The dimensions of a right circular cylinder of maximum volume are
[tex]5\sqrt{6}[/tex] and [tex]10\sqrt{3}[/tex].
Given the radius of sphere is 15 cm.
Let's assume radius of right circular cylinder = r
height of right circular cylinder = h.
Since the cylinder is inscribed in the sphere, their centers will coincide. As a result, the height is divided into two equal portions from the sphere's center. Therefore, we can apply Pythagoras' Theorem to get the cylinder's half-height in terms of radius.
[tex]R^2 = r^2 + (h/2)^2.[/tex]
[tex]r^2 = R^2 - h^2/4.[/tex]
Volume of cylinder = [tex]\pi*r^2*h.[/tex]
Now we can substitute value of [tex]r^2[/tex] in volume of cylinder.
V = [tex]\pi*( R^2 - h^2/4)*h[/tex]
taking R = 15 .
V = [tex]\pi*(225 - h^2/4)*h[/tex]
V = [tex]\pi*225*h - \pi*h^3/4[/tex]
For maximum volume we have to do derivative of volume = 0
derivative with respect to h.
V' = [tex]\pi*225 - 3*\pi*h^2/4[/tex]
V' = 0
[tex]\pi*225 - 3*\pi*h^2/4[/tex]= 0
[tex]3*h^2/4 = 225[/tex]
[tex]h^2 = 75*4.[/tex]
h = 10[tex]\sqrt{3}[/tex]
put the value of h in [tex]r^2 = 225 - h^2/4[/tex]
[tex]r^2[/tex] = 225 - (300/4)
[tex]r^2[/tex] = 150
r = [tex]\sqrt{150}[/tex]
r = 5[tex]\sqrt{6}[/tex].
So the dimensions of a right circular cylinder are 10[tex]\sqrt{3}[/tex] and 5[tex]\sqrt{6}[/tex].
Given Question is incomplete, Complete Question here:
find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 15 cm. what is the maximum volume?
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a coin is placed next to the convex side of a thin spherical glass shell having a radius of curvature of 19.0 cm. reflection from the surface of the shell forms an image of the 1.5-cm-tall coin that is 6.50 cm behind the glass shell. part a where is the coin located? express your answer in centimeters. s
The location of the coin next to the convex side of a thin spherical glass shell is 3.68 cm.
According to the question,
Radius of curvature : 19 cm
Size of image formed : 1.5cm
Distance of coin from glass shell : 6.5cm
The position of the coin placed next to the convex side of a thin spherical glass shell is calculated as follows;
1/d = 1/f - 1/d'
where;
d' is the position of the coin's image
d position of the coin
f is focal length
Focal length = r/2 =19/ 2 = 9.5 cm
=> 1/d = 1/9.5 - (-1/6.5)
=> 1/d = 1/9.5 + 1/6.5
=> 1/d = 0.1052 + 0.1538
=> 1/d = 0.259
=>d = 1/0.259
d = 3.86 cm
Thus, the position of the coin placed next to the convex side of a thin spherical glass shell is 3.86 cm.
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the manufacturer of a new compact car claims that the car will average at least 35 miles per gallon in general highway driving. for 100 test runs, the car averaged 35.5 miles per gallon with a standard deviation of 2.5 miles per gallon. suppose that the manufacturer tests the following hypotheses: h subscript 0 : mu equals 35 h subscript 1 : mu greater than 35 consider the 1% significance level. what is the power of the test if the actual average fuel efficiency is 36 miles per gallon?
The power of the test, if the actual average fuel efficiency is 36 miles per gallon, is 0.5675.
What is the standard deviation?
The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.
We want to test [tex]\mu_0 > 35[/tex] at the level [tex]\alpha=0.01[/tex], where the true mean is [tex]\mu_1=36,\sigma\approx4, n=100[/tex]
The power of a right-tailed test is given by
[tex]1-\beta=P(Z > [z_\alpha-\frac{\sqrt{n}}{\sigma}(\mu_1-\mu_0)])\\\\1-\beta=P(Z > [2.33- \frac{\sqrt{100}}{4}(36-35)])\\\\1-\beta=P(z > -0.17)\\\\power=0.5675[/tex]
Hence, the power of the test, if the actual average fuel efficiency is 36 miles per gallon, is 0.5675.
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A researcher wants to test the hypothesis that on average girls perform better on standardized tests than boys. Since it is true that some boys do better than girls and some girls do better than boys, the researcher must use a two tailed test.
True OR False
The statement of the given hypothesis condition is False.
What is hypothesis testing?
