The composed function for the surface area of the cube for any given volume of an inscribed sphere, A(V) = 24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²
The function used to find the radius r of a sphere given volume V,
r(V) = [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex]
The function used to find the length of the side s of the cube depending on the radius r of the sphere, s(r) = 2r
The function used to find the surface area A of the cube depending on the side of the cube s, A(s) = 6s²
We need to find the composed function for the surface area A of the cube for any given volume V of an inscribed sphere. i.e., A(V)
We have, A(s) = 6s²
Substituting function for s to A(s)
⇒ A(s(r)) = 6(2r)² = 24r²
Substituting function for r into A(s(r)),
⇒ A(s(r(V))) = 24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²
So the function for the surface area of the cube depending on the volume of the inscribed sphere, A(V) = 24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²
The question is incomplete. Find the complete question below:
Consider a cube with an inscribed sphere. The function r(V) = [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex] can be used to find the radius, r, of a sphere given the volume, V . The function s(r) = 2r can be used to find the side length of the cube, s , depending on the radius of the sphere. The function A(s) = 6s² can be used to find the surface area, A , of the cube. Which is the composed function for the surface area of the cube for any given volume of an inscribed sphere?
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Answer:
Answer is D
Step-by-step explanation:
Insert <,>,or = to make the following sentence true. square root of 17 and 4
we can insert > to make the following sentence true that is [tex]\sqrt{17}[/tex] > 4
we have to solve the following sentence
[tex]\sqrt{17}[/tex] --- 4 ( insert <,>, = to make the following sentence true)
what is square root ?
The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is [tex]\sqrt{}[/tex] .
we know that
square root of 17 is 4.12310563
which is 4+ 0.12310563
that is if we add 4+0.12310563 we get 4.12310563
therefore square root of 17 is greater than 4
that is [tex]\sqrt{17}[/tex] > 4
since 4.12310563 > 4
hence, we can insert > to make the following sentence true that is [tex]\sqrt{17}[/tex] > 4
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25 points plus brainliest
Answer:
The first answer is correct
Step-by-step explanation:
y = mx + b is the slope intercept form of a line
15x - 5y = 30 Subtract 15x from both sides
-5y = -15x + 60 Divide both sides by -5
y = 3x -6 The -6 is your y-intercept. It is the point (0.-6) We could stop here because that is the only choice that shows (0,-6), but let's find the x intercept.
The x-intercept is when y = 0
y = 3x -6
0 = 3x - 6 Add 6 to both sides
6 = 3x Divide both side by 3
2 = x This is the point (2,0)
We could have taken the original equation and set x=0 and y=0
15x - 5y = 30
15(0) - 5y = 30
-5y = 30 Divide both sides by -5
y = -6
15x -5y = 30
15x - 5(0) = 30
15x = 30 Divide both sides by 15
x = 2
-
what is the value of 32 ⅗ ?
Answer:
8
Step-by-step explanation:
I attached my answer........
Prove that cos 4θ = 8 cos⁴ θ - 8 cos² θ + 1
Answer:
Step-by-step explanation:
Answer is in the pic.
Answer:
See below for proof.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Trigonometric Identities}\\\\$\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B$\\ \\$\sin^2 \theta + \cos^2 \theta=1$\\\end{minipage}}[/tex]
Use the trigonometric identities to prove the given equation:
[tex]\begin{aligned} \implies \cos 4 \theta & = \cos (2 \theta +2 \theta)\\& = \cos 2 \theta \cos 2 \theta - \sin 2 \theta \sin 2 \theta\\& = \cos^2 2 \theta - \sin^2 2 \theta\\& = \cos^2 2 \theta - (1-\cos^2 2 \theta)\\& = 2\cos^2 2 \theta - 1\\ & = 2\left(\cos 2 \theta \right)^2-1\\& = 2\left(\cos\theta \cos\theta-\sin \theta\sin \theta\right)^2-1\\& = 2\left(\cos^2\theta-\sin ^2\theta\right)^2-1\\& = 2\left(\cos^2\theta-(1-\cos^2\theta)\right)^2-1\\& = 2\left(2\cos^2\theta-1\right)^2-1\\\end{aligned}[/tex]
[tex]\begin{aligned}& = 2\left(4\cos^4\theta-4\cos^2\theta+1\right)-1\\& =8\cos^4\theta-8\cos^2\theta+2-1\\ & =8\cos^4\theta-8\cos^2\theta+1 \end{aligned}[/tex]
