The volume of the given cylinder is V = 1809.56 in³ and the volume of the NBA basketball is V = 448.92 in³.
What are the formulas for finding the volume of a cylinder and a sphere?The formula for the volume of a cylinder is V = π × r² × h cubic units.
Where the radius of the cylinder is represented by 'r' and the height of the cylinder is represented by 'h'.
The formula for the volume of the sphere is V = 4/3 × π × r³ cubic units.
Where the radius of the sphere is represented by 'r'.
Calculation:The given cylinder has a diameter is of 16 inches and a height of 9 inches.
I.e., d = 2r = 16 in and h = 9 in
Then the volume of the cylinder is
V = π × (d/2)² × h
= π × (16/2)² × 9
= π × 64 × 9
= 1809.56 in³
The shape of the NBA basketball is a sphere. The given sphere has a diameter of 9.5 inches.
I.e., d = 2r = 9.5 in
Then the volume of the sphere is
V = 4/3 × π × (d/2)³
= 4/3 × π × (9.5/2)³
= 4/3 × π × (4.75)³
= 4/3 × π × 107.172
= 448.92 in³
Therefore, the volume of the cylinder and the basketball are 1809.56 in³ and 448.92 in³ respectively.
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The following information was obtained from the accounting records of Letty Stores for the financial year ended 30 June 2021:
R
Inventory (1 July 2020)
100 000
Sales
600 000
Purchases
400 000
Sales returns
2 000
Purchases returns
3 000
Drawings: Bank
1 000
Inventory (30 June 2021)
120 000
Additional information:
1. On 29 June 2021, the owner took inventory with a cost price of R20 000 for own use. This transaction has not yet been recorded.
The entity uses the periodic inventory control system.
Required:
Use the information provided above to calculate the cost of sales for the year ended 30 June 2021.
Answer:
333234
Step-by-step explanation:
333234$ for the next 4 years and the ecvation is 69$+-2$
Rationalise the denominator of (12)/(\sqrt(10)+\sqrt(7)+\sqrt(3))
Answer:
\(\frac{12}{\sqrt{10} +\sqrt{7} +\sqrt{3} }=\frac{6\sqrt{147} +6\sqrt{63}-6\sqrt{210} }{21 }\)
Step-by-step explanation:
\(\frac{12}{\sqrt{10} +\sqrt{7} +\sqrt{3} }\)
\(=\frac{12\left( \sqrt{10} -\left( \sqrt{7} +\sqrt{3} \right) \right) }{(\sqrt{10}+(\sqrt{7} +\sqrt{3 } ))( \sqrt{10} -( \sqrt{7} +\sqrt{3}))}\)
\(=\frac{12\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{\sqrt{10^2} -(\sqrt{7} +\sqrt{3})^2}\)
\(\frac{12\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{10-(10+2\sqrt{21} )} }\)
\(=\frac{12\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{-2\sqrt{21} }\)
\(=\frac{-6\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{\sqrt{21} }\)
\(=\frac{-6\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{\sqrt{21} } \times\frac{\sqrt{21} }{\sqrt{21} }\)
\(=\frac{-6\sqrt{21} \left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{21 }\)
\(=\frac{-6\sqrt{210} +6\sqrt{147} +6\sqrt{63} }{21 }\)
\(=\frac{6\sqrt{147} +6\sqrt{63}-6\sqrt{210} }{21 }\)
Remark:
You can simplify moreover if you want to.
Express 31% as a fraction in its lowest form- I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!
Answer:
31/100
Step-by-step explanation:
31% as a fraction can be represented as 0.31 as a decimal. 0.31 as a decimal can be represented as 31/100 as a fraction. Since 31 is a prime number, it cannot be simplified.
The simplest form 31% is 0.31.
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
31% is number
Now, to convert the percent into fraction
=31 /100
As, 31 is prime number having no factor other than 31 and 1 .
So, 31/100= 0.31
Hence, the simplest form 31% is 0.31.
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Graph the circle (x - 3)^2 + (y + 3)^2= 36.
The circle on a graph by drawing the center point and then drawing a circle around it with a radius of 6.
To graph the circle with the equation (x - 3)² + (y + 3)² = 36, we can start by finding the center and radius of the circle.
The equation of a circle in standard form is (x - h)² + (y - k)² = r² (h, k) represents the center of the circle and r represents the radius.
Comparing the given equation with the standard form, we can see that the center of the circle is (3, -3) and the radius is √36 = 6.
Using this information, we can proceed to plot the circle on a graph:
Plot the center point: (3, -3).
From the center point, move 6 units in each direction (up, down, left, and right) to determine the points on the circle.
Up: (3, -3 + 6) = (3, 3)
Down: (3, -3 - 6) = (3, -9)
Left: (3 - 6, -3) = (-3, -3)
Right: (3 + 6, -3) = (9, -3)
Connect the plotted points to form a circle.
