Answer:
The value of r to have maximum profit is 3/25 ft
Step-by-step explanation:
To find:
The size of the sphere so that the profit can be maximized.
Manufacturing cost of the solid sphere = $500/ ft^3
Selling price of sphere (on surface area) = $30 / ft^2
We see that the manufacturing cost dealt with he volume of the sphere where as the selling price dealt with the surface area.
So,
To maximize the profit (P) .
We can say that:
⇒ [tex]P(r)=(unit\ cost)\ (SA) - (unit\ cost)\ (Volume)[/tex]
⇒ [tex]P(r)=(30)\ (4 \pi r^2) - (500)\ (\frac{4\pi r^3}{3} )[/tex]
⇒ [tex]P(r)=(120)\ (2\pi r^2) - (\frac{500\times 4}{3} )\ \pi r^3[/tex]
⇒ [tex]P(r)=(120)\ (\pi r^2) - (\frac{2000}{3} )\ \pi r^3[/tex]
Differentiate "[tex]P[/tex]" and find the "[tex]r[/tex]" value then double differentiate "[tex]P[/tex]", plug the "[tex]r[/tex]" values from [tex]P'[/tex] to find the minimum and maximum values.
⇒ [tex]P(r)'=(120)\ 2\pi r - (\frac{2000}{3} )\ 3\pi r^2[/tex]
⇒ [tex]P(r)'=(240)\ \pi r - (2000)\ \pi r^2[/tex]
Finding r values :
⇒ [tex](240)\ \pi r - (2000)\ \pi r^2 =0[/tex]
Dividing both sides with 240π .
⇒ [tex]r-\frac{25}{3} r^2 =0[/tex] ⇒ [tex]r(1-\frac{25}{3} r) =0[/tex]
⇒ [tex]r=0[/tex] and [tex]r=\frac{3}{25}[/tex]
To find maxima value the double differentiation is :
⇒ [tex]P(r)'=(240)\ \pi r - (2000)\ \pi r^2[/tex] ...first derivative
Double differentiating :
⇒ [tex]P(r)''=(240\pi) - (2000\pi)\ 2(r)[/tex] ...second derivative
⇒ [tex]P(r)''=(240\pi) - (4000\pi)\ (r)[/tex]
Test the value r = 3/25 dividing both sides with 240π
⇒ [tex]1 - \frac{50\pi r}{3}[/tex]
⇒ [tex]1 - \frac{50\times \pi\times 3 }{3\times 25}[/tex]
⇒ [tex]-5.28 < 0[/tex]
It passed the double differentiation test.
Extra work :
Thus:
⇒ [tex]P(r)=(120)\ (\pi r^2) - (\frac{2000}{3} )\ \pi r^3[/tex]
⇒ [tex]P(r)=(120)\times (\pi (\frac{3}{25} )^2) - (\frac{2000}{3} )\times \pi (\frac{3}{25} )^3[/tex]
⇒ [tex]P(r) =1.8095[/tex]
Finally r =3/25 ft that will maximize the profit of the manufacturing company.
What information would most likely be presented in graph form?
Answer:
How Fast something is going say like a car or a chart that tell how much the people you live around like that surtitle thing
Step-by-step explanation:
The point (4,10) is in each scatterplot. In which one is it an outlier?
Answer:
A
Step-by-step explanation:
yy chi u yfgbngny NYC tnfnbfrbcsdv
Answer:
A
Step-by-step explanation:
The number of times per minute that a hummingbird's wings flap is normally distributed with a mean of 145 and a standard deviation of 2. Part A: What is the probability that a randomly selected hummingbird flaps its wings more than 151 times a minute? Part B: What percentage of hummingbirds flap their wings between 141 and 149 times per minute? Part C: A hummingbird that flaps its wings 147 times a minute is in the _______________ percentile.
