Step-by-step explanation:
We can also solve the equation x² + 4x + 4 = 8 by rearranging the terms and using the quadratic formula:
x² + 4x + 4 - 8 = 0
x² + 4x - 4 = 0
Applying the quadratic formula, we have:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 4, and c = -4. Substituting these values, we get:
x = (-4 ± √(4² - 4(1)(-4))) / 2(1)
x = (-4 ± √32) / 2
Simplifying the square root of 32, we get:
x = (-4 ± 4√2) / 2
x = -2 ± 2√2
Therefore, the solutions to the equation x² + 4x + 4 = 8 are x = -2 + 2√2 and x = -2 - 2√2.
which events are independent? check all that apply.each number 1 through 10 is written on a slip of paper, placed in a hat, and randomly picked. sarah picks a number less than 5, keeps it, and then picks an odd number.
The events that are independent are,
1) Henry rolling a multiple of 2 and landing on a red portion of the spinner.
2) Two pairs of socks being randomly chosen from a drawer, Hayden choosing a black pair of socks, putting them on, and then choosing another black pair.
3) Olivia choosing an ace and the dart hitting the bull's-eye
The events that are independent are:1) Henry rolling a multiple of 2 and landing on a red portion of the spinner.
2) Two pairs of socks being randomly chosen from a drawer, Hayden choosing a black pair of socks, putting them on, and then choosing another black pair.
3) Olivia choosing an ace and the dart hitting the bull's-eye.
The other events are dependent because the outcome of the first event affects the outcome of the second event. Specifically
1) Sarah picking a number less than 5 and then picking an odd number. The second event depends on the outcome of the first event.
2) A number cube being rolled and a spinner being spun. The two events are independent of each other, but the outcomes of each event are not independent.
3) Two cards being randomly chosen from a standard deck, and Eliza choosing a jack, replacing it, and then choosing a black card. The outcome of the second event depends on the outcome of the first event, and the outcome of the first event affects the composition of the deck for the second event.
Learn more about independent event here
brainly.com/question/30905572
#SPJ4
The given question is incomplete, the complete question is:
Which events are independent? Check all that apply. Each number 1 through 10 is written on a slip of paper, placed in a hat, and randomly picked. Sarah picks a number less than 5, keeps it, and then picks an odd number. A number cube is rolled and a spinner is spun. Henry rolls a multiple of 2 and lands on a red portion of the spinner. Two cards are randomly chosen from a standard deck. Eliza chooses a jack, replaces it, and then chooses a black card. Two pairs of socks are randomly chosen from a drawer. Hayden chooses a black pair of socks, puts them on, and then chooses another black pair. A card is randomly chosen from a standard deck and a dart is randomly thrown. Olivia chooses an ace and the dart hits the bull’s-eye.
there is a three term arithmetic sequence with the first term 9. if you add 2 to the second term and 20 to the third term it forms a geometric sequence. what is the smallest number the third term in the geometric sequence could be?
The geometric sequence is 9 + 2 + 20 = 29.
The smallest number the third term in the geometric sequence can be is 29.
This is because when you add 2 to the second term and 20 to the third term of the three-term arithmetic sequence with a first term of 9,
the third term of the geometric sequence is 9 + 2 + 20 = 29.
Learn more about geometric sequence
brainly.com/question/30491267
#SPJ11
in a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 47 and a standard deviation of 5. using the empirical rule, what is the approximate percentage of daily phone calls numbering between 42 and 52?
Using empirical rule, the approximate percentage of daily phone calls numbering between 42 and 52 is 68%.
A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, virtually all observed data will lie within three standard deviations (denoted by ) of the mean or average (denoted by ).
The empirical rule specifically states that 68% of observations will fall inside the first standard deviation, 95% will fall within the first two standard deviations, and 99.7% will fall within the first three standard deviations.
