Peter and his 4 brothers combined all him money to buy a video game.If 25% of peters money is $5 how much do all 5 brothers have in total

The value of w will decrease by approximately 235 times the small amount.

Using the power rule and product rule of differentiation, we obtain:

wx(x,y,z) = 6xy - 7yz

wy(x,y,z) = 3x^2 - 7xz + 20yz

wz(x,y,z) = -7xy + 20yz

Next, we evaluate each partial derivative at the given point (3,5,-4) by substituting x = 3, y = 5, and z = -4:

wx(3,5,-4) = 6(3)(5) - 7(5)(-4) = 210

wy(3,5,-4) = 3(3^2) - 7(3)(-4) + 20(5)(-4) = -327

wz(3,5,-4) = -7(3)(5) + 20(5)(-4) = -235

Therefore, the values of the first partial derivatives with respect to x, y, and z, evaluated at the point (3,5,-4), are wx = 210, wy = -327, and wz = -235.

These partial derivatives give us information about how the function w changes as we vary each input variable. For example, wx = 210 indicates that if we increase x by a small amount while holding y and z constant, the value of w will increase by approximately 210 times the small amount. Similarly, wy = -327 tells us that if we increase y by a small amount while holding x and z constant, the value of w will decrease by approximately 327 times the small amount. Finally, wz = -235 tells us that if we increase z by a small amount while holding x and y constant, the value of w will decrease by approximately 235 times the small amount.

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If the probability of event X occurring is the same as the probability of event X occurring given that event Y has already occurred, then: Event X has no effect on the probability of event Y occurring.

So, the correct answer is C.

This is because if the probability of event X occurring is the same as the probability of event X occurring given that event Y has already occurred, it means that event Y has no influence on the probability of event X occurring.

Therefore, events X and Y are independent of each other.

Option A is incorrect because it suggests that event Y is dependent on event X, which is not the case.

Option B is also incorrect because it suggests that both events are dependent on each other.

Option D is incorrect because it suggests that event Y has no effect on the probability of event X occurring, which is not true.

Option E is also incorrect because it includes options A, B, and D which are incorrect.

Option F is also incorrect because we have already established that event X has no effect on the probability of event Y occurring.

Hence the answer of the question is C.

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The set of radian angle measures that is equivalent to [tex]sin^{-1}(-1/2)[/tex] is: c. 7pi/6, 11pi/6.

To find the radian angle measures that are equivalent to [tex]sin^{-1}(-1/2)[/tex], we need to identify angles whose sine function evaluates to -1/2.

The sine function represents the ratio of the length of the side opposite to an angle to the length of the hypotenuse in a right triangle. It takes on values between -1 and 1.

For [tex]sin^{-1}(-1/2)[/tex], we are looking for angles whose sine is equal to -1/2. In other words, we need to find angles where the ratio of the length of the side opposite the angle to the length of the hypotenuse is -1/2.

In the unit circle, the angles 7pi/6 and 11pi/6 correspond to 210 degrees and 330 degrees, respectively. At these angles, the y-coordinate of the corresponding point on the unit circle is -1/2, which satisfies the condition [tex]sin^{-1}(-1/2)[/tex].

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Therefore, the two F-values that divide the area under the F-curve are approximately 0.179 and 4.366 for an F-distribution with degrees of freedom (9,7).

To determine the two F-values that divide the area under the F-curve into a middle 0.95 area and two outside 0.025 areas, we need to consult the F-distribution table. For an F-distribution with degrees of freedom (df) of (9,7), the two values we are looking for correspond to the cumulative probabilities of 0.025 and 0.975.

From the F-distribution table, with numerator degrees of freedom (df1) = 9 and denominator degrees of freedom (df2) = 7, we can find the critical F-values. The critical F-value for the lower tail with cumulative probability 0.025 is approximately 0.179. The critical F-value for the upper tail with cumulative probability 0.975 is approximately 4.366.

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C, that reddish orangish line, it's pointing upwards, so as X increases, Y increases too.

Answer:

Step-by-step explanation:

its c girly

The volume of the rectangular prism is 243 cubic centimeters when the length is 6 cm, the width is 4.5 cm and the height is 9cm.