The probability of a hummingbird flapping its wings more than 151 times per minute is close to 0, the percentage of hummingbirds flapping between 141 and 149 times per minute can be found using the standard normal distribution table or calculator and a hummingbird flapping its wings 147 times per minute is in the 84th percentile.
To solve these problems, we'll use the properties of the normal distribution.
Part A:
We'll standardize the value of 151 using the formula for z-score:
[tex]\( z = \frac{{X - \mu}}{{\sigma}} \)[/tex]
[tex]\( z = \frac{{151 - 145}}{{2}} = \frac{6}{2} = 3 \)[/tex]
Now, we find the probability corresponding to z = 3 using a standard normal distribution table or calculator. The probability of a value being more than 3 standard deviations above the mean is very low, close to 0.
Part B:
We standardize 141 and 149 similarly:
[tex]\( z_{141} = \frac{{141 - 145}}{{2}} = -2 \)[/tex]
[tex]\( z_{149} = \frac{{149 - 145}}{{2}} = 2 \)[/tex]
Then, we find the area between these two z-scores using the standard normal distribution table or calculator. It represents the percentage of hummingbirds flapping between 141 and 149 times per minute.
Part C:
To find the percentile for 147 flaps per minute, we standardize it:
[tex]\( z = \frac{{147 - 145}}{{2}} = 1 \)[/tex]
Then, we find the area to the left of z = 1 using the standard normal distribution table or calculator. This area represents the percentile.
Need help now please
Which model accurately represents the chemical equation 2H2 + O2è 2H2O?
Answer:
B
Step-by-step explanation:
-The balanced chemical reaction of oxygen and water is written as:
[tex]2H_2_{(g)}+O_2_{(g)}->2H_2O_{(l)}[/tex]
-You notice that 2 moles of hydrogen gas reacts with one mole of oxygen gas to form 2 moles of water
-Hence, the correct choice is B
Sandy and Alex are married, with no dependents. They wish to file a joint tax return. Both of them work, but their combined salaries only put them at a slightly above-average income. They would also like to deduct interest paid on their student loans. Recommend an appropriate 1040 form for Sandy and Alex to fill out.
Answer: 1040-A
Step-by-step explanation:
Tax form 1040 is an Internal Revenue Service form that an individual is required to file for a federal income tax return.
One of the shortened form of Tax form 1040 is the 1040-A.
1040-A form enables one to claim some adjustment. This include filing as an household head instead of a single person, claiming dependent and retirement savings, tax deductions, earned income, education, etc.
Form 1040-A is appropriate for the couple as it would allow them have a joint tax return and make tax deductions on their student loans.
Answer:
the other person was correct
The answer is D on edg2020
1 + 4x = -5 + 7x
Help plz
Answer:
x=2
Step-by-step explanation:
1 + 4x = -5 + 7x
Subtract 4x from each side
1 + 4x-4x = -5 + 7x-4x
1 = -5+3x
Add 5 to each side
1+5 = -5+5+3x
6 = 3x
Divide each side by 3
6/3 = 3x/3
2 =x
What is the value of x in the equation 13 x minus 2 (8 + 5 x) = 12 minus 11 x?
a.Negative StartFraction 4 Over 7 EndFraction
b.StartFraction 28 Over 29 EndFraction
c.2
d.4
The value of n in given proportion is 16
Solution:
We have to find the value of "n" in the proportion
Given proportion is:
[tex]\frac{n}{28} = \frac{4}{7}[/tex]
We can solve the above proportion by cross-multiplying
Multiply the numerator of the left-hand fraction by the denominator of the right-hand fraction
Multiply the numerator of the right-hand fraction by the denominator of the left-hand fraction
Set the two products equal to each other
Solve for the variable
[tex]->\frac{n}{28} = \frac{4}{7}[/tex]
[tex]-> 7 * n = 4 * 28[/tex]
[tex]-> n = \frac{4 * 28}{7}[/tex]
[tex]-> n = 4 * 4 = 16[/tex]
Thus the value of n in given proportion is 16
Answer:
the value of n in given proportion is 16
Step-by-step explanation:
If a certain number is added to the numerator of 29/62 and twice the number is subtracted from the denominator, the result is equivalent to 3/4. What is the number? A) 4 B) 5 c)6 d) 7
(15points)
Answer:
Correct option: (d) 7.
