Answer:
The two positive numbers whose product is 81 and whose sum is a minimum are 9 and 9.
Step-by-step explanation:
81 is divisible by 1 and 81, since 81/1 = 81 and 81/81 = 1.
81 is divisible by 3 and 27, since 81/3 = 27 and 81/27 = 3.
81 is divisible by 9, since 81/9 = 9.
Their sums are.
81 + 1 = 82.
3 + 27 = 30
9 + 9 = 18.
So the two positive numbers whose product is 81 and whose sum is a minimum are 9 and 9.
Answer:
The two positive numbers will be 9 and 9.
Step-by-step explanation:
Let the two positive numbers be x and y.
It is given that the product of the number is 81 the sum of them is minimum.
So, the product can be written as [tex]xy=81[/tex].
The sum can be written as [tex]x+y=x+\dfrac{81}{x}[/tex]. It is required to minimize the sum.
Differentiate the sum as,
[tex]x+y=x+\dfrac{81}{x}\\1+y'=1-\dfrac{81}{x^2}=0\\x^2=81\\x=9\\y=\dfrac{81}{x}\\y=9[/tex]
Now, the second derivative of the sum will be,
[tex]y''=2\times \dfrac{81}{x^3}>0[/tex]
So, the second derivative is positive and hence, the sum will be minimum at x=9.
Therefore, the two positive numbers will be 9 and 9.
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A number, one-third of that number , and one-fourth of that number are added. The result is 19 what is the original number
What is greater 3.26 or 3 5/8
John and Jeremy are the local names for two lighthouses that guard a particularly dangerous part of the coast. John blinks every 6 seconds and Jeremy blinks every 4 seconds. They blink together at midnight. How many seconds will pass before they blink together again?
How does a "for every" statement show a ratio comparison?
Twenty-seven minus 1.5 of a number (x) is not more than 36. What is the number?
find two possible factors for the estimated product 2,800
Gina wrote the number 43,628. Then she used the same digits to write a new number. In the new number, she moved the digit 6 one place to the left. Which is the value of 6 in Gina's new number?
To finance her community college education, Sarah takes out a loan for $3700. After a year Sarah decides to pay off the interest, which is 6% of $3700. How much will she pay?
Recall that a prime number is a natural number whose only factors are itself and 1 (for example, 2, 3, 5, . . . ). the goldbach conjecture, posed in 1742, claims that every even number greater than 2 can be expressed as the sum of two primes. for example, 4 = 2 + 2, 6 = 3 + 3, and 8 = 5 + 3. a deductive proof of this conjecture has never been found. test the conjecture for at least 10 even numbers and present an inductive argument for its truth. do you think the conjecture is true? why or why not?
Prime Number is a number whose only factors are itself and one. For example 1,3,5,7,11,13,17,19,23… Now consider the following arguments : Every even number greater than 2 can be expressed as sum of two primes. Now consider the following premises:
Premise 1 : 4 = 2 + 2
Premise 2 : 10 = 5 + 5
Premise 3 : 12 = 5 + 7
Premise 4 : 16 = 5 + 11
Premise 5 : 18 = 5 + 13
Premise 6 : 22 = 11 + 11
Premise 7 : 30 = 7 + 23
Premise 8 : 32 = 3 + 29
Premise 9 : 40 = 3 + 37
Premise 10 : 52 = 5 + 47
Premise 11 : 100 = 3 + 97
Conclusion : every whole number is sum of two prime numbers.
All 11 cases are different, yet the rule applies to all. This outcome offers a strong inductive argument in favor of the conclusion or rule specified. It can be strengthened by additional cases that confirm the rule. Conjecture specified will be true because each number can be specified as sum of two primes. As each whole number will have difference os 1, 2, 3, 5, or 7 between the number and the nearest prime number. Consider the following example :
34 = 31 + 3
36 = 33 + 3
Hence the conjecture “Every number greater than two can ve expressed as the sum of two primes” is true.
A bicycle shop advertised all mountain bikes were priced at 1/4 discount.
Which fraction has a terminating decimal as it's the small expansion?
A) 1/3
B) 1/5
C) 1/7
D) 1/9
The Sanders family and the Wright family each used their sprinklers last summer. The Sanders family's sprinkler was used for 20 hours. The Wright family's sprinkler was used for 35 hours. There was a combined total output of 1025L of water. What was the water output rate for each sprinkler if the sum of the two rates was 40L per hour?
