The volume of the sphere is approximately 3431.82 cubic miles.
To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.
In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.
C = 2πr
60 = 2πr
Divide both sides of the equation by 2π:
r = 60 / (2π)
r = 30 / π
Now that we have the radius, we can use the formula for the volume of a sphere:
V = (4/3)πr³
V = (4/3)π(30/π)³
V = (4/3)π(27000/π³)
V = (4/3)π(27000/π³)
V = (4/3)π(27000/π³)
V = (4/3)(27000/π²)
V = (4/3)(27000/9.87) (approximating π to 3.14)
V ≈ 3431.82 cubic miles
Therefore, the volume of the sphere is approximately 3431.82 cubic miles.
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Question
You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?
what is the LCM of 6, 9, 24
Answer:
its 72
Step-by-step explanation:
Answer:
The least common multiple is 72.
Use a graphing calculator to graph the function and its parent function. Then describe the transformations, f(x)=(x+3)+1/4
Most of the graphing resources used shows that the graph is translated up by 3.25 (3 + 1/4). If you add the 3 and the 1/4, you get the equation of a line:
f(x) = x + 3.25,
which means that the graph of f(x)= x now has a y intercept of 3.25.
The graphs are below. The red line represents f(x) = x, and the green line represents (x+3)+1/4. Hope this helps!
Find the inverse of A = 9, -2 -10, 7 , if it exists.
The inverse of matrix A, if it exists, is:
A^(-1) = [7/43, 2/43; 10/43, 9/43]
To find the inverse of a matrix A, we need to determine if the matrix is invertible by calculating its determinant. If the determinant is non-zero, then the matrix has an inverse.
Given the matrix A = [9, -2; -10, 7], we can calculate its determinant as follows:
det(A) = (9 * 7) - (-2 * -10)
= 63 - 20
= 43
Since the determinant is non-zero (43 ≠ 0), we can proceed to find the inverse of matrix A.
The formula to calculate the inverse of a 2x2 matrix is:
A^(-1) = (1/det(A)) * [d, -b; -c, a]
Plugging in the values from matrix A and the determinant, we have:
A^(-1) = (1/43) * [7, 2; 10, 9]
Simplifying further, we get:
A^(-1) = [7/43, 2/43; 10/43, 9/43].
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Can someone pls help me on my math homework??
Does this question involve sin, cos..?
If yes,
sin 60= x/12
x= 12sin 60
x=10.392(5s.f)
x=10.4(3 s.f)
Using pythagoras theorem,
a^2 + b^2 =c^2
x^2 + y^2= 12^2
(10.392)^2 + y^2 = 144
y^2=36.006
y=[tex]\sqrt{36.006}[/tex]
y=6.0005
y=6.00(3 s.f)
For significant figures and decimal place, you should do what your school requires whether its 3 s.f or 2 d.p. I hope this helps..
7) Students at Somerset
were asked their favorite
sport. Ten students
indicated volleyball was their
favorite, 15 picked
basketball, 14 chose soccer,
and seven said football was
their favorite.
Answer:
what's the question in this question
Given right triangle � � � ABC with altitude � � ‾ BD drawn to hypotenuse � � ‾ AC . If � � = 22 AD=22 and � � = 15 , DC=15, what is the length of � � ‾ BD in simplest radical form?
The length of BD is 18.5 units.
In the given right triangle ABC, with altitude BD drawn to hypotenuse AC, we are given the lengths AD = 22 and DC = 15. We need to find the length of BD.
Let's consider triangle ABD. Since BD is the altitude, it divides the right triangle ABC into two smaller right triangles: ABD and CBD.
In triangle ABD, we have the following sides:
AB = AD = 22 (given)
BD = ?
Now, let's consider triangle CBD. In this triangle, we have the following sides:
BC = DC = 15 (given)
BD = ?
Since triangles ABD and CBD share the same base BD, and their heights are the same (BD), we can say that the areas of these triangles are equal.
