The required positive number whose product is 25 and whose sum is minimum is 5, 5
Sum of Two numbers
Sum of two numbers means adding two same or different number together
Let two positive numbers xy = 25
Divide both side by x
y = [tex]\frac{25}{x}[/tex] ----------Equation (1)
Sum of two positive numbers s = x + y -------Equation (2)
Substitute equation (1) into equation (2)
S = x + [tex]\frac{25}{x}[/tex]
differentiate with respect to x
[tex]\frac{ds}{dx} = \frac{d}{dx} (x + \frac{25}{x} ) = 1 - \frac{25}{x^{2} }[/tex]
[tex]\frac{ds}{dx} = 1-\frac{25}{x^{2} }[/tex] ---------- Equation (3)
[tex]\frac{ds}{dx} = 0[/tex]
[tex]1[/tex][tex]- \frac{25}{x^{2} }[/tex] = 0 ⇒ [tex]x^{2}[/tex] = 25
x = 5
Differentiate equation (3) again
[tex]\frac{d^{2}s }{dx^{2} } = 0 + \frac{50}{x^{2} }[/tex]
hence, at point x = 5, [tex]\frac{d^{2} s}{dx^{2} } = \frac{50}{5^{2} }[/tex] [tex]= \frac{50}{25} = 2[/tex]
Value of s minimum at point x = 5.
substitute the value of x into equation (1)
[tex]y = \frac{25}{x} = \frac{25}{5} = 5[/tex]
Therefore the required positive numbers are 5, 5.
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A flower shop sells bouquets in a basic
arrangement and in a deluxe arrangement.
The table shows the sales of each type for
d days.
Arrangement
Basic
Deluxe
Cost ($)
17
25
Number Sold
8d-7
3d +6
Part A Write an expression that represents the difference between the number of basic
arrangements and deluxe arrangements sold.
Part B The store sells more basic arrangements than deluxe arrangements. After 7 days,
how much money will the store have earned on the number of basic arrangements that
exceeds the number of deluxe arrangements? Explain how you found your answer.
Part A: The formula 5d-13 indicates the distinction between the quantity of basic arrangements and deluxe arrangements sold.
Part B: The difference between the money the store made from basic arrangements and deluxe arrangements is $158.
What does an expression mean?An expression, also known as a mathematical expression, in mathematics is a finite combination of symbols that are well-formed in accordance with principles that depend on the context. Mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, grouping, and integers (constants) to help with logical grammar and operation ordering.
Part A: (8d-7)-(3d+6)
=8d-7-3d-6
=5d-13
Part B: For 7 days, d=7
Cost No. of sold
Basic 17 8(7)-7=49
Deluxe 25 3(7)+6=27
Therefore, Basic=17*49=$833
Deluxe=25*27=$675
Difference=833-675=158
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Bobby bought 3 T-shirts at the mall
and a pair of pants for $16 at the
clothing store. All together he spent $28
for the clothes. How much was each
shirt?
Answer: $4
Step-by-step explanation: we know he spent 28 dollars in total and 16 of those was on a pair of pants so we can subtract 16 from 28 to get 12
we also know he bought 3 shirts in total and because 12/3=4 each shirt must have cost 4 dollars.
We can check the answer by combining the price of the shirts (12)
with the price of the pants (16) because 12+16=28 we know the cost of each shirt has to be $4.
Answer:
Each shirt was 4 dollars.
Step-by-step explanation:
28 - 16 = 12. 12 divided by 3 = 4.
g the center for medicare services reported that there were 295,000 reported appeals for hospitalization and other medicare part a services. for this group, 40% of the first round appeals were successful. suppose ten first round appeals were just received. the results follow a binomial distribution. what is the probability of getting more than two heads? enter answer to four decimal places.
The probability that of getting more than two heads is 0.9537.
Describe the binomial probability?There are just two options for each appeal: either it has been accepted or it wasn't. A binomial probability is employed to answer this question since the chances that one appeal will be permitted is independent of the possibility that any other appeals will be granted.The probability of precisely x successes per n repeated trials is known as a binomial probability, and X has only two possible outcomes.
P(X = x) = Cn,ₓ.pˣ(1 - p)ⁿ⁻ˣ ...eq 1
Where Cn,ₓ represents the number of distinct combinations of x items drawn from a group of n elements, as determined by the formula below.
Cn,ₓ = n!/x!(n - x)!
Where p is the likelihood that anything will happen.
