Answers
Answer:
The two minimum numbers = 5, 5
Step-by-step explanation:
Let the first number = x
let the second number = y
Their sum: x + y = 10
Sum of their squares: = x² + y²
y = 10 - x
f(x) = x² + (10 - x)²
f(x) = x² + 100 - 20x + x²
f(x) = 2x² - 20x + 100
Find the derivative of f(x), to obtain the critical points;
f'(x) = 4x - 20
4x - 20 = 0
4x = 20
x = 5
The value of y is calculated as;
y = 10 - x
y = 10 - 5
y = 5
The two minimum numbers = 5, 5
Related Questions
Find the midpoint of the segment below and enter its coordinates as an ordered pair. If necessary, express the coordinates as fractions, using the slash mark (/) for the fraction bar.
(1,-1) (4,-6)
Answers
If the scale of a map is such that 10 centimeters (cm) represents 25 kilometers (km), then two buildings that are actually 54 km from each other should be how many centimeters apart?
Answers
Step-by-step explanation:
first find the value of 1km
1km= 10/25
1km= 0.4cm
now,
54km= 0.4× 54
= 21.6 cm
A farmer wants to make a rectangular field with a total area of 3200^2. It is surrounded by a fence. It is divided into 3 equal areas by fences. What is the shortest total length of fence with which this can be done?
Answers
Answer:
18133.333... units
Step-by-step explanation:
the shortest circumference for a given area based on rectangles is a square (all sides of equal length).
we cannot split a square completely into 3 equal area squares (only 4).
the best approach is then to split this main square into 3 equal area rectangles (not equal rectangles).
area of square 3200² = 10240000
a third of that area is 3413333.333...
now, splitting the main square into 3 equal "strips" of land creates 3 narrow and long rectangles, which is bad for minimizing the circumference. the best solution is to get as closely as possible to a square shape.
that we get by splitting one side in half and go in as far as the land area allows, which would be
half a side = 1600
3413333.33.../1600 = 2133.33...
so, we get 2 areas of 1600 × 2133.33...
and one area of (3200-2133.33...)×3200 = 1066.66...×3200
the length of fence needed is then
around the main square = 4×3200 = 12800
plus one length of fence between the first 2 parts : 2133.33...
plus one intensive long side between the first 2 parts and the remaining third part : 3200
in total : 18133.33...
to check : the three slices would require the 12800 plus 2 long lines inside between the 3 slices : 2×3200
in total : 19200
and an attempt to simply build one long strip of 3 equal area squares next to each other :
the side length of one such square is
sqrt(341333.33...) = 1847.520861...
as fence we would need 6 times that side length for the top and the bottom of the long strip, 2 times that side length for the sides left and right if the strip, and 2 times inside as additional delimiters between the 3 squares.
in total : (6+2+2) × 1847.520861... = 10×1847.520861...
= 18475.20861...
this is all larger than the original solution.
Question 6 of 10
How many solutions are there to the equation below?
12x + 32=124-7
A 1
B. iniintey many
co
SU
Answers
Answer:
1
Step-by-step explanation:
12x+32=117
12x=85
x=85/12
Select the correct answer.
The variable g varies directly as the cube root of h. If g=128 when h=8, which equation can be used to find other combinations of g and h?
[tex]g \sqrt[3]{h} = 256[/tex]
[tex]g = 64 \sqrt[3]{h} [/tex]
[tex]gh = 1024[/tex]
[tex]g = 16h[/tex]
Answers
the second equation is correct
Step-by-step explanation:
I got it right on the test
7000 litres of water is pumped out if a tank in 42 minutes.how many litres could be pumped out in one hour
Answers
Answer:
10000 litres
Step-by-step explanation:
using proportion
if 7000 litres equals 42 minutes
then, x litres equals 60 minutes
x = (60×7000)÷ 42
x = 10000 litres
What are the coordinates of the point that is 1/5
of the way from A(-7,-4) to
B(3,6)?
A. (-5,0)
B. (-5,-2)
C. (0,3)
O D. (1,4)
Answers
9514 1404 393
Answer:
B. (-5, -2)
Step-by-step explanation:
That point is ...
A + 1/5(B - A)
= (-7, -4) + 1/5(3 -(-7), 6 -(-4)) = (-7, -4) +1/5(10, 10)
= (-7, -4) +(2, 2) = (-5, -2)
The point (-5, -2) is 1/5 of the way from A to B.
A grocery store recently sold 6 cartons of vanilla yogurt and 12 other cartons of yogurt . Based on past data, how many of the next 48 cartons of yogurt sold should you expect to be vanilla?
Answers
There are 6 different cookies on a plate. James will choose 2 of these cookies to pack in his lunch. How many different pairs of 2 cookies can he choose from the 6?