How would I solve these problems
Answer:
1a. -( x + 1)² + 4
1b. y-intercept at y = 3
1c. x-intercepts at x = -3 and x = 1
Derivation of 1b and 1c below
Step-by-step explanation:
Question 1a
The vertex equation form of a parabola is given by
y = a(x-h)² + k where (h, k) are the coordinates of the vertex
If a > 0 then the parabola is facing up(vertex is at a minimum) and if a < 0 then parabola is facing down (vertex at a maximum)
From the graph we see that the parabola is facing down so a = -1
The vertex is at (-1, 4) so h = -1 and k = 4
Therefore the equation of the parabola is
y = -1(x - h)² + k = -1(x- (-1))² + 4 = -1(x + 1)² + 4
y = -( x + 1)² + 4 (Answer 1a)
Question 1b
The y-intercept is the y-value where the parabola crosses the y-axis. From the graph we see that the parabola crosses the y-axis at y = 3 and x = 0
So y-intercept from the graph is 3
To solve algebraically, set x = 0 in the parabola equation and solve for y
We get, for x = 0,
y = - (0 + 1)² + 4
y = -(1²) + 4 = -1 + 4 = 3
Hence verified
Question 1c
There will be two x-intercepts for a parabola. Looking at the graph we see that the parabola intersects the x-axis at two points (-3, 0) and (1, 0). So the two x-intercepts are -3 and 1
Algebraically we can determine the x-intercepts by setting y = 0 and solving for the two values of x
Setting y = 0 in the parabolic equation, we get
y = 0 = -(x + 1)² + 4
Switch sides
-(x + 1)² + 4 = 0
-(x + 1)² = -(x² + 2x + 1) = -x² -2x - 1
-(x + 1)² + 4 = 0
==> -x² -2x - 1 + 4 = 0
==> -x² - 2x +3 = 0
Multiply by -1 both sides
==> x² + 2x - 3 = 0
Solve this quadratic equation by factoring
x² + 2x - 3 = (x - 1)(x + 3) = 0
The solutions are
x - 1 = 0 ==> x = 1
x + 3 = 0 ==> x = -3
Hence verified
Please help with explanation
The perimeter of the sandbox is 2x+2y.
Therefore, the inequality is
[tex]\boxed{2x+2y \leq 20}[/tex]
What is the distance from the origin to point P graphed on the complex plane below?
4
3
2
4
-5-4-3-2-₁
√√7
√29
7
20
-2-
34 32 4
Mark this and return
2 3 45 x
Save and Exit
Next
Submi
Step-by-step explanation:
the point is (2, -5).
the origin is (0, 0).
the distance between 2 points is calculated via Pythagoras due right-angled triangles :
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90° angle). a and b are the legs.
the direct distance is the Hypotenuse, and the x coordinate and y coordinate differences are the legs.
so,
distance² = (2 - 0)² + (-5 - 0)² = 2² + (-5)² = 4 + 25 = 29
distance = sqrt(29) = 5.385164807...
so, the second answer option is correct.
A forest covers 61,000 acres. A survey finds that 0.4% of the forest is old-growth trees. How many acres of old-growth trees are there?
Answer:
2,440 acres of old-growth trees.
Step-by-step explanation:
61,000*0.04=2,440
There are 2,440 acres of old-growth trees.
Hope this helps!
Please mark as brainliest if correct!
Mrs. Genebe worked all year and earned $23,400. How much did she earn per week?
Answer:
$448.766754 per week or $448
Step-by-step explanation:
i gotchu
theres 52.1429 weeks
divide 23,400 by 52.1429
u get $448.766754 per week
a professor wants to randomly select 4 students to go to the board. she decides to randomly select the third student who enters the classroom and every seventh student after that. determine the students who will be going to the board. write down the student numbers.
The total number of students chosen is 4, 13, 22, and 31.
What is random selection?Random selection, also known as random sampling, is a method of selecting members of a population to be included in your study's sample. Random assignment, on the other hand, is a method of dividing the sample into control and experimental groups. The goal is to make the results more generalizable. The goal of selecting a random sample from a larger population is to ensure that the sample is representative of the larger group and less likely to be biased.To determine the students who will be going to the board:
The professor wishes to choose four students at random.She then chose the fourth and ninth students at random.The fourth student is chosen first.Now, using the following term formula, a + d (n - 1).
The second student is up next.
