6. A certain faculty in City Campus is interested in determining if there an association between students' preference for online or face to face instruction and their education level(undergraduate or graduate). 450 students are selected and information collected was as follows: Online | face to face | Total 189 81 270 undergraduate Graduate 102 180 Total 201 159 450 At 0.05 level of significance, is there is sufficient statistical evidence to indicate a signif- icant association between education level and student's preference of instruction(use critical value =3.84)

The least squares regression line minimizes the sum of the mean squared error.

The least squares regression line, also known as the ordinary least squares (OLS) regression line, is a straight line that represents the best fit to a set of data points. It is used to model the relationship between a dependent variable (Y) and one or more independent variables (X) based on the principle of minimizing the sum of the squared differences between the observed data points and the predicted values on the line.

Mean squared error (MSE) is a measure of how well the regression line fits the data points.

It represents the average of the squared differences between the actual values and the predicted values by the regression line.

By minimizing the sum of the squared errors, the least squares regression line finds the line that best fits the data in a linear regression model.

This line is the one that provides the best fit in the sense of minimizing the overall error in the predictions.

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To create a map that identifies different types of angles and lines, draw two parallel lines and a transversal, label the angles formed by the intersection, and identify and label one set each of corresponding angles.

Here are the steps to create a map with the specified requirements:

1. Draw two parallel lines (which will be the "streets") and label them as such.

2. Draw a transversal line (which will be the "highway") that intersects the parallel lines at an angle.

3. Label the angles formed by the intersection of the transversal and the parallel lines. Make sure to include the measures of each angle.

4. Identify and label one set of corresponding angles. Corresponding angles are formed by the intersection of the transversal and the parallel lines and are in corresponding positions.

5. Identify and label one set of alternate interior angles. Alternate interior angles are formed by the intersection of the transversal and the parallel lines and are on opposite sides of the transversal and between the parallel lines.

6. Identify and label one set of complementary angles. Complementary angles are two angles whose sum is 90 degrees.

7. Identify and label one set of supplementary angles. Supplementary angles are two angles whose sum is 180 degrees.

Make sure to include a key that identifies each type of angle and its corresponding label on the map.

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Answer:

Step-by-step explanation: 3×6+1,3×6 is 18+1 is 19/6 is your answer

let's first off, convert the mixed fractions to improper fractions.

\(\stackrel{mixed}{8\frac{2}{5}}\implies \cfrac{8\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{42}{5}}~\hfill \stackrel{mixed}{6\frac{7}{10}} \implies \cfrac{6\cdot 10+7}{10} \implies \stackrel{improper}{\cfrac{67}{10}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{42}{5}-\cfrac{67}{10}\implies \cfrac{(2)42~~ - ~~(1)67}{\underset{\textit{using this LCD}}{10}}\implies \cfrac{84-67}{10}\implies \cfrac{17}{10}\implies 1\frac{7}{10}\)

Answer:

x=4/3

Step-by-step explanation:

The null and alternative hypotheses for this hypothesis test is H₀ : p = 0.93,  Hₐ : p > 0.93.

A hypothesis in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.

Null and alternative hypotheses are used in statistical hypothesis testing. The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

Let 'p' be the population proportion.

Given statement : The new brand of seeds advertises that 93% of the seeds germinate, which is higher than the germination rate of the seeds she is currently using.

Since null hypothesis shows that there is no significant difference between the quantities where as alternative hypothesis believes that there is some  difference,

Hence, the null and alternative hypotheses for this hypothesis test will be :-  H₀ : p = 0.93

          Hₐ : p > 0.93

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Answer:

x=4

Step-by-step explanation:

x

=

4

or

x

=

−

4

Explanation:

First divide throughout by  

2

to get

x

2

=

16

Now take the square root on both sides to get

x

=

±

4

.

You may now substitute the values of  

x

=

4

and

x

=

−

4

back into the original equation and check that it satisfies the equation which it does.

For an independent-measures t statistic, the estimated standard error measures how much difference is reasonable to expect between the sample means for two samples selected from the same population.

True

The reliability of a measure is determined by the standard error of measurement. It is frequently mentioned in standardized testing and it describes how variable a test's measurement error is. A confidence interval for the true score of an element or an individual can be generated using the standard error of measurement.

To ascertain whether there is statistical support that the linked population means are statistically substantially different, the Independent Samples t Test compares the means of two independent groups. An example of a parametric test is the Independent Samples t Test. Additionally called the Independent t Test.

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Answer:

4 methods are there

Step-by-step explanation:

please mark me as brainlist

Y₁(t) = (t, 2t) is the only parametrization of curve L because its equation satisfies the equation of the curve y = 2x.

