The measurements of the cylindrical (round and hollow) drum that minimize the fetched of development are roughly 10.19 yards by 2.46 yards.
How to Solve the Problem?Let's expect that the round and hollow drum includes a stature of h and a span of r.
The volume of a barrel is given by: V = πr^2h.
We know that the drum includes a capacity of 806 cubic yards, so able to compose:
πr^2h = 806
We need to play down the taken a toll of building the drum, which is given by the entirety of the fetched of the beat, foot, and side divider.
The zone of the beat and foot of the drum is given by: A = πr^2.
The fetched of fabric for the beat and foot is $2 per square yard, so the taken a toll of the best and foot is:
C_topbottom = 2A = 2πr^2
The cost of fabric for the side divider is $17 per square yard, and the region of the side divider is given by:
A_side = 2πrh
The whole fetched of building the drum is in this manner:
C = C_topbottom + C_side = 2πr^2 + 17(2πrh) = 2πr^2 + 34πrh
Presently we are able utilize the condition for the volume of the drum to kill h from the fetched condition:
h = 806/(πr^2)
Substituting this expression for h into the taken a toll condition, we get:
C = 2πr^2 + 34πr(806/(πr^2)) = 2πr^2 + 27404/r
To discover the least fetched, we got to take the subordinate of the fetched condition with regard to r and set it rise to to zero:
dC/dr = 4πr - 27404/r^2 =
Fathoming for r, we get:
r = (27404/(4π))^(1/3) ≈ 10.19 yards
Substituting this esteem of r back into the expression for h, we get:
h = 806/(π(10.19)^2) ≈ 2.46 yards
Hence, the measurements of the round and hollow drum that minimize the fetched of development are roughly:
Span: 10.19 yards
Stature: 2.46 yards
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S
Match the system of equations to the number of solutions it has.
y=5z+7
3y-15z = 18
z-2y=6
3z-6y=18
y-3z +6
--2-4
3-12-1
y-z-2
Infinite Solutions
One Solution
#Infinite Solutions #No Solutions :: One Solution
One Solution
No Solutions
Evaluate the expression
12-3y divided by 2 + y(2y-4 divided by y) for y = 3
Here are some integers where a
a
b
C
d
d
d
The mode of the integers is 9
The median of the integers is 8
The range of the integers is 4
Work out the value of a, the value of b, the value of c and the value of d
We know that the mode of the integers is 9, which means that 9 occurs more frequently than any other number in the set of integers.
How to explain the mediWe also know that the median of the integers is 8, which means that when the integers are arranged in order from smallest to largest, the middle number is 8.
Finally, we know that the range of the integers is 4, which means that the difference between the largest and smallest integers in the set is 4.
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Select the correct answer.
If the graphs of the linear equations in a system are parallel, what does that mean about the possible solution(s) of the system?
A. There is no solution.
B. There is exactly one solution
C. There are infinitely many solutions
D.The lines in a system cannot be parallel.
If the graphs of the linear equations in a system are parallel: A. There is no solution.
How to interpret Linear equation Graph?The general form for the equation of a line is:
y = mx + c
where:
m is slope
c is y-intercept
Usually, for two equations to have a solution, they must intersect each other.
However, If the graphs of the two equations are parallel lines, then there will be no solution, and the system is called an inconsistent system because the two lines will never intersect each other.
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ERROR ANALYSIS Describe and correct the error in finding the area of sector XZY when the area of OZ is 255 square feet. X W Z X 115 Let n be the area of sector XZY. 115 255 n≈ 162.35 ft² n 360 =
Answer: The correct answer would be n/255 = 115/360 (N= 81.46)
Step-by-step explanation:
n/255 = 115/360
155/360 = (255)
n = 81.46 ft squared
Find the standard deviation
of the given data.
First, find the mean, X, of the data.
5, 6, 8, 13
Answer:
Step-by-step explanation:
The mean of data is 5.5
Given that
The number of data is = n = 4
The given Numbers are 5, 6, 8, 13
We know
Mean x bar = (sum of data)/(number of data)
= (5 + 6 + 8 + 3)/4
= 22/4
= 5.5
Thus, x bar = 5.5
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The Statue of Liberty in New York Harbor stands at a height of about 305 feet. A group of students in a social studies class is building a scale model of the monument. If the students use a scale of 1 inch: 50 feet, about how tall will their model be? Round your answer to the nearest tenth of an inch if necessary.
Answer:
The answer to your problem is, 6.1 inches
Step-by-step explanation:
So we know that 1 inch of there model in real life is 50 feet.
Divide:
305 / 50
= 6.1 but we are going to use 6
Since it is 6 there model is 6 inches.
But remember we still have that 0.1 which we need to full fill for that:
Note that 6.1 will be in inches.
So it is done.