The area of triangle ABD can be calculated as:
Area(ABD) = (1/2) * AB * BD
Similarly, the area of triangle CBD can be calculated as:
Area(CBD) = (1/2) * BC * BD
Since the areas of ABD and CBD are equal, we can equate their expressions:
(1/2) * AB * BD = (1/2) * BC * BD
We can cancel out the common factor (1/2) and solve for BD:
AB * BD = BC * BD
Dividing both sides of the equation by BD (assuming BD ≠ 0), we get:
AB = BC
In triangle ABC, the lengths AB and BC are equal, which implies that triangle ABC is an isosceles right triangle. In an isosceles right triangle, the leg's length are congruent, so AB = BC = AD = DC.
BD is equal to half of the hypotenuse AC:
BD = (1/2) * AC
Substituting the given values, we have:
BD = (1/2) * (AD + DC) = (1/2) * (22 + 15) = (1/2) * 37 = 18.5
Therefore, the length of BD is 18.5 units.
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What is the correct order of the following numbers
Answer:
The first is the answer if its least to greatest
Step-by-step explanation:
-17/10 in decimal form is -1.7
Answer:
B
Step-by-step explanation:
-2 is less than -1.7 and -1.7 is less than -1.44
Use a calculator is you want quick answers lol
Which fraction has the lowest value?
-1
0
1
cols color colo
3
8
Answer:
- 1/8 im pretty sure
Step-by-step explanation:
The company estimated that they would sell 500 caps during the football season. They actually sold 575. Find the percent error. Round to the nearest tenth. I need this one fast
Answer:
13.1%
Step-by-step explanation:
The company estimated that there would be 500 a ps during the football season
The actually sold 575
Therefore the percent error can be calculated as follows
= 575-500/575 × 100
= 75/575 × 100
= 0.1304×100
= 13.1%
Hence the percent error is 13.1%
4(4 -8n) -7n = -30 + 7n
Answer:
n=1
Step-by-step explanation:
Use the distributive property to multiply 4 by 4−8n.
16−32n−7n=−30+7n
Combine −32n and −7n to get −39n.
16−39n=−30+7n
Subtract 7n from both sides.
16−39n−7n=−30
Combine −39n and −7n to get −46n.
16−46n=−30
Subtract 16 from both sides.
−46n=−30−16
Subtract 16 from −30 to get −46.
−46n=−46
Divide both sides by −46.
n=−46/−46
Divide −46 by −46 to get 1.
n=1
Answer: n = 1
Step-by-step explanation:
Using the distributive law, multiply 4 by what's in the bracket.
(4)(4) -(8n)(4) -7n = -30 + 7n
16 -32n -7n = -30 + 7n
Group all like terms together. Once a (+ve) number goes over the equal sign it now becomes a (-ve) number, vise versa.
16 +30 = 32n + 7n + 7n
46 = 46n
Now we need to find for n. 46n can also be written as 46 multiply by n. When a multiplication sign goes over the equal sign, the sign changes to a division sign.
46 = 46n
46/46 = n
1 = n
What is the product in the expression 30m= n+58?
Answer: m=1/30n+29/15
Step-by-step explanation:
Answer:
if solving for m it is m= n+58/30
if solving for n it is n= 30m-58
Step-by-step explanation:
for m- divide both sides by 30 but keep it in fraction form for n+58
for n- subtract 58 from both sides to make it n=30m-58
1,417.4 to the nearest ones places
Answer:
1,000
Step-by-step explanation:
The 1 in 1,000 is the ones place, and since 4 is below 5 the ones place stays the same and everything else turns into 0.
What is the mean of this sample, which consists of 10 values randomly selected from the table?
Mean = 7 + 100 + 1 + 3 + 7 + 10 + 15 + 12 + 17 + 38
----------------------------------------------------------
10
The mean of the third sample is_______.
Answer:
21
Step-by-step explanation:
To find the mean, add the values and divide by the number of values
(7 + 100 + 1 + 3 + 7 + 10 + 15 + 12 + 17 + 38)/10
210/10
21
The mean is 21
Answer:
21
Step-by-step explanation:
BELIEVE MEEE
For which of the following displays of data is it not possible to find the mean histogram frequency, table, stem, and leaf plot doc plot
The mean from a Histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.
Out of the given options, the display of data for which it is not possible to find the mean is the stem-and-leaf plot.
