The minimum cost to produce the product is $7.
What are functions?
A function from a set X to a set Y allocates exactly one element of Y to each element of X.To determine the minimum cost:
We have to determine the minimum cost of producing this product.
Since [tex]f(x) = 5x^{2} -70x+258[/tex].
Now, consider the equation [tex]5x^{2} -70x+258= 0[/tex].
Dividing the above equation by 5, we get
[tex]x^{2} -70x/5+258/5=0\\x^{2} -14x+258/5=0[/tex]
Now, considering the coefficient of 'x', dividing it by '2' and then adding and subtracting the square of the number which we got after dividing.
Since the coefficient of 'x' is 14, and half of 14 is '7'.
So, adding and subtracting from the above equation.
[tex]x^{2} -14x+(7)^{2} -(7)^{2}+258/5=0\\x^{2} -14x+49 -49+258/5=0\\(x-7)^{2} -49+258/5=0\\(x-7)^{2} +258-245/5=0\\(x-7)^{2} +13/5=0\\5(x-7)^{2} +13=0[/tex]
Now, we have to determine the minimum cost to produce the product.
Since [tex]f(x) = 5x^{2} -70x+258[/tex].
[tex]f'(x) = 10x-70[/tex]
Now, let f'(x)=0
[tex]10x-70=0\\10x=70[/tex]
Therefore, x=7
Now, consider which is greater than 0.
Therefore, x= 7 is the minimum cost.
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Answer: The minimum cost to produce the product is $13.
I apologize for the late answer, hope this helps in the future!
Step-by-step explanation:
To complete the square, we need to rewrite the given function in the form:
f(x) = a(x - h)^2 + k
where (h, k) is the coordinates of the vertex of the parabola defined by the function, and a is a positive constant that determines the shape of the parabola.
We start by factoring out the coefficient of x^2:
f(x) = 5(x^2 - 14x + 51.6)
To complete the square, we need to add and subtract a constant inside the parentheses that will allow us to write the expression inside the parentheses as a perfect square. The constant we need to add and subtract is half of the coefficient of x, squared:
f(x) = 5(x^2 - 14x + 51.6 + (7)^2 - (7)^2)
= 5((x - 7)^2 + 13)
Now we have the function in the desired form, with a = 5, h = 7, and k = 13. Since a is positive, we know that the vertex of the parabola is a minimum. Therefore, the minimum cost of producing the product is $13. So the correct answer is:
5(x − 7)2 + 13
In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height. Use Heron's formula to find the area, in square yards, of ΔABC.
a = 12, b = 11, c = 7
Answer:
12 sqrt (10)
Step-by-step explanation:
S = (12 + 11 + 7) / 2 = 15
A = sqrt (s(s-a)(s-b)(s-c))
= sqrt (15(15-12)(15-11)(15-7))
= sqrt (15*3*4*8)
= sqrt (1440)
= 12 sqrt (10)
Needdddd helpppp someone please
Answer:
none
Step-by-step explanation:
From the markings in the diagram above, we know that corresponding angles of the two triangles are congruent, but since we can make infinite number of triangles with same angle measures as triangle RIE by changing the side lengths, we cannot conclude that the triangles are congruent.
9. Josh and his friends are having a race home from
school. Which of the children actually ran the
fastest on average if their times and the
distances traveled are as follows?
A) Josh - 600 meters in 1200 seconds
B) Harry - 0.8 kilometers in 25 minutes
C) Ali-450 meters in 0.3 hours
D) Matt - 1.5 kilometers in 0.0375 days
Answer:
josh has the fastest average speed of 0.03 km/h
Step-by-step explanation:
shown my working in the image linked . i hope it is helpful how i have worked it out .
I hope its helpful . if you need any more help pls let me know if you can't read it pls let me know . I have tried explaining as much as I can.
pls give brainliest if you found my answer useful :)
find the value of x and y that satisfies both the equaties x/y= 2/3 and y/24=3/4
Answer:[tex]\Large\boxed{x=12~;~y=18}[/tex]
Step-by-step explanation:
Given a system of equations
[tex]1)~\frac{x}{y} =\frac{2}{3}[/tex]
[tex]2)~\frac{y}{24} =\frac{3}{4}[/tex]
Multiply 24 on both sides of 2) equation to isolate y-value
[tex]\frac{y}{24}\times24 =\frac{3}{4}\times24[/tex]
[tex]\Large\boxed{y=18}[/tex]
Substitute the y-value into the 1) equation
[tex]\frac{x}{18} =\frac{2}{3}[/tex]
Multiply 18 on both sides of 1) equation to isolate y-value
[tex]\frac{x}{18}\times18 =\frac{2}{3}\times18[/tex]
[tex]\Large\boxed{x=12}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Wynn is 24 years old and has decided to reduce the number of cups of coffee he buys by 2 cups per day. One cup of coffee typically costs $2.50. Assuming 30 days in a month, if he chooses to invest this money at the end of every 6 months into an investment paying 5.50% compounded semi-annually, how much will he have when he turns 69?