Mean = 47
SD = 5
Using Empirical Formula ,approximate percentage of daily phone calls numbering between 42 and 52
Normal Distribution has bell shape curve
The Empirical Rule states that in a normal distribution
68% of the data falls with in one standard deviation ( -1 to 1)
95% of data falls with in two standard deviations, and (-2 to 2)
99.7% of data falls with in three standard deviations from the mean. (-3 to 3)
z score = ( Value - mean)/SD
Calculate z score for 60
Z = (42 - 47)/5
Z = -1
Calculate z score for 66
Z = (52 - 47)/5
Z = 1
As data lies between -1 and 1 hence with in one standard deviation from the mean Hence using Empirical data approximate percentage of daily phone calls numbering between 42 and 52 is 68%.
Learn more about Empirical rule:
https://brainly.com/question/28873888
#SPJ4
Find the volume of the triangular prism below
We can claim that after answering the above question, the As a result, the triangular prism has a volume of 240 cubic centimetres.
what is prism?A prism is a polyhedron with an n-sided polygonal basis, a second base that is a shifted copy of the first base, and n extra faces (necessarily all parallelograms), with two connecting the corresponding sides of the base. All cross sections that are parallel to the base are translations of it. A prism is a two-sided, solid, three-dimensional object with two faces. It has the same cross-sections, flat sides, and similar bases. Faces of a prism are parallelograms or rectangles with no bases. A prism is a refracting item that is homogeneous, solid, and transparent, contained by two planes that are obliquely oriented to one another. A typical prism has two triangular faces and three parallel rectangular faces. They are made of either glass or metal.
To calculate the volume of a triangular prism, multiply the area of the triangular base by the prism's height.
Triangle area = 1/2 * base * height
Triangle area = 1/2 * 8 cm * 6 cm
Triangle area = 24 cm2
We must now determine the prism's height. The diagram shows that the prism has a height of 10 cm.
Finally, the volume of the triangular prism can be calculated by multiplying the area of the triangle base by the prism's height:
Prism volume = base area * The prism's height
Prism volume = 24 cm2 * 10 cm
Prism volume = 240 cm3
As a result, the triangular prism has a volume of 240 cubic centimeters.
To know more about prism visit:
https://brainly.com/question/27914026
#SPJ1
a force of 6 pounds is required to hold a spring stretched 0.6 feet beyond its natural length. how much work (in foot-pounds) is done in stretching the spring from its natural length to 0.8 feet beyond its natural length?
The amount of work (in foot-pounds) done in stretching a spring from its natural length to 0.8 feet beyond its natural length is 24.
so we have W=6lbs*(0.8ft-0.6ft)
=6lbs*0.2ft
=24ft-lbs.
Work is the measure of the amount of energy required to move an object over a certain distance, so to stretch the spring 0.8 feet beyond its natural length, 24 foot-pounds of work is done.
This can also be understood as the product of the force (6lbs) and the displacement (0.2ft). Work is a scalar quantity, meaning it only has magnitude and not direction.
To know more about scalar quantity click on below link:
https://brainly.com/question/774036#
#SPJ11
IXL
An equilateral triangle with center C is shown below.
(HELP!!)
The area of the equilateral triangle is 36√3 square units
What is area of the equilateral triangle?
Area of an equilateral triangle is equal to(√3/4)a², where an is the length of the triangle's side.
In an equilateral triangle, the center, the centroid, and the circumcenter coincide.
The distance between the center and a vertex is 6cm, which is also the radius of the circumcircle.
The side length is [tex]6(3)^{1/2}[/tex], which is twice the length of the radius.
So, the radius of the circumcircle is 6 cm, and the length of each side of the equilateral triangle is 12 cm.
The area of an equilateral triangle with side length s is given by:
A = (s² * √3) / 4
Substituting s = 12, we get:
A = (12² * √3) / 4
= 36√3
Therefore, the area of the equilateral triangle is 36√3 square units.
To know more about area of the equilateral triangle visit,
https://brainly.com/question/10681095
#SPJ1
i do not understand please help asap
Step-by-step explanation:
Lets assume this is a right triangle.
If you use pythagorean theorem, lets assume the tower is the longest line on the triangle.
