We asked UST employees to tell us how many megabytes of memory (RAM) they have on their computer. We would like to test to see if the mean amount of memory is the same for three different academic departments. We have the memory amounts for six faculty members' machines in the three departments shown below.
Dept. 1 Dept. 2 Dept. 3
1 4096 4096 4096
2 4096 2048 4096
3 4096 2048 8192
computer 4 8192 4096 8192
5 4096 2048 4096
6 2048 8192 2048 Here is the ANOVA table:
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Factor x 5592405 2796203 xxx 0.604
Error xx 80390827 5359388 Total xx 85983232 Calculate the number of degrees of freedom Error.

Protractor postulate: given any angle, we can express its measure as a unique real number from 0 to 180 degrees.

The protractor postulate is a fundamental concept in geometry that establishes a way to measure angles using a protractor. According to this postulate, every angle can be uniquely represented by a real number between 0 and 180 degrees.

A protractor is a geometric tool with a semicircular shape and marked degrees along its edge. To measure an angle using a protractor, we align the center of the protractor with the vertex of the angle and the baseline of the protractor with one side of the angle. We then read the degree measure where the other side of the angle intersects the protractor.

The protractor is divided into 180 degrees, with 0 degrees being the starting point at the baseline of the protractor, and 180 degrees being at the opposite end of the baseline. By aligning the protractor with an angle, we can determine its measure as a real number within this range.

For example, if we measure an angle using a protractor and find that the other side intersects the protractor at 45 degrees, we can express the measure of the angle as 45 degrees. Similarly, if the intersection point is at 90 degrees, the angle measure would be 90 degrees. The protractor postulate guarantees that these angle measures are unique within the range of 0 to 180 degrees.

It is important to note that the protractor postulate assumes that angles can be measured using a protractor and that the measurement is accurate and reliable. The postulate provides a consistent and standardized way to assign a numerical value to an angle, allowing for precise communication and comparison of angles in geometric contexts.

In summary, the protractor postulate establishes that the measure of any angle can be expressed as a unique real number between 0 and 180 degrees. This concept is fundamental in geometry and allows for the measurement, comparison, and communication of angles using a protractor.

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Answer:

Step-by-step explanation:

The loop will run an infinite number of times

The sum of the expression 4∛(x¹⁰) + 5x³∛(8x) in the simplest form will be 14x³ ∛x.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 4∛(x¹⁰) + 5x³∛(8x)

Simplify the expression, then we have

⇒ 4∛(x¹⁰) + 5x³∛(8x)

⇒ 4∛[(x³)³ · x] + 5x³∛(2³ · x)

⇒ 4x³ ∛x + 10x³ ∛x

⇒ 14x³ ∛x

The sum of the expression 4∛(x¹⁰) + 5x³∛(8x) in the simplest form will be 14x³ ∛x.

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The solution to the quadratic equation 7x² + 10 = -127 is \(x = -\frac{i\sqrt{959} }{7} ,x = \frac{i\sqrt{959} }{7}\).

Given the quadratic equation in the question:

7x² + 10 = -127

To solve for x, first subtract 10 from both sides of the equation:

7x² + 10 = -127

7x² + 10 - 10  = -127 - 10

7x²  = -127 - 10

7x²  = -137

Divide both sides by 7:

7x²/7  = -137/7

x² = -137/7

Since the right-hand side of the equation is negative, the equation has no real solutions.

However, if we allow complex numbers, we can take the square root of both sides:

x = ±√( -137/7 )

\(x = -\frac{i\sqrt{959} }{7} \\and\\x = \frac{i\sqrt{959} }{7}\)

Therefore, the solutions \(x = -\frac{i\sqrt{959} }{7} ,x = \frac{i\sqrt{959} }{7}\).

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Answer:

slope is 3

Step-by-step explanation:

10,17

7,8

8-17=-9

7-10=-3

-9/-3=3

the p-value for the test is 0.0016.

(a)The null hypothesis is that the hardness of water from the two different water treatment facilities is the same.

This can be denoted as follows: H0: μ1​=μ2​.

The alternative hypothesis is that the hardness of water from the two different water treatment facilities is different.

This can be denoted as follows:

H1: μ1​≠μ2​.It is given that σ1​=σ2​.