A type of statistical inference known as hypothesis testing uses data from a sample to make inferences about a population parameter or population probability distribution.
Given this, A researcher wants to test the hypothesis that on average girls perform better on standardized tests than boys.
i.e. [tex]\mu_{1} > \mu_{2}[/tex]
">" sign implies that right-tailed test i.e. one-tailed right-sided.
Hence, the given statement is FALSE.
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The parabola y=x^2y=x 2 y, equals, x, squared is reflected across the xxx-axis and then scaled vertically by a factor of 555. What is the equation of the new parabola?.
By using the concept of reflection and scaling, it can be calculated that
New equation of parabola is [tex]y = -5x^2[/tex]
What is reflection and scaling?
Reflection is a mathematical transformation in which a mirror image of an object can be obtained without changing the shape and size of an object.
To draw an object of size proportional to the size of the original object, scaling is used
The equation of the parabola is [tex]y = x^2[/tex]
If it is reflected across x axis, its equation is [tex]y = -x^2[/tex]
Now y = -[tex]x^2[/tex] is scaled vertically by a factor of 5
New equation of parabola
[tex]y = -5x^2[/tex]
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at what speed, as a fraction of c , will a moving rod have a length 60% that of an identical rod at res
As a fraction of c, the length will be 60% at v/c = 0.76
The length of the moving rod = 60%
Using the formula for length contraction-
L = L_o(√(1 - (v²/c²))
Where;
v = The speed of the object
c = The speed of light
L = The length of the object at a moving speed
L_o = The length of the object at rest
Thus,
L = 65%
L_o = 0.65
Substituting the values -
0.65L_o = L_o[√(1 - (v²/c²))]
Dividing both sides by L_o -
0.65 = √(1 - (v²/c²))
Squaring both sides -
0.65² = (1 - (v²/c²))
v²/c² = 1 - 0.65²
v²/c² = 0.5775
Taking the square root of both sides gives;
v/c = 0.76
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. AB :
=
CB =
AC = 4
Answer:
Step-by-step explanation:
its 20
an auditor selects a sample from the file of shipping documents to determine whether invoices were prepared for this sample. this test is to satisfy the audit objective of
An auditor selects a sample of shipping documents to examine whether invoices were created for this sample. The fundamental objective of the audit, Completeness, will be satisfied by this test.
Given,
An auditor picks a sample of shipping papers to examine if the related sales invoices were produced.
We need to determine what kind of audit aim will be the focus of this test's evidence gathering;
Audit purpose;
An audit's objective is to form an unbiased evaluation of the entity's financial statements. It is a component of the opinion if the financial statements give a true and fair picture and have been accurately prepared in accordance with accounting rules.
Here,
The audit objective completion test was carried out by the auditor to acquire proof.
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The question is incomplete. Completed question is given below;
An auditor selects a sample of shipping documents in order to determine if the related sales invoices were prepared. This test would gather evidence concerning which audit objective?
A) Completeness
B) Detail tie-in
C) Occurrence
D) Realizable value
One historic earthquake had a magnitude of 9.0 on the Richter scale. How many times more intense was this than another historic earthquake that had a magnitude of 8.3? (Round your answer to the nearest whole number.)
Answer:
1
Step-by-step explanation:
9/8.3 = 1.0843, rounded to the nearest whole number is 1
WILL GIVE BRAINIEST IF ANSWER ALL QUESTIONS
The value of the the function h(x) at x = 4 is given as follows:
8.7.
The quadratic regression equations for each table are given as follows:
y = -0.127x² + 4.699x - 27.777.y = 32.86x² - 379.14x + 1229.14.How to obtain the value at x = 4?The function for the first item is defined as follows:
h(x) = 50/(5.5 + 8e^(-0.9x)).
At x = 4, the value assumed by the function is obtained replacing the lone instance of x by 4, hence:
h(4) = 50/(5.5 + 8e^(-0.9(4))).
Then a calculator is used to obtain the exact value due to the exponential, hence:
h(4) = 8.7.
How to obtain the regression equations?The regression equations are obtained inserting the points of each table into a quadratic regression calculator.
For the first table, the points are given as follows:
(16, 15), (18, 15.6), (20, 15.7), (21, 15), (23, 13.1), (26, 8.9), (27, 6.6).
Hence the equation is of:
y = -0.127x² + 4.699x - 27.777.
For the second table, the points are given as follows:
(3, 330), (4, 276), (5, 263), (6, 86), (7, 174), (8, 198), (9, 553).
Hence the equation is of:
y = 32.86x² - 379.14x + 1229.14.
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Two angles are
complementary. One angle is six more than
twice the other. What is the measure of each
angle?
Answer:
Step-by-step explanation:
1st angle = (2x+6)° = (56 + 6)°= 62°. 2nd angle = x = 28°. Thus, 62° and 28° are the required angles. Answer.
The frequency table shows how many hours Ashley worked over a thirty day period. Using the frequency table, find the average number of hours Ashley worked per day. (Round to the nearest tenth.)
Responses
A 6.0
B 6.5
C 6.7
D 7.0
E 6.6
The average number of hours that Ashley worked per day is obtained as follows:
Mean = sum of relative frequencies x outcome
What is shown by the relative frequency table?The relative frequency table shows that absolute frequencies of the number of hours worked, that is, the number of days in which each amount of hours was worked.
Then the relative frequencies are obtained by the division of each of the absolute frequencies by the total number of outcomes, which is the sum of all the relative frequencies.
Finally, the mean value is obtained just like the mean of a discrete distribution, with the multiplication of each outcome by it's relative frequency obtained previously.
Missing InformationThe problem is incomplete, hence I gave a general pattern to find the mean of the data-set.
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The difference of 11y from 12y is −4
translate into an equation
then solve for y
A factory makes components used in jet engines, including reinforced steel washers. The washers are required to have a very precise thickness. The thickness of the washers follow a normal distribution with mean 1. 59 millimeters and standard deviation 0. 042 millimeters. A technician randomly samples washers and calculates the mean of their thicknesses, which is. What is the probability that ?.
The probability that [tex]\bar{x}[/tex] < 1.57 for the given mean, standard deviation , and samples is equal to 0.0162.
As given in the question,
Normal distribution with mean 'μ' = 1.59 millimeters
Standard deviation 'σ' = 0.042 millimeters
Sample size 'n' = 20
standard error = σ /√n
= 0.042 / √20
= 0.00933
Probability that [tex]\bar{x}[/tex] < 1.57 is
X = 1.57
s = 0.0093
P( X < 1.57)
= P[ (X -μ)/s < ( 1.57 - 1.59)/ 0.0093]
= P ( z < -2.14 )
Using z - table p value is
= 0.01617
= 0.0162
Therefore, the probability for the [tex]\bar{x}[/tex] < 1.57 is equal to 0.0162.
The complete question is :
A factory makes components used in jet engines, including reinforced steel washers. the washers are required to have a very precise thickness. the thickness of the washers follow a normal distribution with mean 1.59 millimeters and standard deviation 0.042 millimeters. a technician randomly samples n = 20 washers and calculates the mean of their thicknesses, which is x¯. what is the probability that x¯<1.57?
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If rs=12, rt=5, st=7, and points r, s, and t are collinear, what is the relationship between collinear points r, s, and t?.
Answer: The relationship between points R , S , and T is that the sum of the RS and RT will be equal to RT that is RT=RS+ST
Step-by-step explanation:
A ferris wheel is 45 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the Amplitude? meters What is the Midline? y = meters What is the Period? minutes How High are you off of the ground after 4 minutes? meters
If the wheel rotates clockwise, the height function is h(t) = 28.5 + 22.5sin(270 - 36t).
The function's central axis for the height of the Ferris wheel's center is given by h = f(t).
= 6 + 45 ÷ 2 = 6 + 22.5 = 28.5 meters.
The wheel rotates at a speed of 36 degrees per minute since the period of revolution is 10 minutes.
The wheel's direction of rotation—clockwise or counterclockwise—is not specified.
Let's look at both situations:
The present angle, assuming it spins clockwise, is equal to 270 – 36t degrees, where t is the duration in minutes.
Then the height function h = f(t)
= 28.5 + 22.5sin(a)
= 28.5 + 22.5sin(270 - 36t)
If the wheel rotates anti-clockwise, the current angle is
b = 270 + 36t degrees.
Then the height function
h = r(t)
= 28.5 + 22.5sin(b)
= 28.5 + 22.5sin(270 + 36t)
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If the area of the pentagon is 36, what is the area of the larger pentagon?
Answer:
64
Step-by-step explanation:
16 ÷ 12 = 1.33 (rounded to 2 decimal places)
1.33 = scale factor
1.33² = area scale factor
1.33² × 36 = 64 (rounded to a whole number)
Answer: 64 would be the area
Step-by-step explanation:
help fast plsssssssss
Answer:
2 2/3
Step-by-step explanation:
Is the following relation a function?
Answer:
Yes
Step-by-step explanation:
dg's plumbing and heating charges $50 plus $60 per hour for emergency service. bill remembers being billed just over $400 for an emergency call. how long to the nearest hour was the plumber at bill's house?
Answer:
6 hours
Step-by-step explanation:
dg's plumbing and heating charges $50 plus $60 per hour for emergency service. bill remembers being billed just over $400 for an emergency call. how long to the nearest hour was the plumber at bill's house?
60h + 50 > 400
subtract 50 from both sides:
60h > 350
divide both sides by 60:
h > 5.8333
rounded: 6 hours
a ship leaves port at noon and has a bearing of s 23° w. the ship sails at 10 knots. (a) how many nautical miles south and how many nautical miles west will the ship have traveled by 6:00 p.m.? (round your answers to two decimal places.) miles south miles west (b) at 6:00 p.m., the ship changes course to due west. find the ship's bearing and distance from port at 7:00 p.m. (round your answers to one decimal place.) s ° w nautical miles
(a) 52.475nm many nautical miles south and 29.09nm many nautical miles west will the ship have traveled by 6:00 p.m.
(b) at 6:00pm the ship changes course to due west when 36.68° the ship's bearing and distance from port at 7:00 p.m.
Given that,
A ship sets out from port at noon with a bearing of s 23° west and a speed of 10 knots.
We have to find
(a) By the time it gets dark at six o'clock, how far south and west will the ship have sailed? The ship alters its course to head due west at 6:00 p.m. miles south miles west
(b). at 7:00 p.m., determine the ship's bearing and distance from the port. nautical miles in s.
We know that,
(a) For 6:00 p.m
Sin(θ)=opposite/ hypothesis
θ=29
Opposite=west
Hypothesis =60
Sin(29°)=w/60
w=29.09nm
West= 29.09nm
Cos(θ)=adjacent/ hypothesis
θ=29
Adjacent= south
Hypothesis =60
Cos(29°)= south/60
south=52.475nm
Therefore, 52.475nm many nautical miles south and 29.09nm many nautical miles west will the ship have traveled by 6:00 p.m.
(b) tan(θ)=opposite/adjacent
Opposite=29.09nm
Adjacent= 52.475nm
Tan(θ)=29.09nm/52.475nm
θ=36.68°
Therefore, at 6:00pm the ship changes course to due west when 36.68° the ship's bearing and distance from port at 7:00 p.m.
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which assessment finding(s) are likely to cause noncompliance with antiretroviral treatment? select all that apply.
A. Poor understanding of HIV
B. Cognitive impairment
C. Substance abuse
D. Unstable housing
I need help to do this bc my math teacher can’t explain it well-
Answer:
b. 1 1/4
c. 11 3/8
d. 1 4/7
Step-by-step explanation:
b. 3 - 1 3/4
2 4/4 - 1 3/4
[4/4 - 3/4 = 1/4] and [2 - 1 = 1]
1 + 1/4
1 1/4
c. 7 3/8 + 4
Add the whole numbers.
11 3/8
d. 4 - 2 3/7
3 7/7 - 2 3/7
[7/7 - 3/7 = 4/7 and 3 - 2 = 1]
1 + 4/7
1 4/7
May I please have brainliest? Thank you!
Answer:
The goal is to make the denominators the same.
[tex]\frac{numerator}{denominator}[/tex]
Here's how to solve "b" (I explained it so you can do the other ones)
b.
[tex]3 - 1\frac{3}{4}[/tex]
Turn the 3 into a fraction (you can put any number over 1 and it will be the same)
[tex]\frac{3}{1} - 1\frac{3}{4}[/tex]
Next, let's turn the [tex]1\frac{3}{4}[/tex] into an "improper fraction". Right now, it is a mixed number. Multiply the denominator by the whole number on the left, and then add it to the numerator. The denominator will stay the same.
4 * 1 = 4
4 + 3 = 7
[tex]1\frac{3}{4}[/tex] → [tex]\frac{7}{4}[/tex]
Okay, so now we have this:
[tex]\frac{3}{1} - \frac{7}{4}[/tex]
This is getting easier! But to subtract, we have to make the denominators the same. Let's multiply the top and bottom of [tex]\frac{3}{1}[/tex] by 4.
[tex]\frac{3 * 4}{1 * 4} = \frac{12}{4}[/tex]
Now we have:
[tex]\frac{12}{4} -\frac{7}{4}[/tex]
One final step, subtract the numerators! Leave the denominators as they are.
12 - 7 = 5
Our answer is:
[tex]\frac{5}{4}[/tex]
The following data set represents the ages of all six grandchildren in a family. Find the variance for this data set of ages: 6,3,14,11,14,6 round the final answer to one decimal place.
