and y. Rearrange the equation so that it is equal to y.
g(x) = 1/(x + 4)
x = 1/(y + 4)
x(y + 4) = (1/(y + 4))(y + 4)
x(y + 4) = 1
(x(y + 4))/x = 1/x
y + 4 = 1/x
y + 4 - 4 = 1/x - 4
y = 1/x - 4
g⁻¹(x) = 1/x - 4
For the domain, you need to look at where x is located in the equation. For this equation, x is in the denominator by itself. A fraction cannot have a denominator of 0. This means that x cannot be equal to 0. The domain is:
(-∞, 0)∪(0, ∞)
How many solutions are there to the equation
8x - 7 = 2 (2x + 7) - 5
Answer:
x=4
Step-by-step explanation:
8x - 7 =2(2x +7) - 5
8x - 7 =4x +14 - 5
8x - 7 =4x +9
8x - 4x =9 +7
4x =16
x=16 :4
x=4
A moderately active 140 pound person will use 2100 calories per day to maintain that body weight, how many calories per day are necessary to maintain a moderately active 145 pound person
Answer:
2,175 calories
Step-by-step explanation:
140 pound person will use 2100 calories per day
145 pounds person will use x calories per day
Find x
Pounds : calories
140 : 2100 = 145 : x
140/2100 = 145/x
Cross product
140 * x = 2100 * 145
140x = 304,500
Divide both sides by 140
x = 304,500 / 140
= 2,175
Therefore,
145 pounds person will use 2175 calories per day
A health study tracked a group of person for five years. At the beginning of the study, 20% were classified as heavy smokers, 30% as light smokers, and 50% as nonsmokers. Results of the study showed that light smokers were twice as likely as nonsmokers to die during the five-year study, but only half as likely as heavy smokers. A randomly selected participant from the study died during the five-year period. Calculate the probability that the participant was a heavy smoker. g
Answer: 0.421
Step-by-step explanation:
Heavy smoker = 20%
Light smoker = 30%
Non smokers = 50%
We can assume that the probability that a non-smoker is going to die in the next 5 years be y.
Since light smokers were twice as likely as nonsmokers to die during the five-year study, the probability will be:
= 2 × y = 2y
Probability for the Heavy smokers will be:= 2 × 2y = 4y
The expected number of people that will die for each in the next 5 years will be:
Non smoker:
= 50% × y
= 0.5 × y
= 0.5y
Light smoker:
= 30% × 2y
= 0.3 × 2y.
= 0.6y
Heavy smoker:
= 20% × 4y.
= 0.2 × 4y
= 0.8y
Total = 0.5y + 0.6y + 0.8y = 1.9y
The probability that the participant was a heavy smoker will be:
= 0.8y/1.9y
= 0.421
The sum of -3 and x is 5?!
Answer:
is this a question or a comment
Step-by-step explanation:
Factor Please show steps
3^5 + 12^4 − 36^3
Answer:
-25677 = -3^4×317^1
Step-by-step explanation:
Factor the following integer:
-25677
Hint: | Show that 25677 is divisible by 9.
The sum of the digits of 25677 is 2 + 5 + 6 + 7 + 7 = 27, which is divisible by 9. This means 25677 is too
25677 = 9×2853:
-25677 = -9×2853
Hint: | Express 9 as a square.
9 = 3^2:
-25677 = -3^2×2853
Hint: | Show that 2853 is divisible by 9.
The sum of the digits of 2853 is 2 + 8 + 5 + 3 = 18, which is divisible by 9. This means 2853 is too
2853 = 9×317:
-25677 = -3^2×9×317
Hint: | Express 9 as a square.
9 = 3^2:
-25677 = -3^2×3^2×317
Hint: | 3 has no proper divisors.
3 is prime:
-25677 = -3^2×3^2×317
Hint: | Find a divisor of 317 by testing the integers between 2 and sqrt(317)≈17.8 for divisibility.
Because 317 is odd, only test odd numbers for divisibility
317 is not divisible by 3, 5, 7, 9, 11, 13, 15 or 17
Since 317 is not divisible by any integer up to 17, it is prime:
-25677 = -3^2×3^2×317
Hint: | Express -25677 as a product of prime powers.