= 4 + 9(2-1) = 4 + 9(1)= 4 + 9= 13The third student will:
= 4 + 9(3-1)= 4 + 9(2)= 4 + 18= 22The fourth student will:
= 4 + 9(4-1)= 4 + 9(3)= 4+ 27= 31Therefore, the total number of students chosen is 4, 13, 22, and 31.
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Speed and travel time are inversely related, the faster you go, the less time it takes
to get to your destination. If it takes 20 minutes to get to school when you go 30 mph,
how long will it take to get to school if you travel 45 mph? (hint: speed=k/time)
Answer:
Step-by-step explanation:
speed = distance/time
however speed is a compound measure
distance to school = speed x time
= 30mph x 1/3hr
= 10m
time = 10m / 45mph
= 13.3 (recurring)
= 13 mins
Simplify:
4(10+2³-5)
O a. 52
O b. 44
O c. 6892
O d. 17
Answer:
A. 52 is your answer
Step-by-step explanation:
Explained below
Answer:
Ans is a
First you solve the inside of the bracket u will get 4(13)
which will give u 52
jillian is trying to save water, so she reduces the size of her square grass lawn by 8 feet on each side. the area of the smaller lawn is 144 square feet. in the equation (x – 8)2
The dimensions of original lawn are a. 4 feet by 4 feet.
As per the equation and information mentioned in question, x represents the dimension of original lawn. The equation in question represents the relation between area of lawn at side of reduced lawn and it's area. We will solve this equation to find the value of x.
[tex](x - 8)^{2} = 144[/tex]
The expression on Left Hand Side is same as [tex](a - b)^{2}[/tex]. We know, on expansion, we write it as [tex]a^{2} + b^{2} - 2ab[/tex]. Thus, new equation will be -
[tex]x^{2} + 8^{2} - 2*x*8 = 144[/tex]
[tex]x^{2} + 64 + 16x = 144[/tex]
[tex]x^{2} + 16x + 64 - 144 = 0[/tex]
[tex]x^{2} + 16x - 80 = 0[/tex]
[tex]x^{2} + 20x - 4x - 80 = 0[/tex]
x (x + 20) -4 (x + 20) = 0
(x + 20) (x - 4) = 0
So, the two values of x that we get are:
x = 4 and -20.
The dimensions of lawn can not be negative. Hence, the value of x will be x.
Therefore, the dimensions of original lawn are a. 4 feet by 4 feet.
The complete question is -
Jillian is trying to save water, so she reduces the size of her square grass lawn by 8 feet on each side. The area of the smaller lawn is 144 square feet. In the equation [tex](x - 8)^{2} = 144[/tex], x represents the side measure of the original lawn. What were the dimensions of the original lawn?
a. 4 feet by 4 feet
b. 8 + [tex]6\sqrt{2}[/tex] feet by 8 + [tex]6\sqrt{2}[/tex] feet
c. 8 - [tex]6\sqrt{2}[/tex] feet by 8 + [tex]6\sqrt{2}[/tex] feet
d. 20 feet by 20 feet
Solve problems on area of lawn -
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in a random sample of 77 residents of the state of texas, the mean waste recycled per person per day was 1.01.0 pounds with a standard deviation of 0.290.29 pounds. determine the 98�% confidence interval for the mean waste recycled per person per day for the population of texas. assume the population is approximately normal. step 1 of 2 : find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.
Answer:
(0.63789 ; 1.38211 ) is the 98% confidence interval for the mean waste recycled per person per day for the population of texas and Tcritical = 3.143
In a random sample of 7 residents of the state of texas ,the mean waste recycled per person per day was 1.01 pounds and standard deviation 0.29 pounds
we have to find the 98% confidence interval for the mean waste recycled per person per day for the population of texas
Mean, xbar = 1.01
Standard deviation, s = 0.29
Sample size, n = 7
Confidence interval : xbar ± margin of error
Margin of Error = Tcritical * s/sqrt(n)
Degree of freedom (df) = n - 1 = 7 - 1 = 6
Hence Tcritical = 3.143
Margin of Error = 3.143 * 0.29/sqrt(6)
Margin of error = 0.37211
Lower boundary = (1.01 - 0.37211) = 0.63789
Upper boundary = (1.01 + 0.37211) = 1.38211
(0.63789 ; 1.38211 )
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How to find the greatest number of identical arrangements that can be made what is 54 roses and 42 tulips or no flowers left over.
The greatest number of identical arrangements that can be made is 6 arrangements of 7 tulips and 9 roses.
