To find the maximum volume of a cylinder inscribed in a sphere of radius r, we need to use optimization techniques. The cylinder should be such that its height is equal to its diameter and both should be equal to the diameter of the sphere. This means that the cylinder should be a cube with its diagonal equal to the diameter of the sphere.
Let the diameter of the sphere be 2r. The diagonal of the cube is equal to the diameter of the sphere, so its side is r√3. The volume of the cube is (r√3)^3 = 27r^3.
Since the cylinder is inscribed in the sphere, its radius is r and its height is 2r. The volume of the cylinder is πr^2(2r) = 2πr^3.
To maximize the volume of the cylinder, we need to differentiate the volume equation with respect to r and set it equal to zero:
d/dx (2πr^3) = 6πr^2 = 0
This gives us r = 0, which is not a valid solution. Therefore, the maximum volume of the cylinder inscribed in the sphere of radius r is 2πr^3, when the cylinder is a cube with its diagonal equal to the diameter of the sphere.
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prove that lim xâ0 x^4 cos(2/x)=0
To prove that lim x → 0 x^4 cos(2/x)=0, we need to show that for any ε > 0, there exists a δ > 0 such that |x^4 cos(2/x)| < ε whenever 0 < |x| < δ.
First, we note that -1 <= cos(2/x) <= 1 for all x. Therefore, we have:
x^4 <= x^4 cos(2/x) <= x^4 for all x
Taking the limit as x approaches 0 of both sides, we get:
lim x â 0 x^4 <= lim x â 0 x^4 cos(2/x) <= lim x â 0 x^4
Using the fact that lim x â 0 x^4 = 0, we can conclude that:
0 <= lim x â 0 x^4 cos(2/x) <= 0
Thus, by the squeeze theorem, we have:
lim x â 0 x^4 cos(2/x) = 0
Therefore, we have shown that lim x â 0 x^4 cos(2/x) = 0.
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Johnny have 5 Apples in 6 rows how much apples will he have left
It's not entirely clear what is meant by "5 Apples in 6 rows," so I will provide a general answer that could apply to a few different interpretations of the question.
If Johnny has 5 apples and places them in 6 rows, the answer to how many apples he will have left depends on how many apples are in each row and what Johnny does with them. For example, if he eats one apple from each row, he will be left with 5 - 6 = -1 apples, which doesn't make sense. If instead he rearranges the apples into one row, he will still have 5 apples. If he gives away 2 apples, he will have 3 apples left.
In summary, the number of apples Johnny will have left depends on the details of the scenario, including how many apples are in each row and what Johnny does with them.
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What is y=4/5x+2 written in standered form
you need to run stats testing on sales data from two different buffalo wild wings stores to see if there's a correlation between number of employees and customer satisfaction. the test you want is a:
If there is a correlation between the number of employees and customer satisfaction in two different Buffalo Wild Wings stores, we need to perform a Pearson's correlation coefficient analysis.
To run stats testing on sales data from two different Buffalo Wild Wings stores, we need to use a correlation analysis. Specifically, we need to use Pearson's correlation coefficient to determine if there is a relationship between the number of employees and customer satisfaction. The Pearson's correlation coefficient ranges from -1 to +1, with -1 indicating a perfect negative correlation and +1 indicating a perfect positive correlation. If the coefficient is close to zero, it indicates that there is no correlation.
The data we need to collect includes the number of employees in each store and the sales data for a specific period. We also need to gather customer satisfaction data, which can be collected through surveys or other feedback mechanisms. Once we have the data, we can use a statistical software program like SPSS or Excel to perform the correlation analysis.
If the correlation coefficient is positive and statistically significant, it means that there is a relationship between the number of employees and customer satisfaction. This could mean that more employees lead to better customer service, which in turn leads to higher customer satisfaction and sales. However, if the correlation is negative or not statistically significant, it means that there is no relationship between the two variables.
In conclusion, to determine if there is a correlation between the number of employees and customer satisfaction in two different Buffalo Wild Wings stores, we need to perform a Pearson's correlation coefficient analysis. Gathering accurate data and using statistical software will allow us to determine if there is a significant relationship between the variables.
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You have a ten-sided die with numbers 0 to 9. if you roll a prime number, you get 1 point; if you roll a composite number, you lose 1 point. find the expected value of the number of points you get. (hint: 0 and 1 are neither prime nor composite)
The expected value of the number of points you get is 0.
To find the expected value of the number of points you get, we need to calculate the probability of getting each outcome (rolling a prime number or rolling a composite number) and multiply it by the corresponding points.
Here's how we can do that:
There are 10 possible outcomes when rolling the ten-sided die, each with an equal probability of 1/10.
