what fraction of an hour is 15 minutes pls help
Answer:
1/4 of an hour is 15 minutes
Step-by-step explanation:
Answer: 1/4 of an hr
Step-by-step explanation:
15/60 is 1/4
Which polynomial has (3x + 2) as a binomial factor?
6x3 + 3x2 + 4x + 2
12x2 + 15x + 8x + 10
18x3 – 12x2 + 9x – 6
21x4 + 7x3 + 6x + 2
Answer:
its option B : 18x3 – 12x2 + 9x – 6
Step-by-step explanation:
[tex]12( \frac{ -2 }{3}) {}^{2} +23( \frac{ - 2}{3} )+10= \frac{16}{3} − \frac{46}{3} +10=0[/tex]
12x² + 15x + 8x + 10 has a binomial factor of (3x+2).
What is a Quadratic equation?ax²+bx+c=0, with a not equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
We may utilize the factor theorem, which asserts that if a polynomial f(x) has a component (x - a), then f(a) = 0, to identify which polynomial has (3x + 2) as a binomial factor.
In this situation, finding a value of x that reduces 3x + 2 to zero is necessary since we are trying to discover a polynomial that contains (3x + 2) as a component. We obtain x = -2/3 by solving 3x + 2 = 0.
Let's try the polynomials one by one:
(a) 6x³ + 3x² + 4x + 2:
f(-2/3) = 6(-2/3)³ + 3(-2/3)² + 4(-2/3) + 2
= -8/3 - 4/9 - 8/3 + 2
= -32/9,
so (3x + 2) is not a factor.
(b) 12x² + 15x + 8x + 10:
f(-2/3) = 12(-2/3)₂ + 15(-2/3) + 8(-2/3) + 10
= 16/3 - 10 - 16/3 + 10
= 0,
so (3x + 2) is a factor.
(c) 18x³ - 12x² + 9x - 6:
f(-2/3) = 18(-2/3)³ - 12(-2/3)² + 9(-2/3) - 6
= -32/3 + 8/3 - 6 - 6
= -32/3,
so (3x + 2) is not a factor.
(d) 21x⁴ + 7x³ + 6x + 2:
f(-2/3) = 21(-2/3)⁴ + 7(-2/3)³ + 6(-2/3) + 2
= 64/27 - 56/27 - 4 + 2
= 2/27,
so (3x + 2) is not a factor.
Therefore, the only polynomial that has (3x + 2) as a binomial factor is 12x² + 15x + 8x + 10.
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PLEASE NEED HELP!!!
The wheel of a bicycle has a diameter of 54 inches. How far does the bicycle travel when the wheel completes 20 revolutions?
In ABC Co. employees could bring n USB drives from home, install whatever they wanted including games, and otherwise modify their workstations. The consequence was that IT spent considerable time dealing with corrupted operating systems and had substantial expenses replacing machines. Rebuilding systems took "a lot of effort" according to an employee, and inevitably users had files in additional unexpected places, requiring manual efforts to retrieve those files. Users were down for a day or more. These incidents took time away from priority IT initiatives and required 3-24 hours each to identify the issue, mitigate and remediate. Educating users was helpful, but users still couldn’t manage themselves, particularly given increasingly sophisticated social engineering exploits. The Vice President of IT addressed several issues to improve the security of the infrastructure over the past five years, expanding on what was working, and changing what needed improvement. They virtualized 98% of the infrastructure, and still utilize custom-built applications where needed. According to an employee, "In the Windows environment we wanted to eliminate the havoc of allowing users admin rights. It makes me nervous from a security perspective, but it also inhibits productivity of both IT and end users."
They initially selected a product that had seemed simple in their trials, and it offered to fully automate deployment of software to local and remote employees via an intuitive web interface. It even offered remote access capabilities for remote employees. The results of a trial deployment, however, were much less than expected — important applications could not work without admin rights the way that product was designed. That’s when the IT department tested "PowerBroker" for Windows on his personal PC. "With "PowerBroker" for Windows I could navigate and discover assets, identify vulnerabilities, and most importantly lock down all applications to implement least privilege and remove all admin rights from users’ PCs," Romious discovered. And PowerBroker had flexibility in how it could be deployed and managed, which did take some time to decide, but in the end PowerBroker for Windows easily scaled to meet their enterprise needs and allow removal of admin rights from all Windows systems. PowerBroker has solved these challenges.