Thus the answer to your problem is, 6.1 inches
The number of seconds that it takes for a kettle to boil, n, is inversely proportional to its power in kilowatts, p.
The equation of proportionality is n =
270
p
Work out the power of the kettle if it takes 90 seconds to boil.
If your answer is a decimal, give it to 1 d.p.
The power of the kettle if it takes 90 seconds to boil given the inverse proportionality is 3 kilowatts.
What is the power of the kettle?Let
number of seconds that it takes for a kettle to boil = n
power of the kettle = p
n = 270/p
If n = 90 seconds
n = 270/p
90 = 270/p
90 × p = 270
90p = 270
divide both sides by 90
p = 270/90
p = 3 kilowatts
Ultimately, the power of the kettle is 3 kilowatts.
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Devon bought a tie. The tie cost $22.50 before tax. After tax, Devon spent $24.30. What was the percent of sales tax
8% will be the value of sales tax that has been charged on a tie will be.
The tie cost is $22.50
The cost after the tax is $24.30.
The change in the cost will be:
= cost after-tax - cost before tax
=24.30-22.50
=1.8
The percentage change will be
Next, assemble a ratio of the sales tax to the pre-tax cost of the tie.
=Sales tax/Pre-tax value
= (1.8/22.50)*100
=8%
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A hair dryer has a power of 1,200 W. How much electrical energy does it use in minutes?
Answer:
r 0.6 kWh to run for 30 minutes.
Answer:
ok so it takes 1200 watts for a hair dryer to run for a full hour, that means it takes 600 watts, or 600 Wh, or 0.6 kWh to run for 30 minutes
Step-by-step explanation:
Complete the ratio table
The missing values from ratio table are 17 and 28.
We have table as
3 1
48 16
51 x
78 26
84 y
So, the ratio are in proportion then
48 / 16 = 51 /x
3 = 51/x
x= 51/3
x = 17
and, 3/1 = 84/y
y= 84/3
y= 28
Thus, the values are 17 and 28.
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When signing the lease for his $750.00 per month rental property. Stanley will have to pay the first and last months rent and a security deposit equal to 30% of one month's rent. If Stanley currently earns an average bi-weekly net pay of $1,050.00, determine what percent of his monthly pay he will need to save if he wants to save enough money to sign the lease in three month.
Answer:
Step-by-step explanation:
tax
find f(g(2)), g(f(2)) given f(x)=3x+5 and g(x)=-7x+6
The two compositions give:
f(g(2)) = -19g(f(2)) = -71How to evaluate the compositions?Here we have two functions:
f(x) = 3x + 5
g(x) = -7x + 6
And we want to fin the two compositions:
f(g(2))
g(f(2))
First, let's find g(2) = -7*2+ 6 = -14 + 8 = -8
Then:
f(g(2)) = f(-8) = 3*-8 + 5 = -19
Now the other one:
f(2) = 3*2 + 5 = 11
Evaluating g in that:
g(11) = -7*11 + 6 = -77 + 6 = -71
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A florist wants to determine if a new additive would help extend the life of cut flowers longer than the original additive. The florist randomly selects 20 carnations and randomly assigns 10 to the new additive and 10 to the original additive. After three weeks, 6 carnations placed in the new additive still looked healthy and 2 carnations placed in the original additive still looked healthy. The difference in proportions (new – original) for the carnations that still looked healthy after three weeks was 0.4. Assuming there is no difference in the additives, 200 simulated differences in sample proportions are displayed in the dotplot.
Using this dotplot and the difference in proportions from the samples, is there convincing evidence that the new additive was more effective?
A. Yes, because a difference in proportions of 0.4 or more occurred 7 out of 200 times, meaning the difference is statistically significant and the new additive is more effective.
B. Yes, because a difference in proportions of 0.4 or less occurred 193 out of 200 times, meaning the difference is statistically significant and the new additive is more effective.
C. No, because a difference in proportions of 0.4 or more occurred 7 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.
D. No, because a difference in proportions of 0.4 or less occurred 193 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.
C. No, because a difference in proportions of 0.4 or more occurred 7 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.
====================================================
Explanation:
If the new additive was more effective than the old one, then the difference in proportions (new - old) should be fairly large.
Count the dots over the x axis labels of "0.4" through "0.6"
5 dots over "0.4"1 dot over "0.5"1 dot over "0.6"That makes 5+1+1 = 7 dots total.
There are 7 instances where the difference of proportions is 0.4 or larger.
This is out of 200 observations, so 7/200 = 0.035 = 3.5% of the differences have 0.4 or larger.
This is not very significant. The general rule of thumb is to use 5% as the threshold. Some stats textbooks will use 10%. Other times your teacher will specify the significance level. The Greek letter alpha is often used.
Because 3.5% < 5%, we consider the new additive to not be that effective compared to the original additive.
