4. Use the Vertical Angles Theorem to name a pair of congruent angles in the image shown.

A. ZFBC: ZCBX
B. ZFBC; ZGBX
C. ZFBY, ZGBX
D. ZFBY, ZMBG​

Answer:

this type of sampling would be considered a multistage.

The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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The greatest number of comparisons each operation in the method add needs, given a binary search tree with n nodes and height h, is O. (h).

Computer scientists utilize the search method known as binary search to locate a target value within a sorted array. Binary chop, logarithmic search, and half-interval search are other names for it. The binary search compares the target value to the array's center member. If not, the half where the target cannot lie is eliminated, and the search is then carried out on the remaining half while once again comparing the center element's value to the target value. Up till the goal value is found, this process is repeated. if, at the end of the search, the remaining half is empty.

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If u is a combination of v1, v2, v3, it implies that u can be expressed as a linear combination of those vectors. By setting the coefficient of v4 to 0, we can still represent u in the same form while including v4, thereby confirming that u is also a combination of v1, v2, v3, v4.

If u is a combination of v1, v2, v3, it means that we can express u as a linear combination of v1, v2, v3. In other words, we can find coefficients (scalars) such that:

u = c1 * v1 + c2 * v2 + c3 * v3,

where c1, c2, and c3 are scalars.

Now, let's consider the set of vectors v1, v2, v3, v4. We know that u is a combination of v1, v2, v3. So, we can express u as:

u = c1 * v1 + c2 * v2 + c3 * v3.

To show that u is also a combination of v1, v2, v3, v4, we need to demonstrate that we can express u using the same coefficients but also include v4 in the linear combination. In other words, we need to find a scalar c4 such that:

u = c1 * v1 + c2 * v2 + c3 * v3 + c4 * v4.

To do this, we can simply set c4 to 0, because multiplying v4 by 0 does not affect the sum. Therefore, we can express u as a combination of v1, v2, v3, v4 by setting c4 = 0:

u = c1 * v1 + c2 * v2 + c3 * v3 + 0 * v4.

By including v4 with a coefficient of 0, we have not changed the expression of u as a linear combination of v1, v2, v3. Thus, u is indeed a combination of v1, v2, v3, v4.

In summary, if u is a combination of v1, v2, v3, it implies that u can be expressed as a linear combination of those vectors. By setting the coefficient of v4 to 0, we can still represent u in the same form while including v4, thereby confirming that u is also a combination of v1, v2, v3, v4.

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Pilot should take reverse bearing, calculated using atan2(East,North),converted in degrees.

What is radian ?

A radian is a unit of measurement for angles. It is defined as the ratio of the length of an arc of a circle to the radius of that circle. One radian is approximately 57.3 degrees. Radians are often used in mathematics, physics, and engineering because they allow for a more natural way of measuring angles and help simplify certain calculations.

To find the bearing, we can use the formula ,

Bearing = atan2(East, North)

Where East is the number of miles east of the airport and North is the number of miles north of the airport.

The atan2 function is a variation of the arctangent function, which returns the angle (in radians) whose tangent is the quotient of its two arguments. This function is defined for all real arguments and returns a value between -π and π.

So you can convert the bearing from radians to degrees using the formula ,

degrees = bearing * (180/π)

Pilot should take reverse bearing, calculated using atan2(East,North),converted in degrees.

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The number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

We can solve this inequality by introducing an auxiliary variable x4, such that x1 + x2 + x3 + x4 = 11. Here, x1, x2, x3, and x4 are all nonnegative integers.

We can interpret this equation as follows: imagine we have 11 identical objects and we want to distribute them among four boxes (x1, x2, x3, and x4). Each box can contain any number of objects, including zero. The number of solutions to this equation will give us the number of nonnegative integer solutions to the original inequality.

We can use a technique known as stars and bars to count the number of solutions to this equation. Imagine we represent the 11 objects as stars: ***********.

We can then place three bars to divide the stars into four groups, each group representing one of the variables x1, x2, x3, and x4. For example, if we place the first bar after the first star, the second bar after the third star, and the third bar after the fifth star, we get the following arrangement:

| ** | * | ****

This arrangement corresponds to the solution x1=1, x2=2, x3=1, and x4=7. Notice that the number of stars to the left of the first bar gives the value of x1, the number of stars between the first and second bars gives the value of x2, and so on.

We can place the bars in any order, so we need to count the number of ways to arrange three bars among 14 positions (11 stars and 3 bars). This is equivalent to choosing 3 positions out of 14 to place the bars, which can be done in C(14,3) ways.