Here, the test statistic is given by the formula:

t=¯x1−¯x2​SEwhere,SE=Sp2n1​+Sp2n2​where,Sp2=[(n1−1)s21​+(n2−1)s22​)]n1+n2−2Here, n1=n2=n=5

The observed values of water hardness and sample standard deviations for the two facilities can be summarised in the following table: FacilitySample SizeSample MeanSample b

Deviation1(n1​)​x1​s1​2​52​148.8​10.5​22(n2​)​x2​s2​2​52​136.2​9.8​

The pooled variance is given by Sp2=10.54+9.82(5−1)+5−2=10.15The standard error is given by SE=10.155+5=2.261t=¯x1−¯x2​SE=148.8−136.22.261=5.54

Now,

the critical value of t for α=0.05 and 8 degrees of freedom is t0​=2.306. Since t>t0​, the null hypothesis can be rejected.

There is sufficient evidence to conclude that the two water treatment facilities produce water of different hardness at α=0.05.

(b)The p-value is the probability of getting a test statistic at least as extreme as the observed test statistic, assuming the null hypothesis is true.

Since the test is two-tailed, the p-value can be calculated as follows:

p=2P(T>5.54)where T has a t-distribution with 8 degrees of freedom.p=2(0.0008)=0.0016Thus,

the p-value for the test is 0.0016.

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Step-by-step explanation:

triangle BCD ~ triangle EFD so

angle BCD= angle EFD

9x+2=15x-52

6x=54

x=9

angle CBF =9x+2=83°

In the triangle ΔCBD, the angle measure of ∠CBF is 83°.

When the triangles have equal shape, but different sizes. It is called as similar triangles. The corresponding angles are congruent. And the sizes have the same proportionality rate.

Given:

The angle measures,

∠CBD = (9x + 2)°

∠EFD = (15x -52)°

From the diagram,

ΔCBD is similar to ΔEFD.

So, the corresponding angles are equal.

∠CBD = ∠EFD

(9x + 2)° = (15x -52)°

15x - 9x = 52 + 2

6x = 54

x = 9°

And ∠CBF = ∠CBD

So, ∠CBF = (9x + 2)°

Substituting the value of x,

∠CBF = (9(9) + 2)°

∠CBF = 83°

Therefore, the angle measure of ∠CBF is 83°.

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Answer: x^4 + x^3 + 7x^2 + 49x - 30

Step-by-step explanation:

first, we use the distributive property.

x^2 x (x^2 - 2x + 15) + 3x x (x^2 -2x + 15) - 2(x^2 - 2x + 15)

then, we remove the parenthesis.

x^4 - 2x^3 + 15x^2 + 3x^3 - 6x^2 + 45x - 2x^2 + 4x - 30

then, we collect like terms.

x^4 + x^3 + 7x^2 + 49x - 30

Therefore, the center of the circle is located at (0, 6), and the length of the radius is approximately equal to 7.43.

To determine the coordinates of the center and length of the radius of the circle, we need to rewrite the given equation in standard form, which is\((x - h)^2 + (y - k)^2 = r^2\), where (h, k) represents the center coordinates and r represents the radius.

Given equation: \(x^2 + y^2 - 12y - 20.25 = 0\)

To complete the square, we need to add and subtract the appropriate terms on the left side of the equation:

\(x^2 + y^2 - 12y - 20.25 + 36 = 36\)

\(x^2 + (y^2 - 12y + 36) - 20.25 + 36 = 36\)

Simplifying further:

\(x^2 + (y - 6)^2 = 55.25\)

Comparing this equation with the standard form, we can identify the following values:

Center coordinates: (h, k) = (0, 6)

Radius length:\(r^2\) = 55.25, so the radius length is √55.25.

Therefore, the center of the circle is located at (0, 6), and the length of the radius is approximately equal to 7.43.

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estimated sum-114, actual sum-112.97

Step-by-step explanation:

76.6-77

25.5-26

10.87-11

77+26+11=114

76.6+25.5+10.87=112.97

\(y = (1/5) x^5 + Ce^ {(-x^5)}\) is the general solution of the given differential equation.