The total amount he would have at 69 is $343,347.81.
What is the total amount saved?The formula that can be used to determine the future value of the deferred annuity is:
Future value = annuity factor x monthly deposit
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 5.5 /2 = 2.75%n = number of payments = 2 x (69 - 24) = 90Amount he would save every 6 months:
amount saved per day = $2.50 x 2 = $5Amount saved per month : $5 x 30 = $150 Amount saved every 6 months = $150 x 6 = $900Future value : 900 x {[(1.0275^90) - 1] / 0.275}= $343,347.81
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Which of the following is an even function?
A) f(x) = (x – 1)^2
B) f(x) = 8x
C) f(x) = x^2 – x
D) f(x) = 7
Answer:
D) f(x) = 7Step-by-step explanation:
A function is even when f(-x) = f(x) for all x in the domain of f. We can say that the function is simetrical over x axis.
That's all i know, Hope it helps!
Question 9 of 20:
Select the best answer for the question.
9. Select the proper order from least to greatest for 23.76.8.10 -
A. 8,3,10.76.
B.23,10.6.8.
C.8.10 6.2/3.
D.76%10.3.8.
Answer:
Please make the question clearer, but I would say B
Step-by-step explanation:
I am not sure what you mean, to me the question is unclear
A ride at a park has room for 8 children to ride at once.
How many rides are needed to allow 45 children a turn?
Answer:
6
Step-by-step explanation:
45/8=5.625
Since there are .625 children left, we need to add another ride to fill in what's left.
help i dont remember dis stuff from last year
See below for the solution to the systems of equations
How to solve the systems of equations?System of equations 1
Here, we have
3x - 4y = -16
3x + 4y = 8
We start by plotting the graph of both equations
Next, we write out the point of intersection of the equations
See attachment for the equation of the system
From the attached graph, the point of intersection of the equations is (-4/3, 3)
Hence, the solution to the system is (-4/3, 3)
System of equations 2
Here, we have
-x = - 6 + 2y
-18 + 6y = -3x
We start by plotting the graph of both equations
Next, we write out the point of intersection of the equations
See attachment for the equation of the system
From the attached graph, both lines are on each other
This means that the system of equations have infinite many solutions
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20 POINTS TO SOLVE THIS ANSWER!!!
Answer:
V₁ = 104 in.³ , S₂ = 650 in. ²
Step-by-step explanation:
⇒ Ratio = 4/10 = 2/5
⇒ V₁ : V₂ = (ratio)³ = 8/125 {geometric scale}
⇒ S₁ : S₂ = (ratio)² = 4/25
∴ V₁ = 8/125 × V₂ = 1,625 in³ × 8/125 = 104 in.³
⇒ S₂ = 25/4 × S₁ = 104 in² × 25/4 = 650 in.²
Determine whether the sequence converges or diverges. if it converges, find the limit. (if an answer does not exist, enter dne. ) an = n2 n3 5n
The sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.
For given question,
We have been given a sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex]
We need to determine whether the sequence converges or diverges.
From given sequence we have, [tex]a_{n+1}=\frac{(n+1)^2}{(n+1)^3+5(n+1)}[/tex]
We use Ratio Test.
According to Ratio Test, [tex]r=\frac{a_{n+1}}{a_n}[/tex], where sequence converges if and only if |r| < 1.
Consider,
[tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(n+1)^2}{(n+1)^3+5(n+1)}}{\frac{n^2}{n^3+5n}} |\\\\\\= \lim_{n \to \infty} |\frac{(n+1)^2(n^3+5n)}{n^2[(n+1)^3+5(n+1)]} |\\\\=\infty[/tex]
Since [tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |[/tex] is not defined, the sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.
Therefore, the sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.
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In a simple bivariate regression with 60 observations, there will be _____ residuals.
There will be 60 residuals for simple bivariate regression's 60 observations.
According to the statement
We have given that the there is 60 observations and we have to find the number of simple bivariate regression for these observations.
So, For the solution of this problem,
We know that the
A simple linear regression (also known as a bivariate regression) is a linear equation describing the relationship between an explanatory variable and an outcome variable, specifically with the assumption that the explanatory variable influences the outcome variable, and not vice-versa.
And we know that the it is always same for the number as the number of given observations.
That's why there is 60 residuals.
So, There will be 60 residuals for simple bivariate regression's 60 observations.
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PLEASE I NEED THIS FAST there are 3 denominations of bills in a wallet: $1, $5, and $10. there are 5 fewer $5-bills than $1-bills there are half as many $10-bills if there is $115 altogether, find the number of each type of bill in the wallet
The number of $1, $5 and $10 are 49, 44 and 22 respectively.
How to use equation to find the number of bills?There are 3 denominations of bills in a wallet: $1, $5, and $10.
There are 5 fewer $5-bills than $1-bills.
let
x = number of $1 bills
Hence,
number of $5 bills = x - 5
There are half as many $10-bills as $5-bills.
number of $10 bills = 1 / 2 (x - 5)
Therefore,
x + x - 5 + 1 / 2 (x - 5) = 115
2x - 5 + 1 / 2 x - 5 / 2 = 115
2x + 1 / 2 x - 5 - 5 / 2 = 115
5 / 2 x - 7.5 = 115
2.5x = 115 + 7.5
x = 122.5 / 2.5
x = 49
Number of $1 bills = 49
Number of $5 bills = 49 - 5 = 44
Number of $10 bills = 1 / 2 (49 - 5) = 22
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Solve for x.
°x = 196
Enter your answers in the boxes. Enter the smallest answer first.
x= ____ and x= ____
4 andfirst find x by finding its smallest factor
The solution to the given system of equation is -7 and 7
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
Given:
4x² = 196
4x²/4= 196/4
x² = 49
x=√49
x= ±7
Hence, the solution to the given system of equation is -7 and 7
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3. (x,y) → (x + 2,y) → (x, y)
-10-8
-4-2
10
8
6
2
-2
T
ID
-6
-8
-10
9
10
4. (x,
-10-8
HELPPP PLSSSS
1) A translation 2 units right
2) A reflection over the x-axis
is (n x (n +1)) / 2 the same as (n/2)(n+1)
Answer:
nope
Step-by-step explanation:
simplify the first equation
Answer:
yes
Step-by-step explanation:
The associative and commutative properties of multiplication allow you to rearrange the product to the form shown in the question.
Division by 2 is effectively multiplication by 1/2.
[tex](n\times(n+1))/2\qquad\text{given}\\\\=\dfrac{n(n+1)}{2}=\dfrac{n}{2}(n+1)\\\\=\boxed{(n/2)(n+1)}[/tex]
__
Additional comment
Evaluation of the expressions according to the order of operations will proceed differently for the two expressions.
For the first expression, evaluation steps are ...
add 1 to nmultiply the sum by ndivide the product by 2For the second expression, evaluation steps are ...
divide n by 2add 1 to nmultiply the results of these two operationsAs we said above, the properties of multiplication ensure the results are the same either way.
As a practical matter, for integer values of n, one of n and (n+1) will be even. It is usually convenient to divide the even number by 2. This means the evaluation might be ...
((n+1)/2)n . . . . for odd n(n+1)(n/2) . . . . for even nFor certain computer representations of the numbers, results may differ depending on the specific numbers and the order of evaluation.
Determine whether each pair of triangles is congruent. If yes, include the theorem or
postulate that applies and describe the series of rigid motions that map one triangle onto the
other.
A.
4
B.
ΔΔ
C.
D.
The pair of triangles in option A, C and D are congruent triangles.
Pair of triangles are given.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
A) In the given figure, two angles and one side of the one triangle is equal to two angles and one side of the other triangle
By AAS congruence, two triangles are congruent.
B) In the given figure, one angle and one side is equal
So, two triangles are not congruent
C) Here, two sides and one included angle of the one triangle is equal to two sides and one included angle of the other triangle
D) Here, two angles and one included side of the one triangle is equal to two angles and one included side of the other triangle.
Therefore, the pair of triangles in option A, C and D are congruent triangles.
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Consider the steps to solve the equation. 2 5 ( 1 2 y + 20 ) − 4 5 = 9 20 (2y − 1)
Distribute: 1 5 y + 8 − 4 5 = 9 10 y − 9 20
What is the next step after using the distributive property?
*Use the multiplication property of equality to isolate the variable term on one side of the equation.
*Use the multiplication property of equality to isolate the constant on one side of the equation.
*Combine the like terms on the right side of the equation.
*Combine the like terms on the left side of the equation.
Answer:
D
Step-by-step explanation:
I did the assignment
hope this helps :)
evaluate 4 + 6 x 6 / 8
Answer:
8.5
Step-by-step explanation:
4 + (6)(6)/8=
17/2 = 8.5
Answer:
8.5
Step-by-step explanation:
6 x 6 = 36/8 = 4.5 + 4 = 8.5
Area=
What is the area?
Help me asap! Please!! Thanks so much:)
Answer:
area = 10
Step-by-step explanation:
Triangle BOC is a right triangle. You can see this because the slope of BO and OC are negative reciprocals (opposite sign and flipped over) You can calculate the slope, m.
m = (y-Y)/(x-X)
Slope of BO is 4/2,
slope of OC is -2/4.
see image.
So then you can use BO and OC as the base and height in an area calculation.
But first you have to calculate the length of each. Luckily they are the same length. You can use distance formula, but when you have a picture, you can just see to use Pythagorean theorem (distance formula comes from PythagThm anyway)
Both BO and OC have legs length 2 and 4. See image. They are both length sqrt20.
Use Area= 1/2bh to find the area. See image.
(6 1/7 divided by x + 3 5/9) / 4 1/6 = 1 1/3 what is x
let's firstly convert the mixed fractions to improper fractions and them proceed.
[tex]\stackrel{mixed}{6\frac{1}{7}}\implies \cfrac{6\cdot 7+1}{7}\implies \stackrel{improper}{\cfrac{43}{7}} ~\hfill \stackrel{mixed}{3\frac{5}{9}}\implies \cfrac{3\cdot 9+5}{9}\implies \stackrel{improper}{\cfrac{32}{9}} \\\\\\ \stackrel{mixed}{4\frac{1}{6}}\implies \cfrac{4\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{25}{6}} ~\hfill \stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{ ~~ \frac{6\frac{1}{7}}{x}+3\frac{5}{9} ~~ }{4\frac{1}{6}}~~ = ~~1\frac{1}{3}\implies \cfrac{ ~~ \frac{ ~~ \frac{43}{7} ~~ }{x}+\frac{32}{9} ~~ }{\frac{25}{6}}~~ = ~~\cfrac{4}{3}\implies \cfrac{ ~~ \frac{43}{7x}+\frac{32}{9} ~~ }{\frac{25}{6}}~~ = ~~\cfrac{4}{3}[/tex]
[tex]\cfrac{43}{7x}+\cfrac{32}{9}~~ = ~~\cfrac{25}{6}\cdot \cfrac{4}{3}\implies \cfrac{43}{7x}+\cfrac{32}{9}~~ = ~~\cfrac{50}{9}\implies \cfrac{43}{7x}~~ = ~~\cfrac{50}{9}-\cfrac{32}{9} \\\\\\ \cfrac{43}{7x}~~ = ~~\cfrac{18}{9}\implies \cfrac{43}{7x}=2\implies 43=14x\implies \cfrac{43}{14}=x\implies 3\frac{1}{14}=x[/tex]
Franco has enough paint to cover an area of approximately 226 square feet. he needs to paint a cylinder that is 5 feet long. what is the maximum possible radius of the cylinder that can be covered by the paint?
The required radius of the cylinder that can be covered by the paint exists at 3.8 feet.
Franco has enough paint to protect an area of about 226 square feet. He must paint a cylinder that exists 5 feet, and the maximum possible radius of the cylinder that can be covered by the paint exists to be determined.
What is a cylinder?The cylinder exists described as a 3D solid that holds two identical bases joined by a curved surface, at a particular distance.
Here, Franco keeps sufficiently paint to cover an area of about 226 square feet.
Area of the cylinder = 226
Area of the cylinder = πr²h = 226
h = 5 feet and π = 3.14
3.14 [tex]*[/tex] 5 [tex]*[/tex] r² = 226
r² = 226/15.70
[tex]$r = \sqrt{14.70}[/tex]
r = 3.80
Therefore, the required radius of the cylinder that can be covered by the paint exists at 3.8 feet.
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Answer: 4
Step-by-step explanation: I got the answer 4 right on the test
A ________ standard deviation represents an overall wide spread of data points while a ________ standard deviation represents a closely clustered set of points.
Answers are in bold
A larger standard deviation represents an overall wide spread of data points while a smaller standard deviation represents a closely clustered set of points.
Keep in mind the standard deviation cannot be negative. A standard deviation of 0 means that every data value is the same number; hence it is the most clustered set possible. There is no upper limit on how big the standard deviation can be.
If needed, replace "larger" with "large". And if needed, replace "smaller" with "small". I think it will depend on how your teacher wants you to word it. In all honesty, I'm not very good with grammar.
A larger standard deviation represents an overall wide spread of data points while a smaller standard deviation represents a closely clustered set of points.
What is standard deviation?The term "standard deviation refers to a measurement of the data's dispersion from the mean.
A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
The standard deviation cannot be negative, so keep that in mind. The most tightly clustered set of data is one with a standard deviation of 0, which denotes that all the data values are the same.
The size of the standard deviation has no upper bound.
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After working for 25 hours when water made $375. after working for 40 hours lamar made $600. predict how much he would make up to 10 hours of work.
correct 0.34213 to three significant figures
Answer:
0.342
Step-by-step explanation:
round to the given amount of significant figures
Mr Lim had a bag of sweets. After giving each pupil 7 sweets, he had 4 sweets left. If he had given only 5 sweets to each pupil, he would have 4 sweets left. If he had given only 5 sweets to each pupil, he would have 80 sweets left.
i.How many pupils were there in the class?
ii. How many sweets did Mr Lim have?
Solving a system of equations we can see that there are 270 sweets and 38 pupils.
How many pupils and sweets are there?
Let's define the variables:
P = number of pupils.
S= number of sweets.
With the given information, we can write:
7*P + 4 = S
5*P + 80 = S
So we have a system of equations, now we can write:
7*P + 4 = S = 5*P + 80
Solving that for P:
7*P + 4 = 5*P + 80
7*P - 5*P = 80 - 4
2*P = 76
P = 76/2 = 38
There are 38 pupils, and the number of sweets is given by:
S = 7*P + 4 = 7*38 + 4 = 270
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1. Ansley meets her fruends at the movie theter. They had already purchased a bucket of popcorn, and there is only 3/4 left. Ansley eats 1/3 of the remaining popcorn. How much of the bucket did Ansley eat?
2. Jamie bought 6 pool floats to use during the summer. 2/3 of the floats were tellow. How many yellow floats did he buy?
3. Mrs. Jones purchases 2/3 of a pound of cookies for her class. If the cookies are $6.00 per pound, how much did she pay for the cookies?
4.The school band has 24 members. If 1/8 of them play the drums how many members of the band play the drums?
5. Callie spent 1 1/2 hours outside with her sister. They spent half of theat time jumping on their trampoline. How long did they jump on the trampoline?
1. he ate 1/4 of the bucket
2. 4 of the pool floaties are yellow.
3. she paid 4$ for the cookies
4 . 3 members of the band play the drums
5. 45 minutes
Answer:
1. Ansley eats 1/4 of the popcorn bucket
2. He bought 4 yellow floats
3. She pays 4 pounds for the cookies
4. 3 members of the band play the drums
5. They spent 45 minutes jumping on the trampoline
Step-by-step explanation:
If you would like the explanation, I can comment it below (≧∇≦)/ xx
Hope this helps! ♡
Find the volume of the figure. Round your answers to the nearest tenth. It is recommended you use the π button on your calculator to solve.
The volume of the figure is 1, 005. 4 mi³
Volume of a cylinderNote that the figure is a cylinder
The formula for volume of a cylinder is given as;
Volume = πr²h
Where
h = height = 5 mi
r = radius = 8mi
Substitute into the volume
Volume = 3. 142 × 8 × 8 × 5
Volume = 1,005. 4 mi³
Thus, the volume of the figure is 1, 005. 4 mi³
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Find the missing segment in the image below.
Answer:
105.
Step-by-step explanation:
x/120 = 56/64 where x is the length of missing segment
64x = 120*56
x = (120*56)/64
= 105.
Veronica's trail-mix package says there are 7 peanuts for every 3 cashews. Casey's trail-
mix package says there are 63 peanuts and 27 cashews. Are these ratios proportional?
If not, how many peanuts should there have been to make it proportional?
Answer:
Yes, they are proportional.
Step-by-step explanation:
The ratio for Veronica's trail mix is 3:7
The ratio for Casey's trail mix is 27:63 <--- Simplify this number
27:63 simplified is 3:7, which means these ratios are proportional.
hope this helps :)