Step-by-step explanation:
Let the number be denoted by x.
The original fraction is: [tex]\frac{29}{62}[/tex]
Add x to the numerator, i.e. 29 and subtract 2x from the denominator, i.e. 62.
The new fraction is: [tex]\frac{29+x}{62-2x}[/tex]
Now equate the new fraction to [tex]\frac{3}{4}[/tex] and solve for x as follows:
[tex]\frac{29+x}{62-2x}=\frac{3}{4}[/tex]
[tex]4(29+x)=3(62-2x)\\116+4x=186-6x\\4x+6x=186-116\\10x=70\\x=7[/tex]
The value of x is 7.
Thus, the correct option is (d).
What is the midpoint of the straight line segment joining the points (-2, 9) and (3, -2)?
Answer:
x2-x1/y2-y1
-2--2/3-9=-2+2/3-9
=0/-3
cost of x articles at 2 dollars each
Answer:
2x
Step-by-step explanation:
Cost of x articles at 2 dollars each = 2x
The hypotenuse of a right triangle is 12, and one of the legs is 4, what’s the missing leg
Answer:
About 11.31
Step-by-step explanation:
a^2 + b^2 = c^2
4^2 + b^2 = 12^2
16 + b^2 = 144
-16 -16
b^2 = 128
Take the square root of both sides
b= approximately 11.31
What is the approximate volume of the cylinder of 4cm and 9cm? Use 3.14 for π.
The volume of the cylinder is 452.16 cubic centimeter
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
We have to find the volume of cylinder
Radius of cylinder is 4cm and height is 9cm
The formula for volume of cylinder = πr²h
Plug in the values of r and h
Volume = π(4)²(9)
= π×16×9
=3.14×16×9
=452.16 cubic centimeter
Hence, the volume of the cylinder is 452.16 cubic centimeter
To learn more on Three dimensional figure click:
https://brainly.com/question/2400003
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The approximate volume of a cylinder with a radius of 4 cm and a height of 9 cm is 452.16 cm³, using the formula V = πr²h with π approximated as 3.14.
Calculating the Volume of a Cylinder
To find the approximate volume of a cylinder with a radius of 4 cm and a height of 9 cm using 3.14 for π, you can use the formula for the volume of a cylinder, which is V = πr²h. In this case, V = 3.14 × (4 cm)² × 9 cm.
First, calculate the area of the base (which is a circle) by squaring the radius and multiplying by π: Area = π × r² = 3.14 × 4² = 3.14 × 16 = 50.24 cm². Next, multiply the area of the base by the height of the cylinder to get the volume: Volume = Area × Height = 50.24 cm² × 9 cm = 452.16 cm³.
Therefore, the approximate volume of the cylinder is 452.16 cm³.
Which fraction has a terminating decimal as its decimal expansion?
Answer:
fraction which has a terminating decimal as its decimal expansion is:
1/5
Step-by-step explanation:
We are given 4 fractions:
1/3 , 1/5 , 1/7 and 1/9
We have to find which fraction has terminating decimal.
1/3 = 0.33333...
1/5 = 0.2
1/7 = 0.142857142857...
1/9 =0.11111.....
Hence, fraction which has a terminating decimal as its decimal expansion is:
1/5
Final answer:
A fraction will have a terminating decimal if its denominator is a power of 2, a power of 5, or a combination of both since the base of our number system is 10. Examples like 1/8 and 5/16 have terminating decimals because their denominators are powers of 2.
Explanation:
A fraction will have a terminating decimal expansion if its denominator can be written in the form 2n5m, where n and m are nonnegative integers. This is because the base of our number system is 10, which is 2×5. So any fraction with a denominator that is a factor of a power of 10 will have a terminating decimal expansion.