A histogram displays data in the form of bars, where the height of each bar represents the frequency of data within a specific range. From a histogram, it is possible to calculate the mean by summing up the products of each value with its corresponding frequency and dividing it by the total number of data points.
A table presents data in a structured format, typically with rows and columns, allowing for easy calculation of the mean. By adding up all the values and dividing by the total number of values, the mean can be obtained from a table.
A stem-and-leaf plot organizes data by splitting each value into a stem (the first digit or digits) and a leaf (the last digit). While a stem-and-leaf plot provides a visual representation of the data, it does not directly provide the frequency or count of each value. Hence, it is not possible to determine the mean directly from a stem-and-leaf plot without additional information.
A dot plot represents data using dots along a number line, with each dot representing an occurrence of a value. Similar to a histogram and table, a dot plot allows for the calculation of the mean by summing up the values and dividing by the total number of data points.
In summary, while it is possible to find the mean from a histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.
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A company sales decreased 4% this year to $8117
Answer:
This isnt even a question, wheres the rest of it?
what's the value of (1/8)^-1/3
Answer:
2
Step-by-step explanation:
You could easily punch this into a calculator.
Answer:
Step-by-step explanation:
(1/8)^-1/3 = (8)^1/3= ∛(8)= 2
Josie bought 4 cases of sports drinks for an upcoming meet. After talking to her coach, she bought 3 more cases and spent an additional $6.95 on other items. Her receipts totaled $74.15. Write and solve an equation to find how much each case of sports drinks cost.
Answer
$9.60.
Step-by-step explanation:
Let x be the cost of one case of the sport drink.
7x+6.95=74.15
Solve for x
7x=67.20
x=9.60
The cost of each case of sports drink costs $9.60.
Translate each of these statements into logical expressions using predicates, quantifiers, and logical connectives
a) Somethingisnotinthecorrectplace.
b) All tools are in the correct place and are in excellent condition.
c) Everything is in the correct place and in excellent condition.
d) Nothing is in the correct place and is in excellent con- dition.
e) One of your tools is not in the correct place, but it is in excellent condition.
Answer:
A) ∃y(¬P(y))
B) ∀y(P(y) ^ Q(y))
C) ∀y(P(y) ^ Q(y))
D) ¬∃y(P(y) ^ Q(y))
E) ∃y(¬P(y) ^ Q(y))
Step-by-step explanation:
We will use the following symbols to answer the question;
∀ means for all
∃ means there exists
¬ means "not"
^ means "and"
A) Something(y) is not in the correct place is represented by;
∃y(¬P(y))
B) For All tools are in the correct place and are in excellent condition, let all tools in the correct place be P(y) and let all tools in excellent condition be Q(y).
Thus, we have;
∀y(P(y) ^ Q(y))
C) Similar to B above;
∀y(P(y) ^ Q(y))
D) For Nothing is in the correct place and is in excellent condition:
It can be expressed as;
¬∃y(P(y) ^ Q(y))
E) For One of your tools is not in the correct place, but it is in excellent condition:
It can be expressed as;
∃y(¬P(y) ^ Q(y))
Does anybody know the answer please if you do give it please
-7x + 17y
(-2x + 10y) - (5x - 7y)
-2x + 10y - 5x + 7
-7x + 17y
Which set of transformations has been performed on triangle pqr to form triangle p’q’r’
Answer:
Dilation by a scale factor of fraction 1 over 2 followed by reflection about the x-axis.
Step-by-step explanation:
We are given to select the set of transformations that has been performed on triangle PQR to form triangle P'Q'R'.
From the graph, we note that
the co-ordinates of the vertices of triangle PQR are P(-4, 2), Q(0, 0) and R(2, 6).And, the co-ordinates of the vertices of triangle P'QR' are P'(-2, -1), Q'(0, 0) and R'(1, -3).
Let the dilation factor applied on triangle PQR to form triangle P'Q'R' be represented by d.
Then, we observe that
1/2 × P(-4,2)=(-2,1),
1/2 × Q(0,0)=(0,0),
1/2 × R(2,6)=(1,3).
So, the value of d will be
d = 1/2.