The resulting graph should look like this:
| • (3, 3)
|
| •
| •
__|_____________________________
|
|
|
|
| • (3, -3)
The center of the circle is denoted by a solid dot (•) in the graph and the other points lie on the circumference of the circle.
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They are attached below.
14)The sum of the tangent and the sine of the angle is obtained as 1.21.
15)The area of the segment is 95.6 m^2 while the perimeter of the segment is 11.047 m.
16)The angle opposite the largest side is 130°.
What is the trigonometric ratios?The trigonometric ratios are the ratios that are designated as cos, tan and sine. It is important to note that the trigonometric ratios are particular to the right angled triangle. The meaning of the right angle triangle is that one of the angles in the triangle is about 90 degrees.
14)) We can find the hypotenuse by the use of the Pythagoras theorem that is used to find the parts of the right angle triangle.;
a = √2^2 + 3^2
a = √ 4 + 9
a = 3.6
We know that;
tan θ = 2/3 = 0.66
sin θ = 2/3.6 = 0.55
Then;
tan θ + sin θ
0.66 + 0.55
= 1.21
We can see by the use of the trigonometric ratios that we would obtain the sum of the sine and the tangent as 1.21.
15)
The area of the segment is obtained as;
Area of the triangle;
1/2r^2 sinθ
r= radius of the circle
θ = angle of inclination
1/2 * (10)^2 * sin 60
= 43.3
Area of the sector;
60/360 * 3.142 * (10)^2
= 52.3
Therefore the area of the triangle is;
43.3 + 52.3 = 95.6 m
b)The perimeter of the segment;
(2πr * θ/360) + 2rsin(θ/2)
(2 * 3.142 * 60/360) + (2 * 10 * sin (60/2))
1.047 + 10
= 11.047 m
16)
Using;
c^2 = a^2 + b^2 - 2abcos C
20^2 = 13^2 + 9^2 - 2(13 * 9) cos C
400 = 250 - 234cosC
400 - 250 = - 234cosC
150 = - 234cosC
Cos C = -(150/234)
C = Cos-1-(150/234)
C = 130°
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mathhhhhhhhhhh i need help
Answer:
what in the world
Step-by-step explanation:
number 1. is c
number 2. is d
number 3. is a
number 4. is c
number 5. is b
hope this helps
Algebra 1 error analysis
Hello!
I am here with a handful of geometry questions today. Please answer the question based off the image(s) below.
If you are not sure of the answer please leave a comment, DO NOT ANSWER THE QUESTION UNLESS YOU KNOW THE ANSWER. Please don't take me points! Thanks for understanding.
Anyways, please show all of your work and explain your thinking! Thanks!
9514 1404 393
Answer:
square with side length √17 units, so area 17 square units.
Step-by-step explanation:
Each side has a slope with a rise of 1 and a run of 4, or a rise of -4 and a run of 1. The ratios of these numbers are opposite reciprocals, so we know the sides are perpendicular. The sum of squares of these numbers is 17, so we know the sides are √17 and all are the same length. (The Pythagorean theorem tells us this.)
A quadrilateral with equal-length perpendicular sides is a square. This square has side length √17 units and area (√17)² = 17 square units.
Marbleslides: Lines
Answer:
ok
Step-by-step explanation:
Investment A: $800 compounded continuously at 3.5%
Investment B: $900 compounded quarterly at 3%
a. Which investment would be worth more after 20 years? (2 points)
b. How long will it take investment A to triple?
Round to the nearest tenth of a year. (2 points)
Find the volume of this sphere use three
2916 ft³
Step-by-step explanation:Volume helps describe the amount of space that a shape takes up.
Volume of a Sphere
Volume describes the 3-dimensional size of a shape. Since volume is a 3-D measurement, the units should be cubed; this explains why the answer is given in feet cubed. In order to find the volume, we need to use the radius. The radius of a sphere is the distance from the center to the outside. In this case, we are told that the radius is 9 ft.
Volume Formula
Every regular shape has its own volume formula. For a sphere, the formula is:
\(V = \frac{4}{3}\pi r^{3}\)So, to find the volume, all we need to do is plug in the radius. For this sphere, r = 9.
V = 4/3 * 3 * 9³V = 2916When using 3 for pi, the volume of the sphere is 2916 ft³.
Suppose that $7500 is placed in an account that pays 6% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
(b) Find the amount in the account at the end of 2 years
a) The compounded amount in the account at the end of 1 year is $7,950.
b) The compounded amount in the account at the end of 2 years is $8,427.
What is compound interest?Compound interest is the interest added to the principal amount after each period in order to compute the period's interest.
By compounding, we mean that accumulated interest is added to the principal to compute the subsequent interest.
Compound interest is unlike simple interest, which does not compound interest.
The compound interest formula is:
A = P(1 + r/n)^nt
A = Final amount
P = initial principal balance
r = interest rate
n = number of times interest is applied per time period
t = number of time periods elapsed
Since this investment is compounding annually, we can find the final amount at the end of each year using the common formula as follows:
A = P(1 + r)ⁿ
Principal = $7,500
Compound interest rate = 6%
Compounding period = Annually
Amount at the end of Year 1 = $7,950 ($7,500 x 1.06¹)
Amount at the end of Year 2 = $8,427 ($7,500 x 1.06²)
Thus, the compounded amount at the end of year 1 is $7,950 and $8,427 at the end of year 2.
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The following table shows the number and type of properties available in three cities.
City
Key West
Orlando
Miami
Write a matrix that represents the number of each type of property available in Key West.
[ 3 9 13 ] is the Matrix showing all types of property available in key west .
What is matrix ?A matrix is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns to represent a mathematical object or an attribute of such an entity in mathematics.
Calculationgiven in the table that how many types of property are there in the table
its a simple matrix which u can directly see
its a 3 x 1 matrix ...
[3 9 13] this matrix shows the required value
hope this helps...
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Answer: [3 9 13]
Step-by-step explanation:
6.1 Define the term inflation.
Answer:
the action of inflating something or the condition of being inflated.
"the inflation of a balloon"
ASTRONOMY
(in some theories of cosmology) a very brief exponential expansion of the universe postulated to have interrupted the standard linear expansion shortly after the Big Bang.
2.
ECONOMICS
a general increase in prices and fall in the purchasing value of money.
"policies aimed at controlling inflation"
a man gets a job with a salary of 40000 dollars a year. he is promised a 2090 dollars raise each subsequent year. his total earning for a 8-year period is dollars.
Total earnings for an 8-year period is - 378520 dollars.
The salaries, year by year, can be written in a sequence
40000, 40000 + 2090 , 40000 + 2(2090)......
which is an arithmetic sequence, with
a=40,000 , d=2090
and the general term
\(a_{n}\) = 40000 + 2090 (n - 1)
gives the salary at the beginning of year n.
Recall that for the arithmetic sequence,
\(a_{n}\) = \(a + (n - 1 )d\)
the nth partial sum is given by either of the equivalent formulas:
\(S_{n} = \frac{n}{2} [2a + (n - 1 )d ]\)
we find \(S_{8}\) = the sum of the first 8 salaries:
\(S_{n} = \frac{8}{2} [2. 40000 + (8 - 1 )2090 ]\)
= 4 [ 80000 + 7 × 2090 ]
= 4 [ 80000 ++ 14630 ]
= 4 × 94630
= 378520
So, total earnings for an 8-year period is - 378520 dollars.
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The value of y varies inversely as the cube of x, and y=8, when x=2. Find the value of y when x=4
when x = 4, the value of y is 1.
In an inverse variation, the product of the variable and its corresponding value remains constant. Let's denote the constant of variation as k.
According to the given problem, we have the inverse variation equation:
y = k/x^3
To find the value of k, we can substitute the given values for y and x:
8 = k/2^3
8 = k/8
k = 8 * 8
k = 64
Now that we have the constant of variation, we can find the value of y when x = 4:
y = 64/4^3
y = 64/64
y = 1
Therefore, when x = 4, the value of y is 1.
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sue eats 3/8 of a cherry pie. Jan
eats
Answer:
If you're saying Jan ate 1/4 of what was left. How much of the pie did Jan eat?
then the answer is 5/32
Step-by-step explanation:
15% OFF!
Gabe wants to buy a dog collar. The sale price is $3.91. What was the original price?
$
the original price was really "x", which oddly enough is the 100%, but today the collar is on sale at 15% off, that means the sale price is 100% - 15% = 85% of the original price, and we happen to know that's $3.91, so
\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} x & 100\\ 3.91& 85 \end{array} \implies \cfrac{x}{3.91}~~=~~\cfrac{100}{85} \\\\\\ \cfrac{x}{3.91} ~~=~~ \cfrac{20}{17}\implies 17x=78.2\implies x=\cfrac{78.2}{17}\implies x=4.6\)
PLS HELP ME WITH THIS QUESTION PLS SHOW YOUR WORKING OUT
The maximum volume of the cylinder is approximately 1257 cubic centimeters.
What is the maximum volume of the cylinder?The volume V of a right circular cylinder with radius r and height h is given by:
V = πr²h
Substituting the given expressions for the radius and height of the cylinder, we get:
V = πx²(800/πx - x)
Simplifying the expression, we get:
V = 800x - πx³
To find the maximum value of V, we need to find the value of x that maximizes V. We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:
dV/dx = 800 - 3πx² = 0
3πx² = 800
x² = 800/3π
x ≈ 6.43
Substituting this value of x back into the expression for V, we get:
V ≈ 1257
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What additional information is needed to prove the triangles are congruent by the SAS Postulate?
The additional information is needed to prove the triangles are congruent by the SAS Postulate is <ACB = <ACD.
We have, CB = CD
As, The SAS Congruence Theorem states that if two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of another triangle, then the two triangles are congruent.
In triangle ACB and ACD
AC = AC (common)
CB= CD (given)
Now, to prove using SAS rule we need only one angle which is in between the two congruent sides then
<ACB = <ACD
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Please Solve (c-3)^2=100
Answer:
BODMAS RULE
(c-3)²=100
c²-6c+9=100
c²-6c=100-9
c²-6c=91
c²-6c-91=0
then factories
In a data distribution that is skewed left.
The median will be greater than the mean in a left-skewed distribution
We have,
In statistics, skewness is a measure of the asymmetry of a probability distribution around its mean.
A distribution is said to be skewed left if it has a long tail on the left side and the bulk of the data is on the right side.
When the data is skewed left, it means that the distribution is being pulled towards the left side.
This is because there are a few extreme values on the left side that are pulling the mean in that direction.
In contrast, the median is the middle value of the dataset, and it is not influenced by outliers.
For a left-skewed distribution,
The median will be greater than the mean because the mean is being pulled towards the left by the few extreme values.
In a data distribution that is skewed left, the mean will be less than the median.
This is because the mean is sensitive to outliers and is pulled towards the direction of the skewness, while the median is not affected by extreme values and is a more robust measure of central tendency.
Therefore,
The median will be greater than the mean in a left-skewed distribution
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Kristin spends 30% of her savings on a watch and 60% of the
remainder on a dress. What percentage of her savings is left?
Kristin left with the 10% of the savings when she spends thirty percent of her savings on a watch and sixty percent on a dress.
Given that,
Kristin spends thirty percent of her savings on a watch and sixty percent on a dress.
We have to find what portion of her savings is still available.
We know that,
Kristin spends thirty percent of her savings on a watch.
Sixty percent on a dress.
The money she has a 100% in that if she spend 30% on watch she get 70% then if she spend 60% on dress she will have 10%
Therefore, Kristin left with the 10% of the savings when she spends thirty percent of her savings on a watch and sixty percent on a dress.
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Please help will mark Brainly
Answer:
B
Step-by-step explanation:
The domain is the set of \(x\)-values.
Help its a two part question. Big points ans I will give brainliest
The equation of the axis of symmetry of the parabola is equal to x = 4.
How to derive the equation of the axis of symmetry
In this problem we find the representation of a parabola whose axis of symmetry is parallel with y-axis. The axis of symmetry passes through the vertex of the parabola. The definitions of the vertex and the axis of symmetry are, respectively:
Vertex
(x, y) = (h, k)
Axis of symmetry
x = h
If we know that h = - 4, then the equation of axis of symmetry is x = 4.
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Seven years ago, Grogg's dad was 6 times as old as Grogg, and 3 years ago, his dad was 4 times as old as Grogg. How old is Grogg's dad currently?
Answer:
Grogg's dad is 22
Step-by-step explanation:
Let D = dad's current age
Let g = Grogg's current age
6(d - 7) = g - 7 → 6d - 42 = g - 7 → 6d -35 = g
4(d - 3) = g - 3 → 4d -12 = g - 3 → 4d -9 = g
Set the two equations equal to each other and solve for d
6d - 35 = 4d - 9 Subtract 4d from both sides
2d -35 = -9 Add 35 to both sides
2d = 44 Divide both sides by 2
d = 22
Helping in the name of Jesus.
Answer:
Step-by-step explanation:
d = current dad age
g = current grogg age
d-7 = 6(g-7)
d-3 = 4(g-3)
Let's solve the first equation first:
Add 7 to both sides: d - 7 +7 = 6g - 42 + 7 so d = 6g - 35
Substitude d = 6g - 35 for d in d - 3 = 4g - 12
(6g-35)-3 = 4g-12 = 6g-38 = 4g-12
Subtract 4g from both sides: 2g - 38 = -12
Add 38 to both sides: 2g = 26
Easy: g = 13
And now substitude g in for any equations.
d-3 = 52-12
d = 43
Find what percent 768 is of 3,200.
Answer:
3200 of 768 is 416.67%
Step-by-step explanation:
There's your answer hope this helps.
Which expression represents the phrase: 8 less than the product of 6 and a number, x?
Answer:
6x-8
Step-by-step explanation:
Answer:
6x - 8
Step-by-step explanation:
Write the equation of the line that has slope 3 and passes through the point
(-2,5).
In the number 725.78, how does the value of the 7 in the tenths place compare to the value of the 7 in the hundreds place?
Answer:
C. 1/1,000
Step-by-step explanation:
yes or no ?