The given differential equation is:

y' + 5x⁴ y = x⁴

To solve this equation, we can use an integrating factor. First, we need to multiply both sides of the equation by the integrating factor, which is \(e^{(int 5x^4 dx)}\):

\(e^{(int 5x^4 dx) }y' + 5x^{4} e^{(int 5x^4 dx)} y = x^4 e^{(int 5x^4 dx)}\)

The integral of 5x⁴ is (5/5)x⁵ = x, so the integrating factor is \(e^{(x^5)}\):

\(e^{(x^5)} y' + 5x^{4} e^{(x^5)} y = x e^(x^5)\)

Now we can recognize the left-hand side as the product of the derivative of the product of \(e^{(x^5)\)and y:

\((d/dx)[e^{(x^5)} y] = x^4 e^{(x^5)}\)

Integrating both sides with respect to x, we get:

\(e^{(x^5)} y = (1/5) x^5 e^{(x^5)} + C\)

where C is the constant of integration. Dividing both sides by \(e^{(x^5)}\), we get the general solution:

\(y = (1/5) x^5 + Ce^(-x^5)\)

where C is an arbitrary constant.

\(y = (1/5) x^5 + Ce^{(-x^5)}\) is the general solution of the given differential equation.

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Answer:

26

Step-by-step explanation: I'm pretty sure its 26 because if k = 7 then 4 times 7 equals 28. Then you subtract 2. That's how I got 26.

Answer:

Step-by-step explanation:

\(4k-2\\k= 7\\\)

Substitute 7 for k into the given equation

\(4(7)-2\\\\=28-2\\\\=26\)

Answer:

The amount of money originally invested which is the principal P = 5,000

Step-by-step explanation:

Using the compound interest formula, the return on investment can be represented on the interest function as;

f(x) = P(1+r)^x

Where

P is the principal which is the initial investment.

r = rate Proportion

x = time (number of years)

Comparing to the given function;

f(x) = 5,000(1 + 0.04)^x

We can see that;

Principal P = 5,000

Rate r = 0.04

time = x

The amount of money originally invested which is the principal P = 5,000

Answer:

Step-by-step explanation:

If you are saying, Y is more than 9, then use this- Y>9

If you are saying Y more than 9 equals ? then use this- 9+Y=?

Hope i helped you!!

Answer:

D.) u^2 - u-6 = 0 where u = (x-4)

Step-by-step explanation:

Answer: D

Step-by-step explanation:

edge 23

Answer:

Terrence made $30 more than Teresa.

Step-by-step explanation:

Giving the following information:

Terrence earns $450 per week.

Teresa earns $300 per week plus a 6% commission on the total sales of books she sells.

First, we need to structure the total income formula for each:

Terrence= 450

Teresa= 300 + 0.06*x

x= sales

Now, for $2,000 sales of books:

Terrence= $450

Teresa= 300 + 0.06*2,000= $420

Answer:

m = 7 can also be y=7x+1 is positive and shows acceleration or ascending lines steep y axis 1 and x axis 0 ascending to 1 or above and when y = 7  x =1 see attached.

m = -7 is negative and shows deceleration of 1 as we add 1 here too. Or can be any number for y intercept see attached.

Step-by-step explanation:

Answer:

maybe 2

Step-by-step explanation:

im not really sure

The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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Step-by-step explanation:

as we have a point and the slope, we can start with the point-slope form and then transform.

the point-slope form is

y - y1 = a(x - x1)

(x1, y1) being a point on the line, a being the slope.

the slope-interceot form is

y = ax + b

a being the slope again, b being the y-intercept (the y value for x = 0).

so, we have

y - -5 = 5/2 × (x - -4)

y + 5 = 5/2 × (x + 4) = 5x/2 + 5×4/2 = 5x/2 + 10

y = 5x/2 + 5

or

y = (5/2)x + 5

and this is already the slope-intercept form. all done.

A data analyst uses bias()  to find out how much the predicted outcome and the actual outcome of their data model differ.

The act of unfairly favoring or opposing a certain person or item due to allowing your judgment to be influenced by your opinions: The senator charged bias on the part of the media. Journalists must be unbiased and free from political bias.

There is a lack of objectivity in the way we view things. Both intentional and inadvertent biases are possible. When given an option, a person might prefer one shirt over two others if it also happens to be their favorite color.

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Recovered memory in CSA refers to the new development of abusive memories. Repressed memory is when the patient believes the CSA occurred, even though they have no specific memory of the event.

Recovered memory:

The term "recovered memory" implies that at some point the memory must become inaccessible to conscious awareness (as opposed to "continuous memory"). Although the term is not ideal, it is clear that people often fail to report important events, such as known hospitalizations (Loftus, 1993). In 1995, the debate over reclaiming memory was near its most violent climax. Hundreds of people have recovered memories of child sexual abuse (CSA), and sometimes in therapy it is thought that repressed or dissociative memories need to be recovered for a person to 'heal'.