If this is true, lets say that 9^2 (distance from end of slide to base of tower) + x^2 (length of slide) = 23^2 (height of tower)
we get the length of the slide is 21.2 meters.
Find the circumference of each circle.Use your calculators value of pi.Round your answer to the nearest tenth.
Answer:
5) 59.7 in
6) 39.0 mi
7)
8) 50.3 mi
Step-by-step explanation:
5) C = [tex]\pi (19)[/tex]
C = 59.7 in
6) C = [tex]2\pi (6.2)[/tex]
C = 39.0 mi
7) RADIUS IS CUT OFF
use C = [tex]2\pi r[/tex]
8) C = [tex]2\pi (8)[/tex]
C = 50.3 mi
if elisa gets an allowance of $30 per week and spends $10 of it on food and drink, $5 on entertainment and $5 on miscellaneous things, how much does she have available to put aside for savings each week?
Answer: She has 10$ to save
Step-by-step explanation:
Elsia has 30$ to start her week. She spent 10 on food and drink, (30-10=20) 5 on entertainment, (20-5=15), and 5 on Misc. things. (15-5=10). This means that the answer is 10.
Steps:
30-10=20
20-5=15
15-5=10
I hope it helped! :D
reading to children fifty-eight percent of american children (ages 3 to 5 ) are read to every day by someone at home. suppose 5 children are randomly selected. what is the probability that at least 1 is read to every day by someone at home?
To calculate the probability that at least 1 of 5 randomly selected American children (ages 3 to 5) is read to every day by someone at home.
To find the probability that none of the 5 children are read to, we can use the fact that the probability that a single child is not read to every day is 1 - 0.58 = 0.42. We can then use the multiplication rule to find the probability that none of the 5 children are read to, which is (0.42)⁵ = 0.0075. Finally, we can use the complement rule to find the probability that at least 1 child is read to every day, which is 1 - 0.0075 = 0.9925. Therefore, the probability that at least 1 of 5 randomly selected American children (ages 3 to 5) is read to every day by someone at home is 0.9925.
Learn more about probability here: brainly.com/question/30034780
#SPJ4
Please help with #10 and #13!!
The angle of rotation in standard form is 251.5651 degrees.
The length of arc S is approximately 20.94 feet.
How do we solve this?If the point (-1, -3) is on the circle x² + y² = 10, then we can substitute these values for x and y in the equation to obtain:
(-1)² + (-3)² = 10
1 + 9 = 10
So, the point (-1, -3) satisfies the equation of the circle.
To find the angle of rotation in standard form, we need to use the formula:
tan(θ) = y/x
where θ is the angle of rotation.
In this case, x = -1 and y = -3, so we have:
tan(θ) = (-3)/(-1)
tan(θ) = 3
θ = tan⁻¹(3)
Using a calculator, we find:
θ ≈ 1.2490 radians or 71.5651 degrees
To express in standard form, add 180 degrees to the angle in order to obtain an angle between 0 and 360 degrees:
θ ≈ 71.5651 + 180 ≈ 251.5651 degrees
To find the length of an arc S given the radius r and the central angle θ, we use the formula:
S = (θ/360) x 2πr
In this case, r = 15 ft and θ = 1.396 radians
Substituting the values:
S = (1.396/2π) x 2π(15 ft)
S ≈ 1.396 x 15 ft
S ≈ 20.94 ft
Learn more about the length of an arc at: https://brainly.com/question/8020286
#SPJ1
Complete question:
Consider the point (-1, -3), which is on the circle x² + y² = 10. Find the angle of rotation in standard form
Find the length of the arc S when r = 15 ft and θ = 13.96°
The plane traveled 6 mores miles after passing the George Washington Bridge, descending at a 2° angle before landing in the Hudson River.
5a) At what altitude (in feet) did the airplane cross over the G.W. Bridge (e)?
The altitude of the plane at the George Washington Bridge is approximately 0.2095 miles (or 1,106 feet) above sea level, plus whatever the height of the bridge is.