Example:
Consider the fraction 1/8. Since 8 is 23, which is a power of 2, 1/8 has a terminating decimal of 0.125.For the fraction 5/16, the denominator 16 is 24. Because it contains only the prime factor 2, 5/16 has a terminating decimal of 0.3125.In contrast, a fraction like 1/3 does not have a prime factorization that matches the form 2n5m and therefore has a non-terminating decimal expansion (0.333...).
Heather wants to buy new carpet for her living room floor. The floor is in the shape of a rectangle. Its length is 17feet and its width is13 feet. Suppose carpet costs 11
for each square foot. How much will carpet cost for the floor?
Answer:
$2431
Step-by-step explanation:
First we need to find the area
A = l*w
A = 13*17
A =221 ft^2
It cost 11 dollars per square foot so multiply the price times the number of square ft
221*11 =2431
The total cost will be 2431
Final answer:
Heather's new carpet for her rectangular living room floor will cost $2431. This is obtained by calculating the area of the room (221 square feet) and multiplying it by the cost per square foot ($11).
Explanation:
Heather wants to buy new carpet for her living room floor, which is a rectangle with a length of 17 feet and a width of 13 feet. To find out how much the carpet will cost, we need to calculate the area of the floor and then multiply it by the cost per square foot.
First, calculate the area of the floor by multiplying the length by the width:
Area = Length × Width
Area = 17 feet × 13 feet
Area = 221 square feet
Next, multiply the area by the cost of carpet per square foot:
Total cost = Area × Cost per square foot
Total cost = 221 square feet × $11/square foot
Total cost = $2431
Therefore, the carpet will cost Heather $2431 for her living room floor.
NEED HELP ON THIS WILL GIVE CROWN
Matt buys 14 jars of paint. Each jar contains 300 milliliters of paint.
How many liters of paint in all is there in the jars?
4.2 L
42 L
420 L
4,200 L
What are the solution(s) of the quadratic equation 98 – x2 = 0?
x = Plus or minus 2 StartRoot 7 EndRoot
x = Plus or minus 6 StartRoot 3 EndRoot
x = Plus or minus 7 StartRoot 2 EndRoot
no real solution
Answer:
c on ed
Step-by-step explanation:
just took the unit test
Answer:
The answer is c
Step-by-step explanation:
98 - x² = 0
x² = 98
x = ±√98
Lets factor 98
98 | 2
49 | 7
7 | 7
1
So, 98 = 2 . 7 . 7 = 2 . 7²
x = ±√2.7²
x = ±7√2
Hope this helps!!!
One and one half pounds of chocolate are eaten by 5 people . If each person eats the same amount ,find the unite rate in pounds of chocolate per person
Final answer:
To calculate the chocolate per person, divide 1.5 pounds by 5 people, resulting in 0.3 pounds of chocolate per person.
Explanation:
To find the unit rate of chocolate per person, we divide the total amount of chocolate by the number of people:
Start with 1 and 1/2 (or 1.5) pounds of chocolate for 5 people.
Divide 1.5 pounds by 5 people to find the amount each person eats.
1.5 pounds ÷ 5 people = 0.3 pounds per person.
So, each person eats 0.3 pounds of chocolate.
PLEASE HELP!!
IF REAL ANSWER IS PUT, I WILL MARK YOU BRAINLIEST!
Answer:
B
Step-by-step explanation:
It's a trapezoid. The top and bottom sides sum is 18+12 which is 30. the height is 10 and the equation would be 30 times 10 times 1/2. The answer would then be 150.
Answer:
b
Step-by-step explanation:
The time it takes students to complete a statistics quiz has a mean of 20.5 minutes and a standard deviation of 15.4 minutes. What is the probability that a random sample of 40 students will have a mean completing time greater than 25 minutes
Final answer:
To find the probability that the sample mean is between two hours and three hours, calculate the z-scores and use the z-table to find the probability.