To determine which one of the parametric curves Y₁, Y₂, Y₃ is a parametrization of the curve L, we need to compare their equations with the equation of curve L, which is y = 2x.

(i) Comparing the equations of the parametric curves with the equation y = 2x, we find that Y₁(t) = (t, 2t) is a parametrization of curve L.

(ii) The other two parametric curves, Y₂(t) = (-2t, -4t) and Y₃(t) = (2t, t), fail to be parametrizations of curve L because their equations do not satisfy the equation y = 2x.

For Y₂(t), if we substitute the values of x and y from the parametric equations into the equation y = 2x, we get -4t = -4t, which is true. However, the range of the parameter t for Y₂ is not specified, so it does not cover all points on the curve L.

For Y₃(t), substituting the values of x and y into the equation y = 2x, we get t = 2t, which is not true for all values of t. Therefore, Y₃ is not a valid parametrization of curve L.

In conclusion, Y₁(t) = (t, 2t) is the only parametrization of curve L because its equation satisfies the equation of the curve y = 2x.

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(b) Consider the curve L ={(x,y) € Rẻ | y = 2x}, and consider the following three parametric curves: Y₁: R → R², Yı(t) = (t¹, 2t¹), Y2: R→ R², Y2(t) = (-2t, -4t), Y3 : R → R², Y3(t) = (2t, t). (i) Only one of Y₁, Y2, Y3 is a parametrisation of L. Which one is it? (ii) Why do the other two parametric curves fail to be parametrisations of L?

Answer:

The answer is that it is a rational number because it is a terminating decimal

Step-by-step explanation:

0.62581 is a rational number.

Rational numbers are numbers that can be written as the ratio of two integers. For example: 1/2, 3/4, are rational numbers.

Irrational numbers, any real number that cannot be expressed as the quotient of two integers—that is, p/q, where p and q are both integers. For example, there is no number among integers and fractions that equals Square root of√2.

Now the given number is,

0.62581

Now here we see that the numbers after decimal are terminating and non-repeating.

Also the digit after decimal stops.

Hence the number 0.62581 is rational.

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A square-based box with an open top and volume of 4,000 cm³ has minimum surface area when its dimensions are 10√2 cm by 10√2 cm by 20√2 cm.

Let's assume that the box has a square base with side length x and height h. Then, its volume is given by:

V = x^2 * h

We are given that the volume is 4,000 cm³, so we can write:

x^2 * h = 4,000

Solving for h, we get:

h = 4000 / x^2

The amount of material used to construct the box is the sum of the areas of its five faces (four sides and the base). Since the box has an open top, we don't need to consider its area. The area of the base is x^2, and the area of each side is x times the height h. Thus, the total surface area A of the box is given by:

A = x^2 + 4xh

Substituting the expression we found for h, we get:

A = x^2 + 4x(4000 / x^2)

Simplifying and factoring out 4, we get:

A = 4(x^2 + 1000/x)

To find the dimensions of the box that minimize the amount of material used, we need to find the value of x that minimizes A. We can do this by taking the derivative of A with respect to x and setting it equal to zero:

dA/dx = 8x - 4000/x^2 = 0

Solving for x, we get:

x = 10√2

Substituting this value back into the expression we found for h, we get:

h = 20√2

Therefore, the dimensions of the box (in cm) that minimize the amount of material used are:

side length of the base: 10√2 cm

height: 20√2 cm

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The minimum value of y is -1. This can be answered by the concept from equation of a circle.

To find the minimum value of y, we need to rewrite the given equation in terms of y. Completing the square, we have:

x² - 14x + y² - 48y = 0
(x² - 14x + 49) + (y² - 48y + 576) = 49 + 576
(x - 7)² + (y - 24)² = 625

This is the equation of a circle with center (7,24) and radius 25. The minimum value of y occurs at the bottom of the circle, which is the point (7,24-25).

Therefore, the minimum value of y is -1.

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The factorization of \(\rm 125x^9 + 64\) is  \(\rm (5x^3 + 4)(25x^6 - 20x^3 +16)\).

Factorization is nothing but writing a number as the product of smaller numbers.

Given

Polynomial; \(\rm 125x^9 + 64\)

To find the factorization the polynomial equates the equation with zero following all the steps given below.

Then,

The factor of the polynomial is;

\(\rm= 125x^9 + 64\\\\= 125x^9 -100x^6+80x^3+100x^6-80x^3+64 \\\\ =5x^3(25x^6 - 20x^3 +16) +4(25x^6 - 20x^3 +16) \\\\=(5x^3 + 4)(25x^6 - 20x^3 +16)\)

Hence, the factorization of \(\rm 125x^9 + 64\) is  \(\rm (5x^3 + 4)(25x^6 - 20x^3 +16)\).