Answers
Answer:
15
Step-by-step explanation:
He could choose 1 & 2, 1 & 3, 1 & 4, 1 & 5, 1 & 6, 2 & 3, 2 & 4, 2 & 5, 2 & 6, 3 & 4, 3 & 5, 3 & 6, 4 & 5, 4 & 6, 5 & 6
The Pitts Barbecue Company makes three kinds of barbecue sauce: Extra Hot, Hot, and Mild. Pitts’ vice president of marketing estimates that the company can sell 8,000 cases of its Extra Hot sauce plus 10 extra cases for every dollar it spends promoting this sauce; 10,000 cases of Hot sauce plus 8 extra cases for every dollar spent promoting this sauce; and 12,000 cases of its Mild sauce plus 5 extra cases for every dollar spent promoting this sauce. Although each barbecue sauce sells for $10 per case, the cost of producing the different types of sauce varies. It costs the company $6 to produce a case of Extra Hot sauce, $5.50 to produce a case of Hot sauce, and $5.25 to produce a case of Mild sauce. The president of the company wants to make sure the company manufactures at least the minimum amounts of each sauce that the marketing vice president thinks the company can sell. A budget of $25,000 total has been approved for promoting these items of which at least $5,000 must be spent advertising each item. How many cases of each type of sauce should be made, and how do you suggest that the company allocate the promotional budget to maximize profits?
a. Formulate an LP model for this problem.
b. Create a spreadsheet model for this problem, and solve it using Solver.
c. What is the optimal solution?
Answers
Answer:
Case of Extra hot sauce 8000 cases
Case of Hot Sauce 10000 cases
Case of Mild Sauce 12000 + 2000 = 14000
z´(max) = 143500 $
Step-by-step explanation:
Profit of each product:
sale price $ cost $ Profit $
Case of Extra hot sauce 10 6 4
Case of Hot Sauce 10 5.5 4.5
Case of Mild Sauce 10 5.25 4.75
The President of the company already orders the minimum of each case of sauce as follows:
Case of Extra hot sauce 8000
Case of Hot Sauce 10000
Case of Mild Sauce 12000
Let´s call
x₁ quantity of cases of Case of Extra hot sauce over 8000 cases
x₂ quantity of cases of Case of hot sauce over 10000 cases
x₃ quantity of cases of Case of mild sauce over 12000 cases
Then Objective function will be:
z = 4*x₁ + 4.5*x₂ + 4.75*x₃ to maximize
Promoting budget constraint:
each dollar investing in promoting x₁ will become 10*x₁ ( cases)
each dollar investing in promoting x₂ will become 8*x₂(cases )
each dollar investing in promoting x₃ will become 5*x₃ ( cases)
Total investment in promotion is 10000 $ again here we need by sure to invest 5000 $ in promotion for each type of sauce, leaving only extra 10000 $, then:
Constraint due to promotional budge:
10*x₁ + 8*x₂ + 5*x₃ ≤ 10000
General constraints:
x₁ ≥ 0 x₂ ≥0 x₃ ≥ 0 all integers
Then the model is:
z = 4*x₁ + 4.5*x₂ + 4.75*x₃ to maximize
Subject to:
10*x₁ + 8*x₂ + 5*x₃ ≤ 10000
x₁ ≥ 0 x₂ ≥0 x₃ ≥ 0 all integers
After 6 iterations using an on-line solver we got optimal solution:
x₁ = x₂ = 0 x₃ = 2000
z(max) = 9500 $
Then as previous comments, the production will be:
Case of Extra hot sauce 8000 + 0 = 8000
Case of Hot Sauce 10000 + 0 = 10000
Case of Mild Sauce 12000 + 2000 = 14000
The whole profits :
z´ = 4*8000 + 4.5*10000 + 4.75 ( 12000 + 2000)
z´(max) = 32000 + 45000 + 66500
z´(max) = 143500 $
Aditional comments:
If we have n products at the same price it looks obvious that we manufacture the one wich the lowest cost. In this problem, the sales price is the same for the three sauces, and the production cost is the lowest for the Mild sauce, therefore as a consequence, it will be more profitable to manufacture Mild sauce.
-22+14/2(-10)
LAST ONE:)))
Answers
[tex]\huge\textsf {Hey there!}[/tex]
[tex]\mathsf{-22 + \dfrac{14}{2}(-10)}[/tex]
[tex]\mathsf{\dfrac{14}{2}= \boxed{\bf 7}}[/tex]
[tex]\mathsf{= -22 + 7(-10)}[/tex]
[tex]\mathsf{7(-10) =\boxed{\bf -70}}[/tex]
[tex]\mathsf{= -22 + (-70)}[/tex]
[tex]\mathsf{= -22 - 70}[/tex]
[tex]\mathsf{= \boxed{\bf -92}}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf -92}}}\huge\checkmark[/tex]
[tex]\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
-92 is the answer.