What is altitude?Altitude refers to the height of an object or location above a specific reference point, usually the Earth's sea level. In aviation, altitude is often used to describe the height of an aircraft above sea level, and is measured in feet or meters.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It involves the study of trigonometric functions, which are functions of an angle, and are used to relate the angles and sides of a right triangle.
In the given question,
To solve this problem, we need to use trigonometry and the fact that the plane descended at a 2° angle. Let's assume that the altitude of the plane at the George Washington Bridge is h feet.
Using trigonometry, we know that the tangent of the angle of descent is equal to the difference in altitude divided by the horizontal distance traveled. In this case, we have:
tan(2°) = (h - e) / 6
To solve for h, we need to isolate it on one side of the equation. Multiplying both sides by 6, we get:
6 tan(2°) = h - e
Adding e to both sides, we get:
h = 6 tan(2°) + e
We can use a calculator to find the tangent of 2°, which is approximately 0.03492. Substituting this value and the given distance of 6 miles into the equation, we get:
h = 6(0.03492) + e
h = 0.2095 + e
Therefore, the altitude of the plane at the George Washington Bridge is approximately 0.2095 miles (or 1,106 feet) above sea level, plus whatever the height of the bridge is.
To know more about trigonometry, visit:
https://brainly.com/question/29002217
#SPJ1
Darius wrote two integers on the chalkboard. The integers she wrote were 256 and -17. How much larger is 256 than -17?
Answer: 239
Step-by-step explanation:
Darius wrote 2 integers 256 and -17. The question is asking you to solve how much larger is 256 than -17. This means you will subtract 256 by -17 which will give you 239 (256-17). The answer remains positive because 256 is larger
Hope this helps
Answer: They are exactly 273 places away.
Step-by-step explanation:
If a number is larger than another number then you need to subtract it to get the distance. In this case, you look at the subtraction to see how far away they are.
Hope this helps!
Have a blessed day!
how many acres are in a government rectangular survey that consists of the sw 1/4, ne 1/4, and nw 1/4 of section 13, blendon township?
The government rectangular survey consisting SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township covers 480 acres.
We have,
In the Government Rectangular Survey System, a section is a square tract of land measuring 1 mile by 1 mile, covering an area of 640 acres.
Each section is divided into quarters.
If we consider the SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township, the total acreage can be calculated as follows:
SW 1/4:
This represents one-fourth of the section.
The SW 1/4 of Section 13 is 640 acres / 4 = 160 acres.
NE 1/4:
The NE 1/4 of Section 13 is also 160 acres.
NW 1/4:
The NW 1/4 of Section 13 is 160 acres.
To find the total acreage, add up the individual acreages:
160 acres (SW 1/4) + 160 acres (NE 1/4) + 160 acres (NW 1/4)
= 480 acres
Therefore,
The government rectangular survey consisting SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township covers 480 acres.
Learn more about government rectangular surveys here:
https://brainly.com/question/14390891
#SPJ12
Which statements about this system of equations are true? Check all that apply
2 x minus 7 y = negative 13. Negative 2 x + 11 y = 1.
The x-variable will be eliminated when adding the system of equations.
The y-variable will be eliminated when adding the system of equations.
The sum of the system of equations is 4 y = negative 12.
x = 17
y = negative 3
There are infinitely many solutions to the system of equations.
As a result, (x, y) = is the answer to a set of equations. (-17, -3). There aren't an endless number of answers because there is a single one.
What sort of equation would that be?The meaning of an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.
The statements that are true about this system of equations are:
The x-variable will be eliminated when adding the system of equations.
There are infinitely many solutions to the system of equations.
To eliminate the x-variable, we can add the two equations as follows:
(2x - 7y) + (-2x + 11y) = -13 + 1
Simplifying the left-hand side and the right-hand side gives:
4y = -12
Dividing both sides by 4 yields:
y = -3
Substituting y = -3 into either of the original equations gives:
2x - 7(-3) = -13
Simplifying this equation yields:
2x + 21 = -13
Subtracting 21 from both sides yields:
2x = -34
Dividing both sides by 2 yields:
x = -17
Therefore, the solution to the system of equations is (x, y) = (-17, -3). Since there is a unique solution, there are not infinitely many solutions.
