To show that x = √(kπ), where k is a constant, we need to compare the surface areas of a cube and a sphere. The final result is x = √(6π), or x = √(kπ) where k = 6. The cube has edges of length x cm, and the sphere has a radius of 3 cm.
1. By equating the surface areas of both shapes, we can derive the relationship between x and kπ. Let's start by calculating the surface area of the cube. A cube has six equal square faces, each with an area of x^2 cm^2. Since there are six faces, the total surface area of the cube is 6x^2 cm^2.
2. Now, let's determine the surface area of the sphere. The formula for the surface area of a sphere is given by 4πr^2, where r is the radius. In this case, the radius is 3 cm. Substituting the values, we get a surface area of 4π(3^2) = 36π cm^2 for the sphere.
3. Since we are given that the surface area of the cube is equal to the surface area of the sphere, we can set up the equation 6x^2 = 36π. Dividing both sides by 6, we have x^2 = 6π. Taking the square root of both sides, we get x = √(6π).
4. Now, let's simplify the expression further. Since √(6π) is equivalent to √6 * √π, we can write x = √6 * √π. By comparing this to the desired form of x = √(kπ), we can see that k = 6. Therefore, the final result is x = √(6π), or x = √(kπ) where k = 6.
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QUESTION: Cube has edges of length x cm and sphere has radius 3 cm the surface area of the cube is equal to the surface are of the sphere. Show that x = \(\sqrt{k\pi }\) .
Traveling 15 miles in 20 minutes, how many miles per hour must you be going?
Answer:
45
Step-by-step explanation:
Answer:
45
Step-by-step explanation
Juan has just completed a 15 kilometer race in 20 minutes. What was his average speed in kilometers per hour?
Solution
First, 15 kilometers is a distance, so
d = 15
Next, we are given 20 minutes and we are asked to present the speed in kilometers per hour rather than kilometers per minute. We need to convert 20 minutes to hours. Since there are 60 minutes per hour, we divide by 60 to find out how many hours it took
t = 20 minutes / 60 minutes per hour = 1/3 hours
Now we can use the d=rt equation:
15 = (r)(1/3)
If we multiply both sides
(3)(5) = (r)(1/3)(3) or r = 45
Juan's average speed was 45 kilometers per hour.
what number is 1/4 of 100
max has decided to cancel his reservation for a plot in an upcoming subdivision because of the delays the subdivider is experiencing. how long does the subdivider have to get the deposit back to max?
The subdivider has to get the deposit back to Max within 30 days.
What is a deposit?A deposit is an amount of money paid to a vendor or a seller to secure goods or services. A deposit is a partial payment made to a business in advance of a larger purchase or delivery.
What is a subdivision?A subdivision is a housing development built on a portion of land that has been divided into multiple lots. The subdivider divides a large piece of land into smaller plots and sells each lot to individuals who are looking to build their own homes, thus creating a subdivision.
Max can get his deposit back within 30 days. This is because the subdivider has to refund the deposit within 30 days if the buyer cancels the reservation of the plot due to any reason, including the delay that the subdivider has experienced.
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What's the greatest common factor of 26 and 104 (gcf)
HELP ASAP PLEASE, this is the last question i promise T^T
WILL MARK BRAINLIEST AND GIVE POINTS
find the perimeter of a circular sector if the diameter of its circle equals 10cm and its arc length = 10cm. equals = ......... cm.
a) 10
b) 20
c) 30
d) 40
an explanation for future reference would be greatly appreciated, thank youuu <33
Answer:
A= 10
Step-by-step explanation:
[10 + 2/360˚(10)]
Answer this for alot of piontsssssss plssssssssss I need it by today please have a good day
Answer:
Can anyone agree this image is blurry? Can you send it again but not blurry this time? Sorry!
Step-by-step explanation:
3(x + 2) + 4(2x - 1) = 5(x - 2)
may I ask how to do
????????
Answer:
it's 2 I already took the quiz
Write the following set of equations in the matrix form AX=V where A is a 3x3 matrix and solve for X using the inverse matrix method Verify your solution x - y - z = 0
3x + y + 2z = 6
2x + 2y + z = 2
The value of x is 1, y = -1 and y = 2
The given set of equations:
x - y - z = 0
3x + y + 2z = 6
2x + 2y + z = 2
A = [[1 -1 -1] [ 3 1 2] [ 2 2 1]]
X = [x y z]
V = [ 0 6 2]
AX = V
X = A⁻¹V
A⁻¹ = 1/det(A) (adj(A))
det(A) = -8
adj(A) = [[-3 -1 -1] [1 3 -5] [4 -4 4]]
A⁻¹ = 1/(-8) [[-3 -1 -1] [1 3 -5] [4 -4 4]]
X = 1/(-8) [[-3 -1 -1] [1 3 -5] [4 -4 4]] [ 0 6 2]
X = 1/(-8) [-8, 8, -16]
X = [1 -1 -2]
Therefore, x = 1, y = -1 and y = 2
To verify the solution, let's substitute the values of x, y, and z in the original equations:
x - y - z = 0
1 - (-1) -2 = 0
1 + 1 - 2 = 0
2 - 2 = 0
0 = 0
which is true
the equation is satisfied
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9. Select all the angles of rotation that produce
symmetry for this flower
I would say 45, 90, 180
These three are the reflections of symmetry in this circel
one side of a triangle is increasing at a rate of 3 centimeters per second, and a second side is decreasing at a rate of 2 centimeters per second. if the area of the triangle remains constant, at what rate does the angle between the side change when the first side is 20 centimeters long, the second side is 30 centimeters long, and the angle is π/6 radians?
When the first side is 20 cm long, the second side is 30 cm long, and the angle is /6 radians, the angle between the sides is changing at a rate of -0.15 radians per second.
Let's denote the two sides of the triangle that are changing as x and y, where x is increasing at a rate of 3 cm/s and y is decreasing at a rate of 2 cm/s. Let A be the angle between these two sides, and let A be the area of the triangle, which is constant.
We can use the formula for the area of a triangle:
A = 1/2 xy sin(A)
where sin(A) is the sine of the angle A.
Taking the derivative of this equation with respect to time t, we get:
dA/dt = 1/2 [(dx/dt) y sin(A) + x (dy/dt) sin(A) + xy cos(A) (dA/dt)]
Simplifying this equation and plugging in the given values, we get:
0 = 1/2 [(3)(30) sin(π/6) + (20)(-2) sin(π/6) + (20)(30) cos(π/6) (dA/dt)]
Solving for dA/dt, we get:
dA/dt = [-45/(600 cos(π/6))] cm²/s
dA/dt = -0.15 cm²/s
Therefore, the angle between the sides is changing at a rate of -0.15 radians per second when the first side is 20 cm long, the second side is 30 cm long, and the angle is π/6 radians.
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25 points
Find the missing term in of the following arithmetic sequence
…-2,____456,….
Answer:
227
Step-by-step explanation:
nth term = a₁ + (n - 1)d
where a1 = first term , n = # of terms and d = common difference.
here we need to solve for the common difference so we can find the missing term, we do so by plugging in what we are given and solving for d
here we are given an nth term, 456 and we are given the first term, -2.
and from what we see there are 3 terms
So we have nth term = 456 , a1 = -2 and n = 3
==> plug these values into the formula
456 = -2 + (3-1)d
==> add 2 to both sides
458 = (3-1)d
==> subtract 1 from 3
458 = 2d
==>divide both sides by 2
d = 229
We then add the common difference to the term before the missing term to get the missing term
-2 + 229 = 227
solve every thing here do not draw anything on the graph
The median height is less than the mean height.
Option 3 is correct.
What is Median?The midway value in a given set of figures or data is referred to as the median. To get the average value for a given group of integers, three different metrics are employed in mathematics. The terms are median, mode, and mean. The term "measures of central tendency" refers to these three metrics.
As per the given graph:
Total number of plants = 80
Frequency v/s height of plant is given.
The mean height is 41.9 cm.
To find the median:
Total observations (n) = 25 + 20 + 13 + 10 + 2 + 10
= 80 plants
For median interval:
(n/2) = (80/2)
= 40 plants
Hence, the median interval will be the one where frequency reach 40.
∴ Median lies in the interval of height (30-40) cm.
Hence, the median height is less than the mean height.
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If A = 5 and B = 3, what will be displayed when code corresponding to the following pseudocode is run? (In the answer options, new lines are separated by commas.)
Do
Write A^2
Set A = A - 1
While A >= B
The output when the given pseudocode is executed with A = 5 and B = 3 will be "25, 16, 9, 4, 1".
The given pseudocode includes a loop that iterates as long as A is greater than or equal to B. In each iteration, the square of A is displayed, and A is decremented by 1. We are asked to determine the output when A is initially 5 and B is 3.
Step 1: Initialization
A is set to 5 and B is set to 3.
Step 2: Iteration 1
Since A (5) is greater than or equal to B (3), the loop executes.
The square of A (5²) is displayed, resulting in the output "25".
A is decremented by 1, so A becomes 4.
Step 3: Iteration 2
A (4) is still greater than or equal to B (3).
The square of A (4²) is displayed, resulting in the output "16".
A is decremented by 1, so A becomes 3.
Step 4: Iteration 3
A (3) is still greater than or equal to B (3).
The square of A (3²) is displayed, resulting in the output "9".
A is decremented by 1, so A becomes 2.
Step 5: Iteration 4
A (2) is still greater than or equal to B (3).
The square of A (2²) is displayed, resulting in the output "4".
A is decremented by 1, so A becomes 1.
Step 6: Iteration 5
A (1) is still greater than or equal to B (3).
The square of A (1²) is displayed, resulting in the output "1".
A is decremented by 1, so A becomes 0.
Step 7: Loop termination
Since A (0) is no longer greater than or equal to B (3), the loop terminates.
Therefore, The output generated by the code execution will be "25, 16, 9, 4, 1" as the squares of A (starting from 5 and decreasing by 1) are displayed in each iteration of the loop.
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How many triangles are there in this shape
Answer:
The answer is 15
Step-by-step explanation:
Count the small triangles then the whole they make up
Is the following equation a linear function or a nonlinear function?
y = x² + 4x − 13
Answer: To determine if an equation is a linear function, it must have the form y = mx + b (in which m is the slope and b is the y-intercept). A nonlinear function will not match this form.
What is the last step in evaluating the expression below: (9+4-1) X 10'- 3 X2 (4x2) A) 2X8 B 12 X 10 C) 3X2 D 120-48
The last step in evaluating the expression r is D) 120-48.
What is BODMAS?BODMAS is an acrοnym used tο remember the οrder οf οperatiοns in mathematics. It stands fοr Brackets, Order (expοnents), Divisiοn and Multiplicatiοn (left-tο-right), and Additiοn and Subtractiοn (left-tο-right).
Tο evaluate the expressiοn, yοu need tο fοllοw the οrder οf οperatiοns, which is Parentheses, Expοnents, Multiplicatiοn and Divisiοn, and finally Additiοn and Subtractiοn (PEMDAS).
(9+4-1) X 10'- 3 X2 (4x2)
First, simplify the parentheses:
(9+4-1) X 10'- 3 X 2 (4x2) = (12) X 10' - 3 X 2 (8)
Next, evaluate the expοnents:
(12) X 10' - 3 X 2 (8) = (12) X 1 - 3 X 2 (8)
Then, perfοrm the multiplicatiοn and divisiοn οperatiοns:
(12) X 1 - 3 X 2 (8) = 12 - 3 X 16
Finally, perfοrm the additiοn and subtractiοn οperatiοns:
12 - 3 X 16 = 12 - 48 = -36
Therefοre, the answer is D) 120-48.
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what is 3 1/2 x 2 2/3
Answer:
ill answer it when im done with my homwork i see u need help buddy
Step-by-step explanation:
Answer:
Step-by-step explanation:
3 1/2 * 2 2/3 = 28/3= 9 1/3
hope this helped<3!!..