We need to find the volume of a rectangular prism. The volume is determined by using the values length, width, and height. The formula is given as,

V = w × h × l

Where:

w = Width

h = Height

l = Length

We will assume the given data as:

w = 4.5cm

h = 9cm

l = 6 cm

By substuting the values of w,h, and l values in the formula we get:

V = l × h × w

=  6 × 9 × 4.5

= 243

Therefore, the volume of the rectangular prism is 243 cubic centimeters.

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The complete question:

Find the Volume of the Rectangular Prism whose Length is 6cm, width is 4.5 cm and height is 9cm ?

Step-by-step explanation:

The second derivative of y = -7x^6 - 5 is the derivative of the first derivative.

y' = -42x^5

y'' = (d/dx)(-42x^5)

y'' = -210x^4

Therefore, the second derivative of y = -7x^6 - 5 is y'' = -210x^4.

Answer:

Therefore, the two cities are 91.22 degrees apart in latitude and 212.05 degrees apart in longitude.

Step-by-step explanation:

The Haversine formula is:

d = 2r * arcsin(sqrt(sin^2((lat2 - lat1)/2) + cos(lat1) * cos(lat2) * sin^2((lon2 - lon1)/2)))

where:

d is the distance between the two points

r is the radius of the Earth (mean radius = 6,371km)

lat1 and lat2 are the latitude values of the two points

lon1 and lon2 are the longitude values of the two points

Using this formula, we can calculate the distance between Liverpool and Melbourne in terms of latitude and longitude:

Latitude difference = |53.41 - (-37.81)| = 91.22 degrees

Longitude difference = |(-2.99) - 144.96| = 147.95 degrees

Note that the longitude difference is greater than 180 degrees, which means that we need to account for the fact that the two cities are on opposite sides of the 180 degree meridian. To do this, we can subtract the longitude difference from 360 degrees:

Longitude difference = 360 - 147.95 = 212.05 degrees

Therefore, the two cities are 91.22 degrees apart in latitude and 212.05 degrees apart in longitude.

The estimate for cost to renovate the garden is close to $300. The Option C.

The area of the rectangular section is:

= 25 ft x 40 ft

= 1000 sq ft.

The area of the circular fountain is:

= (15/2)^2 x π

≈ 176.71 sq ft.

Given that:

The cost of the sod is $0.30 per square foot.

The estimated cost for renovation will  be:

= 1176.71 sq ft x $0.30/sq ft

= $353.01.

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The 95% confidence interval for b1 is approximately (0.197, 0.703).

The 95% confidence interval for the slope estimate (b1) is given by:

b1 ± t(alpha/2, n-2) * s(e) / (sqrt(SSX) * sqrt(1 - r^2))

where:

t(alpha/2, n-2) is the t-score with alpha/2 probability (alpha = 0.05 for 95% confidence level) and n-2 degrees of freedom

s(e) is the standard error of the estimate for the regression

SSX is the sum of squared deviations of the predictor variable from its mean

r is the correlation coefficient between the predictor and response variables

Substituting the given values, we have:

b1 ± t(0.025, 7) * 2.16 / (sqrt(2.25*8) * sqrt(1 - 0.45^2))

= 0.45 ± 2.365 * 2.16 / (2.121 * 0.676)

= 0.45 ± 1.253

Therefore, the 95% confidence interval for b1 is approximately (0.197, 0.703). So, the answer is (d) (0.11, 0.79).

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The area of the circle is 23. 04 π in²

The formula that is used for calculating the area of a circle is expressed wit the equation;

A = πr²

Such that the parameters are expressed as;

Note that the formula for diameter is expressed as;

Radius = Diameter/2

Substitute the values

Radius = 9.6/2

Divide the values

Radius = 4. 8 in

Substitute the values, we have;

Area = 3.14 × (4.8)²

find the square value, we have;

Area = 3.14 × 23. 04

Multiply the values, we have;

Area = 72. 35 in²

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The probabilities are:

a) P(S^2/σ^2 ≤ 1.8) ≈ 0.8147

b) P(0.85 ≤ S^2/σ^2 ≤ 1.15) ≈ 0.1197

To solve the given problem, we need to use the chi-square distribution. The chi-square distribution is used to analyze the variability of a normally distributed population when the variance is unknown.