In the diagram, angle adc is a central angle and angle measure adc = 60°. What is angle measure ABC?
The measure of angle ABC is 30 degrees. Option B
How to determine the valueIt is important to note the properties of a circle, they include;
Two circles are congruent if they have same radii.Diameter of a circle is the longest chord in the given circleSame chords of a circle subtend the same measure of angles at the center of the circleThe radius that is perpendicular to the chord divides the chord into twoAlso note that the measure of the angle at the circumference is half to twice the measure of the angle at the center.
From the information given, we have that;
<ADC = 60 degrees
This is the angle at the circle
Then,
<ABC is the angle at the circumference
<ABC = <ADC/2 = 60/2 = 30 degrees
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If $x$ is a real number, find $49x^2+14x(19-7x)+(19-7x)^2$
The value of the expression is $-56x² + 266x + 261
What are algebraic expressions?Algebraic expressions are simply described as mathematical expressions that consists of coefficients, certain variables, terms, constants and factors.
Algebraic expressions are also identified with arithmetic operations, such as;
SubtractionMultiplicationDivisionAdditionBracketParenthesesFrom the information given, we have;
$49x^2+14x(19-7x)+(19-7x)^2
expand the bracket, we get;
49x² + 266x - 98x² + 361 - 7x²
Now, collect the like terms, we get;
49x² - 98x² - 7x² + 266x + 361
Add or subtract the values
$-56x² + 266x + 261
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Find the value of a
Answer is 3
Step-by-step explanation:
Use the Ratio Test since Ratio Test guarantee absolutely convergence.
[tex] \frac{ ( - 1) {}^{k + 1}(k + 1) {}^{a} }{5 {}^{k + 1}(3(k + 1) } \times \frac{5 {}^{k}(3k) }{(k) {}^{a} ( - 1) {}^{k} } [/tex]
This simplifes to
[tex] \frac{( - 1) {}^{k} ( - 1) ((k + 1)!) {}^{a} }{5 {}^{k}(5)(3k +1) ! } \times \frac{5 {}^{k} (3k)!}{( - 1) {}^{k} (k!) {}^{a} } [/tex]
[tex] \frac{ - (k + 1) {}^{a} }{5(3k + 3)(3k + 2)(3k + 1)} [/tex]
Take the absolute value
[tex] \frac{(k + 1) {}^{a} }{5(3k + 3)(3k + 2)(3k + 1)} [/tex]
In order for this series to be convergent,
the limit as k approaches infinity must be less than 1.
In order for this series to have a limit less than 1, our numerator and denominator degree must be equal or the denominator must have the larger degree.
Why
If the numerator has a larger degree, our test would make this divergent, so the limit would be infinity
Since the denominator have 3 binomials, our power for the denominator will be 3, this the numerator having a degree of 3 or less as well.
So one of the answer is 3.
solve (2x - 3) (x + 2) = 0
Answer:
x=3/2
x=-2
Step-by-step explanation:
DE bisects AC at point B. AC=a+23
and AB = 3a + 4. Find BC.
Y
X
13
2
X
(X) XS
X₁
IV
The values of AB and BC are equal and equal to
13 units.How to find BCInformation given in the problem includes
DE bisects AC at point B
AC = a + 23
AB = 3a + 4
From the definition of a bisector, point B divides AC into two equal sides, this means that
AB = BC = (1/2) * AC
Substituting the value of AC and AB
AB = 3a + 4 = (1/2) * (a + 23)
3a + 4 = (1/2) * (a + 23)
solving for a
2 * (3a + 4) = a + 23
6a + 8 = a + 23
6a - a = 23 - 8
5a = 15
a = 3
Then we have that:
AB = 3a + 4 = 3(3) + 4 = 9 + 4 = 13
and, AB = BC
so BC = 13
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How to solve a 2 step inequality
Answer: To solve a two-step inequality, undo the addition or subtraction first, using inverse operations, and then undo the multiplication or division. The inverse operation of addition is subtraction and vice versa. Similarly, the inverse operation of multiplication is division and vice versa.
Step-by-step explanation:
Which expression is equivalent to 12/5x -2 A. 12x-2/5 B. 2(2/5x -1) C. 2/5(6x-10) D. 1/5(12x-10)
Answer:
The answer is D.
[tex] \frac{1}{5}(12x - 10)[/tex]
employees receive a 10% discount their shopping at Tesco stores. calculate the weekly benefit to an employee who on average spend£14 each weekday and £22 on each day at the weekend.
The weekly benefit of the employees is A = £ 11.40
Given data ,
Let's calculate the weekly benefit for an employee who spends an average of £14 each weekday and £22 on each day of the weekend, considering the 10% discount they receive at Tesco stores.