The above problem we can use the greatest common factor, we are provided with the information that there are a total of 42 tulips and 54 roses. Now, we will find the greatest common factor of 54 and 42.
42- 54|2
21- 27 | 3
7 - 9
So the greatest common factor of 54 and 42 is 6, here we are left with 7 and 9 which indicates the number of tulips and roses
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what is this equations value for x? |5-2x|>5
The value of equation for x is x > 0.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now the given equation is,
|5-2x| > 5
To solve for let us take x on one side.
So, Subtracting 5 both the side we get,
|5 - 2x - 5| > 5 - 5
Simplifying we get,
|-2x| > 0
Extracting mod we get,
2x > 0
Now since 2 > 0 which is true,
Thus, x > 0
So, the value of equation for x is x > 0.
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A triangle has height of 15 in. And area 120^2 . What is the length of its base
Answer:
16 inches
Step-by-step explanation:
Multiply 120 by 2 to start reversing the triangle area equation.
120*2 = 240.
Now divide by 15
240/15=
16
The length is 16 inches
a racetrack charges $80 each seat in the lower section, $65 for each seat in the upper sections, and $30 for field tickets. there are three times the number of seats in the upper section as compare to the lower section. the revenue from selling all 21,200 seats is $915,000. how many of each ticket were sold at the racetrack?
The number of each ticket sold was:
The upper section contains 5160 seats, the lower section contains 1720 seats, and the field contains 17320 seats.Given Information:
Each seat in the lower section costs $80, each seat in the upper section costs $60, and field tickets cost $40.The upper section has three times the number of seats as the lower section.The total revenue from the sale of all 24,200 tickets is $1,140,000.The steps below can be used to calculate the total number of seats in each section:
Step 1 - In the lower section, enter 'x' as the total number of seats.
So, based on the data provided, the total number of seats in the upper field is '3x'. Let y be the total number of seats in the field.Step 2 - The linear equation that represents total ticket revenue.
80x + 60(3x) + 40y = 1140000260x + 40y = 1140000 ...(1)Step 3 - The linear equation representing the total number of tickets is as follows:
x + 3x + y = 24200y = 24200 - 4x ...(2)Step 4: Change the value of y in the equation (1).
260x + 40(24200 - 4x) = 1140000x = 1720 ticketsStep 5: Change the value of 'x' in equation (2).
y = 24200 - 4(1720)y = 17320 ticketsTherefore, the number of each ticket sold was:
The upper section contains 5160 seats, the lower section contains 1720 seats, and the field contains 17320 seats.Know more about linear equations here:
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The correct question is given below:
A racetrack charges $80 for each seat in the lower section, $60 for each seat in the upper section, and $40 for field tickets. There are three times the amount of seats in the upper section as the lower section. The revenue from selling all 24,200 tickets is $1,140,000. write a system to represent the situation. How many seats are in each section
please help!! (answer is NOT undefined)
[tex]-8\sqrt{-165} \\ \\ =-8\sqrt{-1}\sqrt{165} \\ \\ =\boxed{-8i\sqrt{165}}[/tex]
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form..
Answer:
y = 4/5x + 27/5
or 5y = 4x + 27
or 5y - 4x = 27
Step-by-step explanation:
Look at (-3,3) and (2,7)
So the line rises 4 units and runs 5 units, then slope is 4/5
using m = 4/5, y = 3, x = -3
y = mx + b
3 = 4/5(-3) + b
3 = -12/5 + b
b = 15/5 + 12/5 = 27/5
so y = 4/5x + 27/5
or 5y = 4x + 27
or 5y - 4x = 27
Deanna and Raquel ride a merry-go-round together. Deanna sits on a horse on the outer edge of the merry-go-round, 10 feet from the center of the ride. Raquel sits on a horse that is 2 feet closer to the center than Deanna. This ride makes one full rotation every 15 seconds. When the ride starts spinning, which girl is traveling faster? Explain how you know.
As Deanna is sitting farther from the center she is travelling at a faster rate.
What is circumference of a circle ?Circumference of a circle is the distance around the circle.
We know that merry-go-round covers distance in form of circles and we also know that circumference of a circle is 2πr.
As Deanna sits on a horse on the outer edge of the merry-go-round, 10 feet from the center of the ride it can thought of as the radius.
∴ In one rotation Denna will cover (2πr) feet which is
= (2π×10 feet.
= 62.8 feet in 15 seconds.