The statement "The sum of the system of equations is 4y = -12" is false since the sum of the equations does not simplify to that expression.
The statement "x = 17" is false since the correct solution is x = -17.
The statement "The y-variable will be eliminated when adding the system of equations" is false since adding the equations only eliminated the x-variable.
To know more about Equation visit:
https://brainly.com/question/22688504
#SPJ1
select a random sample of size 2 by writing the five numbers in this population on slips of paper, mixing them, and then selecting two. calculate the mean for your sample.
The mean for the sample is 14.5.
We are asked to select a random sample of size 2 by writing the five numbers in this population on slips of paper, mixing them, and then selecting two. We then have to calculate the mean for the sample. The given numbers are: 12, 17, 8, 13, and 20. Therefore, there are five numbers in the population.
Now, we have to choose any two numbers randomly from the population. Let us suppose that we select 12 and 17 randomly from the population. Therefore, the sample will be {12, 17}. Now, we have to calculate the mean of the sample.
The formula to calculate the mean is: mean = sum of all numbers in the sample / total number of items in the sample. The sum of 12 and 17 is 12 + 17 = 29. Therefore, the sum of all numbers in the sample is 29. Also, the total number of items in the sample is 2.
Therefore, we can calculate the mean as: mean = 29 / 2mean = 14. 5. Therefore, the mean for the sample is 14.5.
To know more about mean refer here:
https://brainly.com/question/26509052
#SPJ11
Jared's average daily balance for the last month was $560. The finance charge was $8. 12. What was the monthly percentage rate? What was the APR?
The monthly percentage rate is 1.45%, and the APR is 17.4%.
To calculate the monthly percentage rate, we can divide the finance charge by the average daily balance, then multiply by 100 to convert to a percentage
Monthly percentage rate = (finance charge / average daily balance) x 100
Monthly percentage rate = ($8.12 / $560) x 100
Monthly percentage rate = 0.0145 x 100
Monthly percentage rate = 1.45%
To calculate the APR (annual percentage rate), we need to multiply the monthly percentage rate by the number of months in a year:
APR = Monthly percentage rate x 12
APR = 1.45% x 12
APR = 17.4%
Learn more about monthly percentage rate here
brainly.com/question/13358341
#SPJ4
Triangle LMN is drawn with vertices at L(−3, −2), M(1, −4), N(−3, −4). Determine the image vertices of L′M′N′ if the preimage is rotated 90° clockwise.
L′(−3, −2), M′(1, −4), N′(−3, −4)
L′(−2, 3), M′(−4, −1), N′(−4, 3)
L′(3, 2), M′(−1, 4), N′(3, 4)
L′(2, 3), M′(4, −1), N′(4, 3)
QUICK HELP 30 POINTS
The image vertices of L′M′N′ are (-2, 3), (-4, -1), and (-4, 3).
What is preimage?
The set of all domain elements for a given function that map to a certain subset of the codomain; (formally) given a function X Y and a subset B Y, the set 1(B) = x X: x B.
Here, we have
Given: Triangle LMN is drawn with vertices at L(−3, −2), M(1, −4), N(−3, −4).
We have to determine the image vertices of L′M′N′ if the preimage is rotated 90° clockwise.
The rule for rotating a point (x, y) 90° clockwise is:
(x,y) ⇒ (y, -x)
The vertices of triangle LMN will be mapped to:
L(-3,-2) ⇒L' (-2, 3)
M(1,-4) ⇒ M'(-4, -1)
N(-3,-4) ⇒ N'(-4, 3)
Hence, the image vertices of L′M′N′ are (-2, 3), (-4, -1), and (-4, 3).
To learn more about the preimage from the given link
https://brainly.com/question/30895103
#SPJ1
a particular triangle has sides of length 14 cm, 8 cm and 9 cm. in centimeters, what is the perimeter of the triangle?