10 appeals are necessary; n = 10.
Because 40% of appeals are successful; p = 0.4.
For the probability of getting at least two heads.
P(X ≥ 2) = 1 - P(X < 1)
P(X < 2) = P(X = 0) + P(X = 1)
Put the values in eq 1 and get the values for X.
P(X < 2) = 0.006 + 0.0403 = 0.0463
Now,
P(X ≥ 2) = 1 - 0.0463
P(X ≥ 2) = 0.9537
Thus, the probability that of getting more than two heads is 0.9537.
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x+3y+z=-8
4x-2y-z=-9
5x+3y+2z=-19
please help me with this
That aint no question
students in a statistics class are conducting a survey to estimate the mean number of units students at their college are enrolled in. the students collect a random sample of 46 students. the mean of the sample is 12.5 units. the sample has a standard deviation of 1.8 units. what is the 95% confidence interval for the average number of units that students in their college are enrolled in? assume that the distribution of individual student enrollment units at this college is approximately normal.
The 95% confidence interval for the average number of units that students in their college are enrolled in is (11.46,12.53)
We are given the number of students, n = 46, and the mean of the sample which is x= 12.5, and the standard deviation of the sample which is s= 1.8 , the formula we are referring to for calculating the confidence interval which is :
x ± t (s/√(n))
since for this case, the degree of freedom is one less than the mean, which is 45, the critical value for the confidence of 95% with the degree of freedom of 45 is 2.015
x + t(s/√(n)) = 12.5 +2.015*(1.8/6.78)= 12.53
x - t(s/√(n))= 12.5 -2.015*(1.8/6.78)= 11.46
The interval is (11.46,12.53)
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Adam's Bikes rents bikes for $19 plus $8 per hour. Nicole paid
$67 to rent a bike. For how many hours did she rent the bike?
Answer:
6 hours.
Step-by-step explanation:
Subtract initial fee from total. (67 - 19 = 48).
Divide by the hourly rate. (48 / 8 = 6).
The bike was rented for 6 hours.
Can someone help me with this please?
The volume of the rectangular prism is the 75 ft cube.
How to find the volume of a prism?The prism below is a rectangular prism.
A rectangular prism is a three-dimensional shape, having six faces, where all the faces (top, bottom, and lateral faces) of the prism are rectangles such that all the pairs of the opposite faces are congruent.
The volume of a rectangular prism can be express as follows:
Volume of a rectangular prism = base area × height
Therefore,
base area of the prism = 25 ft²
height of the prism = 3 ft.
Hence,
Volume of the rectangular prism = 25 × 3
Volume of the rectangular prism = 75 ft³
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When you answer, could you just put the letter of the number you have? Thank you.
In the given triangle KLM with coordinates K(0,2) ,L(2 ,9) ,M(4,2), the sets of points which represent the dilation from the origin is K'(0,8), L'(8, 36) , M'(16, 8) multiply by scale factor 4.
As given in the question,
In the given triangle KLM,
Coordinates of the triangle KLM are given by :
K(0,2) ,L(2 ,9) ,M(4,2)
Dilation from the origin is represented by:
a. K'(0,2) , L'(8,9) , M'(16, 2)
Dilation scale factor does not effect on all the coordinates .
Not a correct option.
b. K'(0,2) , L'(2,36) , M'(16, 2)
Dilation scale factor does not effect on all the coordinates .
Not a correct option.
c. K'(0,8) , L'(8,36) , M'(16, 8)
Multiply by scale factor 4.
Dilation exist.
d. K'(4,6) , L'(6,13) , M'(8, 6)
Scale factor of addition of 4.
Dilation does not exist.
Therefore, in the given triangle KLM with coordinates K(0,2) ,L(2 ,9) ,M(4,2), the sets of points which represent the dilation from the origin is K'(0,8), L'(8, 36) , M'(16, 8) multiply by scale factor 4.
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12. 15-2x) ≤ 11 What is the solution set to the inequality above?
its 4 cause i have done this
First, we isolate the variable on one side of the inequality by subtracting 15 from both sides:
15 - 2x - 15 ≤ 11 - 15
Simplifying the left side, we get:
-2x ≤ -4
Next, we divide both sides by -2. Since we are dividing by a negative number, we need to flip the inequality sign:
-2x/-2 ≥ -4/-2
Simplifying, we get:
x ≥ 2
Therefore, the solution to the inequality 15-2x ≤ 11 is x ≥ 2.
add me cuties
A board game is played by moving a counter S space forward at a time, where S is determined by the following rule: A fair six-sided dice is thrown once. S is half the number shown on the dice if that number is even; otherwise S is twice the number shown on the dice.