First, we'll calculate the total amount spent on weekdays and weekends separately:
Amount spent on weekdays = £14/day x 5 days/week = £70/week
Amount spent on weekends = £22/day x 2 days/week = £44/week
Next, we'll calculate the total amount spent in a week by adding the amounts spent on weekdays and weekends:
On simplifying the equation , we get
Total amount spent in a week = £70 + £44 = £114
Now, we'll calculate the 10% discount on the total amount spent:
10% of £114 = £11.40
Hence , the weekly benefit to the employee who receives a 10% discount on their shopping at Tesco stores would be £11.40
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determine he measures of the angles
Answer:
45
Step-by-step explanation:
Is the function g(x)=8 linear or nonlinear?
Answer:
It's linear
Step-by-step explanation:
Answer:
Linear
Step-by-step explanation:
UCM college administrators claim that the average freshman enrollment over the last 10 years meets the university's capacity of 6,500 students. You believe hypothesize this is inaccurate and believe that UCM is underestimating the number of college freshman. Using a sample of 500
students, you determine a sample mean of 6,600 freshman. Assume o = 1,000 and a = .05.
The t-statistic value of the hypothesis is 2.236
The population mean is equal to 6,500 (H0: μ = 6500)
Alternative hypothesis:
The population mean is greater than 6,500 (Ha: μ > 6500)
We are given the sample mean (x) = 6,600, sample size (n) = 500, population standard deviation (σ) = 1,000, and level of significance (α) = 0.05.
First, we need to calculate the t-statistic using the formula:
t = (X - μ) / (σ / √n)
where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Substituting the given values, we get:
t = (6,600 - 6,500) / (1,000 / √500)
= 2.236
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What is the measure of angle b?
Answer:60 degrees
Step-by-step explanation: The three angles of a triangle add to 180, a right angle is 90 so 180-90-30= 60.
Given that the perimeter of an equilateral triangle is 63 inches, find the height/altitude of the triangle.
The height of the triangle is h = 18.18 inches
Given data ,
In an equilateral triangle, all three sides are equal in length.
Let the length of each side be s
Now , the perimeter of the equilateral triangle is given as 63 inches, so we have:
Perimeter of the triangle = 3s = 63 inches
Dividing both sides by 3, we get:
s = 63/3 = 21 inches
Let's now plot an altitude from one of the equilateral triangle's vertex to the side's midway. As a result, two right-angled triangles will be formed, each with the hypotenuse "s" and sides "s/2" and "h"
From the Pythagoras theorem , we get
(h²) + ((s/2)^2) = s²
Substituting the values we found earlier for "s", we get:
(h²) + ((21/2)²) = 21²
Simplifying further, we have:
(h²) + (10.5²) = 21²
(h²) + 110.25 = 441
Subtracting 110.25 from both sides, we get:
h² = 330.75
On taking square roots on both sides , we get
h = √(330.75)
h ≈ 18.18 inches
Hence , the height of the equilateral triangle is 18.18 inches
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PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
In the above triangle,
1) the sum of side 1 and 2 is: 4x² + 3x + 4
2) the length of side 3 is: 5x³-6x²-12
1) To find the sum of side 1 and side 2, we simply need to add them together.
Side 1 = 3x² - x - 1
Side 2 = x² + 4x + 5
Side 1 + Side 2 = (3x² - x - 1) + (x² + 4x + 5)
= 3x² + x² - x + 4x - 1 + 5
= 4x² + 3x + 4
Therefore, the sum of side 1 and side 2 is = 4x² + 3x + 4
2) We can derive the expression of the thried side by removing the expression in (1) above form the perimeter.
That is;
(5x³-2x² + 3x - 8) - (4x² + 3x + 4)
First we distribute the negative sign
= 5x³-2x² + 3x - 8 + -1 (4x² + 3x + 4)
= 5x³-2x² + 3x - 8 + -1 (4x²) -1( 3x) -1( 4)
= 5x³-2x² + 3x - 8 + -4x² - 3x - 4
Combining like terms we have
= (5x³) (-2x²+-4x²) + (3x +- 3x) + (-8 + - 4)
= 5x³-6x²-12
Hence the missing side (thrid side is) 5x³-6x²-12
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NEED TO BE DONE ASAP ONLY HAVE 2MIN
Answer:
42 units³
Step-by-step explanation:
You want the volume of a rectangular prism that has a base area of 5 1/4 units² and a height of 8 units.
VolumeThe formula for the volume of a prism is ...
V = Bh
where B is the base area and h is the height perpendicular to the base.
Here, we have B = 5 1/4 u² and h = 8 u. The volume is ...
V = (5 1/4 u²)(8 u) = 42 u³
The volume of the prism is 42 cubic units.
The ratio of two numbers is 1 to 3 and the sum of their squares is 250. Find the numbers.
Answer:
Step-by-step explanation:
5 and 15
5^2=25
15^2=225
225+25=250