Repressed Memory:

Repressed memory is a purported psychiatric phenomenon involving the inability to recall autobiographical information, usually traumatic or stressful. The concept has its origins in psychoanalytic theory, where repression is understood as a defense mechanism that keeps painful experiences and unacceptable impulses out of awareness. Repressed memory is a controversial concept, especially in a legal context, where it is used to unjustly and inaccurately accuse individuals, causing significant harm. Meanwhile, a working group from the American Psychological Association has stated that while "most people who were sexually abused in childhood remember some or all of what happened to them, it is possible to remember long-forgotten abuses.

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Answer: 26

Step-by-step explanation:

62-36=26

Answer: 26

You simply have to subtract 36 from 62

Answer:

B

Step-by-step explanation:

Circumference is 3.14*d

Where d is the diameter.

3.14*8000

= 25120

The Earth has a circumference of 25120 miles approximately.

Answer:

B. 25,120 miles.

Step-by-step explanation:

Circumference = π * diameter

= 3.14 * 8000

= 25,120 miles.

Answer:

\( 1 \frac{9}{80} \)

Step-by-step explanation:

To solve this you have to use BODMAS theorem

BODMAS means,

B = brackets

O = of

D = division

M = multiplication

A = addition

S = subtraction

In this sum first you have to do division and then you can do addition

Let's Solve now,

\(m + n \div m - n \\ \frac{4}{5} + \frac{5}{4} \div \frac{4}{5} - \frac{5 }{4} \\ \frac{4}{5} + \frac{5}{4} \times \frac{5}{4} - \frac{5}{4} \\ \frac{4}{5} + \frac{25}{16} - \frac{5}{4} \\ \frac{4 \times 16 + 25 \times 5}{5 \times 16} - \frac{5}{4} \\ \frac{64 + 125}{80} - \frac{5}{4} \\ \frac{189}{80} - \frac{5}{4} \\ \frac{189}{80} - \frac{5 \times 20}{4 \times 20} \\ \frac{189 - 100}{80} \\ \frac{89}{80} \\ = 1 \frac{9}{80} \)

hope this helps you

let me know if you have another questions :-)

The point H could be (1 + √134.56, 5) or (1 - √134.56, 5).

Let’s plot the given points E, F and G on the graph and try to find the missing point H:

Now, the length of the side EF will be:

EF = √((3-1)² + (5-5)²)EF = 2 units

The length of the side FG will be:

FG = √((6-3)² + (1-5)²)FG = √10 units

The length of the side EG will be:

EG = √((6-1)² + (1-5)²)EG = √26 units

Therefore, the total length of the three sides of the fence will be:2 + √10 + √26 units

Now, the perimeter of the fenced area with 4 sides EFGH is:16 = 2 + √10 + √26 + EHThe length of EH will be:

EH = 16 - 2 - √10 - √26EH = 11.60 units

We need to plot the missing point H which is at a distance of 11.60 units from point E along the line passing through points E and F.

Using the slope formula we find that the slope of the line passing through points E and F is: m = (y2 - y1)/(x2 - x1) = (5 - 5)/(3 - 1) = 0Therefore the line passing through E and F is a horizontal line as it has zero slope.

The distance between points E and H is 11.60 units and point H will be on the same horizontal line passing through E and F.Therefore, the x-coordinate of point H will be:

EH = √((x2-x1)² + (y2-y1)²)11.60 = √((x-1)² + (5-5)²)

Solving the above equation:

(x-1)² = 134.56(x-1)

= ±√134.56x

= 1 + √134.56 or x = 1 - √134.56

Therefore, the point H could be (1 + √134.56, 5) or (1 - √134.56, 5).

Point H could be (1 + √134.56, 5) or (1 - √134.56, 5).

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The true statement about the graph is

It is a function with the domain {-6 < x < 0} and the range {0 ≤ y ≤ 5}.

The range refers to all possible value in the out put of a graph.

The out put is the y coordinate and the possible values here is within the interval

0 ≤ y ≤ 5

The domain refers to all possible value in the input of a graph.

The input is the x coordinate and the possible values here is within the interval

-6 ≤ x ≤ 0

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Answer: 64/35

Step-by-step explanation:

8/7 and then divide by 5/8 and you get 1 29/35. 35x1= 35 then add the numerator, 29 and you get 64. so the answer would be 64/35

The graph of the given equation is shown below

From the question, we are to determine the graph that represents the given equation

The given equation is

4x - 3y = -1

The graph of the equation is shown below

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