Now if we do the previous calculation for Raquel with r taken as 8 she will cover:
= 50.24 feet in 15 seconds.
Therefore Deanna is spinning at a faster speed.
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donald is studying the buying habits of all women attending his store. he samples the population by dividing the women into groups by age and randomly selecting a proportionate number of women from each group. he then collects data from the sample. which type of sampling is used?
According to the statement Donald is using Stratified sampling to collects data from the sample.
The correct option is A.
Briefing:A simple random sample is then taken from each separate or subgroup using the stratified sampling survey method, which first divides the population being studied into distinct subgroups or groups known as strata.
The ability to reduce the sample size needed to obtain reliable results is one of the main benefits of stratified sampling.
What accomplishes stratified sampling?When attempting to evaluate data from various subgroups or strata, researchers frequently use stratified random sampling. They can quickly find a population sample that most accurately reflects the entire population they are studying.
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I understand that the question you are looking for is:
Donald is studying the eating habits of all students attending his school. He samples the population by dividing the students into groups by grade level and randomly selecting a proportionate number of students from each group. He then collects data from the sample. Which type of sampling is used?
a. Systematic sampling
b. Convenience sampling
c. Stratified sampling
d. Cluster sampling
A scientist created a scatter plot to represent the heights of four plants over time. Then, she found a line of best-fit to model the height in centimeters of each plant after x days. The equations of each trend line are given in the table.
Trend Line Equations
Plant
Equation of trend line
1
y = three-halves x + three-halves
2
y = 2 x + 1
3
y = one-half x + 3
4
y = three-halves x + 1
According to the trend line equations, which plants are growing at the same rate per day?
The plants which are growing at the same rate are Plant 1 and Plant 4.
Both the plants are growing at the same rate because they have same slope when their growth rate is expressed in the form of equation. Slope may be defined as the amount of steepness of the graph when plotted on graph paper. The slope-intercept form of equation of line is given by y = mx + c where m is the slope of the line and c is the intercept formed by the line. The slope-intercept form of the growth rate equation of Plant 1 is given by y = 3/2x + 3/2 and the slope-intercept form of the growth rate equation of Plant 4 is given by y = 3/2x + 1.
If we compare them from the slope-intercept form of line, then both the Plants have same slope and thus their growth rate is same.
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Answer:
B. 1 and 4
Step-by-step explanation:
Edge 2023
A number d is decreased by 5 and then doubled
Let us assume the given number is x.
If it is decreased by 5 and then doubled, then we can represent that event with an algebraic expression as:
= (x-5) × 2
Formation of equation:
The number decreased by 5 can be written as: x - 5
Now, to double it, we will multiply it by 2 = (x-5) × 2
Therefore, we have the algebraic form of the given condition as :
= (x-5) × 2
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Subtract using a number line.
-3.3-(-0.6)
Plot the minuend and, the difference on the number line.
Answer:
2.7
Step-by-step explanation:
When you subtract a negative number, you are actually adding because the negatives cancel out. So, it will be -3.3+0.6, which is -2.7
hope this helps! ibrahim
Hi there! Your answer is 2.7
Step-by-step explanation:
Add: -3.3+-0.6 = 2.7
When subtracting two negative numbers, this will result in a positive number since the negatives cancel each other out.
Hope this helps! :)
Find the distance between -55 and 63.
Answer:
The distance would be 118
Step-by-step explanation:
The easiest way I solve the distance between a negative number and a positive number is by adding the negative (but making it a positive) and the positive together. If you add 55 and 63 you would get 118. And 118 is the distance between -55 and 63.
I hope this helps!! :)
write the algebraic expression for two less than for times a number
PLEASE SHOW WORK
The expression for the nth term of a sequence is 5n^2
work out the third term in this sequence
Answer:45
Step-by-step explanation:
5n²
5(3)²
5(9)
∴ The third term in the sequence 5n² is 45
Find the total amount given the original price and tax rate. Round to the nearest hundredth if necessary. Original price: $123.28 Tax rate: 7.5%
7.5% = 0.075
0.075 x 123.28 = 9.246
So, the tax will be $9.20.
Total cost would be $132.48.
bro's please help like fr I don't know WHAT IS 4 1/4 TIMES 6 AND PLAESE GIVE ME BOTH SIMP AND NOT THANK YOU <33
Answer:
Exact Form:
51/2
Decimal Form:
25.5
Mixed Number Form:
25 1/2
Step-by-step explanation: