Answers
For the second part, we get that 381.51=(4/3)πr^3, so plugging 381.51 into the equation above we get (3/4)(381.51)/pi=around 91, and r= the cube root of r^3, which would equal around 4.5 here
Related Questions
pre cal/cal master needed
g(x)={ ax-3, x<-2
{ x^2 -2x, x>-2
What value would the function g(x) have point discon. at x=-2 how to find?
Answers
Ok so we want to find what value of a would the function g(x) have point discontinuity at x=-2.
We find this by subsituting -2 where the x is located in the functions x^2 -2x
x^2 -2x
-2^2 - 2(-2) = 8
Now to find a we use ax - 3 and insert -2 for x like the follow
-2a - 3
Next for the limit to exist both limits have to equal the same so we have
-2a - 3 = 8
Now solve for a
-2a - 3 = 8
-2a - 3 + 3 = 8+3
-2a = 11
-2a / -2 = 11 / -2
a = -5.5
So when a is at -5.5 the function is continuous and anything > or < will make it discontinuous. So when -5.5 < a < -5.5 a will have discontinuity.
What is n in a(n-5)+6=bn.(You can use variables in the answer). Please explain, if you can.
Answers
use dis. property for left
an-a5+6=bn
isolate n.
(an-a5+6)/ b= n is the asnwer
i need help 7th grade 13 + p + - 4 3
Answers
13+p-43=
-30+p
Give A={a,b,c},how many subsets does A have including 0?
Answers
----------------------------------------------------------------------
----------------------------------------------------------------------
There are n = 3 elements in the given set, so there are 2^n = 2^3 = 2*2*2 = 8 subsets. Those 8 subsets are listed below
{a,b,c}
{a,b}, {a,c}, {b, c}
{a}, {b}, {c}
{ }
The first row is the original set. Any set is a subset of itself.
The second row represents subsets with exactly 2 elements.
The third row represents subsets with exactly 1 element
The fourth row is the empty set which can be written as [tex]\varnothing[/tex]
py+7=6y+q solve for y
Answers
We know that we are solving for y.
This is a step by step procedure to get the value of y.
First: Move all terms to the left side and set equal to zero.
Second: Then set each factor equal to zero.
The application is:
Given: py+7=6y+q
-6y -7 -6y -7 = 0
(p-6)y = q-7
divide both sides by p-6
y=(q-7)/(p-6)
Answer is y = (q – 7) / (p – 6)
The solution of expression for y as,
⇒ y = (q - 7) / (p - 6)
We have to given that,
An expression is,
⇒ py + 7 = 6y + q
Now, We can simplify the expression for y as,
⇒ py + 7 = 6y + q
Subtract 6y both side,
⇒ py - 6y + 7 = 6y + q - 6y
Subtract 7 both side,
⇒ py - 6y = q - 7
⇒ y (p - 6) = (q - 7)
Divide both side by (p - 6);
⇒ y = (q - 7) / (p - 6)
Therefore, The solution of expression for y as,
⇒ y = (q - 7) / (p - 6)
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A kite flying in the air has a 12 ft line attached to it. Its line is pulled taut and casts an
11 ft shadow. Find the height of the kite. If necessary, round your answer to the nearest tenth.
Answers
h^2 + 10^2 = 12^2
h^2 + 100 = 144
h^2 = 44
h = √44 = appr 6.6
the point (1,1) is the image under the image under rhe translation (x,y) (x+3,y-3)
Answers
The pre-image of the point (1, 1) under the translation (x, y) -> (x+3, y-3) in a coordinate system is the point (-2, 4).
The student's question relates to a translation transformation in mathematics. A translation moves every point of a figure or a space by the same distance in a given direction. In this case, the student has provided a specific translation transformation, which is represented by the formula (x, y)
ightarrow (x+3, y-3). This transformation means that for any point with coordinates (x, y), the translated point will have coordinates where 3 is added to the x-coordinate and 3 is subtracted from the y-coordinate.
If the point (1,1) is an image under this translation, you can find its pre-image by reversing the translation. Thus, subtracting 3 from the x-coordinate of the image and adding 3 to the y-coordinate of the image gives the pre-image coordinates:
Pre-image x-coordinate: 1 - 3 = -2Pre-image y-coordinate: 1 + 3 = 4Therefore, the pre-image of the point (1, 1) under the given translation is (-2, 4).
