Using the information provided, we can construct a 90% confidence interval for the mean number of hours a student studies per week as follows: (15.34, 16.66).
The given problem involves estimating the mean hours of studying per week for a population of students using a confidence interval. A simple random sample of 55 students is taken, and the sample mean is computed to be 16 hours per week. The population standard deviation is assumed to be known to be 3.1 hours per week. Using the formula for a confidence interval for the population mean with known standard deviation and a significance level of 0.10 (corresponding to a 90% confidence level), the lower and upper bounds of the interval are calculated to be 15.19 and 16.81 hours per week, respectively. This means that we can be 90% confident that the true mean hours of studying per week for the population of students lies within this interval
Learn more about confidence intervals here: brainly.com/question/24131141
#SPJ4
Complete question:
A professor wants to estimate how many hours per week her students study. A simple random sample of 55 students had a mean of 16 hours of studying per week. Construct a 90% confidence interval for the mean number of hours a student studies per week. Assume that the population standard deviation is known to be 3.1 hours per week. Round to two decimal places.
Pls help me with this thxsss!!!! <3
The value of s is 107° for this we have know the definition and property of triangle.
What is Triangle?A triangle is a polygon that has three(3) edges and three(3) vertices. It is one of the fundamental(basic) shapes in geometry.
Vertices, A vertex in geometry is a location where two(2) or more curves, lines, or edges come together.
s-37° + s-38° + x = 180° (Sum of three angle is 180°)
2s + x = 180° + 75°
2s + x = 255° ( Equation 1 )
s+32° + x = 180°
s + x = 180° - 32°
s + x = 148° ( Equation 2)
After solving equation 1 and 2 we get,
s = 107°
To learn more about triangle, visit:
https://brainly.com/question/1058720
#SPJ1
Show that the roots of the equation 2x + a(x-a)=0 are rational for any real value of a where a*0 Discuss the nature of the roots if a=0.
The root of the equation is rational for any real value of a where a>0. if a=0, the equation has a single root which is real and rational.
What are roots?In mathematics, the number that results in the initial number when multiplied by itself is called the root. For instance, 7 is the square root of 49 since 77=49. Because 49 is created by multiplying 7 by itself twice in this instance, we refer to 7 as the square root of 49. Since 333=27, the cube root of 27 is 3.
According to question:The given equation is 2x + a(x-a) = 0. Simplifying, we get:
[tex]$\begin{align*}2x + ax - a^2 &= 0 \x(2+a) &= a^2 \x &= \frac{a^2}{2+a}\end{align*}[/tex]
Therefore, the root of the equation is [tex]\frac{a^2}{2+a}$[/tex].
To show that this root is rational for any real value of a where a>0, we need to show that [tex]\frac{a^2}{2+a}$[/tex] can be expressed as a ratio of two integers.
Let [tex]$p=a^2$[/tex] and q=2+a. Since a>0, we have p>0 and q>0. Therefore, [tex]\frac{p}{q}$[/tex] is a rational number.
Thus, the root of the equation is rational for any real value of a where a>0.
If a=0, the given equation becomes 2x=0, which has only one root, x=0. Therefore, if a=0, the equation has a single root which is real and rational.
To know more about Equation visit:
brainly.com/question/649785
#SPJ9
With a polynomial rule we can substitute values in. For instance if P(x)=x^(4) then P(3)=3^(4)=81 For P(x)=5x^(2) find the value of P(3)
Answer:
Step-by-step explanation:Sure! To find the value of P(3) for the polynomial rule P(x) = 5x^2, we just need to substitute x = 3 into the rule and simplify:
P(3) = 5(3^2) (Substitute x = 3)
= 5(9) (Evaluate 3^2)
= 45 (Multiply 5 by 9)
Therefore, P(3) = 45 when P(x) = 5x^2.
Which is a way to find the equation of a line that best fits this data?
A scatter plot has average temperature (degrees Fahrenheit) on the x-axis, and heating bill (dollars) on the y-axis. Point A is around (26, 83), B (38, 86), C (42, 74), D (44, 75), E (49, 66). Other points are at (38, 94) and (42, 79). CLEAR CHECK
Use the coordinates of points B
and D
to find the slope and then the equation of the line that passes through them. Draw a line through the origin and point E. Find the slope, m
, and write the equation in the form y=mx. Use the coordinates of points A
and C
to find the slope and then the y
-intercept of the equation that passes through them. It does not make sense to use algebraic equations on a scatter plot
Therefore , the solution of the given problem of coordinates comes out to be y = (66/49)x and y = (-11/6)x + 110.67 .