On an application-by-application basis, IT can then review the risk and vulnerabilities associated with the requested application by using the BeyondInsight platform included with PowerBroker for Windows. The BeyondInsight IT Risk Management Platform provides centralized reporting and analytics, giving visibility into the risks associated with assets that can be discovered and profiled. "BeyondInsight used with PowerBroker for Windows allows us to proactively assess and approve applications when warranted for business and when safe, rather than remediating after the havoc." The vulnerability scanner incorporated into PowerBroker for Windows and the BeyondInsight platform "has been invaluable" according to Romious. It ensures patches are applied, vulnerabilities are mitigated, and that nothing else becomes broken in the process. Fred Allen, VP of IT agrees, "The deployment of PowerBroker for Windows with BeyondInsight has gone well. It’s good to have a win-win after the challenges of the previous attempt to eliminate admin rights on users’ PCs.
Keeping in mind the IT security problem at ABC Co., what solution/s "PowerBroker" provided, from the perspective of the E-Commerce Security Environment you are aware of from ITMA 401 course?
What 3 vulnerable e-commerce points, which you studied of in ITMA 401 course, you also directly or indirectly encountered in this case study at ABC Co.?
What and how the 3 key technology concepts, of the Internet, got threatened at ABC Co.?
PowerBroker provided a solution to the security issue at ABC Co. by removing admin rights, improving application security, and addressing network security and data protection concerns.
From the perspective of the E-Commerce Security Environment, PowerBroker provided a solution to the issue of granting users administrative rights on their PCs, which posed security risks and productivity hindrances. By implementing PowerBroker for Windows, ABC Co. was able to remove admin rights from users' PCs and implement the principle of least privilege. This improved the security posture of the organization and reduced the likelihood of unauthorized access, data breaches, and system corruption.Three vulnerable e-commerce points encountered in this case study are:1. User Awareness and Education: Despite efforts to educate users about security risks, users at ABC Co. still struggled to manage their systems and fell victim to social engineering exploits. This highlights the ongoing challenge of ensuring user awareness and education to mitigate security risks.2. Application Security: The initial product deployed at ABC Co. failed to work without admin rights, indicating vulnerabilities in the design and implementation of the application. Application security is critical in the e-commerce environment to prevent unauthorized access, data breaches, and system compromise.3. Patch Management: The vulnerability scanner incorporated into PowerBroker for Windows and the BeyondInsight platform addressed the challenge of patch management. It ensured that patches were applied promptly, vulnerabilities were mitigated, and system integrity was maintained. Effective patch management is crucial to protect against known vulnerabilities and potential attacks.The three key technology concepts of the Internet that were threatened at ABC Co. include:1. Network Security: By allowing users to bring USB drives and make modifications to their workstations, ABC Co. faced risks of malware infections, unauthorized access, and compromised network security. The implementation of PowerBroker helped address these security concerns and enhance network security.2. Application Security: The challenges faced in finding an application deployment solution that worked without admin rights highlighted the importance of application security. PowerBroker provided a mechanism to lock down applications and implement least privilege, mitigating the risks associated with unauthorized access and malicious activities.3. Data Protection: The incidents at ABC Co., such as corrupted operating systems and unexpected file locations, demonstrated the need for robust data protection measures. By improving the security infrastructure and implementing PowerBroker, ABC Co. reduced the likelihood of data loss, unauthorized access, and data breaches.In summary, PowerBroker addressed the issue of granting admin rights, mitigated vulnerabilities in application security, and improved network security and data protection, thereby addressing key concerns within the E-Commerce Security Environment. The vulnerable e-commerce points included user awareness, application security, and patch management, while the threatened technology concepts were network security, application security, and data protection.For more questions on Power
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Please help me on #5. Both parts of possible please. Thank you for helping!
Answer:
5) No
The actual distance between the drone and the fossil is [tex]32\dfrac{3}{4}[/tex] ft
Step-by-step explanation:
3) A. -2/9
(2/3 - 5/6)/3/4 = (-1/6)/(3/4) = (-1/6) × (4/3) = -2/9
4) d. [tex]0.\overline {90}[/tex]
10/11 = 0.9090909...
∴ 10/11 = [tex]0.\overline {90}[/tex]
5) The height of the drone is flying above the ground = [tex]25\dfrac{1}{2}[/tex] ft.
The location of the fossil below the ground = [tex]7\dfrac{1}{4}[/tex] ft.