Answer:
31cm
Step-by-step explanation:
14 + 8 + 9 = 31
Make sure to add the cm on the end!
The perimeter of the triangle is 31cm.
The perimeter of the triangle with sides of length 14 cm, 8 cm and 9 cm is 31 cm. This can be calculated by simply adding up the length of each side. To explain, the perimeter of a triangle is the sum of the lengths of all three sides.
In this particular triangle, the length of side 1 is 14 cm, the length of side 2 is 8 cm and the length of side 3 is 9 cm. When we add these three lengths, we get the perimeter of the triangle: 14 cm + 8 cm + 9 cm = 31 cm.
In general, to calculate the perimeter of any triangle, we first have to identify the lengths of all three sides. Then, we simply add these lengths together to get the perimeter.
For example, if the triangle had sides of lengths 4 cm, 5 cm and 6 cm, then the perimeter would be 4 cm + 5 cm + 6 cm = 15 cm.
In conclusion, the perimeter of any triangle can be calculated by adding together the length of each side. In the case of the particular triangle in question, the perimeter is 31 cm.
To know more about perimeter refer here:
https://brainly.com/question/6465134
#SPJ11
Please help
What is the value of x?
Enter your answer in the box.
X =
F
E
L
24
25
1
2 3 4 5
x is the base of given right angled triangle, which is calculated as 7 using the Pythagoras theorem.
Give a brief account on Pythagoras theorem.The Pythagorean theorem, the well-known geometric theorem states that the sum of the squares across the sides of a right triangle equals the square across the hypotenuse (opposite the right angle) – or in general algebraic notation a² + b² = c².
It has long been associated with the Greek mathematician and philosopher Pythagoras (c. 570-500/490 BC), but is actually much older. His four clay tablets in Babylonia, circa 1900 BC to his 1600. Using a very precise calculation of the square root of 2 (the length of the hypotenuse of a right-angled triangle with legs equal to 1) and a special list of integers known as Pythagorean triples, we acquire some knowledge of theorems, indicate and fill them. This phrase is mentioned in his Baudhayana Sulba-sutra of India written between 800 BC and his 400 AD. written.
Given,
DF = 24
DE = 25
Using Pythagoras theorem:
Hypotenuse² = Base² + Perpendicular²
25² = x² + 24²
x² = 25² - 24²
x² = 625 - 576
x² = 49
x = √49
x = 7
To know more about Pythagoras theorem, visit:
https://brainly.com/question/343682
#SPJ1
PLS HELP I NEED HELP ASAP
Answer:
3a + 2b
Step-by-step explanation:
The perimeter of the rectangle is calculated by following formula:
2×(w+l)
w: width, l: lengthLet x represent the missing side length, width,
2(x + 5a - b) = 16a + 2b
Multiply inside the parenthesis 22x + 10a - 2b = 16a + 2b
transfer 10a - 2b to the other side of the equation2x = 16a + 2b - 10a + 2b
Add/subtract like terms2x = 6a + 4b
Divide both sides by 2x = 3a + 2b
Which expression is equivalent to Cube root of 343 x Superscript 9 Baseline y Superscript 12 Baseline z Superscript 6?
7x3y4z2
7x3y6z2
49x3y6z2
49x3y4z2
The value of the cube root [tex]343x^9y^{12}z^6[/tex] is [tex]7x^3y^4z^2[/tex]
A number's cube root is a quantity that when multiplied by itself three or more times, returns the original quantity. The cube root of 27, represented as 327, for instance, is 3 because 3 x 3 x 3 = 27 = 33 when we multiply 3 by itself three times. As a result, we can state that the cube root yields a value that is essentially cubed. Thus, 27 is referred to as the ideal cube. We may deduce what the cube's root is from the word "cube root." It denotes the integer that brought about the cube under the root.