How do I solve this equation? I need a refresher on Algebra.
Answers
Your common denominator is 9x + 9, so
1/(9x+9) = 36/(9x + 9) - (5x + 5)/9
1 - 36 + 5x + 5 / 9x - 9
30x - 30/9x - 9
10x-10/3x - 3
10(x-1)/3(x-1)
10/3
Hope this helped!
Final answer:
To solve an algebraic equation, identify knowns, find suitable equations, simplify algebraically, substitute known values, solve for the unknown, and check if the answer is reasonable.
Explanation:
To solve an algebraic equation, follow these systematic steps:
Firstly, identify the knowns and make a list of what is given or can be inferred from the problem.
Then, find the appropriate equation or set of equations that contain the unknown you need to solve for.
Simplify the algebra by eliminating terms wherever possible. This might require algebraic rearrangement such as dividing terms or multiplying both sides of the equation to isolate the unknown.
Substitute the known values into the equation.
Solve for the unknown and make sure to include units where necessary.
Finally, always check your answer to see if it is reasonable and makes sense.
These steps should yield a solution that is both accurate and verifiable.
The difference between two positive integers is 4. If the smaller is added to the square of the larger, the sum is 68. Find the integers.
Answers
Two positive integers x and y
x - y = 4
x² + y = 68
Findx and y
SolutionAdd the two equations together.
... (x - y) + (x² + y) = (4) + (68)
... x² + x = 72
Rearrange to standard form and factor.
... x² + x - 72 = 0
... (x + 9)(x - 8) = 0
Use the zero product rule to find the solutions. That rule says the product is zero when one or more factors is zero.
... x + 9 = 0 ⇒ x = -9
... x - 8 = 0 ⇒ x = 8 . . . . . . the positive solution
Then we can find y from
... 8 - y = 4
... y = 4 . . . . . . . add y-4 to the equation
The two positive integers are 8 and 4.
To solve for the two positive integers where their difference is 4 and the sum of the smaller and the square of the larger is 68, we set up a quadratic equation and solve for n to find that the integers are 4 and 8.
Explanation:The problem given is a classic algebra question where we are asked to determine two positive integers based on their relationship to each other and an additional numeric condition. We know that the difference between these two numbers is 4, and when the smaller integer is added to the square of the larger, the result is 68.
Let's denote the smaller number as n and the larger number as n+4, since there is a difference of 4 between them. Now, according to the second condition given, we can set up the following equation: n + (n+4)2 = 68.
Expanding the squared term and combining like terms, we get a quadratic equation: n2 + 8n + 16 + n = 68. Simplifying, n2 + 9n + 16 = 68. Further simplification leads to n2 + 9n - 52 = 0. Factoring this quadratic equation, we find the integers that satisfy the equation: n = 4 and n = -13. Since we are looking for positive integers, the solution is n = 4 and n+4 = 8.
Therefore, the two positive integers are 4 and 8.
The length of a table is 6 feet. On a scale drawing, the length is 2 inches. Write three possible scales for the drawing
Answers
Answer:
The three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.
Step-by-step explanation:
It is given that the length of a table is 6 feet. On a scale drawing, the length is 2 inches.
The scale for drawing is
[tex]Scale=\frac{\text{Length in drawing}}{\text{Actual length}}=\text{Length in drawing}:\text{Actual length}[/tex]
First possible scale for the drawing is
2 inch : 6 feet
It can be written as
1 inch : 3 feet
We know that 1 feet = 12 in
1 inch : 36 inch
We know that 1 feet = 30.48 cm
1 inch : 91.44 cm
Therefore the three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.
The three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.
Here, we have,
It is given that the length of a table is 6 feet. On a scale drawing, the length is 2 inches.
The scale for drawing is
scale = length in drawn/actual length
scale = length in drawn : actual length
First possible scale for the drawing is
2 inch : 6 feet
It can be written as
1 inch : 3 feet
We know that 1 feet = 12 in
1 inch : 36 inch
We know that 1 feet = 30.48 cm
1 inch : 91.44 cm
Therefore the three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.