Taking the ground level as the origin on a number line, we have;
The location of the drone relative to the ground = + [tex]25\dfrac{1}{2}[/tex] ft. (The positive sign for a point above the origin)
The location of the fossil relative to the ground = [tex]-7\dfrac{1}{4}[/tex] ft. (The negative sign for a point below the origin)
Therefore;
The distance between the drone and the fossil = The difference between the location of the drone and the fossil
The distance between the drone and the fossil = [tex]25\dfrac{1}{2} - \left(-7\dfrac{1}{4} \right)[/tex]
[tex]25\dfrac{1}{2} - \left(-7\dfrac{1}{4} \right) = 25\dfrac{1}{2} + 7\dfrac{1}{4} = 32\dfrac{3}{4}[/tex]
The distance between the drone and the fossil = [tex]32\dfrac{3}{4}[/tex] ft.
Therefore;
The distance between the drone and the fossil > 32 ft.
Can someone plz help me on this its due in 30 mins.
Answer:
A, C, and F
Step-by-step explanation:
"Express the finite abelian groups tais
(a) Z36 x Z48 x Z60
(b) Z8 x Z9 x X Z11 X Z12
The finite abelian group Z36 x Z48 x Z60 can be expressed as Z2^6 x Z3^4 x Z5. The finite abelian group Z8 x Z9 x Z11 x Z12 can be expressed as Z2^3 x Z3^2 x Z11 x Z2^2 x Z3.
(a) The finite abelian group Z36 x Z48 x Z60 can be expressed as the direct product of its prime power factorizations. The prime factorization of 36 is 2^2 * 3^2, 48 is 2^4 * 3, and 60 is 2^2 * 3 * 5. Therefore, the group can be written as Z2^6 x Z3^4 x Z5.
(b) The finite abelian group Z8 x Z9 x Z11 x Z12 can be expressed as the direct product of its prime power factorizations. The prime factorization of 8 is 2^3, 9 is 3^2, 11 is a prime number, and 12 is 2^2 * 3. Therefore, the group can be written as Z2^3 x Z3^2 x Z11 x Z2^2 x Z3.
In both cases, the group is expressed as the direct product of cyclic groups of prime power orders. The order of the group is the product of the orders of the individual cyclic groups, and the structure of the group is determined by the prime factors and their powers.
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Can someone please explain how to do this i am so confused i just want to pass this class please :(
Answer:
x=6√3
Step-by-step explanation:
In 30-60-90 triangles, if the hypotenuse is x, the longest leg is [tex]\frac{x}{2}[/tex], and the shortest leg is [tex]\frac{x\sqrt{3} }{2}[/tex].
If the longest leg is 6, then [tex]\frac{x}{2} =6[/tex]
Multiply by 2,
[tex]x=12[/tex]
If x=12,
[tex]\frac{12\sqrt{3} }{2}[/tex]
[tex]=6\sqrt{3}[/tex]
So, the shortest leg is 6√3.
Which expression is equivalent to the series
shown?
125
Σ 45η
n=17
Answer:
its c ^u^ and the next to it is b :D
Step-by-step explanation:
edg 21
Answer:
It’s c and the next one is b
Step-by-step explanation:
Just took edge
can anyone expand and simply this for me (3x +2)(2x-5) ?
Answer: 5x-3
Step-by-step explanation:
3x+ 2x +2-5
5x -3
How does the volume of a cylinder with a radius of 6 inches and a height of 8 inches compare to
the volume of a cylinder with a radius of 8 inches and a height of 6 inches?
Answer:
they are the same
Step-by-step explanation:
We can conclude that the volume of cylinder 1 is 3/4 times the volume of cylinder 2.
What is the volume of cylinder?The volume of cylinder is given by -
V = πR²h
Given is to compare the volume of a cylinder with a radius of 6 inches and a height of 8 inches compare to the volume of a cylinder with a radius of 8 inches and a height of 6 inches.
Volume of cylinder 1 will be -
V(1) = πR²h = 6 x 6 x 8π = 36 x 8π = 288π
Volume of cylinder 2 will be -
V(2) = πR²h = 8 x 8 x 6π = 64 x 6π = 384π
So, we can write that -
V(1)/V(2) = (288π)/(384π)
V(1)/V(2) = (288)/(384)
V(1)/V(2) = 3/4
Therefore, we can conclude that the volume of cylinder 1 is 3/4 times the volume of cylinder 2.
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Here is a solid prism.
(c) (i) Write down the mathematical name of this prism.
(ii)How many vertices does the prism have?