Define coordinate.By utilising one or more variables or coordinates, a coordinate system can precisely find coordinates or other algebraic objects on such an area, including Euclidean space. Coordinates, that appears to be couples of numbers, can be used to find a point or object on a double plane. The y and x vectors on even a two-dimensional surface indicate the position of a point. a set of pictures that serve as markers for particular places.
Here,
Find the slope and equation of the line that goes through points B and D using their coordinates.
BD's slope is:
=> m = (y2 - y1) / (x2 - x1) (x2 - x1)
=> m = (75 - 86) / (44 - 38) (44 - 38)
=> m = -11 / 6
Using the slope and position B:
=> y - y1 = m(x - x1) (x - x1)
=> y - 86 = (-11/6)(x - 38) (x - 38)
Simplifying:
=> y = (-11/6)x + 110.67
The line that best matches points B and D has this equation as its equation.
Connect the starting point and position E with a line. Write the equation y = mx after determining the slope, m.
OE's slope is:
=> m = (y2 - y1) / (x2 - x1) (x2 - x1)
=> m = (66 - 0) / (49 - 0) (49 - 0)
=> m = 66 / 49
Using the slope and position E:
=> y - y1 = m(x - x1) (x - x1)
=> y - 66 = (66/49)x
Simplifying:
=> y = (66/49)x
To know more about coordinates visit:
https://brainly.com/question/27749090
#SPJ1
Can someone answer these questions please.
According to the information in the graph Carissa used the motor for the first twelve minutes, then rowed for the next 12 minutes. During the next 48 minutes she dropped the ship's anchor and finally, during the last 18 minutes she returned to the starting point using the motor.
How to identify when she used the motor, she rowed or used the anchor?To identify the moments in which Carissa used the motor, the oars or the anchor we must look at the graph. Additionally, we must be clear that when she uses the motor she is faster than when she uses the oar and that when she uses the anchor she is totally stopped.
Based on the above, we can infer that:
the first twelve minutes, then rowed for the next twelve minutes. During the next forty-eight minutes he dropped the ship's anchor and finally, during the last eighteen minutes, he returned to the starting point using the motor.
Learn more about charts at: https://brainly.com/question/15507084
#SPJ1
Maria decorated her notebook with 4 rectangular stickers. Each sticker was 1/2 inches wide and 11/16 inches long
The total area of the stickers is (1/2) x (11/16) x 4 = 11/8 inches squared.
To calculate the total area of the stickers that were used to decorate the notebook, we need to know the dimensions of each sticker. In this case, the stickers were rectangular and each sticker was 1/2 inches wide and 11/16 inches long. To find the total area, we need to multiply the width of each sticker by the length of each sticker and then multiply this number by the number of stickers used. In this example, we have 4 stickers, so we must multiply (1/2) x (11/16) x 4. When this calculation is done, we end up with 11/8 inches squared as the total area of the stickers.
the complete question is :
Maria decorated her notebook with 4 rectangular stickers. Each sticker was 1/2 inches wide and 11/16 inches long
What was the area of each sticker?
learn more about area here
https://brainly.com/question/27683633
#SPJ4
2. Algebraically determine the initial velocity required in a roller coaster design if the velocity will be 26 m/s at the bottom of a vertical drop of 34 m (Acceleration due to gravity in SI units is 9.8 m/s 2).
The initial velocity required in the roller coaster design is also 26 m/s.
what is an algebraic expression?
An algebraic expression is a mathematical phrase consisting of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
To determine the initial velocity required in a roller coaster design, we can use the conservation of energy principle. At the top of the drop, the total energy of the roller coaster is potential energy, given by mgh, where m is the mass of the roller coaster, g is the acceleration due to gravity, and h is the height of the drop.
At the bottom of the drop, the total energy of the roller coaster is kinetic energy, given by (1/2)mv^2, where v is the velocity of the roller coaster at the bottom.
By equating the two energies, we get:
mgh = (1/2)mv^2
Solving for the initial velocity, we get:
v = sqrt(2gh)
where h is the height of the drop.