There are 4 copies of 3 and 1 copy of 317 in the product:
Answer: -25677 = -3^4×317^1
According to the graph about _____ of households in Africa owns a computer in 2008.
2013 about 1/3 of all households in_______ had a computer.
the number of households with a computer is_______ in all regions overtime
The graph is described in math as a graphical representation or diagram that organizes data or concepts. This graph's dots frequently indicate the relationship of two or more things. A bar chart can then be used to measure the information.
In 2008, nearly 5% of African households owned a computer, according to the graph.In 2013, almost one-third of all Asia homes owned a laptop.Throughout time, the proportion of families that own a computer is increasing across the board.Therefore, the final answer is "5%, Asia, and increasing".
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A contractor has five styles of homes, each with six styles of garages, five styles of decks, and six styles of carpeting. How many different possible homes are there?
Answer:
First, we need to list all the possible selections and the number of options that each selection has:
Style of home: 5 options.
Style of garage: 6 options.
Style of decks: 5 options.
Style of carpeting: 6 options.
The number of different combinations of possible homes is equal to the product between the number of options for each selection.
This is:
C = 5*6*5*6 = 900
So there are 900 possible houses (that are all different in some aspect)
What number should be at pyramid
[tex]\tt Step-by-step~explanation:[/tex]
To solve, we have to look for a pattern.
[tex]\tt Step~1:[/tex]
When you see pyramids like these, they usually tell you to add/multiply the two numbers to get a third number that goes on top. Here, we can see 3 and 4 on the bottom left hand corner. The third number on top of both 3 and 4 is 7. 3 + 4 = 7. Let's check 4 and 5, the middle two numbers. 4 + 5 = 9, and that number is on top of 4 and 5. Therefore, we can confirm that this is an addition pyramid.
[tex]\tt Step~2:[/tex]
Since 7 + 9 is 16 and 9 + 8 is 17, all we need to do in order to get the final number is to add 16 to 17.
[tex]\tt 16 + 17 =33[/tex]
[tex]\large\boxed{\tt Our~final~answer: ~33}[/tex]
A trail runner gets a new map of her favorite mountain.
HELP PLEASE ILL GIVE BRAINLIST
• Her old map has a scale of 1 cm to 100 m.
• Her new map has a scale of 1 cm to 500 m.
If the maps represent the same area, are the distances on the new map longer, shorter, or the same size as the old map? PLEASE HELP
Answer:
Shorter
Step-by-step explanation:
Since in the new map 1 cm is representing a larger area of 500m as compared to the previous map where 1cm represented 100m.
Kylie jarred 12 liters of jam after 2 days. How many days does Kylie need to spend making
jam if she wants to jar 48 liters of jam in all? Solve using unit rates.
days
The graph shows the costs of two types of fruit at a store. A graph measuring cost and amount. Two lines, labeled Cherries and Apples, exit the origin to show that cost increases as amount increases Drag and drop the appropriate symbol to the box to compare the rates of the fruits. cost of apples per lb Response area cost of cherries per lb
The cost of apples per lb is less than cost of cherries per lb.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have the graph shows the costs of two types of fruit at a store. Two lines, labeled Cherries and Apples, exit the origin to show that cost increases as amount increases.
Slope of the line representing apples is smaller than slope of the line representing cherries. This means that the unit rate for cherries is greater than that of apples. So, cost of apples per lb is less than cost of cherries per lb.
Therefore, the cost of apples per lb is less than cost of cherries per lb.
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Mr. Drew wants to build a square sandbox with an area of 225 square feet.
What is the total length of wood Mr. Drew needs to make the sides of the sandbox?
The length of the sandbox will be 15 feet.
What is the area of the square?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.
Given that Mr. Drew wants to build a square sandbox with an area of 225 square feet.
The length will be calculated by using the area formula for square.
Area of square = Length x width
Since the length and width of the square are the same. Then the area of the square can be written as:-
Area of square = ( Length )²
225 = ( Length )²
( Length ) = √225
( Length ) = 15 feet
Therefore, the length of the sandbox will be 15 feet.