The water output rate for the Sanders family's sprinkler was 25 liters per hour, and for the Wright family's sprinkler was 15 liters per hour.
Let the water output rate as "x" liters per hour and the water output rate for the Wright family's sprinkler as "y" liters per hour.
Given that the combined total output of water from both sprinklers was 1025L, we can set up the following equation:
20x + 35y = 1025
We also know that the sum of the two rates is 40L per hour:
x + y = 40
x = 40 - y
Substituting this value of x into the first equation:
20(40 - y) + 35y = 1025
800 - 20y + 35y = 1025
15y = 225
y = 15
Substituting this value of y back into the second equation:
x + 15 = 40
x = 25
Therefore, the water output rate for the Sanders family's sprinkler was 25 liters per hour, and for the Wright family's sprinkler was 15 liters per hour.
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A bottle of medicine contains 40 doses. How many doses are in 3 1/3 bottles?
To calculate the total number of doses in 3 1/3 bottles of medicine, multiply the fraction of bottles (10/3) by the number of doses per bottle (40). The result is 133 1/3 doses.
Explanation:The student is asking how many doses are in 3 1/3 bottles of medicine if one bottle contains 40 doses. To find the answer, we need to multiply the number of bottles by the number of doses per bottle.
Here is the step-by-step calculation:
First, convert 3 1/3 bottles to an improper fraction: 3 1/3 = (3 × 3 + 1)/3 = 10/3 bottles.Next, multiply this value by the number of doses in one bottle to find the total number of doses: (10/3) × 40 doses = 400/3 doses.Finally, simplify the fraction: 400/3 doses = 133 1/3 doses.So, there are 133 1/3 doses in 3 1/3 bottles of medicine.
The school theater department made $2142 and the department sold the same number of tickets each night and each ticket cost $7. How many tickets did the theater department sell each night?
You should get your answer of 306 :)
[tex]\sqrt[7]{2142}[/tex]
^online division .-.
Graph the ellipse with equation x squared divided by nine plus y squared divided by sixteen = 1
Here is the picture of the answer above
The wall in the family room is exactly 12 feet long. Your couch is 10 feet and 6 inches long. Once the couch is placed, how much room is left for your end table?
inches
A number cube is rolled with these results: 64 ones, 67 twos, 73 threes, 59 fours, 72 fives, and 71 sixes. What is the experimental probability of rolling an even number?
Write your answer as a percent, to the nearest tenth of a percent.
A. 51.9%
B. 48.5%
C. 53.6%
D. 46.8%
Answer: B. [tex]48.5\%[/tex]
Step-by-step explanation:
Given : A number cube is rolled with these results:
64 ones, 67 twos, 73 threes, 59 fours, 72 fives, and 71 sixes.
Even numbers : 2,4,6
The number of times of rolling even number = [tex]67+59+71=197[/tex]
Total outcomes = [tex]64+67+73+59+72+71=406[/tex]
Now, the experimental probability of rolling an even number :-
[tex]\dfrac{197}{406}[/tex]
In percent, [tex]\dfrac{197}{406}\times100=48.52216748\approx48.5\%[/tex]
Hence, the experimental probability of rolling an even number = [tex]48.5\%[/tex]
When a day of the week is randomly selected it is a saturday?
5/8 of the 64 musicians in a music contest are guitarist. Some of the guitarist play jazz solos, and the rest play classical solos. The ratio of the number of guitarist playing jazz solos to the total number of guitarist in the contest is 1:4. How many guitarist play classical solos in the contest?
Translate “the perimeter of a rectangle is equal to 2 times the length plus twice the width
The required translated string of “the perimeter of a rectangle is equal to 2 times the length plus twice the width" is,
Perimeter = 2 * length + 2 * width.
Given that,
To translate “the perimeter of a rectangle is equal to 2 times the length plus twice the width."
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
What is the perimeter?Perimeter is the measure of the figure on its circumference.
Here, the given string, “the perimeter of a rectangle is equal to 2 times the length plus twice the width" can be translated in the mathematical form is,
Perimeter = 2 * length + 2 * width.
Thus, the required translated string of “the perimeter of a rectangle is equal to 2 times the length plus twice the width" is,
Perimeter = 2 * length + 2 * width.
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A salesperson's weekly paycheck is 15% less than a second salesperson's paycheck. The two paychecks total $1425. Find the amount of each paycheck.