Step-by-step explanation :
Let's go step by step.
-22 + 14/2(-10)
14/2 is 7, and 7 multiplied by -10 is -70, so we end up with this :
-22 + -70 = -22 - 70
-22 - 70 is -92.
-92 is the answer.
Hope this helps, please mark brainliest!
There are nine counters in a bag numbered from one to nine. If a counter is drawn at random from the bag what is the probability that the number on the counter is not a multiple of three?
Answers
Step-by-step explanation:
jajajsjhshhsejjddjidndjdjdjxndjdkhsjdjddjdkd
The probability is 1/3 that the number on the counter is not a multiple of three.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
We have to determine the probability that the number on the counter is not a multiple of three.
There are nine counters in a bag numbered from one to nine.
If a counter is drawn at random from the bag.
One to nine, there are three numbers are multiple of three that is (3, 6, 9)
Here favorable outcomes = 3
So the probability that the number on the counter is not a multiple of three as
⇒ 3/9
⇒ 1/3
Therefore, the probability is 1/3 that the number on the counter is not a multiple of three.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ2
Which expression is equivalent to:1/m6
Answers
Answer:
A
Step-by-step explanation:
6 is a power. So both C and D are wrong because 6 is being treated as an ordinary integer.
So the answer must be either A or B.
B is not correct because to move an expression from the denominator to the numerator changes the sign in the base (which is m in this question).
A is correct. the power is changed from 6 in the denominator to -6 in the numerator. m is shifted to the numerator as well.
HELPPP!
Carl had two pieces of pizza. One piece had an angle measure of 60. The other one had an angle of 45. He put the two pieces together to make one large angle. What angle do the two pieces of pizza form?
Answers
Answer:
105°, obtuse angle
Step-by-step explanation:
60 + 45 = 105
Hope this helps :D
Why is android sound louder then iPhone???
Answer ASAP
Cause my volume isn’t as loud as android and my speakers work fine and so does the volume?
Answers
Answer:
There are many outcomes or data that needs to be collected... like does the iPhone and android share the same speaker? or are your speaker grills blocked out by something? or is your iPhone old, because they do change the speaker each gen.
Help help help help
Answers
answer: 116⁰
z⁰ for y⁰ because it's
equal
what are the domain and range of this function
Answers
Answer: domain: ARN
Range: y less than or equal to 0
Step-by-step explanation:
The arrows indicate that the lines continue forever, so the domain is all real numbers.
The lines only travel under the x-axis, so the range is y less than or equal to zero.
On a particular game show, there are 8 covered buckets and 2 of them contain a ball.
To win the game, a contestant must select both buckets that contain a ball. Find the
probability that a contestant wins the game if he/she gets to select 4 of the buckets.
Answers
Answer:
0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.
Step-by-step explanation:
The buckets are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
8 covered buckets, so N = 8.
4 buckets are selected, so n = 4.
2 contain a ball, which means that k = 2.
Find the probability that a contestant wins the game if he/she gets to select 4 of the buckets.
This is P(X = 2). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,8,4,2) = \frac{C_{2,2}*C_{6,2}}{C_{8,2}} = 0.2143[/tex]
0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.
Taylor is playing a video game. She eams 15 points when she completes Level 1. Each time she completes a level, she earns three
times as many points as the previous level.
How many points will Taylor earn when she completes Level 6?
Answers
3645 points will Taylor earn when she completes Level 6.
What is a permutation?Permutation is the arrangement of items in which order matters. In this situation order matters repetition allowed.
According to the question,
Taylor is playing a video game. She earns 15 points when she completes Level 1.
Each time she completes a level, she earns three times as many points as the previous level.
= 15 × [tex]3^{6-1}[/tex]
= 15 × [tex]3^{5}[/tex]
= 15 × 243
= 3645
Hence, 3645 points will Taylor earn when she completes Level 6.
Learn more about permutation here
https://brainly.com/question/11710155
#SPJ2
Please helpppp me i
Answers
Answer:
y=-15/2 + 3x/4
Step-by-step explanation:
i need help with this one plz! (marking BRAINLIST) :)
Answers
Answer:
I gotchu man watch this
Step-by-step explanation:
in order to find x u gotta use tan or toh
opposite over hyp
anyway 17*tan(21)
6.525688596
or 6.53
Answer:
Step-by-step explanation:
tan θ = opposite / adjacent
tan 21 = x / 17
17 tan 21 = x
x = 6.52
What transformation of the parent function f(x) is made to get -2f(x)?
A. A reflection of the X axis and a vertical stretch by 2
B. Vertical vertical stretch by 2
C. A reflection on the y axis
D. A reflection in the x axis
Answers
Answer:
A.
Step-by-step explanation:
The negative gives a reflection in the x-axis.