Therefore, the number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

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Answer:

ranalllldooo

Step-by-step explanation:

suiiiiiii

Using translation concepts, the sequence that is used to obtain Figure A'B'C'D' is given by:

Reflection about the y-axis followed by a translation to the left by 2 units.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Considering the vertices, the changes have the following pattern:

(x,y) -> (-x,y) -> (-x -2, y).

At step (x,y) -> (-x,y), the function is reflected over the y-axis. Then, at step (-x,y) -> (-x -2, y), the function is shifted left 2 units, hence the correct option is given by:

Reflection about the y-axis followed by a translation to the left by 2 units.

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Answer:

75 dollars.

Step-by-step explanation:

If 4 gallons of gas costs 15 dollars, then 20 gallons would cost 75 dollars.

Hope this helped!! :D

Answer:

15/4 = 3.75

3.75 x 20 = 75

$75

The root of the equation \(\(f(x) = x^3 - 3x - 1\)\) between -1 and 1, after the second iteration of the False Position method, is approximately -1.

The False Position method involves finding the x-value that corresponds to the x-intercept of the line passing through \(\((a, f(a))\)\) and \(\((b, f(b))\),\)where (a) and (b) are the endpoints of the interval.

Let's begin the iterations:

Iteration 1:

\(\(a = -1\), \(f(a) = (-1)^3 - 3(-1) - 1 = -3\)\)

\(\(b = 1\), \(f(b) = (1)^3 - 3(1) - 1 = -3\)\)

The line passing through (-1, -3) and (1, -3) is (y = -3). The x-intercept of this line is at (x = 0).

Therefore, the new interval becomes [0, 1] since the sign of f(x) changes between\(\(x = -1\) and \(x = 0\).\)

Iteration 2:

\(\(a = 0\), \(f(a) = (0)^3 - 3(0) - 1 = -1\)\)

\(\(b = 1\), \(f(b) = (1)^3 - 3(1) - 1 = -2\)\)

The line passing through\(\((0, -1)\) and \((1, -2)\) is \(y = -x - 1\)\). The x-intercept of this line is at (x = -1).

After the second iteration, the new interval becomes [-1, 1] since the sign of f(x) changes between (x = 0) and (x = -1).

Therefore, the root of the equation \(\(f(x) = x^3 - 3x - 1\)\) between -1 and 1, after the second iteration of the False Position method, is approximately -1.

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Since Quadrilateral CDEF is inscribed in Circle A, the value of x is equal to: B. 33.

Since Quadrilateral CDEF is inscribed in Circle A, we can reasonably infer and logically deduce that line segment DF is the chord of Circle A. Mathematically, an equation which can be used to solve for the value of x in this circle is given by:

m∠DEF + m∠DCF = 180°

Substituting the given parameters into the formula above, we have the following;

(3x + 7)° + (2x + 8)° = 180°

3x + 2x + 8 + 7 = 180°

5x + 15 = 180°

5x = 180° - 15

5x = 165

x = 165/5

x = 33.

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Answer:

No solutions (Maybe)

Step-by-step explanation:

If you input 0 into the equation you get -3=-4, which means it has no solutions.

The hypotheses for this study of the effects of an appetite suppressant are H0: p1 = p2 and Ha: p1 ≠ p2. The placebo group is important in this study because it provides a baseline for comparison with the treatment group.

The hypotheses:

Where p1 is the proportion of subjects who experienced the primary outcome in the sibutramine group and p2 is the proportion of subjects who experienced the primary outcome in the placebo group.

Test statistic:

The test statistic for comparing two proportions is given by:

where SE = sqrt((p1(1-p1) / n1) + (p2(1-p2) / n2))

Using the given data, we have:

So:

Using Table C or software, the P-value is approximately 0.08.

Conclusion:

At a significance level of 0.05, since the P-value is greater than 0.05, we fail to reject the null hypothesis. There is not enough evidence to conclude that there is a difference between the proportions of treatment and placebo subjects who experienced the primary outcome.

The placebo group is important in this study because it provides a baseline for comparison with the treatment group. By comparing the outcomes in the treatment group to the outcomes in the placebo group, we can determine whether any differences are due to the treatment or simply due to chance.

Additionally, the use of a placebo group helps to control for the placebo effect, where patients may experience a positive effect simply because they believe they are receiving treatment, even if the treatment is not actually effective.

This question should be provided with this following information:

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Answer:

Please refer to the attachment

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Thank you

The probability that at least one of them will have a defect is 0.3143

If, defect items = 9%

       Then, non- defect items =  91%

Applying the  binomial formula,      

    Here ,

           x denotes the number of successes desired.

           n denotes the number of trials.

           p denotes the number of successes in a trial.

          q denotes the number of failures in a trial.