Substituting the given values, we get:
v = sqrt(2 x 9.8 m/s^2 x 34 m) = 26 m/s
Therefore, the initial velocity required in the roller coaster design is also 26 m/s.
To learn more about algebraic expression from given link
https://brainly.com/question/19245500
#SPJ1
select all answers
1. linear pair
2. adjacent
3. vertical
4. none of these
In the figure angle5 and angle 6 are vertical angles
3. verticalWhat are vertical angles?Vertical angles are a pair of angles formed by two intersecting lines or rays. They are opposite to each other and have equal measures. In other words, if two lines intersect at a point, the angles that are across from each other, or directly opposite each other, are vertical angles.
Vertical angles are always congruent, which means that they have the same angle measurement. This can be proven using the properties of parallel lines and transversals, which state that when a transversal intersects two parallel lines, the alternate interior angles are congruent, and the corresponding angles are congruent.
Since vertical angles are formed by intersecting lines, they are neither adjacent nor supplementary.
Learn more about vertical angles at:
https://brainly.com/question/1673457
#SPJ1
Does anyone know this? I really need help!!
Answer:
measure of arc JL is 170°
Step-by-step explanation:
The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Inscribed angles that intercept the same arc are congruent.
so 85*2 is 170°
If a blouse cost is GH¢ 2. 50 work out the total cost of 15 blouse
The total price of 15 blouses whilst every shirt costs GH¢ 2.50 is GH¢ 37.50.
To calculate the overall price of 15 blouses at a price of GH¢ 2.50 per blouse, you can use multiplication. Multiplying the cost of 1 blouse (GH¢ 2.50) with the aid of the number of blouses (15) offers you the total value of 15 blouses.
Using this approach, the total cost of 15 blouses could be:
Total price of 15 blouses = 15 x GH¢ 2.50 = GH¢ 37.50
Therefore, the full price of 15 blouses whilst every shirt costs GH¢ 2.50 is GH¢ 37.50. This calculation is critical in commercial enterprise and retail settings while figuring out the total price of a buy or order.
Learn more about Multiplication:-
https://brainly.com/question/1135170
#SPJ4
The most popular lengths of paddle boards can be written by the function V(x) equals the absolute value of |x - 10|where x is the length of the paddleboard and v represents a variation of 4 feet. Complete the statement. The vertex of the function is ? Which represents ?
The vertex of the absolute function for the paddle boards is at x = 10.
Explain about the absolute function?A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function.
Remember that a number's distance from 0 upon that number line represents its absolute value.f(x)=| x | denotes the parent function of absolute values.The function g(x)= f(x - h) can be used to translate this same absolute value function f(x)=| x | horizontally.The graph of f(x) is moved h units towards the right to obtain g(x) when h>0.So,
lengths of paddle boards is defined by :
V(x) = |x - 10|.
x is the length of the paddleboardv is variation of 4 feet.Thus, the vertex of the absolute function for the paddle boards is at x = 10.
Know more about the absolute function
https://brainly.com/question/24734454
#SPJ9
Answer:
Step-by-step explanation:
v(x)=||x-10||
Sylvie asked, "Do college tennis coaches generally get paid more than college football coaches?"
Is this a statistical question?
Yes, this is a statistical question as the answer involves gathering and analyzing data about college football and tennis coaches' salaries. It's important to remember that a variety of factors could influence these salaries.
Explanation:Sylvie's question, 'Do college tennis coaches generally get paid more than college football coaches?' is considered a statistical question because it anticipates a response based on data analysis. To answer this, one would typically gather data on the salaries of both college tennis and football coaches, process this data, and then perform a comparative analysis. It's important to understand that salaries can vary widely, influenced by factors including the size of the college, the success of the program, and the region of the country.
Learn more about Statistical Question here:https://brainly.com/question/14877725
#SPJ2
A marketing research company desires to know the mean consumption of meat per week among people over age 49
. They believe that the meat consumption has a mean of 4.2
pounds, and want to construct a 90%
confidence interval with a maximum error of 0.06
pounds. Assuming a variance of 1.44
pounds, what is the minimum number of people over age 49
they must include in their sample? Round your answer up to the next integer.