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evaluate [(30+6)-3^2] ÷ by 9·2
Answer:
PEMDAS
[(30+6)-3^2] ÷ by 9·2
[(30+6)-9] ÷ by 9·2
[(36)-9] ÷ by 9·2
(27) ÷ by 9·2
Division comes first in this equation. Multiplication & Division goes from left to right when using PEMDAS. Same thing goes for Addition & Subtraction.
[(27) ÷ 9] · 2
(3) · 2
Answer: 6
Hopefully that made sense!
Step-by-step explanation:
_
Step-by-step explanation:
hello..................
From 1960 to 1980, the consumer price index (CPI) increased from 29.6 to
82.4. If a pound of grapes cost $0.14 in 1960 and the price of grapes
increased at the same rate as the CPI from 1960 to 1980, by approximately
how much did the price of a pound of grapes increase from 1960 to 1980?
A. $0.82
B. $0.25
C. $0.39
D. $0.30
The price of pound of grapes increased from 1960 to 1980 is $0.25.
What is a consumer price index?The Consumer price index (CPI) may be a measure of the typical change overtime within the prices paid by urban consumers for a market basket of goods and services.The CPI is one amongst the foremost popular measures of inflation and deflation. The CPI report uses a special survey methodology, prices sample and index weights than the producer index number (PPI), which measures change within the prices received by producers of products and services.Given:
CPI in 1960 = 29.6
CPI in 1980 = 82.4
Price of pound of grapes in 1960 = $0.14
We have to find the increase in the price of pound of grapes from 1960 to 1980.
Now, the rate of increase in the CPI from 1960 to 1980 is given by:
⇒ Rate = (CPI in 1980) / (CPI in 1960)
⇒ Rate = 82.4/29.6
⇒ Rate = 2.78
Now, the price of pound of grapes in 1980 will be calculated as:
⇒ Price of pound of grapes in 1980 = (rate of increase in the CPI from 1960 to 1980) × (Price of pound of grapes in 1960)
⇒ Price of pound of grapes in 1980 = 2.78 × $0.14
⇒ Price of pound of grapes in 1980 = $0.389
Increase in the price of pound of grapes from 1960 to 1980 will be calculated as:
⇒ Increase in the price = (Price of pound of grapes in 1980) - (Price of pound of grapes in 1960)
⇒ Increase in the price = $0.389 - $0.14
⇒ Increase in the price = $0.249
⇒ Increase in the price ≈ $0.25
Therefore, the approximate increase in the price of pound of grapes from 1960 to 1980 is $0.25.
Hence, Option (B) is correct.
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pliz answer my question,start from Qno:15
15 -differences between gymnosperms and angiosperms:
In gymnosperms ovules are exposed but in angiosperm ovules are enclosed in ovary.In angiosperm seeds are enclosed inside the fruits but in gymnosperm seeds are not enclosed inside the fruits.Gymnosperm bear cones instead of flowers but angiosperm bear well developed flowers.16-
They have mammary glands.Their body is covered with hai.Breathing takes place through lungs.17- Uniform acceleration is a change of equal velocity in equal interval of tine.
Non- Uniform acceleration is a change of unequal velocity in equal interval of time.
18- Three equation of motion:
v =u+ats=ut+1/2at^2v^2 = u^2+ 2as Hope this helps!!!The distance around the lake is 0.75 mile. Ryan ran around the lake 3 times on Saturday. How far did he run?
Solve the absolute value equation. If no solution write NO SOLUTION.
-{2x + 3] + 8
12
Answer:
If problem is "-|2x+3|+8=12"
then there is (no solution.)
Step-by-step explanation:
Let's solve your equation step-by-step.
−|2x+3|+8=12
Step 1: Add -8 to both sides.
−|2x+3|+8+−8=12+−8
−|2x+3|=4
Step 2: Divide both sides by -1.
−|2x+3|=4
-1 -1
|2x+3|=−4
Step 3: Solve Absolute Value.
|2x+3|=−4
No solutions Because absolute value is less than 0.