Explanation:
To find the probability that the sample mean is between two hours and three hours, we need to calculate the z-scores corresponding to these values and use the z-table to find the probability.
First, we calculate the z-score for two hours:
z = (2 - 2.5) / (0.25 / sqrt(60)) = -3.16
Next, we calculate the z-score for three hours:
z = (3 - 2.5) / (0.25 / sqrt(60)) = 3.16
Using the z-table, we find that the probability of getting a z-score between -3.16 and 3.16 is approximately 0.9986. Therefore, the probability that the sample mean is between two hours and three hours is approximately 0.9986.
]
find the value of x in the given right triangle
Step-by-step explanation:
It is a right angled triangle so with reference angle 37°
hypotenuse (b) = 10
perpendicular (p) = x
So
tan 37° = p/ b
0.75 = x / 10
x= 0.75/10
Therefore x = 0.075
Hope it will help you :))
A rectangular box has dimensions 4 ft by 5 ft by 2 ft. Increasing each dimension of the box by the same amount yields a new box with volume six times the old. Find how much each dimension of the original box was increased to create the new box. Round your answer to two decimal places.
Answer:
(4+x)(5+x)(5+x) = 700
x^3 + 14x^2 + 65x + 100 = 700
x^3 + 14x^2 + 65x - 600 = 0
x = 4.225
rounding = 4.23
Step-by-step explanation:
Smart takes the bus to work. Unfortunately, he forgets
his lunch at home. Clever grabs the lunch and drives
after the bus. The bus has a 15-minute head start and
is traveling at an average rate of 40 mph. Clever is
traveling at an average rate of 60 mph. How long does
Clever take to catch up to the bus? Draw a diagram to
solve the problem.
Answer:
Speed = Distance / Time
Distance = Speed x Time
Bus: 15 x 40 = 600 m
Clever: 600 / 60 = 10 minutes
Answer = 10 mins
Step-by-step explanation:
hope it helps:) brainlest?!
Find the missing factor BBB that makes the equality true.
21y^4=(B)(7y^3)21y
4
=(B)(7y
3
)
Answer:21y^4= B*7y^3
B=(21y^4)/(7y^3)
B=3y
i think this is correct
Assume that when adults with smartphones are randomly selected, 46% use them in meetings or classes. If 9 adult smartphone users are randomly selected, find the probability that exactly 3 of them use their smartphones in meetings or classes.
Answer:
0.2027 is the probability that exactly 3 out of 9 adults use their smartphones in meetings or classes.
Step-by-step explanation:
We are given the following information:
We treat adult using smartphones in meetings or classes as a success.
P(Adult using smartphone) = 46% = 0.46
Then the number of adults follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 9
We have to evaluate:
[tex]P(x = 3)\\\\= \binom{9}{3}(0.46)^3(1-0.46)^6\\\\= 0.2027[/tex]
0.2027 is the probability that exactly 3 out of 9 adults use their smartphones in meetings or classes.
Final answer:
To find the probability that exactly 3 of the 9 randomly selected adult smartphone users use their smartphones in meetings or classes, we can use the binomial probability formula.
Explanation:
To find the probability that exactly 3 of the 9 randomly selected adult smartphone users use their smartphones in meetings or classes, we can use the binomial probability formula. The binomial probability formula is given by:
P(X=k) = C(n,k) * p^k * (1-p)^(n-k)
where:
P(X=k) is the probability of getting exactly k successes
C(n,k) is the combination formula
p is the probability of success (46% in this case)
n is the total number of trials (9 in this case)
Plugging in the values, we get:
P(X=3) = C(9,3) * (0.46)^3 * (1-0.46)^(9-3)
P(X=3) = 84 * (0.46)^3 * (0.54)^6
P(X=3) = 0.299 (rounded to three decimal places)
Of students taking a course through NCVPS, 7/15 play a sport and 3/5 play a musical instrument.The probability that a NCVPS student plays a sport or a musical instrument is 2/3. What is the probability that a NCVPS student play a sport AND a musical instrument?