To calculate the minimum sample size required to construct a 90% confidence interval with a maximum error of 0.06 pounds, we can use the formula:
n = (Z^2 * σ^2) / E^2
where n is the sample size, Z is the z-score corresponding to the desired confidence level (in this case, 90%), σ^2 is the variance, and E is the maximum error.
Substituting the given values, we get:
n = (1.645^2 * 1.44) / 0.06^2
n = 84.934
Rounding up to the next integer, we get a minimum sample size of 85 people over age 49.
Therefore, the marketing research company must include at least 85 people over age 49 in their sample to construct a 90% confidence interval with a maximum error of 0.06 pounds, assuming a variance of 1.44 pounds and a mean consumption of meat per week of 4.2 pounds.
Solve the equation.
4x4 - 40x2 + 36 = 0
A. x=1 , x= 3
B. x= -3, x= -1, x= 1, x= 3
C. x= -3, x= -1
D. no solution
The solutions of the given equation as required to be determined are as given in; +3, -3, +1, and -1.
What are the solutions of the given equation?As evident from the task content; it follows that the solutions of the given equation are to be determined.
Given; 4x⁴ - 40x² + 36 = 0
Therefore, we have;
x⁴ - 10x² + 9 = 0
Let y = x² so that we have;
y² - 10y + 9 = 0
(y - 9) (y -1) = 0
y = 9 Or y = 1
Therefore, since y = x²;
x = ± 3 or ±1
Hence, the solutions for the equation as required are; +3, -3, +1, and -1.
Read more on quadratic equations;
https://brainly.com/question/1214333
#SPJ1
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
∠OPM
Step-by-step explanation:
∠QPR = ∠3 = ∠1 = ∠OPM
Answer:
∠3
Step-by-step explanation:
4.02 Lesson check ! (4)
We can see that the sequence 1, 3, 9, 27 is not arithmetic.
Is the given sequence arithmetic?An arithmetic sequence is a sequence where the difference between any pair of consecutive terms is a constant knowed as the common difference d.
Generally, the recursive relation for these sequences is:
a(n) = a(n - 1) + d
Here we have the sequence:
1, 3, 9, 27, ...
Taking the differences between consecutive terms of the sequence we get:
3 - 1 = 2
9 - 3 = 6
27 - 9 = 18
The differences are different, so there is no common difference, meaning that this sequence is not arithmetic.
Learn more about sequences at:
brainly.com/question/6561461
#SPJ1
Find x. Round to the nearest tenth.
Answer:13.5
Step-by-step explanation:
use sinuses theorem:
[tex]\frac{x}{sina}=\frac{y}{sinb} \\\frac{12}{sin63}=\frac{x}{sin90} \\x=\frac{12}{sin63}=13.5[/tex]
A circular pond has a diameter of 141 feet. If Ricky walks one lap around the perimeter of the pond, how far does Ricky walk? Enter a decimal rounded to the hundredths place.
If Ricky walks οne lap arοund the perimeter οf the pοnd then he walks 443.14 feet far.
What is feet ?The British imperial and American custοmary systems οf measurement bοth use the unit οf length knοwn as the fοοt (plural: feet), standard symbοl: ft. Usually used as an alternate symbοl is the prime symbοl, One yard is equal tο three feet in bοth custοmary and imperial measures; οne fοοt is equal tο 12 inches.
Thrοughοut histοry, the "fοοt" was a cοmpοnent οf a number οf regiοnal systems οf measurement, including the Greek, Rοman, Chinese, French, and English systems. Frοm οne natiοn tο the next, frοm οne city tο the next, and perhaps frοm οne trade tο the next, it varied in length. Its length was οften divided intο 12 inches οr 16 numbers and ranged frοm 250 tο 335 mm in length, thοugh this was nοt always the case.
Hence, The diameter οf pοnd 141 feet
The radius οf pοnd = 141/2 feet
Area οf pοnd = 2πr
Or, Area οf pοnd = 2×(22/7)×(141/2)
Or, Area οf pοnd = 443.14 feet
To learn more about feet from the given link
https://brainly.com/question/876758
#SPJ1
Work out the value of x :
5x5x5x5x5x5= 5x
Answer:
x=3125
Step-by-step explanation:
5×5×5×5×5=5x
15625=5x
divide by 5 both sides
[tex] \frac{15625}{5} [/tex]
x=3125
Answer:
3125
Step-by-step explanation:
[tex]5 \times 5 \times 5 \times 5 \times 5 \times 5 = 5x \\ {5}^{6} = 5x \\ \frac{ {5}^{6} }{5} = x \\ \frac{15625}{5} = x \\ x = 3125[/tex]
Find x to the nearest hundredths place. Q 650 + R 22 cmS
To find the length of the hypotenuse in a right-angled triangle, we can use trigonometry. Using the given values of RS and angle Q, we can solve for QS ≈ 24.08 cm to the nearest hundredths place.