Substituting, x = 4

                           n = 4

                           p = 0.91 and

                           q = 0.09

The probability that all the chosen items are not defective is:

      P(4 not defective) is given by,        

As a result, the likelihood that any one of the 4 chosen items will be flawed is determined by subtracting the likelihood that none of the 4 items are flawed from 1.

P(at least one defective) is given by,

      P(at least one defective) = 1- P(4 not defective)

                                             = 1 - 0.6857

                                             = 0.3143

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Answer:

The midpoint is (3, -2)

Step-by-step explanation:

\(m = (\frac{x1 + x2}{2}, \frac{y1 + y2}{2})\\m = (\frac{-7 + 13}{2}, \frac{2-6}{2})\\m = (\frac{6}{2}, \frac{-4}{2})\\m = (3, -2)\)

The probability mass function of W is P(W=-3) = 1/27, P(W=-1) = 6/27, P(W=1) = 12/27, and P(W=3) = 8/27.

Let us consider the possible outcomes of three tosses of the biased coin. There are a total of 8 possible outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH, and TTT.

Since a head is twice as likely to occur as a tail, the probability of getting a head is 2/3 and the probability of getting a tail is 1/3.

Let W be a random variable giving the number of heads minus the number of tails in three tosses of the coin. Then, W can take on any value between -3 and 3.

To find the probability mass function (PMF) of W, we need to calculate the probability of each possible outcome. When all three coins come up heads (HHH), W = 3 - 0 = 3. The probability of this outcome is:

P(HHH) = (2/3)^3 = 8/27

When two coins come up heads and one comes up tails (HHT, HTH, THH), W = 2 - 1 = 1. The probability of each of these outcomes is:

P(HHT) = (2/3)^2 × (1/3) = 4/27

P(HTH) = (2/3)^2 × (1/3) = 4/27

P(THH) = (2/3)^2 × (1/3) = 4/27

So, P(W=1) = P(HHT) + P(HTH) + P(THH) = 12/27

When one coin comes up heads and two come up tails (HTT, THT, TTH), W = 1 - 2 = -1. The probability of each of these outcomes is:

P(HTT) = (2/3) × (1/3)^2 = 2/27

P(THT) = (2/3) × (1/3)^2 = 2/27

P(TTH) = (2/3) × (1/3)^2 = 2/27

So, P(W=-1) = P(HTT) + P(THT) + P(TTH) = 6/27

When all three coins come up tails (TTT), W = 0 - 3 = -3. The probability of this outcome is:

P(TTT) = (1/3)^3 = 1/27

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Using the Central Limit Theorem, the given statements are true or false in following

a) True

b) True

c) True

d)True

e) True

a) From the definition of central limit theorem, by law of large number to sample average converge almost slowly to the population average.

So, based on CLT the sample mean be used a3 gond estimator of the population mean assuing that the sample size. sufficiently large i.e ., True.

b) Same reason as (a) , based on CLT the usually considers that sample 51Z6 30 is sufficiently large is true

c) If we generate 1000 samples of Binomial (10;0.3)distribution are plot a histogram then it looks like normal distribution.

So, the Central Limit Theorem be applied to both discrete and continols Fandom variables is true.

d) Whatever be the parent distribution , if sample size ,n is large then sample mean means

converges in probability to the population mean.

So, the given option (d) is true .

e) If population size is normally distributed then sample mean is also normally distributed for all sample size.

So, option(e) is also true.

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Complete question:

Problem Central Limit Theorem) _ Are the following statements true or false?

a)Easy. Based the Central Limit Theorem_ the sample mean be used a3 gond estimator of the population mean assuing that the sample size. sufficiently large.

b)Easy. Then applying the Central Limit Theorem. l usually conziders that sample 51Z6 30 is sufficiently large.

c)Easy. the Central Limit Theorem be applied to both discrete and continols Fandom variables .

d): Assuming that the sample size is sufficiently large the Central Limit Theorem permits draw conclusions about the population based strictly sample data. and without having aIV knowledge about the distribution of the underlying population:

(e) Moderate_ Assuming that the population is normally distributed_ the sampling distribution of the sample mean is normally distributed for samples of all sizes_

The probability of getting exactly four heads when a fair coin is flipped 10 times is 20.51%.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

A coin is filliped 10 times. Each of the flips is independent.

Let's say X is the number of heads in 10 tosses.