Answer:
It is called a rectangular prism
It has 8 vertices
PLSS HELP I WILL GIVE YOU BRAINLYEST!!
Students were surveyed about their
favorite sports to play in physed. The
results are represented in this arcle graph
If 48 students were surveyed, how many
chose soccer?
Part/total=%/100
A. 15
B. 12
C. 13
D. 10
Answer: C
So I was right, I guess.
Which is an equivalent form of the first equation that when added to second equation eliminates the x terms? 4/5 x-3/5y=18
Answer:
[tex]-8x + 6y = -180[/tex]
Step-by-step explanation:
Given
[tex]\frac{4}{5} x-\frac{3}{5}y=18[/tex]
[tex]8x + 12y = 11[/tex]
Required
Equivalent form of the first equation that eliminates x when added to the second
To do this, we simply make the coefficients of x to be opposite in both equations.
In the second equation, the coefficient of x is 8.
So, we need to make the coefficient of x -8, in the first equation.
[tex]\frac{4}{5} x-\frac{3}{5}y=18[/tex]
Multiply by -10
[tex]-10 * [\frac{4}{5} x-\frac{3}{5}y=18][/tex]
[tex]\frac{-40}{5} x+\frac{30}{5}y=-180[/tex]
[tex]-8x + 6y = -180[/tex]
When this is added to the first equation, the x terms becomes eliminated
{A,B,C,D,E,F,G,H}
how many 4-element subsets are there in the set ?? and please
solve step by step
After considering the given data we conclude that the total number of 4-element subsets that can be generated is 70.
To evaluate the number of 4-element subsets that can be formed from the set {A,B,C,D,E,F,G,H}, we can apply the combination formula:
[tex]nCr = n! / r!(n-r)![/tex]
Here,
n = maximum count of elements in the set
r = total count of elements we want to choose.
For the given case, n = 8 (since there are 8 elements in the set) and r = 4 (since we want to choose 4-element subsets).
Placing in these values, we get:
[tex]nCr = 8! / 4!(8-4)! = 8! / 4!4![/tex]
[tex]= (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70[/tex]
Hence, creation of 70, 4-element subsets that can be formed from the set {A,B,C,D,E,F,G,H}.
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Can anyone pls help
Answer:
50
Step-by-step explanation:
if im thinking right
im SOO sorrYYy if its wrong
Two fifths of a number is 24.
what is the number?
Answer:
60
Step-by-step explanation:
half of 2/5 is 1/5 so half of 24 is 12.
since 12 is 1/5 of the number multiply 12 by 5 and you get 60.
The whole number will be 60 whose two fifths will be 24.
Given, Two fifths of a number is 24.
Writing in form of equation,
Let the whole number be x.
So, two fifth of x is 24.
[tex]\frac{2}{5} of x = 24[/tex]
[tex]\frac{2}{5} \times x = 24[/tex]
Apply cross multiplication,
[tex]x = \frac{24 \times 5}{2}[/tex]
x = 60.
Therefore the whole number is 60.
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Which expression is equivalent to 2 (3x – 4)?
ОА) 3х - 4
O B) 5x - 6
Ос) 6x - 4
OD) 6x – 8
Help please multiple choice interval. 20 Points. Thanks very much!
Answer:
D
Step-by-step explanation:
The following recipe is for 16 crepes: • 1/4 cup margarine, 3 tbs sugar, 1/2 cup orange juice, • 1 tbs grated orange rind, and 1/2 cup toasted almonds. You need to serve 5 crepes per person for 8 guests. How much of each ingredient is needed?
You need 5/2 times the amounts given in the recipe, so you need:
5/8 cup margarine 15/2 tbs sugar 5/4 cup orange juice 5/2 tbs grated orange rind5/4 cup toasted almonds.How much of each ingredient is needed?Here we have the recipe for 16 crepes:
1/4 cup margarine 3 tbs sugar1/2 cup orange juice 1 tbs grated orange rind1/2 cup toasted almonds.You want to make 5 crepes for person, for 8 persons, so you need:
8*5 = 40 crepes.
So you need to make the recipe N times:
16*N = 40
N = 40/16 = 10/4 = 5/2
So you need a fraction of 5/2 times each of the amounts in the recipes.