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Answer:

c

Step-by-step explanation:

So, the interest is compounded 6,335 times per year.

To find n, we need to use the formula for compound interest:
\(A = P(1 + r/n)^{(nt)\)

Where:
A = the final amount
P = the principal (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time period (in years)

In this case, we have:

P = $12,000
r = 6.5% = 0.065
n = ?
t = 4 years

We know that the interest is compounded daily, so we need to convert the annual interest rate and the time period to reflect that.

First, we need to find the daily interest rate:

daily rate =\((1 + r/365)^{(365/365) - 1\)
daily rate = (1 + 0.065/365)\(^{(365/365) - 1\)
daily rate = 0.000178

Next, we need to find the number of compounding periods:

n = 365

Finally, we can plug in the values and solve for n:

A = P(1 + r/n)\(^(nt)\)
A = $12,000(1 + 0.000178/365)\(^{\\(365*4)\)
A = $12,000(1.000178)^1460
A = $14,233.29

Now we can use the formula for compound interest in reverse to solve for n:

\(A = P(1 + r/n)^{(nt)\\14,233.29 = 12,000(1 + 0.065/n)^{(n*4)\\1.18611 = (1 + 0.065/n)^(4n)\\\\ln(1.18611) = ln[(1 + 0.065/n)^(4n)]\\0.16946 = 4n ln(1 + 0.065/n)\\n = 4[ln(1.065/1.000178)] / 0.16946\\n = 4[270.309] / 0.16946\\n = 6,334.4\)Therefore, n is approximately 6,334.4. However, since n represents the number of compounding periods and cannot be fractional, we need to round up to the nearest whole number:

n = 6,335

So, the interest is compounded 6,335 times per year.\\

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Answer:

18.2

Step-by-step explanation:

divide 91 by 5

x x x x x. x x x x x x x x x x xx. x

Answer: The first 3 options

Step-by-step explanation:

You have to make sure that the given variable would be able to equal -5. The  \(\geq\) sign in the second and third answer show that the variable could be equivalent to -5.

Answer:

g > -7, f ≤ -5 and g ≥ -5

Step-by-step explanation:

the < and > symbols mean less than and greater than respectively, but not including. Therefore -5 cannot be a valid solution if the range is (for example) g > -5. However, ≤ and ≥ mean less/greater than or equal to, so -5 would be a valid solution for g ≥ -5 (for example).

The linear inequality y</5/2 x - 7 does not have any common solution set with the given inequality.

The solution sets of the linear inequality  are drawn in the graph attached below,

From the graph it is seen that the yellow part represents the inequality y≥-5/2 x - 3

And the green section of the graph represents the other inequality

y<-5/2 x - 7

As we can see in the graph that the two areas are separate. So there are no common points.

Again if we consider the two inequalities as two lines  y= -5/2 x - 3

and y = -5/2 x - 7 . we can see that they both have the same slopes of  -5/2 so they are parallel lines. so they will never intersect.

Therefore we can conclude that the inequality  y</5/2 x - 7 does not have any common solution set with the given inequality.

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Answer:

7.89

Step-by-step explanation:

Answer:

the answer is 7.89

Step-by-step explanation:

39.45/5

7.89

The derivative dy/dt when the x coordinate's rate of change 18 feet is 13.5 feet.

Given,

The radius of the circular track in which the jogger runs = 70 feet

The coordinates of the jogger = (42, 56)

The rate of change in x coordinate = 18 feet/sec

Let (x,y) be the coordinates

We have to find dy/dt;

Then we know x,y satisfies the equation of the circle as

x² + y² = 70²

Let us differentiate this implicit function with respect to t

2x dx/dt + 2y dy/dt = 0

At this point, dx/dt 18 and x = 42. y = 56

Substitute to have

2 × 42 × 18 + 2 × 56 dy/dt = 0

1512 + 112 dy/dt = 0

dy/dt = 1512/112

dy/dt = 13.5 feet

Therefore,

The derivative dy/dt here is 13.5 feet

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The correct option is the fourth one, the slope and y-intercept are different.

Here we have the linear equation:

3x - 5y = 4

We know that it is dilated by a scale factor of 5/3, so let's find the dilation.

We can rewrite the linear equation as:

-5y = 4 - 3x

y =  (3/5)x - 4/5

Now let's apply the dilation:

y = (5/3)*[ (3/5)x - 4/5]

y = x - 4/3

Then we can see that the slope and the y-intercept are different, the correct option is 4.