1. Write out a table showing the possible value of S and their possibilities.
2. Find the probability that, in a single turn, a player moves their counter forward more than 2 spaces.
The table showing the possible value of S and their possibilities is attached below,
The probability that a player moves their counter forward more than 2 spaces is 0.5.
The Probability is the ratio of favorable outcomes to total number of outcomes. The probability of an event must be less than 1 as the sum of all probabilities of events is equal to 1.
Here, If the number on the dice is even, S is half that number; if it is not even, S is double that amount. The table showing the possible value of S and their possibilities is attached below,
Now, finding the probability that a player moves their counter forward more than 2 spaces,
As seen from the table, the number of favorable outcomes where the player moves the counter more than 2 spaces is 3.
The total number of outcomes is 6. so, the probability will be,
Probability [tex]=\frac{3}{6}[/tex]
[tex]=\frac{1}{2} \\\\=0.5[/tex]
Hence, the probability that a player moves their counter forward more than 2 spaces is 0.5.
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you would like to create a rectangular vegetable patch with an area of 32 sq. ft. to grow oranges. the fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. what are the dimensions of the vegetable patch with the least expensive fence? let the variable x denote the length of the east and west sides of the garden and let the variable y denote the length of the north and south sides of the garden. you and your friends individually set up a solution for the optimization problem using these variables. who set up the problem properly?
The maximum and minimum measurements are 5 and -3 respectively.
f ( x ) = -x^3 +3x^2+ 45 x + 10
f' l x ) = 0
0 = - 3x^2 +6x +45
x = 5,- 3.
f ( 4 ) = - ( 4 )^3+ 3( 4 )^ 2 + 45 ( 4 ) + 10 = 174
f ( - 4 ) = - ( - 4 )^3 + 3( - 4 )^2 + 45(- 4) + 10 = - 58
f ( - 3 ) = -(- 3 )^3 + 3 ( - 3)^2 + 45 (- 3) + 10 = - 7 1
+ ( 5 ) = -(5)^3 + 3(5 )^2 +45(5)+ 10 = 185
Absolute maximum = maxis{ f(4 ),f(5),f(-4),f( - 3 )}
= 185 at x=5
Absolute mininum=minis{f(4 ),f(5),f(-4),f( - 3 )}
= - 71 at x= -3
In light of this, the maximum and minimum values are 5 and -3, respectively.
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Catseby ran up 16 flights of stairs. Write an integer to represent this situation
Zero means ????
Answer: 16
Step-by-step explanation:
a pizzeria makes pizzas that are shaped as perfect circles, and measures pizza size by the diameter of a pizza. by surface area, approximately what percent larger is a 16-inch pizza than a 12-inch pizza?
Using the concept of percentage we get 16-inch pizza is 43.75% larger than a 12-inch pizza.
What is the percentage?Percentage means out of hundred. A number that is expressed as a fraction of a hundred is called a percentage. Percentage change = Change in the value / Initial value.
Area of circle = π R²,
Where R is the radius of circle.
Given that size of a pizza is measured by its diameter and surface area.
Diameter of the first pizza = 16 inch
So its radius = 8 inch
Hence area = π×8²
= 64π
And the diameter of the other pizza = 12 inch
So, its radius = 6 inch
Hence its area = π×6²
= 36π
Now the difference in areas of Both the pizza = 64π - 36π
= 28π
Now percentage difference in areas of both pizzas = 28π×100)/64π%
= 2800/64
=43.75%
Hence, 16-inch pizza is 43.75% larger than a 12-inch pizza.
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Identify the correct property of equality to solve each equation. 3 x = 27 x 6 = 5
The correct property of equality to solve each equation. 3 + x = 27 and x + 6 = 5 is subtraction property of equality.
The property of equality defines an equivalence relationship between two variables. The subtraction property of equality refers to the property that two sides of the equation remain equal when the same number is subtracted from both sides of an equation. According to the subtraction property of equality, if two quantities a and b are equal, and if c is subtracted from both a and b, then the difference of a and c and the difference of b and c are equal. Hence, if a = b, a – c = b – c. Using the subtraction property of equality:
3 + x = 27
3 + x -3 = 27 - 3
x = 24
Similarly,
x + 6 – 6 = 5 – 6
x = -1
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Answer:
3+x=27
✔ subtraction property of equality with 3
x/6 = 5
✔ multiplication property of equality with 6
Step-by-step explanation:
Write each ratio as a fraction in simplest form.