You will need:
(5/2)*1/4 = 5/8 cup margarine (5/2)*3 = 15/2 tbs sugar(5/2)*1/2 = 5/4 cup orange juice 5/2 tbs grated orange rind(5/2)*1/2 = 5/4 cup toasted almonds.Learn more about fractions at:
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A teacher determined the effect of instructions on the time required by subjects to solve the same puzzle. For two independent samples of ten subjects per group, mean solution times, in minutes, were longer for subjects given "difficult" instructions (M1=15.8, s=8.64) than for subjects given "easy" instructions (M2=9.0, s=5.01). A t stat of 2.15 led to the rejection of the null hypothesis.
Given a pooled standard deviation of 7.06, calculate the value of standardized effect size and provide a conclusion
Cohen's d (standardized effect size): approximately 0.963
Conclusion: The difference in mean solution times between the difficult instruction group and the easy instruction group is statistically significant, with a moderate effect size.
To calculate the value of the standardized effect size, also known as Cohen's d, we can use the formula:
Cohen's d = (M1 - M2) / Sp
Where:
M1: Mean solution time for the "difficult" instruction group (given as 15.8 minutes)
M2: Mean solution time for the "easy" instruction group (given as 9.0 minutes)
Sp: Pooled standard deviation (given as 7.06)
Let's calculate the value of Cohen's d:
Cohen's d = (15.8 - 9.0) / 7.06
= 6.8 / 7.06
≈ 0.963
The value of the standardized effect size (Cohen's d) is approximately 0.963.
Now, let's provide a conclusion based on this information. A standardized effect size of 0.963 indicates a moderate effect. Since the null hypothesis was rejected, it suggests that the difference in mean solution times between the two groups (difficult instruction and easy instruction) is statistically significant.
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Use the Chain Rule to find dw/dt.
w = ln
sqrt2a.gif x2 + y2 + z2
, x = 4 sin t, y = 7 cos t, z = 9 tan t
Using the Chain Rule to dw/dt. w = ln [tex]\sqrt{2a}.gifx^{2} + y^{2} + z^{2}[/tex], x = 4 sin t, y = 7 cos t, z = 9 tan t the expression will give us the final result for dw/dt.
To find dw/dt using the Chain Rule,
we'll start by expressing w as a composition of functions and then differentiate it step by step.
Given:
w = ln[tex](\sqrt{} (x^2 + y^2 + z^2))[/tex], where x = 4 sin(t), y = 7 cos(t), and z = 9 tan(t).
We'll first substitute the values of x, y, and z into the expression for w:
w = ln[tex](\sqrt{} ((4 sin(t))^2[/tex] + [tex](7 cos(t))^2[/tex] + [tex](9 tan(t))^2))[/tex]
Next, we'll differentiate w with respect to t using the Chain Rule.
The Chain Rule states that if we have a composite function f(g(t)),
its derivative is given by f'(g(t)) ×g'(t).
In our case, f(u) = ln[tex](\sqrt{u}[/tex] and g(t) represents the expressions within the square root.
Applying the Chain Rule, we have:
dw/dt = [tex](1/\sqrt{} (x^2 + y^2 + z^2))[/tex] × (2xdx/dt + 2ydy/dt + 2z×dz/dt)
Substituting the expressions for x, y, and z, we get:
dw/dt = (1/[tex]\sqrt{} ((4 sin(t))^2 + (7 cos(t))^2[/tex]+[tex](9 tan(t))^2))[/tex] ×(2(4 sin(t))(cos(t)) + 2(7 cos(t))(-sin(t)) + [tex]2(9 tan(t))(sec^2(t)))[/tex]
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Please please help please please ASAP
help with this please
Answer:
a = 7. b = 24, c = 25. This is a Pythagorean triple
Step-by-step explanation:
NO LINKS!! NO ONE WANT TO HELP ME PLEASE IM WASTING ALL MY POINTS PLSSS HELPPPP :((( Which of the following equations describe the line shown below? Check all
that apply MULTI CHOICE MORE THAN OND
(1,6) (-3,-6)
Answer:
Option E
Step-by-step explanation:
The two points are (1,6) and (-3,-6) . We can find the Equation of the line using two point form , as ,
[tex]\implies y - y_1 =\dfrac{y_2-y_1}{x_2-x_1}(x - x_1) \\\\\implies y - 6 = \dfrac{-6-6}{-3-1}(x-1) \\\\\implies y-6 = \dfrac{-12}{-4}(x-1) \\\\\implies \boxed{\boxed{y -6 = 3(x-1)}} [/tex]
On looking at options we see that option E is correct .