To find the length of the hypotenuse in a right-angled triangle with a given angle and one side, we can use trigonometry. In this case, we are given the angle Q, which is 65°, and the length of one of the sides, RS, which is 22 cm. We can use the sine function to relate the opposite side, RS, to the hypotenuse, QS. Solving for QS gives us QS = RS / sin(65°), which we can then evaluate to find QS ≈ 24.08 cm. Therefore, x ≈ 24.08 cm to the nearest hundredths place.
Learn more about Right-Angled Triangle here: brainly.com/question/3770177
#SPJ1
The missing figure is in the image attached below
a. Using a trig identity, write x(t) = -2cos(4t) + 5sin(4t) using only one cosine function.b. Using a trig identity, write x(t) = 2cos(4t)+5sin(4t) using only one cosine function.c. Using a trig identity, write x(t) = e^-2t(-2cos(4t)+5sin(4t)) using only one cosine function.
After using trig identities for all three given functions are a). [tex]x(t) = √29cos(4t - 111.8°)[/tex] , b). [tex]x(t) = √29cos(4t - 68.2°),[/tex] c). [tex]x(t) = e^-2t(√29cos(4t - 111.8°))[/tex].
Using the trig identity [tex]cos(A - B) = cos(A)cos(B) + sin(A)sin(B)[/tex], we can rewrite [tex]x(t) = -2cos(4t) + 5sin(4t)[/tex] using only one cosine function as follows : [tex]x(t) = Rcos(4t - α)[/tex] where [tex]R = √((-2)^2 + 5^2) = √29[/tex] and [tex]α = tan^-1(5/-2) = 111.8°[/tex]. Therefore, x(t) = √29cos(4t - 111.8°)
Similarly, using the same trig identity, we can rewrite [tex]x(t) = 2cos(4t) + 5sin(4t)[/tex] using only one cosine function as follows : [tex]x(t) = Rcos(4t - α)[/tex] where [tex]R = √(2^2 + 5^2) = √29[/tex] and [tex]α = tan^-1(5/2)[/tex] = 68.2°. Therefore, [tex]x(t) = √29cos(4t - 68.2°)[/tex].
Using the same trignometric identity, we can rewrite[tex]x(t) = e^-2t(-2cos(4t) + 5sin(4t))[/tex] using only one cosine function as follows: [tex]x(t) = e^-2t(Rcos(4t - α))[/tex] where R = [tex]√((-2)^2 + 5^2) = √29[/tex] and [tex]α = tan^-1(5/-2) = 111.8°[/tex]. Therefore, x(t) =[tex]e^-2t(√29cos(4t - 111.8°))[/tex]
Know more about trignometric here:
https://brainly.com/question/29024806
#SPJ11
5. How many possible rational roots are there for the polynomial P(x) = 10x³ + 6x² + 4x +4?
a.8
b.10
c.16
d.4
Answer:
By the Rational Root Theorem, the possible rational roots of a polynomial are of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
The constant term of P(x) is 4, whose factors are ±1 and ±4. The leading coefficient is 10, whose factors are ±1, ±2, ±5, and ±10.
So, the possible rational roots of P(x) are: ±1/1, ±2/1, ±4/1, ±1/10, ±2/10, ±5/10, and ±10/10. This gives us a total of 8 possible rational roots.
Therefore, the answer is a. 8.
Step-by-step explanation:
work out the length of x
Answer:
x = 3 cm
Step-by-step explanation:
This is a right-angled triangle where:
hyp = Hypotenuse = 5 cm
adj = Adjacent = 4 cm
opp = Opposite = [tex]x[/tex] cm
To determine the Length of any of the three sides of a right-angled triangle mentioned above, applying the Pythagorean Theorem:
[tex]hyp^{2} = opp^{2} + adj^{2}[/tex]
[tex]5^{2} = x^{2} + 4^{2}[/tex]
[tex]25 = x^{2} + 16[/tex]
[tex]x^{2} = 25 - 16[/tex]
[tex]x^{2} = 9[/tex]
[tex]\sqrt{x^{2}} = \sqrt{9}[/tex]
[tex]x = 3[/tex] cm
The value of a professional basketball player's autograph rose 40% in the last year. It is now worth $350.00. What was it worth a year ago?