As sand leaks out of a hole in a contaimer, it forms a conical pile whose altitude is always the same as its radius. If the height of the pile is increasing at a rate of 6in/min, find the rate at which sand is leaking out when the altitude is 10 inches.
The rate at which sand is leaking out when the altitude is 10 inches is
600π inches³ / min.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
The volume of a cone is (1/3)πr²h.
We have,
A conical pile formed due to a leak out of a hole whose radius is equal to its height.
dh/dt = 6 in/min
The rate at which the sand is leaking when height is 10 inches.
We have,
Volume = (1/3)πr²h and h = 10 inches
V = 1/3 πh²h
V = 1/3 πh³
Differentiating both sides.
dV/dt = 1/3 x π x 3 x h² (dh/dt)
dV/dt = π x h² x 6
dV/dt = π x 10² x 6
dV/dt = 600π inches³ / min
Thus,
The rate at which sand is leaking out when the altitude is 10 inches is
600π inches³ / min.
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A two year degree that focuses on natural science, engineering, and mathematics is called an
Associate of science
Answer:
Assosiate in science
Step-by-step explanation:
An Associate of Science (AS) is a 2-year degree offered by most community colleges. Most AS degrees are transfer degrees and provide an academic foundation, but not specific career training. The A.S. degree is intended for students planning to pursue a bachelor’s degree in the areas of math or science.
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(201)3 is equivalente to: (11)10; (10010)2; (11)16; (23)8
It costs $2.80 to make a sandwich at the local deli shop. To make a profit, the deli sells it at a price that is 170% of the cost. The sandwich sells for $ .
What is the constant of proportionality in the equation y = 2.5x?
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]\frac{y}{x}=k[/tex] or [tex]y=kx[/tex]
where
k is the constant of proportionality
In this problem we have
[tex]y=2.5x[/tex]
so
the constant of proportionality k is equal to
[tex]k=2.5[/tex]
therefore
the answer is
[tex]k=2.5[/tex]
The constant of proportionality in the equation [tex]y = 2.5x[/tex] is [tex]\boxed{2.5}.[/tex]
Further explanation:
The relation is defined as the relationship between the input values and output values.
The x coordinates are the domain of the function and the y coordinates are the range of the function.
Given:
The equation is [tex]y = 2.5x.[/tex]
Explanation:
The proportionality equation can be expressed as follows,
[tex]y \propto x[/tex]
The value of [tex]y[/tex] changes as [tex]x[/tex] changes. If the value of [tex]x[/tex] increases then the value of y is also increasing.
The equation can be expressed as follows,
[tex]y = kx[/tex]
The inversely proportional relationship can be expressed as,
[tex]y \propto \dfrac{1}{x}[/tex]
Here, [tex]k[/tex] is the proportionality constant.
The given equation is [tex]y = 2.5x.[/tex]
The y is the independent variable and [tex]x[/tex] is the dependent variable.
The proportionality constant is 2.5.
The constant of proportionality in the equation [tex]y = 2.5x[/tex] is [tex]\boxed{2.5}.[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Ratio and proportion
Keywords: proportional, directly proportional, constant, proportionality equation, y=0.41x, constant of proportionality.
Last year, Gena’s food cart business was $225 in debt. This year, the debt has tripled. Which expressions show how much Gena’s business is currently in debt?
Answer:
Step-by-step explanation:
A & B
The table shows the amount of money in your bank account over a period of 5 weeks. The account does not pay interest. You plan to keep saving at the same rate until you have $650 in the account. Which equation could you use to find the number of weeks, n, it would take to reach your goal?
Answer:
35*n+100=650
Step-by-step explanation:
I got the question right on TTM
Can someone explain this a little better?
Answer:
1. 76,000
2. 8050
3. 240000
Step-by-step explanation:
We know that
1 tens = 10 ones
1 hundreds = 100 ones
1 thousand = 1000 ones
10 thousands = 10000 ones
Using these conversions we get,
1 : [tex]760\text{ hundreds}=760\times 100=76,000[/tex]
2 : [tex]805\text{ tens}=805\times 10=8050[/tex]
3 : [tex]24\text{ ten thousands}=24\times 10000=240000[/tex]
Table can be filled as shown below:
Thousands Ones
Q. no. Hundreds Tens Ones Hundreds Tens Ones
1. 7 6 0 0 0
2. 8 0 5 0
3. 2 4 0 0 0 0
commutative
property of addition of 93+ (68+7)