Given:

The temperature at which a thermostat goes off is normally distributed with variance σ^2.

We are testing the thermostat five times, so we have a sample size of n = 5.

We need to find the probabilities P(S^2/σ^2 ≤ 1.8) and P(0.85 ≤ S^2/σ^2 ≤ 1.15).

a) P(S^2/σ^2 ≤ 1.8):

The chi-square distribution with n - 1 degrees of freedom (df = 4 in this case) is used to calculate the probability.

Using a chi-square table or software, we can find that P(X ≤ 1.8) for df = 4 is approximately 0.8147.

b) P(0.85 ≤ S^2/σ^2 ≤ 1.15):

To find this probability, we need to calculate the cumulative probability of two chi-square values and subtract them.

P(0.85 ≤ S^2/σ^2 ≤ 1.15) = P(S^2/σ^2 ≤ 1.15) - P(S^2/σ^2 ≤ 0.85)

Using the chi-square distribution with df = 4, we find P(X ≤ 1.15) ≈ 0.8264 and P(X ≤ 0.85) ≈ 0.7067.

Therefore, P(0.85 ≤ S^2/σ^2 ≤ 1.15) = 0.8264 - 0.7067 = 0.1197.

So, the probabilities are:

a) P(S^2/σ^2 ≤ 1.8) ≈ 0.8147

b) P(0.85 ≤ S^2/σ^2 ≤ 1.15) ≈ 0.1197

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The answer is B. Normal. For a normal distribution, the mean, median, and mode are all equal to each other.

- Mean: The mean of a normal distribution is the center of the distribution, which is also the highest point of the bell-shaped curve.

- Median: The median of a normal distribution is the same as the mean, since the distribution is symmetric around the center.

- Mode: The mode of a normal distribution is also the same as the mean and median, since the highest point of the curve (i.e. the mode) is at the center of the distribution.

For the other probability distributions:

- A. Uniform: A uniform distribution has no mode (or multiple modes), and the mean and median are equal but different from the mode (if it exists).

- C. Exponential: An exponential distribution has a mode of 0, a median of ln(2)/λ, and a mean of 1/λ. Therefore, the mean, median, and mode are not equal.

- D. Poisson: A Poisson distribution has a mode of the integer part of λ (i.e., the highest probability mass function value). The mean and median are both equal to λ. Therefore, the mode is not necessarily equal to the mean and median.

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The percent of the days in April that it rains is 66.67%.

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 2/3.

A percent is the value of a number out of 100. In order to convert a value to percent, multiply by 100.

Percent of the days that it rains = ( number of days it rains / total number of days) x 100

(2/3) x 100 = 66.67%

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The appropriate null and alternative hypotheses for this research question is H₀: p= 0.69 and Hₐ: p>0.69 respectively.

Assume that p is the proportion of graduates from public, non-profit universities who were in debt from student loans at the time of their graduation.

In the above example, the hypothetical population proportion, or p₀ = 0.69.

According to this, 69% of 'college graduates' from 'public and non-profit' universities have debt from student loans.

Instead of the "alternative hypothesis," which shows a significant difference, the "null hypothesis" is now the "zero difference" hypothesis.

An "alternative hypothesis" that the researcher was interested in testing was if the 69% student loan debt proportion had dramatically grown.

In this instance, the proper "null and alternative" hypotheses are,

The "population proportion" of student loan debt is 69%, or H₀: p= 0.69

The "population proportion" of student loan debt is much higher than 69%, or Hₐ: p>0.69.

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The complete question is:

Does going to a private university increase the chance that a student will graduate with student loan debt? A national poll by the Institute for College Access and Success showed that in 69% of college graduates from public and nonprofit colleges in 2013 had student loan debt. A researcher wanted to see if there was a significant increase in the proportion of student loan debt for public and nonprofit colleges in 2014. Suppose that the researcher surveyed 1500 graduates of public and nonprofit universities and found that 71% of graduates had student loan debt in 2014. Let p be the proportion of all graduates of public nonprofit universities that graduated with student loan debt. What are the appropriate null and alternative hypotheses for this research question?