The cube root 0f [tex]343x^9y^{12}z^6[/tex]
[tex]\sqrt[3]{343x^9y^{12}z^6} \\\sqrt[3]{(7x^3y^4z^2)^3} \\\\\\7x^3y^4z^2[/tex]
learn more about cube root,
https://brainly.com/question/30038389
#SPJ1
What is the area of a circle with the radius of 11.5 meters? Use 3.14 for pi or put pi in your answer for an exact answer.
Answer:
Area = [tex]415.265 m^2[/tex]
Step-by-step explanation:
Area of a circle = [tex]\pi r^2[/tex]
[tex]A = (3.14)(11.5^2)=(3.14)(132.25)=415.265[/tex]
Use the formula V = s³, where V is the volume and s is the edge length of the cube, to solve this problem.
A cube-shaped box has an edge length of 45 meter.
What is the volume of the container?
Enter your answer, as a fraction in simplest form, in the box.
The volume of the container is 91125 cubic meters.
What is volume?
A measurement of three-dimensional space is volume. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.
A sphere is the most basic and typical form of a three-dimensional shape. A sphere's radius is the simplest parameter to measure. The radius of the sphere is used to determine its volume.
Given the edge of a cube is 45 meters.
The formula of volume is V = s³.
The volume of the container is
45³
= 91125 cubic meter.
To learn more about the volume of cuboids, click on the below link:
https://brainly.com/question/12279134
#SPJ9
The difference between numbers tell you how far apart they are on the number line 8 and -16 our units apart because 8 -6 = 14
The answer of the given question based on the number line is the difference between 8 and -16 is not 14, it is 24. and 8 and -16 are 24 units apart on the number line.
What is the use of number line?A number line is a visual representation of the real number system, where numbers are placed in order from left to right, with zero in the center. The number line is an important mathematical tool used in a variety of ways, including:
Understanding and comparing numbers: By plotting numbers on a number line, we can visually see the relative size and position of numbers in relation to each other.
Performing arithmetic operations: The number line can be used to add, subtract, multiply, and divide numbers.
Graphing functions: The number line can be used as the horizontal axis of a graph to plot functions and other mathematical relationships.
Actually, the difference between 8 and -16 is not 14, it is 24.
To find the difference between two numbers on a number line, you need to subtract the smaller number from the larger number. In this case, 8 is larger than -16, so we subtract -16 from 8:
8 - (-16) = 8 + 16 = 24
Therefore, 8 and -16 are 24 units apart on the number line.
To know more about Real number system visit:
https://brainly.com/question/30093910
#SPJ1
an 8-person committee is to be formed from a group of 15 women and 12 men. in how many ways can the committee be formed if the committee must contain four men and four women? if there must be at least two men? if there must be more women than men?
The number of ways to form an 8-person committee with 4 men and 4 women is 9,180. The number of ways to form a committee with at least 2 men is 70,320. The number of ways to form a committee with more women than men is 7,620. This can be solved by the concept of Permutation and Combination.
If the committee must contain four men and four women, there are 7,425 ways to form the committee. If there must be at least two men, there are 58,275 ways to form the committee. If there must be more women than men, there are 26,207,700 ways to form the committee.
To find the number of ways to form a committee with four men and four women, we can use combinations. The number of ways to choose 4 men out of 12 is 495, and the number of ways to choose 4 women out of 15 is 1,365.
To get the total number of ways, we can multiply these numbers:
495 x 1,365 = 7,425.
To find the number of ways to form a committee with at least two men, we need to consider two cases: 2 men and 6 women, and 3 men and 5 women. For the first case, we can choose 2 men out of 12 in 495 ways, and 6 women out of 15 in 5,005 ways. For the second case, we can choose 3 men out of 12 in 2,190 ways, and 5 women out of 15 in 3,003 ways.
To get the total number of ways, we can add these numbers:
495 x 5,005 + 2,190 x 3,003 = 58,275.
To find the number of ways to form a committee with more women than men, we can use a different approach. We can count all the possible committees with 1 man, 2 men, 3 men, and 4 men, and then subtract the committees that have more men than women. There are 15 ways to choose 1 man, 330 ways to choose 2 men, 3,960 ways to choose 3 men, and 12,870 ways to choose 4 men.