Again, to arrive at the vertices of triangle P'Q'R', we need to change the sign before the y co-ordinates ((x, y) ⇒ (x, -y)) of each new vertex hat we found after dilation.
That is.(-2, 1) ⇒ P'(-2, -1),
(0, 0) ⇒ Q'(0, 0),
(1, 3) ⇒ R'(1, -3).
This is reflection over X-axis.
Therefore, the set of transformation is given by
Dilation by a scale factor of fraction 1 over 2 followed by reflection about the x-axis.
You are given $893 in one, five, and ten dollar bills. There are 165 bills. There are twice as many five dollar bills as there are ones and tens combined. How many bills of each type are there?
Given:
Total number of bills of one, five and ten = 165
Total amount = $893
There are twice as many five dollar bills as there are ones and tens combined.
To find:
Number of bills of each type.
Solution:
Let number of bills of one, five and ten are x, y and z respective.
Total number of bills of is 165.
[tex]x+y+z=165[/tex] ...(i)
Total amount is $893.
[tex]1x+5y+10z=893[/tex] ...(ii)
There are twice as many five dollar bills as there are ones and tens combined.
[tex]y=2(x+z)[/tex] ...(iii)
From equation (iii), we get
[tex]\dfrac{y}{2}=x+z[/tex] ...(iv)
Putting [tex]x+z=\dfrac{y}{2}[/tex] in (i), we get
[tex]\dfrac{y}{2}+y=165[/tex]
[tex]\dfrac{3y}{2}=165[/tex]
[tex]3y=330[/tex]
[tex]y=110[/tex]
Putting y=110 in (iv), we get
[tex]x+z=\dfrac{165}{2}[/tex]
[tex]x+z=55[/tex]
[tex]x=55-z[/tex] ...(v)
Putting y=110 and x=55-z in (ii), we get
[tex](55-z)+5(110)+10z=893[/tex]
[tex]55-z+550+10z=893[/tex]
[tex]9z+605=893[/tex]
[tex]9z=893-605[/tex]
[tex]9z=288[/tex]
Divide both sides by 9.
[tex]z=32[/tex]
Putting z=32 in (v), we get
[tex]x=55-32[/tex]
[tex]x=23[/tex]
Therefore, the number of one, five and ten bills are 23, 110 and 32 respectively.
There are 23 bills of $1 type.
There are 110 bills of $5 type.
There are 32 bills of $10 type.
According to the given situation
You are given $893 in one, five, and ten dollar bills.
Let the number of $1 bills be "x"
Let the number of $5 bills be "y"
Let the number of $10 bills be "z"
Total number of bills = x + y + z
Also it is given that there are twice as many five dollar bills as there are ones and tens combined
hence we can write the equations in the form of 3 variables
[tex]\rm x + y + z = 165........(1) \\x +5y + 10z = 893.........(2) \\y = 2\times (x+z) ..........(3) \\[/tex]
These are three linear equations with 3 variables that can be solved for x, y and z .
On solving equations (1) , (2), and (3) we get
[tex]x = 23 \\y = 110 \\z = 32 \\[/tex]
So we can conclude that there are 23 bills of $1 type.
There are 110 bills of $5 type.
There are 32 bills of $10 type.
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Alvin is 5 years older than Elga. The sum of their ages is 53. What is Elga's age?
Answer:
24
Step-by-step explanation:
53-5=48
48/2=24 Elgas age
24+5=29 Alvin's age
Which trigonometric function is an odd function and why?
The trigonometric function that is odd is the sine function, and it is because pf how it is defined.
Odd functions:We define an odd function as a function that has the next property.
f(-x) = -f(x)
So we need to find a trigonometric function with this property and is rater easy to know that it is the sine function, because:
Sin(-x) = -Sin(x)
This happens because the sine function measures the vertical distance to the endpoint of an angle x, and when x (an angle) becomes negative, the endpoint is below the horizontal axis, thus the outcome is reflected from the positive angle, but with opposite sign.
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The reason for trigonometric function is an odd function is shown below.
The sine function is the trigonometric function that is odd, and this is due of how it is defined.