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the function f(x) = sin(x) evaluated at a = 0 represents the derivative of the given limit, lim h→0 cos(h)/h.

we can use the limit definition of the derivative which states that the derivative of a function at a point is equal to the limit of the difference quotient as h approaches 0. In other words, if f(x) is a differentiable function, then

f'(a) = lim h→0 (f(a+h) - f(a))/h

Now, let's look at the given limit:

lim h→0 cos(h)/h

We can rewrite this limit as

lim h→0 [cos(h) - 1 + 1]/h

= lim h→0 [(cos(h) - 1)/h + 1/h]

Using L'Hopital's rule, we can evaluate the first term in the limit:

lim h→0 (cos(h) - 1)/h

= lim h→0 -sin(h)

= 0

Therefore, the given limit is equal to

lim h→0 cos(h)/h = 0 + 1/0

which is undefined.

However, if we consider the function f(x) = sin(x) evaluated at a = 0, then we know that

f'(0) = lim h→0 (f(0+h) - f(0))/h

= lim h→0 (sin(h))/h

= 1

This means that the derivative of f(x) = sin(x) at a = 0 is equal to 1, which is not the same as the given limit.

the function f(x) = sin(x) evaluated at a = 0 represents the derivative of a different limit, not the given limit lim h→0 cos(h)/h.

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Answer:

Hello,

To find amount of inches in 58 centimeters, you need to use the information given.

0.4 inches = 1 centimeter

??? inches = 58 centimeter

58 x 0.4

= 23.20

Hence your answer is 23.2 inches are in 58 centimeters

Hope this helps ^^

In order to construct a confidence interval for the population mean when the population standard deviation is known, two assumptions must be met. Firstly, the sample data must be a simple random sample from the population being studied.

Secondly, the variable being measured must have a normal distribution or the sample size must be sufficiently large. The first assumption of a simple random sample ensures that the sample is representative of the population being studied, which is necessary for valid statistical inference. The second assumption is necessary because the confidence interval calculation relies on the assumption that the sample mean follows a normal distribution. When the variable being measured has a normal distribution, the sample mean will also have a normal distribution regardless of the sample size. When the variable being measured does not have a normal distribution, the sample size must be large enough (typically at least 30) in order for the sample mean to follow a normal distribution due to the central limit theorem. By meeting these two assumptions, we can be confident in the accuracy of the resulting confidence interval for the population mean.

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if the installment option is used, the total amount paid over the 240-month term would be $1,080,000. This includes both the principal amount of $550,000 and the interest accumulated over the repayment period.

To determine the total amount if the installment option is used, we need to calculate the total repayment over the 240-month term.

The installment amount per month is $4,500, and the repayment term is 240 months.

Total repayment = Installment amount per month * Repayment term

Total repayment = $4,500 * 240

Total repayment = $1,080,000

Therefore, if the installment option is used, the total amount paid over the 240-month term would be $1,080,000. This includes both the principal amount of $550,000 and the interest accumulated over the repayment period.

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lets the length be 3x

width be 5x

perimeter = 48

so

3x +5x=48

8x = 48

x =48/8

x= 6

so.

3x = 3×6 = 18

5x = 5×6= 30

hope it will be helpful

In the point (r, θ), r signifies the distance from O to P, while θ represents the angle counterclockwise from the polar axis to the line segment ¯¯¯¯¯¯¯¯OP.

For the point (r, θ), r is the distance from O to P, and θ is the angle counterclockwise from the polar axis to the line segment ¯¯¯¯¯¯¯¯OP.

In polar coordinates, a point is represented by its distance (r) from the origin (O) and the angle (θ) it forms with the positive x-axis. The distance (r) denotes the length of the line segment connecting the origin to the point P. It indicates how far the point is from the origin. The angle (θ) represents the rotation or angular position of the line segment ¯¯¯¯¯¯¯¯OP from the polar axis (positive x-axis) in a counterclockwise direction. It determines the direction in which the point is located relative to the polar axis.

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The integral of (42³ - 2r + 7) dz is equal to (42³ - 2r + 7)z + C.

To integrate the function (42³ - 2r + 7) dz, we treat r as a constant and integrate with respect to z. The integral of a constant with respect to z is simply the constant multiplied by z:

∫ (42³ - 2r + 7) dz = (42³ - 2r + 7)z + C

where C is the constant of integration.

Note: The integral of a constant term (such as 7) with respect to any variable is simply the constant multiplied by the variable. In this case, the variable is z.

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