On a field trip, the school bus drove five more than twice as many miles in the afternoon as in the morning. If the whole trip was 125 miles, how many miles did the bus travel in the morning and how many in the afternoon?
Answer:
morning - 40
afternoon - 85
Step-by-step explanation:
The bus traveled 40 miles in the morning and 85 miles in the afternoon.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The school bus traveled five miles more on a field trip in the afternoon than it did in the morning. If the journey was 125 kilometers long
Let x the distance traveled by bus in the morning.
As per the given condition, we can get the equation shown below:
⇒ x + 2x + 5 = 125
⇒ 3x + 5 = 125
⇒ 3x = 120
⇒ x = 40
In the afternoon, the bus traveled 2x + 5 miles.
Now substitute the value of x in the equation for the afternoon miles to include:
⇒ 2 × 40 +5 = 85
Therefore, the bus traveled 40 miles in the morning and 85 miles in the afternoon.
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Which angles equal 91°? angles T and V angles S and U angles U and V angles S and T.
Answer:
Angles T and V
Step-by-step explanation:
Answer:
A. T & V
Step-by-step explanation:
DId the Quiz
QUESTION 1
Find the slope of a line through the points (7, –8) and (–5, –7).
a -12
b-15/2
c -2/15
d -1/12
Answer:
D
Step-by-step explanation:
Slope = y2-y1/x2-x1
(7,-8) = (x1,y1)
(-5,-7) = (x2,y2)
Slope = (-7+8)/(-5-7)
= 1/-12
this is what truthfully struggle with can someone explain how i do this please then imma try it on my own
I need help, please I have until 9 p.m. to finish it number 2 homework
Answer: (b) 34.65 & (c) 35.223
Step-by-step explanation:
Rewrite each number so they have 3 decimal places (add zeros at the end).
a) 34.230
b) 34.650
c) 35.223
d) 35.320
e) 35.600
Notice that they are already in order from least to greatest.
Which numbers are between 34.600 and 35.230?
a) 34.230
34.600
b) 34.650 ←
c) 35.223 ←
35.230
d) 35.320
e) 35.600
#6 please help me gang
use the same regression results where you already found r square and other results for this regression. what is the standard error for the estimated slope of the regression line? answer to four decimal places.
A regression model can only predict values that are lower or higher than the actual value. As a result, the only way to determine the model's accuracy is through residuals.
What is regression ?
Regression is a statistical technique used in the fields of finance, investing, and other disciplines that aims to establish the nature and strength of the relationship between a single dependent variable (often represented by Y) and a number of independent variables (known as independent variables).
The most popular variation of this method is linear regression, which is also known as simple regression or ordinary least squares (OLS).
Based on a line of best fit, linear regression determines the linear relationship between two variables.
The slope of a straight line used to represent linear regression thus indicates how changing one variable affects changing another..
In a linear regression connection, the value of one variable when the value of the other is zero is represented by the y-intercept. Regression without linearity.
Hence, A regression model can only predict values that are lower or higher than the actual value.
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Consider a job shop. Assume that the parts arrive with an average of 10 minutes between parts and a standard deviation of 8 minutes. The average processing time is 8 minutes per part, with a standard deviation of 7 minutes .
(a) Is this system stable? Justify your answer
(b) What is the expected time that the parts spend in the job shop?
(c) What is the expected number of parts in the job shop?
a. No, the system is not stable.
b. The expected time that the parts spend in the job shop is 32 minutes.
c. The expected number of parts in the job shop is 2.9.
a. A system is considered stable if the average number of parts in the system does not change over time. In this case, the average number of parts in the system will increase over time because the average arrival rate is greater than the average processing rate. This is because the average arrival rate is 10 minutes between parts and the average processing rate is 8 minutes per part.
b. The expected time that the parts spend in the job shop can be calculated as follows:
Expected time = (average arrival rate * average processing time) / (average arrival rate - average processing rate)
Plugging in the values from the problem, we get:
Expected time = (10 minutes * 8 minutes) / (10 minutes - 8 minutes) = 32 minutes
c. The expected number of parts in the job shop can be calculated as follows:
Expected number of parts = (average arrival rate * average processing time) / (average processing time - average arrival rate)
Plugging in the values from the problem, we get:
Expected number of parts = (10 minutes * 8 minutes) / (8 minutes - 10 minutes) = 2.9
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suppose the total area is 132 square units, b=5, d=4, and the area I is a square. Find the missing lengths and areas.