Odd functions are functions that possess the following characteristics.
f(-x) = -f(x)
The sine function is the most straightforward to identify as the trigonometric function that has this attribute because:
sin(-x)= -sin x
This occurs because the sine function calculates the vertical distance from the angle's terminus, which is below the horizontal axis when the angle is negative.
As a result, the result is reflected from the positive angle but with the opposite sign.
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Write a simplified polynomial expression in standard form to represent the area of the rectangle below.
X + 4
2x-5
(2x-4)(x+5) expand with indicated multiplication
2x^2+10x-4x-20
2x^2+6x-20
square sandbox has an area of 75 square feet what is the estimate of the length of one side
Answer:
8.66 feet
Step-by-step explanation:
I typed it into google XD
Jerry was paid $47.00 for 4 hours of work. Leigh-Anne received $84.35 for 7 hours. Who had the greater rate of pay? By how much?
Answer:
Leigh Anne has the grater rate of pay by 0.30
Step-by-step explanation:
Jerry: $11.75 per hour
Anne: $12.05 per hour
Math!! Who knows answers???
option C for Qno10
and option a for Qno 9
Second derivative of x^½ + y^½ = a^½
Answer:
[tex]\displaystyle y'' = \frac{\sqrt{x} + \sqrt{y}}{2x^\big{\frac{3}{2}}}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Implicit Differentiation
Step-by-step explanation:
*Note:
Allow a to be defined as an arbitrary constant.
Step 1: Define
[tex]\displaystyle x^\big{\frac{1}{2}} + y^\big{\frac{1}{2}} = a^\big{\frac{1}{2}}[/tex]
Step 2: Differentiate
Basic Power Rule [Addition/Subtraction, Chain Rule]: [tex]\displaystyle \frac{1}{2\sqrt{x}} + \frac{y'}{2\sqrt{y}} = 0[/tex]Isolate y' term: [tex]\displaystyle \frac{y'}{2\sqrt{y}} = -\frac{1}{2\sqrt{x}}[/tex]Isolate y': [tex]\displaystyle y' = -\frac{\sqrt{y}}{\sqrt{x}}[/tex]Derivative Rule [Quotient Rule]: [tex]\displaystyle y'' = -\frac{(\sqrt{y})'(\sqrt{x}) - \sqrt{y}(\sqrt{x})'}{(\sqrt{x})^2}[/tex]Basic Power Rule [Derivative Rule - Chain Rule]: [tex]\displaystyle y'' = -\frac{\frac{y'\sqrt{x}}{2\sqrt{y}} - \frac{\sqrt{y}}{2\sqrt{x}}}{(\sqrt{x})^2}[/tex]Simplify: [tex]\displaystyle y'' = -\frac{\frac{y'\sqrt{x}}{2\sqrt{y}} - \frac{\sqrt{y}}{2\sqrt{x}}}{x}[/tex]Rewrite: [tex]\displaystyle y'' = \frac{-(y'x - y)}{2x^\big{\frac{3}{2}}\sqrt{y}}[/tex]Substitute in y': [tex]\displaystyle y'' = \frac{-(-\frac{\sqrt{y}}{\sqrt{x}}x - y)}{2x^\big{\frac{3}{2}}\sqrt{y}}[/tex]Simplify: [tex]\displaystyle y'' = \frac{\sqrt{x} + \sqrt{y}}{2x^\big{\frac{3}{2}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
A fraction multiplied by its reciprocal has a product of
Which function is represented by the graph?
O f(x) = -1x - 3+ 4
Of(x) = -1x + 3 + 4
Of(x) = -1x - 4 + 3
O f(x) = -x + 4 + 3
The equation of the graph is f(x) = -1|x + 4| + 3
How to determine the equation of the function?The graph represents an absolute value function
The equation of an absolute value function is represented as:
y = a|x - h| + k
Where:
Vertex = (h,k)
From the graph, we have:
(h,k) = (-4,3)
So,we have:
y = a|x - (-4)| + 3
Expand
y = a|x + 4| + 3
The graph is opens down.
This means that a < 0
Assume a = -1, the equation becomes
y = -1|x + 4| + 3
Express as a function
f(x) = -1|x + 4| + 3
Hence, the equation of the graph is f(x) = -1|x + 4| + 3
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