To prove that the pole of a Simson line perpendicular to one side of a triangle must be one of the vertices of the triangle, we can use the following steps:

Thus, we have shown that the pole of a Simson line perpendicular to one side of a triangle must be one of the vertices of the triangle.

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This scenario where one variable increases, then the other increases, as well describes a positive correlation between two variables. So, correct option is A.

Positive correlation occurs when two variables increase or decrease together, meaning that as the value of one variable increases, the value of the other variable also increases.

For example, if we consider the relationship between the amount of time spent studying and the grade achieved on a test, a positive correlation would exist if students who study more tend to get higher grades.

Positive correlation is often represented by a scatter plot, where the points are clustered around a straight line sloping upwards from left to right.

The correlation coefficient, also known as Pearson's r, can be used to quantify the strength and direction of the relationship between two variables, with a value of +1 indicating a perfect positive correlation and a value of 0 indicating no correlation.

In summary, a positive correlation describes a scenario where two variables increase or decrease together, and is represented by a scatter plot with points clustered around a line sloping upwards from left to right.

So, correct option is A.

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Complete question is:

One variable increases, then the other increases, as well.

Which term would best describe this scenario?

A) positive correlation

B) hypothesis

C) transitional form

D) causation

The expression in terms of x that represents the total amount that Francisco paid at the register is 0.918x.

The total amount that Francisco paid at the register need to first calculate the discounted price after applying the 15% coupon and then add the 8% tax to it.

The discount on the original price is 15% means that Francisco pays only 85% of the original price.

The discounted price as:

Discounted price = 0.85 × x

The 8% tax to the discounted price.

The tax is calculated based on the discounted price not the original price.

The expression for the total amount that Francisco paid at the register is:

Total amount = Discounted price + 8% tax on discounted price

Total amount = 0.85x + 0.08(0.85x)

Total amount = 0.85x + 0.068x

Total amount = 0.918x

The expression in terms of x that represents the total amount that Francisco paid at the register is 0.918x.

This means that Francisco paid 91.8% of the original price after applying the 15% discount and adding the 8% tax.

The expression 0.918x represents the total amount that Francisco paid at the register in terms of the original price x after applying a 15% discount and an 8% tax on the discounted price.

To calculate discounts, taxes and total prices can help consumers make informed decisions about their purchases and manage their finances effectively.

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The radius of convergence for the series [tex]\sum_{n=1}^{\infty}[/tex] xⁿ/(n3ⁿ) is 3.

Given the series is,

[tex]\sum_{n=1}^{\infty}[/tex] xⁿ/(n3ⁿ)

So, here the n th term is given by

aₙ = xⁿ/(n3ⁿ)

Then the (n + 1) the term of the series is given by,

aₙ₊₁ = xⁿ⁺¹/((n + 1)3ⁿ⁺¹)

Now, the value is,

aₙ₊₁/aₙ = (xⁿ⁺¹/((n + 1)3ⁿ⁺¹))/(xⁿ/(n3ⁿ)) = (n/(n + 1))*(x/3)

Now the value of the limit is given by,

[tex]\lim_{n \to \infty}[/tex] |aₙ₊₁/aₙ| = [tex]\lim_{n \to \infty}[/tex] |(n/(n + 1))*(x/3)| = [tex]\lim_{n \to \infty}[/tex] |x/3|*|1/(1 + 1/n)| = (|x|/3)*(1/(1 + 0) = |x|/3

So, now [tex]\lim_{n \to \infty}[/tex] |aₙ₊₁/aₙ| < 1 gives

|x|/3 < 1

|x| < 3

-3 < x < 3

Hence, the radius of convergence = 3.

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Therefore, the critical value for testing the hypothesis at a significance level of 0.005 for a sample of size 30 is -2.756 (rounded to three decimal places).

To find the critical value for testing the hypothesis:

H0: μ = 18.38 (null hypothesis)

Ha: μ < 18.38 (alternative hypothesis)

at a significance level of 0.005 for a sample size of 30, we need to use the t-distribution.

Since the alternative hypothesis is one-tailed (μ < 18.38), we will be looking for the critical value in the left tail of the t-distribution.

The critical value is the value that separates the rejection region from the non-rejection region.

To find the critical value, we can use a t-table or a statistical software. Here, I'll use the t-table.

Since the sample size is 30, the degrees of freedom (df) for this t-test is (n - 1) = (30 - 1) = 29.

Looking up the critical value for a one-tailed test with 29 degrees of freedom and a significance level of 0.005 in the t-table, we find that the critical value is approximately -2.756.

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Part A:

The arithmetic sequence will be approximately,

42 , 36 , 30 , 24 , ....

Given,

The graph of amount of money a movie earns each week after its release where n is the number of weeks after opening, and a(n) is earnings (in millions).

Now,

After reading the graph carefully it can be judged that the the graph is decreasing linearly. Thus the sequence can be framed as,

42 , 36 , 30 , 24 , ....

here the common difference is 6.

Part B:

The movie will earn $16 million in approximately 3.5 -4 weeks.

As from the graph we can see that the earnings will further decline to $15 million in 3.5 weeks.

So for $16 million the required time will be 3.5 to 4 weeks.

Part C:

The movie will approximately earn

Arithmetic sequence,

41 , 34 , 27 , 20..

Complete the sequence,

42 , 36 , 30 , 24 , 18 , 12 , 6 , 0

For total earning,

Add the earning of the respective weeks.

$(42 + 36 + 30 + 24 + 18 + 12 + 6 + 0) million = $168

Hence the total earning of the movie is approximately $168 million.

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Based on the given diagram 1 to 5, each picture represent a number, diagram 5 is 661.

Based on the diagram;

Diagram 1;

90 = 30 + 30 + 30

Each picture in diagram 1 represents 30

Diagram 2:

1 × 1 × 0 = 0

Diagram 3:

30 ÷ 1 = 30

Diagram 4:

22 × 1 - 1 = 21

Hence,

Diagram 5:

1 + 30 × 22 + 0

Using PEMDAS

P = parenthesis

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

1 + 30 × 22 + 0

= 1 + 660 + 0

= 661

Ultimately, diagram 5 equals 661.

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Let

Now

Charge:-

Pay:-

Now earning:-

Answer:

Y = 1.5x + 5

Step-by-step explanation:

To model the amount of money the florist earns for each delivery, we can break it down into the different components involved.

This can be represented by the term "+10".

This can be represented by the term "+2x", where x represents the number of miles.

This can be represented by the term - ( 0.50x + 5 )

Y = 10 + 2x - (0.50x + 5)

Simplify.

Y = 10 + 2x - 0.50x - 5

Combine like terms.

Y = 1.5x + 5

To write y as the sum of a vector in w and a vector orthogonal to w, we first need to find a basis for w. Since w is spanned by bold u 1 and bold u 2, we can use these vectors as our basis for w:
B = {bold u 1, bold u 2}

Now, we can use the orthogonal complement of w, denoted by w⊥, to find a vector that is orthogonal to w. By definition, w⊥ is the set of all vectors that are orthogonal to every vector in w. We can find w⊥ by taking the null space of the matrix whose rows are the basis vectors of w:

A = [bold u 1; bold u 2]

w⊥ = null(A)

Once we have a basis for w⊥, we can find a vector that is orthogonal to w by taking a linear combination of the basis vectors of w⊥. Let's call this vector z:

z = c_1*bold v_1 + c_2*bold v_2 + ... + c_k*bold v_k

where c_1, c_2, ..., c_k are constants, and bold v_1, bold v_2, ..., bold v_k are the basis vectors of w⊥.

Finally, we can express y as the sum of a vector in w and a vector orthogonal to w:

y = a*bold u 1 + b*bold u 2 + z

where a and b are constants that we can find by projecting y onto the basis vectors of w:

a = (y · bold u 1) / (bold u 1 · bold u 1)
b = (y · bold u 2) / (bold u 2 · bold u 2)

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To find the equation of the tangent plane to the surface z = ln(x - 7y) at the point (8, 1, 0), we need to determine the partial derivatives of z with respect to x and y at that point.

First, let's find the partial derivative ∂z/∂x:

∂z/∂x = 1/(x - 7y)

Next, let's find the partial derivative ∂z/∂y:

∂z/∂y = -7/(x - 7y)

Now, let's evaluate these partial derivatives at the point (8, 1, 0):

∂z/∂x = 1/(8 - 7(1)) = 1/(8 - 7) = 1

∂z/∂y = -7/(8 - 7(1)) = -7/(8 - 7) = -7

At the point (8, 1, 0), the partial derivatives are ∂z/∂x = 1 and ∂z/∂y = -7.