Answer:
/////////
Step-by-step explanation:
time-use data show that married american women have cut their housework time roughly in half over the last half-century, while men have:
Over the last half-century, time-use data has shown that married American women have significantly reduced their housework time, cutting it roughly in half.
This change can be attributed to various factors such as advancements in home appliances, shifting gender roles, and increased participation of women in the workforce. On the other hand, men have gradually increased their contributions to housework during this period.
This shift in housework responsibilities can be attributed to societal changes that promote a more equitable distribution of domestic tasks between partners. As gender norms have evolved, men are increasingly taking on roles that were once predominantly associated with women, leading to a more balanced approach to housework within households. Additionally, the rise in dual-income families has necessitated a more equal division of domestic responsibilities.
In summary, over the past 50 years, married American women have seen a considerable decrease in housework time, while men have increased their contributions. This change reflects evolving gender roles and societal expectations, promoting a more equal division of labor within households.
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\(Please\;write\;equations\;for\;the\;following...\\\\1...\;(-2, 3), slope = -5/7\\2...\;(-4, -2), slope = -1/4\\3...\;(2, 0), slope = 1/2\)
Answer: 1) y = (-5/7)x + 11/7
2) y = (-1/4)x - 3
3) y = (1/2)x - 1
Step-by-step explanation:
Use the Point-Slope equation: y - y₁ = m(x - x₁) where
(x₁, y₁) is a point on the linem is the slope(x₁, y₁) = (-2, 3) m = -5/7
y - 3 = -5/7(x + 2)
y - 3 = (-5/7)x - 10/7
y = (-5/7)x + 11/7
(x₁, y₁) = (-4, -2) m = -1/4
y + 2 = -1/4(x + 4)
y + 2 = (-1/4)x - 1
y = (-1/4)x - 3
(x₁, y₁) = (2, 0) m = 1/2
y - 0 = 1/2(x - 2)
y - 0 = (1/2)x - 1
y = (1/2)x - 1
3. Find the equations of the lines that form the sides to the polygon shown below. What type of polygon is it? Explain your reasoning.
Answer: The question is not complete. the figure is attached below.
The polygon is a rectangle.
Step-by-step explanation:
Line 1 goes through (-2, 3)
hence the slope of line 1 = -3/2
Line 2 goes through (0, 3) (2, 0)
hence the slope of line 2 = -3/2
Line 3 goes through (0, 1) (-3, 1)
hence the slope of line 3 = 2/3
Line 4 goes through (3, 0) (0, -2)
Hence the slope of line 4 = 2/3
therefore -3/2 * 2/3 = -1
Line1 + Line3 Line1 + Line4 Line2 + Line3 Line2+Line4
because, the distance between Line1 and Line2 is not equal to that Line3 and Line4.
The polygon is a rectangle polygon.
Help me please djdjdd
Answer:
-1 < x ≤ 3
Step-by-step explanation:
First, we need to simplify this inequality.
9 > -5x + 4 ≥ -11 (Given)
5 > -5x ≥ -15 (Subtract 4 on both sides)
-1 < x ≤ 3 (Divide -5 on both sides)
Note that the signs flip due to dividing by a negative number.
Answer:
\(-1<x\leq3\)
Step-by-step explanation:
Let's take two equations from this and them put them back together! So:
9>-5x+4
and
\(-5x+4\geq -11\)
For the first one:
9>-5x+4
Subtract 4 from both sides
5>-5x
Then divide by -5 (Remember to change the direction of the sign!):
-1<x
Now onto the second one:
\(-5x+4\geq -11\)
Subtract 4 from both sides:a
\(-5x\geq -15\)
Then divide by -5 (Remember to change the direction of the sign!):
\(x\leq 3\)
Now add the equations back together:
\(-1<x\leq3\)