The 2 is a vertical stretch factor 2.
Zeus Computer Chips, Inc., used to have major contracts to produce the Centrino-type chips. The market has been declining during the past three years because of the quad-core chips, which it cannot produce, so Zeus has the unpleasant task of forecasting next year. The task is unpleasant because the firm has not been able to find replacement chips for its product lines. Here is demand over the past 12 quarters:
Two Years
Ago Last Year This Year
I 4800 I 3500 I 3,200
II 3500 II 2700 II 2100
III 4300 III 3500 III 2700
IV 3,000 IV 2,400 IV 1700
Use the decomposition technique to forecast demand for the next four quarters.
Answers
Answer:
1st quarter := 2488.23
2nd quarter = 1646.50
3rd quarter = 1893.98
4th quarter = 1152.93
Step-by-step explanation:
Forecast demand in the next four quarters
intercept ( a ) = 3116.67 - (- 168.25 * 6.5 ) = 4210.29
Slope ( b ) = ( 219041.15 ) - ( 12 * 6.5 * 3,116.67 ) / 650 - ( 12 * ( 6.5)^2 )
= -24059.11 / 143 = -168.25
Forecast demand = a + bt = 4210.29 + 168.25t
1st quarter := 2488.23
2nd quarter = 1646.50
3rd quarter = 1893.98
4th quarter = 1152.93
Values calculated using data from table attached below ( table 2 )
Help me please if you can't don't touch it
Answers
Answer:
C
Step-by-step explanation:
volume of cone= ⅓πr²h
Given: r= 3 in, h= 10 in
Volume of the cone
[tex] = \frac{1}{3} (\pi)(3^{2} )(10)[/tex]
= 30π
= 94.248 in³ (5 s.f.)
≈ 94 in³
please help me this is due today!! it’s number 6
what is the length of AB
Answers
(I think the first one is easier to understand; but obviously it’s the way to prove solution 2)
what is the value of x to the nearest tenth
Answers
Answer:
tan90°=p/b
or,1/0=10/x
therefore x=0
1. What are two possible first steps you could use when solving an equation like `6(x+4)=30?`
Answers
Answer:
Step-by-step explanation:
take 30 devide it by 6 then minose 4 off that and get x=1
Answer:
x = 1
Step-by-step explanation:
6(x + 4) = 30
Simplify.
6x + 24 = 30
Subtract 24 from each side.
6x + 24 - 24 = 30 - 24
Simplify.
6x = 6
Divide each side by 6.
6x ÷ 6 = 6 ÷ 6
Simplify.
x = 1
Use the Pythagorean Theorem to find the missing side
of right triangle RST in simplest radical form.
Answers
Answer:
9
Step-by-step explanation:
hip^2 = cat^2+cat^2
41^2= 40^2 + x^2
1681 = 1600 + x^2
1681-1600 = x^2
81 = x^2 /√
√81 = √x^2
9 = x
In this picture, m∠XOZ = 70° and m∠YOZ = 37°. If m∠XOY = (5x + 16)°, what is the value of x?
Answers
Answer:
x = 3.4
Step-by-step explanation:
You have the value of xoz = 70, yoz = 37 and xoy = 5x+16
Set your formula up as
xoz = yoz + xoy
70 = 37 + 5x + 16
70 - 37 - 16 = 5x
17 = 5x
17 / 5 = x
3.4 = x
[tex]\huge\bold{Given :}[/tex]
m∠XOZ = 70°
m∠YOZ = 37°
m∠XOY = ( 5x + 16 )°
[tex]\huge\bold{To\:find :}[/tex]
The value of x°.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]{\boxed{\mathcal{\red{The\:value\:of\: x° \:is\:3.4° .\:}}}}[/tex]✅
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
We know that,
[tex]\sf\pink{m∠XOZ\:=\:m∠YOZ\:+\:m∠XOY}[/tex]
➪ 70° = 37° + 5x° + 16°
➪ 5x° + 53° = 70°
➪ 5x° = 70° - 53°
➪ 5x° = 17°
➪ x° = [tex] \frac{17° }{5} [/tex]
➪ x° = 3.4°
[tex]\sf\red{Therefore, \:the\: value \:of \:x°\: is \:3.4°.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
✒ 70° = 37° + 5 x 3.4° + 16°
✒ 70° = 37° + 17° + 16°
✒ 70° = 70°
✒ L. H. S. = R. H. S.
[tex]\boxed{Hence\:verified.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
ASAP
How many different arrangements can made using the letters of the word ATHABASCA if...
(a) Each arrangement begins with three A's.
(b) Each arrangement must begin with only two ffs . (The third letter can't be an A)
Answers
Answer:
Poooooop it is poop no cap legit
Step-by-step explanation:pooooooop
Pls believe me the dam answer is poop