The variance for the data set is 18.
What is a variance?
The term variance refers to a statistical measurement of the spread between numbers in a data set. More specifically, variance measures how far each number in the set is from the mean (average), and thus from every other number in the set.
Here we have to find the variance for this data set.
Given data:
The age of six grandchildren in a family is = 6, 3, 14, 11, 14, 6
The mean = 6+3+14+11+14+6/ 6
= 9
The variance = (6-9)² + (3-9)² + (14-9)² +(11-9)² + (14-9)² + (6-9)²/ 6
= 9+36+25+4+25+9/ 9
= 18
Therefore the variance is 18.
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Given the algebraic expression the quantity 125 times x to the seven-thirds power end quantity to the negative one-third power comma, create an equivalent expression.
The expression that results from applying the law of indices and expression is 5x^(-7/3).
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules.
Here,
The resulted expression will be,
(125x)^(7/3)^(-1/3)
125=5^3
(a^n)^m = a^mn
(5x)^3^7/3^-1/3
(5x)^7*-1/3
5x^(-7/3)
The resulted expression will be 5x^(-7/3) using the law of indices and expression.
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2. Find the slope of the line that passes through (-4,4) and (-4,18)
Answer: 14
Step-by-step explanation:
The equation to find slope is y2-y1/x2-x1 or in simpler terms is rise over run.
We see that the y increase by 14 so the rise is 14 and the x is the same so the run is 0. So the slope is 14.
If you can please give me a Brainliest, I only need 1 more to become an Expert, thank you!
I need some help on this fast.
Answer: -2
Step-by-step explanation:
Tom wants to rent a truck for two days and pay no more than $300. How far can he drive the truck if the truck rental cost $49 a day plus $0.40 a mile?
A) 490
B) 505
C) 520
D) 535
Answer:
B
Step-by-step explanation:
for 2 days it's 98
then 300-90=202
202÷0.40=505
The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance that she traveled during these three seconds. t (s) 0 0.5 1.0 1.5 2.0 2.5 3.0 v (t/s)|이 6.2 | 10.8 | 14.9 | 18.1 19.4 20.2 Step 1 We will use either Ls or Rs for the upper and lower estimates. Since the runner's speed is an increasing function, then will give the lower estimate, andR will give the upper estimate. ˇ Step 2 The sub-interval widths At for this situation are At- L--JX
The speed of the runner calculated by the properties of average speed is given by 33.45 feet and the upper limit is 43.45 feet in the last 3 seconds.
The first three seconds of a race saw a runner's speed rapidly grow.
The time is therefore 3 seconds.
The table provides her speed at half-second intervals.
We are aware,
Distance x Time = Speed
Similarly
Distance equals speed x time.
Δt equals 0.5 seconds
Then, the minimum distance travelled overall is equal to
0.5(0 + 6.7 + 9.2 + 14.1 + 17.5 + 19.4).
Terms are multiplied and added.
= 0.5 × 66.9
= 33.45 feet
The maximum distance travelled is equal to
0.5 (6.7 + 9.2 + 14.1 + 17.5 + 19.4 + 20)
= 0.5 × 86.9
= 43.45 feet
As a result, her maximum distance in three seconds is 43.45 feet, and her maximum distance in three seconds is 33.45 feet.
Velocity is the rate at which an item's position changes as perceived from a certain point of view and as measured by a given unit of time (for example, 60 km/h northbound).
Velocity is also the direction at which an object is travelling. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that deals with the motion of bodies.
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A mom mixes 9ounces of juice with 3 ounces of water. What percent of the drink is juice?
Answer: 75%
Step-by-step explanation:
9 + 3 = 12
9/12 = 3/4
3/4 = 75%
what is the area of rectangular region r ? each diagonal of r has length 5. the perimeter of r is 14.
The area of rectangular region r is = 12.
Given:
each diagonal of r has length 5. the perimeter of r is 14.
Let l and b be the length and breadth of a rectangle.
we know that
perimeter of rectangle = 2 ( l + b )
2 ( l + b ) = 14
divide by 2 on both sides
( l + b ) = 14/2
l + b = 7
l = 7 - b
l^2 + b^2 = d^2
( 7 - b )^2 + b^2 = 5^2
7^2 + b^2 - 2 * 7 * b + b^2 = 25
49 + 2b^2 - 14b = 25
2b^2 - 14b + 24 = 0
on solving b = 4,3
Take any one value
b = 4
l = 7 - 4
l = 3
Area of rectangle = l * b
= 4 * 3
= 12
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