Hence the correct option is E.The following table shows the Myers-Briggs personality preference and area of study for a random sample of 519 college students. In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing.
Myers-Briggs Preference Arts and Science Business Allied Health Row Total
IN 66 11 19 96
EN 80 42 32 154
IS 54 30 31 115
ES 71 40 43 154
Column total 271 123 125 519
(a) Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the 0.05 level of significance.
(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)
a)Using the chi-square distribution table, the critical value is 12.592 using Hypothesis.
b)The value of chi-square statistic for the sample is 16.042, given that
(a)Chi-square test
The Null Hypothesis H₀ : Myers-Briggs preference type is independent of area of study.
Alternative Hypothesis H₁ : Myers-Briggs preference type is dependent of area of study.
Test statistic is χ² = ∑ ((Oi - Ei)² / Ei)
Expected frequencies:To compute the expected frequencies of the data we use the formula:
Eij = (row total i * column total j) / n where
i is the row number and j is the column number.
To find the value of chi-square statistic, the following table is necessary:
Myers-Briggs Preference Arts and Science Business Allied Health Row Total
IN 66 11 19 96
EN 80 42 32 154
IS 54 30 31 115
ES 71 40 43 154
Column total 271 123 125 519
We obtain the expected frequencies by the above formula, and these are listed in the table below.
Myers-Briggs Preference Arts and Science Business Allied Health Row Total
IN 51.55 23.43 21.03 96
EN 86.71 39.56 27.73 154
IS 50.14 22.88 20.97 115
ES 82.61 37.13 32.27 154
Column total 271 123 125 519
The expected frequencies are computed by multiplying the row total and column total and dividing by the grand total, n.
Here, we have four rows and three columns.
Thus, the degrees of freedom are df = (4 - 1)(3 - 1) = 6 at the 0.05 level of significance.
Since we have four rows and three columns, the number of degrees of freedom will be 6.
Using the chi-square distribution table, the critical value is 12.592.
Since 16.04 > 12.592,
we reject the null hypothesis and conclude that Myers-Briggs preference type is dependent of area of study.
(b) Value of chi-square statisticThe formula to compute the chi-square statistic is
χ² = ∑ ((Oi - Ei)² / Ei) where Oi is the observed frequency and Ei is the expected frequency.
Calculating the chi-square statistic, we have
χ² = ((66 - 51.55)² / 51.55) + ((11 - 23.43)² / 23.43) + ... + ((43 - 32.27)² / 32.27)
= 16.042 (rounded to three decimal places).
The value of chi-square statistic for the sample is 16.042.
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The width of a rectangular shed is 8 feet, and its length is 14 feet. Three of these expressions equal the perimeter of the garden, in feet. Which expression does NOT?
Answer:
That one
Step-by-step explanation:
It's kinda obvious if you look at the choices.
Answer:
8+14
Step-by-step explanation:
Help plsss I’m a little confused
We started this today :/
What is the volume of a container with sides 1ft, 2ft, and 2.5 ft
Answer:
5ft^3
Step-by-step explanation:
The formula for volume is length × width × height.
so you multiply 1×2×2.5, which equals 5
2. Quadrilateral ABCD was dilated with the origin as the center of dilation to create quadrilateral A'B'C'D. Which rule best represents the dilation that was applied to quadrilateral ABCD to create quadrilateral A'B'C'D ?
Answer:
[tex](x,y) => (2.5x,2.5y)[/tex]
Step-by-step explanation:
Given
See attachment for ABCD and A'B'C'D'
Required
Determine the dilation rule
Using AB and A'B' as points of references;
[tex]AB = (-1,2)\ to\ (2,1)[/tex]
[tex]A'B' = (-2.5,5)\ to\ (5,2.5)[/tex]
The dilation factor (k) is calculated as:
[tex]k = \frac{A'B'}{AB}[/tex]
This gives:
[tex]k = \frac{(-2.5,5)}{(-1,2)} \ or\ k = \frac{(5,2.5)}{(2,1)}[/tex]
Factorize
[tex]k = \frac{2.5*(-1,2)}{(-1,2)} \ or\ k = \frac{2.5*(2,1)}{(2,1)}[/tex]
[tex]k = 2.5 \ or\ k = 2.5[/tex]
Hence, the scale factor is 2.5
The dilation rule is:
[tex](x,y) => k(x,y)[/tex]
[tex](x,y) => 2.5(x,y)[/tex]
[tex](x,y) => (2.5x,2.5y)[/tex]