To count the committees with more men than women, we can use the complement rule. This means we need to count the committees with 4 men and 0, 1, 2, or 3 women, the committees with 3 men and 0 or 1 women, the committees with 2 men and 0 women, and the committee with 1 man and 0 women.
Adding these numbers gives us the total number of committees with more women than men:
15 + 330 + 1,320 + 2,772 + 330 + 15 = 26,207,700
To learn more about Permutation and Combination here:
https://brainly.com/question/28720645#
#SPJ11
A walkway forms one diagonal of a square playground. The walkway is 22m long. How long is a side of the playground?
Answer:
15.556
Step-by-step explanation:
The length of the diagonal of a square is equal to the length of one side of the square multiplied by the square root of 2
22=x√2
The S.S of the two equations : X+2y =5, and 2x+ky=3 in RxR equals phi then k=?
The value of k such that the solution set of the system is empty is any value of k that is not equal to 4.
What is equation?A mathematical statement that expresses the equivalence of two numbers or expressions is known as an equation. It has two sides, the left-hand side (LHS) and the right-hand side (RHS), which are equal and are divided by the equal symbol (=). Variables, constants, and mathematical operations like addition, subtraction, multiplication, and division can all be found in an equation.
To find the value of k such that the solution set of the system of equations X + 2y = 5 and 2x + ky = 3 is the empty set (i.e., the intersection of their solution sets is the empty set), we can use the determinant of the coefficient matrix.
The coefficient matrix for the system is:
| 1 2 |
| 2 k |
The determinant of this matrix is:
[tex]det(| 1 2 |[/tex]
| 2 k |) = (1)(k) - (2)(2) = k - 4
For the solution set of the system to be empty, the determinant must be non-zero, since a zero determinant would indicate that the coefficient matrix is singular and therefore the system has no unique solution.
So, we need to solve the equation k - 4 ≠ 0 for k:
k - 4 ≠ 0
k ≠ 4
To know more about equation:
brainly.com/question/29538993
#SPJ9
suppose that at your favorite restaurant to-go orders arrive at the rate of 10 per hour. assume that the numbers of to-go orders on different hours are independent. the distribution of the average number of to-go orders per hour over 700 random hours is
By using Central Limit Theorem, the distribution of to-go orders per hour over 700 random hours at a restaurant with a rate of 10 per hour can be approximated by a normal distribution with a mean of 10 and a standard deviation of 0.119.
The distribution of the average number of to-go orders per hour over 700 random hours can be approximated by the Central Limit Theorem (CLT). In this case, the population mean (μ) is 10 to-go orders per hour, and the population standard deviation (σ) can be calculated using the Poisson distribution formula:
σ = sqrt(μ) = sqrt(10) ≈ 3.162
The sample size (n) is 700, which is larger than 30, so we can use the CLT to approximate the distribution of the sample means. The mean of the sample means is equal to the population mean, which is 10 to-go orders per hour. The standard deviation of the sample means (also called the standard error) is equal to:
SE = σ / sqrt(n) = 3.162 / sqrt(700) ≈ 0.119
Therefore, the distribution of the average number of to-go orders per hour over 700 random hours is approximately normal with a mean of 10 and a standard deviation of 0.119
To know more about Central Limit Theorem:
https://brainly.com/question/898534
#SPJ4
you have been tracking how long you spend on each course subject during your homework sessions. you want to see what percentage each subject represents. which type of chart would be best for this purpose?
a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.
For visualizing the percentage distribution of different course subjects, a pie chart would be the most suitable type of chart. Pie charts are ideal for displaying the relative proportions of different categories or groups as slices of a circular pie. Each slice of the pie represents a proportion of the whole, which in this case would be the total time spent on all course subjects during homework sessions. The size of each slice will correspond to the percentage of time spent on each course subject. Therefore, a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.
Learn more about time here
https://brainly.com/question/28050940
#SPJ4