The equation of a plane can be expressed as:

z - z0 = (∂z/∂x)(x - x0) + (∂z/∂y)(y - y0)

Using the values we calculated:

z - 0 = 1(x - 8) + (-7)(y - 1)

Simplifying, we get:

z = x - 8 - 7y + 7

Rearranging terms, the equation of the tangent plane to the surface at the point (8, 1, 0) is:

z = x - 7y - 1

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The velocity of airflow during a respiratory cycle is given by v = 0.85 sin(pi t/3) ,t- time in s. One full respiratory cycle takes 6 s, and there are 10 cycles per min. The graph of the velocity function is a sinusoidal wave with amplitude 0.85 and period 6 s.

The given function for velocity during a respiratory cycle is v = 0.85 sin(pi t/3). The velocity is positive during inhalation and negative during exhalation. To find the time for one full respiratory cycle, we need to solve for the values of t that make v=0:

0 = 0.85 sin(pi t/3)

sin(pi t/3) = 0

pi t/3 = n pi

t = 3n, where n is an integer

Thus, one full respiratory cycle takes 6 seconds (when n=2). To find the number of cycles per minute, we can use the formula:

cycles per minute = 60 / time per cycle

Substituting the value of time per cycle, we get:

cycles per minute = 60 / 6 = 10

Therefore, there are 10 cycles per minute.

The graph of the velocity function is a sinusoidal wave with amplitude 0.85 and period 6 seconds. The function starts at 0, reaches a maximum value of 0.85 at t=3 seconds, goes through 0 again at t=6 seconds, reaches a minimum value of -0.85 at t=9 seconds, and returns to 0 at t=12 seconds. The graph repeats itself every 6 seconds, which is the period of the function. Thus, the graph is a sinusoidal wave that oscillates between positive and negative values with a frequency of 1/6 Hz (or 10 cycles per minute).

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Answer:

linear - y= x/2 -19, y = x+25/5

non linear- everything else

Step-by-step explanation:

put it into a calc and look for straight lines (linear)

3y=x^2 is NOT linear (it's a parabola)

y=(x/2)-19 is linear - - - it's a straight line

y= x + 25/5 is linear - - - it's straight line

13y = (1/3)x+5 is linear - - - another straight line

y^3 = x is NOT linear.

Reflection of point across x-axis

preimage (-3, 2)         Image (-3, -2)

Reflection of point across y-axis

preimage (-3, 2)         Image (3, 2)

Here, we have,

to find the coordinates of the reflected image

Reflection is one of the movements in transformation that involve creation of mirror image

Transformation rule for reflection over x-axis at origin (0, 0)) is

(x, y) → (x, -y)

Transformation rule for reflection over line y-axis at origin (0, 0)) is

(x, y) → (-x, y)

The reflection to be done is (-3, 2)

Transformation for reflection over x-axis → (-3, -2)

Transformation for reflection over line y-axis  → (3, 2)

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complete question:

Reflection of point across x-axis

Reflection of point across y-axis

---------------------------------------------------------------------

Reflection of point across x-axis and

then Reflection across y-axis

The missing side length in the triangle is (b) √5

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

The triangle

To find the missing side in a triangle, we can use the pythagoras theorem

So, we have

x² = (2√3)² - (√7)²

Evaluate the difference of exponents

x² = 5

Take the exponent of both sides

x = √5

Hence, the missing side length is (b) √5

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The primary advantage of pooled cross-sectional data over ordinary cross-sectional data is that it provides a larger sample size.

When cross-sectional data from multiple time periods are pooled together, it increases the overall number of observations and thus increases the statistical power of any analysis that is conducted. This larger sample size can also help to reduce the standard errors of estimates and increase the precision of any findings.

However, it is important to note that pooling cross-sectional data does not enable you to ignore the differences in data over time. Rather, it enables you to observe changes in key relationships over time by including observations from different time periods in one data set. Pooling cross-sectional data also does not necessarily enable you to form a panel data set, as this typically requires the same set of individuals or units to be observed over time.

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