Then X is distributed as n = 10 and the probability that the head comes after a single flip is 1/2.

Therefore, the probability of X being exactly 4 will be:

P( X = 4 ) = ₁₀C₄ ( 1/2 )⁴ ( 1 - 1/2 )⁶

P( X = 4 ) = 210 × ( 1/16 ) × ( 1/2 )⁶

P( X = 4 ) = 210 × ( 1/16 ) × ( 1/64 )

P( X = 4 ) = 210/1024

P( X = 4 ) = 105/512

P( X = 4 ) = 0.2051

Hence, the probability is 20.51%.

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Answer:

slope = \(-\frac{1}{3}\)

Step-by-step explanation:

1) Find the slope with the slope formula, \(m = \frac{y_2-y_1}{x_2-x_1}\) (in which \(m\) represents the slope). The \(x_1\) and \(y_1\) represent the x and y values of one point, and the \(x_2\) and \(y_2\) represent the x and y values of another point. Thus, substitute the x and y values of the given points (6, -2) and (-3, 1) into the appropriate places in the formula and solve:

\(m = \frac{(1)-(-2)}{(-3)-(6)} \\m = \frac{1+2}{-3-6} \\m = \frac{3}{-9} \\m = -\frac{1}{3 }\)

Thus, the slope is \(-\frac{1}{3}\).

The center of mass is given by:
(xbar, ybar, zbar) = (Mx/m, My/m, Mz/m)
                  = (0, 16/(3π), 16/(3π))

To find the mass of the wire, we need to integrate the density function over the length of the wire. The length of the wire can be found using the arc length formula:

ds = sqrt(dx^2 + dy^2 + dz^2)
  = sqrt(1 + 4sin^2(t) + 4cos^2(t)) dt
  = sqrt(5) dt

Integrating this from 0 to 2π gives us the length of the wire:

L = ∫_0^(2π) sqrt(5) dt
 = 2πsqrt(5)

Now we can find the mass of the wire:

m = ∫_0^(2π) ρ ds
 = ∫_0^(2π) (x^2 + y^2 + z^2) ds
 = ∫_0^(2π) (t^2 + 4cos^2(t) + 4sin^2(t)) sqrt(5) dt
 = 4πsqrt(5)

To find the center of mass, we need to find the moments about each coordinate axis:

Mx = ∫_0^(2π) ρ x ds
  = ∫_0^(2π) t(t^2 + 4cos^2(t) + 4sin^2(t)) sqrt(5) dt
  = 0 (due to symmetry)

My = ∫_0^(2π) ρ y ds
  = ∫_0^(2π) 2cos^2(t) (t^2 + 4cos^2(t) + 4sin^2(t)) sqrt(5) dt
  = 32π/(3sqrt(5))

Mz = ∫_0^(2π) ρ z ds
  = ∫_0^(2π) 2sin^2(t) (t^2 + 4cos^2(t) + 4sin^2(t)) sqrt(5) dt
  = 32π/(3sqrt(5))

Finally, the center of mass is given by:

(xbar, ybar, zbar) = (Mx/m, My/m, Mz/m)
                  = (0, 16/(3π), 16/(3π))

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We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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In this question, we are asked to determine the sample proportion of Generation Y web users who use the internet to download music, and then perform a hypothesis test to check if there is sufficient evidence to conclude that a majority of Generation Y web users use the internet to download music.

a) The sample proportion is the proportion of individuals in the sample who reported using the internet to download music. In this case, the sample proportion can be calculated as 297/550 = 0.54, or 54%.

b) To perform the hypothesis test, we need to state the null and alternative hypotheses. The null hypothesis is that the proportion of Generation Y web users who use the internet to download music is equal to 0.5, while the alternative hypothesis is that it is greater than 0.5.

Next, we need to check the conditions for the one-proportion z-test, which are:

1) The sample is a simple random sample.

2) The conditions for the Central Limit Theorem are met (np >= 10 and n(1-p) >= 10).

Since the sample is randomly selected and np = 297*0.5 = 148.5 and n(1-p) = 550 - 148.5 = 401.5 are both greater than 10, we can proceed with the one-proportion z-test.

Using a significance level of 0.01, the critical value is 2.33 (calculated using a z-table or calculator). The test statistic can be calculated as\(z = (0.54 - 0.5) / \sqrt{(0.5 * 0.5 / 550)} = 2.16\). Since the test statistic is less than the critical value, we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that a majority of Generation Y web users use the internet to download music at a significance level of 0.01. However, we can conclude that more than half of the sample (54%) reported using the internet to download music.