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A factory makes an oil mixture by mixing oils of grades A and B as follows. For every 2.3 liters of grade A oil, 1.2 liters of grade B oil are mixed in. How many liters of grade A oil and grade B oil will the factory need to make 1000 liters of their oil mixture? Explain your solution.
Answers
Since we don't know the scaling factor, we assign that multiple "x". Then the amounts of each ingredient oil would be:
amount of A = 2.3x
amount of B = 1.2x
add them together to get the required mixture amount.
1000 = 2.3x + 1.2x
1000 = 3.5x
1000/3.5 = x
285.7 = x
this is the scaling factor.
plug x in to find the amounts of each oil type.
A = 2.3(285.7)
A = 657.1 L
B = 1.2(285.7)
B = 342.9 L
how many integers from 1 to 700 are divisible by 2, 5 and 7
Answers
There are 10 integers from 1 to 700 that are divisible by 2, 5, and 7. This is calculated by finding the least common multiple (LCM) of the numbers, which is 70, and then determining how many multiples of 70 are within the given range.
Explanation:The question asks to find out how many integers from 1 to 700 are divisible by 2, 5, and 7. An integer divisible by 2, 5, and 7 is also divisible by their least common multiple (LCM). The LCM of 2, 5, and 7 is 70 since 2 x 5 x 7 = 70. So, the task is to find the number of multiples of 70 between 1 and 700.
To find the number of multiples of 70 in that range, you can use the following steps:
Divide the largest number in the range (700) by 70 to find the highest multiple within the range. ∑(700 ÷ 70 = 10).Since we started from 1 and 70 is the first multiple, the total count is the result of the division.Therefore, there are 10 integers from 1 to 700 that are divisible by 2, 5, and 7.
what is 25.6 divided by 0.5 =
Answers
I hope this helps you alot. God Bless you.
2x+5=10
Solve for x
Answers
Subtract 5 from both sides.
2x + 5 - 5 = 10 - 5
2x = 5
Divide both sides by 2.
2/2x = 5/2
x = 5/2
5/2 can be simplified to 2 1/2 or 2.5.
-5 both sides
2x=5
÷2 both sides
X=5/2
Answer: x=5/2
Check your work:
2 (5/2)+5=10
5+5=10
10=10
Answer is correct
Hope that helps you :)
Let me know if you need any more help :)
8x__=2
10x__= 5
—
2
6x__= 3
—
2
?? Can you fill in the blanks?
Answers
1/2
1/2
I could only understand 1, 2, & 5
You are building a new house on a cartesian plane whose units are measured in miles.
Your house is to be located at the point (6,0). Unfortunately, the
existing gas line follows the curve y=√16x^(2)+6x+19.
It costs 300 dollars per mile to install new pipe connecting your house to the existing line.
What is the least amount of money you could pay to get hooked up to the system?
Answers
[tex]\bf y=\sqrt{16x^2+6x+19}\\\\ -------------------------------\\\\ L(x)=\left[(6-x)^2+(0-\sqrt{16x^2+6x+19})^2 \right]^{\frac{1}{2}} \\\\\\ L(x)=[36-12x+x^2+16x^2+6x+19]^{\frac{1}{2}} \\\\\\ L(x)=(17x^2-6x+55)^{\frac{1}{2}}\\\\ [/tex]
so, that's L(x) equation for the line, simplified, now, let's check its derivative.
[tex]\bf \cfrac{dL}{dx}=\cfrac{1}{2}(17x^2-6x+55)^{-\frac{1}{2}}(34x-6) \\\\\\ \cfrac{dL}{dx}=\cfrac{1}{2}(17x^2-6x+55)^{-\frac{1}{2}}2(17x-3) \\\\\\ \cfrac{dL}{dx}=\cfrac{17x-3}{\sqrt{17x^2-6x+55}}\\\\[/tex]
now, we get critical points when the derivative is 0, or when the denominator is 0, however (usually cusps or asymptotes), but in this case, we won't check the denominator, because it doesn't yield any, so, we'll just zero out the derivative and see what critical points we get.
[tex]\bf 0=17x-3\implies 3=17x\implies \cfrac{3}{17}=x[/tex]
easy enough, so we only got one point... well, is it a minimum though?
well, running a first-derivative test on the left-region and the right-region of 3/17, we get a negative value on the left and a positive value on the right, that means the original function drops and then goes up, check the picture on the right-hand-side.