Answer: 7/25 or 0.28
Step-by-step explanation:
Given that 7/15 play a sport and 3/5 play a musical instrument.
The probability that a NCVPS student play a sport AND a musical instrument means multiplication of the two probabilities
7/15 × 3/5 = 21/75 = 7/25
To win a contest, the number of beans in a jar has to be guessed within 20 of the actual number. If the number of beans in the jar is 645, which equation can be used to find the minimum and maximum number of beans that will win the contest, and what is the maximum guess that could win?
Answer:
Step-by-step explanation:
Let the number of allowable guess be x.
The difference between allowable guess and 645 must not exceed 20.
So, either,
|645 - x| ≤ 20
Or
|x - 645| ≤ 20
where that sign represents the absolute sign.
Hope this Helps!!!
Answer:
| x - 645 | = 20
665
Step-by-step explanation:
We have to guess the amount of beans in a jar to be within 20 of the actual number.
Therefore, the total has to be equal to 20.
We know that the equation required to calculate the minimum and maximum quantity of beans that will win the contest will be:
| x - 645 | = 20
But as we want is the maximum, we break the absolute value and assume "+"
Thus:
x - 645 = 20
fixed for x:
x = 20 + 645
x = 665
The maximum guess you could win is 665
Item 5 A spotlight on the ground shines a beam of light to the top of a tree that is 12 m tall. The beam of light makes an angle of 40° with the ground. What is the distance from the spotlight to the base of the tree, rounded to the nearest meter? 10 m 14 m 16 m 19 m PreviousFinish
Answer:
14 m
Step-by-step explanation:
We are given that
Height of tree=AB=12 m
[tex]\theta=40^{\circ}[/tex]
We have to find the distance from the spotlight to the base of the tree.
We know that
[tex]tan\theta=\frac{perpendicular\;side}{base}[/tex]
[tex]\frac{AB}{BC}=tan40[/tex]
[tex]\frac{12}{BC}=tan40[/tex]
[tex]BC=\frac{12}{tan40}=14.3\approx 14[/tex]
Hence, the distance from the spotlight to the base of the tree=14 m
You mix the letters A, C, Q, U, A, I, N, T, A, N, C, and E thoroughly. Without looking, you select one letter. Find P(Q or C) as a fraction, a decimal, and a percent.
Answer:
P(Q or C) = 0.25
Step-by-step explanation:
We are given the following in the question:
Letters:
A, C, Q, U, A, I, N, T, A, N, C, E
Total number of observations, n = 12
We have to find the probability that a randomly selected letter is Q or C.
Formula:
[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]
P(Q or C) =
[tex]=\dfrac{\text{n(Q or C)}}{n} = \dfrac{3}{12} =0.25 = 25\%[/tex]
Thus,
P(Q or C) = 0.25
Write the standard form of the equation of the circle with its center at (-3,0), and a radius of 6.
What is the equation of the circle in standard form?
Ok i'm so sorry but if you could answer this for me? nobody else will! >0<
Enter the equation of the circle described below.
Center (-3, 0), radius /5
Answer:(X+3)^2 +y^2 =25
This is the correct answer, i just found it out
Calculator question.
Whats is the minimum window that allows r^2=4cos(2theta)
multiple choice
A. [0,2pi]
B. [0,pi]
C. [-2pi,2pi]
D [0,pi/2]
Answer:
D. [0,pi/2]
Step-by-step explanation:
when Ф = 0 in radian
r²= 4cos (2(0))
r² = 4 * 1
r² = 4
∴ r = √4 = 2
r = 2.
when Ф = π/2 in radian
r²= 4cos (2(π/2))
r² = 4 * -1
r² = -4
∴ r = 0