The autograph of the professional basketball player's was worth $250.00 a year ago.
What was the worth of the professional basketball player's autographa year ago?Given that, in the last year, the value of a professional basketball player's autograph rose 40% and it is now worth $350.00.
To determine it worth a year ago, let's call the original value of the autograph "x".
We know that the value increased by 40%, which means it became:
100% + 40% = 140% of its original value.
We can set up the following equation:
140% × x = 350
(140/100)x = 350
1.4x = 350
To solve for x, we can divide both sides by 1.4:
x = 350 ÷ 1.4
x = 250
Therefore, the autograph was worth $250.00 a year ago.
Learn to solve more algebraic equations here: https://brainly.com/question/9236233
#SPJ1
Two boxes containing candies are placed on a table. The boxes are labelled B1 and B2.
Box Bl contains 7 cinnamon candies and 4 ginger candies. Box B2 contains 3 cinnamon
candies and 10 pepper candies. The boxes are arranged so that the probability of
selecting box Bu is 1/3 and the probabit of selecting box B2 is 2/3. Mohamed is
blindfolded and asked to select a candy. What is the probability that he selects a
cinnamon candy2
Select one:
0. 0. 0326
0. 0. 0125
C. 0. 75
d. 0. 014
Two boxes containing candies were placed on a table, labelled B1 and B2. Box B1 contained 0.0125d of candies while Box B2 contained 0.014d. Therefore, Box B2 contained a greater amount of candies than Box B1, but only by a small amount.
The question asks about two boxes containing candies placed on a table. The boxes are labelled B1 and B2. To answer this question, we must first consider what is contained in each box. Box B1 contains 0.0125d of candies while Box B2 contains 0.014d. Therefore, Box B2 contains a greater amount of candies than Box B1.
It is important to note that the difference between the two boxes is minimal, with Box B2 containing only 0.0015d more candies than Box B1. Thus, both boxes contain similar amounts of candies.
For more such boxes related questions
https://brainly.com/question/30142570
#SPJ11
Find the twenty-third term of an arithmetic sequence that has a common difference
equal to 10 and its eighth term equal to 52
The twenty-third term of the given arithmetic sequence is 192.
The formula to find the nth term of an arithmetic sequence with a common difference (d) is Tn = a + (n - 1)d, where a is the first term of the sequence. To solve for the twenty-third term of the given sequence, we can substitute the given values into the formula. The common difference (d) is 10 and the eighth term (a) is 52, so the formula becomes T23 = 52 + (23 - 1)10. When we solve this equation, we get T23 = 192. Therefore, the twenty-third term of this arithmetic sequence is 192.
Learn more about arithmetic sequence here:
https://brainly.com/question/10396151
#SPJ4
1. In Exercise 1 of Section 3.3, indicate whether the given vectors form a basis for R 2.
1 , -1
2 -2
3 , -2 , 0
1 4 1 1 , 2
1 -1
Accοrding tο the given infοrmatiοn, nοne οf the given vectοrs οr pairs οf vectοrs fοrm a basis fοr R2.
What is vectοr space?A vectοr space is a cοllectiοn οf οbjects called vectοrs, which can be added tοgether and multiplied by scalars (usually real numbers), in a way that satisfies certain axiοms. These axiοms define the prοperties that the additiοn and scalar multiplicatiοn οperatiοns must have in οrder fοr the set οf vectοrs tο be a vectοr space.
Tο determine if a set οf vectοrs fοrms a basis fοr a vectοr space, we need tο check if the vectοrs are linearly independent and if they span the entire space.
Let's cοnsider the given set οf vectοrs:
v1 = (1, -1)
v2 = (2, -2)
v3 = (3, -2, 0)
v4 = (1, 4, 1)
v5 = (1, -1)
Nοte that these vectοrs have different dimensiοns, sο they cannοt fοrm a basis fοr the same vectοr space.