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The equation of the tangent line to the curve \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) at the point (1, 0) is y = (2/3)x - 2/3.

To find the equation of the tangent line to the curve at the point (1, 0), we need to find the slope of the tangent line and then use the point-slope form of a linear equation.
Let's differentiate \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) using the quotient rule:

\(y' = [(2x)(x^2 + x + 1) - (x^2 - 1)(2x + 1)] / (x^2 + x + 1)^2\)
Substituting x = 1 into the derivative expression:

\(y'(1) = [(2(1))(1^2 + 1 + 1) - (1^2 - 1)(2(1) + 1)] / (1^2 + 1 + 1)^2\)

        \(= [2(3) - (0)(3)] / (3)^2\)

        = 6/9

        = 2/3

Using the point-slope form y - y₁ = m(x - x₁), where (x₁, y₁) = (1, 0) and m = 2/3 we get,  
y - 0 = (2/3)(x - 1)

y = (2/3)x - 2/3

The point-slope form of a linear equation is given by y - y₁ = m(x - x₁) where (x₁, y₁) is a point on the line, and m is the slope of the line.

Therefore, the equation of the tangent line to the curve y = (x^2 - 1) / (x^2 + x + 1) at the point (1, 0) is y = (2/3)x - 2/3.

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The complete question is:

Find an equation of the tangent line to the given curve at the specified point, \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) at (1,0).

The pigeonhole principle states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon. We can apply this principle to prove the following statements:

(a) Given any seven integers, there will be two that have a difference divisible by 6.

We can divide the integers into six pigeonholes based on their remainders when divided by 6: {0}, {1}, {2}, {3}, {4}, and {5}. Since there are seven integers, by the pigeonhole principle, at least two integers must belong to the same pigeonhole. If two integers belong to the same pigeonhole, then their difference will be divisible by 6.

(b) Given any five integers, there will be two that have a sum or difference divisible by 7.

We can divide the integers into six pigeonholes based on their remainders when divided by 7: {0}, {1}, {2}, {3}, {4}, {5}, and {6}. Since there are five integers, by the pigeonhole principle, at least two integers must belong to the same pigeonhole. If two integers belong to the same pigeonhole, then their sum or difference will be divisible by 7.

Note that if the two integers have the same remainder when divided by 7, then their difference will be divisible by 7. If they have different remainders, then their sum will be divisible by 7.

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Answer:

Step-by-step explanation:

Henry is 3 more than twice Nicholas' age. You can write this as :

H = 3 + 2N

Marcus is 9 less than 6 times Nicholas' age:

M = 6N - 9

Since Henry and Marcus are twins, this means H = N.

3 + 2N = 6N - 9

Add 9 to both sides

12 + 2N = 6N

Subtract 2N from both sides

12 = 4N

Divide both sides by 4 to find N.

N = 12/4 = 3

Answer:

3  ×  10  −  7 (-7 should be in upper top after 10)

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the  

10 . If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Hope this helps.

Answer:

The cost of buying 6 sodas at 79¢ each is greater than the cost of buying 5 sodas and getting 1 free

Step-by-step explanation:

Ella gets a free soda after buying 5 sodas at the regular price of 89¢

Total cost of 6 sodas( 5 + 1 free)

= 89¢ × 5

= 445¢

Same-sized sodas at the local fast food restaurant are 79¢ each.

Total cost of 6 sodas = 79¢ × 6

= 474¢

The cost of buying 6 sodas at 79¢ each is greater than the cost of buying 5 sodas and getting 1 free

Answer:

=> membership fee = $50

=> monthly fee = $55

=> First month = 105$

=> 50 + 55(x)

=> 50 + 55 (15)

=> 50 + 825

=> 875

Workout gym

=> membership fee = $200

=> monthly fee = $45

=> First month = 245$

=> 200 + 45(x)

=> 200 + 45(15)

=> 200 + 675

=> 875

Step-by-step explanation:

Answer:

15 kg, 22.5 kg, 52.5 kg

Step-by-step explanation:

Let the common multiplier of the given ratios be x. Therefore, weights of each bag would be 2x, 3x and 7x

According to the given information:

\(2x + 3x + 7x = 90 \\ 12x = 90 \\ x = \frac{90}{12} \\ x = 7.5 \: \\ \implies \\ 2x = 2 \times 7.5 = 15 \: kg \\ 3x = 3 \times 7.5 = 22.5 \: kg \\ 7x = 7 \times 7.5 = 52.5 \: kg\)

Hence the weight of sand in bag would be 15 kg, 22.5 kg and 52.5 kg