So, it's a minimum, those numbers in red in the picture are the ones I used to check it, but any value on the region will work, even -1,000,000, anyway.
so, at 3/17 is at a minimum... now how many miles, and how much is that?
[tex]\bf f\left( \frac{3}{17} \right)\approx 4.53\qquad \qquad \stackrel{miles}{4.53}\cdot \stackrel{\textit{\$ per mile}}{300}\approx 1360.2[/tex]
I need help I am trying to find ft
Answers
1 foot = 12 inches
divide 69 by 12
69/12 = 5.75 feet
The following data pairs represent the average temperature x (in degrees Fahrenheit) and electricity costs y (in dollars) for different homes: (65, 147), (59, 141), (71, 176), (78, 189), (82, 183), (85, 211), (88, 231), (91, 227), (84, 198), (79, 188), (63, 152), (59, 126) Which of the following values is most likely the closest to the correlation coefficient of the data?
Answers
The correlation coefficient of the given data pairs is most likely closest to 0.8694.
Explanation:The correlation coefficient measures the strength and direction of the relationship between two variables. To find the correlation coefficient, you can use the formula:
r = [n(Σxy) - (Σx)(Σy)] / sqrt{[n(Σx^2) - (Σx)^2][n(Σy^2) - (Σy)^2]}
Using this formula, you can calculate the correlation coefficient for the given data pairs. The closest value to the correlation coefficient will be 0.8694, option d.
The answer closest to the correlation coefficient of the data is 0.835.
To find the correlation coefficient of the given data pairs, we can use the formula:
r = (Σxy - (Σx)(Σy)/n) / sqrt((Σx^2 - (Σx)^2/n)(Σy^2 - (Σy)^2/n))
where Σ represents the sum, n is the number of data pairs, x is the average temperature, y is the electricity cost, and xy is the product of x and y.
To calculate the correlation coefficient, we first need to find the sums and products of the data pairs:
Σx = 65 + 59 + 71 + 78 + 82 + 85 + 88 + 91 + 84 + 79 + 63 + 59 = 924
Σy = 147 + 141 + 176 + 189 + 183 + 211 + 231 + 227 + 198 + 188 + 152 + 126 = 2259
Σxy = (65*147) + (59*141) + (71*176) + (78*189) + (82*183) + (85*211) + (88*231) + (91*227) + (84*198) + (79*188) + (63*152) + (59*126) = 219907
Using these values, we can calculate the correlation coefficient:
r = (219907 - (924*2259)/12) / sqrt((Σx^2 - (Σx)^2/12)(Σy^2 - (Σy)^2/12))
Calculating the remaining sums:
Σx^2 = (65^2) + (59^2) + (71^2) + (78^2) + (82^2) + (85^2) + (88^2) + (91^2) + (84^2) + (79^2) + (63^2) + (59^2) = 73482
Σy^2 = (147^2) + (141^2) + (176^2) + (189^2) + (183^2) + (211^2) + (231^2) + (227^2) + (198^2) + (188^2) + (152^2) + (126^2) = 827259
Plugging in the values:
r = (219907 - (924*2259)/12) / sqrt((73482 - (924^2)/12)(827259 - (2259^2)/12))
After performing the calculations, the correlation coefficient is approximately 0.835.
Therefore, the answer closest to the correlation coefficient of the data is 0.835.
PLEASE ASAP
Trapezoid W ′ X ′ Y ′ Z ′ is the image of trapezoid WXYZ under a dilation through point C. What scale factor was used in the dilation?
− 7/3
− 3/7
3/7
7/3
Answers
Round 754 to the nearest ten
Answers
use properties to find 4 times 23 times 25
Answers
Answer:
2300
Step-by-step explanation:
What is 36 divided by 3/4?
Answers
Explanation: 36 divided by 3/4
36 4 144
____ x ____ = ____ = 48
1 3 3
^
Flip the denominator to numerator
And numerator to denominator
Also divide 144/3
What is the vertex of the graph of y+2x+3 = -(x+2)^2 + 1?
A. (-3,-33)
B. (-3,3)
C. (3,-24)
D. (3,21)
Answers
The graph opens downward too
Irrigation improves the yield of strawberries per acre according to the function S=-(w-2)^2 +50 where S is the number of pints of strawberries grown per acre and w is the acre-feet of water used. Strawberries sell for $3 per pint and water costs $5 per acre-foot. Graph the yield function.
Answers
The yield of strawberries per acre is
S = -(w - 2)² + 50
where
S = number of pints of strawberries per acre
w = acre-feet of water
Strawberries sell for $3 per pint
Water costs $5 per acre-feet.
The yield function is the revenue minus the expenses. It is
Y = (S pints)*($3 per pint) - (w acre-ft)*($5 per acre-ft)
Y = -3(w - 2)² -5w + 150 dollars
A graph of the yield function is shown below.
It indicates that
a) the yield is maximum when the acre-feet is about 1.5;
b) the yield increases between zero and 1.5 acre-feet;
c) the yield decreases quickly when the acre-feet exceed 1.5;
d) the yield vanishes when the acre-feet exceed 8.
Bill gates makes approximately $12 billion a year. On average, how much does he make per minute
Answers
Bill Gates makes approximately $22,831.05 per minute, calculated by dividing his annual earnings of $12 billion by the number of minutes in a year (525,600).
Explanation:To calculate how much Bill Gates makes per minute, we need to start by determining how much he makes per year. According to the question, Bill Gates makes approximately $12 billion a year. To find out how much that is per minute, we need to follow these steps:
Therefore, on average, Bill Gates makes $22,831.05 per minute.
what is 28.5 divided by 5
Answers
How do you write 7/20 as a percentage??
Answers
In decimal form would be 0.35 .
To get the percentage move the decimal to the right 2 times .
:)
Find the quadratic function that is the best fit for f(x) defined by the table below
Answers
We have to calculate a, b and c from the given table
1st Calculate c:
for x = o, y = -1.55
- 1.55 = a(0)² + b(0) + c → then c = -1.55
and the equation becomes: y = ax² + b.x - 1.55
2nd Calculate a and b:
for x = 2 , y = 17.29
17.29 =a(2)² + b(2) - 1.55 → 4a + 2b - 1.55 = 17.29 or 4a + 2b = 18.84 (1)
for x = 4 , y = 54.93
54.93=a(4)² + b(4) - 1.55 → 16a + 4b - 1.55 = 54.93 or 16a + 4b = 56.48 (2)
Now solve the system of 2 equations:
4a + 2b = 18.84 (1)
16a + 4b = 56.48 (2)
And you will find :
a= 2.35 and b = 4.72 . And the final equation is:
y = 2.35.x² + 4.72x - 1.55
The quadratic equation defined by the table is f(x) = 2.35x^2 + 4.72x -1.55
How to determine the function?A quadratic function is represented as:
f(x) = ax^2 + bx + c
Using the table of values, we have:
a(0)^2 + b(0) + c = -1.55
This gives
c = -1.55
Also, we have:
a(2)^2 + b(2) + c = 17.29
4a + 2b -1.55 = 17.29
This gives
4a + 2b = 18.84
Divide through by 2
2a + b = 9.42 --- (2)
Also, we have:
a(4)^2 + b(4) + c = 54.93
16a + 4b -1.55 = 54.93
This gives
16a + 4b = 56.48
Divide through by 4
4a + b = 14.12 ---- (3)
Subtract (2) from (3)
2a = 4.7
Divide by 2
a = 2.35
Substitute a = 2.35 in 4a + b = 14.12
4*2.35 + b = 14.12
Evaluate
b = 4.72
Substitute values for a, b and c in f(x) = ax^2 + bx + c
f(x) = 2.35x^2 + 4.72x -1.55
Hence, the quadratic equation defined by the table is f(x) = 2.35x^2 + 4.72x -1.55
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How are the values of the eights in 880 relared
Answers
the number 880 can be written as:
880 = 800 + 80 + 0
There is 3/4 of a box of cereal remaining. You eat 2/5 of the remaining cereal. What fraction of the box do you eat?
Answers
-------- = ------------- = ------
4(5) 2(5) 10
You eat 3/10 of the box's original contents
Alternatively: (3/4)(2/5) = (3/2)(1/5) = 3/10.