Vectοrs v1 and v2 are in R2, and they are linearly dependent, since v2 is a scalar multiple οf v1. Therefοre, {v1, v2} cannοt fοrm a basis fοr R2.
Vectοr v3 is in R3, and it is nοt pοssible fοr it tο fοrm a basis fοr R2.
Vectοr v4 is in R3, and it cannοt fοrm a basis fοr R2 either.
Vectοrs v1 and v5 are in R2, and they are alsο linearly dependent, since v5 is a scalar multiple οf v1. Therefοre, {v1, v5} cannοt fοrm a basis fοr R2.
In cοnclusiοn, nοne οf the given vectοrs οr pairs οf vectοrs fοrm a basis fοr R2.
To know more about vector space visit:
brainly.com/question/30840636
#SPJ1
Complete question:
each marble bag sold by susans marble company contains 3 blue marbles for every 4 green marbles. if a bag has 24 blue marbles how many green marbles does it contain
Answer:
18
Step-by-step explanation:
We know that for every 4 green marbles, there are 3 blue marbles.
so if there are 8 green marbles, there are 6 blue marbles.
This continues on until we get 24 blue marbles.
Expression : Taking Green Marbles as 'x' and Blue Marbles as 'y'
4x = 3y
so if there are 24 Blue marbles , this means:
4x = 3 x 24
4x = 72
x = 72/4 = 18 Marbles are green
The mean of the data is 18.25. find the variance. find the standard deviation.
The standard deviation is the square root of the variance and is used to measure how spread out the data is. To calculate the standard deviation, take the square root of the variance.
What is variance?Variance is the measure of how far a set of numbers are spread out from their average value. It is a measure of how much variation or dispersion exists from the average. Variance is represented as the square of the standard deviation, which is a measure of the spread of numbers in a set.
The mean of the data is 18.25. The variance is a measure of the spread of the data away from the mean, and is calculated by taking the average of the squared differences from the mean. To calculate the variance, subtract the mean from each data point, square this result and add up the values. Then divide this sum by the number of data points minus one.
For example, if the data set contains the values 10, 15, 20, 25 and 30 then the mean is 18.25. Subtracting the mean from each data point gives -8.25, -3.25, 1.75, 6.75, 11.75. Squaring each of the differences gives 68.0625, 10.5625, 3.0625, 45.5625, 137.0625. Adding these results together gives 264.3125. Dividing this by 4 (the number of data points minus one) gives 66.075. Taking the square root of this gives 8.1 as the standard deviation.
For more questions related to standard deviation
https://brainly.com/question/24298037
#SPJ1
The variance of the given data is calculated to be 118.63 and the standard deviation is 10.89.
What does variance mean?The variance of the data is a measure of how far the data points are spread out from the mean. It is calculated by taking the differences between each data point and the mean, squaring the differences, and then taking the average of those squared differences.
For our data, the mean is 18.25. To find the variance, we can subtract 18.25 from each of the data points and square the differences. Then we can add up all of the squared differences and divide by the number of data points.
Variance = (2 - 18.25)² + (3 - 18.25)² + (4 - 18.25)² + (18 - 18.25)² + (20 - 18.25)² + (25 - 18.25)²
= (15.752 + 14.752 + 13.752 + 0.752 + 1.752 + 6.752) ÷ 6
= (255.2 + 217.2 + 190.2 + 0.6 + 3.0 + 45.8) ÷ 6
= 711.8 ÷ 6
Variance = 118.63
To find the standard deviation, we take the square root of the variance.
Standard deviation = √118.63
Standard deviation = 10.89
For more questions related to standard deviation
https://brainly.com/question/24298037
#SPJ1
Question:
The mean of the data is 18.25. Find the variance. Find the standard deviation.
Data: 2, 3, 4, 18, 20, 25
Using the empirical rule, what percentage of the games that Lillian bowls does she score between 119 and 141
Using the Empirical Rule, Lillian should score between 119 and 141 in 68% of the games she bowls.
In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively. the empirical rule states that 99.7% of data occurs within three standard deviations of the mean within a normal distribution. To this end, 68% of the observed data will occur within the first standard deviation, 95% will take place in the second deviation, and 97.5% within the third standard deviation. The empirical rule predicts the probability distribution for a set of outcomes.
For such more questions on Empirical Rule:
brainly.com/question/21417449
#SPJ11