11 1/3 out of 50 2/3
Answer:
[tex]\frac{17}{76}[/tex]
Step-by-step explanation:
expressing the ratio in fractional form
[tex]\frac{11\frac{1}{3} }{50\frac{2}{3} }[/tex] ← change mixed number to improper fractions
= [tex]\frac{\frac{34}{3} }{\frac{152}{3} }[/tex] ( multiply numerator and denominator by 3 )
= [tex]\frac{34}{152}[/tex] ( divide numerator and denominator by 2 )
= [tex]\frac{17}{76}[/tex] ← in simplest form
Solve the equation:
3/2=4x
x= ____________
Answer:
x = [tex]\frac{3}{8}[/tex]
Step-by-step explanation:
[tex]\frac{3}{2}[/tex] = 4x ( multiply both sides by 2 to clear the fraction )
3 = 8x ( divide both sides by 8 )
[tex]\frac{3}{8}[/tex] = x
Please Help me with this (ASAP) 20 POINTS
The value of y when x = -2, 0,2 is 1/49, 7, 49.
Simplification is an algebraic expression is when we utilize a range of approaches to make algebraic expressions more efficient and compact - in their simplest form - without changing the value of the original expression.
Given function y =[tex]7^{x}[/tex]
We have to determine the y values when x = -2, 0, 2
Now substitute the x values in the given function
If x = -2 then
Y = 7(-2)
Y = 1/49
If x = 0 then
Y = 7(0)
Y = 1
If x = 2 then
Y = 7(2)
Y = 49
Therefore the value of y when x = -2, 0 ,2 is 1/49, 7 , 49
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Multiply and simply: (4 - 3i) (2 + i)
Answer:
11 - 2i
Step-by-step explanation:
Given expression:
[tex](4-3i)(2+i)[/tex]
Expand:
[tex]\implies 4(2+i)-3i(2+i)[/tex]
[tex]\implies 8+4i-6i-3i^2[/tex]
[tex]\implies 8-2i-3i^2[/tex]
Apply the imaginary number rule i² = -1 :
[tex]\implies 8-2i-3(-1)[/tex]
Simplify:
[tex]\implies 8-2i+3[/tex]
[tex]\implies 11-2i[/tex]
Step-by-step explanation:
well, when 2 summed teens are multiplied, every part of one term is multiplied with every part of the other term :
(4 - 3i)(2 + i) = 8 + 4i - 6i - 3i² = 8 - 2i + 3 = 11 - 2i
Solve for n:-
[tex]\sf n - 3n = 14 - 4n[/tex]
Answer:
n = 7
Step-by-step explanation:
The equation is,
→ n - 3n = 14 - 4n
Now the value of n will be,
→ n - 3n = 14 - 4n
→ -2n = 14 - 4n
→ -2n + 4n = 14
→ 2n = 14
→ n = 14/2
→ [ n = 7 ]
Hence, the value of n is 7.
I need help please!
Answer:
All answers other than {7, 11, 15, 19}
Step-by-step explanation:
If we have a Set A, it is a subset of Set B if every element in A is also in B. Set A is a proper subset of Set B if it is a subset of Set B but not equal to Set B.
Using the above information, we know that the proper subset of {7, 11, 15, 19} cannot be itself, so we can rule out the second option.
All of the other options are sets where every element of that set is also an element of {7, 11, 15, 19}. The 3rd option is an empty set, which is a proper subset of any set other than itself, so it is a proper subset of {7, 11, 15, 19}.
Therefore, all of the options except for {7, 11, 15, 19} are valid.
ets
d and simplify these
4(a + 8) =
4(a + 8)
multiply out:
= 4a + 32
What is the remainder when g(x)=2x-3 is divided by
2x^3-9x² + x +q
Answer:9x>6=76
Step-by-step explanation:9x>6=76
can you help me in graph
i came back home now....
Look at the triangles. What information is needed to prove that △ABC∼△DEF?