Prime numbers on the die: 2, 3, 5, 7 (total 4 numbers)
Composite numbers on the die: 4, 6, 8, 9 (total 4 numbers)
For prime numbers (4 possible outcomes):
Probability of rolling a prime number = Number of prime numbers / Total possible outcomes = 4/10 = 2/5
Points gained for rolling a prime number = 1
For composite numbers (4 possible outcomes):
Probability of rolling a composite number = Number of composite numbers / Total possible outcomes = 4/10 = 2/5
Points lost for rolling a composite number = -1
Expected value = (Probability of prime number [tex]\times[/tex]Points gained) + (Probability of composite number [tex]\times[/tex] Points lost)
Expected value = (2/5 [tex]\times[/tex] 1) + (2/5 [tex]\times[/tex] -1)
Expected value = 2/5 - 2/5
Expected value = 0
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If you can help me I’ll be grateful!!!
Answer:
4044.32
Explanation:
6506.08 (total) - 2461.76 (top)=
4044.32 (lateral+top)
Formulae:
total = L + T + B = 2πrh + 2(πr2) = 2πr(h+r)
top= T= πr2
Sara sells dolls at her doll store. If she has a doll that she sells for $15.55, what would be the total cost of the doll if the sales tax were 6% of the sale price?
Answer:
$16.48
Step-by-step explanation:
If 6% is sales tax, that means that the total cost of the doll is 106% of the original cost. (basically 100% is the originall doll, and you add 6% of the tax). If you convert 106% from percentage form to decimal form (which you do by dividing by 100), 106% is the same as 1.06 times the original cost of the doll.
Thus you do 1.06 x 15.55 = 16.483 which rounds down to $16.48
ASAP HELPPP!
Write an equation for the parabola graphed below.
The equation of the parabola graphed below is given as follows:
x = -1/49(y - 2)² - 1.
How to obtain the equation of the parabola?The parabola in the context of this problem is in horizontal form, hence the equation is given as follows:
x = a(y - k)² + h.
In which the parameters are given as follows:
a is the leading coefficient.(h,k) are the coordinates of the vertex.The coordinates of the vertex are given as follows:
(-1, 2).
Hence:
x = a(y - 2)² - 1.
When x = -2, y = -5, hence the leading coefficient a is obtained as follows:
-2 = a(49) - 1
a = -1/49.
Hence the equation is:
x = -1/49(y - 2)² - 1.
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Choose the representation that is INCORRECT and does NOT match the others.
Answer:
The table is the incorrect representation.
A train travels at 110 miles per hour. At this rate, how far will the train travel in 2 1/2 hours
Answer:
275 miles
Step-by-step explanation:
110/2=55
(2*110)+55
=275
Answer:
275 miles
Step-by-step explanation:
110×2=220
110÷2=55
220+55=275
100 POINTS NEED HELP ASSAP
A student is using a weak computer to design a logo. If the weak computer is the only constraint, should the student use the online version of
downloaded version of a graphic design software? (1 point)
O The downloaded version, because the online version usually requires better equipment than the downloaded version.
O The online version, because the downloaded version usually requires better equipment than the online version.
O The online version, because the downloaded version may have limited bandwidth that limits how quickly the designer can work.
O The downloaded version, because the online version may have limited bandwidth that limits how quickly the designer can work
The online version, because the downloaded version usually requires better equipment than the online version.
The online version of the graphic design software is likely the better option for the student using a weak computer. This is because the online version typically runs on the software provider's servers, rather than on the user's computer.
Therefore, the online version does not require as much processing power or memory from the user's computer, making it more accessible to those with weaker or older machines.
Additionally, the online version may also have the advantage of automatic updates, so the student can always have the latest version of the software without needing to manually download and install updates.
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Annie has $9,000 in an account that earns 5% interest compounded annually.
To the nearest cent, how much interest will she earn in 2 years?
Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
$
Answer:
B=$18900.00
Step-by-step explanation:
B=?
P=9000
r=5%=0.05
t=2
B=p(1+r)t
B=9000×(1+0.05)×2
B=9000×(1.05)×2
B=9000×2.1
B=18900
What is the y-intercept the equation y=(x+4)2? The equation you wrote to answer the last question should help you. (Only enter the y-coordinate.)
Answer:
x-intercepts: (-4,0)
y-intercepts: (0,16)
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
have a great day and thx for your inquiry :)
How does y=5x and y=5x-4 are related
These two equations have the same slope, slope = 5.
They have different intercepts (the origin (0,0) and (0, -4)).
These lines are parallel.
Find the values of x and y in the picture
Answer:
x = 56y = 75Step-by-step explanation:
You want the measures of the angles marked x° and y° in the given diagram.
Inscribed angleThe measure of an inscribed angle is half the measure of the arc it intercepts. This means any inscribed angles that intercept the same arc will have the same measure.
The inscribed angles with vertices J and K both intercept arc FH, so both have the marked measure of 56°.
x = 56
Angle at chordsThe angle where the chords cross (y°) will be half the sum of the arcs those chords intercept. Here, those are arcs FH and JK.
Given that half the arc measure is the measure of the intercepting inscribed angle, we can simply sum the inscribed angles to get y°:
y° = 56° +19° = 75°
y = 75
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What is the area of the shape below?
15 m
15 m
17 m
7m
Answer:
(1/2)(15)(7 + 15) = (1/2)(22)(15) = 165 m^2
Answer:
165m²
Step-by-step explanation:
First you make it into a triangle and rectangle. The rectangle would be 15x7. The triangle would be 1/2x15x8.
15x7=105
1/2x15x8=60
105+60=165 meters squared
Answer Immeditely Please
Answer:
9
Step-by-step explanation:
This situation creates 3 similar triangles, so the lengths of corresponding sides are proportional.
1/3 = 3/x
x = 3 × 3
x = 9
Please help I also need to round to the nearest tenth is necessary
The volume and the surface area is 85.33π in³ and 16π in² respectively.
Given that a sphere of diameter 8 in, we will find it surface area and volume,
Surface area of a sphere = 4π × radius²
= 4π × (8/2)² [∵ diameter = 2 × radius]
= 16π in²
Volume of a sphere = 4π/3 × radius³
= 4π/3 × 4³
= 256π/3
= 85.33π in³
Hence the volume and the surface area is 85.33π in³ and 16π in² respectively.
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Of the 95children in 6th grade 3/5 went to holiday parties how many students went to holiday parties in all?
Answer:
57
Step-by-step explanation:
95/5 x 3 = 57
solve for x show steps
Answer:
x ≈ 50.7
Step-by-step explanation:
x/sin 90 = 23/sin(180-90-63) = 23/sin 27
x = (23 X sin 90) / sin 27
≈ 50.7
WILL GIVE BRAINLIST TO BEST ANSWER
Find the value of x that makes lines u and v parallel
If those two angles = 180, then lines u and v are parallel.
90 + (x+102) = 180
192 + x = 180
x = 180-192
x = -12
So if x = -12, then lines u and v are parallel.
Answer:
x = -12
Step-by-step explanation:
We know that the right angle measuring 90° on line u and the (x + 102)° angle are both same side interior angles. When two lines are parallel, the measure of their same interior angles are always equal to 180. Thus, we can solve for x by making the sum of the 90° right angle and the (x + 102)° angle equal to 180:90 + x + 102 = 180
192 + x = 180
x = -12
Therefore, in order for lines u and v to be parallel, the value of x must be -12
In the diagram below, AABC= ADEF. Complete the statement ZA =
C
A
B
F
D
In the diagram, if ΔABC= ΔDEF, then angle A is congruent to angle D.
Option C.
What are similar triangles?Similar triangles are triangles that have the same shape, but not necessarily the same size. In other words, their corresponding angles are equal, and their corresponding sides are proportional in length.
Two triangles are considered similar if they satisfy one of the following conditions:
AA SimilaritySSS SimilaritySAS SimilarityABC ≅ DEF
∠A ≅ ∠ D
Thus, two triangles are similar if their corresponding angles are congruent, and their corresponding sides are in proportion, so angle A of triangle ABC is congruent to angle D of triangle DEF.
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The range of the data in the 4th of July parade is blank the range of data in the New Year’s Day parade
The range of the data on the 4th of July parade is greater than the range of the data in the New Years's Day parade.
A dataset's range, which reflects the gap among its greatest and lowest values, is measured statistically.
By deducting lowest value from the greatest value, it is computed. If range of total data is wider in Fourth of July parade than it is in the New Year's Day parade, then highest and lowest figures in Fourth of July parade will be further apart than highest and lowest values in New Year's Day parade.
For example, if highest value in 4th of July parade is 100 and lowest value is 10, then total range is 100 - 20 = 80.
If the highest value in the New Year's Day parade is 60 and the lowest value is 20, then the range is 60 - 20 = 40.
Thus, here range of the data in 4th of July parade is greater than range of the data in the New Year's Day parade.
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Fifteen words were randomly selected from a book. The line plot shows the number of letters in each of the 15 words.
What is the mean length of the words?
Just type the number No Units.
The mean length of the words that are given above in a line plot would be = 4
How to calculate the mean length of given words?The total number of words that where selected form the book = 15
The number of letters in each word is represented above in a line plot such as follows;
words with one letter = 3 ×1 = 3 letters
words with two letters = 2×2 = 4
Words with 3 letters = 1×3 = 3
words with four letters =4×4 = 16
words with six letters = 2 × 6 = 12
words with seven letters = 2×7 = 14
Words with eight letters = 1×8 = 8
Total word length = 3+4+3+16+12+14+8 = 60
But mean = total of given data/number of data
= 60/15
= 4
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PLEASE HELP ASAP
Find the missing side in each triangle using any method. Check your answers using a different method. Round answers to the nearest whole number
AC = ? units
DE = ? units
In triangle ABC, the length of AC is 13 units
In triangle DEF, the length of DE is 24 units
By pythagoras theorem we find the missing length
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
In triangle ABC, we have to find length of AC
AC² = 5² + 12²
=25+144
=169
AC=13 units
In triangle DEF, we have to find length of DE
DF² =DE² + EF²
26²=DE² + 10²
676=DE² + 100
576=DE²
DE=24 units
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whats is 8000 lb =
to
8000 pounds is equal to 4 tons.
A pound is a unit of weight that is approximately equal to 16 ounces, while a ton is a unit of weight equal to 2000 pounds.
Therefore, to convert pounds to tons, you divide the weight in pounds by 2000.
8000 pounds is the weight that we want to convert to tons.
Dividing 8000 by 2000 gives us 4
which means that 8000 pounds is equal to 4 tons.
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please help my answers are wrong
The proof that shows that sides SP is congruent to side TR is explained below.
How to Prove that Sides SP and TR are Congruent to Each Other?First, using the given information, we have to establish that both triangles are congruent to each other, then state that the two sides are congruent since corresponding parts of congruent triangles are congruent.
Therefore, the correct proof is:
Statement Reason
1. QP ≅ QR; SQ ≅ TQ 1. Given
2. <SQP ≅ <TQR 2. Vertical Angle Theorem
3. ΔSQP ≅ ΔTQR 3. SAS congruence theorem
4. SP ≅ TR 4. Corresponding parts of congruent
triangles are congruent.
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This graph represents an exponential function.
Complete the sentences.
The function's y-intercept is ___ , and the equation of its asymptote is ___. The graph shows that the function ____ by a factor of ____ each time x increases by 1. This function can be represented by the equation _____ .
The function's y-intercept is 4, and the equation of its asymptote is y = 0. The graph shows that the function increases by a factor of [tex]\frac{3}{2}[/tex] each time x increases by 1. This function can be represented by the equation [tex]y = 4(\frac{3}{2})^x[/tex].
What is an exponential function?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, base, or constant.Based on the graph, we would calculate the value of a and b as follows;
[tex]f(x) = a(b)^x[/tex]
4 = a(b)⁰
a = 4
Next, we would determine value of b as follows;
6 = 4(b)¹
6 = 4b
b = 6/4
b = 3/2
Therefore, the required exponential function is given by;
[tex]y = 4(\frac{3}{2})^x[/tex]
In conclusion, the graph shows that the exponential function increases by a factor of [tex]\frac{3}{2}[/tex] or 1.5 each time x increases by 1.
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10.8.5: assigning bedrooms to daughters. (a) a family has four daughters. their home has three bedrooms for the girls. two of the bedrooms are only big enough for one girl. the other bedroom will have two girls. how many ways are there to assign the girls to bedrooms?
Answer: 12 different ways.
Step-by-step explanation:
For a set of M elements, the number of combinations of N elements (N ≤ M) is given by:
In this case, we know that there is a room that can hold two of the girls, then the number of combinations of the two girls that can be in that room is:
So these are the different combinations for the larger room.
So we assume that two girls already have a room, then we have two girls left and two rooms left.
For the first room, there are two possible girls that can be in, let's choose one of them.
For the last room, we have only one girl left, so we have one option.
The total number of combinations will be equal to the product between the number of options for each event (where the events are assigning the girls to the rooms)
Then the number of different outcomes is:
C = 6*2*1 = 12
There are 12 different ways.
when we draw small and large samples from the same population, small samples group of answer choices produce a more peaked and narrower distribution. vary more from the population mean result in more degrees of freedom
When we draw small and large samples from the same population, small samples produce a more peaked and narrower distribution.
This phenomenon is due to the presence of fewer degrees of freedom associated with the small samples. Variations between sample and population mean result in fewer degrees of freedom, which results in a greater variation between samples and the population mean.
Degrees of freedom (df) is a statistical measure that quantifies the number of values in the final calculation of a statistic that are free to vary. When we sample data from a population, we calculate the sample mean, standard deviation, and other statistics
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