Options are listed at the bottom
Looking at the triangles, the information needed to prove that ABC∼△DEF is AC = 10
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shows that pair of equivalent sides are
AB and DE, BC and FE, then AC and DF
The solution is worked out using sides BC and FE, then AC and DF
BC / AC = FE / DF
8 / AC = 16 / 20
reducing the fraction 16/20 gives
8 / AC = 8 / 10
hence AC = 10
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Solve. −1 − 10x < −1
The solution to the inequality is x > 0
What is Inequality?Inequality in mathematics differentiate two values, if one is less than, greater than, or not equal to another value
Evaluate the equation by letting the unknow to be on one side
−1 − 10x < −1
-10x < -1+1
Add +1 to both sides
= -1-10x+1 < -1+1
= -10x < 0
Divide both sides by -10 same factor and flip the relation because of negative factor
= -10x /-10 > 0/-10
= x > 0
Therefore the solution to the inequality is x>0
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One online bookstore charges $10 per book and $8 for shipping. Another online bookstore charges $12 per book and offers free shipping. For what number of books is the cost the same ?
Answer:
The number of books bought in each store would be 4 The amount spent will be the same in either store.
Step-by-step explanation:
Comment
The question has to make the assumption that no matter how many books are bought from store 1, the shipping charge is 8 dollars. Otherwise there is no solution.
Givens
Book1: 10 and 8 dollars total for shipping
Book2: 12 dollars, no shipping costs.
Equation
12x = 10x + 8 Subtract 10x from both sides
Solution
12x - 10x = 10x - 10x + 8 Combine
2x = 8 Divide both sides by 2
2x/2 = 8/2
x = 4
Replace the star astrict (*) with a digit that allows you to reduce the fraction. If there are two * in the same fraction, replace them with the same digit. Find all possible values of * in each fraction. This is the one that I got stumped in...
12*/23* This is a fraction. Fill it in. Remember, you have to fill it in, so it can get reduced.
Please answer by 3:00PM Pacific time Sunday november 6th 2022
The star asterisk in the fraction 12*/23* is being replaced by all the possible values as outlined
1 to be 11/21
2 to be 61/116
4 to be 62/117
5 to be 25/47
6 to be 63/118
8 to be 64/119
0 to be 12/23
What are fractions?In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a chunk or section taken from a whole, which can be any number, and can represent any amount.
The fractions with different numerators and denominators when compared with another fraction but the same value with the fraction are said to be equivalent fractions.
The asterisk value is replaced with digit in each case, and the fraction formed is reduced to their equivalent forms as below
12*/23* * replaced by 1 and reduced to be 11/21
12*/23* * replaced by 2 and reduced to be 61/116
12*/23* * replaced by 4 and reduced to be 62/117
12*/23* * replaced by 5 and reduced to be 25/47
12*/23* * replaced by 6 and reduced to be 63/118
12*/23* * replaced by 8 and reduced to be 64/119
12*/23* * replaced by 0 and reduced to be 12/23
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what is the answer to this question?
3 5/6+ (-1 1/6)=
Drag the tiles to the correct boxes. Not all tiles will be used.
Determine which steps are used to find the product shown. Put the steps in the order in which they would be performed.
Determine which steps are used to find the product shown. Put the steps in the order in which they would be performed.
See photo below. Comment for more clarification.
an environmental agency is analyzing soil samples from 50 farms for lead contamination. eight of the farms have dangerously high levels of lead. ten farms are randomly selected from the sample. using technology, how many ways could two contaminated farms and eight noncontaminated farms be chosen?
Number of ways , two contaminated and 8 non- contaminated farms be choosen is 3,304,845,180.
Permutation and Combination
Combination is a mathematical way to arranging the set of values randomly.
ⁿCᵣ = n! / r! (n-r)!
we have given that ,
total number of farms for lead contamination = 50
Number of farms have dangerously high level of lead = 8
so, number of non- containmated farms ( no high level of lead ) = 50-8 = 42
We have to find the number of ways to choose two contaminated farms and eight non- contaminated farms. Two containmated farms are selected from 8 containated farms and 8 non- contaminated farms are selected from 42 farms .
Number of ways for selecting two containmated farms = ⁸C₂ = 8!/2!×6! = 8×7/2 = 28
Number of ways for selecting eight non-containmated farms from 42 farms = ⁴²C₈
= 42! / 8! 34! = 42×41×---×35/8×7×----×1
= 118013185
The total number of ways to obtain 2 containmated farms and 8 non- contaminated farms in 10 farms selected is then product of number of ways to select the 2 containmated farms and number of ways to select 8 non-containmated farms .
= 118030185× 28 = 3,304,845,180
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